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Solution of generalized shifted linear systems with complex symmetric matrices
NASA Astrophysics Data System (ADS)
Sogabe, Tomohiro; Hoshi, Takeo; Zhang, Shao-Liang; Fujiwara, Takeo
We develop the shifted COCG method [R. Takayama, T. Hoshi, T. Sogabe, S.-L. Zhang, T. Fujiwara, Linear algebraic calculation of Green's function for large-scale electronic structure theory, Phys. Rev. B 73 (165108) (2006) 1-9] and the shifted WQMR method [T. Sogabe, T. Hoshi, S.-L. Zhang, T. Fujiwara, On a weighted quasi-residual minimization strategy of the QMR method for solving complex symmetric shifted linear systems, Electron. Trans. Numer. Anal. 31 (2008) 126-140] for solving generalized shifted linear systems with complex symmetric matrices that arise from the electronic structure theory. The complex symmetric Lanczos process with a suitable bilinear form plays an important role in the development of the methods. The numerical examples indicate that the methods are highly attractive when the inner linear systems can efficiently be solved.
Conjugate gradient type methods for linear systems with complex symmetric coefficient matrices
NASA Technical Reports Server (NTRS)
Freund, Roland
We consider conjugate gradient type methods for the solution of large sparse linear system Ax equals b with complex symmetric coefficient matrices A equals A(T). Such linear systems arise in important applications, such as the numerical solution of the complex Helmholtz equation. Furthermore, most complex non-Hermitian linear systems which occur in practice are actually complex symmetric. We investigate conjugate gradient type iterations which are based on a variant of the nonsymmetric Lanczos algorithm for complex symmetric matrices. We propose a new approach with iterates defined by a quasi-minimal residual property. The resulting algorithm presents several advantages over the standard biconjugate gradient method. We also include some remarks on the obvious approach to general complex linear systems by solving equivalent real linear systems for the real and imaginary parts of x. Finally, numerical experiments for linear systems arising from the complex Helmholtz equation are reported.
Iterative methods for the solution of very large complex symmetric linear systems of equations in electrodynamics
Clemens, M.; Weiland, T.
In the field of computational electrodynamics the discretization of Maxwell`s equations using the Finite Integration Theory (FIT) yields very large, sparse, complex symmetric linear systems of equations. For this class of complex non-Hermitian systems a number of conjugate gradient-type algorithms is considered. The complex version of the biconjugate gradient (BiCG) method by Jacobs can be extended to a whole class of methods for complex-symmetric algorithms SCBiCG(T, n), which only require one matrix vector multiplication per iteration step. In this class the well-known conjugate orthogonal conjugate gradient (COCG) method for complex-symmetric systems corresponds to the case n = 0. The case n = 1 yields the BiCGCR method which corresponds to the conjugate residual algorithm for the real-valued case. These methods in combination with a minimal residual smoothing process are applied separately to practical 3D electro-quasistatical and eddy-current problems in electrodynamics. The practical performance of the SCBiCG methods is compared with other methods such as QMR and TFQMR.
Reversibility of a Symmetric Linear Cellular Automata
NASA Astrophysics Data System (ADS)
Del Rey, A. Martín; Sánchez, G. Rodríguez
The characterization of the size of the cellular space of a particular type of reversible symmetric linear cellular automata is introduced in this paper. Specifically, it is shown that those symmetric linear cellular with 2k + 1 cells, and whose transition matrix is a k-diagonal square band matrix with nonzero entries equal to 1 are reversible. Furthermore, in this case the inverse cellular automata are explicitly computed. Moreover, the reversibility condition is also studied for a general number of cells.
Small diameter symmetric networks from linear groups
NASA Technical Reports Server (NTRS)
Campbell, Lowell; Carlsson, Gunnar E.; Dinneen, Michael J.; Faber, Vance; Fellows, Michael R.; Langston, Michael A.; Moore, James W.; Multihaupt, Andrew P.; Sexton, Harlan B.
In this note is reported a collection of constructions of symmetric networks that provide the largest known values for the number of nodes that can be placed in a network of a given degree and diameter. Some of the constructions are in the range of current potential engineering significance. The constructions are Cayley graphs of linear groups obtained by experimental computation.
On the Complex Symmetric and Skew-Symmetric Operators with a Simple Spectrum
NASA Astrophysics Data System (ADS)
Zagorodnyuk, Sergey M.
In this paper we obtain necessary and sufficient conditions for a linear bounded operator in a Hilbert space H to have a three-diagonal complex symmetric matrix with non-zero elements on the first sub-diagonal in an orthonormal basis in H. It is shown that a set of all such operators is a proper subset of a set of all complex symmetric operators with a simple spectrum. Similar necessary and sufficient conditions are obtained for a linear bounded operator in H to have a three-diagonal complex skew-symmetric matrix with non-zero elements on the first sub-diagonal in an orthonormal basis in H.
Block Lanczos tridiagonalization of complex symmetric matrices
NASA Astrophysics Data System (ADS)
Qiao, Sanzheng; Liu, Guohong; Xu, Wei
The classic Lanczos method is an effective method for tridiagonalizing real symmetric matrices. Its block algorithm can significantly improve performance by exploiting memory hierarchies. In this paper, we present a block Lanczos method for tridiagonalizing complex symmetric matrices. Also, we propose a novel componentwise technique for detecting the loss of orthogonality to stablize the block Lanczos algorithm. Our experiments have shown our componentwise technique can reduce the number of orthogonalizations.
Experimental scheme for unambiguous discrimination of linearly independent symmetric states
Jimenez, O.; Burgos-Inostroza, E.; Delgado, A.; Saavedra, C.; Sanchez-Lozano, X.
We propose an experimental setup for discriminating four linearly independent nonorthogonal symmetric quantum states. The setup is based on linear optics only and can be configured to implement both optimal unambiguous state discrimination [Chefles and Barnett, Phys. Lett. A 250, 223 (1998)] and minimum error discrimination. In both cases, the setup is characterized by an optimal success probability. The experimental setup can be generalized to the case of discrimination among N linearly nonorthogonal symmetric quantum states. We also study the discrimination between two incoherent superpositions of symmetric states. In this case, the setup also achieves an optimal success probability in the case of unambiguous discrimination as well as minimum error discrimination.
Linear quadratic optimal control for symmetric systems
NASA Technical Reports Server (NTRS)
Lewis, J. H.; Martin, C. F.
Special symmetries are present in many control problems. This paper addresses the problem of determining linear-quadratic optimal control problems whose solutions preserve the symmetry of the initial linear control system.
On the symmetrization of rotational spectra for freely rotating linear molecules
NASA Astrophysics Data System (ADS)
Borysow, Aleksandra; Moraldi, Massimo
It is demonstrated that the symmetrization of a quantum mechanical rotational spectrum of freely rotating linear molecules by means of the Egelstaff transformation produces a symmetric spectrum whose first two even moments coincide with the corresponding classical moments.
Nonlinear light behaviors near phase transition in non-parity-time-symmetric complex waveguides.
Nixon, Sean; Yang, Jianke
Many classes of non-parity-time (PT)-symmetric waveguides with arbitrary gain and loss distributions still possess all-real linear spectrum or exhibit phase transition. In this Letter, nonlinear light behaviors in these complex waveguides are probed analytically near a phase transition. Using multi-scale perturbation methods, a nonlinear ordinary differential equation (ODE) is derived for the light's amplitude evolution. This ODE predicts that a single class of these non-PT-symmetric waveguides supports soliton families and amplitude-oscillating solutions both above and below linear phase transition, in close analogy with PT-symmetric systems. For the other classes of waveguides, the light's intensity always amplifies under the effect of nonlinearity, even if the waveguide is below the linear phase transition. These analytical predictions are confirmed by direct computations of the full system.
Experimental beta limits of symmetric linear heliac configurations
Spanjers, G.G.; Nelson, B.A.; Ribe, F.L.; Jarboe, T.R. )
Helically symmetric heliac equilibria [H. P. Furth, [ital Plasma] [ital Physics] [ital and] [ital Controlled] [ital Fusion] [ital Research] (International Atomic Energy Agency, Vienna, 1966), Vol. 1, p. 103] are formed on the High Beta Q Machine (HBQM) [C. M. Greenfield, Phys. Fluids B [bold 2], 133 (1990)] by using a fast-rising central conductor (hardcore) current in conjunction with a shock-heated [ital l]=1 stellarator configuration. The equilibria are found to possess a high global beta and the plasma pressure is approximately a flux-surface quantity. Under the effects of plasma, the magnetic well is found to deepen and the rotational transform is greatly increased and becomes highly sheared, owing to plasma currents induced by the fast-rising hardcore current. In the second phase of the experiment, the equilibrium fields of the symmetric heliac are lowered while maintaining the same shock heating in an attempt to raise the global beta. No substantial change in global beta is seen, indicating that the configuration forms at the beta limit in the shock-heated HBQM, and that the plasma beta seen in the first phase of the experiment is the symmetric heliac beta limit.
Efficient linear algebra routines for symmetric matrices stored in packed form.
Ahlrichs, Reinhart; Tsereteli, Kakha
Quantum chemistry methods require various linear algebra routines for symmetric matrices, for example, diagonalization or Cholesky decomposition for positive matrices. We present a small set of these basic routines that are efficient and minimize memory requirements.
On the Lanczos Method for Solving Symmetric Linear Systems with Several Right-Hand-Sides.
CHART .NAJ l k ) Lnu On the Lanzos Method for Solving Symmetric Linear Systems with Several Right-Hand- Sides Youcef ad . ~ ~~Technical Report YALEU...hand sides . The methods examined are suitable for the case where the right sides are not too different from one another as is often the case in time...equivalent to the block Lanctos algorithm. On the Lanczos Method for Solving Symmetric Linear Systems with Several Right-Hand- Sides Youcef Saad 1 Technical
Scattering of linear and nonlinear waves in a waveguide array with a PT-symmetric defect
Dmitriev, Sergey V.; Suchkov, Sergey V.; Sukhorukov, Andrey A.; Kivshar, Yuri S.
We study the scattering of linear and nonlinear waves in a long waveguide array with a parity-time (PT)-symmetric defect created by two waveguides with balanced gain and loss. We present exact solutions for the scattering of linear waves on such a defect, and then demonstrate numerically that the linear theory can describe, with a good accuracy, the soliton scattering in the case of weak nonlinearity. We reveal that the reflected and transmitted linear and nonlinear waves can be amplified substantially after interaction with the PT-symmetric defect thus allowing an active control of the wave scattering in the array.
Complex PT-symmetric nonlinear Schrödinger equation and Burgers equation.
Yan, Zhenya
The complex -symmetric nonlinear wave models have drawn much attention in recent years since the complex -symmetric extensions of the Korteweg-de Vries (KdV) equation were presented in 2007. In this review, we focus on the study of the complex -symmetric nonlinear Schrödinger equation and Burgers equation. First of all, we briefly introduce the basic property of complex symmetry. We then report on exact solutions of one- and two-dimensional nonlinear Schrödinger equations (known as the Gross-Pitaevskii equation in Bose-Einstein condensates) with several complex -symmetric potentials. Finally, some complex -symmetric extension principles are used to generate some complex -symmetric nonlinear wave equations starting from both -symmetric (e.g. the KdV equation) and non- -symmetric (e.g. the Burgers equation) nonlinear wave equations. In particular, we discuss exact solutions of some representative ones of the complex -symmetric Burgers equation in detail.
Algorithm 937: MINRES-QLP for Symmetric and Hermitian Linear Equations and Least-Squares Problems
Choi, Sou-Cheng T.; Saunders, Michael A.
We describe algorithm MINRES-QLP and its FORTRAN 90 implementation for solving symmetric or Hermitian linear systems or least-squares problems. If the system is singular, MINRES-QLP computes the unique minimum-length solution (also known as the pseudoinverse solution), which generally eludes MINRES. In all cases, it overcomes a potential instability in the original MINRES algorithm. A positive-definite pre-conditioner may be supplied. Our FORTRAN 90 implementation illustrates a design pattern that allows users to make problem data known to the solver but hidden and secure from other program units. In particular, we circumvent the need for reverse communication. Example test programs input and solve real or complex problems specified in Matrix Market format. While we focus here on a FORTRAN 90 implementation, we also provide and maintain MATLAB versions of MINRES and MINRES-QLP. PMID:25328255
Generalized Householder transformations for the complex symmetric eigenvalue problem
NASA Astrophysics Data System (ADS)
Noble, J. H.; Lubasch, M.; Jentschura, U. D.
We present an intuitive and scalable algorithm for the diagonalization of complex symmetric matrices, which arise from the projection of pseudo-Hermitian and complex scaled Hamiltonians onto a suitable basis set of "trial" states. The algorithm diagonalizes complex and symmetric (non-Hermitian) matrices and is easily implemented in modern computer languages. It is based on generalized Householder transformations and relies on iterative similarity transformations T → T' = Q T T Q, where Q is a complex and orthogonal, but not unitary, matrix, i.e. Q T = Q -1 but Q + ≠ Q -1. We present numerical reference data to support the scalability of the algorithm. We construct the generalized Householder transformations from the notion that the conserved scalar product of eigenstates Ψ n and Ψ m of a pseudo-Hermitian quantum mechanical Hamiltonian can be reformulated in terms of the generalized indefinite inner product ∫ d x Ψ n ( x, t) Ψ m ( x, t), where the integrand is locally defined, and complex conjugation is avoided. A few example calculations are described which illustrate the physical origin of the ideas used in the construction of the algorithm.
Symmetric linear systems - An application of algebraic systems theory
NASA Technical Reports Server (NTRS)
Hazewinkel, M.; Martin, C.
Dynamical systems which contain several identical subsystems occur in a variety of applications ranging from command and control systems and discretization of partial differential equations, to the stability augmentation of pairs of helicopters lifting a large mass. Linear models for such systems display certain obvious symmetries. In this paper, we discuss how these symmetries can be incorporated into a mathematical model that utilizes the modern theory of algebraic systems. Such systems are inherently related to the representation theory of algebras over fields. We will show that any control scheme which respects the dynamical structure either implicitly or explicitly uses the underlying algebra.
A new Krylov-subspace method for symmetric indefinite linear systems
Freund, R.W.; Nachtigal, N.M.
Many important applications involve the solution of large linear systems with symmetric, but indefinite coefficient matrices. For example, such systems arise in incompressible flow computations and as subproblems in optimization algorithms for linear and nonlinear programs. Existing Krylov-subspace iterations for symmetric indefinite systems, such as SYMMLQ and MINRES, require the use of symmetric positive definite preconditioners, which is a rather unnatural restriction when the matrix itself is highly indefinite with both many positive and many negative eigenvalues. In this note, the authors describe a new Krylov-subspace iteration for solving symmetric indefinite linear systems that can be combined with arbitrary symmetric preconditioners. The algorithm can be interpreted as a special case of the quasi-minimal residual method for general non-Hermitian linear systems, and like the latter, it produces iterates defined by a quasi-minimal residual property. The proposed method has the same work and storage requirements per iteration as SYMMLQ or MINRES, however, it usually converges in considerably fewer iterations. Results of numerical experiments are reported.
Scattering amplitudes for the rationally extended PT symmetric complex potentials
NASA Astrophysics Data System (ADS)
Kumari, Nisha; Yadav, Rajesh Kumar; Khare, Avinash; Bagchi, Bijan; Mandal, Bhabani Prasad
In this paper, we consider the rational extensions of two different classes of PT symmetric complex potentials namely the asymptotically vanishing Scarf II and asymptotically non-vanishing Rosen-Morse II [ RM-II] and obtain the accompanying bound state eigenfunctions in terms of the exceptional Xm Jacobi polynomials and a certain class of orthogonal polynomials. By considering the asymptotic behavior of the exceptional polynomials, we also derive the reflection and transmission amplitudes for them and discuss the various novel properties of the corresponding amplitudes.
Symmetric and Asymmetric Tendencies in Stable Complex Systems
Tan, James P. L.
A commonly used approach to study stability in a complex system is by analyzing the Jacobian matrix at an equilibrium point of a dynamical system. The equilibrium point is stable if all eigenvalues have negative real parts. Here, by obtaining eigenvalue bounds of the Jacobian, we show that stable complex systems will favor mutualistic and competitive relationships that are asymmetrical (non-reciprocative) and trophic relationships that are symmetrical (reciprocative). Additionally, we define a measure called the interdependence diversity that quantifies how distributed the dependencies are between the dynamical variables in the system. We find that increasing interdependence diversity has a destabilizing effect on the equilibrium point, and the effect is greater for trophic relationships than for mutualistic and competitive relationships. These predictions are consistent with empirical observations in ecology. More importantly, our findings suggest stabilization algorithms that can apply very generally to a variety of complex systems. PMID:27545722
Symmetric and Asymmetric Tendencies in Stable Complex Systems.
Tan, James P L
A commonly used approach to study stability in a complex system is by analyzing the Jacobian matrix at an equilibrium point of a dynamical system. The equilibrium point is stable if all eigenvalues have negative real parts. Here, by obtaining eigenvalue bounds of the Jacobian, we show that stable complex systems will favor mutualistic and competitive relationships that are asymmetrical (non-reciprocative) and trophic relationships that are symmetrical (reciprocative). Additionally, we define a measure called the interdependence diversity that quantifies how distributed the dependencies are between the dynamical variables in the system. We find that increasing interdependence diversity has a destabilizing effect on the equilibrium point, and the effect is greater for trophic relationships than for mutualistic and competitive relationships. These predictions are consistent with empirical observations in ecology. More importantly, our findings suggest stabilization algorithms that can apply very generally to a variety of complex systems.
Talbot self-imaging in PT-symmetric complex crystals
NASA Astrophysics Data System (ADS)
Longhi, Stefano
The Talbot effect, i.e., the self-imaging property of a periodic wave in near-field diffraction, is a remarkable interference phenomenon in paraxial systems with continuous translational invariance. In crystals, i.e., systems with discrete translational invariance, self-imaging has been regarded so far as a rare effect, restricted to special sets of initial field distributions. Here it is shown that in a class of gapless PT-symmetric complex crystals at the symmetry-breaking threshold Talbot revivals can arise for almost any initial periodic wave distribution which is commensurate with the lattice period. A possible experimental realization of commensurate Talbot self-imaging for light pulses in complex "temporal" crystals, realized in an optical dispersive fiber loop with amplitude and phase modulators, is briefly discussed.
Spherically symmetric analysis on open FLRW solution in non-linear massive gravity
Chiang, Chien-I; Izumi, Keisuke; Chen, Pisin E-mail: email@example.com
We study non-linear massive gravity in the spherically symmetric context. Our main motivation is to investigate the effect of helicity-0 mode which remains elusive after analysis of cosmological perturbation around an open Friedmann-Lemaitre-Robertson-Walker (FLRW) universe. The non-linear form of the effective energy-momentum tensor stemming from the mass term is derived for the spherically symmetric case. Only in the special case where the area of the two sphere is not deviated away from the FLRW universe, the effective energy momentum tensor becomes completely the same as that of cosmological constant. This opens a window for discriminating the non-linear massive gravity from general relativity (GR). Indeed, by further solving these spherically symmetric gravitational equations of motion in vacuum to the linear order, we obtain a solution which has an arbitrary time-dependent parameter. In GR, this parameter is a constant and corresponds to the mass of a star. Our result means that Birkhoff's theorem no longer holds in the non-linear massive gravity and suggests that energy can probably be emitted superluminously (with infinite speed) on the self-accelerating background by the helicity-0 mode, which could be a potential plague of this theory.
Theoretical study of ignition reactions of linear symmetrical monoethers as potential diesel fuel additives: DFT calculations
NASA Astrophysics Data System (ADS)
Marrouni, Karim El; Abou-Rachid, Hakima; Kaliaguine, Serge
This work investigates the chemical reactivity of four linear symmetrical monoethers with molecular oxygen. Such oxygenated compounds may be considered as potential diesel fuel additives in order to reduce the ignition delay in diesel fuel engines. For this purpose, a kinetic study is proposed to clarify the relation between the molecular structure of the fuel molecule and its ignition properties. To this end, DFT calculations were performed for these reactions using B3LYP/6-311G(d,p) and BH&HLYP/6-311G(d,p) to determine structures, energies, and vibrational frequencies of stationary points as well as activated complexes involved in each gas-phase combustion initiation reaction of the monoethers CH3OCH3, C2H5OC2H5, C3H7OC3H7, or C4H9OC4H9 with molecular oxygen. This theoretical kinetic study was carried out using electronic structure results and the transition state theory, to assess the rate constants for all studied combustion reactions. As it has been shown in our previous work [Abou-Rachid et al., J Mol Struct (Theochem) 2003, 621, 293], the cetane number (CN) of a pure organic molecule depends on the initiation rate of its homogeneous gas-phase reaction with molecular oxygen. Indeed, the calculated initiation rate constants of the H-abstraction process of linear monoethers with O2 show a very good correlation with experimental CN data of these pure compounds at T D 1,000 K. This temperature is representative of the operating conditions of a diesel fuel engine.0
Classical irregular blocks, Hill's equation and PT-symmetric periodic complex potentials
NASA Astrophysics Data System (ADS)
Piatek, Marcin; Pietrykowski, Artur R.
The Schrödinger eigenvalue problems for the Whittaker-Hill potential {Q}_2(x) = 1/2{h}^2 cos 4x + 4hμ cos 2x and the periodic complex potential {Q}_1(x)=1/4{h}^2{e}^{-} 4ix} + 2{h}^2 cos 2x are studied using their realizations in two-dimensional conformal field theory (2dCFT). It is shown that for the weak coupling (small) h ∈ ℝ and non-integer Floquet parameter ν ∉ ℤ spectra of hamiltonians ℋi = - d2/d x 2 + Q i( x), i = 1, 2 and corresponding two linearly independent eigenfunctions are given by the classical limit of the "single flavor" and "two flavors" ( N f = 1 , 2) irregular conformal blocks. It is known that complex nonhermitian hamiltonians which are PT-symmetric (= invariant under simultaneous parity P and time reversal T transformations) can have real eigenvalues. The hamiltonian ℋ1 is PT-symmetric for h, x ∈ ℝ. It is found that ℋ1 has a real spectrum in the weak coupling region for ν ∈ ℝ ℤ. This fact in an elementary way follows from a definition of the N f = 1 classical irregular block. Thus, ℋ1 can serve as yet another new model for testing postulates of PT-symmetric quantum mechanics.
Generation of Symmetric Dicke States of Remote Qubits with Linear Optics
Thiel, C.; Zanthier, J. von; Bastin, T.; Solano, E.; Agarwal, G. S.
We propose a method for generating all symmetric Dicke states, either in the long-lived internal levels of N massive particles or in the polarization degrees of freedom of photonic qubits, using linear optical tools only. By means of a suitable multiphoton detection technique, erasing Welcher-Weg information, our proposed scheme allows the generation and measurement of an important class of entangled multiqubit states.
Neutrinoless double beta decay in the left-right symmetric models for linear seesaw
NASA Astrophysics Data System (ADS)
Gu, Pei-Hong
In a class of left-right symmetric models for linear seesaw, a neutrinoless double beta decay induced by the left- and right-handed charged currents together will only depend on the breaking details of left-right and electroweak symmetries. This neutrinoless double beta decay can reach the experimental sensitivities if the right-handed charged gauge boson is below the 100TeV scale.
More Results on the Convergence of Iterative Methods for the Symmetric Linear Complementarity Problem.
earlier paper, our present analysis applies only to the symmetric linear complementarity problem . Various applications to a strictly convex quadratic...characterization requires no such constraint qualification as (F). There is yet another approach to apply an iterative method for solving the strictly convex ...described a Lagrangian relaxation algorithm for a constrained matrix problem which is formulated as a strictly convex separable quadratic program. They
The development of an algebraic multigrid algorithm for symmetric positive definite linear systems
Vanek, P.; Mandel, J.; Brezina, M.
An algebraic multigrid algorithm for symmetric, positive definite linear systems is developed based on the concept of prolongation by smoothed aggregation. Coarse levels are generated automatically. We present a set of requirements motivated heuristically by a convergence theory. The algorithm then attempts to satisfy the requirements. Input to the method are the coefficient matrix and zero energy modes, which are determined from nodal coordinates and knowledge of the differential equation. Efficiency of the resulting algorithm is demonstrated by computational results on real world problems from solid elasticity, plate blending, and shells.
Buckling Behavior of Long Symmetrically Laminated Plates Subjected to Shear and Linearly Varying Axial Edge Loads
NASA Technical Reports Server (NTRS)
Nemeth, Michael P.
A parametric study of the buckling behavior of infinitely long symmetrically laminated anisotropic plates that are subjected to linearly varying edge loads, uniform shear loads, or combinations of these loads is presented. The study focuses on the effects of the shape of linearly varying edge load distribution, plate orthotropy, and plate flexural anisotropy on plate buckling behavior. In addition, the study exmines the interaction of linearly varying edge loads and uniform shear loads with plate flexural anisotropy and orthotropy. Results obtained by using a special purpose nondimensional analysis that is well suited for parametric studies of clamped and simply supported plates are presented for [+/- theta](sub s), thin graphite-epoxy laminates that are representative of spacecraft structural components. Also, numerous generic buckling-design charts are presented for a wide range of nondimensional parameters that are applicable to a broad class of laminate constructions. These charts show explicitly the effects of flexural orthotropy and flexural anisotropy on plate buckling behavior for linearly varying edge loads, uniform shear loads, or combinations of these loads. The most important finding of the present study is that specially orthotropic and flexurally anisotropic plates that are subjected to an axial edge load distribution that is tension dominated can support shear loads that are larger in magnitude than the shear buckling load.
Observation of Bloch oscillations in complex PT-symmetric photonic lattices
Wimmer, Martin; Miri, Mohammed-Ali; Christodoulides, Demetrios; Peschel, Ulf
Light propagation in periodic environments is often associated with a number of interesting and potentially useful processes. If a crystalline optical potential is also linearly ramped, light can undergo periodic Bloch oscillations, a direct outcome of localized Wannier-Stark states and their equidistant eigenvalue spectrum. Even though these effects have been extensively explored in conservative settings, this is by no means the case in non-Hermitian photonic lattices encompassing both amplification and attenuation. Quite recently, Bloch oscillations have been predicted in parity-time-symmetric structures involving gain and loss in a balanced fashion. While in a complex bulk medium, one intuitively expects that light will typically follow the path of highest amplification, in a periodic system this behavior can be substantially altered by the underlying band structure. Here, we report the first experimental observation of Bloch oscillations in parity-time-symmetric mesh lattices. We show that these revivals exhibit unusual properties like secondary emissions and resonant restoration of PT symmetry. In addition, we present a versatile method for reconstructing the real and imaginary components of the band structure by directly monitoring the light evolution during a cycle of these oscillations. PMID:26639941
Comparison of Finite Differences and WKB approximation Methods for PT symmetric complex potentials
NASA Astrophysics Data System (ADS)
Naceri, Leila; Chekkal, Meziane; Hammou, Amine B.
We consider the one dimensional schrödinger eigenvalue problem on a finite domain (Strum-Liouville problem) for several PT-symmetric complex potentials, studied by Bender and Jones using the WKB approximation method. We make a comparison between the solutions of theses PT-symmetric complex potentials using both the finite difference method (FDM) and the WKB approximation method and show quantitative and qualitative agreement between the two methods.
Symmetric and asymmetric solitons in linearly coupled Bose-Einstein condensates trapped in optical lattices
Gubeskys, Arthur; Malomed, Boris A.
We study spontaneous symmetry breaking in a system of two parallel quasi-one-dimensional traps (cores), equipped with optical lattices (OLs) and filled with a Bose-Einstein condensate (BEC). The cores are linearly coupled by tunneling (the model may also be interpreted in terms of spatial solitons in parallel planar optical waveguides with a periodic modulation of the refractive index). Analysis of the corresponding system of linearly coupled Gross-Pitaevskii equations (GPEs) reveals that spectral band gaps of the single GPE split into subgaps. Symmetry breaking in two-component BEC solitons is studied in cases of the attractive (AA) and repulsive (RR) nonlinearity in both traps; the mixed situation, with repulsion in one trap and attraction in the other (RA), is considered too. In all the cases, stable asymmetric solitons are found, bifurcating from symmetric or antisymmetric ones (and destabilizing them), in the AA and RR systems, respectively. In either case, bistability is predicted, with a nonbifurcating stable branch, either antisymmetric or symmetric, coexisting with asymmetric ones. Solitons destabilized by the bifurcation tend to rearrange themselves into their stable asymmetric counterparts. In addition to the fundamental solitons, branches of twisted (odd) solitons in the AA system, and twisted bound states of fundamental solitons in both AA and RR systems, are found too. The impact of a phase mismatch, {delta}, between the OLs in the two cores is also studied. It is concluded that {delta}={pi}/2 only mildly deforms the picture, while {delta}={pi} changes it drastically, replacing the symmetry-breaking bifurcations by pseudobifurcations, with the branch of asymmetric solutions asymptotically approaching its symmetric or antisymmetric counterpart (in the AA and RR system, respectively), rather than splitting off from it. Also considered is a related model, for a binary BEC in a single-core trap with the OL, assuming that the two species (representing
On the stability of the non-symmetric BEM/FEM coupling in linear elasticity
NASA Astrophysics Data System (ADS)
Steinbach, Olaf
In this paper we discuss the use of single and double layer boundary integral equations for the numerical solution of linear elasticity problems with boundary conditions of mixed type, and the one-equation coupling of finite and boundary element methods to solve a free space transmission problem. In particular we present a sufficient and necessary condition which ensures stability of the coupled approach for any choice of finite and boundary elements. These results justify the coupling of collocation and Galerkin one-equation boundary element methods with finite elements as used in many engineering and industrial applications. Hence one may avoid the use of the symmetric formulation of boundary integral equations, which is, although well established from a mathematical point of view and also used in some engineering applications, not so much accepted in particular in industrial applications.
Stability of soliton families in nonlinear Schrödinger equations with non-parity-time-symmetric complex potentials
NASA Astrophysics Data System (ADS)
Yang, Jianke; Nixon, Sean
Stability of soliton families in one-dimensional nonlinear Schrödinger equations with non-parity-time (PT)-symmetric complex potentials is investigated numerically. It is shown that these solitons can be linearly stable in a wide range of parameter values both below and above phase transition. In addition, a pseudo-Hamiltonian-Hopf bifurcation is revealed, where pairs of purely-imaginary eigenvalues in the linear-stability spectra of solitons collide and bifurcate off the imaginary axis, creating oscillatory instability, which resembles Hamiltonian-Hopf bifurcations of solitons in Hamiltonian systems even though the present system is dissipative and non-Hamiltonian. The most important numerical finding is that, eigenvalues of linear-stability operators of these solitons appear in quartets (λ , - λ ,λ* , -λ*), similar to conservative systems and PT-symmetric systems. This quartet eigenvalue symmetry is very surprising for non- PT-symmetric systems, and it has far-reaching consequences on the stability behaviors of solitons.
Spatial turning bands simulation of anisotropic non-linear models of coregionalization with symmetric cross-covariances
NASA Astrophysics Data System (ADS)
Marcotte, D.
The turning bands method (TBM) is a commonly used method of simulation for large Gaussian fields, its O(N) complexity being unsurpassed (N denotes the number of points to simulate). TBM can be implemented either in the spatial or the spectral domains. In the multivariate anisotropic case, spatial versions of TBM are currently available only for the linear model of coregionalization (LMC). For anisotropic non-LMC with symmetrical covariances only the spectral version is currently available. The spectral domain approach can be slow in the case of non-differentiable covariances due to the numerous frequencies to sample. Here a derivation of the equations is provided for simulating the anisotropic non-LMC directly in the spatial domain and the method is illustrated with two synthetic examples. The approach allows the specification of many different direct and cross-covariance components, each with possibly different geometric anisotropies and different model types. The complexity of the new multivariate approach remains O(N). Hence, a case of two variables defining an anisotropic non-LMC is simulated over one billion points in less than one hour on a desktop computer. These results help enlarge the scope of application of the TBM. The method can be easily implemented in any existing TBM program.
Linear perturbation analysis of hairy black holes in shift-symmetric Horndeski theories: Odd-parity perturbations
NASA Astrophysics Data System (ADS)
Takahashi, Kazufumi; Suyama, Teruaki
We analyze the mode stability of odd-parity perturbations of black holes with linearly time-dependent scalar hair in shift-symmetric Horndeski theories. We show that a large class of black hole solutions in these theories suffer from ghost or gradient instability, while there are some classes of solutions that are stable under linear odd-parity perturbations in the context of mode analysis.
Collision-induced absorption in mixtures of symmetrical linear and tetrahedral molecules - Methane-nitrogen
NASA Technical Reports Server (NTRS)
Birnbaum, G.; Borysow, A.; Buechele, A.
The far infrared absorption of a CH4-N2 mixture was measured at 297, 195, and 162 K from 30 to 650/cm. The spectral invariants gamma1 and alpha1, proportional, respectively, to the zeroth and first spectral moments, due to bimolecular collisions between CH4 and N2 were obtained from these data and compared with theoretical values. The theory for collision-induced dipoles between a tetrahedral and a diatomic or symmetrical linear molecule includes contributions not previously considered. Whereas the theoretical values of gamma1 are only somewhat greater than experiment at all temperatures, the theoretical values of alpha1 are significantly lower than the experimental values. From the theoretical spectral moments for the various induced dipole components, the parameters of the BC shape were computed, and theoretical spectra were constructed. Good agreement was obtained at the lower frequencies, but with increasing frequencies the theoretical spectra were increasingly less intense than the experimental spectra. Although the accuracy of the theoretical results may suffer from the lack of a reliable potential function, it does not appear that this high frequency discrepancy can be removed by any conceivable modification in the potential.
Parametric symmetries in exactly solvable real and PT symmetric complex potentials
NASA Astrophysics Data System (ADS)
Yadav, Rajesh Kumar; Khare, Avinash; Bagchi, Bijan; Kumari, Nisha; Mandal, Bhabani Prasad
In this paper, we discuss the parametric symmetries in different exactly solvable systems characterized by real or complex PT symmetric potentials. We focus our attention on the conventional potentials such as the generalized Pöschl Teller (GPT), Scarf-I, and PT symmetric Scarf-II which are invariant under certain parametric transformations. The resulting set of potentials is shown to yield a completely different behavior of the bound state solutions. Further, the supersymmetric partner potentials acquire different forms under such parametric transformations leading to new sets of exactly solvable real and PT symmetric complex potentials. These potentials are also observed to be shape invariant (SI) in nature. We subsequently take up a study of the newly discovered rationally extended SI potentials, corresponding to the above mentioned conventional potentials, whose bound state solutions are associated with the exceptional orthogonal polynomials (EOPs). We discuss the transformations of the corresponding Casimir operator employing the properties of the so(2, 1) algebra.
Localized modes in χ(2 ) media with non-PT -symmetric complex localized potentials
NASA Astrophysics Data System (ADS)
Moreira, F. C.; Cavalcanti, S. B.
We study the existence and the stability of solitons in quadratic nonlinear media with spatially localized non-PT -symmetric tunable modulation of the linear refractive index. The properties of nonlinear modes bifurcating from a linear limit of a small fundamental harmonic field are investigated. The modes bifurcating from the linear mode of the second harmonic may exist even above the real phase breaking threshold. The stability intervals for different values of the propagation constant and gain-loss gradient are obtained. Examples of dynamics and excitations of solitons obtained by numerical simulations are also given.
Response of Seismometer with Symmetric Triaxial Sensor Configuration to Complex Ground Motion
NASA Astrophysics Data System (ADS)
Graizer, V.
Most instruments used in seismological practice to record ground motion in all directions use three sensors oriented toward North, East and upward. In this standard configuration horizontal and vertical sensors differ in their construction because of gravity acceleration always applied to a vertical sensor. An alternative way of symmetric sensor configuration was first introduced by Galperin (1955) for petroleum exploration. In this arrangement three identical sensors are also positioned orthogonally to each other but are tilted at the same angle of 54.7 degrees to the vertical axis (triaxial system of coordinate balanced on its corner). Records obtained using symmetric configuration must be rotated into an earth referenced X, Y, Z coordinate system. A number of recent seismological instruments (e.g., broadband seismometers Streckeisen STS-2, Trillium of Nanometrics and Cronos of Kinemetrics) are using symmetric sensor configuration. In most of seismological studies it is assumed that rotational (rocking and torsion) components of earthquake ground motion are small enough to be neglected. However, recently examples were shown when rotational components are significant relative to translational components of motions. Response of pendulums installed in standard configuration (vertical and two horizontals) to complex input motion that includes rotations has been studied in a number of publications. We consider the response of pendulums in a symmetric sensor configuration to complex input motions including rotations, and the resultant triaxial system response. Possible implications of using symmetric sensor configuration in strong motion studies are discussed. Considering benefits of equal design of all three sensors in symmetric configuration, and as a result potentially lower cost of the three-component accelerograph, it may be useful for strong motion measurements not requiring high resolution post signal processing. The disadvantage of this configuration is that if
A single Lanczos propagation method for calculating transition amplitudes. III. S-matrix elements with a complex-symmetric Hamiltonian
NASA Astrophysics Data System (ADS)
Li, Shenmin; Li, Guohui; Guo, Hua
The recently proposed single Lanczos propagation method [J. Chem. Phys. 111, 9944 (1999); ibid. 114, 1467 (2001)] is extended to complex-symmetric Hamiltonians. It is shown that the complex-symmetric Lanczos algorithm possesses several useful numerical properties similar to those observed in real-symmetric cases, which enable one to compute multiple transition amplitudes with a single Lanczos propagation. The usefulness of the method is illustrated in calculating the S-matrix elements for the collinear H+H2 reaction.
A Family of Symmetric Linear Multistep Methods for the Numerical Solution of the Schroedinger Equation and Related Problems
Anastassi, Z. A.; Simos, T. E.
We develop a new family of explicit symmetric linear multistep methods for the efficient numerical solution of the Schroedinger equation and related problems with oscillatory solution. The new methods are trigonometrically fitted and have improved intervals of periodicity as compared to the corresponding classical method with constant coefficients and other methods from the literature. We also apply the methods along with other known methods to real periodic problems, in order to measure their efficiency.
Symmetrized complex amplitudes for He double photoionization from the time-dependent close coupling and exterior complex scaling methods
Horner, D.A.; Colgan, J.; Martin, F.; McCurdy, C.W.; Pindzola, M.S.; Rescigno, T.N.
Symmetrized complex amplitudes for the double photoionization of helium are computed by the time-dependent close-coupling and exterior complex scaling methods, and it is demonstrated that both methods are capable of the direct calculation of these amplitudes. The results are found to be in excellent agreement with each other and in very good agreement with results of other ab initio methods and experiment.
Complex linear superfields, supercurrents and supergravities
NASA Astrophysics Data System (ADS)
Kočí, P.; Koutrolikos, K.; von Unge, R.
We present expressions for the supercurrents generated by a generic 4 D, N=1 theory of complex linear superfield Σ. We verify that these expressions satisfy the appropriate superspace conservation equations. Furthermore, we discuss the component projection in order to derive expressions for the energy-momentum tensor, the supersymmetry current and the R-symmetry current when available. In addition, we discuss aspects of the coupling of the theory to supergravity. Specifically, we present a straightforward method to select the appropriate formulations of supergravity that one must use in order to do the coupling. This procedure is controlled by a superfield X originating from the Super-Poincaré invariance of ccthe theory. We apply these results to examples of theories with higher derivative terms.
Preconditioning the bidomain model with almost linear complexity
NASA Astrophysics Data System (ADS)
Pierre, Charles
The bidomain model is widely used in electro-cardiology to simulate spreading of excitation in the myocardium and electrocardiograms. It consists of a system of two parabolic reaction diffusion equations coupled with an ODE system. Its discretisation displays an ill-conditioned system matrix to be inverted at each time step: simulations based on the bidomain model therefore are associated with high computational costs. In this paper we propose a preconditioning for the bidomain model either for an isolated heart or in an extended framework including a coupling with the surrounding tissues (the torso). The preconditioning is based on a formulation of the discrete problem that is shown to be symmetric positive semi-definite. A block LU decomposition of the system together with a heuristic approximation (referred to as the monodomain approximation) are the key ingredients for the preconditioning definition. Numerical results are provided for two test cases: a 2D test case on a realistic slice of the thorax based on a segmented heart medical image geometry, a 3D test case involving a small cubic slab of tissue with orthotropic anisotropy. The analysis of the resulting computational cost (both in terms of CPU time and of iteration number) shows an almost linear complexity with the problem size, i.e. of type nlog α( n) (for some constant α) which is optimal complexity for such problems.
Modeling and minimizing CAPRI round 30 symmetrical protein complexes from CASP-11 structural models.
El Houasli, Marwa; Maigret, Bernard; Devignes, Marie-Dominique; Ghoorah, Anisah W; Grudinin, Sergei; Ritchie, David W
Many of the modeling targets in the blind CASP-11/CAPRI-30 experiment were protein homo-dimers and homo-tetramers. Here, we perform a retrospective docking-based analysis of the perfectly symmetrical CAPRI Round 30 targets whose crystal structures have been published. Starting from the CASP "stage-2" fold prediction models, we show that using our recently developed "SAM" polar Fourier symmetry docking algorithm combined with NAMD energy minimization often gives acceptable or better 3D models of the target complexes. We also use SAM to analyze the overall quality of all CASP structural models for the selected targets from a docking-based perspective. We demonstrate that docking only CASP "center" structures for the selected targets provides a fruitful and economical docking strategy. Furthermore, our results show that many of the CASP models are dockable in the sense that they can lead to acceptable or better models of symmetrical complexes. Even though SAM is very fast, using docking and NAMD energy minimization to pull out acceptable docking models from a large ensemble of docked CASP models is computationally expensive. Nonetheless, thanks to our SAM docking algorithm, we expect that applying our docking protocol on a modern computer cluster will give us the ability to routinely model 3D structures of symmetrical protein complexes from CASP-quality models. Proteins 2017; 85:463-469. © 2016 Wiley Periodicals, Inc.
General theory of spherically symmetric boundary-value problems of the linear transport theory.
NASA Technical Reports Server (NTRS)
Kanal, M.
A general theory of spherically symmetric boundary-value problems of the one-speed neutron transport theory is presented. The formulation is also applicable to the 'gray' problems of radiative transfer. The Green's function for the purely absorbing medium is utilized in obtaining the normal mode expansion of the angular densities for both interior and exterior problems. As the integral equations for unknown coefficients are regular, a general class of reduction operators is introduced to reduce such regular integral equations to singular ones with a Cauchy-type kernel. Such operators then permit one to solve the singular integral equations by the standard techniques due to Muskhelishvili. We discuss several spherically symmetric problems. However, the treatment is kept sufficiently general to deal with problems lacking azimuthal symmetry. In particular the procedure seems to work for regions whose boundary coincides with one of the coordinate surfaces for which the Helmholtz equation is separable.
Gap solitons in parity-time-symmetric mixed linear-nonlinear optical lattices with fourth-order diffraction
NASA Astrophysics Data System (ADS)
Zhu, Xing; Shi, Zhiwei; Li, Huagang
We report on the existence and stability of fundamental and out-of-phase dipole gap solitons in parity-time (PT)-symmetric mixed linear-nonlinear optical lattices with a fourth-order diffraction. These solitons exist in the semi-infinite gap. For fundamental gap solitons, they can bifurcate from the higher edge of the first Bloch band, solitons are stable in the low power region. For dipole gap solitons, they cannot bifurcate from the higher edge of the first Bloch band, they can stably exist in the moderate power region. The coupling constant of the fourth-order diffraction can influence the stability of these gap solitons.
Structural tailoring effects on the magnetic behavior of symmetric and asymmetric cubane-type Ni complexes.
Ponomaryov, Alexey N; Kim, Namseok; Hwang, Jaewon; Nojiri, Hiroyuki; van Tol, Johan; Ozarowski, Andrew; Park, Jena; Jang, Zeehoon; Suh, Byoungjin; Yoon, Sungho; Choi, Kwang-Yong
Using two kinds of carboxylate ligands with small but significant differences in steric size, symmetric and asymmetric Fe(II) and Ni(II) cubanes have been synthesized in a controlled fashion. Fast sweeping pulsed field measurements showed magnetization hysteresis loops for two cubane-type molecular complexes, [Ni4(μ-OMe)4(O2CAr(4F-Ph))4(HOMe)8] and [Ni4(μ-OMe)4(O2CAr(Tol))4(HOMe)6], thus suggesting single-molecule magnet behavior. To differentiate the magnetic properties between the symmetric and asymmetric cubanes, detailed electron paramagnetic resonance (EPR) measurements were performed. From the EPR data, taken at various frequencies and temperatures, zero-field splitting parameters D, E, and other higher-order parameters for both cubane samples were extracted. Compared to the symmetric Ni-cubane, the asymmetric one shows an increase in the D and E values by about 20%, thereby suggesting structural engineering effects on the magnetic properties. By using the magnetic parameters determined by EPR, a static magnetization curve at 2 K and a temperature dependence of the magnetic susceptibility were simulated. A good agreement between theoretical and experimental data confirms the validity of the values obtained from EPR measurements.
A Symmetrical Tetramer for S. aureus Pyruvate Carboxylase in Complex with Coenzyme A
Yu, L.; Xiang, S; Lasso, G; Gil, D; Valle, M; Tong, L
Pyruvate carboxylase (PC) is a conserved metabolic enzyme with important cellular functions. We report crystallographic and cryo-electron microscopy (EM) studies of Staphylococcus aureus PC (SaPC) in complex with acetyl-CoA, an allosteric activator, and mutagenesis, biochemical, and structural studies of the biotin binding site of its carboxyltransferase (CT) domain. The disease-causing A610T mutation abolishes catalytic activity by blocking biotin binding to the CT active site, and Thr908 might play a catalytic role in the CT reaction. The crystal structure of SaPC in complex with CoA reveals a symmetrical tetramer, with one CoA molecule bound to each monomer, and cryo-EM studies confirm the symmetrical nature of the tetramer. These observations are in sharp contrast to the highly asymmetrical tetramer of Rhizobium etli PC in complex with ethyl-CoA. Our structural information suggests that acetyl-CoA promotes a conformation for the dimer of the biotin carboxylase domain of PC that might be catalytically more competent.
Circularly-symmetric complex normal ratio distribution for scalar transmissibility functions. Part I: Fundamentals
NASA Astrophysics Data System (ADS)
Yan, Wang-Ji; Ren, Wei-Xin
Recent advances in signal processing and structural dynamics have spurred the adoption of transmissibility functions in academia and industry alike. Due to the inherent randomness of measurement and variability of environmental conditions, uncertainty impacts its applications. This study is focused on statistical inference for raw scalar transmissibility functions modeled as complex ratio random variables. The goal is achieved through companion papers. This paper (Part I) is dedicated to dealing with a formal mathematical proof. New theorems on multivariate circularly-symmetric complex normal ratio distribution are proved on the basis of principle of probabilistic transformation of continuous random vectors. The closed-form distributional formulas for multivariate ratios of correlated circularly-symmetric complex normal random variables are analytically derived. Afterwards, several properties are deduced as corollaries and lemmas to the new theorems. Monte Carlo simulation (MCS) is utilized to verify the accuracy of some representative cases. This work lays the mathematical groundwork to find probabilistic models for raw scalar transmissibility functions, which are to be expounded in detail in Part II of this study.
Non-linear resonances in the forced responses of plates. I - Symmetric responses of circular plates
NASA Technical Reports Server (NTRS)
Sridhar, S.; Mook, D. T.; Nayfeh, A. H.
The dynamic analogue of the von Karman equations is used to study the symmetric response of a circular plate to a harmonic excitation when the frequency of the excitation is near one of the natural frequencies. It is shown that, in general, when there is no internal resonance (i.e., the natural frequencies are not commensurable), only the mode having a frequency near that of the excitation is strongly excited (i.e., is needed to represent the response in the first approximation). A clamped, circular plate is used as a numerical example to show that, when there is an internal resonance, more than one of the modes involved in this resonance can be strongly excited; moreover, when more than one mode is strongly excited, the lower modes can dominate the response, even when the frequency of the excitation is near that of the highest mode. This possibility was not revealed by any of the earlier studies which were based on the same governing equations.
The fractional dimensional spatiotemporal accessible solitons supported by PT-symmetric complex potential
NASA Astrophysics Data System (ADS)
Zhong, Wei-Ping; Belić, Milivoj; Zhang, Yiqi
Using the separation variable technique, the properties of localized accessible soliton family supported by a parity-time (PT) symmetric complex potential in fractional dimension (FD) 2 < D ≤ 3 are investigated in strongly nonlocal nonlinear media. Analytical solution of the FD Schrödinger equation in the limit of strongly nonlocal nonlinearity, given in terms of the generalized Laguerre and the Gegenbauer polynomials in spherical coordinates, is obtained. Some dynamical characteristics of the accessible solitons and a specific angular expression, such as the spatiotemporal distribution, the angular distribution and external profiles of the analytical solution, are displayed for some peculiar quantum numbers. We expect that the FD accessible solitons will find various applications in science and technology in the future.
Malachite green mediates homodimerization of antibody VL domains to form a fluorescent ternary complex with singular symmetric interfaces
Szent-Gyorgyi, Chris; Stanfield, Robyn L.; Andreko, Susan; Dempsey, Alison; Ahmed, Mushtaq; Capek, Sara; Waggoner, Alan; Wilson, Ian A.; Bruchez, Marcel P.
We report that a symmetric small molecule ligand mediates the assembly of antibody light chain variable domains (VLs) into a correspondent symmetric ternary complex with novel interfaces. The L5* Fluorogen Activating Protein (FAP) is a VL domain that binds malachite green dye (MG) to activate intense fluorescence. Crystallography of liganded L5* reveals a 2:1 protein:ligand complex with inclusive C2 symmetry, where MG is almost entirely encapsulated between an antiparallel arrangement of the two VL domains. Unliganded L5* VL domains crystallize as a similar antiparallel VL/VL homodimer. The complementarity determining regions (CDRs) are spatially oriented to form novel VL/VL and VL/ligand interfaces that tightly constrain a propeller conformer of MG. Binding equilibrium analysis suggests highly cooperative assembly to form a very stable VL/MG/VL complex, such that MG behaves as a strong chemical inducer of dimerization. Fusion of two VL domains into a single protein tightens MG binding over 1,000-fold to low picomolar affinity without altering the large binding enthalpy, suggesting that bonding interactions with ligand and restriction of domain movements make independent contributions to binding. Fluorescence activation of a symmetrical fluorogen provides a selection mechanism for the isolation and directed evolution of ternary complexes where unnatural symmetric binding interfaces are favored over canonical antibody interfaces. As exemplified by L5*, these self-reporting complexes may be useful as modulators of protein association or as high affinity protein tags and capture reagents. PMID:23978698
Malachite green mediates homodimerization of antibody VL domains to form a fluorescent ternary complex with singular symmetric interfaces.
Szent-Gyorgyi, Chris; Stanfield, Robyn L; Andreko, Susan; Dempsey, Alison; Ahmed, Mushtaq; Capek, Sarah; Waggoner, Alan S; Wilson, Ian A; Bruchez, Marcel P
We report that a symmetric small-molecule ligand mediates the assembly of antibody light chain variable domains (VLs) into a correspondent symmetric ternary complex with novel interfaces. The L5* fluorogen activating protein is a VL domain that binds malachite green (MG) dye to activate intense fluorescence. Crystallography of liganded L5* reveals a 2:1 protein:ligand complex with inclusive C2 symmetry, where MG is almost entirely encapsulated between an antiparallel arrangement of the two VL domains. Unliganded L5* VL domains crystallize as a similar antiparallel VL/VL homodimer. The complementarity-determining regions are spatially oriented to form novel VL/VL and VL/ligand interfaces that tightly constrain a propeller conformer of MG. Binding equilibrium analysis suggests highly cooperative assembly to form a very stable VL/MG/VL complex, such that MG behaves as a strong chemical inducer of dimerization. Fusion of two VL domains into a single protein tightens MG binding over 1000-fold to low picomolar affinity without altering the large binding enthalpy, suggesting that bonding interactions with ligand and restriction of domain movements make independent contributions to binding. Fluorescence activation of a symmetrical fluorogen provides a selection mechanism for the isolation and directed evolution of ternary complexes where unnatural symmetric binding interfaces are favored over canonical antibody interfaces. As exemplified by L5*, these self-reporting complexes may be useful as modulators of protein association or as high-affinity protein tags and capture reagents.
Linear relation on the correlation in complex networks
NASA Astrophysics Data System (ADS)
Ma, C. W.; Szeto, K. Y.
Correlation in complex networks follows a linear relation between the degree of a node and the total degrees of its neighbors for six different classes of real networks. This general linear relation is an extension of the Aboav-Weaire law in two-dimensional cellular structures and provides a simple and different perspective on the correlation in complex networks, which is complementary to an existing description using Pearson correlation coefficients and a power law fit. Analytical expression for this linear relation for three standard models of complex networks: the Erdos-Renyi, Watts-Strogatz, and Barabasi-Albert networks is provided. The slope and intercept of this linear relation are described by a single parameter a together with the first and second moment of the degree distribution of the network. The assortivity of the network can be related to the sign of the intercept.
Influence of composition fluctuations on the linear viscoelastic properties of symmetric diblock copolymers near the order-disorder transition
Hickey, Robert J.; Gillard, Timothy M.; Lodge, Timothy P.; Bates, Frank S.
Rheological evidence of composition fluctuations in disordered diblock copolymers near the order disorder transition (ODT) has been documented in the literature over the past three decades, characterized by a failure of time–temperature superposition (tTS) to reduce linear dynamic mechanical spectroscopy (DMS) data in the terminal viscoelastic regime to a temperature-independent form. However, for some materials, most notably poly(styrene-b-isoprene) (PS–PI), no signature of these rheological features has been found. We present small-angle X-ray scattering (SAXS) results on symmetric poly(cyclohexylethylene-b-ethylene) (PCHE–PE) diblock copolymers that confirm the presence of fluctuations in the disordered state and DMS measurements that also show no sign of the features ascribed to composition fluctuations. Assessment of DMS results published on five different diblock copolymer systems leads us to conclude that the effects of composition fluctuations can be masked by highly asymmetric block dynamics, thereby resolving a long-standing disagreement in the literature and reinforcing the importance of mechanical contrast in understanding the dynamics of ordered and disordered block polymers.
A study on the interaction between two rumors in homogeneous complex networks under symmetric conditions
NASA Astrophysics Data System (ADS)
Jie, Renlong; Qiao, Jian; Xu, Genjiu; Meng, Yingying
The propagating dynamics of more than one rumor has received a substantial amount of attention in recent years. To investigate the effects of interactions between two rumors under symmetric conditions, we built a model based on an ordinary differential equation system while assuming that each individual's spreading rate after receiving one rumor depends on whether he/she knows the other rumor. In certain cases, two rumors accelerate the spread of each other, while in a portion of the other cases they impede or decelerate the spread of each other. We discuss these effects by dividing the total population into nine groups that correspond to nine states, and we subsequently build the mean-field equations for the two-rumor interaction based on the SIR model in a homogeneous complex network, and we find their numerical solution with varying interaction factors for the rates of spreading and becoming disinterested. The results show that when we change these interaction factors, the density curves of the nine states and their maximum values will change accordingly by a series of rules, which demonstrates the corresponding effects when there is a positive or negative interaction between the two rumors. Our work could establish a foundation for further study of this issue.
Fluorescence study of protein-lipid complexes with a new symmetric squarylium probe.
Ioffe, Valeriya M; Gorbenko, Galyna P; Deligeorgiev, Todor; Gadjev, Nikolai; Vasilev, Aleksey
The novel symmetric squarylium derivative SQ-1 has been synthesized and tested for its sensitivity to the formation of protein-lipid complexes. SQ-1 binding to the model membranes composed of zwitterionic lipid phosphatidylcholine (PC) and its mixtures with anionic lipid cardiolipin (CL) in different molar ratios was found to be controlled mainly by hydrophobic interactions. Lysozyme (Lz) and ribonuclease A (RNase) exerted an influence on the probe association with lipid vesicles resulting presumably from the competition between SQ-1 and the proteins for bilayer free volume and modification of its properties. The magnitude of this effect was much higher for lysozyme which may stem from the amphipathy of protein alpha-helix involved in the membrane binding. Varying membrane composition provides evidence for the dye sensitivity to both hydrophobic and electrostatic protein-lipid interactions. Fluorescence anisotropy studies uncovered the restriction of SQ-1 rotational mobility in lipid environment in the presence of Lz and RNase being indicative of the incorporation of the proteins into bilayer interior. The results of binding, fluorescence quenching and kinetic experiments suggested lysozyme-induced local lipid demixing upon protein association with negatively charged membranes with threshold concentration of CL for the lipid demixing being 10 mol%.
Lanczos-type variants of the COCR method for complex nonsymmetric linear systems
NASA Astrophysics Data System (ADS)
Jing, Yan-Fei; Huang, Ting-Zhu; Zhang, Yong; Li, Liang; Cheng, Guang-Hui; Ren, Zhi-Gang; Duan, Yong; Sogabe, Tomohiro; Carpentieri, Bruno
Motivated by the celebrated extending applications of the well-established complex Biconjugate Gradient (CBiCG) method to deal with large three-dimensional electromagnetic scattering problems by Pocock and Walker [M.D. Pocock, S.P. Walker, The complex Bi-conjugate Gradient solver applied to large electromagnetic scattering problems, computational costs, and cost scalings, IEEE Trans. Antennas Propagat. 45 (1997) 140-146], three Lanczos-type variants of the recent Conjugate A-Orthogonal Conjugate Residual (COCR) method of Sogabe and Zhang [T. Sogabe, S.-L. Zhang, A COCR method for solving complex symmetric linear systems, J. Comput. Appl. Math. 199 (2007) 297-303] are explored for the solution of complex nonsymmetric linear systems. The first two can be respectively considered as mathematically equivalent but numerically improved popularizing versions of the BiCR and CRS methods for complex systems presented in Sogabe's Ph.D. Dissertation. And the last one is somewhat new and is a stabilized and more smoothly converging variant of the first two in some circumstances. The presented algorithms are with the hope of obtaining smoother and, hopefully, faster convergence behavior in comparison with the CBiCG method as well as its two corresponding variants. This motivation is demonstrated by numerical experiments performed on some selective matrices borrowed from The University of Florida Sparse Matrix Collection by Davis.
Vacuum systems of linear accelerators of the NICA injection complex
NASA Astrophysics Data System (ADS)
Kosachev, V. V.; Bazanov, A. M.; Butenko, A. V.; Galimov, A. R.; Nesterov, A. V.; Pivin, R. V.; Smirnov, A. V.
The NICA project, which includes several accelerators of charged particles, is under construction in the Laboratory of High Energy Physics, Joint Institute for Nuclear Research (JINR), Dubna. Obtaining the required vacuum conditions is one of the key points in implementing the project, because reaching the required ion lifetime at all stages of particle acceleration is what determines the effective luminosity of the experiments in the long run. Currently, modernization of the vacuum system of the injection complex of the LU-20 linear accelerator of light ions, one of oldest accelerators in the JINR, is being carried out and the new HILAC linear accelerator for the acceleration of gold ions in the collider mode of the NICA complex is being installed. At the end parts of the linear accelerators, the residual gas pressure must be approximately 10-5 Pa, which is determined by the maximum amplitude of the RF electric field used for the acceleration of ions.
Solving complex-valued linear systems via equivalent real formulations
Most algorithms used in preconditioned iterative methods are generally applicable to complex valued linear systems, with real valued linear systems simply being a special case. However, most iterative solver packages available today focus exclusively on real valued systems, or deal with complex valued systems as an afterthought. One obvious approach to addressing this problem is to recast the complex problem into one of a several equivalent real forms and then use a real valued solver to solve the related system. However, well-known theoretical results showing unfavorable spectral properties for the equivalent real forms have diminished enthusiasm for this approach. At the same time, experience has shown that there are situations where using an equivalent real form can be very effective. In this paper, the authors explore this approach, giving both theoretical and experimental evidence that an equivalent real form can be useful for a number of practical situations. Furthermore, they show that by making good use of some of the advance features of modem solver packages, they can easily generate equivalent real form preconditioners that are computationally efficient and mathematically identical to their complex counterparts. Using their techniques, they are able to solve very ill-conditioned complex valued linear systems for a variety of large scale applications. However, more importantly, they shed more light on the effectiveness of equivalent real forms and more clearly delineate how and when they should be used.
Parity-time symmetric complex-coupled distributed feedback laser with excellent immunity to external optical feedback
NASA Astrophysics Data System (ADS)
Ke, Cheng; Li, Xun; Xi, Yanping
In this paper, we propose an external optical feedback resistant distributed feedback (DFB) laser diode (LD) by exploiting parity-time symmetric complex coupling. With its complex refractive index followed a parity-time symmetry, the grating shows a strongly asymmetric reflection to the contra-propagating light inside the DFB cavity, which effectively rejects the returning light from one end. Consequently, the DFB LD is much less sensitive to external optical feedback. On the contrary, the transmissivity of such grating is still symmetric so that the output light of the DFB LD is not affected. Numerical simulation result shows that the lasing wavelength drift can be less than 0.2 nm with a SMSR exceeding 45 dB under a coherent external optical feedback as high as -10 dB.
Linear polynuclear helicates as a link between discrete supramolecular complexes and programmed infinite polymetallic chains.
Dalla-Favera, Natalia; Hamacek, Josef; Borkovec, Michal; Jeannerat, Damien; Gumy, Frédéric; Bünzli, Jean-Claude G; Ercolani, Gianfranco; Piguet, Claude
The contribution of the solvation energies to the assembly of polynuclear helicates reduces the free energy of intermetallic repulsion, DeltaE(MM), in condensed phase to such an extent that stable D(3)-symmetrical tetranuclear lanthanide-containing triple-stranded helicates [Ln(4)(L4)(3)](12+) are quantitatively produced at millimolar concentrations, despite the twelve positive charge borne by these complexes. A detailed modelling of the formation constants using statistical factors, adapted to self-assembly processes involving intra- and intermolecular connections, provides a set of five microscopic parameters, which can be successfully used for rationalizing the stepwise generation of linear bi-, tri- and tetranuclear analogues. Photophysical studies of [Eu(4)(L4)(3)](12+) confirm the existence of two different binding sites producing differentiated metal-centred emission at low temperature, which transforms into single site luminescence at room temperature because of intramolecular energy funelling processes.
Multikernel linear mixed models for complex phenotype prediction
Weissbrod, Omer; Geiger, Dan; Rosset, Saharon
Linear mixed models (LMMs) and their extensions have recently become the method of choice in phenotype prediction for complex traits. However, LMM use to date has typically been limited by assuming simple genetic architectures. Here, we present multikernel linear mixed model (MKLMM), a predictive modeling framework that extends the standard LMM using multiple-kernel machine learning approaches. MKLMM can model genetic interactions and is particularly suitable for modeling complex local interactions between nearby variants. We additionally present MKLMM-Adapt, which automatically infers interaction types across multiple genomic regions. In an analysis of eight case-control data sets from the Wellcome Trust Case Control Consortium and more than a hundred mouse phenotypes, MKLMM-Adapt consistently outperforms competing methods in phenotype prediction. MKLMM is as computationally efficient as standard LMMs and does not require storage of genotypes, thus achieving state-of-the-art predictive power without compromising computational feasibility or genomic privacy. PMID:27302636
Metal-metal multiple bonding in C3-symmetric bimetallic complexes of the first row transition metals.
Krogman, Jeremy P; Thomas, Christine M
Metal-metal multiple bonds have been an intense area of focus in inorganic chemistry for many decades as a result of their fundamentally interesting bonding properties, as well as their potential applications in multielectron transfer and small molecule activation processes. Much of what is known in this field revolves around 2nd and 3rd row transition metals, with fundamental knowledge lacking in the area of bonds between elements of the first transition series. The smaller size and tendency of first row ions to adopt high-spin electron configurations weaken metal-metal interactions and serve to complicate the interpretation of the electronic structure and bonding in bimetallic species containing first row transition metals. Furthermore, traditional tetragonal "paddlewheel" complexes dominate the metal-metal multiple bond literature, and only recently have researchers begun to take advantage of the weaker ligand field in three-fold symmetric bimetallic complexes to encourage more favourable metal-metal bonding interactions. In the past 5 years, several research groups have exploited three-fold symmetric frameworks to investigate new trends in metal-metal bonding involving the first row transition metals. This feature article serves to highlight recent achievements in this area and to use C3-symmetric systems as a model to better understand the fundamental aspects of multiple bonds featuring first row transition metals.
Parity-time-symmetric solitons in trapped Bose-Einstein condensates and the influence of varying complex potentials: A variational approach.
Devassy, Lini; Jisha, Chandroth P; Alberucci, Alessandro; Kuriakose, V C
Dynamics and properties of nonlinear matter waves in a trapped BEC subject to a PT-symmetric linear potential, with the trap in the form of a super-Gaussian potential, are investigated via a variational approach accounting for the complex nature of the soliton. In the process, we address how the shape of the imaginary part of the potential, that is, a gain-loss mechanism, affects the self-localization and the stability of the condensate. Variational results are found to be in good agreement with full numerical simulations for predicting the shape, width, and chemical potential of the condensate until the PT breaking point. Variational computation also predicts the existence of solitary solution only above a threshold in the particle number as the gain-loss is increased, in agreement with numerical simulations.
Branched-linear polyion complexes at variable charge densities
NASA Astrophysics Data System (ADS)
Angelescu, Daniel G.; Linse, Per
Structural behavior of complexes formed by a charged and branched copolymer and an oppositely charged and linear polyion was examined by Monte Carlo simulations employing a coarse-grained bead-spring model. The fractional bead charge and the branching density were systematically varied; the former between 0e and 1e and the latter such that both the comb-polymer and the bottle-brush limits were included. The number of beads of the main chain of the branched copolymer and of the linear polyion was always kept constant and equal, and a single side-chain length was used. Our analysis involved characterization of the complex as well as investigation of size, shape, and flexibility of the charged moieties. An interplay between Coulomb interaction and side-chain repulsion governed the structure of the polyion complex. At strong Coulomb interaction, the complexes underwent a gradual transition from a globular structure at low branching density to an extended one at high branching density. As the electrostatic coupling was decreased, the transition was smoothened and shifted to lower branching density, and, eventually, a behavior similar to that found for neutral branched polymer was observed. Structural analogies and dissimilarities with uncharged branched polymers in poor solutions are discussed.
Linearized simulation of flow over wind farms and complex terrains.
Segalini, Antonio
The flow over complex terrains and wind farms is estimated here by numerically solving the linearized Navier-Stokes equations. The equations are linearized around the unperturbed incoming wind profile, here assumed logarithmic. The Boussinesq approximation is used to model the Reynolds stress with a prescribed turbulent eddy viscosity profile. Without requiring the boundary-layer approximation, two new linear equations are obtained for the vertical velocity and the wall-normal vorticity, with a reduction in the computational cost by a factor of 8 when compared with a primitive-variables formulation. The presence of terrain elevation is introduced as a vertical coordinate shift, while forestry or wind turbines are included as body forces, without any assumption about the wake structure for the turbines. The model is first validated against some available experiments and simulations, and then a simulation of a wind farm over a Gaussian hill is performed. The speed-up effect of the hill is clearly beneficial in terms of the available momentum upstream of the crest, while downstream of it the opposite can be said as the turbines face a decreased wind speed. Also, the presence of the hill introduces an additional spanwise velocity component that may also affect the turbines' operations. The linear superposition of the flow over the hill and the flow over the farm alone provided a first estimation of the wind speed along the farm, with discrepancies of the same order of magnitude for the spanwise velocity. Finally, the possibility of using a parabolic set of equations to obtain the turbulent kinetic energy after the linearized model is investigated with promising results.This article is part of the themed issue 'Wind energy in complex terrains'.
Trellis complexity bounds for decoding linear block codes
NASA Technical Reports Server (NTRS)
Kiely, A. B.; Dolinar, S.; Ekroot, L.; Mceliece, R. J.; Lin, W.
We consider the problem of finding a trellis for a linear block code that minimizes one or more measures of trellis complexity. The domain of optimization may be different permutations of the same code or different codes with the same parameters. Constraints on trellises, including relationships between the minimal trellis of a code and that of the dual code, are used to derive bounds on complexity. We define a partial ordering on trellises: If a trellis is optimum with respect to this partial ordering, if has the desirable property that it simultaneously minimizes all of the complexity measures examined. We examine properties of such optimal trellises and give examples of optimal permutations of codes, most notably the (48,24,12) quadratic residue code.
Measurement of refractive index profile of non-symmetric, complex silica preforms with high refractive index differences
NASA Astrophysics Data System (ADS)
Probostova, Jana; Slanicka, Jiri; Mrazek, Jan; Podrazky, Ondrej; Benda, Adam; Peterka, Pavel
Refractive index profile measurement is a key instrument for characterization of optical properties of preforms, which are used for drawing of high-quality optical fibers. Common industrial optical preform analyzers have been designed for measurement of simple symmetric structures such as step-index or graded-index preforms with refractive index close to the silica (n=1.457 at 633 nm). However, these conditions are usually far from more complex structures used in fiber lasers or in fiber sensor area. Preforms for the drawing of advanced optical fibers, such as Bragg, microstructure or photonic crystal fibers, are usually constituted from stacks with non-symmetric internal structure or composed of alternating layers with high refractive index contrasts. In this paper we present comparison of refractive index profile measurements of simple as well as complex structures with high refractive index differences simulating the Bragg structures. Commercial Photon Kinetics 2600 preform analyzer was used for the refractive index profile measurements. A set of concentrically arranged silica tubes was welded to form a complex preforms. Free space between the tubes was filled by immersion with varying refractive indices to simulate the Bragg structure. Up to three tubes were used for the analysis and the refractive indices of immersion were changed from 1.4 to 1.5. When refractive index of immersion was independently measured the structure of preform was defined. Profiles of these "known" structures were compared to measured data processed by originally proposed algorithm. The work provides an extension of issues of refractive index profile measurements in non-symmetric complex silica structures by a commercial preform analyzer and proposes more convenient methods of numeric data processing.
Evaluation of out-of-core computer programs for the solution of symmetric banded linear equations. [simultaneous equations
NASA Technical Reports Server (NTRS)
Dunham, R. S.
FORTRAN coded out-of-core equation solvers that solve using direct methods symmetric banded systems of simultaneous algebraic equations. Banded, frontal and column (skyline) solvers were studied as well as solvers that can partition the working area and thus could fit into any available core. Comparison timings are presented for several typical two dimensional and three dimensional continuum type grids of elements with and without midside nodes. Extensive conclusions are also given.
Seismic Sensor orientation by complex linear least squares
NASA Astrophysics Data System (ADS)
Grigoli, Francesco; Cesca, Simone; Krieger, Lars; Olcay, Manuel; Tassara, Carlos; Sobiesiak, Monika; Dahm, Torsten
Poorly known orientation of the horizontal components of seismic sensors is a common problem that limits data analysis and interpretation for several acquisition setups, including linear arrays of geophones deployed in borehole installations, ocean bottom seismometers deployed at the sea-floor and surface seismic arrays. To solve this problem we propose an inversion method based on complex linear least squares method. Relative orientation angles, with respect to a reference sensor, are retrieved by minimizing the l2-norm between the complex traces (hodograms) of adjacent pairs of sensors in a least-squares sense. The absolute orientations are obtained in a second step by the polarization analysis of stacked seismograms of a seismic event with known location. This methodology can be applied without restrictions, if the plane wave approximation for wavefields recorded by each pair of sensors is valid. In most cases, it is possible to satisfy this condition by low-pass filtering the recorded waveform. The main advantage of our methodology is that, finding the estimation of the relative orientations of seismic sensors in complex domain is a linear inverse problem, which allows a direct solution corresponding to the global minimum of a misfit function. It is also possible to use simultaneously more than one independent dataset (e.g. using several seismic events simultaneously) to better constrain the solution of the inverse problem itself. Furthermore, by a computational point of view, our method results faster than the relative orientation methods based on waveform cross-correlation. Our methodology can be also applied for testing the correct orientation/alignment of multicomponent land stations in seismological arrays or temporary networks and for determining the absolute orientation of OBS stations and borehole arrays. We first apply our method to real data resembling two different acquisition setups: a borehole sensor array deployed in a gas field located in the
Circularly-symmetric complex normal ratio distribution for scalar transmissibility functions. Part II: Probabilistic model and validation
NASA Astrophysics Data System (ADS)
Yan, Wang-Ji; Ren, Wei-Xin
In Part I of this study, some new theorems, corollaries and lemmas on circularly-symmetric complex normal ratio distribution have been mathematically proved. This part II paper is dedicated to providing a rigorous treatment of statistical properties of raw scalar transmissibility functions at an arbitrary frequency line. On the basis of statistics of raw FFT coefficients and circularly-symmetric complex normal ratio distribution, explicit closed-form probabilistic models are established for both multivariate and univariate scalar transmissibility functions. Also, remarks on the independence of transmissibility functions at different frequency lines and the shape of the probability density function (PDF) of univariate case are presented. The statistical structures of probabilistic models are concise, compact and easy-implemented with a low computational effort. They hold for general stationary vector processes, either Gaussian stochastic processes or non-Gaussian stochastic processes. The accuracy of proposed models is verified using numerical example as well as field test data of a high-rise building and a long-span cable-stayed bridge. This study yields new insights into the qualitative analysis of the uncertainty of scalar transmissibility functions, which paves the way for developing new statistical methodologies for modal analysis, model updating or damage detection using responses only without input information.
Investigation of the 1D symmetrical linear graded superconductor-dielectric photonic crystals and its potential applications as an optimized low temperature sensors
NASA Astrophysics Data System (ADS)
Baraket, Zina; Zaghdoudi, Jihene; Kanzari, Mounir
Based on the Transfer Matrix Method (TMM) and the two fluid model for a superconductor and by taking account of the thermal expansion effect and thermo optical effects, we theoretically investigates the transmittance spectra of a one dimensional superconductor -dielectric photonic crystal (PC) designed as ((HLS)5/(SLH)5) made up of a BiGeO12(H), SiO2(L) and YaBO2CuO7 (S). The transmittance spectra shows that the system realizes a tunable filter which depends on a nonlinear relation with temperature. It's found that the symmetrical application of a linear deformation d(m) = d0+(m-1).δd(m) where d0 is the initial thickness of the layer m, δd(m) is the elementary added thickness at each layer. This linear gradation of the thickness permits to improve the temperature sensitivity of the system which acts as an optimized low temperature sensor.
Cu(2+), Zn(2+), and Ni(2+) Complexes of C2-Symmetric Pseudopeptides with an Aromatic Central Spacer.
Gorla, Lingaraju; Martí-Centelles, Vicente; Freimuth, Lena; Altava, Belén; Burguete, M Isabel; Luis, Santiago V
Two new tetradentate C2-symmetric pseudopeptidic ligands derived from Val and Phe containing two amino and two amido groups and a central o-substituted aromatic spacer have been prepared. Their complexes with Cu(2+), Zn(2+), and Ni(2+) have been studied by potentiometry, UV-vis spectrophotometry, FT-IR, and ESI-MS. The presence of the aromatic spacer provides Cu(2+) complexes with stability constants several orders of magnitude higher than those observed for related ligands containing aliphatic central spacers. Besides, the formation of [MH-2L] complex species is favored. Crystal structures for the corresponding Cu(2+) and Ni(2+) have been obtained, revealing the metal atom in an essentially square-planar geometry, although, in several instances, the oxygen atom of an amide carbonyl of a second complex species can act as a fifth coordination site. In the case of Zn(2+), the only crystal structure obtained displays a square-pyramidal arrangement of the metal center. Finally, preliminary experiments show the catalytic activity of some of these complexes, in particular, Zn(2+) complexes, for epoxide ring-opening with using aniline as the nucleophile in a ligand accelerated process.
Data bank homology search algorithm with linear computation complexity.
Strelets, V B; Ptitsyn, A A; Milanesi, L; Lim, H A
A new algorithm for data bank homology search is proposed. The principal advantages of the new algorithm are: (i) linear computation complexity; (ii) low memory requirements; and (iii) high sensitivity to the presence of local region homology. The algorithm first calculates indicative matrices of k-tuple 'realization' in the query sequence and then searches for an appropriate number of matching k-tuples within a narrow range in database sequences. It does not require k-tuple coordinates tabulation and in-memory placement for database sequences. The algorithm is implemented in a program for execution on PC-compatible computers and tested on PIR and GenBank databases with good results. A few modifications designed to improve the selectivity are also discussed. As an application example, the search for homology of the mouse homeotic protein HOX 3.1 is given.
On the experimental verification of quantum complexity in linear optics
NASA Astrophysics Data System (ADS)
Carolan, Jacques; Meinecke, Jasmin D. A.; Shadbolt, Peter J.; Russell, Nicholas J.; Ismail, Nur; Wörhoff, Kerstin; Rudolph, Terry; Thompson, Mark G.; O'Brien, Jeremy L.; Matthews, Jonathan C. F.; Laing, Anthony
Quantum computers promise to solve certain problems that are forever intractable to classical computers. The first of these devices are likely to tackle bespoke problems suited to their own particular physical capabilities. Sampling the probability distribution from many bosons interfering quantum-mechanically is conjectured to be intractable to a classical computer but solvable with photons in linear optics. However, the complexity of this type of problem means its solution is mathematically unverifiable, so the task of establishing successful operation becomes one of gathering sufficiently convincing circumstantial or experimental evidence. Here, we develop scalable methods to experimentally establish correct operation for this class of computation, which we implement for three, four and five photons in integrated optical circuits, on Hilbert spaces of up to 50,000 dimensions. Our broad approach is practical for all quantum computational architectures where formal verification methods for quantum algorithms are either intractable or unknown.
C{sub 2}-symmetric Copper(II) complexes as chiral Lewis acids
Evans, D.A.; Murry, J.A.; Matt, P. von
Two new Cu(II)-derived Lewis acid catalysts 1 and 2 have been prepared and their utility as catalysts in the Diels-Alder reaction documented. While complex 1 is effective in catalyzing the cycloaddition of unsaturated aldehyde dienophiles with cyclopentadiene complex 2 is optimal for imide dienophiles. This study provides a rational basis for the design of Lewis acids based on the coordinating capacity of cationic Cu(II) complexes which possess sufficient Lewis acidity to catalyze a range of synthetically useful Diels-Alder reactions. In particular, documentation of the importance of counterion structure in the use of cationic metal centers as Lewis acids has been made for the first time.
Synthesis and in vitro antitumor activity of novel iridium(III) complexes with enantiopure C2-symmetrical vicinal diamine ligands.
Yang, Qing; Chang, Jun; Song, Jiao; Qian, Meng-Ting; Yu, Jian-Ming; Sun, Xun
Four novel iridium(III) complexes with enantiopure C2-symmetrical vicinal diamine ligands were designed, synthesized, and characterized by FT-IR, NMR, and MS. The cytotoxicities of all of the complexes against the human solid tumor cell lines A2780, A549, KB, and MDA-MB-231 were evaluated. Both R,R-configured complexes (R,R)-5a and (R,R)-5b exhibited more potent or similar activity compared with oxaliplatin, whereas their corresponding (S,S)-isomers (S,S)-5a and (S,S)-5b were found to be mostly inactive. As indicated by the activation of caspase-3, the cleavage of PARP, and the upregulation of p53, the preliminary mechanism studies revealed that the mode of cell death initiated by (R,R)-5a in A2780 cells was predominantly p53-mediated apoptosis. In addition, the structure of (R,R)-5a was unambiguously confirmed through single crystal X-ray structure determination.
SOD activity and DNA binding properties of a new symmetric porphyrin Schiff base ligand and its metal complexes.
Çay, Sevim; Köse, Muhammet; Tümer, Ferhan; Gölcü, Ayşegül; Tümer, Mehmet
4-Methoxy-2,6-bis(hydroxymethyl)phenol (1) was prepared from the reaction of 4-methoxyphenol and formaldehyde. The compound (1) was then oxidized to the 4-methoxy-2,6-diformylphenol (2) compound. Molecular structure of compound (2) was determined by X-ray diffraction method. A new symmetric porphyrin Schiff base ligand 4-methoxy-2,6-bis[5-(4-iminophenyl)-10,15,20-triphenylporphyrin]phenol (L) was prepared from the reaction of the 5-(4-aminophenyl)-10,15,20-triphenylporphyrin (TTP-NH2) and the compound (2) in the toluene solution. The metal complexes (Cu(II), Fe(III), Mn(III), Pt(II) and Zn(II)) of the ligand (L) were synthesized and characterized by the spectroscopic and analytical methods. The DNA (fish sperm FSdsDNA) binding studies of the ligand and its complexes were performed using UV-vis spectroscopy. Additionally, superoxide dismutase activities of the porphyrin Schiff base metal complexes were investigated. Additionally, electrochemical, photoluminescence and thermal properties of the compounds were investigated.
Unpacking the Complexity of Linear Equations from a Cognitive Load Theory Perspective
ERIC Educational Resources Information Center
Ngu, Bing Hiong; Phan, Huy P.
The degree of element interactivity determines the complexity and therefore the intrinsic cognitive load of linear equations. The unpacking of linear equations at the level of operational and relational lines allows the classification of linear equations in a hierarchical level of complexity. Mapping similar operational and relational lines across…
Asymmetric Michael addition of nitroalkanes to nitroalkenes catalyzed by C2-symmetric tridentate bis(oxazoline) and bis(thiazoline) zinc complexes.
Lu, Shao-Feng; Du, Da-Ming; Xu, Jiaxi; Zhang, Shi-Wei
The first asymmetric synthesis of 1,3-dinitro compounds through Michael addition of nitroalkanes to nitroalkenes catalyzed by C2-symmetric chiral tridentate bis(oxazoline) and bis(thiazoline) zinc complexes was achieved with high enantioselectivities (up to 95% ee).
Complex modes and solvability of nonclassical linear systems
NASA Astrophysics Data System (ADS)
Caughey, T. K.; Ma, F.
Some basic properties of nonclassical linear systems are examined to determine necessary and sufficient conditions under which nonclassical linear systems can be decoupled or become solvable in n-space. It was found that a necessary and sufficient condition under which a nonclassical system can be decoupled is for the coefficient matrices M, C, and K (where M is the mass matrix, C is the damping matrix, and K is the stiffness matrix) to be diagonalizable and pairwise commutative.
Dinuclear fluoro-peroxovanadium(v) complexes with symmetric and asymmetric peroxo bridges: syntheses, structures and DFT studies.
Chrappová, Jana; Schwendt, Peter; Sivák, Michal; Repiský, Michal; Malkin, Vladimir G; Marek, Jaromír
Two new dinuclear fluoro peroxovanadium(v) complexes, Cs3[V2O2(O2)4F] x H2O (1) and Cs3[V2O2(O2)3F3] x 2HF x H2O (2), were prepared and characterized by elemental analysis, IR spectroscopy, thermal analysis and X-ray crystallography. While the anion in possesses an asymmetric structure with a micro-eta1:eta2 bridging peroxo group, the [V2O2(O2)3F3]3- ion in exhibits a symmetrical structure with a unique mu-fluoro and micro-eta2:eta2 peroxo double bridge. The X-ray structure data were compared with equilibrium and vibrationally-averaged (effective) DFT calculated geometries. The decomposition reactions of and in aqueous solution were studied by 51V NMR spectroscopy. The calculations of vibrationally averaged NMR chemical shifts (DFT-GIAO) were used to support the empirical assignment of NMR signals and afforded excellent agreement with experimental values for the studied peroxovanadium species. The ESI mass spectra of the prepared compounds are in accordance with the assignment of NMR spectra and with DFT study.
Complex Craniofacial Changes in Blind Cave-Dwelling Fish Are Mediated by Genetically Symmetric and Asymmetric Loci
Gross, Joshua B.; Krutzler, Amanda J.; Carlson, Brian M.
The genetic regulators of regressive craniofacial morphologies are poorly understood. To shed light on this problem, we examined the freshwater fish Astyanax mexicanus, a species with surface-dwelling and multiple independent eyeless cave-dwelling forms. Changes affecting the skull in cavefish include morphological alterations to the intramembranous circumorbital bones encircling the eye. Many of these modifications, however, have evolved separately from eye loss, such as fragmentation of the third suborbital bone. To understand the genetic architecture of these eye-independent craniofacial alterations, we developed and scored 33 phenotypes in the context of an F2 hybrid mapping pedigree bred from Pachón cavefish and surface fish. We discovered several individuals exhibiting dramatic left–right differences in bone formation, such as extensive fragmentation on the right side only. This observation, along with well-known eye size asymmetry in natural cave-dwelling animals, led us to further evaluate left–right genetic differences for the craniofacial complex. We discovered three phenotypes, inclusive of bone fragmentation and fusion, which demonstrated a directional heritable basis only on one side. Interestingly, the overall areas of affected bones were genetically symmetric. Phenotypic effect plots of these novel craniofacial QTL revealed that cave alleles are associated with abnormal conditions such as bony fusion and fragmentation. Moreover, many linked loci overlapped with other cave-associated traits, suggesting regressive craniofacial changes may evolve through linkage or as antagonistic pleiotropic consequences of cave-associated adaptations. These novel findings illuminate significant craniofacial changes accompanying evolution in complete darkness and reveal complex changes to the skull differentially influenced by genetic changes affecting the left and right sides. PMID:24496009
Symmetrical Diphosphatetraazacyclooctatetraenes.
aryl, alkyl, perfluoroalkyl and perfluoroalkylether radcalsl Rf is selected from perfluoroalkyl and perfluoroalkylether radicals 20 as represented by...process for synthesizing symmetrical diphosphatetraazacyclooctatetraenes by reacting perfluoroalkyl or perfluoroalkylether amidine with a...symmetrical diphosphatetraazacyclooctatetraene. The substituent Rf can he selected from perfluoroalkyl and pertluoroalkylether groups as represented hy the
Generalized Vibrational Perturbation Theory for Rotovibrational Energies of Linear, Symmetric and Asymmetric Tops: Theory, Approximations, and Automated Approaches to Deal with Medium-to-Large Molecular Systems
Piccardo, Matteo; Bloino, Julien; Barone, Vincenzo
Models going beyond the rigid-rotor and the harmonic oscillator levels are mandatory for providing accurate theoretical predictions for several spectroscopic properties. Different strategies have been devised for this purpose. Among them, the treatment by perturbation theory of the molecular Hamiltonian after its expansion in power series of products of vibrational and rotational operators, also referred to as vibrational perturbation theory (VPT), is particularly appealing for its computational efficiency to treat medium-to-large systems. Moreover, generalized (GVPT) strategies combining the use of perturbative and variational formalisms can be adopted to further improve the accuracy of the results, with the first approach used for weakly coupled terms, and the second one to handle tightly coupled ones. In this context, the GVPT formulation for asymmetric, symmetric, and linear tops is revisited and fully generalized to both minima and first-order saddle points of the molecular potential energy surface. The computational strategies and approximations that can be adopted in dealing with GVPT computations are pointed out, with a particular attention devoted to the treatment of symmetry and degeneracies. A number of tests and applications are discussed, to show the possibilities of the developments, as regards both the variety of treatable systems and eligible methods. © 2015 Wiley Periodicals, Inc. PMID:26345131
Generalized Vibrational Perturbation Theory for Rotovibrational Energies of Linear, Symmetric and Asymmetric Tops: Theory, Approximations, and Automated Approaches to Deal with Medium-to-Large Molecular Systems.
Piccardo, Matteo; Bloino, Julien; Barone, Vincenzo
Models going beyond the rigid-rotor and the harmonic oscillator levels are mandatory for providing accurate theoretical predictions for several spectroscopic properties. Different strategies have been devised for this purpose. Among them, the treatment by perturbation theory of the molecular Hamiltonian after its expansion in power series of products of vibrational and rotational operators, also referred to as vibrational perturbation theory (VPT), is particularly appealing for its computational efficiency to treat medium-to-large systems. Moreover, generalized (GVPT) strategies combining the use of perturbative and variational formalisms can be adopted to further improve the accuracy of the results, with the first approach used for weakly coupled terms, and the second one to handle tightly coupled ones. In this context, the GVPT formulation for asymmetric, symmetric, and linear tops is revisited and fully generalized to both minima and first-order saddle points of the molecular potential energy surface. The computational strategies and approximations that can be adopted in dealing with GVPT computations are pointed out, with a particular attention devoted to the treatment of symmetry and degeneracies. A number of tests and applications are discussed, to show the possibilities of the developments, as regards both the variety of treatable systems and eligible methods.
On the Solutions of Some Linear Complex Quaternionic Equations
İpek, Ahmet
Some complex quaternionic equations in the type AX − XB = C are investigated. For convenience, these equations were called generalized Sylvester-quaternion equations, which include the Sylvester equation as special cases. By the real matrix representations of complex quaternions, the necessary and sufficient conditions for the solvability and the general expressions of the solutions are obtained. PMID:25101318
Linear and nonlinear rheology of architecturally complex polymers
NASA Astrophysics Data System (ADS)
Kapnistos, Michail
We investigated the linear and nonlinear rheology of several model polymeric materials ranging from combs with linear or star-like backbone to third generation dendrimers and cyclic polymers (with no free ends or branches). These systems are governed by topological interactions, which influence their mechanical properties. We combined experiments with theoretical models in order to identify the factors that affect the mechanical response of polymers of various architectures. All polymeric materials exhibited some universal features that were assigned to their microscopic motions. The tube model and the concept of hierarchy of motions along with the dynamic tube dilation (DTD) were the key elements to understand the rheology of branched polymer melts and solutions. We also performed nonlinear experiments in solutions of branched polymers obtaining an extensive dataset of damping functions in combs. We found evidence that the above ideas and mainly DTD, are also present during nonlinear deformations. Apart for the experiments, we modified the existent tube model, improving several shortcomings. The topological free ends of combs were treated simultaneously with the branches and included the effect of polydispersity in a direct manner. The equations were integrated with a user-friendly computer interface for modeling the linear viscoelastic data of several polymer architectures. We explored the role of polymer topology in rheology with the use of model polymers. We found universal principles that govern the mechanical response and linked the microstructure with macroscopic experiments. The extended experimental data have revealed some issues not explained by current theoretical model that need to be addressed in the future.
Linear Dichroism Characteristics of Ethidium and Proflavine Supercoiled DNA Complexes
of Ethidium-and Proflavine -Supercoi led DNA Complexes CHARLES E. SWENBERG, 1 SUSAN E. CARBERRV, 2 * and NICHOLAS E. GEACINTOV' SRadliationl Biochenitr...drug were stained with EB, photographed under uv light, molecules, EB and proflavine (PF) (Figure 1), and the bands were quantitated by densitometry
Ramond, P. . Dept. of Physics)
The Wolfenstein parametrization is extended to the quark masses in the deep ultraviolet, and an algorithm to derive symmetric textures which are compatible with existing data is developed. It is found that there are only five such textures.
Ramond, P.
The Wolfenstein parametrization is extended to the quark masses in the deep ultraviolet, and an algorithm to derive symmetric textures which are compatible with existing data is developed. It is found that there are only five such textures.
Quantifying Stability in Complex Networks: From Linear to Basin Stability
NASA Astrophysics Data System (ADS)
Kurths, Jürgen
The human brain, power grids, arrays of coupled lasers and the Amazon rainforest are all characterized by multistability. The likelihood that these systems will remain in the most desirable of their many stable states depends on their stability against significant perturbations, particularly in a state space populated by undesirable states. Here we claim that the traditional linearization-based approach to stability is in several cases too local to adequately assess how stable a state is. Instead, we quantify it in terms of basin stability, a new measure related to the volume of the basin of attraction. Basin stability is non-local, nonlinear and easily applicable, even to high-dimensional systems. It provides a long-sought-after explanation for the surprisingly regular topologies of neural networks and power grids, which have eluded theoretical description based solely on linear stability. Specifically, we employ a component-wise version of basin stability, a nonlinear inspection scheme, to investigate how a grid's degree of stability is influenced by certain patterns in the wiring topology. Various statistics from our ensemble simulations all support one main finding: The widespread and cheapest of all connection schemes, namely dead ends and dead trees, strongly diminish stability. For the Northern European power system we demonstrate that the inverse is also true: `Healing' dead ends by addition of transmission lines substantially enhances stability. This indicates a crucial smart-design principle for tomorrow's sustainable power grids: add just a few more lines to avoid dead ends. Further, we analyse the particular function of certain network motifs to promote the stability of the system. Here we uncover the impact of so-called detour motifs on the appearance of nodes with a poor stability score and discuss the implications for power grid design. Moreover, it will be shown that basin stability enables uncovering the mechanism for explosive synchronization and
Synthesis, characterization and crystal structure of Cu(II) complex of trans-cyclohexane-1,2-diamine: Application in synthesis of symmetrical biaryls
NASA Astrophysics Data System (ADS)
Agrahari, Bhumika; Layek, Samaresh; Kumari, Shweta; Anuradha; Ganguly, Rakesh; Pathak, Devendra D.
A new Cu(II) complex [Cu(cyhxn)2(H2O)2][OTf]2 was synthesised by the reaction of ligand cyhxn (cyhxn = trans-cyclohexane-1,2-diamine) with Cu(OTf)2 in methanol at room temperature. The complex was fully characterized by elemental analysis (CHN), FT-IR, UV-Vis and EPR spectroscopic techniques. The structure of the complex was confirmed by single crystal X-ray diffraction study. The EPR spectrum is isotropic type having giso = 2.078, which indicates a distorted octahedral geometry of the complex. The complex was found to be an active homogeneous catalyst for the homocoupling reactions of arylboronic acid to obtain symmetrical biaryls at room temperature in methanol without the use of any additives such as a base and or an oxidant.
The solution of the optimization problem of small energy complexes using linear programming methods
NASA Astrophysics Data System (ADS)
Ivanin, O. A.; Director, L. B.
Linear programming methods were used for solving the optimization problem of schemes and operation modes of distributed generation energy complexes. Applicability conditions of simplex method, applied to energy complexes, including installations of renewable energy (solar, wind), diesel-generators and energy storage, considered. The analysis of decomposition algorithms for various schemes of energy complexes was made. The results of optimization calculations for energy complexes, operated autonomously and as a part of distribution grid, are presented.
Complex transition metal hydrides: linear correlation of countercation electronegativity versus T-D bond lengths.
Humphries, T D; Sheppard, D A; Buckley, C E
For homoleptic 18-electron complex hydrides, an inverse linear correlation has been established between the T-deuterium bond length (T = Fe, Co, Ni) and the average electronegativity of the metal countercations. This relationship can be further employed towards aiding structural solutions and predicting physical properties of novel complex transition metal hydrides.
{PT}-symmetric optical superlattices
NASA Astrophysics Data System (ADS)
Longhi, Stefano
The spectral and localization properties of {PT}-symmetric optical superlattices, either infinitely extended or truncated at one side, are theoretically investigated, and the criteria that ensure a real energy spectrum are derived. The analysis is applied to the case of superlattices describing a complex ( {PT}-symmetric) extension of the Harper Hamiltonian in the rational case.
Amore, Paolo; Fernández, Francisco M.; Garcia, Javier; Gutierrez, German
We study both analytically and numerically the spectrum of inhomogeneous strings with PT-symmetric density. We discuss an exactly solvable model of PT-symmetric string which is isospectral to the uniform string; for more general strings, we calculate exactly the sum rules Z(p)≡∑{sub n=1}{sup ∞}1/E{sub n}{sup p}, with p=1,2,… and find explicit expressions which can be used to obtain bounds on the lowest eigenvalue. A detailed numerical calculation is carried out for two non-solvable models depending on a parameter, obtaining precise estimates of the critical values where pair of real eigenvalues become complex. -- Highlights: •PT-symmetric Hamiltonians exhibit real eigenvalues when PT symmetry is unbroken. •We study PT-symmetric strings with complex density. •They exhibit regions of unbroken PT symmetry. •We calculate the critical parameters at the boundaries of those regions. •There are exact real sum rules for some particular complex densities.
Synthesis, spectral characterization, DNA binding ability and antibacterial screening of copper(II) complexes of symmetrical NOON tetradentate Schiff bases bearing different bridges
NASA Astrophysics Data System (ADS)
Bahaffi, Saleh O.; Abdel Aziz, Ayman A.; El-Naggar, Maher M.
A novel series of four copper(II) complexes were synthesized by thermal reaction of copper acetate salt with symmetrical tetradentate Schiff bases, N,N'bis(o-vanillin)4,5-dimethyl-l,2-phenylenediamine (H2L1), N,N'bis(salicylaldehyde)4,5-dimethyl-1,2-phenylenediamine (H2L2), N,N'bis(o-vanillin)4,5-dichloro-1,2-phenylenediamine (H2L3) and N,N'bis(salicylaldehyde)4,5-dichloro-1,2-phenylenediamine (H2L4), respectively. All the new synthesized complexes were characterized by using of microanalysis, FT-IR, UV-Vis, magnetic measurements, ESR, and conductance measurements, respectively. The data revealed that all the Schiff bases (H2L1-4) coordinate in their deprotonated forms and behave as tetradentate NOON coordinated ligands. Moreover, their copper(II) complexes have square planar geometry with general formula [CuL1-4]. The binding of the complexes with calf thymus DNA (CT-DNA) was investigated by UV-Vis spectrophotometry, fluorescence quenching and viscosity measurements. The results indicated that the complexes bind to CT-DNA through an intercalative mode. From the biological activity view, the copper(II) complexes and their parent ligands were screened for their in vitro antibacterial activity against the bacterial species Staphylococcus aureus, Staphylococcus epidermidis, Escherichia coli and Pseudomonas aeruginosai by well diffusion method. The complexes showed an increased activity in comparison to some standard drugs.
Some comparisons of complexity in dictionary-based and linear computational models.
Gnecco, Giorgio; Kůrková, Věra; Sanguineti, Marcello
Neural networks provide a more flexible approximation of functions than traditional linear regression. In the latter, one can only adjust the coefficients in linear combinations of fixed sets of functions, such as orthogonal polynomials or Hermite functions, while for neural networks, one may also adjust the parameters of the functions which are being combined. However, some useful properties of linear approximators (such as uniqueness, homogeneity, and continuity of best approximation operators) are not satisfied by neural networks. Moreover, optimization of parameters in neural networks becomes more difficult than in linear regression. Experimental results suggest that these drawbacks of neural networks are offset by substantially lower model complexity, allowing accuracy of approximation even in high-dimensional cases. We give some theoretical results comparing requirements on model complexity for two types of approximators, the traditional linear ones and so called variable-basis types, which include neural networks, radial, and kernel models. We compare upper bounds on worst-case errors in variable-basis approximation with lower bounds on such errors for any linear approximator. Using methods from nonlinear approximation and integral representations tailored to computational units, we describe some cases where neural networks outperform any linear approximator.
Symmetrical P4 cleavage at cobalt half sandwich complexes [(η5-C5H5)Co(L)] (L = CO, NHC)--a computational case study on the mechanism of symmetrical P4 degradation to P2 ligands.
Zarzycki, Bartosz; Bickelhaupt, F Matthias; Radius, Udo
A full theoretical mechanistic investigation on the symmetrical cleavage of P4 at the active complex fragments [(η(5)-C5H5)Co(L)] (L = CO, (i)Pr2Im; (i)Pr2Im = 1,3-di-iso-propylimidazolin-2-ylidene), which results in the formation of the complex [{(η(5)-C5H5)Co}2(μ,η(2:2)-P2)2] 9, is presented. The overall reaction mechanism is a complex, multistep process. Rate-determining steps of the reaction sequence are two consecutive dissociations of the co-ligands L, which induce the decisive structural rearrangements of the P4 unit. The choice of the co-ligand L ( = CO, (i)Pr2Im) influences the kinetic barrier as well as the energy balance of the overall reaction path significantly. The calculations further reveal a strong influence of the entropic effect on the overall reaction. As a consequence, the energy balance of the overall formation of 9 starting from [(η(5)-C5H5)Co(CO)] precursors is almost thermoneutral and has to overcome high kinetic barriers, whereas the reaction starting from [(η(5)-C5H5)Co((i)Pr2Im)] precursors is exothermic, featuring lower transition barriers with stabilized intermediates. From the direct comparison of both reaction coordinates it seems that the entropic effect of the co-ligands is even stronger than their electronic influence, as for both investigated systems the reactions' energy profiles are almost identical up to intermediate [{(η(5)-C5H5)Co(L)}2(μ,η(2:2)-P4)] 5 (L = CO, (i)Pr2Im). After the formation of 5, the first CO dissociation step renders the reaction endothermic for L = CO, whereas in the case of (i)Pr2Im dissociation the reaction progresses exothermically. Energy decomposition analysis and fragment analysis provide a picture of the bonding mechanisms between the metal complex fragments and P4 in the case of the most significant intermediates and the final product.
Structures of KcsA in Complex with Symmetrical Quaternary Ammonium Compounds Reveal a Hydrophobic Binding Site
Potassium channels allow for the passive movement of potassium ions across the cell membrane and are instrumental in controlling the membrane potential in all cell types. Quaternary ammonium (QA) compounds block potassium channels and have long been used to study the functional and structural properties of these channels. Here we describe the interaction between three symmetrical hydrophobic QAs and the prokaryotic potassium channel KcsA. The structures demonstrate the presence of a hydrophobic pocket between the inner helices of KcsA and provide insight into the binding site and blocking mechanism of hydrophobic QAs. The structures also reveal a structurally hidden pathway between the central cavity and the outside membrane environment reminiscent of the lateral fenestration observed in sodium channels that can be accessed through small conformational changes in the pore wall. We propose that the hydrophobic binding pocket stabilizes the alkyl chains of long-chain QA molecules and may play a key role in hydrophobic drug binding in general. PMID:25093676
Synthesis, crystal structure, DFT study and photocatalytic property of a new Ni(II) complex of a symmetric N2O4-donor bis-Schiff base ligand
NASA Astrophysics Data System (ADS)
Wang, Hu; Meng, Xiangmin; Fan, Chuanbin; Fan, Yuhua; Bi, Caifeng
A new complex, Ni(C22H26N2O10S2)·2CH3OH, with a sexidentate (N2O4) symmetric bis-Schiff base ligand (C22H26N2O10S2 = 1,2-bis(2-methoxy-6-formylphenoxy)ethane-2-aminoethane-sulfonic acid) has been synthesized and characterized by physico-chemical and spectroscopic methods. The X-ray crystal structure shows that the Ni(II) atom of the complex is six-coordinated by two nitrogens from Cdbnd N groups, two oxygens from ether groups and two hydroxyl oxygens from sulfonic acid groups in the mono-ligand, forming a distorted octahedral geometry. Theoretical study of the complex is carried out by density functional theory (DFT) method and the B3LYP method employing the 6-3l+G* basis set. Moreover, the complex proved to be good candidate for the photocatalytic degradation of methylene blue.
Direct Synthesis of Symmetrical Azines from Alcohols and Hydrazine Catalyzed by a Ruthenium Pincer Complex: Effect of Hydrogen Bonding
Azines (2,3-diazabuta-1,3-dienes) are a widely used class of compounds with conjugated C=N double bonds. Herein, we present a direct synthesis of azines from alcohols and hydrazine hydrate. The reaction, catalyzed by a ruthenium pincer complex, evolves dihydrogen and can be run in a base-free version. The dehydrogenative coupling of benzylic and aliphatic alcohols led to good conversions and yields. Spectroscopic evidence for a hydrazine-coordinated dearomatized ruthenium pincer complex was obtained. Isolation of a supramolecular crystalline compound provided evidence for the important role of hydrogen bonding networks under the reaction conditions. PMID:27990319
1. Mono([8]annulene)Uranium(4) half-sandwich complexes, 2. Novel syntheses of symmetrically substituted cyclooctatetetraenes
Boussie, T.R.
A reproducible, high-yield synthesis of mono([8]annulene)uranium(4)dichloride (1) is reported, along with the X-ray crystal structural of the bis(pyridine) adduct. Metathesis reactions of the half-sandwich complex 1 with a variety of simple alkyl and alkoxy reagents failed to generate any isolable mono-ring complexes. Reactions of 1 with polydentate, delocalized anions did produce stable derivatives, including mono([8]annulene)uranium(4)bis(acetylacetonate) (4). An X-ray crystal structure of 4 is reported.
1. Mono((8)annulene)Uranium(4) half-sandwich complexes, 2. Novel syntheses of symmetrically substituted cyclooctatetetraenes
Boussie, T.R.
A reproducible, high-yield synthesis of mono((8)annulene)uranium(4)dichloride (1) is reported, along with the X-ray crystal structural of the bis(pyridine) adduct. Metathesis reactions of the half-sandwich complex 1 with a variety of simple alkyl and alkoxy reagents failed to generate any isolable mono-ring complexes. Reactions of 1 with polydentate, delocalized anions did produce stable derivatives, including mono((8)annulene)uranium(4)bis(acetylacetonate) (4). An X-ray crystal structure of 4 is reported.
ERIC Educational Resources Information Center
de Villiers, Michael
Symmetry is found in the visual arts, architecture and design of artefacts since the earliest time. Many natural objects, both organic and inorganic, display symmetry: from microscopic crystals and sub-atomic particles to macro-cosmic galaxies. Today it features strongly in higher mathematics such as Linear and Abstract Algebra, Projective and…
Linear-scaling first-principles molecular dynamics of complex biological systems with the Conquest code
NASA Astrophysics Data System (ADS)
Otsuka, Takao; Taiji, Makoto; Bowler, David R.; Miyazaki, Tsuyoshi
The recent progress of linear-scaling or O(N) methods in density functional theory (DFT) is remarkable. In this paper, we show that all-atom molecular dynamics simulations of complex biological systems based on DFT are now possible using our linear-scaling DFT code Conquest. We first overview the calculation methods used in Conquest and explain the method introduced recently to realise efficient and robust first-principles molecular dynamics (FPMD) with O(N) DFT. Then, we show that we can perform reliable all-atom FPMD simulations of a hydrated DNA model containing about 3400 atoms. We also report that the velocity scaling method is both reliable and useful for controlling the temperature of the FPMD simulation of this system. From these results, we conclude that reliable FPMD simulations of complex biological systems are now possible with Conquest.
Linear hexanuclear nickel complexes with rich electrochemical features and facility to reduction
NASA Astrophysics Data System (ADS)
Wang, Wen-Zhen; Zhao, Dan; Zhao, Meng-Jiao; Li, Haoyong; Liu, Shuang; Ismayilov, Rayyat H.; Lee, Gene-Hsiang; Peng, Shie-Ming
Two novel linear hexanuclear nickel complexes [Ni6(μ6-dpznda)4Cl2](PF6)2(1) and [Ni6(μ6-dpznda)4(NCS)2](PF6)2(2) (H2dpznda = N2,N7-di(pyrazin-2-yl)-1,8-naphthyridine-2,7-diamine) were synthesized and structurally characterized. Both the two complexes consist of a linear metal chain and four supporting ligands which are helically wrapped around the metal core. The single crystal X-ray structural analysis showed that the complex 1 belonged to rhombohedral system, space group R-3 with a = b = 34.2051(8), c = 20.7751(5) Å, V = 21050.2(9) Å3 and Z = 9. Direct-current magnetic susceptibility measurements showed weak antiferromagnetic interactions with coupling parameters of g = 2.04 and J = -8.27 cm-1 for 1 and g = 2.02 and J = -12.62 cm-1 for 2, respectively (Ĥ = -JŜ1Ŝ2, S1 = S2 = 1). The decrease of magnetic moments at low temperature was partly attributed to ZFS. The electrochemical study on complex 1 shows rich features and facility to reduction in its cyclic voltammogram by displaying four reversible redox couples at E1/2 = +0.01, -0.29, -0.64 and -0.73 V (vs. Ag/AgCl).
The uranium-Xylidyl Blue I complex and its application in linear sweep polarography.
Zhao, Z; Cai, X; Li, P
The linear sweep polarographic wave of the uranium-Xylidyl Blue I complex in ethylenediamine-1,10-phenanthroline-hydrochloric acid medium has been studied. The complex, corresponding to UO(2)(XBI)(2-)(2) with log beta' = 9.09 (by polarography), 8.81 (by spectrophotometry), is strongly adsorbed on the surface of the mercury electrode. The polarographic wave is attributed to the reduction of Xylidyl Blue I in the complex. The method is very sensitive with a detection limit of 3 x 10(-8)M. The wave height is proportional to the concentration of uranium over the range 8 x 10(-8)-7 x 10(-6)M. Solvent extraction is used to separate possible interferences. The recommended procedure has been applied to the determination of trace amounts of uranium in ores.
Steric hindrances create a discrete linear Dy4 complex exhibiting SMM behaviour.
Lin, Shuang-Yan; Zhao, Lang; Ke, Hongshan; Guo, Yun-Nan; Tang, Jinkui; Guo, Yang; Dou, Jianmin
Two linear tetranuclear lanthanide complexes of general formula [Ln(4)(L)(2)(C(6)H(5)COO)(12)(MeOH)(4)], where HL = 2,6-bis((furan-2-ylmethylimino)methyl)-4-methylphenol, () and Ln(III) = Dy(III) (1) and Gd(III) (2), have been synthesized and characterized. The crystal structural analysis demonstrates that two Schiff-base ligands inhibit the growth of benzoate bridged 1D chains, leading to the isolation of discrete tetranuclear complexes due to their steric hindrances. Every Ln(III) ion is coordinated by eight donor atoms in a distorted bicapped trigonal-prismatic arrangement. Alternating current (ac) susceptibility measurements of complex 1 reveal a frequency- and temperature-dependent out-of-phase signal under zero dc field, typical of single-molecule magnet (SMM) behaviour with an anisotropic barrier Δ(eff) = 17.2 K.
Dual emission and excited-state mixed-valence in a quasi-symmetric dinuclear Ru-Ru complex.
Kreitner, Christoph; Grabolle, Markus; Resch-Genger, Ute; Heinze, Katja
The synthesis and characterization of the new dinuclear dipeptide [(EtOOC-tpy)Ru(tpy-NHCO-tpy)Ru(tpy-NHCOCH3)](4+) 3(4+) of the bis(terpyridine)ruthenium amino acid [(HOOC-tpy)Ru(tpy-NH2)](2+) 1(2+) are described, and the properties of the dipeptide are compared to those of the mononuclear complex [(EtOOC-tpy)Ru(tpy-NHCOCH3)](2+) 4(2+) carrying the same functional groups. 3(4+) is designed to serve a high electronic similarity of the two ruthenium sites despite the intrinsic asymmetry arising from the amide bridge. This is confirmed via UV-vis absorption and NMR spectroscopy as well as cyclic voltammetry. 4(2+) and 3(4+) are emissive at room temperature, as expected. Moreover, 3(4+) exhibits dual emission from two different triplet states with different energies and lifetimes at room temperature. This is ascribed to the presence of a unique thermal equilibrium between coexisting [Ru(II)(tpy-NHCO-tpy(·-))Ru(III)] and [Ru(III)(tpy-NHCO-tpy(·-))Ru(II)] states leading to an unprecedented excited-state Ru(II)Ru(III) mixed-valent system via the radical anion bridge tpy-NHCO-tpy(·-). The mixed-valent cation 3(5+), on the other hand, shows no measurable interaction of the Ru(II)Ru(III) centers via the neutral bridge tpy-NHCO-tpy (Robin-Day class I). Reduction of 3(4+) to the radical cation 3(3+) by decamethylcobaltocene is bridge-centered as evidenced by rapid-freeze electron paramagnetic resonance spectroscopy. Interestingly, all attempts to observe 3(3+) via NMR and UV-vis absorption spectroscopy only led to the detection of the diamagnetic complex 3-H(3+) in which the bridging amide is deprotonated. Hence 3-H(3+) (and 4-H(+)) appear to reduce protons to dihydrogen. The ease of single and double deprotonation of 4(2+) and 3(4+) to 4-H(+), 3-H(3+), and 3-2H(2+) was demonstrated using a strong base and was studied using NMR and UV-vis absorption spectroscopies. The equilibrating excited triplet states of 3(4+) are reductively quenched by N,N-dimethylaniline assisted by
Surface chemistry of the linear chromium chain complex on GaN(0001)
Lung, C.-H.; Peng, S.-M.; Chang, C.-C.
Better understanding about the chemistry of the organometallic chain complexes reacting on the solid surface can foster concepts of nanowire fabrication which are central to the continued advance of the electronic and optoelectronic industries. In this study, the adsorption and thermal reactivity of a trinuclear chromium chain complex, tetrakis (2,2{sup '}-dipyridylamino)chromium(VI) chloride, on the GaN(0001) surface were investigated using x-ray photoelectron spectroscopy, temperature-programmed desorption, and static secondary ion mass spectrometry in order to obtain some insight into the bonding changes involved in the reaction of the linear metal chain complex on the compound semiconductor surface. One of the two terminal Cr-Cl bonds of the complex may be cleaved upon adsorption at 110 K, leading to the formation of the Ga-Cl bonds on the surface, although some complexes remained intact upon adsorption and bonded strongly to the surface. No ligand was dissociated from the chromium chain complex during the adsorption. The Cl-cleaved complex residue preserved its original chemical configuration. Both the Cl-cleaved and the intact complexes in the first layer were stable on the surface in the substrate temperature range between 110 and 260 K. A partial decomposition in which some ligands were dissociated from the adsorbed complex took place before the substrate temperature reaching 400 K. Additional Cr-Cl bonds were disrupted, resulting in a larger population of Ga-Cl bonds on the surface. Further thermal reaction at higher temperatures led to the dominance of the Ga-Cl bonding for the Cl presence on the surface. Surface etching of Ga by the dissociated Cl atoms started at a substrate temperature of {approx}525 K and the etching rate reached its maximum at {approx}590 K.
Development of a C3-symmetric benzohydroxamate tripod: Trimetallic complexation with Fe(III), Cr(III) and Al(III)
NASA Astrophysics Data System (ADS)
Baral, Minati; Gupta, Amit; Kanungo, B. K.
The design, synthesis and physicochemical characterization of a C3-symmetry Benzene-1,3,5-tricarbonylhydroxamate tripod, noted here as BTHA, are described. The chelator was built from a benzene as an anchor, symmetrically extended by three hydroxamate as ligating moieties, each bearing O, O donor sites. A combination of absorption spectrophotometry, potentiometry and theoretical investigations are used to explore the complexation behavior of the ligand with some trivalent metal ions: Fe(III), Cr(III), and Al(III). Three protonation constants were calculated for the ligand in a pH range of 2-11 in a highly aqueous medium (9:1 H2O: DMSO). A high rigidity in the molecular structure restricts the formation of 1:1 (M/L) metal encapsulation but shows a high binding efficiency for a 3:1 metal ligand stoichiometry giving formation constant (in β unit) 28.73, 26.13 and 19.69 for [M3L]; Mdbnd Fe(III), Al(III) and Cr(III) respectively, and may be considered as an efficient Fe-carrier. The spectrophotometric study reveals of interesting electronic transitions occurred during the complexation. BTHA exhibits a peak at 238 nm in acidic pH and with the increase of pH, a new peak appeared at 270 nm. A substantial shifting in both of the peaks in presence of the metal ions implicates a s coordination between ligand and metal ions. Moreover, complexation of BTHA with iron shows three distinct colors, violet, reddish orange and yellow in different pH, enables the ligand to be considered for the use as colorimetric sensor.
Metal-metal interactions in linear tri-, penta-, hepta-, and nona-nuclear ruthenium string complexes.
Niskanen, Mika; Hirva, Pipsa; Haukka, Matti
Density functional theory (DFT) methodology was used to examine the structural properties of linear metal string complexes: [Ru(3)(dpa)(4)X(2)] (X = Cl(-), CN(-), NCS(-), dpa = dipyridylamine(-)), [Ru(5)(tpda)(4)Cl(2)], and hypothetical, not yet synthesized complexes [Ru(7)(tpta)(4)Cl(2)] and [Ru(9)(ppta)(4)Cl(2)] (tpda = tri-α-pyridyldiamine(2-), tpta = tetra-α-pyridyltriamine(3-), ppta = penta-α-pyridyltetraamine(4-)). Our specific focus was on the two longest structures and on comparison of the string complexes and unsupported ruthenium backboned chain complexes, which have weaker ruthenium-ruthenium interactions. The electronic structures were studied with the aid of visualized frontier molecular orbitals, and Bader's quantum theory of atoms in molecules (QTAIM) was used to study the interactions between ruthenium atoms. The electron density was found to be highest and distributed most evenly between the ruthenium atoms in the hypothetical [Ru(7)(tpta)(4)Cl(2)] and [Ru(9)(ppta)(4)Cl(2)] string complexes.
Up-converted fluorescence from photosynthetic light-harvesting complexes linearly dependent on excitation intensity.
Leiger, Kristjan; Freiberg, Arvi
Weak up-converted fluorescence related to bacteriochlorophyll a was recorded from various detergent-isolated and membrane-embedded light-harvesting pigment-protein complexes as well as from the functional membranes of photosynthetic purple bacteria under continuous-wave infrared laser excitation at 1064 nm, far outside the optically allowed singlet absorption bands of the chromophore. The fluorescence increases linearly with the excitation power, distinguishing it from the previously observed two-photon excited fluorescence upon femtosecond pulse excitation. Possible mechanisms of this excitation are discussed.
Variational theory of complex rays applied to shell structures: in-plane inertia, quasi-symmetric ray distribution, and orthotropic materials
NASA Astrophysics Data System (ADS)
Cattabiani, Alessandro; Barbarulo, Andrea; Riou, Hervé; Ladevèze, Pierre
Recently, interest of aerospace and automotive industries on medium-frequency vibrational behavior of composite shell structures has grown due to their high specific stiffness and fatigue resistance. Conventional methods such as the finite element method and the statistical energy analysis are not suitable for the medium-frequency bandwidth. Conversely, the variational theory of complex rays (VTCR) is taking place as an ad-hoc technique to tackle such frequency band. It is a Trefftz method based on a weak variational formulation. Equilibrium equations are met using exact solutions as shape functions. The variational problem imposes boundary conditions in weak form. The present paper extends VTCR to orthotropic shell structures. Moreover, several new enhancements are introduced. Now, we use a quasi-symmetric ray distribution which can greatly reduce computational costs, and addresses in-plane inertia which was neglected in previous works. Some relevant numerical examples are presented to show the strategy and results are compared with a FEM reference to study performances.
Synthesis and characterization of a series of transition metal complexes with a new symmetrical polyoxaaza macroacyclic Schiff base ligand: X-ray crystal structure of cobalt(II) and nickel(II) complexes and their antibacterial properties
NASA Astrophysics Data System (ADS)
Keypour, Hassan; Shayesteh, Maryam; Rezaeivala, Majid; Chalabian, Firoozeh; Valencia, Laura
A new symmetrical [N4O2] hexadentate Schiff base ligand, (E)-N-(pyridin-2-ylmethylene)-2-(3-(2-((E)-pyridin-2-lmethyleneamino)phenoxy)naphthalen-2-yloxy)benzenamine, abbreviated to L, and its complexes of Ni(II), Cu(II), Zn(II), Co(II), Cd(II) and Mn(II) have been synthesized in the presence of metal ions. The complexes were structurally characterized by elemental analyses, IR, UV-Vis, NMR and molar conductivity. The crystal structures of two complexes, [NiL(ONO2)2]·2H2O and [CoLCl2]CH3OH·0.5H2O, have been determined by a single crystal X-ray diffraction study. In these complexes, the ligand is coordinated in a neutral form via pyridine and azomethine nitrogen atoms. The metal ions complete their six coordination with two coordinated nitrate or chloride ions, forming a distorted octahedral geometry. The synthesized compounds have antibacterial activity against the three Gram-positive bacteria: Enterococcus faecalis, Bacillus cereus and Staphylococcus epid and also against the three Gram-negative bacteria: Citrobacter freundii, Enterobacter aerogenes and Salmonella typhi. The activity data show that the complexes are more potent antibacterials than the parent Schiff base.
Synthesis and characterization of a series of transition metal complexes with a new symmetrical polyoxaaza macroacyclic Schiff base ligand: X-ray crystal structure of cobalt(II) and nickel(II) complexes and their antibacterial properties.
Keypour, Hassan; Shayesteh, Maryam; Rezaeivala, Majid; Chalabian, Firoozeh; Valencia, Laura
A new symmetrical [N4O2] hexadentate Schiff base ligand, (E)-N-(pyridin-2-ylmethylene)-2-(3-(2-((E)-pyridin-2-lmethyleneamino)phenoxy)naphthalen-2-yloxy)benzenamine, abbreviated to L, and its complexes of Ni(II), Cu(II), Zn(II), Co(II), Cd(II) and Mn(II) have been synthesized in the presence of metal ions. The complexes were structurally characterized by elemental analyses, IR, UV-Vis, NMR and molar conductivity. The crystal structures of two complexes, [NiL(ONO2)2]·2H2O and [CoLCl2]CH3OH·0.5H2O, have been determined by a single crystal X-ray diffraction study. In these complexes, the ligand is coordinated in a neutral form via pyridine and azomethine nitrogen atoms. The metal ions complete their six coordination with two coordinated nitrate or chloride ions, forming a distorted octahedral geometry. The synthesized compounds have antibacterial activity against the three Gram-positive bacteria: Enterococcus faecalis, Bacillus cereus and Staphylococcus epid and also against the three Gram-negative bacteria: Citrobacter freundii, Enterobacter aerogenes and Salmonella typhi. The activity data show that the complexes are more potent antibacterials than the parent Schiff base.
Ab initio anharmonic vibrational frequency predictions for linear proton-bound complexes OC-H(+)-CO and N(2)-H(+)-N(2).
Terrill, Kasia; Nesbitt, David J
Ab initio anharmonic transition frequencies are calculated for strongly coupled (i) asymmetric and (ii) symmetric proton stretching modes in the X-H(+)-X linear ionic hydrogen bonded complexes for OCHCO(+) and N(2)HN(2)(+). The optimized potential surface is calculated in these two coordinates for each molecular ion at CCSD(T)/aug-cc-pVnZ (n = 2-4) levels and extrapolated to the complete-basis-set limit (CBS). Slices through both 2D surfaces reveal a relatively soft potential in the asymmetric proton stretching coordinate at near equilibrium geometries, which rapidly becomes a double minimum potential with increasing symmetric proton acceptor center of mass separation. Eigenvalues are obtained by solution of the 2D Schrödinger equation with potential/kinetic energy coupling explicity taken into account, converged in a distributed Gaussian basis set as a function of grid density. The asymmetric proton stretch fundamental frequency for N(2)HN(2)(+) is predicted at 848 cm(-1), with strong negative anharmonicity in the progression characteristic of a shallow "particle in a box" potential. The corresponding proton stretch fundamental for OCHCO(+) is anomalously low at 386 cm(-1), but with a strong alternation in the vibrational spacing due to the presence of a shallow D(infinityh) transition state barrier (Delta = 398 cm(-1)) between the two equivalent minimum geometries. Calculation of a 2D dipole moment surface and transition matrix elements reveals surprisingly strong combination and difference bands with appreciable intensity throughout the 300-1500 cm(-1) region. Corrected for zero point (DeltaZPE) and thermal vibrational excitation (DeltaE(vib)) at 300 K, the single and double dissociation energies in these complexes are in excellent agreement with thermochemical gas phase ion data.
LINPACK. Simultaneous Linear Algebraic Equations
Miller, M.A.
LINPACK is a collection of FORTRAN subroutines which analyze and solve various classes of systems of simultaneous linear algebraic equations. The collection deals with general, banded, symmetric indefinite, symmetric positive definite, triangular, and tridiagonal square matrices, as well as with least squares problems and the QR and singular value decompositions of rectangular matrices. A subroutine-naming convention is employed in which each subroutine name consists of five letters which represent a coded specification (TXXYY) of the computation done by that subroutine. The first letter, T, indicates the matrix data type. Standard FORTRAN allows the use of three such types: S REAL, D DOUBLE PRECISION, and C COMPLEX. In addition, some FORTRAN systems allow a double-precision complex type: Z COMPLEX*16. The second and third letters of the subroutine name, XX, indicate the form of the matrix or its decomposition: GE General, GB General band, PO Positive definite, PP Positive definite packed, PB Positive definite band, SI Symmetric indefinite, SP Symmetric indefinite packed, HI Hermitian indefinite, HP Hermitian indefinite packed, TR Triangular, GT General tridiagonal, PT Positive definite tridiagonal, CH Cholesky decomposition, QR Orthogonal-triangular decomposition, SV Singular value decomposition. The final two letters, YY, indicate the computation done by the particular subroutine: FA Factor, CO Factor and estimate condition, SL Solve, DI Determinant and/or inverse and/or inertia, DC Decompose, UD Update, DD Downdate, EX Exchange. The LINPACK package also includes a set of routines to perform basic vector operations called the Basic Linear Algebra Subprograms (BLAS).
LINPACK. Simultaneous Linear Algebraic Equations
Dongarra, J.J.
LINPACK is a collection of FORTRAN subroutines which analyze and solve various classes of systems of simultaneous linear algebraic equations. The collection deals with general, banded, symmetric indefinite, symmetric positive definite, triangular, and tridiagonal square matrices, as well as with least squares problems and the QR and singular value decompositions of rectangular matrices. A subroutine-naming convention is employed in which each subroutine name consists of five letters which represent a coded specification (TXXYY) of the computation done by that subroutine. The first letter, T, indicates the matrix data type. Standard FORTRAN allows the use of three such types: S REAL, D DOUBLE PRECISION, and C COMPLEX. In addition, some FORTRAN systems allow a double-precision complex type: Z COMPLEX*16. The second and third letters of the subroutine name, XX, indicate the form of the matrix or its decomposition: GE General, GB General band, PO Positive definite, PP Positive definite packed, PB Positive definite band, SI Symmetric indefinite, SP Symmetric indefinite packed, HI Hermitian indefinite, HP Hermitian indefinite packed, TR Triangular, GT General tridiagonal, PT Positive definite tridiagonal, CH Cholesky decomposition, QR Orthogonal-triangular decomposition, SV Singular value decomposition. The final two letters, YY, indicate the computation done by the particular subroutine: FA Factor, CO Factor and estimate condition, SL Solve, DI Determinant and/or inverse and/or inertia, DC Decompose, UD Update, DD Downdate, EX Exchange. The LINPACK package also includes a set of routines to perform basic vector operations called the Basic Linear Algebra Subprograms (BLAS).
Distress Propagation in Complex Networks: The Case of Non-Linear DebtRank
Bardoscia, Marco; Caccioli, Fabio; Perotti, Juan Ignacio; Vivaldo, Gianna; Caldarelli, Guido
We consider a dynamical model of distress propagation on complex networks, which we apply to the study of financial contagion in networks of banks connected to each other by direct exposures. The model that we consider is an extension of the DebtRank algorithm, recently introduced in the literature. The mechanics of distress propagation is very simple: When a bank suffers a loss, distress propagates to its creditors, who in turn suffer losses, and so on. The original DebtRank assumes that losses are propagated linearly between connected banks. Here we relax this assumption and introduce a one-parameter family of non-linear propagation functions. As a case study, we apply this algorithm to a data-set of 183 European banks, and we study how the stability of the system depends on the non-linearity parameter under different stress-test scenarios. We find that the system is characterized by a transition between a regime where small shocks can be amplified and a regime where shocks do not propagate, and that the overall stability of the system increases between 2008 and 2013. PMID:27701457
Distress Propagation in Complex Networks: The Case of Non-Linear DebtRank.
Bardoscia, Marco; Caccioli, Fabio; Perotti, Juan Ignacio; Vivaldo, Gianna; Caldarelli, Guido
We consider a dynamical model of distress propagation on complex networks, which we apply to the study of financial contagion in networks of banks connected to each other by direct exposures. The model that we consider is an extension of the DebtRank algorithm, recently introduced in the literature. The mechanics of distress propagation is very simple: When a bank suffers a loss, distress propagates to its creditors, who in turn suffer losses, and so on. The original DebtRank assumes that losses are propagated linearly between connected banks. Here we relax this assumption and introduce a one-parameter family of non-linear propagation functions. As a case study, we apply this algorithm to a data-set of 183 European banks, and we study how the stability of the system depends on the non-linearity parameter under different stress-test scenarios. We find that the system is characterized by a transition between a regime where small shocks can be amplified and a regime where shocks do not propagate, and that the overall stability of the system increases between 2008 and 2013.
Two Dimensional Symmetric Correlation Functions of the S Operator and Two Dimensional Fourier Transforms: Considering the Line Coupling for P and R Lines of Linear Molecules
NASA Technical Reports Server (NTRS)
Ma, Q.; Boulet, C.; Tipping, R. H.
The refinement of the Robert-Bonamy (RB) formalism by considering the line coupling for isotropic Raman Q lines of linear molecules developed in our previous study [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] has been extended to infrared P and R lines. In these calculations, the main task is to derive diagonal and off-diagonal matrix elements of the Liouville operator iS1 - S2 introduced in the formalism. When one considers the line coupling for isotropic Raman Q lines where their initial and final rotational quantum numbers are identical, the derivations of off-diagonal elements do not require extra correlation functions of the ^S operator and their Fourier transforms except for those used in deriving diagonal elements. In contrast, the derivations for infrared P and R lines become more difficult because they require a lot of new correlation functions and their Fourier transforms. By introducing two dimensional correlation functions labeled by two tensor ranks and making variable changes to become even functions, the derivations only require the latters' two dimensional Fourier transforms evaluated at two modulation frequencies characterizing the averaged energy gap and the frequency detuning between the two coupled transitions. With the coordinate representation, it is easy to accurately derive these two dimensional correlation functions. Meanwhile, by using the sampling theory one is able to effectively evaluate their two dimensional Fourier transforms. Thus, the obstacles in considering the line coupling for P and R lines have been overcome. Numerical calculations have been carried out for the half-widths of both the isotropic Raman Q lines and the infrared P and R lines of C2H2 broadened by N2. In comparison with values derived from the RB formalism, new calculated values are significantly reduced and become closer to measurements.
Two dimensional symmetric correlation functions of the S-circumflex operator and two dimensional Fourier transforms: Considering the line coupling for P and R lines of linear molecules
Ma, Q.; Tipping, R. H.
The refinement of the Robert-Bonamy (RB) formalism by considering the line coupling for isotropic Raman Q lines of linear molecules developed in our previous study [Q. Ma, C. Boulet, and R. H. Tipping, J. Chem. Phys. 139, 034305 (2013)] has been extended to infrared P and R lines. In these calculations, the main task is to derive diagonal and off-diagonal matrix elements of the Liouville operator iS{sub 1} − S{sub 2} introduced in the formalism. When one considers the line coupling for isotropic Raman Q lines where their initial and final rotational quantum numbers are identical, the derivations of off-diagonal elements do not require extra correlation functions of the S-circumflex operator and their Fourier transforms except for those used in deriving diagonal elements. In contrast, the derivations for infrared P and R lines become more difficult because they require a lot of new correlation functions and their Fourier transforms. By introducing two dimensional correlation functions labeled by two tensor ranks and making variable changes to become even functions, the derivations only require the latters' two dimensional Fourier transforms evaluated at two modulation frequencies characterizing the averaged energy gap and the frequency detuning between the two coupled transitions. With the coordinate representation, it is easy to accurately derive these two dimensional correlation functions. Meanwhile, by using the sampling theory one is able to effectively evaluate their two dimensional Fourier transforms. Thus, the obstacles in considering the line coupling for P and R lines have been overcome. Numerical calculations have been carried out for the half-widths of both the isotropic Raman Q lines and the infrared P and R lines of C{sub 2}H{sub 2} broadened by N{sub 2}. In comparison with values derived from the RB formalism, new calculated values are significantly reduced and become closer to measurements.
Probabilistic cloning of three symmetric states
Jimenez, O.; Bergou, J.; Delgado, A.
We study the probabilistic cloning of three symmetric states. These states are defined by a single complex quantity, the inner product among them. We show that three different probabilistic cloning machines are necessary to optimally clone all possible families of three symmetric states. We also show that the optimal cloning probability of generating M copies out of one original can be cast as the quotient between the success probability of unambiguously discriminating one and M copies of symmetric states.
Anomalous Light Scattering by Topological PT-symmetric Particle Arrays
Ling, C. W.; Choi, Ka Hei; Mok, T. C.; Zhang, Zhao-Qing; Fung, Kin Hung
Robust topological edge modes may evolve into complex-frequency modes when a physical system becomes non-Hermitian. We show that, while having negligible forward optical extinction cross section, a conjugate pair of such complex topological edge modes in a non-Hermitian -symmetric system can give rise to an anomalous sideway scattering when they are simultaneously excited by a plane wave. We propose a realization of such scattering state in a linear array of subwavelength resonators coated with gain media. The prediction is based on an analytical two-band model and verified by rigorous numerical simulation using multiple-multipole scattering theory. The result suggests an extreme situation where leakage of classical information is unnoticeable to the transmitter and the receiver when such a -symmetric unit is inserted into the communication channel. PMID:27905504
Anomalous Light Scattering by Topological PT-symmetric Particle Arrays
NASA Astrophysics Data System (ADS)
Ling, C. W.; Choi, Ka Hei; Mok, T. C.; Zhang, Zhao-Qing; Fung, Kin Hung
Robust topological edge modes may evolve into complex-frequency modes when a physical system becomes non-Hermitian. We show that, while having negligible forward optical extinction cross section, a conjugate pair of such complex topological edge modes in a non-Hermitian -symmetric system can give rise to an anomalous sideway scattering when they are simultaneously excited by a plane wave. We propose a realization of such scattering state in a linear array of subwavelength resonators coated with gain media. The prediction is based on an analytical two-band model and verified by rigorous numerical simulation using multiple-multipole scattering theory. The result suggests an extreme situation where leakage of classical information is unnoticeable to the transmitter and the receiver when such a -symmetric unit is inserted into the communication channel.
Waste management under multiple complexities: Inexact piecewise-linearization-based fuzzy flexible programming
Sun Wei; Huang, Guo H.; Lv Ying; Li Gongchen
Highlights: Black-Right-Pointing-Pointer Inexact piecewise-linearization-based fuzzy flexible programming is proposed. Black-Right-Pointing-Pointer It's the first application to waste management under multiple complexities. Black-Right-Pointing-Pointer It tackles nonlinear economies-of-scale effects in interval-parameter constraints. Black-Right-Pointing-Pointer It estimates costs more accurately than the linear-regression-based model. Black-Right-Pointing-Pointer Uncertainties are decreased and more satisfactory interval solutions are obtained. - Abstract: To tackle nonlinear economies-of-scale (EOS) effects in interval-parameter constraints for a representative waste management problem, an inexact piecewise-linearization-based fuzzy flexible programming (IPFP) model is developed. In IPFP, interval parameters for waste amounts and transportation/operation costs can be quantified; aspiration levels for net system costs, as well as tolerance intervals for both capacities of waste treatment facilities and waste generation rates can be reflected; and the nonlinear EOS effects transformed from objective function to constraints can be approximated. An interactive algorithm is proposed for solving the IPFP model, which in nature is an interval-parameter mixed-integer quadratically constrained programming model. To demonstrate the IPFP's advantages, two alternative models are developed to compare their performances. One is a conventional linear-regression-based inexact fuzzy programming model (IPFP2) and the other is an IPFP model with all right-hand-sides of fussy constraints being the corresponding interval numbers (IPFP3). The comparison results between IPFP and IPFP2 indicate that the optimized waste amounts would have the similar patterns in both models. However, when dealing with EOS effects in constraints, the IPFP2 may underestimate the net system costs while the IPFP can estimate the costs more accurately. The comparison results between IPFP and IPFP3 indicate
Preparation, linear and NLO properties of DNA-CTMA-SBE complexes
NASA Astrophysics Data System (ADS)
Manea, Ana-Maria; Rau, Ileana; Kajzar, Francois; Meghea, Aurelia
Synthesis of deoxyribonucleic acid (DNA) - was cetyltrimethylammonium (CTMA) - sea buckthorn extract (SBE) at different concentrations is decribed. The complexes were processed into good optical quality thin films by spin coating on different substrates such as: glass, silica and ITO covered glass substrates. SBE contains many bioactive substances that can be used in the treatment of several diseases, such as cardiovascular disease, cancer, and acute mountain sickness. The obtained thin films were characterized for their spectroscopic, fluorescent, linear and nonlinear optical properties as function of SBE concentration. The third-order nonlinear optical (NLO) properties of thin films were determined by the optical third-harmonic generation technique at 1 064.2 nm fundamental wavelength.
FORTRAN subroutines for out-of-core solutions of large complex linear systems
NASA Technical Reports Server (NTRS)
Yip, E. L.
The design and usage of two main subprograms using direct methods to solve large linear complex systems, of the form Ax = b, whose coeffficient matrices are too large to be stored in core are described. The first main subprogram is for systems whose coefficient matrices are of a particular sparse structure, namely, the matrix A can be written in the form B + D, where B is a block-banded system, and D has only a few columns of nonzeros. Key elements of the algorithms used in the subprograms include: the data structure, the strategy for preserving numerical stability, the adaptability of the algorithms for dense systems as well as for block-profile systems.
Experimental and theoretical study of lanthanide complexes based on linear and macrocyclic polyaminopolycarboxylic acids containing pyrazolylethyl arms.
Pérez-Mayoral, Elena; Soriano, Elena; Cerdán, Sebastián; Ballesteros, Paloma
We report the synthesis of two novel Gd(III)-complexes derived from linear and macrocyclic polyaminopolycarboxylic acids 1 and 2, which contain a 3,5- dimethylpyrazolyl-ethyl arm, and a study of their relaxivity properties. The relationships between the experimental and theoretical results have provided interesting information about the kinetic and thermodynamic stability of these complexes.
Optimal symmetric flight studies
NASA Technical Reports Server (NTRS)
Weston, A. R.; Menon, P. K. A.; Bilimoria, K. D.; Cliff, E. M.; Kelley, H. J.
Several topics in optimal symmetric flight of airbreathing vehicles are examined. In one study, an approximation scheme designed for onboard real-time energy management of climb-dash is developed and calculations for a high-performance aircraft presented. In another, a vehicle model intermediate in complexity between energy and point-mass models is explored and some quirks in optimal flight characteristics peculiar to the model uncovered. In yet another study, energy-modelling procedures are re-examined with a view to stretching the range of validity of zeroth-order approximation by special choice of state variables. In a final study, time-fuel tradeoffs in cruise-dash are examined for the consequences of nonconvexities appearing in the classical steady cruise-dash model. Two appendices provide retrospective looks at two early publications on energy modelling and related optimal control theory.
Linear-type S-bridged triruthenium complexes with aliphatic aminothiolate ligands: synthesis, characterization, and properties.
Matsuura, Noriyuki; Igashira-Kamiyama, Asako; Kawamoto, Tatsuya; Konno, Takumi
Treatment of [RuCl(2)(DMSO)(4)] with 2-aminoethanethiol (Haet) in ethanol gave a dicationic triruthenium complex, [Ru[Ru(aet)(3)](2)]Cl(2) ([1]Cl(2)). Complex [1]Cl(2) was also obtained by treatment of RuCl(3).nH(2)O with excess Haet in water. When [1](2+) was chromatographed on a cation-exchange column of SP-Sephadex C-25, meso (DeltaLambda) and racemic (DeltaDelta/LambdaLambda) isomers of the corresponding tricationic complex, [Ru[Ru(aet)(3)](2)](3+) ([2](3+)), were eluted with aqueous NaNO(3). The racemic isomer of [2](3+) was optically resolved into DeltaDelta and LambdaLambda isomers by using [Sb(2)(R,R-tartrato)(2)](2-) as a resolving agent. The molecular structures of DeltaLambda- and DeltaDelta/LambdaLambda-[2](NO(3))(3) were determined by X-ray crystallography. In these complexes, the central Ru atom is coordinated by six thiolato groups from two terminal fac-(S)-[Ru(aet)(3)] units in an octahedral geometry, forming a linear-type S-bridged triruthenium structure. The spectroelectrochemical studies on the electronic absorption and CD spectra, together with the electrochemical studies, demonstrated that [1](2+) and [2](3+) are interconvertible with each other through a one-electron redox process, retaining the chirality of the triruthenium structure. Their electronic structures were investigated on the basis of EPR and magnetic susceptibility measurements, which indicated that [1](2+) and [2](3+) have spin ground states of S(t) = 0 and S(t) = 1/2, respectively. The corresponding L-cysteinato complex, [Ru[Ru(L-cys-N,S)(3)](2)](3-), which was formed from RuCl(3).nH(2)O and excess L-cysteine (L-H(2)cys) in water followed by air oxidation, is also presented.
Waste management under multiple complexities: inexact piecewise-linearization-based fuzzy flexible programming.
Sun, Wei; Huang, Guo H; Lv, Ying; Li, Gongchen
To tackle nonlinear economies-of-scale (EOS) effects in interval-parameter constraints for a representative waste management problem, an inexact piecewise-linearization-based fuzzy flexible programming (IPFP) model is developed. In IPFP, interval parameters for waste amounts and transportation/operation costs can be quantified; aspiration levels for net system costs, as well as tolerance intervals for both capacities of waste treatment facilities and waste generation rates can be reflected; and the nonlinear EOS effects transformed from objective function to constraints can be approximated. An interactive algorithm is proposed for solving the IPFP model, which in nature is an interval-parameter mixed-integer quadratically constrained programming model. To demonstrate the IPFP's advantages, two alternative models are developed to compare their performances. One is a conventional linear-regression-based inexact fuzzy programming model (IPFP2) and the other is an IPFP model with all right-hand-sides of fussy constraints being the corresponding interval numbers (IPFP3). The comparison results between IPFP and IPFP2 indicate that the optimized waste amounts would have the similar patterns in both models. However, when dealing with EOS effects in constraints, the IPFP2 may underestimate the net system costs while the IPFP can estimate the costs more accurately. The comparison results between IPFP and IPFP3 indicate that their solutions would be significantly different. The decreased system uncertainties in IPFP's solutions demonstrate its effectiveness for providing more satisfactory interval solutions than IPFP3. Following its first application to waste management, the IPFP can be potentially applied to other environmental problems under multiple complexities.
Modifications to Axially Symmetric Simulations Using New DSMC (2007) Algorithms
NASA Technical Reports Server (NTRS)
Liechty, Derek S.
Several modifications aimed at improving physical accuracy are proposed for solving axially symmetric problems building on the DSMC (2007) algorithms introduced by Bird. Originally developed to solve nonequilibrium, rarefied flows, the DSMC method is now regularly used to solve complex problems over a wide range of Knudsen numbers. These new algorithms include features such as nearest neighbor collisions excluding the previous collision partners, separate collision and sampling cells, automatically adaptive variable time steps, a modified no-time counter procedure for collisions, and discontinuous and event-driven physical processes. Axially symmetric solutions require radial weighting for the simulated molecules since the molecules near the axis represent fewer real molecules than those farther away from the axis due to the difference in volume of the cells. In the present methodology, these radial weighting factors are continuous, linear functions that vary with the radial position of each simulated molecule. It is shown that how one defines the number of tentative collisions greatly influences the mean collision time near the axis. The method by which the grid is treated for axially symmetric problems also plays an important role near the axis, especially for scalar pressure. A new method to treat how the molecules are traced through the grid is proposed to alleviate the decrease in scalar pressure at the axis near the surface. Also, a modification to the duplication buffer is proposed to vary the duplicated molecular velocities while retaining the molecular kinetic energy and axially symmetric nature of the problem.
The linear ubiquitin chain assembly complex regulates TRAIL-induced gene activation and cell death.
Lafont, Elodie; Kantari-Mimoun, Chahrazade; Draber, Peter; De Miguel, Diego; Hartwig, Torsten; Reichert, Matthias; Kupka, Sebastian; Shimizu, Yutaka; Taraborrelli, Lucia; Spit, Maureen; Sprick, Martin R; Walczak, Henning
The linear ubiquitin chain assembly complex (LUBAC) is the only known E3 ubiquitin ligase which catalyses the generation of linear ubiquitin linkages de novo LUBAC is a crucial component of various immune receptor signalling pathways. Here, we show that LUBAC forms part of the TRAIL-R-associated complex I as well as of the cytoplasmic TRAIL-induced complex II In both of these complexes, HOIP limits caspase-8 activity and, consequently, apoptosis whilst being itself cleaved in a caspase-8-dependent manner. Yet, by limiting the formation of a RIPK1/RIPK3/MLKL-containing complex, LUBAC also restricts TRAIL-induced necroptosis. We identify RIPK1 and caspase-8 as linearly ubiquitinated targets of LUBAC following TRAIL stimulation. Contrary to its role in preventing TRAIL-induced RIPK1-independent apoptosis, HOIP presence, but not its activity, is required for preventing necroptosis. By promoting recruitment of the IKK complex to complex I, LUBAC also promotes TRAIL-induced activation of NF-κB and, consequently, the production of cytokines, downstream of FADD, caspase-8 and cIAP1/2. Hence, LUBAC controls the TRAIL signalling outcome from complex I and II, two platforms which both trigger cell death and gene activation.
Sexual display complexity varies non-linearly with age and predicts breeding status in greater flamingos
Perrot, Charlotte; Béchet, Arnaud; Hanzen, Céline; Arnaud, Antoine; Pradel, Roger; Cézilly, Frank
The long-lived greater flamingo (Phoenicopterus roseus) is famous for performing conspicuous group displays during which adults try to acquire a new mate each year with varying success. We examined variation in the sexual display complexity (SDC) of wild flamingos aged between 4 and 37 yrs. SDC was defined as the product of richness (the number of different display movements) and versatility (the number of transitions between movements) within a 5 min behavioral sequence. In both sexes, date in the pairing season had a linear and positive effect on SDC, whereas age had a quadratic effect, with SDC increasing until about age 20yrs, and declining afterwards. SDC better explained pairing patterns than age, and positively influenced the probability of becoming a breeder. Our results thus support the idea that SDC is an honest signal of individual quality and further suggest that senescence in display could be an overlooked aspect of reproductive decline in species with no or weak pair bonding. PMID:27883016
Sexual display complexity varies non-linearly with age and predicts breeding status in greater flamingos.
Perrot, Charlotte; Béchet, Arnaud; Hanzen, Céline; Arnaud, Antoine; Pradel, Roger; Cézilly, Frank
The long-lived greater flamingo (Phoenicopterus roseus) is famous for performing conspicuous group displays during which adults try to acquire a new mate each year with varying success. We examined variation in the sexual display complexity (SDC) of wild flamingos aged between 4 and 37 yrs. SDC was defined as the product of richness (the number of different display movements) and versatility (the number of transitions between movements) within a 5 min behavioral sequence. In both sexes, date in the pairing season had a linear and positive effect on SDC, whereas age had a quadratic effect, with SDC increasing until about age 20yrs, and declining afterwards. SDC better explained pairing patterns than age, and positively influenced the probability of becoming a breeder. Our results thus support the idea that SDC is an honest signal of individual quality and further suggest that senescence in display could be an overlooked aspect of reproductive decline in species with no or weak pair bonding.
T-Matrix Modeling of Linear Depolarization by Morphologically Complex Soot and Soot-Containing Aerosols
NASA Technical Reports Server (NTRS)
Mishchenko, Michael I.; Liu, Li; Mackowski, Daniel W.
We use state-of-the-art public-domain Fortran codes based on the T-matrix method to calculate orientation and ensemble averaged scattering matrix elements for a variety of morphologically complex black carbon (BC) and BC-containing aerosol particles, with a special emphasis on the linear depolarization ratio (LDR). We explain theoretically the quasi-Rayleigh LDR peak at side-scattering angles typical of low-density soot fractals and conclude that the measurement of this feature enables one to evaluate the compactness state of BC clusters and trace the evolution of low-density fluffy fractals into densely packed aggregates. We show that small backscattering LDRs measured with groundbased, airborne, and spaceborne lidars for fresh smoke generally agree with the values predicted theoretically for fluffy BC fractals and densely packed near-spheroidal BC aggregates. To reproduce higher lidar LDRs observed for aged smoke, one needs alternative particle models such as shape mixtures of BC spheroids or cylinders.
The linear and non-linear characterization of dust ion acoustic mode in complex plasma in presence of dynamical charging of dust
Bhattacharjee, Saurav Das, Nilakshi
A systematic theoretical investigation has been carried out on the role of dust charging dynamics on the nature and stability of DIA (Dust Ion Acoustic) mode in complex plasma. The study has been made for both linear and non-linear scale regime of DIA mode. The observed results have been characterized in terms of background plasma responses towards dust surface responsible for dust charge fluctuation, invoking important dusty plasma parameters, especially the ion flow speed and dust size. The linear analyses confirm the nature of instability in DIA mode in presence of dust charge fluctuation. The instability shows a damping of DIA mode in subsonic flow regime followed by a gradual growth in instability in supersonic limit of ion flow. The strength of non-linearity and their existence domain is found to be driven by different dusty plasma parameters. As dust is ubiquitous in interstellar medium with plasma background, the study also addresses the possible effect of dust charging dynamics in gravito-electrostatic characterization and the stability of dust molecular clouds especially in proto-planetary disc. The observations are influential and interesting towards the understanding of dust settling mechanism and formation of dust environments in different regions in space.
Conformally symmetric traversable wormholes
Boehmer, Christian G.; Harko, Tiberiu; Lobo, Francisco S. N.
Exact solutions of traversable wormholes are found under the assumption of spherical symmetry and the existence of a nonstatic conformal symmetry, which presents a more systematic approach in searching for exact wormhole solutions. In this work, a wide variety of solutions are deduced by considering choices for the form function, a specific linear equation of state relating the energy density and the pressure anisotropy, and various phantom wormhole geometries are explored. A large class of solutions impose that the spatial distribution of the exotic matter is restricted to the throat neighborhood, with a cutoff of the stress-energy tensor at a finite junction interface, although asymptotically flat exact solutions are also found. Using the 'volume integral quantifier', it is found that the conformally symmetric phantom wormhole geometries may, in principle, be constructed by infinitesimally small amounts of averaged null energy condition violating matter. Considering the tidal acceleration traversability conditions for the phantom wormhole geometry, specific wormhole dimensions and the traversal velocity are also deduced.
Linear precoding based on polynomial expansion: reducing complexity in massive MIMO.
Mueller, Axel; Kammoun, Abla; Björnson, Emil; Debbah, Mérouane
Massive multiple-input multiple-output (MIMO) techniques have the potential to bring tremendous improvements in spectral efficiency to future communication systems. Counterintuitively, the practical issues of having uncertain channel knowledge, high propagation losses, and implementing optimal non-linear precoding are solved more or less automatically by enlarging system dimensions. However, the computational precoding complexity grows with the system dimensions. For example, the close-to-optimal and relatively "antenna-efficient" regularized zero-forcing (RZF) precoding is very complicated to implement in practice, since it requires fast inversions of large matrices in every coherence period. Motivated by the high performance of RZF, we propose to replace the matrix inversion and multiplication by a truncated polynomial expansion (TPE), thereby obtaining the new TPE precoding scheme which is more suitable for real-time hardware implementation and significantly reduces the delay to the first transmitted symbol. The degree of the matrix polynomial can be adapted to the available hardware resources and enables smooth transition between simple maximum ratio transmission and more advanced RZF. By deriving new random matrix results, we obtain a deterministic expression for the asymptotic signal-to-interference-and-noise ratio (SINR) achieved by TPE precoding in massive MIMO systems. Furthermore, we provide a closed-form expression for the polynomial coefficients that maximizes this SINR. To maintain a fixed per-user rate loss as compared to RZF, the polynomial degree does not need to scale with the system, but it should be increased with the quality of the channel knowledge and the signal-to-noise ratio.
A linear S-bridged trinuclear cobalt(III) complex with 2-aminobenzenethiol: Synthesis, crystal structure, and spectroscopic characterization.
Panja, Anangamohan; Moore, Curtis E; Eichhorn, David M
Treatment of cobalt(II) perchlorate hexahydrate with 2 molar equiv. of 2-aminobenzenethiol (Habt) in acetonitrile afforded a tricationic tricobalt complex, [Co{Co(abt)3}2](ClO4)3·2CH3CN, by aerial oxidation. The molecular structure of the meso (ΔΛ) form of the complex was determined by X-ray crystallography. In the complex cation, the central Co is coordinated by six thiolate groups from two terminal fac(S)-[Co(abt)3] units in an octahedral geometry, forming a linear S-bridged tricobalt structure.
Upscaling Radionuclide Retardation?Linking the Surface Complexation and Ion Exchange Mechanistic Approach to a Linear Kd Approach
Zavarin, M; Carle, S; Maxwell, R
The LLNL near-field hydrologic source term (HST) model is based on a mechanistic approach to radionuclide retardation-that is, a thermodynamic description of chemical processes governing retardation in the near field, such as aqueous speciation, surface complexation, ion exchange, and precipitation The mechanistic approach allows for radionuclide retardation to vary both in space and time as a function of the complex reaction chemistry of the medium. This level of complexity is necessary for near-field HST transport modeling because of the non-linear reaction chemistry expected close to the radiologic source. Large-scale Corrective Action Unit (CAU) models-into which the near-field HST model results feed-require that the complexity of the mechanistic approach be reduced to a more manageable form (e.g. Linear, Langmuir, or Freundlich sorption isotherms, etc). The linear sorption isotherm (or K{sub d}) approach is likely the most simple approach for large-scale CAU models. It may also be the most appropriate since the reaction chemistry away from the near field is expected to be less complex and relatively steady state. However, if the radionuclide retardation approaches in near-field HST and large-scale CAU models are different, they must be proved consistent. In this report, we develop a method to link the near-field HST and large-scale CAU model radionuclide retardation approaches.
Light propagation in periodically modulated complex waveguides
NASA Astrophysics Data System (ADS)
Nixon, Sean; Yang, Jianke
Light propagation in optical waveguides with periodically modulated index of refraction and alternating gain and loss are investigated for linear and nonlinear systems. Based on a multiscale perturbation analysis, it is shown that for many non-parity-time- (PT -) symmetric waveguides, their linear spectrum is partially complex; thus light exponentially grows or decays upon propagation, and this growth or decay is not altered by nonlinearity. However, several classes of non-PT -symmetric waveguides are also identified to possess all-real linear spectrum. For PT -symmetric waveguides, phase transition is predicted analytically. In the nonlinear regime longitudinally periodic and transversely quasilocalized modes are found for PT -symmetric waveguides both above and below phase transition. These nonlinear modes are stable under evolution and can develop from initially weak initial conditions.
Evaluation of one-dimensional potential energy surfaces for prediction of spectroscopic properties of hydrogen bonds in linear bonded complexes.
Jouypazadeh, Hamidreza; Farrokhpour, Hossein; Solimannejad, Mohammad
This work evaluated the reliability of the one-dimensional potential energy surface for calculating the spectroscopic properties (rovibrational constants and rotational line energies) of hydrogen bonds in linear bonded complexes by comparing theoretical results with the corresponding experimental results. For this purpose, two hydrogen bonded complexes were selected: the HCN···HCN homodimer and the HCN···HF heterodimer. The one-dimensional potential energy surfaces related to the hydrogen bonds in these complexes were calculated using different computational methods and basis sets. The calculated potential curve of each complex was fitted to an analytical one-dimensional potential function to obtain the potential parameters. The obtained analytical potential function of each complex was used in a two-particle Schrödinger equation to obtain the rovibrational energy levels of the hydrogen bond. Using the calculated rovibrational levels, the rovibrational spectra and constants of each complex were calculated and compared with experimental data available from the literature. Compared with experimental data, the calculated one-dimensional potential energy surface at the QCISD/aug-cc-pVDZ level of theory was found to predict the spectroscopic properties of hydrogen bonds better than the potential curves obtained using other computational methods, especially for the HCN···HCN homodimer complex. Generally, the results obtained for the HCN···HCN homodimer complex were closer to experimental data than those obtained for the HCN···HF heterodimer complex. The investigation performed in this work showed that the one-dimensional potential curve related to the hydrogen bond between two linear molecules can be used to predict the spectroscopic constants of hydrogen bonds. Graphical abstract Potential energy curves of HCN···HCN and HCN···HF complexes calculated at the different computational levels.
On the linear classification of even and odd permutation matrices and the complexity of computing the permanent
NASA Astrophysics Data System (ADS)
Babenko, A. V.; Vyalyi, M. N.
The problem of linear classification of the parity of permutation matrices is studied. This problem is related to the analysis of complexity of a class of algorithms designed for computing the permanent of a matrix that generalizes the Kasteleyn algorithm. Exponential lower bounds on the magnitude of the coefficients of the functional that classifies the even and odd permutation matrices in the case of the field of real numbers and similar linear lower bounds on the rank of the classifying map for the case of the field of characteristic 2 are obtained.
Symmetric States Requiring System Asymmetry
NASA Astrophysics Data System (ADS)
Nishikawa, Takashi; Motter, Adilson E.
Spontaneous synchronization has long served as a paradigm for behavioral uniformity that can emerge from interactions in complex systems. When the interacting entities are identical and their coupling patterns are also identical, the complete synchronization of the entire network is the state inheriting the system symmetry. As in other systems subject to symmetry breaking, such symmetric states are not always stable. Here, we report on the discovery of the converse of symmetry breaking—the scenario in which complete synchronization is not stable for identically coupled identical oscillators but becomes stable when, and only when, the oscillator parameters are judiciously tuned to nonidentical values, thereby breaking the system symmetry to preserve the state symmetry. Aside from demonstrating that diversity can facilitate and even be required for uniformity and consensus, this suggests a mechanism for convergent forms of pattern formation in which initially asymmetric patterns evolve into symmetric ones.
Transmission of linear regression patterns between time series: From relationship in time series to complex networks
NASA Astrophysics Data System (ADS)
Gao, Xiangyun; An, Haizhong; Fang, Wei; Huang, Xuan; Li, Huajiao; Zhong, Weiqiong; Ding, Yinghui
The linear regression parameters between two time series can be different under different lengths of observation period. If we study the whole period by the sliding window of a short period, the change of the linear regression parameters is a process of dynamic transmission over time. We tackle fundamental research that presents a simple and efficient computational scheme: a linear regression patterns transmission algorithm, which transforms linear regression patterns into directed and weighted networks. The linear regression patterns (nodes) are defined by the combination of intervals of the linear regression parameters and the results of the significance testing under different sizes of the sliding window. The transmissions between adjacent patterns are defined as edges, and the weights of the edges are the frequency of the transmissions. The major patterns, the distance, and the medium in the process of the transmission can be captured. The statistical results of weighted out-degree and betweenness centrality are mapped on timelines, which shows the features of the distribution of the results. Many measurements in different areas that involve two related time series variables could take advantage of this algorithm to characterize the dynamic relationships between the time series from a new perspective.
Transmission of linear regression patterns between time series: from relationship in time series to complex networks.
Gao, Xiangyun; An, Haizhong; Fang, Wei; Huang, Xuan; Li, Huajiao; Zhong, Weiqiong; Ding, Yinghui
The linear regression parameters between two time series can be different under different lengths of observation period. If we study the whole period by the sliding window of a short period, the change of the linear regression parameters is a process of dynamic transmission over time. We tackle fundamental research that presents a simple and efficient computational scheme: a linear regression patterns transmission algorithm, which transforms linear regression patterns into directed and weighted networks. The linear regression patterns (nodes) are defined by the combination of intervals of the linear regression parameters and the results of the significance testing under different sizes of the sliding window. The transmissions between adjacent patterns are defined as edges, and the weights of the edges are the frequency of the transmissions. The major patterns, the distance, and the medium in the process of the transmission can be captured. The statistical results of weighted out-degree and betweenness centrality are mapped on timelines, which shows the features of the distribution of the results. Many measurements in different areas that involve two related time series variables could take advantage of this algorithm to characterize the dynamic relationships between the time series from a new perspective.
Solution NMR characterization of an unusual distal H-bond network in the active site of the cyanide-inhibited, human heme oxygenase complex of the symmetric substrate, 2,4-dimethyldeuterohemin.
Li, Yiming; Syvitski, Ray T; Auclair, Karine; Wilks, Angela; Ortiz De Montellano, Paul R; La Mar, Gerd N
The presence of variable static hemin orientational disorder about the alpha-gamma-meso axis in the substrate complexes of mammalian heme oxygenase, together with the incomplete averaging of a second, dynamic disorder, for each hemin orientation, has led to NMR spectra with severe spectral overlap and loss of key two-dimensional correlations that seriously interfere with structural characterization in solution. We demonstrate that the symmetric substrate, 2,4-dimethyldeuterohemin, yields a single solution species for which the dynamic disorder is sufficiently rapid to allow effective and informative (1)H NMR structural characterization. A much more extensive, effective, and definitive NMR characterization of the cyanide-inhibited, symmetric heme complex of human heme oxygenase shows that the active site structure, with some minor differences, is essentially the same as that for the native protohemin in solution and crystal. A unique distal network that involves particularly strong hydrogen bonds, as well as inter-aromatic contacts, is described that is proposed to stabilize the position of the catalytically critical distal helix Asp-140 carboxylate (Liu, Y., Koenigs Lightning, L., Huang, H., Moënne-Loccoz, P., Schuller, D. J., Poulos, T. L., Loehr, T. M., and Ortiz de Montellano, P. R. (2000) J. Biol. Chem. 275, 34501-34507). The potential role of this network in placing a water molecule to stabilize the hydroperoxy species and as a template for the condensation of the distal helix upon substrate binding are discussed.
Unravelling raked linear dunes to explain the coexistence of bedforms in complex dunefields
NASA Astrophysics Data System (ADS)
Lü, Ping; Narteau, Clément; Dong, Zhibao; Rozier, Olivier; Courrech Du Pont, Sylvain
Raked linear dunes keep a constant orientation for considerable distances with a marked asymmetry between a periodic pattern of semi-crescentic structures on one side and a continuous slope on the other. Here we show that this shape is associated with a steady-state dune type arising from the coexistence of two dune growth mechanisms. Primary ridges elongate in the direction of the resultant sand flux. Semi-crescentic structures result from the development of superimposed dunes growing perpendicularly to the maximum gross bedform-normal transport. In the particular case of raked linear dunes, these two mechanisms produces primary and secondary ridges with similar height but with different orientations, which are oblique to each other. The raked pattern develops preferentially on the leeward side of the primary ridges according to the direction of propagation of the superimposed bedforms. As shown by numerical modelling, raked linear dunes occur where both these oblique orientations and dynamics are met.
Unravelling raked linear dunes to explain the coexistence of bedforms in complex dunefields
Lü, Ping; Narteau, Clément; Dong, Zhibao; Rozier, Olivier; Courrech du Pont, Sylvain
Raked linear dunes keep a constant orientation for considerable distances with a marked asymmetry between a periodic pattern of semi-crescentic structures on one side and a continuous slope on the other. Here we show that this shape is associated with a steady-state dune type arising from the coexistence of two dune growth mechanisms. Primary ridges elongate in the direction of the resultant sand flux. Semi-crescentic structures result from the development of superimposed dunes growing perpendicularly to the maximum gross bedform-normal transport. In the particular case of raked linear dunes, these two mechanisms produces primary and secondary ridges with similar height but with different orientations, which are oblique to each other. The raked pattern develops preferentially on the leeward side of the primary ridges according to the direction of propagation of the superimposed bedforms. As shown by numerical modelling, raked linear dunes occur where both these oblique orientations and dynamics are met. PMID:28128195
NASA Astrophysics Data System (ADS)
Dunajewski, Adam; Dusza, Jacek J.; Rosado Muñoz, Alfredo
The article presents a proposal for the description of human gait as a periodic and symmetric process. Firstly, the data for researches was obtained in the Laboratory of Group SATI in the School of Engineering of University of Valencia. Then, the periodical model - Mean Double Step (MDS) was made. Finally, on the basis of MDS, the symmetrical models - Left Mean Double Step and Right Mean Double Step (LMDS and RMDS) could be created. The method of various functional extensions was used. Symmetrical gait models can be used to calculate the coefficients of asymmetry at any time or phase of the gait. In this way it is possible to create asymmetry, function which better describes human gait dysfunction. The paper also describes an algorithm for calculating symmetric models, and shows exemplary results based on the experimental data.
Normalized linear variance decay dimension density and its application of dynamical complexity detection in physiological (fMRI) time series
NASA Astrophysics Data System (ADS)
Xie, Xiaoping; Zhao, Xiaohu; Fang, Youtong; Cao, Zhitong; He, Guoguang
The upper and lower bounds of the linear variance decay (LVD) dimension density are analytically deduced using multivariate series with uncorrelated and perfectly correlated component series. Then, the normalized LVD dimension density ( δ) is introduced. In order to measure the complexity of a scalar series with δ, a pseudo-multivariate series was constructed from the scalar time series using time-delay embedding. Thus, δ is used to characterize the complexity of the pseudo-multivariate series. The results from the model systems and fMRI data of anxiety subjects reveal that this method can be used to analyze short and noisy time series.
Antitumor activities and interaction with DNA of oxaliplatin-type platinum complexes with linear or branched alkoxyacetates as leaving groups.
Yin, Runting; Gou, Shaohua; Liu, Xia; Lou, Liguang
Five oxaliplatin-typed platinum complexes containing trans-1R, 2R-diaminocyclohexane chelating platinum cores, characteristic of linear or branched alkoxycarboxylates as leaving groups, were biologically evaluated. These compounds showed higher antitumor activity, lower toxicity in vivo than cisplatin or oxaliplatin. And the results revealed that the antitumor activity and interaction with DNA of these compounds were highly related to the nature of leaving groups. Among these complexes, 5a, cis-(trans-1R, 2R-diaminocyclohexane) bis (2-tert-butoxyacetate) platinum(II), showed the highest antitumor activity and the lowest toxicity.
Discovery of a complex linearly polarized spectrum of Betelgeuse dominated by depolarization of the continuum
NASA Astrophysics Data System (ADS)
Aurière, M.; López Ariste, A.; Mathias, P.; Lèbre, A.; Josselin, E.; Montargès, M.; Petit, P.; Chiavassa, A.; Paletou, F.; Fabas, N.; Konstantinova-Antova, R.; Donati, J.-F.; Grunhut, J. H.; Wade, G. A.; Herpin, F.; Kervella, P.; Perrin, G.; Tessore, B.
Context. Betelgeuse is an M supergiant that harbors spots and giant granules at its surface and presents linear polarization of its continuum. Aims: We have previously discovered linear polarization signatures associated with individual lines in the spectra of cool and evolved stars. Here, we investigate whether a similar linearly polarized spectrum exists for Betelgeuse. Methods: We used the spectropolarimeter Narval, combining multiple polarimetric sequences to obtain high signal-to-noise ratio spectra of individual lines, as well as the least-squares deconvolution (LSD) approach, to investigate the presence of an averaged linearly polarized profile for the photospheric lines. Results: We have discovered the existence of a linearly polarized spectrum for Betelgeuse, detecting a rather strong signal (at a few times 10-4 of the continuum intensity level), both in individual lines and in the LSD profiles. Studying its properties and the signal observed for the resonant Na i D lines, we conclude that we are mainly observing depolarization of the continuum by the absorption lines. The linear polarization of the Betelgeuse continuum is due to the anisotropy of the radiation field induced by brightness spots at the surface and Rayleigh scattering in the atmosphere. We have developed a geometrical model to interpret the observed polarization, from which we infer the presence of two brightness spots and their positions on the surface of Betelgeuse. We show that applying the model to each velocity bin along the Stokes Q and U profiles allows the derivation of a map of the bright spots. We use the Narval linear polarization observations of Betelgeuse obtained over a period of 1.4 yr to study the evolution of the spots and of the atmosphere. Conclusions: Our study of the linearly polarized spectrum of Betelgeuse provides a novel method for studying the evolution of brightness spots at its surface and complements quasi-simultaneous observations obtained with PIONIER at the
Evaluation of the parameters of 1:1 charge transfer complexes from spectrophotometric data by non-linear numerical method
NASA Astrophysics Data System (ADS)
Grebenyuk, Serhiy A.; Perepichka, Igor F.; Popov, Anatolii F.
The non-linear numerical method for evaluation of equilibrium constants and molar extinction coefficients of molecular complexes from a spectrophotometric experiment is described, which in contrast to linear models has no limitations with respect to concentrations of the components. The proposed procedure is applied to donor-acceptor interaction in solution between N-ethyl carbazole (EtCz) and 7,7,8,8-tetracyanoquinodimethane (TCNQ) or n-hexyl 2,5,7-trinitro-9-dicyanomethylenefluorene-4-carboxylate (HexDTFC) to evaluate the method and to obtain the parameters of charge transfer complexes (CTCs) formation. Association constants ( K) and molar extinction coefficients ( ɛ) of CTCs derived from non-linear approach (EtCz-TCNQ: K=2.49±0.19 M -1; ɛ=2950±160 M -1 cm -1. EtCz-HexDTFC: K=12.1±0.3 M -1; ɛ=1335±24 M -1 cm -1) are close to that from linear models but show lower standard errors in parameter estimations.
Panprasitwech, Oranit; Laohakosol, Vichian; Chaichana, Tuangrat
Explicit formulae for continued fractions with symmetric patterns in their partial quotients are constructed in the field of formal power series. Similar to the work of Cohn in 1996, which generalized the so-called folding lemma to {kappa}-fold symmetry, the notion of {kappa}-duplicating symmetric continued fractions is investigated using a modification of the 1995 technique due to Clemens, Merrill and Roeder.
Inhibiting complex IL-17A and IL-17RA interactions with a linear peptide
Liu, Shenping; Desharnais, Joel; Sahasrabudhe, Parag V.; Jin, Ping; Li, Wei; Oates, Bryan D.; Shanker, Suman; Banker, Mary Ellen; Chrunyk, Boris A.; Song, Xi; Feng, Xidong; Griffor, Matt; Jimenez, Judith; Chen, Gang; Tumelty, David; Bhat, Abhijit; Bradshaw, Curt W.; Woodnutt, Gary; Lappe, Rodney W.; Thorarensen, Atli; Qiu, Xiayang; Withka, Jane M.; Wood, Lauren D.
IL-17A is a pro-inflammatory cytokine that has been implicated in autoimmune and inflammatory diseases. Monoclonal antibodies inhibiting IL-17A signaling have demonstrated remarkable efficacy, but an oral therapy is still lacking. A high affinity IL-17A peptide antagonist (HAP) of 15 residues was identified through phage-display screening followed by saturation mutagenesis optimization and amino acid substitutions. HAP binds specifically to IL-17A and inhibits the interaction of the cytokine with its receptor, IL-17RA. Tested in primary human cells, HAP blocked the production of multiple inflammatory cytokines. Crystal structure studies revealed that two HAP molecules bind to one IL-17A dimer symmetrically. The N-terminal portions of HAP form a β-strand that inserts between two IL-17A monomers while the C-terminal section forms an α helix that directly blocks IL-17RA from binding to the same region of IL-17A. This mode of inhibition suggests opportunities for developing peptide antagonists against this challenging target. PMID:27184415
Linear-dichroic infrared spectral analysis of Cu(I)?homocysteine complex
NASA Astrophysics Data System (ADS)
Ivanova, B. B.; Arnaudov, M. G.; Bontchev, P. R.
The interaction between homocysteine (HCysSH) and Cu(II) leads to the formation of a yellow complex [Cu I(HCysS-SCysH) 2]Cl (1) after redox processes in the Cu(II)-homocysteine system resulting in dimerization of the ligand and formation of a mononuclear Cu(I) complex with two dimers. The structure of (1) was obtained by IR-LD spectral analysis of a solid amorphous sample oriented in nematic liquid crystal medium. The original technique for orientation developed here and the polarized IR spectra thus obtained, permit the determination of the complexation sites and coordination mode of diamagnetic complexes. In the complex (1), Cu(I) is coordinated through the two O atoms of one COO - group of each of the ligands and the metal ion coordination sphere represents a distorted tetrahedron.
How Linearity and Structural Complexity Interact and Affect the Recognition of Italian Derived Words
ERIC Educational Resources Information Center
Bridgers, Franca Ferrari; Kacinik, Natalie
The majority of words in most languages consist of derived poly-morphemic words but a cross-linguistic review of the literature (Amenta and Crepaldi in Front Psychol 3:232-243, 2012) shows a contradictory picture with respect to how such words are represented and processed. The current study examined the effects of linearity and structural…
Estimation of Complex Generalized Linear Mixed Models for Measurement and Growth
ERIC Educational Resources Information Center
Jeon, Minjeong
Maximum likelihood (ML) estimation of generalized linear mixed models (GLMMs) is technically challenging because of the intractable likelihoods that involve high dimensional integrations over random effects. The problem is magnified when the random effects have a crossed design and thus the data cannot be reduced to small independent clusters. A…
Three-dimensional forward modelling and inversion of complex resistivity based on the improved quasi-linear approximation
NASA Astrophysics Data System (ADS)
Liu, Y.; Li, T.; Zhu, C.; Zhang, R.; Wu, Y.
Three-dimensional (3-D) electromagnetic (EM) forward modelling and inversion continues to be an important issue for the correct interpretation of EM data.To this end,approximate solutions have been developed that allow the construction of relatively fast forward modelling and inversion schemes.We have developed an improved quasi-linear approximation which is more appropriate in solving the linear equation for greatly shortening calculation time.We achieved this by using green's function properties.Then we introduced the improved quasi-linear approximation to spectral induced polarization (SIP) to tackle the problem of the resolution and the efficiency.The localized quasi-linear (LQL) approximation theory is appropriate for multisource array-type surveys assuming that the normal field is slowly varying within the inhomogeneity domain.However,the normal field of attenuates severely which dose not satisfy the assumption of the LQL approximation.As a consenquence,the imaginary part is not accurate when LQL approximation is adopted for the simulation.The improved quasi-linear approximation provide a new approach with the same resolution of QL approximation and much less calculation time.We have also constructed three-dimensional SIP forward modeling based on improved quasi-linear approximation method.It only takes 0.8s for forward modeling when inhomogeneity domain is divided into 2000 blocks.Beyond that, we have introduced the Cole-Cole model to the algorithm and complete the three-dimensional complex resistivity conjugate gradient inversion with parameter restraint.The model trial results show that this method can obtain good inversion results in physical parameters such as zero frequency resistivity, polarization.The results demonstrate the stability and the efficiency of the improved quasi-linear approximation and the method may be a practical solution for3-D EM forward modelling and inversion of SIP.
The Role of Symmetric-Stretch Vibration in Asymmetric-Stretch Vibrational Frequency Shift: the Case of 2CH Excitation Infrared Spectra of Acetylene-Hydrogen Van Der Waals Complex
NASA Astrophysics Data System (ADS)
Hou, Dan; Ma, Yong-Tao; Zhang, Xiao-Long; Zhai, Yu; Li, Hui
Direct infrared spectra predictions for van der Waals (vdW) complexes rely on accurate intra-molecular vibrationally excited inter-molecular potential. Due to computational cost increasing with number of freedom, constructing an effective reduced-dimension potential energy surface, which only includes direct relevant intra- molecular modes, is the most feasible way and widely used in the recent potential studies. However, because of strong intra-molecular vibrational coupling, some indirect relevant modes are also play important roles in simulating infrared spectra of vdW complexes. The questions are how many intra-molecular modes are needed, and which modes are most important in determining the effective potential and direct infrared spectra simulations. Here, we explore these issues using a simple, flexible and efficient vibration-averaged approach, and apply the method to vdW complex C_2H_2-H_2. With initial examination of the intra-molecular vibrational coupling, an effective seven-dimensional ab initio potential energy surface(PES) for C_2H_2-H_2, which explicitly takes into account the Q_1,Q_2 symmetric-stretch and Q_3 asymmetric-stretch normal modes of the C_2H_2 monomer, has been generated. Analytic four-dimensional PESs are obtained by least-squares fitting vibrationally averaged interaction energies for νb{3}(C_2H_2)=0 and 1 to the Morse/long-range(MLR) potential function form. We provide the first prediction of the infrared spectra and band origin shifts for C_2H_2-H_2 dimer. We particularly examine the dependence of the symmetric-stretch normal mode on asymmetric-stretch frequency shift for the complex.
A Low-Complexity ESPRIT-Based DOA Estimation Method for Co-Prime Linear Arrays
Sun, Fenggang; Gao, Bin; Chen, Lizhen; Lan, Peng
The problem of direction-of-arrival (DOA) estimation is investigated for co-prime array, where the co-prime array consists of two uniform sparse linear subarrays with extended inter-element spacing. For each sparse subarray, true DOAs are mapped into several equivalent angles impinging on the traditional uniform linear array with half-wavelength spacing. Then, by applying the estimation of signal parameters via rotational invariance technique (ESPRIT), the equivalent DOAs are estimated, and the candidate DOAs are recovered according to the relationship among equivalent and true DOAs. Finally, the true DOAs are estimated by combining the results of the two subarrays. The proposed method achieves a better complexity–performance tradeoff as compared to other existing methods. PMID:27571079
Prediction of partitioning between complex organic mixtures and water: application of polyparameter linear free energy relationships
Satoshi Endo; Torsten C. Schmidt
Equilibrium partitioning between nonaqueous phase liquids (NAPLs) and water is a governing process for contaminants leaching from NAPLs. This study introduces a polyparameter linear free energy relationship (PP-LFER) approach as a more general tool to predict NAPL-water partitioning coefficients. The approach was evaluated using 441 experimental partitioning data from 30 references. Experimental fuel-water partitioning coefficients were generally well reproduced by existing PP-LFERs for pure solvents using either a volume-fraction weighted sum of partitioning coefficients K (linear model, R{sup 2} = 0.983, root-mean-squared error (rmse) = 0.23) or a volume-fraction weighted sum of log K (log linear model, R{sup 2} = 0.976, rmse = 0.28). Using the linear model, estimations were, in most cases, within a factor of 2 from the experimental values, regardless of the type of compounds and the presence of a fuel additive. In contrast, the log linear model considerably underestimated partitioning coefficients in the presence of strong solute-solvent hydrogen bonding. For coal tar-water partitioning coefficients (K{sub coal tar/w}), new PP-LFER equations were calculated based on experimental log K{sub coal tar/w} values of 35 compounds. The resulting regression equation was log K{sub coal tar/w} = 0.40({+-}0.33) + 0.34({+-}0.32)E + 0.61({+-}0.57)S - 0.55({+-}0.61)A - 5.07({+-}0.61)B + 3.22({+-}0.35)V with the rmse equal to 0.21, where E, S, A, B, and V are Abraham's solute descriptors. Partitioning coefficients for phenol and alcohols, were closer to the experimental values than to those estimated by the SP-LFER approach with octanol-water partitioning coefficients. The values of the coefficients also provide insight into the properties of coal tar in terms of molecular interactions with solutes. 45 refs., 5 figs., 4 tabs.
Nonlinear rheology of entangled symmetric and asymmetric star polymers
NASA Astrophysics Data System (ADS)
Tezel, Amy Kathleen
Polymer architecture has a significant effect on the material properties of polymer melts and solutions. These topological differences are important because they either prohibit or allow different relaxation mechanisms when the system is perturbed from equilibrium. In the past three decades, significant progress has been made describing the response of entangled polymer liquids to small perturbations (the linear viscoelastic regime), however when flow is added, the situation becomes more complex. In flow, it has been suggested that a relaxation mechanism known as convective constraint release (CCR) will dominate the relaxation response of entangled polymers at shear rates in between the inverse of the longest relaxation time (taul) and the inverse of the Rouse time (tauR). Initial experiments using linear polymers could only provide a limited test of this mechanism because the window of relevant shear rates is small. Star polymers, however, provide an excellent system with which to test the accuracy of CCR because of the wide range of shear rates at which it is expected to dominate. We have proposed both a steady state and transient model that incorporates CCR in a straightforward way and favorably compared its predictions of stresses with those measured experimentally. Asymmetric stars are intriguing because they are very similar to both linear chains and symmetric stars. Currently work is being done in other groups to quantitatively describe asymmetric stars in the linear viscoelastic regime. We have synthesized our own batch of asymmetric stars and have conducted the first study of asymmetric stars in the nonlinear regime. These results are examined in the context of previous work done on linear and symmetric star polymers.
Euclidean Closed Linear Transformations of Complex Spacetime and generally of Complex Spaces of dimension four endowed with the Same or Different Metric
NASA Astrophysics Data System (ADS)
Vossos, Spyridon; Vossos, Elias
Relativity Theory and the corresponding Relativistic Quantum Mechanics are the fundamental theories of physics. Special Relativity (SR) relates the frames of Relativistic Inertial observers (RIOs), through Linear Spacetime Transformation (LSTT) of linear spacetime. Classic Special Relativity uses real spacetime endowed with Lorentz metric and the frames of two RIOs with parallel spatial axes are always related through Lorentz Boost (LB). This cancels the transitive attribute in parallelism, when three RIOs are related, because LB is not closed transformation, causing Thomas Rotation. In this presentation, we consider closed LSTT of Complex Spacetime, so there is no necessity for spatial axes rotation and all the frames are chosen having parallel spatial axes. The solution is expressed by a 4x4 matrix (Λ) containing components of the complex velocity of one Observer wrt another and two functions depended by the metric of Spacetime. Demanding isometric transformation, it emerges a class of metrics that are in accordance with the closed LSTT and the transformation matrix contains one parameter ω depended by the metric of Spacetime. In case that we relate RIOs with steady metric, it emerges one steady number (ωI ) depended by the metric of Spacetime of the specific SR. If ωI is an imaginary number, the elements of the Λ are complex numbers, so the corresponding spacetime is necessarily complex and there exists real Universal Speed (UI). The specific value ωI =±i gives Vossos transformation (VT) endowed with Lorentz metric (for gii=1) of complex spacetime and invariant spacetime interval (or equivalently invariant speed of light in vacuum), which produce the theory of Euclidean Complex Relativistic Mechanics (ECRMs). If ωI is a real number (ωI #0) the elements of the Λ are real numbers, so the corresponding spacetime is real, but there exist imaginary UI. The specific value ωI =0 gives Galileo Transformation (GT) with the invariant time, in which any other
Theoretical and experimental investigations on linear and nonlinear optical response of metal complexes doped PMMA films
NASA Astrophysics Data System (ADS)
Praveen, P. A.; Babu, R. Ramesh; Ramamurthi, K.
Metal organic complexes, diaceto bis benzimidazole cobalt(II) and diaceto bis benzimidazole copper(II), are synthesized by a simple chemical route. The synthesized powders are doped in PMMA with 1, 3, 5 wt% and deposited as free standing films of thickness ∼1 μm. For theoretical simulation, metal organic complex (MOC) embedded into the PMMA matrix is subjected to polarizability and hyperpolarizability calculations using the PM6 algorithm in MOPAC2012 package. It is found that the minimum interaction distance between PMMA and MOC is about 34 nm and does not vary with respect to the dopant. The copper complex shows higher interaction energy with the polymer matrix than the cobalt complex. Time dependent Hartree Fock approach is used to calculate the α, β and γ values for static, 0.25 and 0.5 eV energies; the cobalt complex shows higher polarizability and hyperpolarizability than the copper complex. Experimentally, the optical absorption, thermo-optic coefficient, nonlinear absorption coefficient and nonlinear refractive index of the samples are determined. The thermo-optic coefficients of the samples are seen to increase with increasing dopant concentration. From open aperture Z-scan studies the films are found to exhibit reverse saturable absorption behaviour, and from the closed aperture Z-scan all samples are found to exhibit self-focusing effects. The calculated third order susceptibility is in the order of 10‑5 esu. The optical limiting properties are studied at 650 nm using a 20 mW laser and all the samples are found to exhibit good optical limiting in the operating wavelength.
Systems of Differential Equations with Skew-Symmetric, Orthogonal Matrices
ERIC Educational Resources Information Center
Glaister, P.
The solution of a system of linear, inhomogeneous differential equations is discussed. The particular class considered is where the coefficient matrix is skew-symmetric and orthogonal, and where the forcing terms are sinusoidal. More general matrices are also considered.
An immobilized symmetrical bis-(NHC) palladium complex as a highly efficient and recyclable Suzuki-Miyaura catalyst in aerobic aqueous media.
Begum, Tahshina; Mondal, Manoj; Borpuzari, Manash Protim; Kar, Rahul; Kalita, Golap; Gogoi, Pradip K; Bora, Utpal
A bis-N-heterocyclic carbene (NHC) functionalized with chloropropyltriethoxysilane over silica was used to synthesize a well-defined immobilized palladium complex. This complex is a suitable and easily retrievable catalyst for Suzuki-Miyaura cross-coupling reactions under mild aqueous conditions. Excellent yields and conversions were obtained with low palladium loadings (down to 0.03 mol% Pd). The catalyst can be reused up to six cycles without the loss of its activity. The catalytic role of the NHC complex of palladium during coupling between bromobenzene and phenylboronic acid was investigated theoretically. The oxidative addition step is predicted to be endothermic in agreement with the experimental conditions.
Structure of an Antibody in Complex with Its Mucin Domain Linear Epitope That Is Protective against Ebola Virus
Olal, Daniel; Kuehne, Ana I.; Bale, Shridhar; Halfmann, Peter; Hashiguchi, Takao; Fusco, Marnie L.; Lee, Jeffrey E.; King, Liam B.; Kawaoka, Yoshihiro; Dye, John M.
Antibody 14G7 is protective against lethal Ebola virus challenge and recognizes a distinct linear epitope in the prominent mucin-like domain of the Ebola virus glycoprotein GP. The structure of 14G7 in complex with its linear peptide epitope has now been determined to 2.8 Å. The structure shows that this GP sequence forms a tandem β-hairpin structure that binds deeply into a cleft in the antibody-combining site. A key threonine at the apex of one turn is critical for antibody interaction and is conserved among all Ebola viruses. This work provides further insight into the mechanism of protection by antibodies that target the protruding, highly accessible mucin-like domain of Ebola virus and the structural framework for understanding and characterizing candidate immunotherapeutics. PMID:22171276
Computational study of the linear proton bound ion-molecule complexes of HCNH+ with HCN and HNC
NASA Astrophysics Data System (ADS)
Eric Cotton, C.; Francisco, Joseph S.; Klemperer, William
This work reports the results of a high level ab initio study of the linear proton bound ion-molecule complex of HCNH+ with HCN and its isomer HNC. The energetics, equilibrium geometries, and predicted equilibrium rotational constants of three strongly interacting ion-molecule complexes are reported from calculations performed at the coupled-cluster calculations including singles, doubles, and perturbative triple excitations (CCSD(T))/aug-cc-pVnZ (n = 2-5) level of theory. Harmonic vibrational frequencies from calculations performed at the CCSD(T)/aug-cc-pVnZ (n = 2-4) level of theory are presented. Additional calculations are performed at the CCSD(T)-F12b/VnZ-F12 level of theory, and the associated energetics, equilibrium geometries, and equilibrium spectroscopic properties are reported. Anharmonicity is treated with the vibrational configuration interaction method, and the predicted anharmonic vibrational frequencies are reported. The results of these calculations show that of the four possible linear interactions of HCNH+ with HCN and HNC, there are three strongly interacting proton bound complexes. Further, the study presents results that the fourth possible interaction provides the basis for a novel HNC to HCN isomerization pathway in the interstellar medium.
Braids, shuffles and symmetrizers
NASA Astrophysics Data System (ADS)
Isaev, A. P.; Ogievetsky, O. V.
Multiplicative analogues of the shuffle elements of the braid group rings are introduced; in local representations they give rise to certain graded associative algebras (b-shuffle algebras). For the Hecke and BMW algebras, the (anti)-symmetrizers have simple expressions in terms of the multiplicative shuffles. The (anti)-symmetrizers can be expressed in terms of the highest multiplicative 1-shuffles (for the Hecke and BMW algebras) and in terms of the highest additive 1-shuffles (for the Hecke algebras). The spectra and multiplicities of eigenvalues of the operators of the multiplication by the multiplicative and additive 1-shuffles are examined. Dedicated to the memory of Aleosha Zamolodchikov.
Our Expedition in Linear Neutral Platinum-Acetylide Complexes: The Preparation of Micro/nanostructure Materials, Complicated Topologies, and Dye-Sensitized Solar Cells.
Xu, Lin; Yang, Hai-Bo
During the past few decades, the construction of various kinds of platinum-acetylide complexes has attracted considerable attention, because of their wide applications in photovoltaic cells, non-linear optics, and bio-imaging materials. Among these platinum-acetylide complexes, the linear neutral platinum-acetylide complexes, due to their attractive properties, such as well-defined linear geometry, synthetic accessibility, and intriguing photoproperties, have emerged as a rising star in this field. In this personal account, we will discuss how we entered the field of linear neutral platinum-acetylide chemistry and what we found in this field. The preparation of various types of linear neutral platinum-acetylide complexes and their applications in the areas of micro/nanostructure materials, complicated topologies, and dye-sensitized solar cells will be summarized in this account.
Souza Dutra, A. de; Santos, V. G. C. S. dos; Amaro de Faria, A. C. Jr.
Some kinks for non-Hermitian quantum field theories in 1+1 dimensions are constructed. A class of models where the soliton energies are stable and real are found. Although these kinks are not Hermitian, they are symmetric under PT transformations.
Octanuclear and nonanuclear supramolecular copper(II) complexes with linear "tritopic" ligands: structural and magnetic studies.
Milway, Victoria A; Niel, Virginie; Abedin, Tareque S M; Xu, Zhiqiang; Thompson, Laurence K; Grove, Hilde; Miller, David O; Parsons, Stewart R
The structures and magnetic properties of self-assembled copper(II) clusters and grids with the "tritopic" ligands 2poap (a), Cl2poap (b), m2poap (c), Cl2pomp (d), and 2pomp (e) are described [ligands derived by reaction of 4-R-2,6-pyridinedicarboxylic hydrazide (R = H, Cl, MeO) with 2-pyridinemethylimidate (a-c, respectively) or 2-acetylpyridine (d, R = Cl; e, R = H)]. Cl2poap and Cl2pomp self-assemble with Cu(NO(3))(2) to form octanuclear "pinwheel" cluster complexes [Cu(8)(Cl2poap-2H)(4)(NO(3))(8)].20H(2)O (1) and [Cu(8)(Cl2pomp-2H)(4)(NO(3))(8)].15H(2)O (2), built on a square [2 x 2] grid with four pendant copper arms, using "mild" reaction conditions. Similar reactions of Cl2pomp and 2pomp with Cu(ClO(4))(2) produce pinwheel clusters [Cu(8)(Cl2pomp-2H)(4)(H(2)O)(8)](ClO(4))(8).7H(2)O (3) and [Cu(8)(2pomp-2H)(4)(H(2)O)(8)](ClO(4))(8) (4), respectively. Heating a solution of 1 in MeOH/H(2)O produces a [3 x 3] nonanuclear square grid complex, [Cu(9)(Cl2poap-H)(3)(Cl2poap-2H)(3)](NO(3))(9).18H(2)O (5), which is also produced by direct reaction of the ligand and metal salt under similar conditions. Reaction of m2poap with Cu(NO(3))(2) produces only the [3 x 3] grid [Cu(9)(m2poap-H)(2)(m2poap-2H)(4)](NO(3))(8).17H(2)O (6) under similar conditions. Mixing the tritopic ligand 2poap with pyridine-2,6-dicarboxylic acid (picd) in the presence of Cu(NO(3))(2) produces a remarkable mixed ligand, nonanuclear grid complex [Cu(9)(2poap-H)(4)(picd-H)(3)(picd-2H)](NO(3))(9).9H(2)O (7), in which aromatic pi-stacking interactions are important in stabilizing the structure. Complexes 1-3 and 5-7 involve single oxygen atom (alkoxide) bridging connections between adjacent copper centers, while complex 4 has an unprecedented mixed micro-(N-N) and micro-O metal ion connectivity. Compound 1 (C(76)H(92)N(44)Cu(8)O(50)Cl(4)) crystallizes in the tetragonal system, space group I, with a = 21.645(1) A, c = 12.950(1) A, and Z = 2. Compound 2 (C(84)H(88)N(36)O(44)Cl(4)Cu(8)) crystallizes in
The Additive and Logical Complexities of Linear and Bilinear Arithmetic Algorithms,
of vectors, CV, cyclic convolution of vectors, CCV, and matrix multiplication, MM, are among the central problems of algebraic complexity theory , cf...a basi, set of vertices of D. (Lo(D) could be the set . of all vertices of D of indegree 0 but for D = D(A) we always choose Lo(D) as the set of...the directions of edges of D(A) and choose the set of input-variables of A as the basic set Lo(D) of the new digraph, D(A). Then our construction
EMG-torque Relation in Chronic Stroke: A Novel EMG Complexity Representation with A Linear Electrode Array.
Zhang, Xu; Wang, Dongqing; Yu, Zaiyang; Chen, Xiang; Li, Sheng; Zhou, Ping
This study examines the electromyogram (EMG) - torque relation for chronic stroke survivors using a novel EMG complexity representation. Ten stroke subjects performed a series of submaximal isometric elbow flexion tasks using their affected and contralateral arms, respectively, while a 20-channel linear electrode array was used to record surface EMG from the biceps brachii muscles. The sample entropy (SampEn) of surface EMG signals was calculated with both global and local tolerance schemes. A regression analysis was performed between SampEn of each channel's surface EMG and elbow flexion torque. It was found that a linear regression can be used to well describe the relation between surface EMG SampEn and the torque. Each channel's root mean square (RMS) amplitude of surface EMG signal in the different torque level was computed to determine the channel with the highest EMG amplitude. The slope of the regression (observed from the channel with the highest EMG amplitude) was smaller on the impaired side than on the non-impaired side in 8 of the 10 subjects, regardless of the tolerance scheme (global or local) and the range of torques (full or matched range) used for comparison. The surface EMG signals from the channels above the estimated muscle innervation zones demonstrated significantly lower levels of complexity compared with other channels between innervation zones and muscle tendons. The study provides a novel point of view of the EMG-torque relation in the complexity domain, and reveals its alterations post stroke, which are associated with complex neural and muscular changes post stroke. The slope difference between channels with regard to innervation zones also confirms the relevance of electrode position in surface EMG analysis.
Spectral, morphological, linear and nonlinear optical properties of nanostructured benzimidazole metal complex thin films.
Praveen, P A; Ramesh Babu, R; Jothivenkatachalam, K; Ramamurthi, K
Metal organic materials are widely investigated to find their suitability for nonlinear optical applications due to the advantage of combined organic and inorganic properties. In this work benzimidazole based metal organic thin films of dichlorobis (1H-Benzimidazole) Co(II) and dichlorobis (1H-Benzimidazole) Cu(II) were deposited by chemical bath deposition method. The deposited films were annealed at 100, 150 and 200 °C to investigate the effect of annealing on the properties of thin films. Surface homogeneity of the films was increased with the annealing temperature due to the surface diffusion of the films and the same was evidently shown by Raman spectroscopy and Atomic Force Microscopy studies. But annealing the films at 200 °C yielded bulk patches on the surface due to the distortion of molecules. Linear and nonlinear optical properties of the films annealed at 150 °C showed relatively higher transmittance and improved nonlinear optical properties than the other as prepared and annealed samples.
Temperature effects on EPR spectra of a linear chain copper complex-copper calcium acetate hexahydrate
NASA Astrophysics Data System (ADS)
De, D. K.
The observed angular dependence of the electron paramagnetic resonance linewidth in the ab and ac planes of CuCa(AC)2, 6H2O in the temperature interval 77K-12K was explained by considering dipolar interactions along with hyperfine and isotropic exchange interactions in these two planes. It was found that this so called linear-chain copper compound can be better described by a three dimensional paramagnet. The exchange interaction is very nearly isotropic with values Jab = 0.0098 cm-1 and Jc = 0.0103 cm-1. The values of the A⊥ derived from the linewidth fit in the ab plane are 14G at 77K and 60.5G at 1.2K. Due to insufficiency of data in the ac plane, the fit was done with the measured value of A∥. Although the exchange interaction has been found to be temperature independent the hyperfine interaction increases very much at low temperatures. The high temperature (300-460K) EPR spectra are quite different from the low temperature spectra. High temperature differential thermal analyses and thermogravimetric analyses have been carried out and corroborated with the EPR findings.
Modelling and prediction of complex non-linear processes by using Pareto multi-objective genetic programming
NASA Astrophysics Data System (ADS)
Jamali, A.; Khaleghi, E.; Gholaminezhad, I.; Nariman-zadeh, N.
In this paper, a new multi-objective genetic programming (GP) with a diversity preserving mechanism and a real number alteration operator is presented and successfully used for Pareto optimal modelling of some complex non-linear systems using some input-output data. In this study, two different input-output data-sets of a non-linear mathematical model and of an explosive cutting process are considered separately in three-objective optimisation processes. The pertinent conflicting objective functions that have been considered for such Pareto optimisations are namely, training error (TE), prediction error (PE), and the length of tree (complexity of the network) (TL) of the GP models. Such three-objective optimisation implementations leads to some non-dominated choices of GP-type models for both cases representing the trade-offs among those objective functions. Therefore, optimal Pareto fronts of such GP models exhibit the trade-off among the corresponding conflicting objectives and, thus, provide different non-dominated optimal choices of GP-type models. Moreover, the results show that no significant optimality in TE and PE may occur when the TL of the corresponding GP model exceeds some values.
Resonances for Symmetric Two-Barrier Potentials
ERIC Educational Resources Information Center
Fernandez, Francisco M.
We describe a method for the accurate calculation of bound-state and resonance energies for one-dimensional potentials. We calculate the shape resonances for symmetric two-barrier potentials and compare them with those coming from the Siegert approximation, the complex scaling method and the box-stabilization method. A comparison of the…
Symmetrical reproductive compatibility of two species in the Ciona intestinalis (Ascidiacea) species complex, a model for marine genomics and developmental biology.
Sato, Atsuko; Shimeld, Sebastian M; Bishop, John D D
The sea squirt Ciona intestinalis species complex is a widely used model system for genomics and developmental biology, as well as ecology. Contrary to previous reports, here we show no difference in the success of development and hatching between hybrid and conspecific crosses between the two species within this complex known as types A and B, from a region in the English Channel where they are sympatric. We grew laboratory hybrids in the field for three months, and successfully obtained reproductive adults. In back-crosses of F1 laboratory hybrids to parental types, normal larvae were obtained. We conclude that hybrid crosses generate viable offspring and the resulting hybrids are interfertile with types A and B. However we also show that introgression in the natural sympatric population remains low. We discuss possible pre-zygotic and post-zygotic mechanisms which reproductively isolate these species.
The FA Core Complex Contains a Homo-dimeric Catalytic Module for the Symmetric Mono-ubiquitination of FANCI-FANCD2.
Swuec, Paolo; Renault, Ludovic; Borg, Aaron; Shah, Fenil; Murphy, Vincent J; van Twest, Sylvie; Snijders, Ambrosius P; Deans, Andrew J; Costa, Alessandro
Activation of the main DNA interstrand crosslink repair pathway in higher eukaryotes requires mono-ubiquitination of FANCI and FANCD2 by FANCL, the E3 ligase subunit of the Fanconi anemia core complex. FANCI and FANCD2 form a stable complex; however, the molecular basis of their ubiquitination is ill defined. FANCD2 mono-ubiquitination by FANCL is stimulated by the presence of the FANCB and FAAP100 core complex components, through an unknown mechanism. How FANCI mono-ubiquitination is achieved remains unclear. Here, we use structural electron microscopy, combined with crosslink-coupled mass spectrometry, to find that FANCB, FANCL, and FAAP100 form a dimer of trimers, containing two FANCL molecules that are ideally poised to target both FANCI and FANCD2 for mono-ubiquitination. The FANCC-FANCE-FANCF subunits bridge between FANCB-FANCL-FAAP100 and the FANCI-FANCD2 substrate. A transient interaction with FANCC-FANCE-FANCF alters the FANCI-FANCD2 configuration, stabilizing the dimerization interface. Our data provide a model to explain how equivalent mono-ubiquitination of FANCI and FANCD2 occurs.
A (Not Really) Complex Method for Finding Solutions to Linear Differential Equations. Modules and Monographs in Undergraduate Mathematics and Its Applications Project. UMAP Unit 497.
ERIC Educational Resources Information Center
Uebelacker, James W.
This module considers ordinary linear differential equations with constant coefficients. The "complex method" used to find solutions is discussed, with numerous examples. The unit includes both problem sets and an exam, with answers provided for both. (MP)
Organometallic complexes of bulky, optically active, C3-symmetric tris(4S-isopropyl-5,5-dimethyl-2-oxazolinyl)phenylborate (ToP*)
Xu, Songchen; Magoon, Yitzhak; Reinig, Regina R.; ...
A bulky, optically active monoanionic scorpionate ligand, tris(4S-isopropyl-5,5-dimethyl-2-oxazolinyl)phenylborate (ToP*), is synthesized from the naturally occurring amino acid l-valine as its lithium salt, Li[ToP*] (1). That compound is readily converted to the thallium complex Tl[ToP*] (2) and to the acid derivative H[ToP*] (3). Group 7 tricarbonyl complexes ToP*M(CO)3 (M = Mn (4), Re (5)) are synthesized by the reaction of MBr(CO)5 and Li[ToP*] and are crystallographically characterized. The νCO bands in their infrared spectra indicate that π back-donation in the rhenium compounds is greater with ToP* than with non-methylated tris(4S-isopropyl-2-oxazolinyl)phenylborate (ToP). The reaction of H[ToP*] and ZnEt2 gives ToP*ZnEt (6), whilemore » ToP*ZnCl (7) is synthesized from Li[ToP*] and ZnCl2. The reaction of ToP*ZnCl and KOtBu followed by addition of PhSiH3 provides the zinc hydride complex ToP*ZnH (8). In this study, compound 8 is the first example of a crystallographically characterized optically active zinc hydride. We tested its catalytic reactivity in the cross-dehydrocoupling of silanes and alcohols, which provided Si-chiral silanes with moderate enantioselectivity.« less
Rome, J.A.; Harris, J.H.
A fusion reactor device is provided in which the magnetic fields for plasma confinement in a toroidal configuration is produced by a plurality of symmetrical modular coils arranged to form a symmetric modular torsatron referred to as a symmotron. Each of the identical modular coils is helically deformed and comprise one field period of the torsatron. Helical segments of each coil are connected by means of toroidally directed windbacks which may also provide part of the vertical field required for positioning the plasma. The stray fields of the windback segments may be compensated by toroidal coils. A variety of magnetic confinement flux surface configurations may be produced by proper modulation of the winding pitch of the helical segments of the coils, as in a conventional torsatron, winding the helix on a noncircular cross section and varying the poloidal and radial location of the windbacks and the compensating toroidal ring coils.
Chen, Yan; Feng, Huijuan; Ma, Jiayao; Peng, Rui; You, Zhong
The traditional waterbomb origami, produced from a pattern consisting of a series of vertices where six creases meet, is one of the most widely used origami patterns. From a rigid origami viewpoint, it generally has multiple degrees of freedom, but when the pattern is folded symmetrically, the mobility reduces to one. This paper presents a thorough kinematic investigation on symmetric folding of the waterbomb pattern. It has been found that the pattern can have two folding paths under certain circumstance. Moreover, the pattern can be used to fold thick panels. Not only do the additional constraints imposed to fold the thick panels lead to single degree of freedom folding, but the folding process is also kinematically equivalent to the origami of zero-thickness sheets. The findings pave the way for the pattern being readily used to fold deployable structures ranging from flat roofs to large solar panels.
NASA Astrophysics Data System (ADS)
Chen, Yan; Feng, Huijuan; Ma, Jiayao; Peng, Rui; You, Zhong
The traditional waterbomb origami, produced from a pattern consisting of a series of vertices where six creases meet, is one of the most widely used origami patterns. From a rigid origami viewpoint, it generally has multiple degrees of freedom, but when the pattern is folded symmetrically, the mobility reduces to one. This paper presents a thorough kinematic investigation on symmetric folding of the waterbomb pattern. It has been found that the pattern can have two folding paths under certain circumstance. Moreover, the pattern can be used to fold thick panels. Not only do the additional constraints imposed to fold the thick panels lead to single degree of freedom folding, but the folding process is also kinematically equivalent to the origami of zero-thickness sheets. The findings pave the way for the pattern being readily used to fold deployable structures ranging from flat roofs to large solar panels.
Integrability of PT-symmetric dimers
NASA Astrophysics Data System (ADS)
Pickton, J.; Susanto, H.
The coupled discrete linear and Kerr nonlinear Schrödinger equations with gain and loss describing transport on dimers with parity-time (PT)-symmetric potentials are considered. The model is relevant among others to experiments in optical couplers and proposals on Bose-Einstein condensates in PT-symmetric double-well potentials. It is known that the models are integrable. Here, the integrability is exploited further to construct the phase portraits of the system. A pendulum equation with a linear potential and a constant force for the phase difference between the fields is obtained, which explains the presence of unbounded solutions above a critical threshold parameter. The behavior of all solutions of the system, including changes in the topological structure of the phase plane, is then discussed.
Static cylindrically symmetric spacetimes
NASA Astrophysics Data System (ADS)
Fjällborg, Mikael
We prove the existence of static solutions to the cylindrically symmetric Einstein Vlasov system, and we show that the matter cylinder has finite extension in two of the three spatial dimensions. The same results are also proved for a quite general class of equations of state for perfect fluids coupled to the Einstein equations, extending the class of equations of state considered by Bicak et al (2004 Class. Quantum Grav.21 1583). We also obtain this result for the Vlasov Poisson system.
N≥ 𝟐 symmetric superpolynomials
NASA Astrophysics Data System (ADS)
Alarie-Vézina, L.; Lapointe, L.; Mathieu, P.
The theory of symmetric functions has been extended to the case where each variable is paired with an anticommuting one. The resulting expressions, dubbed superpolynomials, provide the natural N =1 supersymmetric version of the classical bases of symmetric functions. Here we consider the case where more than one independent anticommuting variable is attached to each ordinary variable. First, the N =2 super-version of the monomial, elementary, homogeneous symmetric functions, as well as the power sums, is constructed systematically (using an exterior-differential formalism for the multiplicative bases), these functions being now indexed by a novel type of superpartitions. Moreover, the scalar product of power sums turns out to have a natural N =2 generalization which preserves the duality between the monomial and homogeneous bases. All these results are then generalized to an arbitrary value of N . Finally, for N =2 , the scalar product and the homogeneous functions are shown to have a one-parameter deformation, a result that prepares the ground for the yet-to-be-defined N =2 Jack superpolynomials.
Linear oxygen-sensing response from a rhenium complex induced by heavy atom: synthesis, characterization, photophysical study and sensing performance.
Wan, Pu; Zhao, Lun; Wang, Lisha; Xu, Guangyang
In this paper, we synthesized a Br-containing ligand of 2-(4-bromophenyl)-5-(pyridin-2-yl)-1,3,4-oxadiazole and its corresponding Re(I) complex. Their synthesis, characterization, single crystal structure, electronic transitions and photophysical property were presented and discussed in detail. This Re(I) complex was found to be a yellow emitter with slim π→π* radiative decay contribution, and its emission was also found to be sensitive towards O2. By doping this Re(I) complex into a polymer matrix, the oxygen-sensing performance of the resulted composite nanofibers was also investigated. Owing to the porous structure of the supporting matrix, the optimal sample gave the highest sensitivity of 3.91 with short response time of only 9 s. In addition, the linearity of the Stern-Volmer plots was greatly improved due to the highly pure emissive center triggered by heavy-atom turbulence effect from Br atom, as indicted by theoretical calculation result.
Linear oxygen-sensing response from a rhenium complex induced by heavy atom: Synthesis, characterization, photophysical study and sensing performance
NASA Astrophysics Data System (ADS)
Pu, Wan; Lun, Zhao; Lisha, Wang; Guangyang, Xu
In this paper, we synthesized a Br-containing ligand of 2-(4-bromophenyl)-5-(pyridin-2-yl)-1,3,4-oxadiazole and its corresponding Re(I) complex. Their synthesis, characterization, single crystal structure, electronic transitions and photophysical property were presented and discussed in detail. This Re(I) complex was found to be a yellow emitter with slim π → π* radiative decay contribution, and its emission was also found to be sensitive towards O2. By doping this Re(I) complex into a polymer matrix, the oxygen-sensing performance of the resulted composite nanofibers was also investigated. Owing to the porous structure of the supporting matrix, the optimal sample gave the highest sensitivity of 3.91 with short response time of only 9 s. In addition, the linearity of the Stern-Volmer plots was greatly improved due to the highly pure emissive center triggered by heavy-atom turbulence effect from Br atom, as indicted by theoretical calculation result.
Stereoselectivity in the formation of tris-diimine complexes of Fe(II), Ru(II), and Os(II) with a C2-symmetric chiral derivative of 2,2'-bipyridine.
Drahonovský, Dusan; Knof, Ulrich; Jungo, Laurence; Belser, Thomas; Neels, Antonia; Labat, Gaël Charles; Stoeckli-Evans, Helen; von Zelewsky, Alex
A C2-symmetric enantiopure 4,5-bis(pinene)-2,2'-bipyridine ligand (-)-L was used to investigate the diastereoselectivity in the formation of [ML3]2+ coordination species (M = Fe(II), Ru(II), Os(II), Zn(II), Cd(II), Cu(II), Ni(II)), and [ML2Cl2] (M = Ru(II), Os(II)). The X-ray structures of the [ML3]2+ complexes were determined for Delta-[FeL3](PF6)2, Delta-[RuL3](PF6)2, Lambda-[RuL3](PF6)2, Delta-[OsL3](PF6)2, and Lambda-[OsL3](TfO)2. All of these compounds were also characterized by NMR, CD and UV/VIS absorption spectroscopy. The [FeL3]2+ diastereoisomers were studied in equilibrated solutions at various temperatures and in several solvents. The [RuL3]2+ complexes, which are thermally stable up to 200 degrees C, were photochemically equilibrated.
Symmetric States on the Octonionic Bloch Ball
NASA Astrophysics Data System (ADS)
Graydon, Matthew
Finite-dimensional homogeneous self-dual cones arise as natural candidates for convex sets of states and effects in a variety of approaches towards understanding the foundations of quantum theory in terms of information-theoretic concepts. The positive cone of the ten-dimensional Jordan-algebraic spin factor is one particular instantiation of such a convex set in generalized frameworks for quantum theory. We consider a projection of the regular 9-simplex onto the octonionic projective line to form a highly symmetric structure of ten octonionic quantum states on the surface of the octonionic Bloch ball. A uniform subnormalization of these ten symmetric states yields a symmetric informationally complete octonionic quantum measurement. We discuss a Quantum Bayesian reformulation of octonionic quantum formalism for the description of two-dimensional physical systems. We also describe a canonical embedding of the octonionic Bloch ball into an ambient space for states in usual complex quantum theory.
Active and passive symmetrization of Runge-Kutta Lobatto IIIA methods
NASA Astrophysics Data System (ADS)
Gorgey, A.; Chan, R. P. K.
Symmetrization of the Runge-Kutta Gauss methods have been shown to be robust in solving stiff linear and nonlinear initial value ordinary differential equations [4]. The most efficient way of applying symmmetrization was found to be passive symmetrization with passive extrapolation. In this paper we investigate symmetrization of the Lobatto IIIA methods. We show numerically that the same strategy of using passive symmetrization applied with passive extrapolation of the Lobbatto IIIA methods is also most efficient in solving the nonlinear problems tested.
Complex linear minimum mean-squared-error equalization of spatially quadrature-amplitude-modulated signals in holographic data storage
NASA Astrophysics Data System (ADS)
Sato, Takanori; Kanno, Kazutaka; Bunsen, Masatoshi
We applied complex linear minimum mean-squared-error equalization to spatially quadrature-amplitude-modulated signals in holographic data storage (HDS). The equalization technique can improve dispersion in constellation outputs due to intersymbol interference. We confirm the effectiveness of the equalization technique in numerical simulations and basic optical experiments. Our numerical results have shown that intersymbol interference of a retrieved signal in a HDS system can be improved by using the equalization technique. In our experiments, a mean squared error (MSE), which indicates the deviation from an ideal signal, has been used for quantitatively evaluating the dispersion of equalized signals. Our equalization technique has been able to improve the MSE. However, symbols in the equalized signal have remained inseparable. To further improve the MSE and make the symbols separable, reducing errors in repeated measurements is our future task.
Linear ubiquitin chain assembly complex coordinates late thymic T-cell differentiation and regulatory T-cell homeostasis
Teh, Charis E.; Lalaoui, Najoua; Jain, Reema; Policheni, Antonia N.; Heinlein, Melanie; Alvarez-Diaz, Silvia; Sheridan, Julie M.; Rieser, Eva; Deuser, Stefanie; Darding, Maurice; Koay, Hui-Fern; Hu, Yifang; Kupresanin, Fiona; O'Reilly, Lorraine A.; Godfrey, Dale I.; Smyth, Gordon K.; Bouillet, Philippe; Strasser, Andreas; Walczak, Henning; Silke, John; Gray, Daniel H. D.
The linear ubiquitin chain assembly complex (LUBAC) is essential for innate immunity in mice and humans, yet its role in adaptive immunity is unclear. Here we show that the LUBAC components HOIP, HOIL-1 and SHARPIN have essential roles in late thymocyte differentiation, FOXP3+ regulatory T (Treg)-cell development and Treg cell homeostasis. LUBAC activity is not required to prevent TNF-induced apoptosis or necroptosis but is necessary for the transcriptional programme of the penultimate stage of thymocyte differentiation. Treg cell-specific ablation of HOIP causes severe Treg cell deficiency and lethal immune pathology, revealing an ongoing requirement of LUBAC activity for Treg cell homeostasis. These data reveal stage-specific requirements for LUBAC in coordinating the signals required for T-cell differentiation. PMID:27857075
Symmetric missile dynamic instabilities: A review
NASA Astrophysics Data System (ADS)
Murphy, C. H.
Dynamic instabilities observed for symmetric missiles and projectiles arise from a large variety of causes. These include unstable linear damping moments, and different nonlinear in-plane and out-of-plane damping moments for nonspinning re-entry vehicles, nonlinear Magnus moments for spinning missiles, and internal resonance with moving payload components. If aerodynamic trim is present, linear spin-yaw resonance can occur as well as nonlinear subharmonic motions and a number of other limit motions. This report gives a complete survey of these possibilities with a number of actual case histories.
Symmetric covalent linkage of N-(6-aminohexyl)-5-chloro-1-naphthalenesulfonamide (W-7) results in novel derivatives with increased inhibitory activities against calcium/calmodulin complex.
Yokokura, H; Osawa, M; Inoue, T; Umezawa, I; Naito, Y; Ikura, M; Hidaka, H
A useful calmodulin (CaM) antagonist, N-(6-aminohexyl)-5-chloro-1-naphthalenesulfonamide (W-7), was invented by Hidaka et al. in 1978 (J. Pharmacol. Exp. Ther. 207, 8-15). Here, we have designed new CaM antagonists on the basis of the three-dimensional structure of Ca2+/CaM complexed with W-7. Eleven new compounds all share a similar architecture, in which two W-7 molecules are linked between their aminohexyl termini by a linker with different functionalities. A wide range of inhibitory activities against Ca2+/CaM-dependent protein kinase I (CaM kinase I) has been observed with these self-crosslinked W-7 analogs, (W-7)2. In vitro competitive CaM kinase I assays using CaM kinase I and nuclear magnetic resonance studies indicated that one (W-7)2 molecule binds to one CaM molecule as expected, with the two chloronaphthalene rings of (W-7)2 being anchored separately to the N- and C-terminal hydrophobic pockets of Ca2+/CaM. The most potent compound, N,N'-bis[6-(5-chloro-1-naphthalenesulfonyl)-amino-1-hexyl]-p-xylen e-diamine ((W-7)2 - 10), inhibits CaM kinase I activity at an IC50 value of 0.23 microM; about 75 times more effectively than W-7. The length and basicity of the linker sequence in (W-7)2 significantly contribute to inhibitory activity. The present study opens an avenue for developing powerful CaM antagonists that could be used at low doses in vivo.
Large Energy Barrier and Magnetization Hysteresis at 5 K for a Symmetric {Dy2} Complex with Spherical Tricapped Trigonal Prismatic Dy(III) Ions.
Mazarakioti, Eleni C; Regier, Jeffery; Cunha-Silva, Luís; Wernsdorfer, Wolfgang; Pilkington, Melanie; Tang, Jinkui; Stamatatos, Theocharis C
The introduction of the Schiff base ligand N-salicylidene-2-amino-5-chlorobenzoic acid (sacbH2) in 4f-metal chemistry has afforded a new dinuclear complex, [Dy2(NO3)4(sacbH)2(H2O)2(MeCN)2] (1), with the metal ions adopting a rare spherical tricapped trigonal prismatic coordination geometry. The deprotonated phenoxido O atoms of the organic chelate occupy the axial triangular faces of the prism and were found to be very close to the main anisotropy axes of the two Dy(III) ions. As a result, the {Dy(III)2} compound exhibits frequency- and temperature-dependent out-of-phase ac signals below ∼25 K in the absence of a static dc field, yielding an energy barrier of 109.3(1) K for the reversal of magnetization. Fast and efficient quantum tunneling of magnetization, attributed to the strong tails of signals below ∼15 K, was suppressed through the application of a small dc field, yielding entirely visible χM″ signals below 27 K. Single-crystal magnetic hysteresis studies confirmed the single-molecule magnet (SMM) behavior of 1; the hysteresis loops appear at temperatures below ∼5 K, which is one of the highest blocking temperatures in the field of 4f-SMMs to date. This joint magneto-structural and ab initio study demonstrates the ability of more common coordination numbers (i.e., 9), but with rare coordination geometries (i.e., spherical tricapped trigonal prismatic), to promote axiality that enhances the molecular anisotropy and subsequently the magnetization dynamics of the system.
On obtaining spectrally accurate solutions of linear differential equations with complex interfaces using the immersed interface method
NASA Astrophysics Data System (ADS)
Ray, Sudipta; Saha, Sandeep
Numerical solution of engineering problems with interfacial discontinuities requires exact implementation of the jump conditions else the accuracy deteriorates significantly; particularly, achieving spectral accuracy has been limited due to complex interface geometry and Gibbs phenomenon. We adopt a novel implementation of the immersed-interface method that satisfies the jump conditions at the interfaces exactly, in conjunction with the Chebyshev-collocation method. We consider solutions to linear second order ordinary and partial differential equations having a discontinuity in their zeroth and first derivatives across an interface traced by a complex curve. The solutions obtained demonstrate the ability of the proposed method to achieve spectral accuracy for discontinuous solutions across tortuous interfaces. The solution methodology is illustrated using two model problems: (i) an ordinary differential equation with jump conditions forced by an infinitely differentiable function, (ii) Poisson's equation having a discontinuous solution across interfaces that are ellipses of varying aspect ratio. The use of more polynomials in the direction of the major axis than the minor axis of the ellipse increases the convergence rate of the solution.
Complex-number representation of informed basis functions in general linear modeling of Functional Magnetic Resonance Imaging.
Wang, Pengwei; Wang, Zhishun; He, Lianghua
Functional Magnetic Resonance Imaging (fMRI), measuring Blood Oxygen Level-Dependent (BOLD), is a widely used tool to reveal spatiotemporal pattern of neural activity in human brain. Standard analysis of fMRI data relies on a general linear model and the model is constructed by convolving the task stimuli with a hypothesized hemodynamic response function (HRF). To capture possible phase shifts in the observed BOLD response, the informed basis functions including canonical HRF and its temporal derivative, have been proposed to extend the hypothesized hemodynamic response in order to obtain a good fitting model. Different t contrasts are constructed from the estimated model parameters for detecting the neural activity between different task conditions. However, the estimated model parameters corresponding to the orthogonal basis functions have different physical meanings. It remains unclear how to combine the neural features detected by the two basis functions and construct t contrasts for further analyses. In this paper, we have proposed a novel method for representing multiple basis functions in complex domain to model the task-driven fMRI data. Using this method, we can treat each pair of model parameters, corresponding respectively to canonical HRF and its temporal derivative, as one complex number for each task condition. Using the specific rule we have defined, we can conveniently perform arithmetical operations on the estimated model parameters and generate different t contrasts. We validate this method using the fMRI data acquired from twenty-two healthy participants who underwent an auditory stimulation task.
Convexity and symmetrization in relativistic theories
NASA Astrophysics Data System (ADS)
Ruggeri, T.
There is a strong motivation for the desire to have symmetric hyperbolic field equations in thermodynamics, because they guarantee well-posedness of Cauchy problems. A generic quasi-linear first order system of balance laws — in the non-relativistic case — can be shown to be symmetric hyperbolic, if the entropy density is concave with respect to the variables. In relativistic thermodynamics this is not so. This paper shows that there exists a scalar quantity in relativistic thermodynamics whose concavity guarantees a symmetric hyperbolic system. But that quantity — we call it —bar h — is not the entropy, although it is closely related to it. It is formed by contracting the entropy flux vector — ha with a privileged time-like congruencebar ξ _α . It is also shown that the convexity of h plus the requirement that all speeds be smaller than the speed of light c provide symmetric hyperbolic field equations for all choices of the direction of time. At this level of generality the physical meaning of —h is unknown. However, in many circumstances it is equal to the entropy. This is so, of course, in the non-relativistic limit but also in the non-dissipative relativistic fluid and even in relativistic extended thermodynamics for a non-degenerate gas.
Linear Free Energy Relationships for Metal-Ligand Complexation: Bidentate Binding to Negatively-Charged Oxygen Donor Atoms
Carbonaro, Richard F.; Atalay, Yasemin B.; Di Toro, Dominic M.
Stability constants for metal complexation to bidentate ligands containing negatively-charged oxygen donor atoms can be estimated from the following linear free energy relationship (LFER): log KML = χOO(αO log KHL,1 + αO log KHL,2) where KML is the metal-ligand stability constant for a 1:1 complex, KHL,1 and KHL,2 are the proton-ligand stability constants (the ligand pKa values), and αO is the Irving-Rossotti slope. The parameter χOO is metal specific and has slightly different values for 5 and 6 membered chelate rings. LFERs are presented for 21 different metal ions and are accurate to within approximately 0.30 log units in predictions of log KML values. Ligands selected for use in LFER development include dicarboxylic acids, carboxyphenols, and ortho-diphenols. For ortho-hydroxybenzaldehydes, α-hydroxycarboxylic acids, and α-ketocarboxylic acids, a modification of the LFER where log KHL,2 is set equal to zero is required. The chemical interpretation of χOO is that it accounts for the extra stability afforded to metal complexes by the chelate effect. Cu-NOM binding constants calculated from the bidentate LFERs are similar in magnitude to those used in WHAM 6. This LFER can be used to make log KML predictions for small organic molecules. Since natural organic matter (NOM) contains many of the same functional groups (i.e. carboxylic acids, phenols, alcohols), the LFER log KML predictions shed light on the range of appropriate values for use in modeling metal partitioning in natural systems. PMID:21833149
Linear free energy relationships for metal-ligand complexation: Bidentate binding to negatively-charged oxygen donor atoms
NASA Astrophysics Data System (ADS)
Carbonaro, Richard F.; Atalay, Yasemin B.; Di Toro, Dominic M.
Stability constants for metal complexation to bidentate ligands containing negatively-charged oxygen donor atoms can be estimated from the following linear free energy relationship (LFER): log KML = χOO( αO log KHL,1 + αO log KHL,2) where KML is the metal-ligand stability constant for a 1:1 complex, KHL,1 and KHL,2 are the proton-ligand stability constants (the ligand p Ka values), and αO is the Irving-Rossotti slope. The parameter χOO is metal specific and has slightly different values for five and six membered chelate rings. LFERs are presented for 21 different metal ions and are accurate to within approximately 0.30 log units in predictions of log KML values. Ligands selected for use in LFER development include dicarboxylic acids, carboxyphenols, and ortho-diphenols. For ortho-hydroxybenzaldehydes, α-hydroxycarboxylic acids, and α-ketocarboxylic acids, a modification of the LFER where log KHL,2 is set equal to zero is required. The chemical interpretation of χOO is that it accounts for the extra stability afforded to metal complexes by the chelate effect. Cu-NOM binding constants calculated from the bidentate LFERs are similar in magnitude to those used in WHAM 6. This LFER can be used to make log KML predictions for small organic molecules. Since natural organic matter (NOM) contains many of the same functional groups (i.e. carboxylic acids, phenols, alcohols), the LFER log KML predictions shed light on the range of appropriate values for use in modeling metal partitioning in natural systems.
Construction of dynamics and time-ordered exponential for unbounded non-symmetric Hamiltonians
Futakuchi, Shinichiro; Usui, Kouta
We prove under certain assumptions that there exists a solution of the Schrödinger or the Heisenberg equation of motion generated by a linear operator H acting in some complex Hilbert space H, which may be unbounded, not symmetric, or not normal. We also prove that, under the same assumptions, there exists a time evolution operator in the interaction picture and that the evolution operator enjoys a useful series expansion formula. This expansion is considered to be one of the mathematically rigorous realizations of so-called "time-ordered exponential," which is familiar in the physics literature. We apply the general theory to prove the existence of dynamics for the mathematical model of Quantum Electrodynamics quantized in the Lorenz gauge, the interaction Hamiltonian of which is not even symmetric or normal.
Stochastic thermodynamics for Ising chain and symmetric exclusion process
NASA Astrophysics Data System (ADS)
Toral, R.; Van den Broeck, C.; Escaff, D.; Lindenberg, Katja
We verify the finite-time fluctuation theorem for a linear Ising chain in contact with heat reservoirs at its ends. Analytic results are derived for a chain consisting of two spins. The system can be mapped onto a model for particle transport, namely, the symmetric exclusion process in contact with thermal and particle reservoirs. We modify the symmetric exclusion process to represent a thermal engine and reproduce universal features of the efficiency at maximum power.
Generalized symmetric extension for size-limited multirate filter banks.
Bamberger, R H; Eddins, S L; Nuri, V
A multirate (MR) filter bank is called size-limited if the total number of output samples equals the number of input samples. A method called symmetric extension improved performance in subband image compression systems compared to the earlier method of circular convolution. However, the symmetric extension method was developed only for two-band uniform filter banks, and required even-length linear phase analysis filters. The authors generalize the symmetric extension method to the M-band, possibly nonuniform filter banks, where M=/>2. The length restriction on the analysis filters is relaxed.
Social complexity, modernity and suicide: an assessment of Durkheim's suicide from the perspective of a non-linear analysis of complex social systems.
Condorelli, Rosalia
Can we share even today the same vision of modernity which Durkheim left us by its suicide analysis? or can society 'surprise us'? The answer to these questions can be inspired by several studies which found that beginning the second half of the twentieth century suicides in western countries more industrialized and modernized do not increase in a constant, linear way as modernization and social fragmentation process increases, as well as Durkheim's theory seems to lead us to predict. Despite continued modernizing process, they found stabilizing or falling overall suicide rate trends. Therefore, a gradual process of adaptation to the stress of modernization associated to low social integration levels seems to be activated in modern society. Assuming this perspective, the paper highlights as this tendency may be understood in the light of the new concept of social systems as complex adaptive systems, systems which are able to adapt to environmental perturbations and generate as a whole surprising, emergent effects due to nonlinear interactions among their components. So, in the frame of Nonlinear Dynamical System Modeling, we formalize the logic of suicide decision-making process responsible for changes at aggregate level in suicide growth rates by a nonlinear differential equation structured in a logistic way, and in so doing we attempt to capture the mechanism underlying the change process in suicide growth rate and to test the hypothesis that system's dynamics exhibits a restrained increase process as expression of an adaptation process to the liquidity of social ties in modern society. In particular, a Nonlinear Logistic Map is applied to suicide data in a modern society such as the Italian one from 1875 to 2010. The analytic results, seeming to confirm the idea of the activation of an adaptation process to the liquidity of social ties, constitutes an opportunity for a more general reflection on the current configuration of modern society, by relating the
Determination of the interaction parameter and topological scaling features of symmetric star polymers in dilute solution.
Rai, Durgesh K; Beaucage, Gregory; Ratkanthwar, Kedar; Beaucage, Peter; Ramachandran, Ramnath; Hadjichristidis, Nikos
Star polymers provide model architectures to understand the dynamic and rheological effects of chain confinement for a range of complex topological structures like branched polymers, colloids, and micelles. It is important to describe the structure of such macromolecular topologies using small-angle neutron and x-ray scattering to facilitate understanding of their structure-property relationships. Modeling of scattering from linear, Gaussian polymers, such as in the melt, has applied the random phase approximation using the Debye polymer scattering function. The Flory-Huggins interaction parameter can be obtained using neutron scattering by this method. Gaussian scaling no longer applies for more complicated chain topologies or when chains are in good solvents. For symmetric star polymers, chain scaling can differ from ν=0.5(d(f)=2) due to excluded volume, steric interaction between arms, and enhanced density due to branching. Further, correlation between arms in a symmetric star leads to an interference term in the scattering function first described by Benoit for Gaussian chains. In this work, a scattering function is derived which accounts for interarm correlations in symmetric star polymers as well as the polymer-solvent interaction parameter for chains of arbitrary scaling dimension using a hybrid Unified scattering function. The approach is demonstrated for linear, four-arm and eight-arm polyisoprene stars in deuterated p-xylene.
Synthesis of linear and cyclic peptide-PEG-lipids for stabilization and targeting of cationic liposome-DNA complexes.
Ewert, Kai K; Kotamraju, Venkata Ramana; Majzoub, Ramsey N; Steffes, Victoria M; Wonder, Emily A; Teesalu, Tambet; Ruoslahti, Erkki; Safinya, Cyrus R
Because nucleic acids (NAs) have immense potential value as therapeutics, the development of safe and effective synthetic NA vectors continues to attract much attention. In vivo applications of NA vectors require stabilized, nanometer-scale particles, but the commonly used approaches of steric stabilization with a polymer coat (e.g., PEGylation; PEG=poly(ethylene glycol)) interfere with attachment to cells, uptake, and endosomal escape. Conjugation of peptides to PEG-lipids can improve cell attachment and uptake for cationic liposome-DNA (CL-DNA) complexes. We present several synthetic approaches to peptide-PEG-lipids and discuss their merits and drawbacks. A lipid-PEG-amine building block served as the common key intermediate in all synthetic routes. Assembling the entire peptide-PEG-lipid by manual solid phase peptide synthesis (employing a lipid-PEG-carboxylic acid) allowed gram-scale synthesis but is mostly applicable to linear peptides connected via their N-terminus. Conjugation via thiol-maleimide or strain-promoted (copper-free) azide-alkyne cycloaddition chemistry is highly amenable to on-demand preparation of peptide-PEG-lipids, and the appropriate PEG-lipid precursors are available in a single chemical step from the lipid-PEG-amine building block. Azide-alkyne cycloaddition is especially suitable for disulfide-bridged peptides such as iRGD (cyclic CRGDKGPDC). Added at 10 mol% of a cationic/neutral lipid mixture, the peptide-PEG-lipids stabilize the size of CL-DNA complexes. They also affect cell attachment and uptake of nanoparticles in a peptide-dependent manner, thereby providing a platform for preparing stabilized, affinity-targeted CL-DNA nanoparticles.
Control of linear modes in cylindrical resistive magnetohydrodynamics with a resistive wall, plasma rotation, and complex gain
Brennan, D. P.; Finn, J. M.
Feedback stabilization of magnetohydrodynamic (MHD) modes in a tokamak is studied in a cylindrical model with a resistive wall, plasma resistivity, viscosity, and toroidal rotation. The control is based on a linear combination of the normal and tangential components of the magnetic field just inside the resistive wall. The feedback includes complex gain, for both the normal and for the tangential components, and it is known that the imaginary part of the feedback for the former is equivalent to plasma rotation [J. M. Finn and L. Chacon, Phys. Plasmas 11, 1866 (2004)]. The work includes (1) analysis with a reduced resistive MHD model for a tokamak with finite β and with stepfunction current density and pressure profiles, and (2) computations with a full compressible visco-resistive MHD model with smooth decreasing profiles of current density and pressure. The equilibria are stable for β = 0 and the marginal stability values β{sub rp,rw} < β{sub rp,iw} < β{sub ip,rw} < β{sub ip,iw} (resistive plasma, resistive wall; resistive plasma, ideal wall; ideal plasma, resistive wall; and ideal plasma, ideal wall) are computed for both models. The main results are: (a) imaginary gain with normal sensors or plasma rotation stabilizes below β{sub rp,iw} because rotation suppresses the diffusion of flux from the plasma out through the wall and, more surprisingly, (b) rotation or imaginary gain with normal sensors destabilizes above β{sub rp,iw} because it prevents the feedback flux from entering the plasma through the resistive wall to form a virtual wall. A method of using complex gain G{sub i} to optimize in the presence of rotation in this regime with β > β{sub rp,iw} is presented. The effect of imaginary gain with tangential sensors is more complicated but essentially destabilizes above and below β{sub rp,iw}.
Static spherically symmetric wormholes with isotropic pressure
NASA Astrophysics Data System (ADS)
Cataldo, Mauricio; Liempi, Luis; Rodríguez, Pablo
In this paper we study static spherically symmetric wormhole solutions sustained by matter sources with isotropic pressure. We show that such spherical wormholes do not exist in the framework of zero-tidal-force wormholes. On the other hand, it is shown that for the often used power-law shape function there are no spherically symmetric traversable wormholes sustained by sources with a linear equation of state p = ωρ for the isotropic pressure, independently of the form of the redshift function ϕ (r). We consider a solution obtained by Tolman at 1939 for describing static spheres of isotropic fluids, and show that it also may describe wormhole spacetimes with a power-law redshift function, which leads to a polynomial shape function, generalizing a power-law shape function, and inducing a solid angle deficit.
PT-Symmetric Quantum Liouvillean Dynamics
NASA Astrophysics Data System (ADS)
Prosen, Tomaž
We discuss a combination of unitary and antiunitary symmetry of quantum Liouvillean dynamics, in the context of open quantum systems, which implies a D2 symmetry of the complex Liouvillean spectrum. For sufficiently weak system-bath coupling, it implies a uniform decay rate for all coherences, i.e., off-diagonal elements of the system's density matrix taken in the eigenbasis of the Hamiltonian. As an example, we discuss symmetrically boundary driven open XXZ spin 1/2 chains.
Theoretical prediction of the linear isomers for rare gas-carbon disulfide complexes: He-CS₂, Ne-CS₂, and Ar-CS₂.
Zang, Limin; Dai, Wei; Zheng, Limin; Duan, Chuanxi; Lu, Yunpeng; Yang, Minghui
Theoretical studies of the potential energy surfaces (PESs) and bound states are performed for rare gas-carbon disulfide complexes, He-CS2, Ne-CS2, and Ar-CS2. Three two-dimensional intermolecular PESs are constructed from ab initio data points which are calculated at the CCSD(T) level with aug-cc-pVTZ basis set supplemented with bond functions. We find that the three PESs have very similar features and each PES can be characterized by a global T-shaped minimum, two equivalent local linear minima, and the saddle points between them. The T-shaped isomer is energetically more stable than the linear isomer for each complex. The linear isomers, which have not been observed in experiment so far, are predicted from our PESs and further identified by bound state calculations. Moreover, we assign several intermolecular vibrational states for both the T-shaped and linear isomers of the three complexes via the analysis of wavefunctions. The corresponding vibrational frequencies are calculated from the bound state energies for these assigned states. These frequencies could be helpful for further experimental studies, especially for the linear isomers. We also calculate the rovibrational transition frequencies for the three T-shaped isomers and the pure rotational transition frequencies for the linear isomers, respectively. The accuracy of the PESs is validated by the good agreement between theoretical and experimental results for the rovibrational transition frequencies and spectroscopic parameters.
Porcine Reproductive and Respiratory Syndrome Virus nsp1α Inhibits NF-κB Activation by Targeting the Linear Ubiquitin Chain Assembly Complex.
Jing, Huiyuan; Fang, Liurong; Ding, Zhen; Wang, Dang; Hao, Wenqi; Gao, Li; Ke, Wenting; Chen, Huanchun; Xiao, Shaobo
Linear ubiquitination, a newly discovered posttranslational modification, is catalyzed by the linear ubiquitin chain assembly complex (LUBAC), which is composed of three subunits: one catalytic subunit HOIP and two accessory molecules, HOIL-1L and SHARPIN. Accumulating evidence suggests that linear ubiquitination plays a crucial role in innate immune signaling and especially in the activation of the NF-κB pathway by conjugating linear polyubiquitin chains to NF-κB essential modulator (NEMO, also called IKKγ), the regulatory subunit of the IKK complex. Porcine reproductive and respiratory syndrome virus (PRRSV), an Arterivirus that has devastated the swine industry worldwide, is an ideal model to study the host's disordered inflammatory responses after viral infection. Here, we found that LUBAC-induced NF-κB and proinflammatory cytokine expression can be inhibited in the early phase of PRRSV infection. Screening the PRRSV-encoded proteins showed that nonstructural protein 1α (nsp1α) suppresses LUBAC-mediated NF-κB activation and its CTE domain is required for the inhibition. Mechanistically, nsp1α binds to HOIP/HOIL-1L and impairs the interaction between HOIP and SHARPIN, thus reducing the LUBAC-dependent linear ubiquitination of NEMO. Moreover, PRRSV infection also blocks LUBAC complex formation and NEMO linear-ubiquitination, the important step for transducing NF-κB signaling. This unexpected finding demonstrates a previously unrecognized role of PRRSV nsp1α in modulating LUBAC signaling and explains an additional mechanism of immune modulation by PRRSV.
Complexes Formed in Solution Between Vanadium(IV)/(V) and the Cyclic Dihydroxamic Acid Putrebactin or Linear Suberodihydroxamic Acid
An aerobic solution prepared from V(IV) and the cyclic dihydroxamic acid putrebactin (pbH2) in 1:1 H2O/CH3OH at pH = 2 turned from blue to orange and gave a signal in the positive ion electrospray ionization mass spectrometry (ESI-MS) at m/zobs 437.0 attributed to the monooxoV(V) species [VVO(pb)]+ ([C16H26N4O7V]+, m/zcalc 437.3). A solution prepared as above gave a signal in the 51V NMR spectrum at δV = −443.3 ppm (VOCl3, δV = 0 ppm) and was electron paramagnetic resonance silent, consistent with the presence of [VVO(pb)]+. The formation of [VVO(pb)]+ was invariant of [V(IV)]:[pbH2] and of pH values over pH = 2–7. In contrast, an aerobic solution prepared from V(IV) and the linear dihydroxamic acid suberodihydroxamic acid (sbhaH4) in 1:1 H2O/CH3OH at pH values of 2, 5, or 7 gave multiple signals in the positive and negative ion ESI-MS, which were assigned to monomeric or dimeric V(V)– or V(IV)–sbhaH4 complexes or mixed-valence V(V)/(IV)–sbhaH4 complexes. The complexity of the V-sbhaH4 system has been attributed to dimerization (2[VVO(sbhaH2)]+ ↔ [(VVO)2(sbhaH2)2]2+), deprotonation ([VVO(sbhaH2)]+ – H+ ↔ [VVO(sbhaH)]0), and oxidation ([VIVO(sbhaH2)]0 –e– ↔ [VVO(sbhaH2)]+) phenomena and could be described as the sum of two pH-dependent vectors, the first comprising the deprotonation of hydroxamate (low pH) to hydroximate (high pH) and the second comprising the oxidation of V(IV) (low pH) to V(V) (high pH). Macrocyclic pbH2 was preorganized to form [VVO(pb)]+, which would provide an entropy-based increase in its thermodynamic stability compared to V(V)–sbhaH4 complexes. The half-wave potentials from solutions of [V(IV)]:[pbH2] (1:1) or [V(IV)]:[sbhaH4] (1:2) at pH = 2 were E1/2 −335 or −352 mV, respectively, which differed from the expected trend (E1/2 [VO(pb)]+/0 < VV/IV–sbhaH4). The complex solution speciation of the V(V)/(IV)–sbhaH4 system prevented the determination of half-wave potentials for single species. The characterization
PT -symmetric model of immune response
NASA Astrophysics Data System (ADS)
Bender, Carl M.; Ghatak, Ananya; Gianfreda, Mariagiovanna
The study of PT -symmetric physical systems began in 1998 as a complex generalization of conventional quantum mechanics, but beginning in 2007 experiments began to be published in which the predicted PT phase transition was clearly observed in classical rather than in quantum-mechanical systems. This paper examines the classical PT phase transition in dynamical-system models that are moderately accurate representations of antigen-antibody systems. A surprising conclusion that can be drawn from these models is that it might be possible treat a serious disease in which the antigen concentration grows out of bounds (and the host dies) by injecting a small dose of a second (different) antigen. In this case a PT -symmetric analysis shows there are two possible favorable outcomes. In the unbroken-PT -symmetric phase the disease becomes chronic and is no longer lethal, while in the appropriate broken-PT -symmetric phase the concentration of lethal antigen goes to zero and the disease is completely cured.
Stable parity-time-symmetric nonlinear modes and excitations in a derivative nonlinear Schrödinger equation
NASA Astrophysics Data System (ADS)
Chen, Yong; Yan, Zhenya
The effect of derivative nonlinearity and parity-time-symmetric (PT -symmetric) potentials on the wave propagation dynamics is explored in the derivative nonlinear Schrödinger equation, where the physically interesting Scarf-II and harmonic-Hermite-Gaussian potentials are chosen. We study numerically the regions of unbroken and broken linear PT -symmetric phases and find some stable bright solitons of this model in a wide range of potential parameters even though the corresponding linear PT -symmetric phases are broken. The semielastic interactions between particular bright solitons and exotic incident waves are illustrated such that we find that particular nonlinear modes almost keep their shapes after interactions even if the exotic incident waves have evidently been changed. Moreover, we exert the adiabatic switching on PT -symmetric potential parameters such that a stable nonlinear mode with the unbroken linear PT -symmetric phase can be excited to another stable nonlinear mode belonging to the broken linear PT -symmetric phase.
A Complex Insertion Sequence Cluster at a Point of Interaction between the Linear Plasmid SCP1 and the Linear Chromosome of Streptomyces coelicolor A3(2)
Yamasaki, Masayuki; Miyashita, Kiyotaka; Cullum, John; Kinashi, Haruyasu
The giant linear plasmid SCP1 can integrate into the central region of the linear chromosome of Streptomyces coelicolor A3(2). Nucleotide sequence analysis around the target site for SCP1 integration in strain M145 identified a total of five copies of four insertion sequences (ISs) in a 6.5-kb DNA stretch. Three of the four (IS468, IS469, and IS470) are new IS elements, and the other is IS466. All of these elements contain one open reading frame which encodes a transposase-like protein. Two copies of IS468 (IS468A and -B) are tandemly aligned at the left end of the cluster. Following these, IS469 and IS466 are located in a tail-to-tail orientation with 69.3% identity to each other. IS470 is located at the right end of the cluster. The activities of IS466 and IS468 were demonstrated by transposition experiments and sequence comparison of several copies, respectively. PMID:10809688
Inversion-symmetric topological insulators
NASA Astrophysics Data System (ADS)
Hughes, Taylor L.; Prodan, Emil; Bernevig, B. Andrei
We analyze translationally invariant insulators with inversion symmetry that fall outside the current established classification of topological insulators. These insulators exhibit no edge or surface modes in the energy spectrum and hence they are not edge metals when the Fermi level is in the bulk gap. However, they do exhibit protected modes in the entanglement spectrum localized on the cut between two entangled regions. Their entanglement entropy cannot be made to vanish adiabatically, and hence the insulators can be called topological. There is a direct connection between the inversion eigenvalues of the Hamiltonian band structure and the midgap states in the entanglement spectrum. The classification of protected entanglement levels is given by an integer N, which is the difference between the negative inversion eigenvalues at inversion symmetric points in the Brillouin zone, taken in sets of 2. When the Hamiltonian describes a Chern insulator or a nontrivial time-reversal invariant topological insulator, the entirety of the entanglement spectrum exhibits spectral flow. If the Chern number is zero for the former, or time reversal is broken in the latter, the entanglement spectrum does not have spectral flow, but, depending on the inversion eigenvalues, can still exhibit protected midgap bands similar to impurity bands in normal semiconductors. Although spectral flow is broken (implying the absence of real edge or surface modes in the original Hamiltonian), the midgap entanglement bands cannot be adiabatically removed, and the insulator is "topological." We analyze the linear response of these insulators and provide proofs and examples of when the inversion eigenvalues determine a nontrivial charge polarization, a quantum Hall effect, an anisotropic three-dimensional (3D) quantum Hall effect, or a magnetoelectric polarization. In one dimension, we establish a link between the product of the inversion eigenvalues of all occupied bands at all inversion
Highly Effective Non-Viral Antitumor Gene Therapy System Comprised of Biocompatible Small Plasmid Complex Particles Consisting of pDNA, Anionic Polysaccharide, and Fully Deprotected Linear Polyethylenimine
Koyama, Yoshiyuki; Sugiura, Kikuya; Yoshihara, Chieko; Inaba, Toshio; Ito, Tomoko
We have reported that ternary complexes of plasmid DNA with conventional linear polyethylenimine (l-PEI) and certain polyanions were very stably dispersed, and, with no cryoprotectant, they could be freeze-dried and re-hydrated without the loss of transfection ability. These properties enabled the preparation of a concentrated suspension of very small pDNA complex, by preparing the complexes at highly diluted conditions, followed by condensation via lyophilization-and-rehydration procedure. Recently, a high potency linear polyethylenimine having no residual protective groups, i.e., Polyethylenimine "Max" (PEI "Max"), is available, which has been reported to induce much higher gene expression than conventional l-PEI. We tried to prepare the small DNA/PEI "Max"/polyanion complexes by a similar freeze-drying method. Small complex particles could be obtained without apparent aggregation, but transfection activity of the rehydrated complexes was severely reduced. Complex-preparation conditions were investigated in details to achieve the freeze-dried DNA/PEI "Max"/polyanion small ternary complexes with high transfection efficiency. DNA/PEI "Max"/polyanion complexes containing cytokine-coding plasmids were then prepared, and their anti-tumor therapeutic efficacy was examined in tumor-bearing mice. PMID:26213961
Linear optimal control of tokamak fusion devices
Kessel, C.E.; Firestone, M.A.; Conn, R.W.
The control of plasma position, shape and current in a tokamak fusion reactor is examined using linear optimal control. These advanced tokamaks are characterized by non up-down symmetric coils and structure, thick structure surrounding the plasma, eddy currents, shaped plasmas, superconducting coils, vertically unstable plasmas, and hybrid function coils providing ohmic heating, vertical field, radial field, and shaping field. Models of the electromagnetic environment in a tokamak are derived and used to construct control gains that are tested in nonlinear simulations with initial perturbations. The issues of applying linear optimal control to advanced tokamaks are addressed, including complex equilibrium control, choice of cost functional weights, the coil voltage limit, discrete control, and order reduction. Results indicate that the linear optimal control is a feasible technique for controlling advanced tokamaks where the more common classical control will be severely strained or will not work. 28 refs., 13 figs.
A Free-Knot Spline Modeling Framework for Piecewise Linear Logistic Regression in Complex Samples with Body Mass Index and Mortality as an Example
Keith, Scott W.; Allison, David B.
This paper details the design, evaluation, and implementation of a framework for detecting and modeling non-linearity between a binary outcome and a continuous predictor variable adjusted for covariates in complex samples. The framework provides familiar-looking parameterizations of output in terms of linear slope coefficients and odds ratios. Estimation methods focus on maximum likelihood optimization of piecewise linear free-knot splines formulated as B-splines. Correctly specifying the optimal number and positions of the knots improves the model, but is marked by computational intensity and numerical instability. Our inference methods utilize both parametric and non-parametric bootstrapping. Unlike other non-linear modeling packages, this framework is designed to incorporate multistage survey sample designs common to nationally representative datasets. We illustrate the approach and evaluate its performance in specifying the correct number of knots under various conditions with an example using body mass index (BMI, kg/m2) and the complex multistage sampling design from the Third National Health and Nutrition Examination Survey to simulate binary mortality outcomes data having realistic non-linear sample-weighted risk associations with BMI. BMI and mortality data provide a particularly apt example and area of application since BMI is commonly recorded in large health surveys with complex designs, often categorized for modeling, and non-linearly related to mortality. When complex sample design considerations were ignored, our method was generally similar to or more accurate than two common model selection procedures, Schwarz's Bayesian Information Criterion (BIC) and Akaike's Information Criterion (AIC), in terms of correctly selecting the correct number of knots. Our approach provided accurate knot selections when complex sampling weights were incorporated, while AIC and BIC were not effective under these conditions. PMID:25610831
Representation of Fuzzy Symmetric Relations
Std Z39-18 REPRESENTATION OF FUZZY SYMMETRIC RELATIONS L. Valverde Dept. de Matematiques i Estadistica Universitat Politecnica de Catalunya Avda...REPRESENTATION OF FUZZY SYMMETRIC RELATIONS L. "Valverde* Dept. de Matematiques i Estadistica Universitat Politecnica de Catalunya Avda. Diagonal, 649
Solitonic dynamics and excitations of the nonlinear Schrödinger equation with third-order dispersion in non-Hermitian PT-symmetric potentials.
Chen, Yong; Yan, Zhenya
Solitons are of the important significant in many fields of nonlinear science such as nonlinear optics, Bose-Einstein condensates, plamas physics, biology, fluid mechanics, and etc. The stable solitons have been captured not only theoretically and experimentally in both linear and nonlinear Schrödinger (NLS) equations in the presence of non-Hermitian potentials since the concept of the parity-time -symmetry was introduced in 1998. In this paper, we present novel bright solitons of the NLS equation with third-order dispersion in some complex -symmetric potentials (e.g., physically relevant -symmetric Scarff-II-like and harmonic-Gaussian potentials). We find stable nonlinear modes even if the respective linear -symmetric phases are broken. Moreover, we also use the adiabatic changes of the control parameters to excite the initial modes related to exact solitons to reach stable nonlinear modes. The elastic interactions of two solitons are exhibited in the third-order NLS equation with -symmetric potentials. Our results predict the dynamical phenomena of soliton equations in the presence of third-order dispersion and -symmetric potentials arising in nonlinear fiber optics and other physically relevant fields.
Solitonic dynamics and excitations of the nonlinear Schrödinger equation with third-order dispersion in non-Hermitian PT-symmetric potentials
Chen, Yong; Yan, Zhenya
Solitons are of the important significant in many fields of nonlinear science such as nonlinear optics, Bose-Einstein condensates, plamas physics, biology, fluid mechanics, and etc. The stable solitons have been captured not only theoretically and experimentally in both linear and nonlinear Schrödinger (NLS) equations in the presence of non-Hermitian potentials since the concept of the parity-time -symmetry was introduced in 1998. In this paper, we present novel bright solitons of the NLS equation with third-order dispersion in some complex -symmetric potentials (e.g., physically relevant -symmetric Scarff-II-like and harmonic-Gaussian potentials). We find stable nonlinear modes even if the respective linear -symmetric phases are broken. Moreover, we also use the adiabatic changes of the control parameters to excite the initial modes related to exact solitons to reach stable nonlinear modes. The elastic interactions of two solitons are exhibited in the third-order NLS equation with -symmetric potentials. Our results predict the dynamical phenomena of soliton equations in the presence of third-order dispersion and -symmetric potentials arising in nonlinear fiber optics and other physically relevant fields. PMID:27002543
Tensor species and symmetric functions.
Méndez, M
An equivariant representation of the symmetric group Sn (equivariant representation from here on) is defined as a particular type of tensor species. For any tensor species R the characteristic generating function of R is defined in a way that generalizes the Frobenius characters of representations of the symmetric groups. If R is an equivariant representation, then the characteristic is a homogeneous symmetric function. The combinatorial operations on equivariant representations correspond to formal operations on the respective characteristic functions. In particular, substitution of equivariant representations corresponds to plethysm of symmetric functions. Equivariant representations are constructed that have as characteristic the elementary, complete, and Schur functions. Bijective proofs are given for the formulas that connect them with the monomial symmetric functions. PMID:11607233
Linear-dendritic supramolecular complexes as nanoscale reaction vessels for "green" chemistry. Diels-Alder reactions between fullerene C60 and polycyclic aromatic hydrocarbons in aqueous medium.
Simonyan, Arsen; Gitsov, Ivan
This study describes the first Diels-Alder (DA) reaction performed in aqueous medium with highly hydrophobic compounds-fullerene (C 60) as the dienophile and anthracene (An) or tetracene (Tet) as the dienes, respectively. The reactions are performed in nanocontainers, constructed by self-assembly of linear-dendritic amphiphilic copolymers with poly(ethylene glycol), PEG or poly(ethylene oxide), PEO as the hydrophilic blocks and poly(benzyl ether) monodendrons as the hydrophobic fragments: G3PEO13k, dG3 and dG2. Comparative studies under identical conditions are carried out with an amphiphilic linear-linear copolymer, poly(styrene)1800- block-PEO2100, PSt-PEO, and the nonionic surfactant Igepal CO-720, IP720. The binding affinity of supermolecules built of these amphiphiles toward the DA reagents decreases in the following order: G3PEO13k > dG3 > PSt-PEO > dG2 > IP720. The kinetic constant of binding is evaluated for tetracene and decreases in a similar fashion: 5 x 10 (-7) M/min (G3PEO13k), through 4 x 10 (-7) M/min (PSt-PEO) down to 1.5 x 10 (-7) M/min for IP720. The mobility of substrates encapsulated in the micellar core, estimated by pyrene fluorescence decay, is 95-121 ns for the micelles of the linear-dendritic copolymers and notably higher for PSt-PEO (152 ns), revealing the much denser interior of the linear analogue. The apparent kinetic constant for the DA reaction of C 60 and Tet within the G3PEO13k supermolecule in aqueous medium is markedly higher than in organic solvent (toluene), 208 vs 1.82 M /min. With G3PEO13k the conversions reach 49% for the DA reaction between C 60 and An, and 55% for C 60 and Tet. Besides the monoadduct (26.5% yield) the reaction with An produces exclusively increasing amounts of D 2 h -symmetric antipodal bis-adduct, whose yield reaches up to 22.5% after 48 h. In addition to the environmentally friendly conditions notable advantages of the synthetic strategy described are the extended stability of the linear
Symmetric multilayer megampere X-pinch
Shelkovenko, T. A.; Pikuz, S. A.; McBride, R. D.; Knapp, P. F.; Wilhelm, G.; Sinars, D. B.; Hammer, D. A.; Orlov, N. Yu.
Raising the power of X-ray emission from an X-pinch by increasing the pinch current to the megampere level requires the corresponding increase in the initial linear mass of the load. This can be achieved by increasing either the number of wires or their diameter. In both cases, special measures should be undertaken to prevent the formation of a complicated configuration with an uncontrolled spatial structure in the region of wire crossing, because such a structure breaks the symmetry of the neck formed in the crossing region, destabilizes plasma formation, and degrades X-ray generation. To improve the symmetry of the wire crossing region, X-pinch configurations with a regular multilayer arrangement of wires in this region were proposed and implemented. The results of experiments with various symmetric X-pinch configurations on the COBRA facility at currents of {approx}1MA are presented. It is shown that an X-pinch with a symmetric crossing region consisting of several layers of wires made of different materials can be successfully used in megampere facilities. The most efficient combinations of wires in symmetric multilayer X-pinches are found in which only one hot spot forms and that are characterized by a high and stable soft X-ray yield.
A Pyridine-Based Ligand with Two Hydrazine Functions for Lanthanide Chelation: Remarkable Kinetic Inertness for a Linear, Bishydrated Complex.
Bonnet, Célia S; Laine, Sophie; Buron, Frédéric; Tircsó, Gyula; Pallier, Agnès; Helm, Lothar; Suzenet, Franck; Tóth, Éva
To study the influence of hydrazine functions in the ligand skeleton, we designed the heptadentate HYD ligand (2,2',2″,2‴-(2,2'-(pyridine-2,6-diyl)bis(2-methylhydrazine-2,1,1-triyl)) tetraacetic acid) and compared the thermodynamic, kinetic, and relaxation properties of its Ln(3+) complexes to those of the parent pyridine (Py) analogues without hydrazine (Py = 2,6-pyridinebis(methanamine)-N,N,N',N'-tetraacetic acid). The protonation constants of HYD were determined by pH-potentiometric measurements, and assigned by a combination of UV-visible and NMR spectroscopies. The protonation sequence is rather unusual and illustrates that small structural changes can strongly influence ligand basicity. The first protonation step occurs on the pyridine nitrogen in the basic region, followed by two hydrazine nitrogens and the carboxylate groups at acidic pH. Contrary to Py, HYD self-aggregates through a pH-dependent process (from pH ca. 4). Thermodynamic stability constants have been obtained by pH-potentiometry and UV-visible spectrophotometry for various Ln(3+) and physiological cations (Zn(2+), Ca(2+), Cu(2+)). LnHYD stability constants show the same trend as those of LnDTPA complexes along the Ln(3+) series, with log K = 18.33 for Gd(3+), comparable to the Py analogue. CuHYD has a particularly high stability (log K > 19) preventing its determination from pH-potentiometric measurements. The stability constant of CuPy was also revisited and found to be underestimated in previous studies, highlighting that UV-visible spectrophotometry is often indispensable to obtain reliable stability constants for Cu(2+) chelates. The dissociation of GdL, assessed by studying the Cu(2+)-exchange reaction, occurs mainly via an acid-catalyzed process, with limited contribution from direct Cu(2+) attack. The kinetic inertness of GdHYD is remarkable for a linear bishydrated chelate; the 25-fold increase in the dissociation half-life with respect to the monohydrated commercial contrast agent
Novel linear piezoelectric motor for precision position stage
NASA Astrophysics Data System (ADS)
Chen, Chao; Shi, Yunlai; Zhang, Jun; Wang, Junshan
Conventional servomotor and stepping motor face challenges in nanometer positioning stages due to the complex structure, motion transformation mechanism, and slow dynamic response, especially directly driven by linear motor. A new butterfly-shaped linear piezoelectric motor for linear motion is presented. A two-degree precision position stage driven by the proposed linear ultrasonic motor possesses a simple and compact configuration, which makes the system obtain shorter driving chain. Firstly, the working principle of the linear ultrasonic motor is analyzed. The oscillation orbits of two driving feet on the stator are produced successively by using the anti-symmetric and symmetric vibration modes of the piezoelectric composite structure, and the slider pressed on the driving feet can be propelled twice in only one vibration cycle. Then with the derivation of the dynamic equation of the piezoelectric actuator and transient response model, start-upstart-up and settling state characteristics of the proposed linear actuator is investigated theoretically and experimentally, and is applicable to evaluate step resolution of the precision platform driven by the actuator. Moreover the structure of the two-degree position stage system is described and a special precision displacement measurement system is built. Finally, the characteristics of the two-degree position stage are studied. In the closed-loop condition the positioning accuracy of plus or minus <0.5 μm is experimentally obtained for the stage propelled by the piezoelectric motor. A precision position stage based the proposed butterfly-shaped linear piezoelectric is theoretically and experimentally investigated.
Decay Structure for Symmetric Hyperbolic Systems with Non-Symmetric Relaxation and its Application
NASA Astrophysics Data System (ADS)
Ueda, Yoshihiro; Duan, Renjun; Kawashima, Shuichi
This paper is concerned with the decay structure for linear symmetric hyperbolic systems with relaxation. When the relaxation matrix is symmetric, the dissipative structure of the systems is completely characterized by the Kawashima-Shizuta stability condition formulated in Umeda et al. (Jpn J Appl Math 1:435-457, 1984) and Shizuta and Kawashima (Hokkaido Math J 14:249-275, 1985) and we obtain the asymptotic stability result together with the explicit time-decay rate under that stability condition. However, some physical models which satisfy the stability condition have non-symmetric relaxation term (for example, the Timoshenko system and the Euler-Maxwell system). Moreover, it had been already known that the dissipative structure of such systems is weaker than the standard type and is of the regularity-loss type (see Duan in J Hyperbolic Differ Equ 8:375-413, 2011; Ide et al. in Math Models Meth Appl Sci 18:647-667, 2008; Ide and Kawashima in Math Models Meth Appl Sci 18:1001-1025, 2008; Ueda et al. in SIAM J Math Anal 2012; Ueda and Kawashima in Methods Appl Anal 2012). Therefore our purpose in this paper is to formulate a new structural condition which includes the Kawashima-Shizuta condition, and to analyze the weak dissipative structure for general systems with non-symmetric relaxation.
Dosimetric characterization of hypofractionated Gamma Knife radiosurgery of large or complex brain tumors versus linear accelerator-based treatments.
Dong, Peng; Pérez-Andújar, Angélica; Pinnaduwage, Dilini; Braunstein, Steve; Theodosopoulos, Philip; McDermott, Michael; Sneed, Penny; Ma, Lijun
OBJECTIVE Noninvasive Gamma Knife (GK) platforms, such as the relocatable frame and on-board imaging, have enabled hypofractionated GK radiosurgery of large or complex brain lesions. This study aimed to characterize the dosimetric quality of such treatments against linear accelerator-based delivery systems that include the CyberKnife (CK) and volumetric modulated arc therapy (VMAT). METHODS Ten patients treated with VMAT at the authors' institution for large brain tumors (> 3 cm in maximum diameter) were selected for the study. The median prescription dose was 25 Gy (range 20-30 Gy) in 5 fractions. The median planning target volume (PTV) was 9.57 cm(3) (range 1.94-24.81 cm(3)). Treatment planning was performed using Eclipse External Beam Planning V11 for VMAT on the Varian TrueBeam system, Multiplan V4.5 for the CyberKnife VSI System, and Leksell GammaPlan V10.2 for the Gamma Knife Perfexion system. The percentage of the PTV receiving at least the prescription dose was normalized to be identical across all platforms for individual cases. The prescription isodose value for the PTV, conformity index, Paddick gradient index, mean and maximum doses for organs at risk, and normal brain dose at variable isodose volumes ranging from the 5-Gy isodose volume (V5) to the 15-Gy isodose volume (V15) were compared for all of the cases. RESULTS The mean Paddick gradient index was 2.6 ± 0.2, 3.2 ± 0.5, and 4.3 ± 1.0 for GK, CK, and VMAT, respectively (p < 0.002). The mean V15 was 7.5 ± 3.7 cm(3) (range 1.53-13.29 cm(3)), 9.8 ± 5.5 cm(3) (range 2.07-18.45 cm(3)), and 16.1 ± 10.6 cm(3) (range 3.58-36.53 cm(3)) for GK, CK, and VMAT, respectively (p ≤ 0.03, paired 2-tailed t-tests). However, the average conformity index was 1.18, 1.12, and 1.21 for GK, CK, and VMAT, respectively (p > 0.06). The average prescription isodose values were 52% (range 47%-69%), 60% (range 46%-68%), and 88% (range 70%-94%) for GK, CK, and VMAT, respectively, thus producing significant variations in
Backbone dynamics of a symmetric calmodulin dimer in complex with the calmodulin-binding domain of the basic-helix-loop-helix transcription factor SEF2-1/E2-2: a highly dynamic complex.
Larsson, Göran; Schleucher, Jürgen; Onions, Jacqueline; Hermann, Stefan; Grundström, Thomas; Wijmenga, Sybren S
Calmodulin (CaM) interacts specifically as a dimer with some dimeric basic-Helix-Loop-Helix (bHLH) transcription factors via a novel high affinity binding mode. Here we report a study of the backbone dynamics by (15)N-spin relaxation on the CaM dimer in complex with a dimeric peptide that mimics the CaM binding region of the bHLH transcription factor SEF2-1. The relaxation data were measured at multiple magnetic fields, and analyzed in a model-free manner using in-house written software designed to detect nanosecond internal motion. Besides picosecond motions, all residues also experience internal motion with an effective correlation time of approximately 2.5 ns with squared order parameter (S(2)) of approximately 0.75. Hydrodynamic calculations suggest that this can be attributed to motions of the N- and C-terminal domains of the CaM dimer in the complex. Moreover, residues with significant exchange broadening are found. They are clustered in the CaM:SEF2-1mp binding interface, the CaM:CaM dimer interface, and in the flexible helix connecting the CaM N- and C-terminal domains, and have similar exchange times (approximately 50 micros), suggesting a cooperative mechanism probably caused by protein:protein interactions. The dynamic features presented here support the conclusion that the conformationally heterogeneous bHLH mimicking peptide trapped inside the CaM dimer exchanges between different binding sites on both nanosecond and microsecond timescales. Nature has thus found a way to specifically recognize a relatively ill-fitting target. This novel mode of target-specific binding, which neither belongs to lock-and-key nor induced-fit binding, is characterized by dimerization and continuous exchange between multiple flexible binding alternatives.
A Cyclic Alkyl(amino)carbene as Two-Atom π-Chromophore Leading to the First Phosphorescent Linear Cu(I) Complexes.
Gernert, Markus; Müller, Ulrich; Haehnel, Martin; Pflaum, Jens; Steffen, Andreas
The members of a series of linear and trigonal copper(I) complexes bearing a cyclic alkyl(amino)carbene (CAAC) ligand show surprising photophysical properties compared to those of the corresponding N-heterocyclic carbene (NHC) complexes. Whereas the linear NHC complexes [CuX(NHC)] are almost non-emissive, [CuX(CAAC)] (X=Cl, Br, I) and [Cu(CAAC)2 ]PF6 show very bright emissions from their triplet excited states in the blue to green region, displaying quantum yields of up to 65 % in the solid state, even though the π-acceptor comprises only the carbene C and N atoms with no other π conjugation. [Cu(CAAC)2 ]PF6 is the fastest Cu(I) -based triplet state emitter characterized to date, not displaying thermally activated delayed fluorescence (TADF), with an intrinsic lifetime of only 10.6 μs, that is, kr =9.4×10(4) s(-1) , competitive with many Pt(II) - and Ir(III) -based emitters. In order to test the stability of such linear copper CAAC complexes in devices, some of our compounds have been applied in proof-of-principle organic light-emitting diodes (OLEDs). This case study thus demonstrates for the first time the use of CAACs as suitable π-chromophores for Cu(I) -based phosphorescent emitters, and their implementation in OLEDs underlines the general applicability of this class of ligands in materials science.
Structure Effect of Some New Anticancer Pt(II) Complexes of Amino Acid Derivatives with Small Branched or Linear Hydrocarbon Chains on Their DNA Interaction.
Kantoury, Mahshid; Eslami Moghadam, Mahboube; Tarlani, Ali Akbar; Divsalar, Adeleh
The aim of this study was to investigate the structure effect and identify the modes of binding of amino acid-Pt complexes to DNA molecule for cancer treatment. Hence, three novel water soluble platinum complexes, [Pt(phen)(R-gly)]NO3 (where phen is 1,10-phenanthroline, R-gly is methyl, amyl, and isopentyl-glycine), have been synthesized and characterized by spectroscopic methods, conductivity measurements, and chemical analysis. The anticancer activities of synthesized complexes were investigated against human breast cancer cell line of MDA-MB 231. The 50% cytotoxic concentration values were determined to be 42.5, 58, and 70 μm for methyl-, amyl-, and isopentyl-gly complexes, respectively. These complexes were interacted with calf thymus DNA (ct-DNA) via positive cooperative interaction. The modes of binding of the complexes to DNA were investigated by fluorescence spectroscopy and circular dichroism in combination with a molecular docking study. The result indicates that complexes with small or branched hydrocarbon chains can intercalate with DNA. This is while amyl complexes with linear chains interacted additionally via groove binding. The results of the negative value of Gibbs energy for binding of isopentyl-platinum to DNA and those of the molecular docking were coherent. Furthermore, the docking results demonstrated that hydrophobic interaction plays an important role in the complex-DNA interaction.
Sampling and error analysis of radial symmetric interpolation for fast hologram generation.
Lee, Seok; Chang, Hyunsung; Wey, Hocheon; Nam, Dongkyung
In this paper, we present a fast hologram pattern generation method by radial symmetric interpolation, which exploits concentric redundancy of a point hologram pattern to reduce computational complexity in hologram pattern calculation, and analyze the quality degradation sources in the proposed method. Compared to the analytic method in which phase and amplitude information is directly calculated from a wave equation, in our method a Fresnel zone plate is periodically sampled along a diagonal line and the wave information of a point hologram is calculated by linear interpolation. During these sampling and interpolation processes, the wave information can be modified from the original signal and the reconstruction quality can be degraded compared to the analytic pattern calculation method. The effects of sampling and linear interpolation are investigated in spatial and frequency domains.
Nonlinear waves in PT -symmetric systems
NASA Astrophysics Data System (ADS)
Konotop, Vladimir V.; Yang, Jianke; Zezyulin, Dmitry A.
Recent progress on nonlinear properties of parity-time (PT )-symmetric systems is comprehensively reviewed in this article. PT symmetry started out in non-Hermitian quantum mechanics, where complex potentials obeying PT symmetry could exhibit all-real spectra. This concept later spread out to optics, Bose-Einstein condensates, electronic circuits, and many other physical fields, where a judicious balancing of gain and loss constitutes a PT -symmetric system. The natural inclusion of nonlinearity into these PT systems then gave rise to a wide array of new phenomena which have no counterparts in traditional dissipative systems. Examples include the existence of continuous families of nonlinear modes and integrals of motion, stabilization of nonlinear modes above PT -symmetry phase transition, symmetry breaking of nonlinear modes, distinctive soliton dynamics, and many others. In this article, nonlinear PT -symmetric systems arising from various physical disciplines are presented, nonlinear properties of these systems are thoroughly elucidated, and relevant experimental results are described. In addition, emerging applications of PT symmetry are pointed out.
Taming the Exceptional Points of Parity-Time Symmetric Acoustics
NASA Astrophysics Data System (ADS)
Dubois, Marc; Shi, Chengzhi; Chen, Yun; Cheng, Lei; Ramezani, Hamidreza; Wang, Yuan; Zhang, Xiang
Parity-time (PT) symmetric concept and development lead to a wide range of applications including coherent perfect absorbers, single mode lasers, unidirectional cloaking and sensing, and optical isolators. These new applications and devices emerge from the existence of a phase transition in PT symmetric complex-valued potential obtained by balancing gain and loss materials. However, the systematic extension of such devices is adjourned by the key challenge in the management of the complex scattering process within the structure in order to engineer PT phase and exceptional points. Here, based on active acoustic elements, we experimentally demonstrate the simultaneous control of complex-valued potentials and multiple interference inside the structure at any given frequency. This method broadens the scope of applications for PT symmetric devices in many fields including optics, microwaves, electronics, which are crucial for sensing, imaging, cloaking, lasing, absorbing, etc.
Influence of the anions on the structure and magnetic properties of a series of bis(μ-diphenoxo)-bridged linear trinuclear copper(II) complexes: an experimental and theoretical study.
Botana, Luis; Ruiz, José; Seco, José Manuel; Mota, Antonio J; Rodríguez-Diéguez, Antonio; Sillanpää, Reijo; Colacio, Enrique
The reaction of H(2)L (N,N'-dimethyl-N,N'-bis(2-hydroxy-3-methoxy-5-methylbenzyl)-ethylenediamine) with different copper salts, in methanol and using a H(2)L/Cu = 2 : 3 molar ratio, led to four new bis(μ-diphenoxo)-bridged Cu(3) complexes of general formula [{Cu(S)(μ-L)}(2)Cu(H(2)O)(2n)]X(2) (S = CH(3)OH, n = 1 and X = BF(4)(-) for (1) or ClO(4)(-) for (2); S = Br(3)(-) anion and n = 1 without any X species for (3); S = H(2)O, n = 0 and X = NO(3)(-) for (4)). The use in the same reaction conditions of 4,4'-bipyridine (4,4'-bipy) as connector led to the chain complex [{Cu(μ-4,4'-bipy)(0.5)(μ-L)}(2)Cu(H(2)O)(2n)](ClO(4))(2)·17H(2)O (5). The structure of the centrosymmetric trinuclear unit in (1)-(5) consists of two [Cu(L)] fragments connected through two phenoxo bridging groups to the central copper(II) ion giving rise to a linear arrangement of the copper(II) ions, where the ligand acts in a compartmental form wrapping the metal centre with a N(2)O(2) tetradentate bridging mode. The coordination polyhedron of the symmetrically related external copper atoms exhibits a geometry very close to square-pyramidal, whereas the central copper(II) atom displays either a tetragonally elongated octahedral geometry or a square-planar geometry. Owing to the steric hindrance promoted by the methoxy groups at the phenyl rings, the whole Cu(3) structure is not planar but folded along the line connecting the phenoxo bridging oxygen atoms of the same ligand. Temperature dependence of the magnetic susceptibility of complexes (1)-(5) was measured, showing strong antiferromagnetic interactions between the central and external atoms through the bis(μ-phenoxo) groups. DFT calculations were also performed (a) to support the experimental values of the coupling constant (J(1)) between the nearest-neighbouring copper atoms, (b) to determine the magnitude of the interactions between next-nearest copper(II) atoms (J(2)) and (c) to study magneto-structural correlations for this kind of bis
Differential salt-induced dissociation of the p53 protein complexes with circular and linear plasmid DNA substrates suggest involvement of a sliding mechanism.
Šebest, Peter; Brázdová, Marie; Fojta, Miroslav; Pivoňková, Hana
A study of the effects of salt conditions on the association and dissociation of wild type p53 with different ~3 kbp long plasmid DNA substrates (supercoiled, relaxed circular and linear, containing or lacking a specific p53 binding site, p53CON) using immunoprecipitation at magnetic beads is presented. Salt concentrations above 200 mM strongly affected association of the p53 protein to any plasmid DNA substrate. Strikingly different behavior was observed when dissociation of pre-formed p53-DNA complexes in increased salt concentrations was studied. While contribution from the p53CON to the stability of the p53-DNA complexes was detected between 100 and 170 mM KCl, p53 complexes with circular DNAs (but not linear) exhibited considerable resistance towards salt treatment for KCl concentrations as high as 2 M provided that the p53 basic C-terminal DNA binding site (CTDBS) was available for DNA binding. On the contrary, when the CTDBS was blocked by antibody used for immunoprecipitation, all p53-DNA complexes were completely dissociated from the p53 protein in KCl concentrations≥200 mM under the same conditions. These observations suggest: (a) different ways for association and dissociation of the p53-DNA complexes in the presence of the CTDBS; and (b) a critical role for a sliding mechanism, mediated by the C-terminal domain, in the dissociation process.
A Non-Linear Mixed Spectral Finite-Difference 3-D Model of Planetary Boundary-Layer Flow over Complex Terrain and Its Application
NASA Astrophysics Data System (ADS)
Weng, W.; Taylor, P. A.
Based on the early linear and Non-Linear Mixed Spectral Finite-Difference (MSFD and NLMSFD) models, a 3-D non-linear model of planetary boundary-layer flow (NLMSFD-PBL) was developed to study neutral PBL flow over complex terrain. The model assumes upwind or zero-order profiles of mean and turbulence variables about which perturbation quantities are calculated due to the effects of the terrain. In early models, the mean zero-order wind profile was assumed to be a simple logarithmic surface-layer profile and Reynolds stresses were constant throughout the depth of the model domain. This formally limits the applications of model to the surface-layer flow. The new model utilizes the results of early 1-D planetary boundary layer model of Weng and Taylor as the zero-order or upstream profiles of mean and turbulent quantities. The limitations associated with the original MSFD/NLMSFD model (e.g. logarithmic wind profile and constant shear stress layer) are relaxed. The effect of earth's rotation is also included in the model. Model results for planetary boundary-layer flow over complex terrain are discussed, particularly, the flow over Askervein hill - the site of a detailed and much referenced field study of flow over hills in the 1980s. This type of modelling of flow over complex terrain has important applications for wind energy resource assessment and wind farm design.
Molecular properties of a bis(ketoiminato)-bis(tricarbonyliron) complex obtained by symmetric cleavage from acetophenone azine. Idealized symmetry in anti and syn isomers studied by X-ray diffraction, NMR and density functional theory
NASA Astrophysics Data System (ADS)
Zimniak, Andrzej; Bakalarski, Grzegorz
Distinct anti and syn isomers of the bis(μ 2-acetophenoniminato)-bis(tricarbonyliron) obtained from iron dodecacarbonyl and 1,4-dimethyl-1,4-diphenyl-2,3-diazabuta-1,3-diene by symmetric cleavage of the azine have been compared in terms of molecular deviations from symmetry. The study was carried out by the analysis of intra- and intermolecular close contacts in crystals, quantum chemical DFT calculations for the isolated molecules and by NMR in solution. In the crystalline state the intramolecular contacts and also the symmetry perturbations were more strongly expressed in the syn form as compared with anti, and the same relation was perceived in the DFT-optimized single molecules. However, in solution only symmetric conformations were observed for both isomers anti and syn by 1H and 13C NMR at room temperature and at -70°C.
Characterization of Generalized Young Measures Generated by Symmetric Gradients
NASA Astrophysics Data System (ADS)
De Philippis, Guido; Rindler, Filip
This work establishes a characterization theorem for (generalized) Young measures generated by symmetric derivatives of functions of bounded deformation (BD) in the spirit of the classical Kinderlehrer-Pedregal theorem. Our result places such Young measures in duality with symmetric-quasiconvex functions with linear growth. The "local" proof strategy combines blow-up arguments with the singular structure theorem in BD (the analogue of Alberti's rank-one theorem in BV), which was recently proved by the authors. As an application of our characterization theorem we show how an atomic part in a BD-Young measure can be split off in generating sequences.
On the optimum bit orders with respect to the state complexity of trellis diagrams for binary linear codes
NASA Technical Reports Server (NTRS)
Kasami, Tadao; Takata, Toyoo; Fujiwara, Toru; Lin, Shu
It was shown earlier that for a punctured Reed-Muller (RM) code or a primitive BCH code, which contains a punctured RM code of the same minimum distance as a large subcode, the state complexity of the minimal trellis diagram is much greater than that for an equivalent code obtained by a proper permutation on the bit positions. To find a permutation on the bit positions for a given code that minimizes the state complexity of its minimal trellis diagram is an interesting and challenging problem. This permutation problem is related to the generalized Hamming weight hierarchy of a code, and is shown that for RM codes, the standard binary order of bit positions is optimum at every bit position with respect to the state complexity of a minimal trellis diagram by using a theorem due to Wei. The state complexity of trellis diagram for the extended and permuted (64, 24) BCH code is discussed.
Self-assembly behavior of a linear-star supramolecular amphiphile based on host-guest complexation.
Wang, Juan; Wang, Xing; Yang, Fei; Shen, Hong; You, Yezi; Wu, Decheng
A star polymer, β-cyclodextrin-poly(l-lactide) (β-CD-PLLA), and a linear polymer, azobenzene-poly(ethylene glycol) (Azo-PEG), could self-assemble into a supramolecular amphiphilic copolymer (β-CD-PLLA@Azo-PEG) based on the host-guest interaction between β-CD and azobenzene moieties. This linear-star supramolecular amphiphilic copolymer further self-assembled into a variety of morphologies, including sphere-like micelle, carambola-like micelle, naan-like micelle, shuttle-like lamellae, tube-like fiber, and random curled-up lamellae, by tuning the length of hydrophilic or hydrophobic chains. The variation of morphology was closely related to the topological structure and block ratio of the supramolecular amphiphiles. These self-assembly structures could disassemble upon an ultraviolet (UV) light irradiation.
Synthesis and spectral studies on metal complexes of s-triazine based ligand and non linear optical properties
NASA Astrophysics Data System (ADS)
Shanmugakala, R.; Tharmaraj, P.; Sheela, C. D.
A series of transition metal complexes of type [ML] and [ML2]Cl2 (where M = Cu(II), Ni(II), Co(II) have synthesized from 2-phenylamino-4,6-dichloro-s-triazine and 3,5-dimethyl pyrazole; their characteristics have been investigated by means of elemental analyses, magnetic susceptibility, molar conductance, IR, UV-Vis, Mass, NMR and ESR spectra. The electrochemical behavior of copper(II) complexes we have studied, by using cyclic voltammetry. The ESR spectra of copper(II) complexes are recorded at 300 K and 77 K and their salient features are appropriately reported. Spectral datas, we found, show that the ligand acts as a neutral tridentate, and coordinates through the triazine ring nitrogen and pyrazolyl ring nitrogen atoms to the metal ion. Evident from our findings, the metal(II) complexes of [ML] type exhibit square pyramidal geometry, and that of [ML2]Cl2 exhibit octahedral geometry. The in vitro antimicrobial activities of the ligand and its complexes are evaluated against Bacillus subtilis, Micrococcus luteus, Staphylococcus aureus, Staphylococcus epidermidis, Streptococcus mutans, Escherichia coli, Enterobacter aerogenes, Klebsiella pneumoniae, Proteus vulgaris, Cryptococcus neoformans, Pseudomonas aeruginosa, Salmonella typhi, Serratia marcescens, Shigella flexneri, Vibrio cholera, Vibris parahaemolyticus, Aspergillus niger, Candida albicans and Penicillium oxalicum by well-diffusion method. The second harmonic generation efficiency of the ligand and its complexes are determined and compared with urea and KDP.
On the Huygens principle for bianisotropic mediums with symmetric permittivity and permeability dyadics
NASA Astrophysics Data System (ADS)
Faryad, Muhammad; Lakhtakia, Akhlesh
Mathematical statements of the Huygens principle relate the electric and magnetic field phasors at an arbitrary location in a source-free region enclosed by a surface to the tangential components of the electric and magnetic field phasors over that surface, via the dyadic Green functions applicable to the linear homogeneous medium occupying that region. We have mathematically formulated the Huygens principle for the electric and magnetic field phasors when the permittivity and permeability dyadics of the medium are symmetric, the symmetric parts of the two magnetoelectric dyadics of the medium are negative of each other, and both magnetoelectric dyadics also contain anti-symmetric terms. We have also formulated the Huygens principle for the electric (resp. magnetic) field phasor in a medium whose permittivity (resp. permeability) is scalar, the permeability (resp. permittivity) is symmetric, the symmetric parts of the two magnetoelectric dyadics reduce to dissimilar scalars, and anti-symmetric parts of the two magnetoelectric dyadics are identical.
Plane symmetric thin-shell wormholes: Solutions and stability
Lemos, Jose P. S.; Lobo, Francisco S. N.
Using the cut-and-paste procedure, we construct static and dynamic, plane symmetric wormholes by surgically grafting together two spacetimes of plane symmetric vacuum solutions with a negative cosmological constant. These plane symmetric wormholes can be interpreted as domain walls connecting different universes, having planar topology, and upon compactification of one or two coordinates, cylindrical topology or toroidal topology, respectively. A stability analysis is carried out for the dynamic case by taking into account specific equations of state, and a linearized stability analysis around static solutions is also explored. It is found that thin-shell wormholes made of a dark energy fluid or of a cosmological constant fluid are stable, while thin-shell wormholes made of phantom energy are unstable.
SYMTRAN - A Time-dependent Symmetric Tandem Mirror Transport Code
Hua, D; Fowler, T
A time-dependent version of the steady-state radial transport model in symmetric tandem mirrors in Ref. [1] has been coded up and first tests performed. Our code, named SYMTRAN, is an adaptation of the earlier SPHERE code for spheromaks, now modified for tandem mirror physics. Motivated by Post's new concept of kinetic stabilization of symmetric mirrors, it is an extension of the earlier TAMRAC rate-equation code omitting radial transport [2], which successfully accounted for experimental results in TMX. The SYMTRAN code differs from the earlier tandem mirror radial transport code TMT in that our code is focused on axisymmetric tandem mirrors and classical diffusion, whereas TMT emphasized non-ambipolar transport in TMX and MFTF-B due to yin-yang plugs and non-symmetric transitions between the plugs and axisymmetric center cell. Both codes exhibit interesting but different non-linear behavior.
A reconfigurable parity-time symmetric meta-atom for polarization and phase control (Conference Presentation)
NASA Astrophysics Data System (ADS)
Baum, Brian; Dionne, Jennifer; Alaeian, Hadiseh; Jankovic, Vladan; Lawrence, Mark
Metasurfaces offer exotic optical properties, which often originate from carefully designed material geometries. With locked geometries, these metasurfaces are difficult or impossible to change post-fabrication. Here, we theoretically explore a nano-scale coaxial structure capable of adjustably manipulating the polarization, phase, and spatial distribution of light through the introduction of parity-time (PT) symmetric perturbations. Coaxial waveguides possess degenerate modes, corresponding to different orbital angular momentum (OAM) states. The degeneracy of OAM modes can be lifted through the introduction of any non-zero amount of gain and loss into the structure in a way that matches the azimuthal periodicity of the degenerate mode pair. New hybrid complex conjugate modes are created which lose their pure OAM nature and are either amplifying or lossy. We confirm this behavior using both a Hamiltonian formulation and degenerate perturbation theory, and propose this selective excitation and absorption scheme as a new method of filtering for mode division multiplexing in on-chip nanophotonic systems. In addition to the creation of new hybrid modes, we show that these PT-symmetric perturbations in coaxial apertures are capable of converting incident circularly polarized light into linearly polarized light with unity efficiency. Further, due to the localization of field intensity within the gain sections, it is possible to rotate linear polarization and induce up to a pi-phase shift. We describe how our PT-symmetric coaxial aperture could function as a reconfigurable meta-atom for phase, amplitude, and polarization controlled meta-surfaces, and discuss routes toward unity-efficiency, reconfigurable holography.
Linearized gravity in terms of differential forms
NASA Astrophysics Data System (ADS)
Baykal, Ahmet; Dereli, Tekin
A technique to linearize gravitational field equations is developed in which the perturbation metric coefficients are treated as second rank, symmetric, 1-form fields belonging to the Minkowski background spacetime by using the exterior algebra of differential forms.
Linear units improve articulation between social and physical constructs: An example from caregiver parameterization for children supported by complex medical technologies
NASA Astrophysics Data System (ADS)
Bezruczko, N.; Stanley, T.; Battle, M.; Latty, C.
Despite broad sweeping pronouncements by international research organizations that social sciences are being integrated into global research programs, little attention has been directed toward obstacles blocking productive collaborations. In particular, social sciences routinely implement nonlinear, ordinal measures, which fundamentally inhibit integration with overarching scientific paradigms. The widely promoted general linear model in contemporary social science methods is largely based on untransformed scores and ratings, which are neither objective nor linear. This issue has historically separated physical and social sciences, which this report now asserts is unnecessary. In this research, nonlinear, subjective caregiver ratings of confidence to care for children supported by complex, medical technologies were transformed to an objective scale defined by logits (N=70). Transparent linear units from this transformation provided foundational insights into measurement properties of a social- humanistic caregiving construct, which clarified physical and social caregiver implications. Parameterized items and ratings were also subjected to multivariate hierarchical analysis, then decomposed to demonstrate theoretical coherence (R2 >.50), which provided further support for convergence of mathematical parameterization, physical expectations, and a social-humanistic construct. These results present substantial support for improving integration of social sciences with contemporary scientific research programs by emphasizing construction of common variables with objective, linear units.
Synthesis of a symmetrical dithiirane
Allakverdiev, M.A.; Farzaliev, V.M.; Mamedov, C.I.
The reaction of p-xylene with epichlorohydrin in the presence of aluminum chloride gave 1,4-dimethyl-2,5-bis(1-chloro-2-hydroxypropyl) benzene, which serves as the starting compound for the synthesis of the corresponding symmetrical dithiirane.
Prior Distributions on Symmetric Groups
ERIC Educational Resources Information Center
Gupta, Jayanti; Damien, Paul
Fully and partially ranked data arise in a variety of contexts. From a Bayesian perspective, attention has focused on distance-based models; in particular, the Mallows model and extensions thereof. In this paper, a class of prior distributions, the "Binary Tree," is developed on the symmetric group. The attractive features of the class are: it…
Supercritical Flow Past Symmetrical Airfoils.
about quasi-elliptic airfoil sections. The method was later extended by Boerstoel [1967] to present a catalog of solutions for certain body shapes. Bauer...Lecture Notes in Economics and Mathematical Systems, Springer- Verlag, New York, 1972. Boerstoel , J. W., "A Survey of Symmetrical Transonic Potential
Particle-vortex symmetric liquid
NASA Astrophysics Data System (ADS)
Mulligan, Michael
We introduce an effective theory with manifest particle-vortex symmetry for disordered thin films undergoing a magnetic field-tuned superconductor-insulator transition. The theory may enable one to access both the critical properties of the strong-disorder limit, which has recently been confirmed by Breznay et al. [Proc. Natl. Acad. Sci. USA 113, 280 (2016), 10.1073/pnas.1522435113] to exhibit particle-vortex symmetric electrical response, and the nearby metallic phase discovered earlier by Mason and Kapitulnik [Phys. Rev. Lett. 82, 5341 (1999), 10.1103/PhysRevLett.82.5341] in less disordered samples. Within the effective theory, the Cooper-pair and field-induced vortex degrees of freedom are simultaneously incorporated into an electrically neutral Dirac fermion minimally coupled to a (emergent) Chern-Simons gauge field. A derivation of the theory follows upon mapping the superconductor-insulator transition to the integer quantum Hall plateau transition and the subsequent use of Son's particle-hole symmetric composite Fermi liquid. Remarkably, particle-vortex symmetric response does not require the introduction of disorder; rather, it results when the Dirac fermions exhibit vanishing Hall effect. The theory predicts approximately equal (diagonal) thermopower and Nernst signal with a deviation parameterized by the measured electrical Hall response at the symmetric point.
Thermophoresis of Axially Symmetric Bodies
Sweden Abstract. Thermophoresis of axially symmetric bodies is investigated to first order in the Knudsen-mimber, Kn. The study is made in the limit...derived. Asymptotic solutions are studied. INTRODUCTION Thermophoresis as a phenomenon has been known for a long time, and several authors have approached
A symmetric bipolar nebula around MWC 922.
Tuthill, P G; Lloyd, J P
We report regular and symmetric structure around dust-enshrouded Be star MWC 922 obtained with infrared imaging. Biconical lobes that appear nearly square in aspect, forming this "Red Square" nebula, are crossed by a series of rungs that terminate in bright knots or "vortices," and an equatorial dark band crossing the core delimits twin hyperbolic arcs. The intricate yet cleanly constructed forms that comprise the skeleton of the object argue for minimal perturbation from global turbulent or chaotic effects. We also report the presence of a linear comb structure, which may arise from optically projected shadows of a periodic feature in the inner regions, such as corrugations in the rim of a circumstellar disk. The sequence of nested polar rings draws comparison with the triple-ring system seen around the only naked-eye supernova in recent history: SN1987A.
PEP-FOLD3: faster de novo structure prediction for linear peptides in solution and in complex
Lamiable, Alexis; Thévenet, Pierre; Rey, Julien; Vavrusa, Marek; Derreumaux, Philippe; Tufféry, Pierre
Structure determination of linear peptides of 5–50 amino acids in aqueous solution and interacting with proteins is a key aspect in structural biology. PEP-FOLD3 is a novel computational framework, that allows both (i) de novo free or biased prediction for linear peptides between 5 and 50 amino acids, and (ii) the generation of native-like conformations of peptides interacting with a protein when the interaction site is known in advance. PEP-FOLD3 is fast, and usually returns solutions in a few minutes. Testing PEP-FOLD3 on 56 peptides in aqueous solution led to experimental-like conformations for 80% of the targets. Using a benchmark of 61 peptide–protein targets starting from the unbound form of the protein receptor, PEP-FOLD3 was able to generate peptide poses deviating on average by 3.3Å from the experimental conformation and return a native-like pose in the first 10 clusters for 52% of the targets. PEP-FOLD3 is available at http://bioserv.rpbs.univ-paris-diderot.fr/services/PEP-FOLD3. PMID:27131374
Hepatitis B Virus-Induced Parkin-Dependent Recruitment of Linear Ubiquitin Assembly Complex (LUBAC) to Mitochondria and Attenuation of Innate Immunity
Khan, Mohsin; Syed, Gulam Hussain; Kim, Seong-Jun; Siddiqui, Aleem
Hepatitis B virus (HBV) suppresses innate immune signaling to establish persistent infection. Although HBV is a DNA virus, its pre-genomic RNA (pgRNA) can be sensed by RIG-I and activates MAVS to mediate interferon (IFN) λ synthesis. Despite of the activation of RIG-I-MAVS axis by pgRNA, the underlying mechanism explaining how HBV infection fails to induce interferon-αβ (IFN) synthesis remained uncharacterized. We demonstrate that HBV induced parkin is able to recruit the linear ubiquitin assembly complex (LUBAC) to mitochondria and abrogates IFN β synthesis. Parkin interacts with MAVS, accumulates unanchored linear polyubiquitin chains on MAVS via LUBAC, to disrupt MAVS signalosome and attenuate IRF3 activation. This study highlights the novel role of parkin in antiviral signaling which involves LUBAC being recruited to the mitochondria. These results provide avenues of investigations on the role of mitochondrial dynamics in innate immunity. PMID:27348524
Synthesis, structure, catalytic and calculated non-linear optical properties of cis- and trans-, mer-chlorobis(triphenyl phosphine/triphenyl arsine)-dipicolinato ruthenium III complexes
NASA Astrophysics Data System (ADS)
Trivedi, Manoj; Nagarajan, R.; Kumar, Abhinav; Singh, Narendra K.; Rath, Nigam P.
The new mononuclear Ru III complexes cis-, mer-[Ru( k3-dipic)(EPh 3) 2Cl]·2H 2O (E = P ( 1), As ( 2)), (L = 2,6-pyridyldicarboxylate; dipic) have been synthesized and characterized. The X-ray crystal structure of 1 reveals that the coordination geometry around the Ru III center is distorted octahedral in which three sites are occupied by tridentate dipic ligand and remaining three sites are occupied by two mutually cis triphenyl phosphine ligands and one chloride ions. In chloroform solvent, cis-, mer-[Ru( k3-dipic)(EPh 3) 2Cl]·2H 2O (E = P ( 1), As ( 2)) complexes undergoes thermal rearrangement to more stable trans-, mer-[Ru( k3-dipic)(EPh 3) 2Cl] (E = P( 3), As( 4)) complexes. Complexes 1 and 2 show rhombic EPR spectral features, while complex 3 and 4 show tetragonal distortion. The new Ru III complexes 1 and 2 display both Ru III-Ru II reduction and Ru III-Ru IV oxidation processes. These geometric isomers exhibit textbook differences both in spectroscopic as well as structural properties in the solid state. The new complexes 1 and 2 were found to catalyze the oxidation of alcohols to carbonyl derivatives using N-methyl morpholine- N-oxide as co-oxidant. The first static hyperpolarizability ( β) for all of the complexes have been investigated by density functional theory (DFT) which suggests β value increases from trans to cis form. Also, the solvent-induced effects on the non-linear optical properties (NLO) were studied by using self-consistent reaction field (SCRF) method. As the solvent polarity increases, the β value increases monotonically. The electronic absorption bands of 1 have been assigned by time dependent density functional theory (TD-DFT).
Nonlinear localized modes in PT-symmetric optical media with competing gain and loss
Midya, Bikashkali; Roychoudhury, Rajkumar
The existence and stability of the nonlinear spatial localized modes are investigated in parity-time symmetric optical media characterized by a generic complex hyperbolic refractive index distribution with competing gain and loss profile. The exact analytical expression of the localized modes are found for all values of the competing parameter and in the presence of both the self-focusing and self-defocusing Kerr nonlinearity. The effects of competing gain/loss profile on the stability structure of these localized modes are discussed with the help of linear stability analysis followed by the direct numerical simulation of the governing equation. The spatial localized modes in two-dimensional geometry as well as the transverse power-flow density associated with these localized modes are also examined. -- Highlights: • Existence of localized modes is investigated in PT-symmetric complex potentials. • Exact analytical expression of the localized modes is obtained. • Effect of gain/loss profile on the stability of these localized modes is discussed. • Localized modes in 2D and associated transverse power-flow density are also examined.
Thin-shell wormholes: Linearization stability
Poisson, E.; Visser, M.
The class of spherically symmetric thin-shell wormholes provides a particularly elegant collection of exemplars for the study of traversable Lorentzian wormholes. In the present paper we consider linearized (spherically symmetric) perturbations around some assumed static solution of the Einstein field equations. This permits us to relate stability issues to the (linearized) equation of state of the exotic matter which is located at the wormhole throat. {copyright} 1995 The American Physical Society.
A free-knot spline modeling framework for piecewise linear logistic regression in complex samples with body mass index and mortality as an example.
Keith, Scott W; Allison, David B
This paper details the design, evaluation, and implementation of a framework for detecting and modeling nonlinearity between a binary outcome and a continuous predictor variable adjusted for covariates in complex samples. The framework provides familiar-looking parameterizations of output in terms of linear slope coefficients and odds ratios. Estimation methods focus on maximum likelihood optimization of piecewise linear free-knot splines formulated as B-splines. Correctly specifying the optimal number and positions of the knots improves the model, but is marked by computational intensity and numerical instability. Our inference methods utilize both parametric and nonparametric bootstrapping. Unlike other nonlinear modeling packages, this framework is designed to incorporate multistage survey sample designs common to nationally representative datasets. We illustrate the approach and evaluate its performance in specifying the correct number of knots under various conditions with an example using body mass index (BMI; kg/m(2)) and the complex multi-stage sampling design from the Third National Health and Nutrition Examination Survey to simulate binary mortality outcomes data having realistic nonlinear sample-weighted risk associations with BMI. BMI and mortality data provide a particularly apt example and area of application since BMI is commonly recorded in large health surveys with complex designs, often categorized for modeling, and nonlinearly related to mortality. When complex sample design considerations were ignored, our method was generally similar to or more accurate than two common model selection procedures, Schwarz's Bayesian Information Criterion (BIC) and Akaike's Information Criterion (AIC), in terms of correctly selecting the correct number of knots. Our approach provided accurate knot selections when complex sampling weights were incorporated, while AIC and BIC were not effective under these conditions.
Non-Real Eigenvalues for PT-Symmetric Double Wells
NASA Astrophysics Data System (ADS)
Benbernou, Amina; Boussekkine, Naima; Mecherout, Nawal; Ramond, Thierry; Sjöstrand, Johannes
We study small, PT-symmetric perturbations of self-adjoint double-well Schrödinger operators in dimension {n≥ 1}. We prove that the eigenvalues stay real for a very small perturbation, then bifurcate to the complex plane as the perturbation gets stronger.
Copper(II) complex formation with a linear peptide encompassing the putative cell binding site of angiogenin.
La Mendola, Diego; Magrì, Antonio; Vagliasindi, Laura I; Hansson, Örjan; Bonomo, Raffaele P; Rizzarelli, Enrico
Angiogenin is one of the more potent angiogenic factors known, whose activity may be affected by the presence of copper ions. Copper(II) complexes with the peptides encompassing the putative endothelial cell binding domain of angiogenin, Ac-KNGNPHREN-NH(2) and Ac-PHREN-NH(2), have been characterized by potentiometric, UV-vis, CD and EPR spectroscopic methods. The coordination features of all the copper complex species derived by both peptides are practically the same, as predictable because of the presence of a proline residue within their aminoacidic sequence. In particular, Ac-PHREN-NH(2) is really the aminoacidic sequence involved in the binding to copper(II). Thermodynamic and spectroscopic evidence are given that side chain oxygen donor atom of glutamyl residue is involved in the copper binding up to physiological pH. EPR parameters suggest that the carboxylate group is still involved also in the predominant species [Cu(L)H(-2)], the metal coordination environment being probably formed by N(Im), 2N(-), H(2)O in equatorial plane and an oxygen atom from COO(-) in apical position, or vice versa, with the carboxylate oxygen atom in the copper coordination plane and the water molecule confined to one of the apical positions. Moreover, the comparison with the thermodynamic and spectroscopic results in the case of the copper(ii) complex species formed by the single point mutated peptide, Ac-PHRQN-NH(2), provides further evidence of the presence of carboxylate oxygen atom in the copper coordination sphere.
Synthesis of molecular wires of linear and branched bis(terpyridine)-complex oligomers and electrochemical observation of through-bond redox conduction.
Nishimori, Yoshihiko; Kanaizuka, Katsuhiko; Murata, Masaki; Nishihara, Hiroshi
Films of linear and branched oligomer wires of Fe(tpy)2 (tpy = 2,2':6',2''-terpyridine) were constructed on a gold-electrode surface by the interfacial stepwise coordination method, in which a surface-anchoring ligand, (tpy-C6H4N=NC6H4-S)2 (1), two bridging ligands, 1,4-(tpy)2C6H4 (3) and 1,3,5-(C[triple bond]C-tpy)3C6H3 (4), and metal ions were used. The quantitative complexation of the ligands and Fe(II) ions was monitored by electrochemical measurements in up to eight complexation cycles for linear oligomers of 3 and in up to four cycles for branched oligomers of 4. STM observation of branched oligomers at low surface coverage showed an even distribution of nanodots of uniform size and shape, which suggests the quantitative formation of dendritic structures. The electron-transport mechanism and kinetics for the redox reaction of the films of linear and branched oligomer wires were analyzed by potential-step chronoamperometry (PSCA). The unique current-versus-time behavior observed under all conditions indicates that electron conduction occurs not by diffusional motion but by successive electron hopping between neighboring redox sites within a molecular wire. Redox conduction in a single molecular wire in a redox-polymer film has not been reported previously. The analysis provided the rate constant for electron transfer between the electrode and the nearest redox-complex moiety, k1 (s(-1)), as well as that for intrawire electron transfer between neighboring redox-complex moieties, k2 (cm2 mol(-1) s(-1)). The strong effect of the electrolyte concentration on both k1 and k2 indicates that the counterion motion limits the electron-hopping rate at lower electrolyte concentrations. Analysis of the dependence of k1 and k2 on the potential gave intrinsic kinetic parameters without overpotential effects: (k1(0) = 110 s(-1), k2(0) = 2.6x10(12) cm2 mol(-1) s(-1) for [n Fe3], and k1(0) = 100 s(-1), k2(0) = 4.1x10(11) cm2 mol(-1) s(-1) for [n Fe4] (n = number of complexation
Geometry and Symmetric Coherent States of Three Qubits Systems
NASA Astrophysics Data System (ADS)
Guo, Xiao-Kan
In this paper, we first generalize the previous results that relate 1- and 2-qubit geometries to complex and quaternionic Möbius transformations respectively, to the case of 3-qubit states under octonionic Möbius transformations. This completes the correspondence between the qubit geometries and the four normed division algebras. Thereby, new systems of symmetric coherent states with 2 and 3 qubits can be constructed by mapping the spin coherent states to their antipodal symmetric ponits on the generalized Bloch spheres via Möbius transformations in corresponding dimensions. Finally, potential applications of the normed division algebras in physics are discussed.
Bunch-Kaufman factorization for real symmetric indefinite banded matrices
NASA Technical Reports Server (NTRS)
Jones, Mark T.; Patrick, Merrell L.
The Bunch-Kaufman algorithm for factoring symmetric indefinite matrices was rejected for banded matrices because it destroys the banded structure of the matrix. Herein, it is shown that for a subclass of real symmetric matrices which arise in solving the generalized eigenvalue problem using Lanczos's method, the Bunch-Kaufman algorithm does not result in major destruction of the bandwidth. Space time complexities of the algorithm are given and used to show that the Bunch-Kaufman algorithm is a significant improvement over LU factorization.
Reversible Switching between Nonquenched and Quenched States in Nanoscale Linear Arrays of Plant Light-Harvesting Antenna Complexes
A simple and robust nanolithographic method that allows sub-100 nm chemical patterning on a range of oxide surfaces was developed in order to fabricate nanoarrays of plant light-harvesting LHCII complexes. The site-specific immobilization and the preserved functionality of the LHCII complexes were confirmed by fluorescence emission spectroscopy. Nanopatterned LHCII trimers could be reversibly switched between fluorescent and quenched states by controlling the detergent concentration in the imaging buffer. A 3-fold quenching of the average fluorescence intensity was accompanied by a decrease in the average (amplitude-weighted) fluorescence lifetime from approximately 2.24 ns to approximately 0.4 ns, attributed to the intrinsic ability of LHCII to switch between fluorescent and quenched states upon changes in its conformational state. The nanopatterning methodology was extended by immobilizing a second protein, the enhanced green fluorescent protein (EGFP), onto LHCII-free areas of the chemically patterned surfaces. This very simple surface chemistry, which allows simultaneous selective immobilization and therefore sorting of the two types of protein molecules on the surface, is a key underpinning step toward the integration of LHCII into switchable biohybrid antenna constructs. PMID:24988144
Working With Socially and Medically Complex Patients: When Care Transitions Are Circular, Overlapping, and Continual Rather Than Linear and Finite.
Roberts, Shauna R; Crigler, Jane; Ramirez, Cristina; Sisco, Deborah; Early, Gerald L
The care coordination program described here evolved from 5 years of trial and learning related to how to best serve our high-cost, high-utilizing, chronically ill, urban core patient population. In addition to medical complexity, they have daily challenges characteristic of persons served by Safety-Net health systems. Many have unstable health insurance status. Others have insecure housing. A number of patients have a history of substance use and mental illness. Many have fractured social supports. Although some of the best-known care transition models have been successful in reducing rehospitalizations and cost among patients studied, these models were developed for a relatively high functioning patient population with social support. We describe a successful approach targeted at working with patients who require a more intense and lengthy care coordination intervention to self-manage and reduce the cost of caring for their medical conditions. Using a diverse team and a set of replicable processes, we have demonstrated statistically significant reduction in the use of hospital and emergency services. Our intervention leverages the strengths and resilience of patients, focuses on trust and self-management, and targets heterogeneous "high-utilizer" patients with medical and social complexity.
Spatiotemporal localized modes in PT-symmetric optical media
NASA Astrophysics Data System (ADS)
Wang, Yue-Yue; Dai, Chao-Qing; Wang, Xiao-Gang
We firstly obtain spatiotemporal localized mode solutions of a (3+1)-dimensional nonlinear Schrödinger equation in PT-symmetric potentials, and then discuss the linear stability of LMs, which are also tested by means of direct simulations. Moreover, phase switches and transverse power-flow density associated with these localized modes have also been examined. At last, we investigate the dynamical behaviors of spatiotemporal LMs in three kinds of inhomogeneous media.
Linear coding of complex sound spectra by discharge rate in neurons of the medial nucleus of the trapezoid body (MNTB) and its inputs
Koka, Kanthaiah; Tollin, Daniel J.
The interaural level difference (ILD) cue to sound location is first encoded in the lateral superior olive (LSO). ILD sensitivity results because the LSO receives excitatory input from the ipsilateral cochlear nucleus and inhibitory input indirectly from the contralateral cochlear nucleus via glycinergic neurons of the ipsilateral medial nucleus of the trapezoid body (MNTB). It is hypothesized that in order for LSO neurons to encode ILDs, the sound spectra at both ears must be accurately encoded via spike rate by their afferents. This spectral-coding hypothesis has not been directly tested in MNTB, likely because MNTB neurons have been mostly described and studied recently in regards to their abilities to encode temporal aspects of sounds, not spectral. Here, we test the hypothesis that MNTB neurons and their inputs from the cochlear nucleus and auditory nerve code sound spectra via discharge rate. The Random Spectral Shape (RSS) method was used to estimate how the levels of 100-ms duration spectrally stationary stimuli were weighted, both linearly and non-linearly, across a wide band of frequencies. In general, MNTB neurons, and their globular bushy cell inputs, were found to be well-modeled by a linear weighting of spectra demonstrating that the pathways through the MNTB can accurately encode sound spectra including those resulting from the acoustical cues to sound location provided by head-related directional transfer functions (DTFs). Together with the anatomical and biophysical specializations for timing in the MNTB-LSO complex, these mechanisms may allow ILDs to be computed for complex stimuli with rapid spectrotemporally-modulated envelopes such as speech and animal vocalizations and moving sound sources. PMID:25565971
Canonical distributions on Riemannian homogeneous k-symmetric spaces
NASA Astrophysics Data System (ADS)
Balashchenko, Vitaly V.
It is known that distributions generated by almost product structures are applicable, in particular, to some problems in the theory of Monge-Ampère equations. In this paper, we characterize canonical distributions defined by canonical almost product structures on Riemannian homogeneous k-symmetric spaces in the sense of types AF (anti-foliation), F (foliation), TGF (totally geodesic foliation). Algebraic criteria for all these types on k-symmetric spaces of orders k = 4, 5, 6 were obtained. Note that canonical distributions on homogeneous k-symmetric spaces are closely related to special canonical almost complex structures and f-structures, which were recently applied by I. Khemar to studying elliptic integrable systems.
Accessing the exceptional points of parity-time symmetric acoustics
Shi, Chengzhi; Dubois, Marc; Chen, Yun; Cheng, Lei; Ramezani, Hamidreza; Wang, Yuan; Zhang, Xiang
Parity-time (PT) symmetric systems experience phase transition between PT exact and broken phases at exceptional point. These PT phase transitions contribute significantly to the design of single mode lasers, coherent perfect absorbers, isolators, and diodes. However, such exceptional points are extremely difficult to access in practice because of the dispersive behaviour of most loss and gain materials required in PT symmetric systems. Here we introduce a method to systematically tame these exceptional points and control PT phases. Our experimental demonstration hinges on an active acoustic element that realizes a complex-valued potential and simultaneously controls the multiple interference in the structure. The manipulation of exceptional points offers new routes to broaden applications for PT symmetric physics in acoustics, optics, microwaves and electronics, which are essential for sensing, communication and imaging. PMID:27025443
Symmetric quadratic Hamiltonians with pseudo-Hermitian matrix representation
Fernández, Francisco M.
We prove that any symmetric Hamiltonian that is a quadratic function of the coordinates and momenta has a pseudo-Hermitian adjoint or regular matrix representation. The eigenvalues of the latter matrix are the natural frequencies of the Hamiltonian operator. When all the eigenvalues of the matrix are real, then the spectrum of the symmetric Hamiltonian is real and the operator is Hermitian. As illustrative examples we choose the quadratic Hamiltonians that model a pair of coupled resonators with balanced gain and loss, the electromagnetic self-force on an oscillating charged particle and an active LRC circuit. -- Highlights: •Symmetric quadratic operators are useful models for many physical applications. •Any such operator exhibits a pseudo-Hermitian matrix representation. •Its eigenvalues are the natural frequencies of the Hamiltonian operator. •The eigenvalues may be real or complex and describe a phase transition.
Linear electric field mass spectrometry
McComas, D.J.; Nordholt, J.E.
A mass spectrometer and methods for mass spectrometry are described. The apparatus is compact and of low weight and has a low power requirement, making it suitable for use on a space satellite and as a portable detector for the presence of substances. High mass resolution measurements are made by timing ions moving through a gridless cylindrically symmetric linear electric field. 8 figs.
Linear electric field mass spectrometry
McComas, David J.; Nordholt, Jane E.
A mass spectrometer and methods for mass spectrometry. The apparatus is compact and of low weight and has a low power requirement, making it suitable for use on a space satellite and as a portable detector for the presence of substances. High mass resolution measurements are made by timing ions moving through a gridless cylindrically symmetric linear electric field.
Nonlinear wave dynamics near phase transition in PT-symmetric localized potentials
NASA Astrophysics Data System (ADS)
Nixon, Sean; Yang, Jianke
Nonlinear wave propagation in parity-time symmetric localized potentials is investigated analytically near a phase-transition point where a pair of real eigenvalues of the potential coalesce and bifurcate into the complex plane. Necessary conditions for a phase transition to occur are derived based on a generalization of the Krein signature. Using the multi-scale perturbation analysis, a reduced nonlinear ordinary differential equation (ODE) is derived for the amplitude of localized solutions near phase transition. Above the phase transition, this ODE predicts a family of stable solitons not bifurcating from linear (infinitesimal) modes under a certain sign of nonlinearity. In addition, it predicts periodically-oscillating nonlinear modes away from solitons. Under the opposite sign of nonlinearity, it predicts unbounded growth of solutions. Below the phase transition, solution dynamics is predicted as well. All analytical results are compared to direct computations of the full system and good agreement is observed.
On the complex non-linear interaction between bacteria and redox dynamics in sediments and its effects on water quality
NASA Astrophysics Data System (ADS)
Sanchez-Vila, X.; Rubol, S.; Fernandez-Garcia, D.
Despite the fact that the prognoses on the availability of resources related to different climate scenarios have been already formulated, the complex hydrological and biogeochemical reactions taking place in different compartments in natural environmental media are poorly understood, especially regarding the interactions between water bodies, and the reactions taking place at soil-water interfaces. Amongst them, the inter-relationship between hydrology, chemistry and biology has important implications in natural (rivers, lakes) and man-made water facilities (lagoons, artificial recharge pounds, reservoirs, slow infiltration systems, etc). The consequences involve environment, economic, social and health-risk aspects. At the current stage, only limited explanations are available to understand the implications of these relationships on ecosystem services, water quality and water quantity. Therefore, there is an urgent need to seek a full understanding of these physical-biogeochemical processes in water-bodies, sediments and biota and its implications in ecological and health risk. We present a soil column experiment and a mathematical model which aim to study the mutual interplay between water and bacteria activity in porous media, the corresponding dynamics and the feedback on nutrient cycling by using a multidisciplinary approach.
Gómez-Hernández, J Jaime
It is difficult to define complexity in modeling. Complexity is often associated with uncertainty since modeling uncertainty is an intrinsically difficult task. However, modeling uncertainty does not require, necessarily, complex models, in the sense of a model requiring an unmanageable number of degrees of freedom to characterize the aquifer. The relationship between complexity, uncertainty, heterogeneity, and stochastic modeling is not simple. Aquifer models should be able to quantify the uncertainty of their predictions, which can be done using stochastic models that produce heterogeneous realizations of aquifer parameters. This is the type of complexity addressed in this article.
Modeling Symmetric Macromolecular Structures in Rosetta3
DiMaio, Frank; Leaver-Fay, Andrew; Bradley, Phil; Baker, David; André, Ingemar
Symmetric protein assemblies play important roles in many biochemical processes. However, the large size of such systems is challenging for traditional structure modeling methods. This paper describes the implementation of a general framework for modeling arbitrary symmetric systems in Rosetta3. We describe the various types of symmetries relevant to the study of protein structure that may be modeled using Rosetta's symmetric framework. We then describe how this symmetric framework is efficiently implemented within Rosetta, which restricts the conformational search space by sampling only symmetric degrees of freedom, and explicitly simulates only a subset of the interacting monomers. Finally, we describe structure prediction and design applications that utilize the Rosetta3 symmetric modeling capabilities, and provide a guide to running simulations on symmetric systems. PMID:21731614
Linear analysis of a force reflective teleoperator
NASA Technical Reports Server (NTRS)
Biggers, Klaus B.; Jacobsen, Stephen C.; Davis, Clark C.
Complex force reflective teleoperation systems are often very difficult to analyze due to the large number of components and control loops involved. One mode of a force reflective teleoperator is described. An analysis of the performance of the system based on a linear analysis of the general full order model is presented. Reduced order models are derived and correlated with the full order models. Basic effects of force feedback and position feedback are examined and the effects of time delays between the master and slave are studied. The results show that with symmetrical position-position control of teleoperators, a basic trade off must be made between the intersystem stiffness of the teleoperator, and the impedance felt by the operator in free space.
Homogeneous solvation controlled photoreduction of cobalt(III) complexes in aqueous 2-methyl-2-propanol solutions. Linear solvation energy relationship and cyclic voltammetric analyses
NASA Astrophysics Data System (ADS)
Anbalagan, K.; Lydia, I. Sharmila
The effect of solvent participation on the ligand-to-metal charge transfer (LMCT, L → Co III) reduction of the of Co III(en) 2Br(RC 6H 4NH 2) 2+ where R = m-OCH 3, p-F, H, m-CH 3, p-CH 3,p-OC 2H 5 and p-OCH 3 were examined in aqueous 2-methyl-2-propanol (Bu tOH) solutions. The change in the reduction behavior of Co III centre was also examined through cyclic voltammetric studies. The observed reduction in quantum yield due to LMCT excitation can mainly be accounted using linear solvation energy relationship (LSER) comprising model correlation equations. These consist of empirical parameters such as Grunwald-Winstein's solvent ionizing power, Y, Dimroth-Richardt's solvent micro-polarity parameter, ETN, Gutmann's donor number, DN N, along with Kamlet-Taft's solvatochromic parameters (hydrogen bond acceptor acidity/basicity α/ β and solvent dipolarity/polarizability, π*). The origin of solvent effect is found to be due to microscopic interaction between the solvent donor and the nitrogen-bound hydrogen of the ligand. Cyclic voltammograms show an irreversible reduction of Co III in DMF using Glassy Carbon Electrode, GCE, the redox peaks for the aniline complexes appear at -0.20 and 0.525 V. Irradiation of the complexes with UV light ( λ = 254 nm) in binary mixtures produce Co IIaq and the concentration of this species are highly dependent on xalc ( xalc = mole fraction of alcohol). The observed quantum yield (log ΦCo(II)) is found to be linearly related to mole fraction of organic co-solvent added in the mixture, therefore, log ΦCo(II) = 26.41 × 10 -2 when x2 = 0.0094 and 43.75 × 10 -2 when x2 = 0.076 for a typical complex Co III(en) 2Br( p-OCH 3C 6H 4NH 2) 2+ in aqueous 2-methyl-2-propanol at 300 K. Cyclic voltammetry and LSER analyses illustrate the variation of reduction property of Co(III) by the aryl ligand and homogeneous solvation of the excited state of the complex Co III(en) 2Br(RC 6H 4NH 2) 2+ in H 2O/Bu tOH mixtures.
Special symmetric quark mass matrices
NASA Astrophysics Data System (ADS)
Silva-Marcos, J. I.
We give a procedure to construct a special class of symmetric quark mass matrices near the democratic limit of equal Yukawa couplings for each sector. It is shown that within appropriate weak-bases, the requirements of symmetry and arg[det(M)]=0 are very strong conditions, that necessarily lead to a Cabibbo angle given by Vus=sqrt(md/ms), and to Vcb~ms/mb, in first order. In addition, we prove that the recently classified ansätze, which also reproduce these mixing matrix relations, and which were based on the hypothesis of the Universal Strength for Yukawa couplings, where all Yukawa couplings have equal moduli while the flavour dependence is only in their phases, are, in fact, particular cases of the generalized symmetric quark mass matrix ansätze we construct here. In an excellent numerical example, the experimental values on all quark mixings and masses are accommodated, and the CP violation phase parameter is shown to be crucially dependent on the values of mu and Vus.
An iteration for indefinite and non-symmetric systems and its application to the Navier-Stokes equations
Wathen, A.; Golub, G.
A simple fixed point linearisation of the Navier-Stokes equations leads to the Oseen problem which after appropriate discretisation yields large sparse linear systems with coefficient matrices of the form (A B{sup T} B -C). Here A is non-symmetric but its symmetric part is positive definite, and C is symmetric and positive semi-definite. Such systems arise in other situations. In this talk we will describe and present some analysis for an iteration based on an indefinite and symmetric preconditioner of the form (D B{sup T} B -C).
Nonlinear modes in finite-dimensional PT-symmetric systems.
Zezyulin, D A; Konotop, V V
By rearrangements of waveguide arrays with gain and losses one can simulate transformations among parity-time (PT-) symmetric systems not affecting their pure real linear spectra. Subject to such transformations, however, the nonlinear properties of the systems undergo significant changes. On an example of an array of four waveguides described by the discrete nonlinear Schrödinger equation with dissipation and gain, we show that the equivalence of the underlying linear spectra does not imply similarity of the structure or stability of the nonlinear modes in the arrays. Even the existence of one-parametric families of nonlinear modes is not guaranteed by the PT symmetry of a newly obtained system. In addition, the stability is not directly related to the PT symmetry: stable nonlinear modes exist even when the spectrum of the linear array is not purely real. We use a graph representation of PT-symmetric networks allowing for a simple illustration of linearly equivalent networks and indicating their possible experimental design.
PT-symmetric phase in kagome-based photonic lattices.
Chern, Gia-Wei; Saxena, Avadh
The kagome lattice is a two-dimensional network of corner-sharing triangles and is often associated with geometrical frustration. In particular, the frustrated coupling between waveguide modes in a kagome array leads to a dispersionless flat band consisting of spatially localized modes. Here we propose a complex photonic lattice by placing PT-symmetric dimers at the kagome lattice points. Each dimer corresponds to a pair of strongly coupled waveguides. With balanced arrangement of gain and loss on individual dimers, the system exhibits a PT-symmetric phase for finite gain/loss parameter up to a critical value. The beam evolution in this complex kagome waveguide array exhibits a novel oscillatory rotation of optical power along the propagation distance. Long-lived local chiral structures originating from the nearly flat bands of the kagome structure are observed when the lattice is subject to a narrow beam excitation.
Theory of Complex Linear Systems.
realizations, solution of operational differential equations, reachability, controllability, observability, duality, state feedback, assignability, state ... observers , regulators, and stability. A summary of these results is contained in this report. (Author)
Walking dynamics are symmetric (enough)
Ankaralı, M. Mert; Sefati, Shahin; Madhav, Manu S.; Long, Andrew; Bastian, Amy J.; Cowan, Noah J.
Many biological phenomena such as locomotion, circadian cycles and breathing are rhythmic in nature and can be modelled as rhythmic dynamical systems. Dynamical systems modelling often involves neglecting certain characteristics of a physical system as a modelling convenience. For example, human locomotion is frequently treated as symmetric about the sagittal plane. In this work, we test this assumption by examining human walking dynamics around the steady state (limit-cycle). Here, we adapt statistical cross-validation in order to examine whether there are statistically significant asymmetries and, even if so, test the consequences of assuming bilateral symmetry anyway. Indeed, we identify significant asymmetries in the dynamics of human walking, but nevertheless show that ignoring these asymmetries results in a more consistent and predictive model. In general, neglecting evident characteristics of a system can be more than a modelling convenience—it can produce a better model. PMID:26236826
PT -symmetric slowing down of decoherence
NASA Astrophysics Data System (ADS)
Gardas, Bartłomiej; Deffner, Sebastian; Saxena, Avadh
We investigate P T -symmetric quantum systems ultraweakly coupled to an environment. We find that such open systems evolve under P T -symmetric, purely dephasing and unital dynamics. The dynamical map describing the evolution is then determined explicitly using a quantum canonical transformation. Furthermore, we provide an explanation of why P T -symmetric dephasing-type interactions lead to a critical slowing down of decoherence. This effect is further exemplified with an experimentally relevant system, a P T -symmetric qubit easily realizable, e.g., in optical or microcavity experiments.
PT-symmetric slowing down of decoherence
Gardas, Bartlomiej; Deffner, Sebastian; Saxena, Avadh Behari
Here, we invesmore » tigate PT-symmetric quantum systems ultraweakly coupled to an environment. We find that such open systems evolve under PT-symmetric, purely dephasing and unital dynamics. The dynamical map describing the evolution is then determined explicitly using a quantum canonical transformation. Furthermore, we provide an explanation of why PT-symmetric dephasing-type interactions lead to a critical slowing down of decoherence. This effect is further exemplified with an experimentally relevant system, a PT-symmetric qubit easily realizable, e.g., in optical or microcavity experiments.« less
Computing symmetric colorings of the dihedral group
NASA Astrophysics Data System (ADS)
Zelenyuk, Yuliya
A symmetry on a group G is a mapping G ∋ x ↦ gx-1 g ∈ G, where g ∈ G. A subset A ⊆ G is symmetric if it is invariant under some symmetry, that is, A = gA-1g. The notion of symmetry has interesting relations to enumerative combinatorics. A coloring is symmetric if χ(gx-1g) = χ(x) for some g ∈ G. We discuss an approach how to compute the number of symmetric r-colorings for any finite group. Using this approach we derive the formula for the number of symmetric r-colorings of the dihedral group D3.
Drift waves in helically symmetric stellarators
Rafiq, T.; Hegna, C.
The local linear stability of electron drift waves and ion temperature gradient modes (ITG) is investigated in a quasihelically symmetric (QHS) stellarator and a conventional asymmetric (Mirror) stellarator. The geometric details of the different equilibria are emphasized. Eigenvalue equations for the models are derived using the ballooning mode formalism and solved numerically using a standard shooting technique in a fully three-dimensional stellarator configuration. While the eigenfunctions have a similar shape in both magnetic geometries, they are slightly more localized along the field line in the QHS case. The most unstable electron drift modes are strongly localized at the symmetry points (where stellarator symmetry is present) and in the regions where normal curvature is unfavorable and magnitude of the local magnetic shear and magnetic field is minimum. The presence of a large positive local magnetic shear in the bad curvature region is found to be destabilizing. Electron drift modes are found to be more affected by the normal curvature than by the geodesic curvature. The threshold of stability of the ITG modes in terms of {eta}{sub i} is found to be 2/3 in this fluid model consistent with the smallest threshold for toroidal geometry with adiabatic electrons. Optimization to favorable drift wave stability has small field line curvature, short connection lengths, the proper combination of geodesic curvature and local magnetic shear, large values of local magnetic shear, and the compression of flux surfaces in the unfavorable curvature region.
Super Bloch oscillation in a PT symmetric system
NASA Astrophysics Data System (ADS)
Turker, Z.; Yuce, C.
Wannier-Stark ladder in a PT symmetric system is generally complex that leads to amplified/damped Bloch oscillation. We show that a non-amplified wave packet oscillation with very large amplitude can be realized in a non-Hermitian tight binding lattice if certain conditions are satisfied. We show that pseudo PT symmetry guarantees the reality of the quasi energy spectrum in our system.
Stable parity-time-symmetric nonlinear modes and excitations in a derivative nonlinear Schrödinger equation.
Chen, Yong; Yan, Zhenya
The effect of derivative nonlinearity and parity-time-symmetric (PT-symmetric) potentials on the wave propagation dynamics is explored in the derivative nonlinear Schrödinger equation, where the physically interesting Scarf-II and harmonic-Hermite-Gaussian potentials are chosen. We study numerically the regions of unbroken and broken linear PT-symmetric phases and find some stable bright solitons of this model in a wide range of potential parameters even though the corresponding linear PT-symmetric phases are broken. The semielastic interactions between particular bright solitons and exotic incident waves are illustrated such that we find that particular nonlinear modes almost keep their shapes after interactions even if the exotic incident waves have evidently been changed. Moreover, we exert the adiabatic switching on PT-symmetric potential parameters such that a stable nonlinear mode with the unbroken linear PT-symmetric phase can be excited to another stable nonlinear mode belonging to the broken linear PT-symmetric phase.
On the characterization of dynamic supramolecular systems: a general mathematical association model for linear supramolecular copolymers and application on a complex two-component hydrogen-bonding system.
Odille, Fabrice G J; Jónsson, Stefán; Stjernqvist, Susann; Rydén, Tobias; Wärnmark, Kenneth
A general mathematical model for the characterization of the dynamic (kinetically labile) association of supramolecular assemblies in solution is presented. It is an extension of the equal K (EK) model by the stringent use of linear algebra to allow for the simultaneous presence of an unlimited number of different units in the resulting assemblies. It allows for the analysis of highly complex dynamic equilibrium systems in solution, including both supramolecular homo- and copolymers without the recourse to extensive approximations, in a field in which other analytical methods are difficult. The derived mathematical methodology makes it possible to analyze dynamic systems such as supramolecular copolymers regarding for instance the degree of polymerization, the distribution of a given monomer in different copolymers as well as its position in an aggregate. It is to date the only general means to characterize weak supramolecular systems. The model was fitted to NMR dilution titration data by using the program Matlab, and a detailed algorithm for the optimization of the different parameters has been developed. The methodology is applied to a case study, a hydrogen-bonded supramolecular system, salen 4+porphyrin 5. The system is formally a two-component system but in reality a three-component system. This results in a complex dynamic system in which all monomers are associated to each other by hydrogen bonding with different association constants, resulting in homo- and copolymers 4n5m as well as cyclic structures 6 and 7, in addition to free 4 and 5. The system was analyzed by extensive NMR dilution titrations at variable temperatures. All chemical shifts observed at different temperatures were used in the fitting to obtain the DeltaH degrees and DeltaS degrees values producing the best global fit. From the derived general mathematical expressions, system 4+5 could be characterized with respect to above-mentioned parameters.
Continuity and Separation in Symmetric Topologies
ERIC Educational Resources Information Center
Harris, J.; Lynch, M.
In this note, it is shown that in a symmetric topological space, the pairs of sets separated by the topology determine the topology itself. It is then shown that when the codomain is symmetric, functions which separate only those pairs of sets that are already separated are continuous, generalizing a result found by M. Lynch.
Critical binding and electron scattering by symmetric-top polar molecules.
Garrett, W R
Quantum treatments of electron interactions with polar symmetric-top rotor molecules show features not present in the treatment of the linear-polar-rotor model. For symmetric tops possessing non-zero angular momentum about the symmetry axis, a new critical dipole can be defined that guarantees an infinite set of dipole-bound states independent of the values of the components of the inertial tensor. Additionally, for this same class, the scattering cross section diverges for all nonzero values of dipole moments and inertial moments, similar to solutions for the fixed linear dipole. Additional predictions are presented for electron affinities and rotational resonances of these systems.
Critical binding and electron scattering by symmetric-top polar molecules
Garrett, W. R.
Quantum treatments of electron interactions with polar symmetric-top rotor molecules show features not present in the treatment of the linear-polar-rotor model. For symmetric tops possessing non-zero angular momentum about the symmetry axis, a new critical dipole can be defined that guarantees an infinite set of dipole-bound states independent of the values of the components of the inertial tensor. Additionally, for this same class, the scattering cross section diverges for all nonzero values of dipole moments and inertial moments, similar to solutions for the fixed linear dipole. Additional predictions are presented for electron affinities and rotational resonances of these systems.
Robust synchronization of fractional-order complex dynamical networks with parametric uncertainties
NASA Astrophysics Data System (ADS)
Wong, W. K.; Li, Hongjie; Leung, S. Y. S.
The study investigates robust synchronization of fractional-order complex dynamical networks with parametric uncertainties. Based on the properties of the kronecker product and the stability of the fractional-order system, the robust synchronization criteria are derived by applying the nonlinear control. These criteria are in the form of linear matrix inequalities which can be readily solved by applying the LMI toolbox. The coupling configuration matrix is not necessary to be symmetric or irreducible, and the inner coupling matrix needs not to be symmetric, diagonal or positive definite. Two numerical examples are provided to demonstrate the validity of the presented synchronization scheme.
Baryon symmetric big bang cosmology
NASA Technical Reports Server (NTRS)
Stecker, F. W.
Both the quantum theory and Einsteins theory of special relativity lead to the supposition that matter and antimatter were produced in equal quantities during the big bang. It is noted that local matter/antimatter asymmetries may be reconciled with universal symmetry by assuming (1) a slight imbalance of matter over antimatter in the early universe, annihilation, and a subsequent remainder of matter; (2) localized regions of excess for one or the other type of matter as an initial condition; and (3) an extremely dense, high temperature state with zero net baryon number; i.e., matter/antimatter symmetry. Attention is given to the third assumption, which is the simplest and the most in keeping with current knowledge of the cosmos, especially as pertains the universality of 3 K background radiation. Mechanisms of galaxy formation are discussed, whereby matter and antimatter might have collided and annihilated each other, or have coexisted (and continue to coexist) at vast distances. It is pointed out that baryon symmetric big bang cosmology could probably be proved if an antinucleus could be detected in cosmic radiation.
Organometallic complexes of bulky, optically active, C3-symmetric tris(4S-isopropyl-5,5-dimethyl-2-oxazolinyl)phenylborate (ToP*)
Xu, Songchen; Magoon, Yitzhak; Reinig, Regina R.; Schmidt, Bradley M.; Ellern, Arkady; Sadow, Aaron D.
A bulky, optically active monoanionic scorpionate ligand, tris(4S-isopropyl-5,5-dimethyl-2-oxazolinyl)phenylborate (ToP*), is synthesized from the naturally occurring amino acid l-valine as its lithium salt, Li[ToP*] (1). That compound is readily converted to the thallium complex Tl[ToP*] (2) and to the acid derivative H[ToP*] (3). Group 7 tricarbonyl complexes ToP*M(CO)3 (M = Mn (4), Re (5)) are synthesized by the reaction of MBr(CO)5 and Li[ToP*] and are crystallographically characterized. The νCO bands in their infrared spectra indicate that π back-donation in the rhenium compounds is greater with ToP* than with non-methylated tris(4S-isopropyl-2-oxazolinyl)phenylborate (ToP). The reaction of H[ToP*] and ZnEt2 gives ToP*ZnEt (6), while ToP*ZnCl (7) is synthesized from Li[ToP*] and ZnCl2. The reaction of ToP*ZnCl and KOtBu followed by addition of PhSiH3 provides the zinc hydride complex ToP*ZnH (8). In this study, compound 8 is the first example of a crystallographically characterized optically active zinc hydride. We tested its catalytic reactivity in the cross-dehydrocoupling of silanes and alcohols, which provided Si-chiral silanes with moderate enantioselectivity.
Diagonalization of the symmetrized discrete i th right shift operator
NASA Astrophysics Data System (ADS)
Fuentes, Marc
In this paper, we consider the symmetric part of the so-called ith right shift operator. We determine its eigenvalues as also the associated eigenvectors in a complete and closed form. The proposed proof is elementary, using only basical skills such as Trigonometry, Arithmetic and Linear algebra. The first section is devoted to the introduction of the tackled problem. Second and third parts contain almost all the ?technical? stuff of the proofE Afterwards, we continue with the end of the proof, provide a graphical illustration of the results, as well as an application on the polyhedral ?sandwiching? of a special compact of arising in Signal theory.
Charged axially-symmetric solution in f( T) gravity theory
NASA Astrophysics Data System (ADS)
Nashed, G. G. L.
In present article, an axially symmetric tetrad field has been applied to the charged field equations of f( T) gravity theory. Some constraints have been imposed to solve the resulting non-linear partial differential equations. An exact non-vacuum charged solution with three constants of integration is derived. The solution does not have non-trivial scalar torsion, T={T^i}_{jk}{S_i}^{jk}. Total conserved charges, using Poincaré gauge version, are calculated to understand the physical meaning of the three constants of integration. It has been shown that these constants are gravitational mass, angular momentum of the rotating source and charge parameter.
Dispersion in a bent-solenoid channel with symmetric focusing
Wang, Chun-xi
Longitudinal ionization cooling of a muon beam is essential for muon colliders and will be useful for neutrino factories. Bent-solenoid channels with symmetric focusing has been considered for beam focusing and for generating the required dispersion in the ``emittance exchange'' scheme of longitudinal cooling. In this paper, we derive the Hamiltonian that governs the linear beam dynamics of a bent-solenoid channel, solve the single-particle dynamics, and give equations for determining the lattice functions, in particular, the dispersion functions.
Recursive partitioned inversion of large (1500 x 1500) symmetric matrices
NASA Technical Reports Server (NTRS)
Putney, B. H.; Brownd, J. E.; Gomez, R. A.
A recursive algorithm was designed to invert large, dense, symmetric, positive definite matrices using small amounts of computer core, i.e., a small fraction of the core needed to store the complete matrix. The described algorithm is a generalized Gaussian elimination technique. Other algorithms are also discussed for the Cholesky decomposition and step inversion techniques. The purpose of the inversion algorithm is to solve large linear systems of normal equations generated by working geodetic problems. The algorithm was incorporated into a computer program called SOLVE. In the past the SOLVE program has been used in obtaining solutions published as the Goddard earth models.
Static spherically symmetric solutions in f(G) gravity
NASA Astrophysics Data System (ADS)
Sharif, M.; Fatima, H. Ismat
We investigate interior solutions for static spherically symmetric metric in the background of f(G) gravity. We use the technique of conformal Killing motions to solve the field equations with both isotropic and anisotropic matter distributions. These solutions are then used to obtain density, radial and tangential pressures for power-law f(G) model. For anisotropic case, we assume a linear equation-of-state and investigate solutions for the equation-of-state parameter ω = -1.5. We check physical validity of the solutions through energy conditions and also examine its stability. Finally, we study equilibrium configuration using Tolman-Oppenheimer-Volkoff equation.
O-X mode conversion in a non-symmetric torus at electron cyclotron frequencies
NASA Astrophysics Data System (ADS)
Weitzner, Harold
Earlier work on linear wave propagation over a symmetric background state, is simplified and extended to non-symmetric equilibria. With the exception of one special case, which reduces to the case of a perpendicularly stratified medium, it is shown that mode conversion in symmetric or non-symmetric equilibria satisfies the same set of equations. An examination of the coupling of the geometrical ray optics solution to the mode conversion system provides a relatively simple and physical characterization of the incoming wave structure necessary to achieve effective mode conversion. Part of the work was done while visiting the Max=Planck-Insititute-for Plasmaphysics, Greifswald , Germany. its support is gratefully acknowledged. DE-FG-86ER53223.
Observation of optical solitons in PT-symmetric lattices
Wimmer, Martin; Regensburger, Alois; Miri, Mohammad-Ali; Bersch, Christoph; Christodoulides, Demetrios N.; Peschel, Ulf
Controlling light transport in nonlinear active environments is a topic of considerable interest in the field of optics. In such complex arrangements, of particular importance is to devise strategies to subdue chaotic behaviour even in the presence of gain/loss and nonlinearity, which often assume adversarial roles. Quite recently, notions of parity-time (PT) symmetry have been suggested in photonic settings as a means to enforce stable energy flow in platforms that simultaneously employ both amplification and attenuation. Here we report the experimental observation of optical solitons in PT-symmetric lattices. Unlike other non-conservative nonlinear arrangements where self-trapped states appear as fixed points in the parameter space of the governing equations, discrete PT solitons form a continuous parametric family of solutions. The possibility of synthesizing PT-symmetric saturable absorbers, where a nonlinear wave finds a lossless path through an otherwise absorptive system is also demonstrated. PMID:26215165
Modulational instability in a PT-symmetric vector nonlinear Schrödinger system
NASA Astrophysics Data System (ADS)
Cole, J. T.; Makris, K. G.; Musslimani, Z. H.; Christodoulides, D. N.; Rotter, S.
A class of exact multi-component constant intensity solutions to a vector nonlinear Schrödinger (NLS) system in the presence of an external PT-symmetric complex potential is constructed. This type of uniform wave pattern displays a non-trivial phase whose spatial dependence is induced by the lattice structure. In this regard, light can propagate without scattering while retaining its original form despite the presence of inhomogeneous gain and loss. These constant-intensity continuous waves are then used to perform a modulational instability analysis in the presence of both non-hermitian media and cubic nonlinearity. A linear stability eigenvalue problem is formulated that governs the dynamical evolution of the periodic perturbation and its spectrum is numerically determined using Fourier-Floquet-Bloch theory. In the self-focusing case, we identify an intensity threshold above which the constant-intensity modes are modulationally unstable for any Floquet-Bloch momentum belonging to the first Brillouin zone. The picture in the self-defocusing case is different. Contrary to the bulk vector case, where instability develops only when the waves are strongly coupled, here an instability occurs in the strong and weak coupling regimes. The linear stability results are supplemented with direct (nonlinear) numerical simulations.
NASA Astrophysics Data System (ADS)
Sidorin, Anatoly
In linear accelerators the particles are accelerated by either electrostatic fields or oscillating Radio Frequency (RF) fields. Accordingly the linear accelerators are divided in three large groups: electrostatic, induction and RF accelerators. Overview of the different types of accelerators is given. Stability of longitudinal and transverse motion in the RF linear accelerators is briefly discussed. The methods of beam focusing in linacs are described.
Complete list of the first integrals of dynamic equations of a multidimensional solid in a nonconservative field under the assumption of linear damping
NASA Astrophysics Data System (ADS)
Shamolin, M. V.
The dynamic part of equations of motion is investigated for a dynamically symmetric multidimensional solid in a nonconservative force field in the presence of the following force in the case when the solid is under the action of a pair of forces. In this case, there is additional linear damping in the system. The new case of complete integrability is found in transcendental (in the sense of complex analysis) functions, which are expressed through a finite combination of elementary functions.
Martingale Rosenthal inequalities in symmetric spaces
Astashkin, S V
We establish inequalities similar to the classical Rosenthal inequalities for sequences of martingale differences in general symmetric spaces; a central role is played here by the predictable quadratic characteristic of a martingale. Bibliography: 26 titles.
Lax Operator for Macdonald Symmetric Functions
NASA Astrophysics Data System (ADS)
Nazarov, Maxim; Sklyanin, Evgeny
Using the Lax operator formalism, we construct a family of pairwise commuting operators such that the Macdonald symmetric functions of infinitely many variables and of two parameters q, t are their eigenfunctions. We express our operators in terms of the Hall-Littlewood symmetric functions of the variables and of the parameter t corresponding to the partitions with one part only. Our expression is based on the notion of Baker-Akhiezer function.
Symmetric point four-point functions at one loop in QCD
NASA Astrophysics Data System (ADS)
Gracey, J. A.
We evaluate the quartic ghost and quark Green's functions as well as the gluon-ghost, gluon-quark and ghost-quark four-point functions of quantum chromodynamics at one loop at the fully symmetric point in a linear covariant gauge. Similar expressions for the analogous Green's functions in quantum electrodynamics are also provided.
A linear Hf isotope-age array despite different granitoid sources and complex Archean geodynamics: Example from the Pietersburg block (South Africa)
NASA Astrophysics Data System (ADS)
Laurent, Oscar; Zeh, Armin
Combined U-Pb and Lu-Hf isotope data from zircon populations are widely used to constrain Hadean-Archean crustal evolution. Linear Hf isotope-age arrays are interpreted to reflect the protracted, internal reworking of crust derived from the (depleted) mantle during a short-lived magmatic event, and related 176Lu/177Hf ratios are used to constrain the composition of the reworked crustal reservoir. Results of this study, however, indicate that Hf isotope-age arrays can also result from complex geodynamic processes and crust-mantle interactions, as shown by U-Pb and Lu-Hf isotope analyses of zircons from well characterized granitoids of the Pietersburg Block (PB), northern Kaapvaal Craton (South Africa). Apart from scarce remnants of Paleoarchean crust, most granitoids of the PB with ages between 2.94 and 2.05 Ga (n = 32) define a straight Hf isotope-age array with low 176Lu/177Hf of 0.0022, although they show a wide compositional range, were derived from various sources and emplaced successively in different geodynamic settings. The crustal evolution occurred in five stages: (I) predominately mafic crust formation in an intra-oceanic environment (3.4-3.0 Ga); (II) voluminous TTG crust formation in an early accretionary orogen (3.0-2.92 Ga); (III) internal TTG crust reworking and subduction of TTG-derived sediments in an Andean-type setting (2.89-2.75 Ga); (IV) (post-)collisional high-K magmatism from both mantle and crustal sources (2.71-2.67 Ga); and (V) alkaline magmatism in an intra-cratonic environment (2.05-2.03 Ga). The inferred array results from voluminous TTG crust formation during stage II, and involvement of this crust during all subsequent stages by two different processes: (i) internal crust reworking through both partial melting and assimilation at 2.89-2.75 Ga, leading to the formation of biotite granites coeval with minor TTGs, and (ii) subduction of TTG-derived sediments underneath the PB, causing enrichment of the mantle that subsequently became
Two-dimensional solitons in conservative and parity-time-symmetric triple-core waveguides with cubic-quintic nonlinearity
NASA Astrophysics Data System (ADS)
Feijoo, David; Zezyulin, Dmitry A.; Konotop, Vladimir V.
We analyze a system of three two-dimensional nonlinear Schrödinger equations coupled by linear terms and with the cubic-quintic (focusing-defocusing) nonlinearity. We consider two versions of the model: conservative and parity-time (PT ) symmetric. These models describe triple-core nonlinear optical waveguides, with balanced gain and losses in the PT -symmetric case. We obtain families of soliton solutions and discuss their stability. The latter study is performed using a linear stability analysis and checked with direct numerical simulations of the evolutional system of equations. Stable solitons are found in the conservative and PT -symmetric cases. Interactions and collisions between the conservative and PT -symmetric solitons are briefly investigated, as well.
Synchronization analysis of delayed complex networks with time-varying couplings
NASA Astrophysics Data System (ADS)
Li, Ping; Yi, Zhang
In this paper, a new method is presented to analyze the linear stability of the synchronized state in arbitrarily coupled complex dynamical systems with time delays. The coupling configurations are not restricted to the symmetric and irreducible connections or the non-negative off-diagonal links. The stability criteria are obtained by using Lyapunov-Krasovskii functional method and subspace projection method. These criteria reveal the relationship between coupling matrices and stability of the dynamical networks.
Benign symmetrical lipomatosis and pellagra associated with alcoholism.
Filgueiras, Fernanda de Marca; Stolarczuk, Dionne de Almeida; Gripp, Alexandre Carlos; Succi, Isabel Cristina Brasil
A 42-year-old male patient, alcoholic, presented showing signs of tumors in the neck and around the shoulders, scaly, erythematous-violaceous lesions and some bullous lesions in sun-exposed areas of upper and lower limbs. Based on clinical features, laboratory tests and imaging studies we have established the diagnosis of pellagra associated with benign symmetrical lipomatosis, both justified by chronic alcoholism. Treated with intravenous B-complex and oriented about the importance of alcohol withdrawal, the patient showed complete remission of skin lesions, but with no change in the lipomatosis.
The Topology of Three-Dimensional Symmetric Tensor Fields
NASA Technical Reports Server (NTRS)
Lavin, Yingmei; Levy, Yuval; Hesselink, Lambertus
We study the topology of 3-D symmetric tensor fields. The goal is to represent their complex structure by a simple set of carefully chosen points and lines analogous to vector field topology. The basic constituents of tensor topology are the degenerate points, or points where eigenvalues are equal to each other. First, we introduce a new method for locating 3-D degenerate points. We then extract the topological skeletons of the eigenvector fields and use them for a compact, comprehensive description of the tensor field. Finally, we demonstrate the use of tensor field topology for the interpretation of the two-force Boussinesq problem.
Architecture of the symmetric core of the nuclear pore.
Lin, Daniel H; Stuwe, Tobias; Schilbach, Sandra; Rundlet, Emily J; Perriches, Thibaud; Mobbs, George; Fan, Yanbin; Thierbach, Karsten; Huber, Ferdinand M; Collins, Leslie N; Davenport, Andrew M; Jeon, Young E; Hoelz, André
The nuclear pore complex (NPC) controls the transport of macromolecules between the nucleus and cytoplasm, but its molecular architecture has thus far remained poorly defined. We biochemically reconstituted NPC core protomers and elucidated the underlying protein-protein interaction network. Flexible linker sequences, rather than interactions between the structured core scaffold nucleoporins, mediate the assembly of the inner ring complex and its attachment to the NPC coat. X-ray crystallographic analysis of these scaffold nucleoporins revealed the molecular details of their interactions with the flexible linker sequences and enabled construction of full-length atomic structures. By docking these structures into the cryoelectron tomographic reconstruction of the intact human NPC and validating their placement with our nucleoporin interactome, we built a composite structure of the NPC symmetric core that contains ~320,000 residues and accounts for ~56 megadaltons of the NPC's structured mass. Our approach provides a paradigm for the structure determination of similarly complex macromolecular assemblies.
The Stark Effect in Linear Potentials
ERIC Educational Resources Information Center
Robinett, R. W.
We examine the Stark effect (the second-order shifts in the energy spectrum due to an external constant force) for two one-dimensional model quantum mechanical systems described by linear potentials, the so-called quantum bouncer (defined by V(z) = Fz for z greater than 0 and V(z) = [infinity] for z less than 0) and the symmetric linear potential…
CAST: Contraction Algorithm for Symmetric Tensors
Rajbhandari, Samyam; NIkam, Akshay; Lai, Pai-Wei; Stock, Kevin; Krishnamoorthy, Sriram; Sadayappan, Ponnuswamy
Tensor contractions represent the most compute-intensive core kernels in ab initio computational quantum chemistry and nuclear physics. Symmetries in these tensor contractions makes them difficult to load balance and scale to large distributed systems. In this paper, we develop an efficient and scalable algorithm to contract symmetric tensors. We introduce a novel approach that avoids data redistribution in contracting symmetric tensors while also avoiding redundant storage and maintaining load balance. We present experimental results on two parallel supercomputers for several symmetric contractions that appear in the CCSD quantum chemistry method. We also present a novel approach to tensor redistribution that can take advantage of parallel hyperplanes when the initial distribution has replicated dimensions, and use collective broadcast when the final distribution has replicated dimensions, making the algorithm very efficient.
Communication-avoiding symmetric-indefinite factorization
Ballard, Grey Malone; Becker, Dulcenia; Demmel, James; Dongarra, Jack; Druinsky, Alex; Peled, Inon; Schwartz, Oded; Toledo, Sivan; Yamazaki, Ichitaro
We describe and analyze a novel symmetric triangular factorization algorithm. The algorithm is essentially a block version of Aasen's triangular tridiagonalization. It factors a dense symmetric matrix A as the product A=PLTLTPT where P is a permutation matrix, L is lower triangular, and T is block tridiagonal and banded. The algorithm is the first symmetric-indefinite communication-avoiding factorization: it performs an asymptotically optimal amount of communication in a two-level memory hierarchy for almost any cache-line size. Adaptations of the algorithm to parallel computers are likely to be communication efficient as well; one such adaptation has been recently published. As a result, the current paper describes the algorithm, proves that it is numerically stable, and proves that it is communication optimal.
Communication-avoiding symmetric-indefinite factorization
Ballard, Grey Malone; Becker, Dulcenia; Demmel, James; ...
We describe and analyze a novel symmetric triangular factorization algorithm. The algorithm is essentially a block version of Aasen's triangular tridiagonalization. It factors a dense symmetric matrix A as the product A=PLTLTPT where P is a permutation matrix, L is lower triangular, and T is block tridiagonal and banded. The algorithm is the first symmetric-indefinite communication-avoiding factorization: it performs an asymptotically optimal amount of communication in a two-level memory hierarchy for almost any cache-line size. Adaptations of the algorithm to parallel computers are likely to be communication efficient as well; one such adaptation has been recently published. As a result,more » the current paper describes the algorithm, proves that it is numerically stable, and proves that it is communication optimal.« less
On symmetric and upwind TVD schemes
NASA Technical Reports Server (NTRS)
Yee, H. C.
A class of explicit and implicit total variation diminishing (TVD) schemes for the compressible Euler and Navier-Stokes equations was developed. They do not generate spurious oscillations across shocks and contact discontinuities. In general, shocks can be captured within 1 to 2 grid points. For the inviscid case, these schemes are divided into upwind TVD schemes and symmetric (nonupwind) TVD schemes. The upwind TVD scheme is based on the second-order TVD scheme. The symmetric TVD scheme is a generalization of Roe's and Davis' TVD Lax-Wendroff scheme. The performance of these schemes on some viscous and inviscid airfoil steady-state calculations is investigated. The symmetric and upwind TVD schemes are compared.
The Robust Assembly of Small Symmetric Nanoshells
Wagner, Jef; Zandi, Roya
Highly symmetric nanoshells are found in many biological systems, such as clathrin cages and viral shells. Many studies have shown that symmetric shells appear in nature as a result of the free-energy minimization of a generic interaction between their constituent subunits. We examine the physical basis for the formation of symmetric shells, and by using a minimal model, demonstrate that these structures can readily grow from the irreversible addition of identical subunits. Our model of nanoshell assembly shows that the spontaneous curvature regulates the size of the shell while the mechanical properties of the subunit determine the symmetry of the assembled structure. Understanding the minimum requirements for the formation of closed nanoshells is a necessary step toward engineering of nanocontainers, which will have far-reaching impact in both material science and medicine. PMID:26331253
The Robust Assembly of Small Symmetric Nanoshells.
Wagner, Jef; Zandi, Roya
Highly symmetric nanoshells are found in many biological systems, such as clathrin cages and viral shells. Many studies have shown that symmetric shells appear in nature as a result of the free-energy minimization of a generic interaction between their constituent subunits. We examine the physical basis for the formation of symmetric shells, and by using a minimal model, demonstrate that these structures can readily grow from the irreversible addition of identical subunits. Our model of nanoshell assembly shows that the spontaneous curvature regulates the size of the shell while the mechanical properties of the subunit determine the symmetry of the assembled structure. Understanding the minimum requirements for the formation of closed nanoshells is a necessary step toward engineering of nanocontainers, which will have far-reaching impact in both material science and medicine.
Christofilos, N.C.; Polk, I.J.
Improvements in linear particle accelerators are described. A drift tube system for a linear ion accelerator reduces gap capacity between adjacent drift tube ends. This is accomplished by reducing the ratio of the diameter of the drift tube to the diameter of the resonant cavity. Concentration of magnetic field intensity at the longitudinal midpoint of the external sunface of each drift tube is reduced by increasing the external drift tube diameter at the longitudinal center region.
Self-bending symmetric cusp beams
Gong, Lei; Liu, Wei-Wei; Lu, Yao; Li, Yin-Mei; Ren, Yu-Xuan
A type of self-bending symmetric cusp beams with four accelerating intensity maxima is theoretically and experimentally presented. Distinguished from the reported regular polygon beams, the symmetric cusp beams simultaneously exhibit peculiar features of natural autofocusing and self-acceleration during propagation. Further, such beams take the shape of a fine longitudinal needle-like structure at the focal region and possess the strong ability of self-healing over obstacles. All these intriguing properties were verified experimentally. Particularly, the spatial profile of the reconstructed beam exhibits spatially sculpted optical structure with four siamesed curved arms. Thus, we anticipate that the structured beam will benefit optical guiding and optofluidics in surprising ways.
All-optical symmetric ternary logic gate
NASA Astrophysics Data System (ADS)
Chattopadhyay, Tanay
Symmetric ternary number (radix=3) has three logical states (1¯, 0, 1). It is very much useful in carry free arithmetical operation. Beside this, the logical operation using this type of number system is also effective in high speed computation and communication in multi-valued logic. In this literature all-optical circuits for three basic symmetrical ternary logical operations (inversion, MIN and MAX) are proposed and described. Numerical simulation verifies the theoretical model. In this present scheme the different ternary logical states are represented by different polarized state of light. Terahertz optical asymmetric demultiplexer (TOAD) based interferometric switch has been used categorically in this manuscript.
Properties of a symmetric RHIC insertion
Lee, S.Y.
This report evaluates the lattice functions of the symmetric insertion proposed by A.G. Ruggiero for the RHIC insertion. The crossing geometry, Inner and Outer matching sections, and chromatic properties are studied in detail. Some properties of the missing dipole dispersion correction scheme are also discussed. We found that the chromatic properties of the symmetric insertion is not better than the antisymmetric insertion. The problem is that the four family sextupole correction scheme seems not able to improve the chromatic distortion. Analytic understanding of the failure of the four family sextupole correction scheme will be very useful. 9 figs., 1 tab.
Quantum fidelity of symmetric multipartite states
NASA Astrophysics Data System (ADS)
Neven, A.; Mathonet, P.; Gühne, O.; Bastin, T.
For two symmetric quantum states one may be interested in maximizing the overlap under local operations applied to one of them. The question arises whether the maximal overlap can be obtained by applying the same local operation to each party. We show that for two symmetric multiqubit states and local unitary transformations this is the case; the maximal overlap can be reached by applying the same unitary matrix everywhere. For local invertible operations (stochastic local operations assisted by classical communication equivalence), however, we present counterexamples, demonstrating that considering the same operation everywhere is not enough.
Observational tests of Baryon symmetric cosmology
NASA Technical Reports Server (NTRS)
Stecker, F. W.
Observational evidence for Baryon symmetric (matter/antimatter) cosmology and future observational tests are reviewed. The most significant consequences of Baryon symmetric cosmology lie in the prediction of an observable cosmic background of gamma radiation from the decay of pi(0)-mesons produced in nucleon-antinucleon annihilations. Equations for the prediction of the amma ray background spectrum for the case of high redshifts are presented. The theoretical and observational plots of the background spectrum are shown to be in good agreement. Measurement of cosmic ray antiprotons and the use of high energy neutrino astronomy to look for antimatter elsewhere in the universe are also addressed.
Synthesis, crystal structures and magnetic properties of bis(μ-dialkoxo)-bridged linear trinuclear copper(II) complexes with aminoalcohol ligands: a theoretical/experimental magneto-structural study.
Seppälä, Petri; Colacio, Enrique; Mota, Antonio J; Sillanpää, Reijo
The bis(μ-dialkoxo)-bridged trinuclear copper(II) complexes [Cu(3)(ap)(4)(ClO(4))(2)EtOH] (1), [Cu(3)(ap)(4)(NO(3))(2)] (2), [Cu(3)(ap)(4)Br(2)] (3) and [Cu(3)(ae)(4)(NO(3))(2)] (4) (ae = 2-aminoethanolato and ap = 3-aminopropanolato) have been synthesised via self-assembly from chelating aminoalcohol ligands with the corresponding copper(II) salts. The complexes are characterised by single-crystal X-ray diffraction analyses and variable temperature magnetic measurements. The crystal structures of complexes 1-4 consist of slightly bent linear or linear trinuclear [Cu(3)(aa)(4)](2+) (aa = aminoalcoholato) units to which the perchlorate, nitrate or bromide anions are weakly coordinated. The adjacent trinuclear units of 1-4 are connected together by hydrogen bonds and bridging nitrate or bromide anions resulting in the formation of 2D layers. Magnetic studies of 1, 2 and 4 show that J values vary from -379 to +36.0 cm(-1) as the Cu-O-Cu angle (θ) and the out-of-plane shift of the carbon atom of the bridging alkoxo group (τ) vary from 103.7 to 94.4° and from 0.9 to 35.5°, respectively. Magnetic exchange coupling constants calculated by DFT methods are of the same nature and magnitude as the experimental ones. For complexes 1, 2 and 4, which have complementarity effects between the θ and τ angles (small θ values are associated with large τ values and vice versa), an almost linear relationship between the calculated J values with θ angles could be established, thus supporting that the θ and τ angles are the two key structural factors that determine the magnetic exchange coupling for such a type of compounds. Complex 3 does not obey this linear correlation because of the existence of counter-complementarity effects between these angles (small θ values are associated with small τ values and vice versa). It is of interest that the theoretical calculations for the magnetic exchange interaction between next-nearest neighbours indicate that the usual
Accuracy assessment of the linear Poisson-Boltzmann equation and reparametrization of the OBC generalized Born model for nucleic acids and nucleic acid-protein complexes.
Fogolari, Federico; Corazza, Alessandra; Esposito, Gennaro
The generalized Born model in the Onufriev, Bashford, and Case (Onufriev et al., Proteins: Struct Funct Genet 2004, 55, 383) implementation has emerged as one of the best compromises between accuracy and speed of computation. For simulations of nucleic acids, however, a number of issues should be addressed: (1) the generalized Born model is based on a linear model and the linearization of the reference Poisson-Boltmann equation may be questioned for highly charged systems as nucleic acids; (2) although much attention has been given to potentials, solvation forces could be much less sensitive to linearization than the potentials; and (3) the accuracy of the Onufriev-Bashford-Case (OBC) model for nucleic acids depends on fine tuning of parameters. Here, we show that the linearization of the Poisson Boltzmann equation has mild effects on computed forces, and that with optimal choice of the OBC model parameters, solvation forces, essential for molecular dynamics simulations, agree well with those computed using the reference Poisson-Boltzmann model.
Integrability and vesture for harmonic maps into symmetric spaces
NASA Astrophysics Data System (ADS)
Beheshti, Shabnam; Tahvildar-Zadeh, Shadi
After formulating the notion of integrability for axially symmetric harmonic maps from ℝ3 into symmetric spaces, we give a complete and rigorous proof that, subject to some mild restrictions on the target, all such maps are integrable. Furthermore, we prove that a variant of the inverse scattering method, called vesture (dressing) can always be used to generate new solutions for the harmonic map equations starting from any given solution. In particular, we show that the problem of finding N-solitonic harmonic maps into a non-compact Grassmann manifold SU(p,q)/S(U(p) × U(q)) is completely reducible via the vesture (dressing) method to a problem in linear algebra which we prove is solvable in general. We illustrate this method, and establish its agreement with previously known special cases, by explicitly computing a 1-solitonic harmonic map for the two cases (p = 1,q = 1) and (p = 2,q = 1) and showing that the family of solutions obtained in each case contains respectively the Kerr family of solutions to the Einstein vacuum equations, and the Kerr-Newman family of solutions to the Einstein-Maxwell equations in the hyperextreme sector of the corresponding parameters.
Modelling of partially-resolved oceanic symmetric instability
NASA Astrophysics Data System (ADS)
Bachman, S. D.; Taylor, J. R.
A series of idealized numerical models have been developed to investigate the effects of partially resolved symmetric instability (SI) in oceanic general circulation models. An analysis of the energetics of symmetric instability is used to argue that the mixed layer can be at least partially restratified even when some SI modes are absent due to either large horizontal viscosity or coarse model resolution. Linear stability analysis reveals that in the idealized models the amount of restratification can be predicted as a function of the grid spacing and viscosity. The models themselves are used to demonstrate these predictions and reveal three possible outcomes in steady-state: (1) incomplete restratification due to viscosity, (2) incomplete restratification due to resolution, and (3) excessive restratification due to anisotropy of the viscosity. The third outcome occurs even on a high-resolution isotropic grid and in two separate numerical models, and thus appears to be a sort of robust numerical feature. The three outcomes are used to recommend criteria that a successful SI parameterization should satisfy.
An almost symmetric Strang splitting scheme for nonlinear evolution equations.
Einkemmer, Lukas; Ostermann, Alexander
In this paper we consider splitting methods for the time integration of parabolic and certain classes of hyperbolic partial differential equations, where one partial flow cannot be computed exactly. Instead, we use a numerical approximation based on the linearization of the vector field. This is of interest in applications as it allows us to apply splitting methods to a wider class of problems from the sciences. However, in the situation described, the classic Strang splitting scheme, while still being a method of second order, is not longer symmetric. This, in turn, implies that the construction of higher order methods by composition is limited to order three only. To remedy this situation, based on previous work in the context of ordinary differential equations, we construct a class of Strang splitting schemes that are symmetric up to a desired order. We show rigorously that, under suitable assumptions on the nonlinearity, these methods are of second order and can then be used to construct higher order methods by composition. In addition, we illustrate the theoretical results by conducting numerical experiments for the Brusselator system and the KdV equation.
An almost symmetric Strang splitting scheme for nonlinear evolution equations☆
Einkemmer, Lukas; Ostermann, Alexander
In this paper we consider splitting methods for the time integration of parabolic and certain classes of hyperbolic partial differential equations, where one partial flow cannot be computed exactly. Instead, we use a numerical approximation based on the linearization of the vector field. This is of interest in applications as it allows us to apply splitting methods to a wider class of problems from the sciences. However, in the situation described, the classic Strang splitting scheme, while still being a method of second order, is not longer symmetric. This, in turn, implies that the construction of higher order methods by composition is limited to order three only. To remedy this situation, based on previous work in the context of ordinary differential equations, we construct a class of Strang splitting schemes that are symmetric up to a desired order. We show rigorously that, under suitable assumptions on the nonlinearity, these methods are of second order and can then be used to construct higher order methods by composition. In addition, we illustrate the theoretical results by conducting numerical experiments for the Brusselator system and the KdV equation. PMID:25844017
A modified direct preconditioner for indefinite symmetric Toeplitz systems
Concus, P.; Saylor, P.
A modification is presented of the classical $O(n{sup 2})$ algorithm of Trench for the direct solution of Toeplitz systems of equations. The Trench algorithm can be guaranteed to be stable only for matrices that are (symmetric) positive definite; it is generally unstable otherwise. The modification permits extension of the algorithm to compute an approximate inverse in the indefinite symmetric case, for which the unmodified algorithm breaks down when principal submatrices are singular. As a preconditioner, this approximate inverse has an advantage that only matrix-vector multiplications are required for the solution of a linear system, without forward and backward solves. The approximate inverse so obtained can be sufficiently accurate, moreover that, when it is used as a preconditioner for the applications investigated, subsequent iteration may not even be necessary. Numerical results are given for several test matrices. The perturbation to the original matrix that defines the modification is related to a perturbation in a quantity generated in the Trench algorithm; the associated stability of the Trench algorithm is discussed.
A modified direct preconditioner for indefinite symmetric Toeplitz systems
Concus, P. California Univ., Berkeley, CA . Dept. of Mathematics); Saylor, P. . Dept. of Computer Science)
A modification is presented of the classical O(n[sup 2]) algorithm of Trench for the direct solution of Toeplitz systems of equations. The Trench algorithm can be guaranteed to be stable only for matrices that are (symmetric) positive definite; it is generally unstable otherwise. The modification permits extension of the algorithm to compute an approximate inverse in the indefinite symmetric case, for which the unmodified algorithm breaks down when principal submatrices are singular. As a preconditioner, this approximate inverse has an advantage that only matrix-vector multiplications are required for the solution of a linear system, without forward and backward solves. The approximate inverse so obtained can be sufficiently accurate, moreover, that, when it is used as a preconditioner for the applications investigated, subsequent iteration may not even be necessary. Numerical results are given for several test matrices. The perturbation to the original matrix that defines the modification is related to a perturbation in a quantity generated in the Trench algorithm; the associated stability of the Trench algorithm is discussed.
A modified direct preconditioner for indefinite symmetric Toeplitz systems
Concus, P. |; Saylor, P.
A modification is presented of the classical O(n{sup 2}) algorithm of Trench for the direct solution of Toeplitz systems of equations. The Trench algorithm can be guaranteed to be stable only for matrices that are (symmetric) positive definite; it is generally unstable otherwise. The modification permits extension of the algorithm to compute an approximate inverse in the indefinite symmetric case, for which the unmodified algorithm breaks down when principal submatrices are singular. As a preconditioner, this approximate inverse has an advantage that only matrix-vector multiplications are required for the solution of a linear system, without forward and backward solves. The approximate inverse so obtained can be sufficiently accurate, moreover, that, when it is used as a preconditioner for the applications investigated, subsequent iteration may not even be necessary. Numerical results are given for several test matrices. The perturbation to the original matrix that defines the modification is related to a perturbation in a quantity generated in the Trench algorithm; the associated stability of the Trench algorithm is discussed.
Super-symmetric informationally complete measurements
Zhu, Huangjun
Symmetric informationally complete measurements (SICs in short) are highly symmetric structures in the Hilbert space. They possess many nice properties which render them an ideal candidate for fiducial measurements. The symmetry of SICs is intimately connected with the geometry of the quantum state space and also has profound implications for foundational studies. Here we explore those SICs that are most symmetric according to a natural criterion and show that all of them are covariant with respect to the Heisenberg–Weyl groups, which are characterized by the discrete analog of the canonical commutation relation. Moreover, their symmetry groups are subgroups of the Clifford groups. In particular, we prove that the SIC in dimension 2, the Hesse SIC in dimension 3, and the set of Hoggar lines in dimension 8 are the only three SICs up to unitary equivalence whose symmetry groups act transitively on pairs of SIC projectors. Our work not only provides valuable insight about SICs, Heisenberg–Weyl groups, and Clifford groups, but also offers a new approach and perspective for studying many other discrete symmetric structures behind finite state quantum mechanics, such as mutually unbiased bases and discrete Wigner functions.
Onthe static and spherically symmetric gravitational field
NASA Astrophysics Data System (ADS)
Gottlieb, Ioan; Maftei, Gheorghe; Mociutchi, Cleopatra
Starting from a generalization of Einstein 's theory of gravitation, proposed by one of the authors (Cleopatra Mociutchi), the authors study a particular spherical symmetric case. Among other one obtain the compatibility conditions for the existence of the static and spherically symmetruic gravitational filed in the case of extended Einstein equation.
The deuterium puzzle in the symmetric universe
NASA Technical Reports Server (NTRS)
Leroy, B.; Nicolle, J. P.; Schatzman, E.
An attempt was made to use deuterium abundance in the symmetric universe to prove that no nucleosynthesis takes place during annihilation and therefore neutrons were loss before nucleosynthesis. Data cover nucleosynthesis during the radiative era, cross section estimates, maximum abundance of He-4 at the end of nucleosynthesis area, and loss rate.
Dissociative recombination of highly symmetric polyatomic ions.
Douguet, Nicolas; Orel, Ann E; Greene, Chris H; Kokoouline, Viatcheslav
A general first-principles theory of dissociative recombination is developed for highly symmetric molecular ions and applied to H(3)O(+) and CH(3)(+), which play an important role in astrophysical, combustion, and laboratory plasma environments. The theoretical cross sections obtained for the dissociative recombination of the two ions are in good agreement with existing experimental data from storage ring experiments.
Super-symmetric informationally complete measurements
NASA Astrophysics Data System (ADS)
Zhu, Huangjun
Symmetric informationally complete measurements (SICs in short) are highly symmetric structures in the Hilbert space. They possess many nice properties which render them an ideal candidate for fiducial measurements. The symmetry of SICs is intimately connected with the geometry of the quantum state space and also has profound implications for foundational studies. Here we explore those SICs that are most symmetric according to a natural criterion and show that all of them are covariant with respect to the Heisenberg-Weyl groups, which are characterized by the discrete analog of the canonical commutation relation. Moreover, their symmetry groups are subgroups of the Clifford groups. In particular, we prove that the SIC in dimension 2, the Hesse SIC in dimension 3, and the set of Hoggar lines in dimension 8 are the only three SICs up to unitary equivalence whose symmetry groups act transitively on pairs of SIC projectors. Our work not only provides valuable insight about SICs, Heisenberg-Weyl groups, and Clifford groups, but also offers a new approach and perspective for studying many other discrete symmetric structures behind finite state quantum mechanics, such as mutually unbiased bases and discrete Wigner functions.
Alfvén modes in the Madison Symmetric Torus
NASA Astrophysics Data System (ADS)
Li, M.; Breizman, B. N.; Zheng, L. J.; Lin, L.; Ding, W. X.; Brower, D. L.
This work presents a theoretical and computational analysis of core-localized energetic particle driven modes observed near the magnetic axis in the Madison Symmetric Torus [L. Lin, W. X. Ding, D. L. Brower et al., Phys. Plasmas 20, 030701 (2013)]. Using measured safety factor and plasma pressure profiles as input, the linear ideal MHD code Adaptive EiGenfunction Independent Solution (AEGIS) [L. J. Zheng and M. Kotschenreuther, J. Comput. Phys. 211, 748 (2006)] reveals Alfvénic modes close to the measured frequencies. The AEGIS results together with a reduced analytical model demonstrate that the modes are essentially "cylindrical" and dominated by a single poloidal component (m = 1). The modes are localized at the plasma core where the magnetic shear is weak and continuum damping is minimal. Detailed analysis establishes constraints on the safety factor and plasma pressure, under which two modes can exist simultaneously.
On the locally rotationally symmetric Einstein-Maxwell perfect fluid
NASA Astrophysics Data System (ADS)
Pugliese, D.; Valiente Kroon, J. A.
We examine the stability of Einstein-Maxwell perfect fluid configurations with a privileged radial direction by means of a 1+1+2-tetrad formalism. We use this formalism to cast in a quasilinear symmetric hyperbolic form the equations describing the evolution of the system. This hyperbolic reduction is used to discuss the stability of linear perturbations in some special cases. By restricting the analysis to isotropic fluid configurations, we assume a constant electrical conductivity coefficient for the fluid. As a result of this analysis we provide a complete classification and characterization of various stable and unstable configurations. We find, in particular, that in many cases the stability conditions are strongly determined by the constitutive equations and the electric conductivity. A threshold for the emergence of the instability appears in both contracting and expanding systems.
Vibration-rotation double resonance effects in symmetrical top molecules.
NASA Technical Reports Server (NTRS)
Marantz, H.; Frenkel, L.; Sullivan, T.
Rotational transitions in symmetrical top molecules in the wavelength regions of 1-3 mm are sufficiently strong to be observed directly on an oscilloscope. Changes in the vibrational level populations induced by laser radiations affect the intensity of the rotational transitions. Observation of the microwave lines under the influence of chopped laser radiation shows a variety of interesting and potentially informative effects. At pressures above a few tenths of a torr the effect of laser radiation is to reduce the microwave response. This is true for all microwave lines at all those laser frequencies which are absorbed by the gas, and this effect is roughly proportional to the absorption coefficient. The rise and decay times of this effect increase with pressure and the the linear dimensions of the absorption cell. At low pressures the microwave response may increase, decrease, or remain unaffected depending on the observed microwave transitions and the specific laser line applied to the gas.
Classification of static plane symmetric spacetime via Noether gauge symmetries
NASA Astrophysics Data System (ADS)
Jhangeer, Adil; Iftikhar, Nazish; Naz, Tayyaba
In this paper, general static plane symmetric spacetime is classified with respect to Noether operators. For this purpose, Noether theorem is used which yields a set of linear partial differential equations (PDEs) with unknown radial functions A(r), B(r) and F(r). Further, these PDEs are solved by taking different possibilities of radial functions. In the first case, all radial functions are considered same, while two functions are taken proportional to each other in second case, which further discussed by taking four different relationships between A(r), B(r) and F(r). For all cases, different forms of unknown functions of radial factor r are reported for nontrivial Noether operators with non-zero gauge term. At the end, a list of conserved quantities for each Noether operator Tables 1-4 is presented.
Two loop QCD vertices at the symmetric point
Gracey, J. A.
We compute the triple gluon, quark-gluon and ghost-gluon vertices of QCD at the symmetric subtraction point at two loops in the MS scheme. In addition we renormalize each of the three vertices in their respective momentum subtraction schemes, MOMggg, MOMq and MOMh. The conversion functions of all the wave functions, coupling constant and gauge parameter renormalization constants of each of the schemes relative to MS are determined analytically. These are then used to derive the three loop anomalous dimensions of the gluon, quark, Faddeev-Popov ghost and gauge parameter as well as the {beta} function in an arbitrary linear covariant gauge for each MOM scheme. There is good agreement of the latter with earlier Landau gauge numerical estimates of Chetyrkin and Seidensticker.
Cylindrically symmetric cosmological model of the universe in modified gravity
NASA Astrophysics Data System (ADS)
Mishra, B.; Vadrevu, Samhita
In this paper, we have constructed the cosmological models of the universe in a cylindrically symmetric space time in two classes of f(R,T) gravity (Harko et al. in Phys. Rev. D 84:024020, 2011). We have discussed two cases: one in the linear form and the other in the quadratic form of R. The matter is considered to be in the form of perfect fluid. It is observed that in the first case, the pressure and energy density remain the same, which reduces to a Zeldovich fluid. In the second case we have studied the quadratic function of f(R,T) gravity in the form f(R)=λ(R+R2) and f(T)=λ T. In the second case the pressure is in the negative domain and the energy density is in the positive domain, which confirms that the equation of state parameter is negative. The physical properties of the constructed models are studied.
Mueller matrix decomposition for extraction of individual polarization parameters from complex turbid media exhibiting multiple scattering, optical activity, and linear birefringence.
Ghosh, Nirmalya; Wood, Michael F G; Vitkin, I Alex
Linear birefringence and optical activity are two common optical polarization effects present in biological tissue, and determination of these properties has useful biomedical applications. However, measurement and unique interpretation of these parameters in tissue is hindered by strong multiple scattering effects and by the fact that these and other polarization effects are often present simultaneously. We have investigated the efficacy of a Mueller matrix decomposition methodology to extract the individual intrinsic polarimetry characteristics (linear retardance delta and optical rotation psi, in particular) from a multiply scattering medium exhibiting simultaneous linear birefringence and optical activity. In the experimental studies, a photoelastic modulation polarimeter was used to record Mueller matrices from polyacrylamide phantoms having strain-induced birefringence, sucrose-induced optical activity, and polystyrene microspheres-induced scattering. Decomposition of the Mueller matrices recorded in the forward detection geometry from these phantoms with controlled polarization properties yielded reasonable estimates for delta and psi parameters. The confounding effects of scattering, the propagation path of multiple scattered photons, and detection geometry on the estimated values for delta and psi were further investigated using polarization-sensitive Monte Carlo simulations. The results show that in the forward detection geometry, the effects of scattering induced linear retardance and diattenuation are weak, and the decomposition of the Mueller matrix can retrieve the intrinsic values for delta and psi with reasonable accuracy. The ability of this approach to extract the individual intrinsic polarimetry characteristics should prove valuable in diagnostic photomedicine, for example, in quantifying the small optical rotations due to the presence of glucose in tissue and for monitoring changes in tissue birefringence as a signature of tissue abnormality.
Linear ubiquitination in immunity.
Shimizu, Yutaka; Taraborrelli, Lucia; Walczak, Henning
Linear ubiquitination is a post-translational protein modification recently discovered to be crucial for innate and adaptive immune signaling. The function of linear ubiquitin chains is regulated at multiple levels: generation, recognition, and removal. These chains are generated by the linear ubiquitin chain assembly complex (LUBAC), the only known ubiquitin E3 capable of forming the linear ubiquitin linkage de novo. LUBAC is not only relevant for activation of nuclear factor-κB (NF-κB) and mitogen-activated protein kinases (MAPKs) in various signaling pathways, but importantly, it also regulates cell death downstream of immune receptors capable of inducing this response. Recognition of the linear ubiquitin linkage is specifically mediated by certain ubiquitin receptors, which is crucial for translation into the intended signaling outputs. LUBAC deficiency results in attenuated gene activation and increased cell death, causing pathologic conditions in both, mice, and humans. Removal of ubiquitin chains is mediated by deubiquitinases (DUBs). Two of them, OTULIN and CYLD, are constitutively associated with LUBAC. Here, we review the current knowledge on linear ubiquitination in immune signaling pathways and the biochemical mechanisms as to how linear polyubiquitin exerts its functions distinctly from those of other ubiquitin linkage types.
Future non-linear stability for solutions of the Einstein-Vlasov system of Bianchi types II and VI0
NASA Astrophysics Data System (ADS)
Nungesser, Ernesto
In a recent paper [E. Nungesser, "Future non-linear stability for reflection symmetric solutions of the Einstein-Vlasov system of Bianchi types II and VI0," Annales Henri Poincare (2012), 10.1007/s00023-012-0201-0], we have treated the future nonlinear stability for reflection symmetric solutions of the Einstein-Vlasov system of Bianchi types II and VI0. We have been able now to remove the reflection symmetry assumption, thus treating the non-diagonal case. Apart from the increasing complexity, the methods have been essentially the same as in the diagonal case, showing that they are thus quite powerful. Here, the challenge was to put the equations in a form that permits the use of the previous results. We are able to conclude that after a possible basis change, the future of the non-diagonal spacetimes in consideration is asymptotically diagonal.
Permutation inference for the general linear model
Winkler, Anderson M.; Ridgway, Gerard R.; Webster, Matthew A.; Smith, Stephen M.; Nichols, Thomas E.
Permutation methods can provide exact control of false positives and allow the use of non-standard statistics, making only weak assumptions about the data. With the availability of fast and inexpensive computing, their main limitation would be some lack of flexibility to work with arbitrary experimental designs. In this paper we report on results on approximate permutation methods that are more flexible with respect to the experimental design and nuisance variables, and conduct detailed simulations to identify the best method for settings that are typical for imaging research scenarios. We present a generic framework for permutation inference for complex general linear models (glms) when the errors are exchangeable and/or have a symmetric distribution, and show that, even in the presence of nuisance effects, these permutation inferences are powerful while providing excellent control of false positives in a wide range of common and relevant imaging research scenarios. We also demonstrate how the inference on glm parameters, originally intended for independent data, can be used in certain special but useful cases in which independence is violated. Detailed examples of common neuroimaging applications are provided, as well as a complete algorithm – the "randomise" algorithm – for permutation inference with the glm. PMID:24530839
The effects of linear assembly of two carbazole groups on acid-base and DNA-binding properties of a ruthenium(II) complex.
Chen, Xi; Xue, Long-Xin; Ju, Chun-Chuan; Wang, Ke-Zhi
A novel Ru(II) complex of [Ru(bpy)2(Hbcpip)](ClO4)2 {where bpy=2,2-bipyridine, Hbcpip=2-(4-(9H-3,9'-bicarbazol-9-yl)phenyl)-1H-imidazo[4,5-f][1,10]phenanthroline} is synthesized and characterized. Calf-thymus DNA-binding properties of the complex were studied by UV-vis absorption and luminescence titrations, steady-state emission quenching by [Fe(CN)6](4-), DNA competitive binding with ethidium bromide, thermal denaturation and DNA viscosity measurements. The results indicate that the complex partially intercalated into the DNA with a binding constant of (5.5±1.4)×10(5) M(-1) in buffered 50 mM NaCl. The acid-base properties of the complex were also studied by UV-visible and luminescence spectrophotometric pH titrations, and ground- and excited-state acidity ionization constant values were derived.
Propagation and attenuation characteristics of azimuthal symmetric surface waves in un-magnetized plasma column
NASA Astrophysics Data System (ADS)
Li, Wenqiu; Wang, Gang; Xiang, Dong; Su, Xiaobao
Phase and attenuation properties of azimuthal symmetric surface waves are investigated analytically in an un-magnetized cylindrical plasma column based on the transcendental dispersion relation. A novel method of calculating the wave power deposition in terms of complex electric conductivity is proposed. Electron density distribution is obtained theoretically through charged particle balance theory. It is shown that the effect of the electron temperature on the dispersion curve can be neglected when kzα < 1. Both the phase/attenuation characteristics and wave energy deposition properties of the azimuthal symmetric surface wave have an evident dependence on the electron density and the electron collision frequency.
Axially symmetric static sources of gravitational field
NASA Astrophysics Data System (ADS)
Hernandez-Pastora, J. L.; Herrera, L.; Martin, J.
A general procedure to find static and axially symmetric, interior solutions to the Einstein equations is presented. All the so obtained solutions, verify the energy conditions for a wide range of values of the parameters, and match smoothly to some exterior solution of the Weyl family, thereby representing globally regular models describing non-spherical sources of gravitational field. In the spherically symmetric limit, all our models converge to the well known incompressible perfect fluid solution. The key stone of our approach is based on an ansatz allowing to define the interior metric in terms of the exterior metric functions evaluated at the boundary source. Some particular sources are obtained, and the physical variables of the energy-momentum tensor are calculated explicitly, as well as the geometry of the source in terms of the relativistic multipole moments. The total mass of different configurations is also calculated, it is shown to be equal to the monopole of the exterior solution.
Multipartite maximally entangled states in symmetric scenarios
NASA Astrophysics Data System (ADS)
González-Guillén, Carlos E.
We consider the class of (N+1)-partite states suitable for protocols where there is a powerful party, the authority, and the other N parties play the same role, namely, the state of their system lies in the symmetric Hilbert space. We show that, within this scenario, there is a "maximally entangled state" that can be transform by a local operations and classical communication protocol into any other state. In addition, we show how to use the protocol efficiently, including the construction of the state, and discuss security issues for possible applications to cryptographic protocols. As an immediate consequence we recover a sequential protocol that implements the 1-to-N symmetric cloning.
Theory of connectivity for formally symmetric operators
Herrera, Ismael
A previous paper introduced the notion of complete connectivity conditions and developed variational principles for diffraction problems subjected to such restrictions. Here, an abstract definition of formally symmetric operators is given and it is shown that the problem of connecting solutions of equations associated with this kind of operators leads to complete connectivity conditions. The variational principles previously developed as well as a present more general one are thus applicable. The problem of connecting solutions defined in different regions is basic for finite element formulations. Formally symmetric operators occur in many branches of science and engineering. Applications are given here to potential theory, wave propagation, elasticity, and a general class of boundary integral equations. PMID:16592459
On the global behaviour of symmetric Skyrmions
NASA Astrophysics Data System (ADS)
Yang, Yisong
It is shown that the chiral angle, θ( r), of the hedgehog (symmetric) Skyrmions with an arbitrary baryon number, is a strictly decreasing or increasing function. For large values of r>0, θ( r) is strictly convex or concave. As r→∞, θ( r) and θ'( r) approach their limit values at the rate O r -α for any α∈(0,2).
PT symmetric Aubry-Andre model
NASA Astrophysics Data System (ADS)
Yuce, C.
PT symmetric Aubry-Andre model describes an array of N coupled optical waveguides with position-dependent gain and loss. We show that the reality of the spectrum depends sensitively on the degree of quasi-periodicity for small number of lattice sites. We obtain the Hofstadter butterfly spectrum and discuss the existence of the phase transition from extended to localized states. We show that rapidly changing periodical gain/loss materials almost conserve the total intensity.
Solitons in PT-symmetric nonlinear lattices
Abdullaev, Fatkhulla Kh.; Konotop, Vladimir V.; Zezyulin, Dmitry A.; Kartashov, Yaroslav V.
The existence of localized modes supported by the PT-symmetric nonlinear lattices is reported. The system considered reveals unusual properties: unlike other typical dissipative systems, it possesses families (branches) of solutions, which can be parametrized by the propagation constant; relatively narrow localized modes appear to be stable, even when the conservative nonlinear lattice potential is absent; and finally, the system supports stable multipole solutions.
Diagnostic and Therapeutic Advances: Distal Symmetric Polyneuropathy
Callaghan, Brian C.; Price, Raymond S.; Feldman, Eva L.
Importance Peripheral neuropathy is a highly prevalent and morbid condition affecting 2–7% of the population. Patients frequently suffer from pain and are at risk of falls, ulcerations, and amputations. We aimed to review recent diagnostic and therapeutic advances in peripheral neuropathy in distal symmetric polyneuropathy, the most common subtype of peripheral neuropathy. Observations and Advances Current evidence supports limited routine laboratory testing in patients with distal symmetric polyneuropathy. Patients without a known cause should have a complete blood count, comprehensive metabolic panel, B12, serum protein electrophoresis with immunofixation, fasting glucose, and a glucose tolerance test. The presence of atypical features such as asymmetry, non-length-dependence, motor predominance, acute or subacute onset, and/or prominent autonomic involvement should prompt a consultation with a neurologist or neuromuscular specialist. Electrodiagnostic tests and magnetic resonance imaging of the neuroaxis are the main drivers of the cost of the diagnostic evaluation, but evidence supporting their use is lacking. Strong evidence supports the use of tricyclic antidepressants, serotonin and norepinephrine reuptake inhibitors, and voltage-gated calcium channel ligands in the treatment of neuropathic pain. More intensive glucose control substantially reduces the incidence of distal symmetric polyneuropathy in patients with type 1 diabetes, but does not in type 2 diabetes. Conclusions and Relevance The opportunity exists to improve guideline concordant testing in distal symmetric polyneuropathy patients. Moreover, the role of electrodiagnostic tests needs to be further defined, and interventions to reduce magnetic resonance imaging use in this population are needed. Even though several efficacious medications exist for neuropathic pain treatment, pain is still under-recognized and undertreated. New disease modifying medications are needed to prevent and treat
Wave equation on spherically symmetric Lorentzian metrics
Bokhari, Ashfaque H.; Al-Dweik, Ahmad Y.; Zaman, F. D.; Kara, A. H.; Karim, M.
Wave equation on a general spherically symmetric spacetime metric is constructed. Noether symmetries of the equation in terms of explicit functions of {theta} and {phi} are derived subject to certain differential constraints. By restricting the metric to flat Friedman case the Noether symmetries of the wave equation are presented. Invertible transformations are constructed from a specific subalgebra of these Noether symmetries to convert the wave equation with variable coefficients to the one with constant coefficients.
Scattering from a PT symmetric standing wave
NASA Astrophysics Data System (ADS)
Yuce, C.
We study the Kapitza-Dirac diffraction of a free beam particle in the presence of a PT symmetric standing wave. We discuss that the momentum and total probability are not conserved in the non-Hermitian scattering process. We show that the average momentum gain/loss does not vanish over a period even if the non-Hermitian optical potential changes periodically in time. We give the resonance conditions at which large momentum transfer is produced.
Time-symmetric electrodynamics and quantum measurement
NASA Astrophysics Data System (ADS)
Pegg, D. T.
The application of the Wheeler-Feynman theory of time-symmetric electrodynamics to obtain definite answers to questions concerning the objective existence of quantum states in an optical EPR type of experiment is discussed. This theory allows the influence of the detector on the system being studied to be taken into account. The result is an entirely fresh understanding of experiments of the Kocher-Commins type.
Compensator configurations for load currents' symmetrization
NASA Astrophysics Data System (ADS)
Rusinaru, D.; Manescu, L. G.; Dinu, R. C.
This paper approaches aspects regarding the mitigation effects of asymmetries in 3-phase 3-wire networks. The measure consisting in connecting of load current symmetrization devices at the load coupling point is presented. A time-variation of compensators parameters is determined as a function of the time-recorded electrical values. The general sizing principle of the load current symmetrization reactive components is based on a simple equivalent model of the unbalanced 3-phase loads. By using these compensators a certain control of the power components transits is ensured in the network. The control is based on the variations laws of the compensators parameters as functions of the recorded electrical values: [B] = [T]·[M]. The link between compensator parameters and measured values is ensured by a transformation matrix [T] for each operation conditions of the supply network. Additional conditions for improving of energy and efficiency performance of the compensator are considered: i.e. reactive power compensation. The compensator sizing algorithm was implemented into a MATLAB environment software, which generate the time-evolution of the parameters of load current symmetrization device. The input data of application takes into account time-recording of the electrical values. By using the compensator sizing software, some results were achieved for the case of a consumer connected at 20 kV busbar of a distribution substation, during 24 hours measurement session. Even the sizing of the compensators aimed some additional network operation aspects (power factor correction) correlated with the total or major load symmetrizations, the harmonics aspects of the network values were neglected.
Symmetrical peripheral gangrene associated with peripartum cardiomyopathy
Jaryal, Ajay; Raina, Sujeet; Thakur, Surender; Sontakke, Tushar
Symmetrical peripheral gangrene (SPG) is a rare clinical entity. It was first described in late 19th century and since then has been reported with array of medical conditions mainly those complicated with shock, sepsis, and disseminated intravascular coagulation (DIC). Here in, we describe a parturient with peripartum cardiomyopathy (PPCM) and SPG. Clinicians should be aware of this entity as early recognition can help in reducing morbidity and mortality. PMID:23984243
Replication of avocado sunblotch viroid: evidence for a symmetric pathway with two rolling circles and hammerhead ribozyme processing.
Daròs, J A; Marcos, J F; Hernández, C; Flores, R
The structure of a series of RNAs extracted from avocado infected by the 247-nt avocado sunblotch viroid (ASBVd) was investigated. The identification of multistranded complexes containing circular ASBVd RNAs of (+) and (-) polarity suggests that replication of ASBVd proceeds through a symmetric pathway with two rolling circles where these two circular RNAs are the templates. This is in contrast to the replication of potato spindle tuber viroid and probably of most of its related viroids, which proceeds via an asymmetric pathway where circular (+)-strand and linear multimeric (-)-strand RNAs are the two templates. Linear (+) and (-) ASBVd RNAs of subgenomic length (137 nt and about 148 nt, respectively) and one linear (+)-strand ASBVd RNA of supragenomic length (383-384 nt) were also found in viroid-infected tissue. The two linear (+)-strand RNAs have the same 5'- and 3'-terminal sequences, with the supragenomic species being a fusion product of the monomeric and subgenomic (+)-strand ASBVd RNAs. The 3' termini of these two (+)-strand molecules, which at least in the subgenomic RNA has an extra nontemplate cytidylate residue, could represent sites of either premature termination of the (+)-strands or specific initiation of the (-)-strands. The 5' termini of sub- and supragenomic (+)-strand and the 5' terminus of the subgenomic (-)-strand ASBVd RNA are identical to those produced in the in vitro self-cleavage reactions of (+) and (-) dimeric ASBVd RNAs, respectively. These observations strongly suggest that the hammerhead structures which mediate the in vitro self-cleavage reactions are also operative in vivo. Images Fig. 1 Fig. 3 Fig. 4 Fig. 5 PMID:7809126
NASA Astrophysics Data System (ADS)
Morel, Danielle; Levy, William B.
Information processing in the brain is metabolically expensive and energy usage by the different components of the nervous system is not well understood. In a continuing effort to explore the costs and constraints of information processing at the single neuron level, dendritic processes are being studied. More specifically, the role of various ion channel conductances is explored in terms of integrating dendritic excitatory synaptic input. Biophysical simulations of dendritic behavior show that the complexity of voltage-dependent, non-linear dendritic conductances can produce simplicity in the form of linear synaptic integration. Over increasing levels of synaptic activity, it is shown that two types of voltage-dependent conductances produce linearization over a limited range. This range is determined by the parameters defining the ion channel and the 'passive' properties of the dendrite. A persistent sodium and a transient A-type potassium channel were considered at steady-state transmembrane potentials in the vicinity of and hyperpolarized to the threshold for action potential initiation. The persistent sodium is seen to amplify and linearize the synaptic input over a short range of low synaptic activity. In contrast, the A-type potassium channel has a broader linearization range but tends to operate at higher levels of synaptic bombardment. Given equivalent 'passive' dendritic properties, the persistent sodium is found to be less costly than the A-type potassium in linearizing synaptic input.
Construction of an enterobactin analogue with symmetrically arranged monomer subunits of ferritin.
Nakajima, Hiroshi; Kondo, Mio; Nakane, Taiki; Abe, Satoshi; Nakao, Takahiro; Watanabe, Yoshihito; Ueno, Takafumi
A set of three catecholamide ligands mimicking the structure of enterobactin was constructed on ferritin, where the 3-fold symmetric arrangement of the monomer subunits served as a foundation to form a coordination space. Similar to enterobactin, the ligands showed strong affinity for the ferric ion and formed a tris-catechoyl complex. Crystallography revealed that the complex was embedded in the entrance of the 3-fold axis channel.
Spherically symmetric thick branes cosmological evolution
NASA Astrophysics Data System (ADS)
Bernardini, A. E.; Cavalcanti, R. T.; da Rocha, Roldão
Spherically symmetric time-dependent solutions for the 5D system of a scalar field canonically coupled to gravity are obtained and identified as an extension of recent results obtained by Ahmed et al. (JHEP 1404:061. arXiv:1312.3576 [hep-th], 2014). The corresponding cosmology of models with regularized branes generated by such a 5D scalar field scenario is also investigated. It has been shown that the anisotropic evolution of the warp factor and consequently the Hubble like parameter are both driven by the radial coordinate on the brane, which leads to an emergent thick brane-world scenario with spherically symmetric time dependent warp factor. Meanwhile, the separability of variables depending on fifth dimension, , which is exhibited by the equations of motion, allows one to recover the extra dimensional profiles obtained in Ahmed et al. (2014), namely the extra dimensional part of the scale (warp) factor and the scalar field dependence on . Therefore, our results are mainly concerned with the time dependence of a spherically symmetric warp factor. Besides evincing possibilities for obtaining asymmetric stable brane-world scenarios, the extra dimensional profiles here obtained can also be reduced to those ones investigated in Ahmed et al. (2014).
Distal symmetrical polyneuropathy: definition for clinical research.
England, J D; Gronseth, G S; Franklin, G; Miller, R G; Asbury, A K; Carter, G T; Cohen, J A; Fisher, M A; Howard, J F; Kinsella, L J; Latov, N; Lewis, R A; Low, P A; Sumner, A J
The objective of this report was to develop a case definition of "distal symmetrical polyneuropathy" to standardize and facilitate clinical research and epidemiological studies. A formalized consensus process was employed to reach agreement after a systematic review and classification of evidence from the literature. The literature indicates that symptoms alone have relatively poor diagnostic accuracy in predicting the presence of polyneuropathy; signs are better predictors of polyneuropathy than symptoms; and single abnormalities on examination are less sensitive than multiple abnormalities in predicting the presence of polyneuropathy. The combination of neuropathic symptoms, signs, and electrodiagnostic findings provides the most accurate diagnosis of distal symmetrical polyneuropathy. A set of case definitions was rank ordered by likelihood of disease. The highest likelihood of polyneuropathy (useful for clinical trials) occurs with a combination of multiple symptoms, multiple signs, and abnormal electrodiagnostic studies. A modest likelihood of polyneuropathy (useful for field or epidemiological studies) occurs with a combination of multiple symptoms and multiple signs when the results of electrodiagnostic studies are not available. A lower likelihood of polyneuropathy occurs when electrodiagnostic studies and signs are discordant. For research purposes, the best approach for defining distal symmetrical polyneuropathy is a set of case definitions rank ordered by estimated likelihood of disease. The inclusion of this formalized case definition in clinical and epidemiological research studies will ensure greater consistency of case selection.
Symmetric smoothing filters from global consistency constraints.
Haque, Sheikh Mohammadul; Pai, Gautam P; Govindu, Venu Madhav
Many patch-based image denoising methods can be viewed as data-dependent smoothing filters that carry out a weighted averaging of similar pixels. It has recently been argued that these averaging filters can be improved using their doubly stochastic approximation, which are symmetric and stable smoothing operators. In this paper, we introduce a simple principle of consistency that argues that the relative similarities between pixels as imputed by the averaging matrix should be preserved in the filtered output. The resultant consistency filter has the theoretically desirable properties of being symmetric and stable, and is a generalized doubly stochastic matrix. In addition, we can also interpret our consistency filter as a specific form of Laplacian regularization. Thus, our approach unifies two strands of image denoising methods, i.e., symmetric smoothing filters and spectral graph theory. Our consistency filter provides high-quality image denoising and significantly outperforms the doubly stochastic version. We present a thorough analysis of the properties of our proposed consistency filter and compare its performance with that of other significant methods for image denoising in the literature.
Corelation between Complexity and Stability in Multicellular Organisms
NASA Astrophysics Data System (ADS)
Werman, Steven D.; Qaddour, Jihad; Deyoung, Gary; Misra, Prasanta K.
We present a model to study the corelation between the complexity and stability of unicellular and multicellular organisms. We state the postulates made by us and define the thermodynamic functions and other parameters used to formulate the problem. We have also used several theorems based on reasonable assumptions to analyze the functional interactions which are non-symmetric, non-local and non-instantaneous. The mathematical model developed by using these hypotheses is explained in detail and a set of non-linear equations for each type of organism is presented. We present the results obtained by us by solving these equations.
Calculating vibrational spectra without determining excited eigenstates: Solving the complex linear equations of damped response theory for vibrational configuration interaction and vibrational coupled cluster states.
Godtliebsen, Ian H; Christiansen, Ove
It is demonstrated how vibrational IR and Raman spectra can be calculated from damped response functions using anharmonic vibrational wave function calculations, without determining the potentially very many eigenstates of the system. We present an implementation for vibrational configuration interaction and vibrational coupled cluster, and describe how the complex equations can be solved using iterative techniques employing only real trial vectors and real matrix-vector transformations. Using this algorithm, arbitrary frequency intervals can be scanned independent of the number of excited states. Sample calculations are presented for the IR-spectrum of water, Raman spectra of pyridine and a pyridine-silver complex, as well as for the infra-red spectrum of oxazole, and vibrational corrections to the polarizability of formaldehyde.
Calculating vibrational spectra without determining excited eigenstates: Solving the complex linear equations of damped response theory for vibrational configuration interaction and vibrational coupled cluster states
NASA Astrophysics Data System (ADS)
Godtliebsen, Ian H.; Christiansen, Ove
It is demonstrated how vibrational IR and Raman spectra can be calculated from damped response functions using anharmonic vibrational wave function calculations, without determining the potentially very many eigenstates of the system. We present an implementation for vibrational configuration interaction and vibrational coupled cluster, and describe how the complex equations can be solved using iterative techniques employing only real trial vectors and real matrix-vector transformations. Using this algorithm, arbitrary frequency intervals can be scanned independent of the number of excited states. Sample calculations are presented for the IR-spectrum of water, Raman spectra of pyridine and a pyridine-silver complex, as well as for the infra-red spectrum of oxazole, and vibrational corrections to the polarizability of formaldehyde.
Mo and W dihalide complexes with uncommon trigonal-prismatic geometry imposed by the linear tetraphosphine ancillary ligand and their reactivities toward diazoalkanes.
Seino, Hidetake; Watanabe, Daisuke; Ohnishi, Takeshi; Arita, Chirima; Mizobe, Yasushi
New Mo and W tetraphosphine-dihalide complexes [MX2(kappa4-P4)] (2, MX=MoCl, MoBr, WBr; P4=meso-o-C6H4(PPhCH2CH2PPh2)2) with uncommon trigonal-prismatic geometries have been prepared. Treatment of ethyl diazoacetate with 2 (MX=MoCl) resulted in catalytic carbenoid-group coupling to give diethyl maleate and fumarate, whereas reactions of 2 with trimethylsilyldiazoalkane formed the diazoalkane complexes trans-[MX(NN=CHSiMe3)-(kappa4-P4)]+ (3+) and cis,mer-[MoCl2(NN=CHSiMe3)(kappa3-P4)]. The molecular structures of 2 (MX=MoCl) and 3[PF6] (MX=WBr) were crystallographically determined.
Propagation Effects on the Breakdown of a Linear Amplifier Model: Complex-Mass Schrödinger Equation Driven by the Square of a Gaussian Field
NASA Astrophysics Data System (ADS)
Mounaix, Philippe; Collet, Pierre; Lebowitz, Joel L.
Solutions to the equation [InlineMediaObject not available: see fulltext.] are investigated, where S( x, t) is a complex Gaussian field with zero mean and specified covariance, and m≠0 is a complex mass with Im( m) ≥ 0. For real m this equation describes the backscattering of a smoothed laser beam by an optically active medium. Assuming that S( x, t) is the sum of a finite number of independent complex Gaussian random variables, we obtain an expression for the value of λ at which the q th moment of [InlineMediaObject not available: see fulltext.] w.r.t. the Gaussian field S diverges. This value is found to be less or equal for all m ≠ 0, Im( m) ≥ 0 and | m|<+∞ than for | m| = +∞, i.e. when the [InlineMediaObject not available: see fulltext.] term is absent. Our solution is based on a distributional formulation of the Feynman path-integral and the Paley-Wiener theorem.
Ordinary versus PT-symmetric Φ³ quantum field theory
Bender, Carl M.; Branchina, Vincenzo; Messina, Emanuele
A quantum-mechanical theory is PT-symmetric if it is described by a Hamiltonian that commutes with PT, where the operator P performs space reflection and the operator T performs time reversal. A PT-symmetric Hamiltonian often has a parametric region of unbroken PT symmetry in which the energy eigenvalues are all real. There may also be a region of broken PT symmetry in which some of the eigenvalues are complex. These regions are separated by a phase transition that has been repeatedly observed in laboratory experiments. This paper focuses on the properties of a PT-symmetric igΦ³ quantum field theory. This quantum field theory is the analog of the PT-symmetric quantum-mechanical theory described by the Hamiltonian H=p²+ix³, whose eigenvalues have been rigorously shown to be all real. This paper compares the renormalization group properties of a conventional Hermitian gΦ³ quantum field theory with those of the PT-symmetric igΦ³ quantum field theory. It is shown that while the conventional gΦ³ theory in d=6 dimensions is asymptotically free, the igΦ³ theory is like a gΦ⁴ theory in d=4 dimensions; it is energetically stable, perturbatively renormalizable, and trivial.
Ordinary versus PT-symmetric Φ³ quantum field theory
Bender, Carl M.; Branchina, Vincenzo; Messina, Emanuele
A quantum-mechanical theory is PT-symmetric if it is described by a Hamiltonian that commutes with PT, where the operator P performs space reflection and the operator T performs time reversal. A PT-symmetric Hamiltonian often has a parametric region of unbroken PT symmetry in which the energy eigenvalues are all real. There may also be a region of broken PT symmetry in which some of the eigenvalues are complex. These regions are separated by a phase transition that has been repeatedly observed in laboratory experiments. This paper focuses on the properties of a PT-symmetric igΦ³ quantum field theory. This quantum fieldmore » theory is the analog of the PT-symmetric quantum-mechanical theory described by the Hamiltonian H=p²+ix³, whose eigenvalues have been rigorously shown to be all real. This paper compares the renormalization group properties of a conventional Hermitian gΦ³ quantum field theory with those of the PT-symmetric igΦ³ quantum field theory. It is shown that while the conventional gΦ³ theory in d=6 dimensions is asymptotically free, the igΦ³ theory is like a gΦ⁴ theory in d=4 dimensions; it is energetically stable, perturbatively renormalizable, and trivial.« less
Nonthermal and geometric effects on the symmetric and anti-symmetric surface waves in a Lorentzian dusty plasma slab
Lee, Myoung-Jae; Jung, Young-Dae
The nonthermal and geometric effects on the propagation of the surface dust acoustic waves are investigated in a Lorentzian dusty plasma slab. The symmetric and anti-symmetric dispersion modes of the dust acoustic waves are obtained by the plasma dielectric function with the spectral reflection conditions the slab geometry. The variation of the nonthermal and geometric effects on the symmetric and the anti-symmetric modes of the surface plasma waves is also discussed.
Colgate, S.A.
An improvement is presented in linear accelerators for charged particles with respect to the stable focusing of the particle beam. The improvement consists of providing a radial electric field transverse to the accelerating electric fields and angularly introducing the beam of particles in the field. The results of the foregoing is to achieve a beam which spirals about the axis of the acceleration path. The combination of the electric fields and angular motion of the particles cooperate to provide a stable and focused particle beam.
Asymmetric and symmetric meta-correlations in financial markets
NASA Astrophysics Data System (ADS)
Li, Xiaohui; Shen, Xiangying; Huang, Jiping
In financial markets, the relation between fluctuations of stock prices and trading behaviors is complex. It is intriguing to quantify this kind of meta-correlation between market fluctuations and the synchronous behaviors. We refine the theoretical index leverage model proposed by Reigneron et al., to exactly quantify the meta-correlation under various levels of price fluctuations [Reigneron P A, Allez R and Bouchaud J P 2011 Physica A 390 3026]. The characteristics of meta-correlations in times of market losses, are found to be significantly different in Chinese and American financial markets. In addition, unlike the asymmetric results at the daily scale, the correlation behaviors are found to be symmetric at the high-frequency scale. Project supported by the National Natural Science Foundation of China (Grant No. 11222544), the Fok Ying Tung Education Foundation (Grant No. 131008), and the Program for New Century Excellent Talents in University, China (Grant No. NCET-12-0121).
NASA Technical Reports Server (NTRS)
2006-01-01[figure removed for brevity, see original site] Context image for PIA03667 Linear Clouds These clouds are located near the edge of the south polar region. The cloud tops are the puffy white features in the bottom half of the image. Image information: VIS instrument. Latitude -80.1N, Longitude 52.1E. 17 meter/pixel resolution. Note: this THEMIS visual image has not been radiometrically nor geometrically calibrated for this preliminary release. An empirical correction has been performed to remove instrumental effects. A linear shift has been applied in the cross-track and down-track direction to approximate spacecraft and planetary motion. Fully calibrated and geometrically projected images will be released through the Planetary Data System in accordance with Project policies at a later time. NASA's Jet Propulsion Laboratory manages the 2001 Mars Odyssey mission for NASA's Office of Space Science, Washington, D.C. The Thermal Emission Imaging System (THEMIS) was developed by Arizona State University, Tempe, in collaboration with Raytheon Santa Barbara Remote Sensing. The THEMIS investigation is led by Dr. Philip Christensen at Arizona State University. Lockheed Martin Astronautics, Denver, is the prime contractor for the Odyssey project, and developed and built the orbiter. Mission operations are conducted jointly from Lockheed Martin and from JPL, a division of the California Institute of Technology in Pasadena.
On stable solitons and interactions of the generalized Gross-Pitaevskii equation with P T - and non- P T -symmetric potentials
NASA Astrophysics Data System (ADS)
Yan, Zhenya; Chen, Yong; Wen, Zichao
We report the bright solitons of the generalized Gross-Pitaevskii (GP) equation with some types of physically relevant parity-time- ( P T -) and non- P T -symmetric potentials. We find that the constant momentum coefficient Γ can modulate the linear stability and complicated transverse power-flows (not always from the gain toward loss) of nonlinear modes. However, the varying momentum coefficient Γ ( x ) can modulate both unbroken linear P T -symmetric phases and stability of nonlinear modes. Particularly, the nonlinearity can excite the unstable linear mode (i.e., broken linear P T -symmetric phase) to stable nonlinear modes. Moreover, we also find stable bright solitons in the presence of non- P T -symmetric harmonic-Gaussian potential. The interactions of two bright solitons are also illustrated in P T -symmetric potentials. Finally, we consider nonlinear modes and transverse power-flows in the three-dimensional (3D) GP equation with the generalized P T -symmetric Scarff-II potential.
Development of the complex general linear model in the Fourier domain: application to fMRI multiple input-output evoked responses for single subjects.
Rio, Daniel E; Rawlings, Robert R; Woltz, Lawrence A; Gilman, Jodi; Hommer, Daniel W
A linear time-invariant model based on statistical time series analysis in the Fourier domain for single subjects is further developed and applied to functional MRI (fMRI) blood-oxygen level-dependent (BOLD) multivariate data. This methodology was originally developed to analyze multiple stimulus input evoked response BOLD data. However, to analyze clinical data generated using a repeated measures experimental design, the model has been extended to handle multivariate time series data and demonstrated on control and alcoholic subjects taken from data previously analyzed in the temporal domain. Analysis of BOLD data is typically carried out in the time domain where the data has a high temporal correlation. These analyses generally employ parametric models of the hemodynamic response function (HRF) where prewhitening of the data is attempted using autoregressive (AR) models for the noise. However, this data can be analyzed in the Fourier domain. Here, assumptions made on the noise structure are less restrictive, and hypothesis tests can be constructed based on voxel-specific nonparametric estimates of the hemodynamic transfer function (HRF in the Fourier domain). This is especially important for experimental designs involving multiple states (either stimulus or drug induced) that may alter the form of the response function.
Application of non-linear angle synchronous spectrofluorimetry to the determination of complex mixtures of drugs in urine: A comparative study
NASA Astrophysics Data System (ADS)
Murillo Pulgarín, J. A.; Alañón Molina, A.; Boras, N.
Synchronous fluorescence spectroscopy (SFS) is a rapid, sensitive and non-destructive method suitable for the analysis of multifluorophoric mixtures. In this study non linear variable angle synchronous spectrofluorimetry was applied to the determination of three fluoroquinololes in urine. Although this technique provides very good results, total resolution of multicomponent mixtures is not always achieved when the spectral profiles strongly overlap. Partial least-squares regression (PLS-1) was utilized to a develop calibration model that related synchronous fluorescence spectra to the analytical concentration of fluoroquinolones in the presence of urine. The same multicomponent mixture was determined using excitation emission matrix fluorescence (EEMF) along with N-way partial least squares regression (N-PLS and U-PLS). The determination was carried out in micellar medium 0.01 M with a pH of 4.8 provided by 0.2 M sodium acetate/acetic acid buffer. A central composite design was selected to obtain a calibration matrix of 25 standards plus a blank sample. The proposed methods were validated by application to a test set of synthetic samples. The results show that SFS with PLS-1 is a better method compared to EEMF with N-PLS or U-PLS because of the low RMSEP values of the former.
Whorled hairless nevus of the scalp, linear hyperpigmentation, and telangiectatic nevi of the lower limbs: a novel variant of the "phacomatosis complex".
Castori, Marco; Scarciolla, Oronzo; Morlino, Silvia; Manente, Liborio; Biscaglia, Assunta; Fragasso, Alberto; Grammatico, Paola
The term "phacomatosis" refers to a growing number of sporadic genetic skin disorders characterized by the combination of two or more different nevi and possibly resulting from non-allelic twin spotting. While phacomatosis pigmentovascularis (PPV) and pigmentokeratotica represent the most common patterns, some patients do not fit with either condition and are temporarily classified as unique phenotypes. We report on an 8-year-old boy with striking right hemihypoplasia, resulting in limb asymmetry and fixed dislocation of right hip. Skin on the affected side showed three distinct nevi: (i) A whorled, hairless nevus of the scalp in close proximity with (ii) epidermal hyperpigmentation following lines of Blaschko on the neck and right upper limb, and (iii) multiple telangiectatic nevi of the right lower limb and hemiscrotum. Didymosis atricho-melanotica was proposed for the combination of adjacent patchy congenital alopecia and linear hyperpigmentation, while phacomatosis atricho-pigmento-vascularis appears to define the entire cutaneous phenotype, thus implying the involvement of three neighboring loci influencing the development of distinct constituents of the skin. Given the striking asymmetry of the observed phenotype, the effect of mosaicism (either genomic or functional) for a mutation in a single gene with pleiotropic action and influenced by the lateralization pattern of early development cannot be excluded.
Nonlinear reversal of the PT -symmetric phase transition in a system of coupled semiconductor microring resonators
NASA Astrophysics Data System (ADS)
Hassan, Absar U.; Hodaei, Hossein; Miri, Mohammad-Ali; Khajavikhan, Mercedeh; Christodoulides, Demetrios N.
A system of two coupled semiconductor-based resonators is studied when lasing around an exceptional point. We show that the presence of nonlinear saturation effects can have important ramifications on the transition behavior of this system. In sharp contrast with linear PT -symmetric configurations, nonlinear processes are capable of reversing the order in which the symmetry breaking occurs. Yet, even in the nonlinear regime, the resulting non-Hermitian states still retain the structural form of the corresponding linear eigenvectors expected above and below the phase-transition point. The conclusions of our analysis are in agreement with experimental data.
High-efficiency Fresnel lens fabricated by axially symmetric photoalignment method.
Huang, Yao-Han; Ko, Shih-Wei; Chu, Shu-Chun; Fuh, Andy Ying-Guey
In this study, a Fresnel lens with radial and azimuthal liquid crystal (LC) alignments in the odd and even zones was fabricated using the photoalignment technique based on an azo dye doped in LC cells. The lens has approximately 35% focusing efficiency as determined using a linearly polarized probe beam. In addition, the lens converts the input linear polarization into axially symmetrical polarization at the focal plane. The fabricated Fresnel lens is polarization-independent and has electrically controllable focusing efficiency. Moreover, the far-field pattern of a probe beam through the device placed between the polarizers agrees with the pattern obtained from the simulation.
Towards an exact theory of linear absorbance and circular dichroism of pigment-protein complexes: Importance of non-secular contributions
Dinh, Thanh-Chung; Renger, Thomas
A challenge for the theory of optical spectra of pigment-protein complexes is the equal strength of the pigment-pigment and the pigment-protein couplings. Treating both on an equal footing so far can only be managed by numerically costly approaches. Here, we exploit recent results on a normal mode analysis derived spectral density that revealed the dominance of the diagonal matrix elements of the exciton-vibrational coupling in the exciton state representation. We use a cumulant expansion technique that treats the diagonal parts exactly, includes an infinite summation of the off-diagonal parts in secular and Markov approximations, and provides a systematic perturbative way to include non-secular and non-Markov corrections. The theory is applied to a model dimer and to chlorophyll (Chl) a and Chl b homodimers of the reconstituted water-soluble chlorophyll-binding protein (WSCP) from cauliflower. The model calculations reveal that the non-secular/non-Markov effects redistribute oscillator strength from the strong to the weak exciton transition in absorbance and they diminish the rotational strength of the exciton transitions in circular dichroism. The magnitude of these corrections is in a few percent range of the overall signal, providing a quantitative explanation of the success of time-local convolution-less density matrix theory applied earlier. A close examination of the optical spectra of Chl a and Chl b homodimers in WSCP suggests that the opening angle between Q{sub y} transition dipole moments in Chl b homodimers is larger by about 9{sup ∘} than for Chl a homodimers for which a crystal structure of a related WSCP complex exists. It remains to be investigated whether this change is due to a different mutual geometry of the pigments or due to the different electronic structures of Chl a and Chl b.
Towards an exact theory of linear absorbance and circular dichroism of pigment-protein complexes: Importance of non-secular contributions
NASA Astrophysics Data System (ADS)
Dinh, Thanh-Chung; Renger, Thomas
A challenge for the theory of optical spectra of pigment-protein complexes is the equal strength of the pigment-pigment and the pigment-protein couplings. Treating both on an equal footing so far can only be managed by numerically costly approaches. Here, we exploit recent results on a normal mode analysis derived spectral density that revealed the dominance of the diagonal matrix elements of the exciton-vibrational coupling in the exciton state representation. We use a cumulant expansion technique that treats the diagonal parts exactly, includes an infinite summation of the off-diagonal parts in secular and Markov approximations, and provides a systematic perturbative way to include non-secular and non-Markov corrections. The theory is applied to a model dimer and to chlorophyll (Chl) a and Chl b homodimers of the reconstituted water-soluble chlorophyll-binding protein (WSCP) from cauliflower. The model calculations reveal that the non-secular/non-Markov effects redistribute oscillator strength from the strong to the weak exciton transition in absorbance and they diminish the rotational strength of the exciton transitions in circular dichroism. The magnitude of these corrections is in a few percent range of the overall signal, providing a quantitative explanation of the success of time-local convolution-less density matrix theory applied earlier. A close examination of the optical spectra of Chl a and Chl b homodimers in WSCP suggests that the opening angle between Qy transition dipole moments in Chl b homodimers is larger by about 9∘ than for Chl a homodimers for which a crystal structure of a related WSCP complex exists. It remains to be investigated whether this change is due to a different mutual geometry of the pigments or due to the different electronic structures of Chl a and Chl b.
Four-coordinate nickel(II) and copper(II) complex based ONO tridentate Schiff base ligands: synthesis, molecular structure, electrochemical, linear and nonlinear properties, and computational study.
Novoa, Néstor; Roisnel, Thierry; Hamon, Paul; Kahlal, Samia; Manzur, Carolina; Ngo, Hoang Minh; Ledoux-Rak, Isabelle; Saillard, Jean-Yves; Carrillo, David; Hamon, Jean-René
We report the synthesis, characterization, crystal structures, nonlinear-optical (NLO) properties, and density functional theory (DFT) calculations of nickel(ii) and copper(ii) complex based ONO tridentate Schiff base ligands: two mononuclear compounds, [Ni(An-ONO)(NC5H5)] (5) and [Cu(An-ONO)(4-NC5H4C(CH3)3)] (6), and two heterobimetallic species, [M(Fc-ONO)(NC5H5)] (M = Ni, 7; Cu, 8), where An-ONOH2 (3) and Fc-ONOH2 (4) are the 1 : 1 condensation products of 2-aminophenol and p-anisoylacetone and ferrocenoylacetone, respectively. These compounds were characterised by microanalysis, FT-IR and X-ray crystallography in the solid state and in solution by UV-vis and (1)H and (13)C NMR spectroscopy. The crystal structures of 3-5, 7 and 8 have been determined and show for Schiff base complexes 5, 7 and 8 a four-coordinated square-planar environment for nickel and copper ions. The electrochemical behavior of all derivatives 3-8 was investigated by cyclic voltammetry in dichloromethane, and discussed on the basis of DFT-computed electronic structures of the neutral and oxidized forms of the compounds. The second-order NLO responses of 3-8 have been determined by harmonic light scattering measurements using a 10(-2) M solution of dichloromethane and working with a 1.91 μm incident wavelength, giving rather high β1.91 values of 350 and 290 × 10(-30) esu for the mononuclear species 5 and 6, respectively. The assignment and the nature of the electronic transitions observed in the UV-vis spectra were analyzed using time-dependent (TD) DFT calculations. They are dominated by LMCT, MLCT and π-π* transitions.
Towards an exact theory of linear absorbance and circular dichroism of pigment-protein complexes: importance of non-secular contributions.
Dinh, Thanh-Chung; Renger, Thomas
A challenge for the theory of optical spectra of pigment-protein complexes is the equal strength of the pigment-pigment and the pigment-protein couplings. Treating both on an equal footing so far can only be managed by numerically costly approaches. Here, we exploit recent results on a normal mode analysis derived spectral density that revealed the dominance of the diagonal matrix elements of the exciton-vibrational coupling in the exciton state representation. We use a cumulant expansion technique that treats the diagonal parts exactly, includes an infinite summation of the off-diagonal parts in secular and Markov approximations, and provides a systematic perturbative way to include non-secular and non-Markov corrections. The theory is applied to a model dimer and to chlorophyll (Chl) a and Chl b homodimers of the reconstituted water-soluble chlorophyll-binding protein (WSCP) from cauliflower. The model calculations reveal that the non-secular/non-Markov effects redistribute oscillator strength from the strong to the weak exciton transition in absorbance and they diminish the rotational strength of the exciton transitions in circular dichroism. The magnitude of these corrections is in a few percent range of the overall signal, providing a quantitative explanation of the success of time-local convolution-less density matrix theory applied earlier. A close examination of the optical spectra of Chl a and Chl b homodimers in WSCP suggests that the opening angle between Qy transition dipole moments in Chl b homodimers is larger by about 9(∘) than for Chl a homodimers for which a crystal structure of a related WSCP complex exists. It remains to be investigated whether this change is due to a different mutual geometry of the pigments or due to the different electronic structures of Chl a and Chl b.
Symmetrical and anti-symmetrical coherent perfect absorption for acoustic waves
Wei, Pengjiang; Croënne, Charles; Tak Chu, Sai; Li, Jensen
We investigate tunable acoustic absorption enabled by the coherent control of input waves. It relies on coherent perfect absorption originally proposed in optics. By designing appropriate acoustic metamaterial structures with resonating effective bulk modulus or density, we show that complete absorption of incident waves impinging on the metamaterial can be achieved for either symmetrical or anti-symmetrical inputs in the forward and backward directions. By adjusting the relative phase between the two incident beams, absorption can be tuned effectively from unity to zero, making coherent control useful in applications like acoustic modulators, noise controllers, transducers, and switches.
A synthetic method to access symmetric and non-symmetric 2-(N,N'-disubstituted)guanidinebenzothiazoles.
Cruz, Alejandro; Padilla-Martínez, Itzia I; García-Báez, Efrén V
Symmetric and non-symmetric 2-(N-H, N-methyl, N-ethylenyl and N-aryl)guanidinebenzothiazoles were synthesized from the reaction of ammonia, methylamine, pyrrolidine and aniline with dimethyl benzo[d]thiazol-2-yl-carbonodithioimidate as intermediate. The products were characterized by ¹H-, ¹³C-NMR spectroscopy and three of them by X-ray diffraction analysis. HN-phenyl protons formed intramolecular hydrogen bonds that assist the stereochemistry of the second substituent, whereas the HN-alkyl protons were involved in intermolecular hydrogen bonding.
Symmetrical band-pass loudspeaker systems
NASA Astrophysics Data System (ADS)
Matusiak, Grzegorz Piotr
Loudspeaker systems are analyzed in a doctoral dissertation. The dissertation concerns loudspeaker systems, which are known as subwoofers or band-pass loudspeaker systems. Their advantages include: high- quality sound reproduction in the low-frequency range, small dimensions, small nonlinear distortions and the fact that they can be placed anywhere in a room or car. Band-pass loudspeaker systems are used widely in the so- called Home Theatre as well as to provide sound in cinema, theatre, concert, discotheque, opera, operetta, philharmonic and amphitheater halls, at open-air concerts, and so on. Various designs are mass-produced by a large number of manufacturers. The study covers an analysis of band-pass loudspeaker systems to which the frequency transformation, i.e. the reactance transformation, has been applied. Since this is a symmetrical transformation, amplitude frequency responses of the studied band-pass systems are also symmetrical (logarithmic scale of a frequency). As a result, the high-pass loudspeaker system design method, known as the Thiele-Small, Benson analysis, can be employed. The investigations include the formulation of band-pass system equations (fourth, sixth and eighth-order polynomials) and the subsequent derivation of relations for the calculation of system parameters. The obtained results enable the calculation of optimum designs for prescribed alignments, e.g. (Chebyshev) equal-ripple, (Butterworth) maximally flat, or quasi-maximally flat (QB). The analysis covers fourth, sixth and eighth-order symmetrical systems. Eighth-order systems have been divided into three kinds according to three ways of physical realization. The doctoral dissertation includes band-pass loudspeaker systems, which can be designed with active or passive filters or without the filter. Designed systems consist of a loudspeaker whose front of a diaphragm is loaded with a Helmholtz resonator, i.e. an enclosure with a vent, which radiates sound outwards. The back is
Symmetric Toeplitz-Structured Compressed Sensing Matrices
NASA Astrophysics Data System (ADS)
Huang, Tao; Fan, Yi-Zheng; Zhu, Ming
How to construct a suitable measurement matrix is an important topic in compressed sensing. A significant part of the recent work is that the measurement matrices are not completely random on the entries but exhibit some considerable structures. In this paper, we proved that a symmetric Toeplitz matrix and its variant can be used as measurement matrices and recovery signal with high probability. Compared with random matrices (e.g. Gaussian and Bernoulli matrices) and some structured matrices (e.g. Toeplitz and circulant matrices), we need to generate fewer independent entries to obtain the measurement matrix while the effectiveness of the recovery keeps good.
Scalar resonances in axially symmetric spacetimes
NASA Astrophysics Data System (ADS)
Ranea-Sandoval, Ignacio F.; Vucetich, Héctor
We study properties of resonant solutions to the scalar wave equation in several axially symmetric spacetimes. We prove that nonaxial resonant modes do not exist neither in the Lanczos dust cylinder, the extreme (2 + 1) dimensional Bañados-Taitelboim-Zanelli (BTZ) spacetime nor in a class of simple rotating wormhole solutions. Moreover, we find unstable solutions to the wave equation in the Lanczos dust cylinder and in the r2 < 0 region of the extreme (2 + 1) dimensional BTZ spacetime, two solutions that possess closed timelike curves. Similarities with previous results obtained for the Kerr spacetime are explored.
Quantum asymmetric cryptography with symmetric keys
NASA Astrophysics Data System (ADS)
Gao, Fei; Wen, Qiaoyan; Qin, Sujuan; Zhu, Fuchen
Based on quantum encryption, we present a new idea for quantum public-key cryptography (QPKC) and construct a whole theoretical framework of a QPKC system. We show that the quantum-mechanical nature renders it feasible and reasonable to use symmetric keys in such a scheme, which is quite different from that in conventional public-key cryptography. The security of our scheme is analyzed and some features are discussed. Furthermore, the state-estimation attack to a prior QPKC scheme is demonstrated.
Synthesis of controllers for symmetric systems
NASA Astrophysics Data System (ADS)
Ameur Abid, Chiheb; Zouari, Belhassen
This article deals with supervisory control problem for coloured Petri (CP) nets. Considering a CP-net, we build a condensed version of the ordinary state-space, namely the symbolic reachability graph (SRG). This latter graph allows to cope with state-space explosion problem for symmetric systems. The control specification can be expressed in terms of either forbidden states or forbidden sequences of transitions. According to these specifications, we derive the controller by applying the theory of regions on the basis of the SRG. Thanks to expressiveness power of CP-nets, the obtained controller to be connected to the plant model is reduced to one single place.
Anisotropy of bituminous mixture in the linear viscoelastic domain
NASA Astrophysics Data System (ADS)
Di Benedetto, Hervé; Sauzéat, Cédric; Clec'h, Pauline
Some anisotropic properties in the linear viscoelastic domain of bituminous mixtures compacted with a French LPC wheel compactor are highlighted in this paper. Bituminous mixture is generally considered as isotropic even if the compaction process on road or in laboratory induces anisotropic properties. Tension-compression complex modulus tests have been performed on parallelepipedic specimens in two directions: (i) direction of compactor wheel movement (direction I, which is horizontal) and (ii) direction of compaction (direction II, which is vertical). These tests consist in measuring sinusoidal axial and lateral strains as well as sinusoidal axial stress, when sinusoidal axial loading is applied on the specimen. Different loading frequencies and temperatures are applied. Two complex moduli, EI ^{*} and E_{II}^{*}, and four complex Poisson's ratios, ν_{{II-I}}^{*}, ν_{{III-I}}^{*}, ν_{{I-II}}^{*} and ν_{{III-II}}^{*}, were obtained. The vertical direction appears softer than the other ones for the highest frequencies. There are very few differences between the two directions I and II for parameters concerning viscous effects (phase angles φ(EI) and φ(E_{II}), and shift factors). The four Poisson's ratios reveal anisotropic properties but rheological tensor can be considered as symmetric when considering very similar values obtained for the two measured parameters (I-II and II-I)
The transition from symmetric to baroclinic instability in the Eady model
NASA Astrophysics Data System (ADS)
Stamper, Megan A.; Taylor, John R.
Here, we explore the transition from symmetric instability to ageostrophic baroclinic instability in the Eady model; an idealised representation of a submesoscale mixed layer front. We revisit the linear stability problem considered by Stone (J Atmos Sci, 23, 390-400, (Stone 1966)), Stone (J Atmos Sci, 27, 721-726, (Stone 1970)), Stone (J Atmos Sci, 29, 419-426, (Stone 1972)) with a particular focus on three-dimensional `mixed modes' (which are neither purely symmetric or baroclinic) and find that these modes can have growth rates within just a few percent of the corresponding two-dimensional growth rate maximum. In addition, we perform very high resolution numerical simulations allowing an exploration of the transition from symmetric to baroclinic instability. Three-dimensional mixed modes represent the largest contribution to the turbulent kinetic energy during the transition period between symmetric and baroclinic instability. In each simulation, we see the development of sharp fronts with associated high rms vertical velocities of up to 30 mm s-1. Furthermore, we see significant transfer of energy to small scales, demonstrated by time-integrated mixing and energy dissipation by small-scale three-dimensional turbulence totalling about 30 % of the initial kinetic energy in all cases.
Electroweak Baryogenesis in R-symmetric Supersymmetry
Fok, R.; Kribs, Graham D.; Martin, Adam; Tsai, Yuhsin
We demonstrate that electroweak baryogenesis can occur in a supersymmetric model with an exact R-symmetry. The minimal R-symmetric supersymmetric model contains chiral superfields in the adjoint representation, giving Dirac gaugino masses, and an additional set of "R-partner" Higgs superfields, giving R-symmetric \\mu-terms. New superpotential couplings between the adjoints and the Higgs fields can simultaneously increase the strength of the electroweak phase transition and provide additional tree-level contributions to the lightest Higgs mass. Notably, no light stop is present in this framework, and in fact, we require both stops to be above a few TeV to provide sufficient radiative corrections to the lightest Higgs mass to bring it up to 125 GeV. Large CP-violating phases in the gaugino/higgsino sector allow us to match the baryon asymmetry of the Universe with no constraints from electric dipole moments due to R-symmetry. We briefly discuss some of the more interesting phenomenology, particularly of the of the lightest CP-odd scalar.
Fast numerical determination of symmetric sparsity patterns
Carter, R.G.
The author considers a function g: {Re}{sup n} {yields} {Re}{sup n} for which the Jacobian is symmetric and sparse. Such functions often arise, for instance, in numerical optimization, where g is the gradient of some objective function f so that the Jacobian of g is the Hessian of f. In many such applications one can generate extremely efficient algorithms by taking advantage of the sparsity structure of the problem if this pattern is known a priori. Unfortunately, determining such sparsity structures by hand is often difficult and prone to error. If one suspects a mistake has been made, or if g is a {open_quotes}black box{close_quotes} so that the true structure is completely unknown, one often has no alternative but to compute the entire matrix by finite differences - a prohibitively expensive task for large problems. The author shows that it is possible to numerically determine symmetric sparsity patterns using a relatively small number of g evaluations. Numerical results are shown for n up to 100,000 in which all nonzeros in the Jacobian are correctly identified in about one-hundredth of the time required to estimate the sparsity structure by a full finite difference calculation. When a good initial guess for the sparsity structure is available, numerical results are presented for n up to 500,000, in which all missing nonzeros are correctly located almost five-thousand times faster than would be possible with a full finite difference calculation.
The modelling of symmetric airfoil vortex generators
NASA Technical Reports Server (NTRS)
Reichert, B. A.; Wendt, B. J.
An experimental study is conducted to determine the dependence of vortex generator geometry and impinging flow conditions on shed vortex circulation and crossplane peak vorticity for one type of vortex generator. The vortex generator is a symmetric airfoil having a NACA 0012 cross-sectional profile. The geometry and flow parameters varied include angle-of-attack alfa, chordlength c, span h, and Mach number M. The vortex generators are mounted either in isolation or in a symmetric counter-rotating array configuration on the inside surface of a straight pipe. The turbulent boundary layer thickness to pipe radius ratio is delta/R = 0. 17. Circulation and peak vorticity data are derived from crossplane velocity measurements conducted at or about 1 chord downstream of the vortex generator trailing edge. Shed vortex circulation is observed to be proportional to M, alfa, and h/delta. With these parameters held constant, circulation is observed to fall off in monotonic fashion with increasing airfoil aspect ratio AR. Shed vortex peak vorticity is also observed to be proportional to M, alfa, and h/delta. Unlike circulation, however, peak vorticity is observed to increase with increasing aspect ratio, reaching a peak value at AR approx. 2.0 before falling off.
Spherically Symmetric Solutions of Light Galileon
NASA Astrophysics Data System (ADS)
Momeni, D.; Houndjo, M. J. S.; Güdekli, E.; Rodrigues, M. E.; Alvarenga, F. G.; Myrzakulov, R.
We have been studied the model of light Galileon with translational shift symmetry ϕ → ϕ + c. The matter Lagrangian is presented in the form {L}_{φ }= -η (partial φ )2+β G^{μ ν }partial _{μ }φ partial _{ν }φ . We have been addressed two issues: the first is that, we have been proven that, this type of Galileons belong to the modified matter-curvature models of gravity in type of f(R,R^{μ ν }T_{μ ν }m). Secondly, we have been investigated exact solution for spherically symmetric geometries in this model. We have been found an exact solution with singularity at r = 0 in null coordinates. We have been proven that the solution has also a non-divergence current vector norm. This solution can be considered as an special solution which has been investigated in literature before, in which the Galileon's field is non-static (time dependence). Our scalar-shift symmetrized Galileon has the simple form of ϕ = t, which it is remembered by us dilaton field.
Compressible flow about symmetrical Joukowski profiles
NASA Technical Reports Server (NTRS)
Kaplan, Carl
The method of Poggi is employed for the determination of the effects of compressibility upon the flow past an obstacle. A general expression for the velocity increment due to compressibility is obtained. The general result holds whatever the shape of the obstacle; but, in order to obtain the complete solution, it is necessary to know a certain Fourier expansion of the square of the velocity of flow past the obstacle. An application is made to the case flow of a symmetrical Joukowski profile with a sharp trailing edge, fixed in a stream of an arbitrary angle of attack and with the circulation determined by the Kutta condition. The results are obtained in a closed form and are exact insofar as the second approximation to the compressible flow is concerned, the first approximation being the result for the corresponding incompressible flow. Formulas for lift and moment analogous to the Blasius formulas in incompressible flow are developed and are applied to thin symmetrical Joukowski profiles for small angles of attack.
General theory for multiple input-output perturbations in complex molecular systems. 1. Linear QSPR electronegativity models in physical, organic, and medicinal chemistry.
González-Díaz, Humberto; Arrasate, Sonia; Gómez-SanJuan, Asier; Sotomayor, Nuria; Lete, Esther; Besada-Porto, Lina; Ruso, Juan M
In general perturbation methods starts with a known exact solution of a problem and add "small" variation terms in order to approach to a solution for a related problem without known exact solution. Perturbation theory has been widely used in almost all areas of science. Bhor's quantum model, Heisenberg's matrix mechanincs, Feyman diagrams, and Poincare's chaos model or "butterfly effect" in complex systems are examples of perturbation theories. On the other hand, the study of Quantitative Structure-Property Relationships (QSPR) in molecular complex systems is an ideal area for the application of perturbation theory. There are several problems with exact experimental solutions (new chemical reactions, physicochemical properties, drug activity and distribution, metabolic networks, etc.) in public databases like CHEMBL. However, in all these cases, we have an even larger list of related problems without known solutions. We need to know the change in all these properties after a perturbation of initial boundary conditions. It means, when we test large sets of similar, but different, compounds and/or chemical reactions under the slightly different conditions (temperature, time, solvents, enzymes, assays, protein targets, tissues, partition systems, organisms, etc.). However, to the best of our knowledge, there is no QSPR general-purpose perturbation theory to solve this problem. In this work, firstly we review general aspects and applications of both perturbation theory and QSPR models. Secondly, we formulate a general-purpose perturbation theory for multiple-boundary QSPR problems. Last, we develop three new QSPR-Perturbation theory models. The first model classify correctly >100,000 pairs of intra-molecular carbolithiations with 75-95% of Accuracy (Ac), Sensitivity (Sn), and Specificity (Sp). The model predicts probabilities of variations in the yield and enantiomeric excess of reactions due to at least one perturbation in boundary conditions (solvent, temperature
Solitary Waves of a $$\\mathcal {P}$$ $$\\mathcal {T}$$-Symmetric Nonlinear Dirac Equation
Cuevas-Maraver, Jesus; Kevrekidis, Panayotis G.; Saxena, Avadh; ...
In our study we consider we consider a prototypical example of a mathcalP mathcalT-symmetric Dirac model. We discuss the underlying linear limit of the model and identify the threshold of the mathcalP mathcalT -phase transition in an analytical form. We then focus on the examination of the nonlinear model. We consider the continuation in the mathcalP mathcalT -symmetric model of the solutions of the corresponding Hamiltonian model and find that the solutions can be continued robustly as stable ones all the way up to the mathcalP mathcalT-transition threshold. In the latter, they degenerate into linear waves. We also examine themore » dynamics of the model. Given the stability of the waveforms in the mathcalP mathcalT-exact phase, we consider them as initial conditions for parameters outside of that phase. We also find that both oscillatory dynamics and exponential growth may arise, depending on the size of the corresponding "quench". The former can be characterized by an interesting form of bifrequency solutions that have been predicted on the basis of the SU symmetry. Finally, we explore some special, analytically tractable, but not mathcalP mathcalT-symmetric solutions in the massless limit of t- e model.« less
An Approximate Solution and Master Curves for Buckling of Symmetrically Laminated Composite Cylinders
NASA Technical Reports Server (NTRS)
Nemeth, Michael P.
Nondimensional linear-bifurcation buckling equations for balanced, symmetrically laminated cylinders with negligible shell-wall anisotropies and subjected to uniform axial compression loads are presented. These equations are solved exactly for the practical case of simply supported ends. Nondimensional quantities are used to characterize the buckling behavior that consist of a stiffness-weighted length-to-radius parameter, a stiffness-weighted shell-thinness parameter, a shell-wall nonhomogeneity parameter, two orthotropy parameters, and a nondimensional buckling load. Ranges for the nondimensional parameters are established that encompass a wide range of laminated-wall constructions and numerous generic plots of nondimensional buckling load versus a stiffness-weighted length-to-radius ratio are presented for various combinations of the other parameters. These plots are expected to include many practical cases of interest to designers. Additionally, these plots show how the parameter values affect the distribution and size of the festoons forming each response curve and how they affect the attenuation of each response curve to the corresponding solution for an infinitely long cylinder. To aid in preliminary design studies, approximate formulas for the nondimensional buckling load are derived, and validated against the corresponding exact solution, that give the attenuated buckling response of an infinitely long cylinder in terms of the nondimensional parameters presented herein. A relatively small number of "master curves" are identified that give a nondimensional measure of the buckling load of an infinitely long cylinder as a function of the orthotropy and wall inhomogeneity parameters. These curves reduce greatly the complexity of the design-variable space as compared to representations that use dimensional quantities as design variables. As a result of their inherent simplicity, these master curves are anticipated to be useful in the ongoing development of
Spatial-frequency Fourier polarimetry of the complex degree of mutual anisotropy of linear and circular birefringence in the diagnostics of oncological changes in morphological structure of biological tissues
Ushenko, Yu A; Gorskii, M P; Dubolazov, A V; Motrich, A V; Ushenko, V A; Sidor, M I
Theory of polarisation-correlation analysis of laser images of histological sections of biopsy material from cervix tissue based on spatial frequency selection of linear and circular birefringence mechanisms is formulated. Comparative results of measuring the coordinate distributions of the complex degree of mutual anisotropy (CDMA), produced by fibrillar networks formed by myosin and collagen fibres of cervix tissue in different pathological conditions, namely, pre-cancer (dysplasia) and cancer (adenocarcinoma), are presented. The values and variation ranges of statistical (moments of the first - fourth order), correlation (excess-autocorrelation functions), and fractal (slopes of approximating curves and dispersion of extrema of logarithmic dependences of power spectra) parameters of the CDMA coordinate distributions are studied. Objective criteria for pathology diagnostics and differentiation of its severity degree are determined. (image processing)
Spatial-frequency Fourier polarimetry of the complex degree of mutual anisotropy of linear and circular birefringence in the diagnostics of oncological changes in morphological structure of biological tissues
NASA Astrophysics Data System (ADS)
Ushenko, Yu A.; Gorskii, M. P.; Dubolazov, A. V.; Motrich, A. V.; Ushenko, V. A.; Sidor, M. I.
Theory of polarisation-correlation analysis of laser images of histological sections of biopsy material from cervix tissue based on spatial frequency selection of linear and circular birefringence mechanisms is formulated. Comparative results of measuring the coordinate distributions of the complex degree of mutual anisotropy (CDMA), produced by fibrillar networks formed by myosin and collagen fibres of cervix tissue in different pathological conditions, namely, pre-cancer (dysplasia) and cancer (adenocarcinoma), are presented. The values and variation ranges of statistical (moments of the first — fourth order), correlation (excess-autocorrelation functions), and fractal (slopes of approximating curves and dispersion of extrema of logarithmic dependences of power spectra) parameters of the CDMA coordinate distributions are studied. Objective criteria for pathology diagnostics and differentiation of its severity degree are determined.
Minimal Left-Right Symmetric Dark Matter.
Heeck, Julian; Patra, Sudhanwa
We show that left-right symmetric models can easily accommodate stable TeV-scale dark matter particles without the need for an ad hoc stabilizing symmetry. The stability of a newly introduced multiplet either arises accidentally as in the minimal dark matter framework or comes courtesy of the remaining unbroken Z_{2} subgroup of B-L. Only one new parameter is introduced: the mass of the new multiplet. As minimal examples, we study left-right fermion triplets and quintuplets and show that they can form viable two-component dark matter. This approach is, in particular, valid for SU(2)×SU(2)×U(1) models that explain the recent diboson excess at ATLAS in terms of a new charged gauge boson of mass 2 TeV.
Cracked shells under skew-symmetric loading
NASA Technical Reports Server (NTRS)
Lelale, F.
A shell containing a through crack in one of the principal planes of curvature and under general skew-symmetric loading is considered. By employing a Reissner type shell theory which takes into account the effect of transverse shear strains, all boundary conditions on the crack surfaces are satisfied separately. Consequently, unlike those obtained from the classical shell theory, the angular distributions of the stress components around the crack tips are shown to be identical to the distributions obtained from the plane and antiplane elasticity solutions. Extensive results are given for axially and circumferentially cracked cylindrical shells, spherical shells, and toroidal shells under uniform inplane shearing, out of plane shearing, and torsion. The effect of orthotropy on the results is also studied.
Highly symmetric POVMs and their informational power
NASA Astrophysics Data System (ADS)
Słomczyński, Wojciech; Szymusiak, Anna
We discuss the dependence of the Shannon entropy of normalized finite rank-1 POVMs on the choice of the input state, looking for the states that minimize this quantity. To distinguish the class of measurements where the problem can be solved analytically, we introduce the notion of highly symmetric POVMs and classify them in dimension 2 (for qubits). In this case, we prove that the entropy is minimal, and hence, the relative entropy (informational power) is maximal, if and only if the input state is orthogonal to one of the states constituting a POVM. The method used in the proof, employing the Michel theory of critical points for group action, the Hermite interpolation, and the structure of invariant polynomials for unitary-antiunitary groups, can also be applied in higher dimensions and for other entropy-like functions. The links between entropy minimization and entropic uncertainty relations, the Wehrl entropy, and the quantum dynamical entropy are described.
Symmetric Satellite Swarms and Choreographic Crystals.
Boyle, Latham; Khoo, Jun Yong; Smith, Kendrick
In this Letter, we introduce a natural dynamical analogue of crystalline order, which we call choreographic order. In an ordinary (static) crystal, a high degree of symmetry may be achieved through a careful arrangement of the fundamental repeated elements. In the dynamical analogue, a high degree of symmetry may be achieved by having the fundamental elements perform a carefully choreographed dance. For starters, we show how to construct and classify all symmetric satellite constellations. Then we explain how to generalize these ideas to construct and classify choreographic crystals more broadly. We introduce a quantity, called the "choreography" of a given configuration. We discuss the possibility that some (naturally occurring or artificial) many-body or condensed-matter systems may exhibit choreographic order, and suggest natural experimental signatures that could be used to identify and characterize such systems.
Diamond Turning of Nonrotationally Symmetric Surfaces.
NASA Astrophysics Data System (ADS)
Falter, Peter John
Conventional techniques for ultraprecision turning have been successfully applied to the generation of optical quality surfaces. These resulting geometries however have been limited to surfaces of revolution. To investigate the machining of more general geometries, equipment has been developed to allow the production of accurate non -rotationally symmetric optical surfaces. This apparatus utilizes high speed digital control and a piezoelectric tool servo in conjunction with a workpiece-based metrology frame to synchronize tool position with spindle rotation. Machining experiments have been conducted to investigate the limits of producibility and the mechanics of this type of turning. The influences of tool forces, machine dynamics and metrology/control equipment on the accuracy of the finished part have also been determined.
Partial transpose criteria for symmetric states
NASA Astrophysics Data System (ADS)
Bohnet-Waldraff, F.; Braun, D.; Giraud, O.
We express the positive-partial-transpose (PPT) separability criterion for symmetric states of multiqubit systems in terms of matrix inequalities based on the recently introduced tensor representation for spin states. We construct a matrix from the tensor representation of the state and show that it is similar to the partial transpose of the density matrix written in the computational basis. Furthermore, the positivity of this matrix is equivalent to the positivity of a correlation matrix constructed from tensor products of Pauli operators. This allows for a more transparent experimental interpretation of the PPT criteria for an arbitrary spin-j state. The unitary matrices connecting our matrix to the partial transpose of the state generalize the so-called magic basis that plays a central role in Wootters' explicit formula for the concurrence of a two-qubit system and the Bell bases used for the teleportation of a one- or two-qubit state.
Pseudo-Z symmetric space-times
NASA Astrophysics Data System (ADS)
Mantica, Carlo Alberto; Suh, Young Jin
In this paper, we investigate Pseudo-Z symmetric space-time manifolds. First, we deal with elementary properties showing that the associated form Ak is closed: in the case the Ricci tensor results to be Weyl compatible. This notion was recently introduced by one of the present authors. The consequences of the Weyl compatibility on the magnetic part of the Weyl tensor are pointed out. This determines the Petrov types of such space times. Finally, we investigate some interesting properties of (PZS)4 space-time; in particular, we take into consideration perfect fluid and scalar field space-time, and interesting properties are pointed out, including the Petrov classification. In the case of scalar field space-time, it is shown that the scalar field satisfies a generalized eikonal equation. Further, it is shown that the integral curves of the gradient field are geodesics. A classical method to find a general integral is presented.
Tensor eigenvalues and entanglement of symmetric states
NASA Astrophysics Data System (ADS)
Bohnet-Waldraff, F.; Braun, D.; Giraud, O.
Tensor eigenvalues and eigenvectors have been introduced in the recent mathematical literature as a generalization of the usual matrix eigenvalues and eigenvectors. We apply this formalism to a tensor that describes a multipartite symmetric state or a spin state, and we investigate to what extent the corresponding tensor eigenvalues contain information about the multipartite entanglement (or, equivalently, the quantumness) of the state. This extends previous results connecting entanglement to spectral properties related to the state. We show that if the smallest tensor eigenvalue is negative, the state is detected as entangled. While for spin-1 states the positivity of the smallest tensor eigenvalue is equivalent to separability, we show that for higher values of the angular momentum there is a correlation between entanglement and the value of the smallest tensor eigenvalue.
Symmetric Satellite Swarms and Choreographic Crystals
NASA Astrophysics Data System (ADS)
Boyle, Latham; Khoo, Jun Yong; Smith, Kendrick
In this Letter, we introduce a natural dynamical analogue of crystalline order, which we call choreographic order. In an ordinary (static) crystal, a high degree of symmetry may be achieved through a careful arrangement of the fundamental repeated elements. In the dynamical analogue, a high degree of symmetry may be achieved by having the fundamental elements perform a carefully choreographed dance. For starters, we show how to construct and classify all symmetric satellite constellations. Then we explain how to generalize these ideas to construct and classify choreographic crystals more broadly. We introduce a quantity, called the "choreography" of a given configuration. We discuss the possibility that some (naturally occurring or artificial) many-body or condensed-matter systems may exhibit choreographic order, and suggest natural experimental signatures that could be used to identify and characterize such systems.
Predictive equations to estimate spinal loads in symmetric lifting tasks.
Arjmand, N; Plamondon, A; Shirazi-Adl, A; Larivière, C; Parnianpour, M
Response surface methodology is used to establish robust and user-friendly predictive equations that relate responses of a complex detailed trunk finite element biomechanical model to its input variables during sagittal symmetric static lifting activities. Four input variables (thorax flexion angle, lumbar/pelvis ratio, load magnitude, and load position) and four model responses (L4-L5 and L5-S1 disc compression and anterior-posterior shear forces) are considered. Full factorial design of experiments accounting for all combinations of input levels is employed. Quadratic predictive equations for the spinal loads at the L4-S1 disc mid-heights are obtained by regression analysis with adequate goodness-of-fit (R(2)>98%, p<0.05, and low root-mean-squared-error values compared with the range of predicted spine loads). Results indicate that intradiscal pressure values at the L4-L5 disc estimated based on the predictive equations are in close agreement with available in vivo data measured under similar loadings and postures. Combinations of input (posture and loading) variable levels that yield spine loads beyond the tolerance compression limit of 3400 N are identified using contour plots. Ergonomists and bioengineers, faced with the dilemma of using either complex but more accurate models on one hand or less accurate but simple models on the other hand, have thereby easy-to-use predictive equations that quantifies spinal loads and risk of injury under different occupational tasks of interest.
Symmetry-restrained flexible fitting for symmetric EM maps
Chan, Kwok-Yan; Gumbart, James; McGreevy, Ryan; Watermeyer, Jean M.; Sewell, B. Trevor; Schulten, Klaus
Summary Many large biological macromolecules have inherent structural symmetry, being composed of a few distinct subunits, repeated in a symmetric array. These complexes are often not amenable to traditional high-resolution structural determination methods, but can be imaged in functionally relevant states using cryo-electron microscopy (cryo-EM). A number of methods for fitting atomic-scale structures into cryo-EM maps have been developed, including the molecular dynamics flexible fitting (MDFF) method. However, quality and resolution of the cryo-EM map are the major determinants of a method's success. In order to incorporate knowledge of structural symmetry into the fitting procedure, we developed the symmetry-restrained MDFF method. The new method adds to the cryo-EM map-derived potential further restraints on the allowed conformations of a complex during fitting, thereby improving the quality of the resultant structure. The benefit of using symmetry-based restraints during fitting, particularly for medium to low-resolution data, is demonstrated for three different systems. PMID:21893283
Cutting force predication based on integration of symmetric fuzzy number and finite element method.
Wang, Zhanli; Hu, Yanjuan; Wang, Yao; Dong, Chao; Pang, Zaixiang
In the process of turning, pointing at the uncertain phenomenon of cutting which is caused by the disturbance of random factors, for determining the uncertain scope of cutting force, the integrated symmetric fuzzy number and the finite element method (FEM) are used in the prediction of cutting force. The method used symmetric fuzzy number to establish fuzzy function between cutting force and three factors and obtained the uncertain interval of cutting force by linear programming. At the same time, the change curve of cutting force with time was directly simulated by using thermal-mechanical coupling FEM; also the nonuniform stress field and temperature distribution of workpiece, tool, and chip under the action of thermal-mechanical coupling were simulated. The experimental result shows that the method is effective for the uncertain prediction of cutting force.
Cutting Force Predication Based on Integration of Symmetric Fuzzy Number and Finite Element Method
Wang, Zhanli; Hu, Yanjuan; Wang, Yao; Dong, Chao; Pang, Zaixiang
In the process of turning, pointing at the uncertain phenomenon of cutting which is caused by the disturbance of random factors, for determining the uncertain scope of cutting force, the integrated symmetric fuzzy number and the finite element method (FEM) are used in the prediction of cutting force. The method used symmetric fuzzy number to establish fuzzy function between cutting force and three factors and obtained the uncertain interval of cutting force by linear programming. At the same time, the change curve of cutting force with time was directly simulated by using thermal-mechanical coupling FEM; also the nonuniform stress field and temperature distribution of workpiece, tool, and chip under the action of thermal-mechanical coupling were simulated. The experimental result shows that the method is effective for the uncertain prediction of cutting force. PMID:24790556
Error reduction in retrievals of atmospheric species from symmetrically measured lidar sounding absorption spectra.
Chen, Jeffrey R; Numata, Kenji; Wu, Stewart T
We report new methods for retrieving atmospheric constituents from symmetrically-measured lidar-sounding absorption spectra. The forward model accounts for laser line-center frequency noise and broadened line-shape, and is essentially linearized by linking estimated optical-depths to the mixing ratios. Errors from the spectral distortion and laser frequency drift are substantially reduced by averaging optical-depths at each pair of symmetric wavelength channels. Retrieval errors from measurement noise and model bias are analyzed parametrically and numerically for multiple atmospheric layers, to provide deeper insight. Errors from surface height and reflectance variations are reduced to tolerable levels by "averaging before log" with pulse-by-pulse ranging knowledge incorporated.
Symmetric RBF classifier for nonlinear detection in multiple-antenna-aided systems.
Chen, Sheng; Wolfgang, Andreas; Harris, Chris J; Hanzo, Lajos
In this paper, we propose a powerful symmetric radial basis function (RBF) classifier for nonlinear detection in the so-called "overloaded" multiple-antenna-aided communication systems. By exploiting the inherent symmetry property of the optimal Bayesian detector, the proposed symmetric RBF classifier is capable of approaching the optimal classification performance using noisy training data. The classifier construction process is robust to the choice of the RBF width and is computationally efficient. The proposed solution is capable of providing a signal-to-noise ratio (SNR) gain in excess of 8 dB against the powerful linear minimum bit error rate (BER) benchmark, when supporting four users with the aid of two receive antennas or seven users with four receive antenna elements.
Evolution of recombination rates in a multi-locus, haploid-selection, symmetric-viability model.
Chasnov, J R; Ye, Felix Xiaofeng
A fast algorithm for computing multi-locus recombination is extended to include a recombination-modifier locus. This algorithm and a linear stability analysis is used to investigate the evolution of recombination rates in a multi-locus, haploid-selection, symmetric-viability model for which stable equilibria have recently been determined. When the starting equilibrium is symmetric with two selected loci, we show analytically that modifier alleles that reduce recombination always invade. When the starting equilibrium is monomorphic, and there is a fixed nonzero recombination rate between the modifier locus and the selected loci, we determine analytical conditions for which a modifier allele can invade. In particular, we show that a gap exists between the recombination rates of modifiers that can invade and the recombination rate that specifies the lower stability boundary of the monomorphic equilibrium. A numerical investigation shows that a similar gap exists in a weakened form when the starting equilibrium is fully polymorphic but asymmetric.
Focal symmetrical encephalomalacia in a goat.
Oliveira, Diego M; Pimentel, Luciano A; Pessoa, André F; Dantas, Antônio F M; Uzal, Francisco; Riet-Correa, Franklin
Focal symmetrical encephalomalacia (FSE) is the most prominent lesion seen in the chronic form of enterotoxemia caused by Clostridium perfringens type D in sheep. However, this lesion has not been reported in goats. The current paper reports a case of FSE in a goat from the state of Paraíba in the Brazilian semiarid region. As reported by the farmer, 30, 4-48-month-old animals from a flock of 150 goats died after showing nervous signs, including blindness and recumbence, for periods varying between 1 and 14 days. The flock was grazing native pasture supplemented with wheat and corn bran. Additionally, lactating goats were supplemented with soybeans. A 4-month-old goat with nervous signs was examined clinically and then necropsied 3 days after the onset of clinical signs. Bilateral, focal, and symmetrical areas of brown discoloration were observed in the internal capsule and thalamus. Histologic lesions in these areas consisted of multifocal, bilateral malacia with a few neutrophils; endothelial cell swelling; perivascular edema; and hemorrhages. The etiology of these lesions was not determined. However, FSE is considered pathognomonic for C. perfringens type D enterotoxemia in sheep, and it is speculated that this microorganism was the etiologic agent in the present case. The flock had been vaccinated against type D enterotoxemia only once, approximately 3 months before the beginning of the outbreak. Insufficient immunity due to the incorrect vaccination protocol, low efficacy of the vaccine used, and a diet including large amounts of highly fermentable carbohydrates were suspected to be predisposing factors for this outbreak.
Topological Analyses of Symmetric Eruptive Prominences
NASA Astrophysics Data System (ADS)
Panasenco, O.; Martin, S. F.
Erupting prominences (filaments) that we have analyzed from Hα Doppler data at Helio Research and from SOHO/EIT 304 Å, show strong coherency between their chirality, the direction of the vertical and lateral motions of the top of the prominences, and the directions of twisting of their legs. These coherent properties in erupting prominences occur in two patterns of opposite helicity; they constitute a form of dynamic chirality called the ``roll effect." Viewed from the positive network side as they erupt, many symmetrically-erupting dextral prominences develop rolling motion toward the observer along with right-hand helicity in the left leg and left-hand helicity in the right leg. Many symmetricaly-erupting sinistral prominences, also viewed from the positive network field side, have the opposite pattern: rolling motion at the top away from the observer, left-hand helical twist in the left leg, and right-hand twist in the right leg. We have analysed the motions seen in the famous movie of the ``Grand Daddy" erupting prominence and found that it has all the motions that define the roll effect. From our analyses of this and other symmetric erupting prominences, we show that the roll effect is an alternative to the popular hypothetical configuration of an eruptive prominence as a twisted flux rope or flux tube. Instead we find that a simple flat ribbon can be bent such that it reproduces nearly all of the observed forms. The flat ribbon is the most logical beginning topology because observed prominence spines already have this topology prior to eruption and an initial long magnetic ribbon with parallel, non-twisted threads, as a basic form, can be bent into many more and different geometrical forms than a flux rope.
Static, cylindrically symmetric strings in general relativity with cosmological constant
Linet, B.
The static, cylindrically symmetric solutions to Einstein's equations with a cosmological term describing cosmic strings are determined. The discussion depends on the sign of the cosmological constant.
Symmetrization of grey-scale images based on dilation
NASA Astrophysics Data System (ADS)
Tuzikov, Alexander V.; Krivonos, O. V.
We generalize set symmetrization transformations based on Minkowski addition to symmetrization transformations for numerical functions. For this purpose two types of function representation are used. The first one is umbra representation, when symmetrization transformations are performed to the set of points under the graph of a function. This corresponds to introducing of transformations using gray-scale dilation. The second representation of a function is based on a family of threshold sets. Flat function symmetrization transformations are generated by corresponding set transformations operating on threshold sets.
Entanglement equivalence of N-qubit symmetric states
Mathonet, P.; Krins, S.; Bastin, T.; Godefroid, M.; Solano, E.
We study the interconversion of multipartite symmetric N-qubit states under stochastic local operations and classical communication (SLOCC). We demonstrate that if two symmetric states can be connected with a nonsymmetric invertible local operation (ILO), then they belong necessarily to the separable, W, or Greenberger-Horne-Zeilinger (GHZ) entanglement class, establishing a practical method of discriminating subsets of entanglement classes. Furthermore, we prove that there always exists a symmetric ILO connecting any pair of symmetric N-qubit states equivalent under SLOCC, simplifying the requirements for experimental implementations of local interconversion of those states.
Extracting pure endmembers using symmetric sparse representation for hyperspectral imagery
NASA Astrophysics Data System (ADS)
Sun, Weiwei; Liu, Chun; Sun, Yanwei; Li, Weiyue; Li, Jialin
This article proposes a symmetric sparse representation (SSR) method to extract pure endmembers from hyperspectral imagery (HSI). The SSR combines the features of the linear unmixing model and the sparse subspace clustering model of endmembers, and it assumes that the desired endmembers and all the HSI pixel points can be sparsely represented by each other. It formulates the endmember extraction problem into a famous program of archetypal analysis, and accordingly, extracting pure endmembers can be transformed as finding the archetypes in the minimal convex hull containing all the HSI pixel points. The vector quantization scheme is adopted to help in carefully choosing the initial pure endmembers, and the archetypal analysis program is solved using the simple projected gradient algorithm. Seven state-of-the-art methods are implemented to make comparisons with the SSR on both synthetic and real hyperspectral images. Experimental results show that the SSR outperforms all the seven methods in spectral angle distance and root-mean-square error, and it can be a good alternative choice for extracting pure endmembers from HSI data.
Stochastic modeling of cell growth with symmetric or asymmetric division
NASA Astrophysics Data System (ADS)
Marantan, Andrew; Amir, Ariel
We consider a class of biologically motivated stochastic processes in which a unicellular organism divides its resources (volume or damaged proteins, in particular) symmetrically or asymmetrically between its progeny. Assuming the final amount of the resource is controlled by a growth policy and subject to additive and multiplicative noise, we derive the recursive integral equation describing the evolution of the resource distribution over subsequent generations and use it to study the properties of stable resource distributions. We find conditions under which a unique stable resource distribution exists and calculate its moments for the class of affine linear growth policies. Moreover, we apply an asymptotic analysis to elucidate the conditions under which the stable distribution (when it exists) has a power-law tail. Finally, we use the results of this asymptotic analysis along with the moment equations to draw a stability phase diagram for the system that reveals the counterintuitive result that asymmetry serves to increase stability while at the same time widening the stable distribution. We also briefly discuss how cells can divide damaged proteins asymmetrically between their progeny as a form of damage control. In the appendixes, motivated by the asymmetric division of cell volume in Saccharomyces cerevisiae, we extend our results to the case wherein mother and daughter cells follow different growth policies.
Hybrid Transmission Line for ECRH in the Helically Symmetric Experiment
NASA Astrophysics Data System (ADS)
Radder, J. W.; Likin, K. M.; Anderson, F. S. B.; Anderson, D. T.
The HSX oversized, mode-converting ECRH transmission line has been upgraded to a hybrid system to increase launched microwave power and reduce electrical arcing. Filtering of high-order, spurious modes ensures efficient coupling to a Gaussian beam for optimal electron heating. A Vlasov mode converter and two phase-correcting ellipsoidal mirrors convert the TE02 gyrotron output mode to a symmetric, linearly polarized, microwave beam. A swappable twist reflector plate rotates beam polarization for 2nd-harmonic X-mode or fundamental O-mode ECRH. Long distances are traversed by coupling the beam to a dual-mode (TE11 + TM11), smooth, circular cross-section waveguide. This system has been successfully tested without arcing for 50 ms pulses and over 100 kW of launched power. Analysis of the microwave beam for 50 kW, 2 ms microwave pulses reveals agreement with predicted beam shapes at two beam locations. The new system has also demonstrated increased plasma stored energy for ECRH plasmas with equal launched power.
Nonlinear coupling of tearing fluctuations in the Madison Symmetric Torus
Sarff, J.S.; Assadi, S.; Almagri, A.F.; Cekic, M.; Den Hartog, D.J.; Fiksel, G.; Hokin, S.A.; Ji, H.; Prager, S.C.; Shen, W.; Sidikman, K.L.; Stoneking, M.R. )
Three-wave, nonlinear, tearing mode coupling has been measured in the Madison Symmetric Torus (MST) reversed-field pinch (RFP) [Fusion Technol. [bold 19], 131 (1991)] using bispectral analysis of edge magnetic fluctuations resolved in [ital k]-space.'' The strength of nonlinear three-wave interactions satisfying the sum rules [ital m][sub 1]+[ital m][sub 2]=[ital m][sub 3] and [ital n][sub 1]+[ital n][sub 2]=[ital n][sub 3] is measured by the bicoherency. In the RFP, [ital m]=1, [ital n][similar to]2[ital R]/[ital a] (6 for MST) internally resonant modes are linearly unstable and grow to large amplitude. Large values of bicoherency occur for two [ital m]=1 modes coupled to an [ital m]=2 mode and the coupling of intermediate toroidal modes, e.g., [ital n]=6 and 7 coupled to [ital n]=13. These experimental bispectral features agree with predicted bispectral features derived from magnetohydrodynamic (MHD) computation. However, in the experiment, enhanced coupling occurs in the crash'' phase of a sawtooth oscillation concomitant with a broadened mode spectrum suggesting the onset of a nonlinear cascade.
Calix[3]carbazole: A C3-symmetrical receptor for barium ion
NASA Astrophysics Data System (ADS)
Yang, Zhaozheng; Tian, Zhangmin; Yang, Peng; Deng, Tuo; Li, Gang; Zhou, Xue; Chen, Yan; Zhao, Liang; Shen, Hongyan
The binding ability of calix[3]carbazole (1) to metal ions has been investigated. It is found that 1 could serve as a non crown ether based, C3-symmetrical receptor for Ba2 + via the marriage of cation-π and cation-dipole interactions. FID assay further illustrates that 1 could selectively interact with Ba2 + over Pd2 +. A possible binding mechanism for [1-Ba2 +] complex is proposed.
Design and Synthesis of C2-Symmetric N-Heterocyclic Carbene Precursors and Metal Carbenoids
Albright, Abigail; Eddings, Daniel; Black, Regina; Welch, Christopher J.; Gerasimchuk, Nikolay N.; Gawley, Robert E.
Chiral, C2-symmetric imidazolium and imidazolinium ions, as well as the corresponding copper or silver bound carbenoids, have been prepared. Structural study of these compounds by X-ray crystallography reveals a chiral pocket that surrounds the putative carbene site or the metal-carbene bond, at carbon 2, in three of the four ligands prepared. Preliminary investigation into the application of these complexes has shown one of them to be highly enantioselective in the hydrosilylation of acetophenone. PMID:21823580
Competing {PT} potentials and the re-entrant {PT}-symmetric phase: a particle in a box
NASA Astrophysics Data System (ADS)
Joglekar, Yogesh N.; Bagchi, Bijan
We investigate the effects of competition between two complex, {PT}-symmetric potentials on the {PT}-symmetric phase of a 'particle in a box'. These potentials, given by VZ(x) = iZsign(x) and Vξ(x) = iξ[δ(x - a) - δ(x + a)], represent long-range and localized gain/loss regions, respectively. We obtain the {PT}-symmetric phase in the (Z, ξ) plane, and find that for locations ±a near the edge of the box, surprisingly, the {PT}-symmetric phase is strengthened by additional losses to the loss region. Consequently, we predict that a broken {PT}-symmetry will be restored by increasing the strength ξ of the localized potential. By comparing the results for this problem and its lattice counterpart, we show that a robust {PT}-symmetric phase in the continuum is consistent with the fragile phase on the lattice. Our results demonstrate that systems with multiple, {PT}-symmetric potentials show unique, unexpected properties.
Full S matrix calculation via a single real-symmetric Lanczos recursion: the Lanczos artificial boundary inhomogeneity method.
Zhang, Hong; Smith, Sean C
We present an efficient and robust method for the calculation of all S matrix elements (elastic, inelastic, and reactive) over an arbitrary energy range from a single real-symmetric Lanczos recursion. Our new method transforms the fundamental equations associated with Light's artificial boundary inhomogeneity approach from the primary representation (original grid or basis representation of the Hamiltonian or its function) into a single tridiagonal Lanczos representation, thereby affording an iterative version of the original algorithm with greatly superior scaling properties. The method has important advantages over existing iterative quantum dynamical scattering methods: (a) the numerically intensive matrix propagation proceeds with real symmetric algebra, which is inherently more stable than its complex symmetric counterpart; (b) no complex absorbing potential or real damping operator is required, saving much of the exterior grid space which is commonly needed to support these operators and also removing the associated parameter dependence. Test calculations are presented for the collinear H+H(2) reaction, revealing excellent performance characteristics.
Supersymmetric Model of a Bose-Einstein Condensate in a 𝓟𝓣-Symmetric Double-delta Trap
NASA Astrophysics Data System (ADS)
Abt, Nikolas; Cartarius, Holger; Wunner, Günter
The most important properties of a Bose-Einstein condensate subject to balanced gain and loss can be modelled by a Gross-Pitaevskii equation with an external 𝓟𝓣-symmetric double-delta potential. We study its linear variant with a supersymmetric extension. It is shown that both in the 𝓟𝓣-symmetric as well as in the 𝓟𝓣-broken phase arbitrary stationary states can be removed in a supersymmetric partner potential without changing the energy eigenvalues of the other state. The characteristic structure of the singular delta potential in the supersymmetry formalism is discussed, and the applicability of the formalism to the nonlinear Gross-Pitaevskii equation is analysed. In the latter case the formalism could be used to remove 𝓟𝓣-broken states introducing an instability to the stationary 𝓟𝓣-symmetric states.
Group Lifting Structures For Multirate Filter Banks, II: Linear Phase Filter Banks
Brislawn, Christopher M
The theory of group lifting structures is applied to linear phase lifting factorizations for the two nontrivial classes of two-channel linear phase perfect reconstruction filter banks, the whole-and half-sample symmetric classes. Group lifting structures defined for the reversible and irreversible classes of whole-and half-sample symmetric filter banks are shown to satisfy the hypotheses of the uniqueness theorem for group lifting structures. It follows that linear phase lifting factorizations of whole-and half-sample symmetric filter banks are therefore independent of the factorization methods used to compute them. These results cover the specification of user-defined whole-sample symmetric filter banks in Part 2 of the ISO JPEG 2000 standard.
Tunneling control using classical non-linear oscillator
Kar, Susmita; Bhattacharyya, S. P.
A quantum particle is placed in symmetric double well potential which is coupled to a classical non-linear oscillator via a coupling function. With different spatial symmetry of the coupling and under various controlling fashions, the tunneling of the quantum particle can be enhanced or suppressed, or totally destroyed.
Symmetry matters: photodissociation dynamics of symmetrically versus asymmetrically substituted phenols.
Karsili, Tolga N V; Wenge, Andreas M; Marchetti, Barbara; Ashfold, Michael N R
We report a combined experimental (H (Rydberg) atom photofragment translational spectroscopy) and theoretical (ab initio electronic structure and vibronic coupling calculations) study of the effects of symmetry on the photodissociation dynamics of phenols. Ultraviolet photoexcitation to the bound S1((1)ππ*) state of many phenols leads to some O-H bond fission by tunneling through the barrier under the conical intersection (CI) between the S1 and dissociative S2((1)πσ*) potential energy surfaces in the R(O-H) stretch coordinate. Careful analysis of the total kinetic energy release spectra of the resulting products shows that the radicals formed following S1 ← S0 excitation of phenol and symmetrically substituted phenols like 4-fluorophenol all carry an odd number of quanta in vibrational mode ν(16a), whereas those deriving from asymmetrically substituted systems like 3-fluorophenol or 4-methoxyphenol do not. This contrasting behavior can be traced back to symmetry. Symmetrically substituted phenols exist in two equivalent rotamers, which interconvert by tunneling through the barrier to OH torsional motion. Their states are thus best considered in the non-rigid G4 molecular symmetry group, wherein radiationless transfer from the S1 to S2 state requires a coupling mode of a2 symmetry. Of the three a2 symmetry parent modes, the out-of-plane ring puckering mode ν(16a) shows much the largest interstate coupling constant in the vicinity of the S1/S2 CI. The nuclear motions associated with ν(16a) are orthogonal to the dissociation coordinate, and are thus retained in the radical products. Introducing asymmetry (even a non-linear substituent in the 4-position) lifts the degeneracy of the rotamers, and lowers the molecular symmetry to Cs. Many more parent motions satisfy the reduced (a'') symmetry requirement to enable S1/S2 coupling, the most effective of which is OH torsion. This motion 'disappears' on O-H bond fission; symmetry thus imposes no restriction to
X-ray studies of crystalline complexes involving amino acids and peptides. XLIII. Adipic acid complexes of L- and DL-lysine.
Sharma, Alok; Thamotharan, S; Roy, Siddhartha; Vijayan, M
The asymmetric unit of the DL-lysine complex of adipic acid [bis(DL-lysinium) adipate], 2C6H15N2O2+.C6H8O(4)2-, contains a zwitterionic singly charged lysinium cation and half a doubly charged adipate anion (the complete anion has inversion symmetry). That of the L-lysine complex (lysinium hydrogen adipate), C6H15N2O2+.C6H9O4-, consists of a lysinium cation and a singly charged hydrogen adipate anion. In both structures, the lysinium cations organize into layers interconnected by adipate or hydrogen adipate anions. However, the arrangement of the molecular ions in the layer is profoundly different in the DL- and L-lysine complexes. The hydrogen adipate anions in the L-lysine complex form linear arrays in which adjacent ions are interconnected by a symmetric O...H...O hydrogen bond.
The Caenorhabditis elegans septin complex is nonpolar
John, Corinne M; Hite, Richard K; Weirich, Christine S; Fitzgerald, Daniel J; Jawhari, Hatim; Faty, Mahamadou; Schläpfer, Dominik; Kroschewski, Ruth; Winkler, Fritz K; Walz, Tom; Barral, Yves; Steinmetz, Michel O
Septins are conserved GTPases that form heteromultimeric complexes and assemble into filaments that play a critical role in cell division and polarity. Results from budding and fission yeast indicate that septin complexes form around a tetrameric core. However, the molecular structure of the core and its influence on the polarity of septin complexes and filaments is poorly defined. The septin complex of the nematode Caenorhabditis elegans is formed entirely by the core septins UNC-59 and UNC-61. We show that UNC-59 and UNC-61 form a dimer of coiled-coil-mediated heterodimers. By electron microscopy, this heterotetramer appears as a linear arrangement of four densities representing the four septin subunits. Fusion of GFP to the N termini of UNC-59 and UNC-61 and subsequent electron microscopic visualization suggests that the sequence of septin subunits is UNC-59/UNC-61/UNC-61/UNC-59. Visualization of GFP extensions fused to the extremity of the C-terminal coiled coils indicates that these extend laterally from the heterotetrameric core. Together, our study establishes that the septin core complex is symmetric, and suggests that septins form nonpolar filaments. PMID:17599066
Vibration control of large linear quadratic symmetric systems. Ph.D. Thesis
NASA Technical Reports Server (NTRS)
Jeon, G. J.
Some unique properties on a class of the second order lambda matrices were found and applied to determine a damping matrix of the decoupled subsystem in such a way that the damped system would have preassigned eigenvalues without disturbing the stiffness matrix. The resulting system was realized as a time invariant velocity only feedback control system with desired poles. Another approach using optimal control theory was also applied to the decoupled system in such a way that the mode spillover problem could be eliminated. The procedures were tested successfully by numerical examples.
No-scalar-hair theorem for spherically symmetric reflecting stars
NASA Astrophysics Data System (ADS)
Hod, Shahar
It is proved that spherically symmetric compact reflecting objects cannot support static bound-state configurations made of scalar fields whose self-interaction potential V (ψ2) is a monotonically increasing function of its argument. Our theorem rules out, in particular, the existence of massive scalar hair outside the surface of a spherically symmetric compact reflecting star.
47 CFR 51.711 - Symmetrical reciprocal compensation.
Code of Federal Regulations, 2011 CFR
... 47 Telecommunication 3 2011-10-01 2011-10-01 false Symmetrical reciprocal compensation. 51.711... (CONTINUED) INTERCONNECTION Reciprocal Compensation for Transport and Termination of Telecommunications Traffic § 51.711 Symmetrical reciprocal compensation. (a) Rates for transport and termination...
47 CFR 51.711 - Symmetrical reciprocal compensation.
Code of Federal Regulations, 2010 CFR
... 47 Telecommunication 3 2010-10-01 2010-10-01 false Symmetrical reciprocal compensation. 51.711... (CONTINUED) INTERCONNECTION Reciprocal Compensation for Transport and Termination of Telecommunications Traffic § 51.711 Symmetrical reciprocal compensation. (a) Rates for transport and termination...
Solution of dense systems of linear equations in electromagnetic scattering calculations
Rahola, J.
The discrete-dipole approximation (DDA) is a method for calculating the scattering of light by an irregular particle. The DDA has been used for example in calculations of optical properties of cosmic dust. In this method the particle is approximated by interacting electromagnetic dipoles. Computationally the DDA method includes the solution of large dense systems of linear equations where the coefficient matrix is complex symmetric. In the author`s work, the linear systems of equations are solved by various iterative methods such as the conjugate gradient method applied to the normal equations and QMR. The linear systems have rather low condition numbers due to which many iterative methods perform quite well even without any preconditioning. Some possible preconditioning strategies are discussed. Finally, some fast special methods for computing the matrix-vector product in the iterative methods are considered. In some cases, the matrix-vector product can be computed with the fast Fourier transform, which enables the author to solve dense linear systems of hundreds of thousands of unknowns.
Do capuchin monkeys (Sapajus apella) prefer symmetrical face shapes?
Paukner, Annika; Wooddell, Lauren J.; Lefevre, Carmen; Lonsdorf, Eric; Lonsdorf, Elizabeth
In humans, facial symmetry has been linked to an individual's genetic quality, and facial symmetry has a small yet significant effect on ratings of facial attractiveness. The same evolutionary processes underlying these phenomena may also convey a selective advantage to symmetrical individuals of other primate species, yet to date, few studies have examined sensitivity to facial symmetry in non-human primates. Here we presented images of symmetrical and asymmetrical human and monkey faces to tufted capuchin monkeys (Sapajus apella), and hypothesized that capuchins would visually prefer symmetrical faces of opposite sex conspecifics. Instead, we found that male capuchins preferentially attended to symmetrical male conspecific faces whereas female capuchins did not appear to discriminate between symmetrical and asymmetrical faces. These results suggest that male capuchin monkeys may use facial symmetry to judge male quality in intra-male competition. PMID:28182489
Differences in the Visual Perception of Symmetric Patterns in Orangutans (Pongo pygmaeus abelii) and Two Human Cultural Groups: A Comparative Eye-Tracking Study.
Mühlenbeck, Cordelia; Liebal, Katja; Pritsch, Carla; Jacobsen, Thomas
Symmetric structures are of importance in relation to aesthetic preference. To investigate whether the preference for symmetric patterns is unique to humans, independent of their cultural background, we compared two human populations with distinct cultural backgrounds (Namibian hunter-gatherers and German town dwellers) with one species of non-human great apes (Orangutans) in their viewing behavior regarding symmetric and asymmetric patterns in two levels of complexity. In addition, the human participants were asked to give their aesthetic evaluation of a subset of the presented patterns. The results showed that humans of both cultural groups fixated on symmetric patterns for a longer period of time, regardless of the pattern's complexity. On the contrary, Orangutans did not clearly differentiate between symmetric and asymmetric patterns, but were much faster in processing the presented stimuli and scanned the complete screen, while both human groups rested on the symmetric pattern after a short scanning time. The aesthetic evaluation test revealed that the fixation preference for symmetric patterns did not match with the aesthetic evaluation in the Hai//om group, whereas in the German group aesthetic evaluation was in accordance with the fixation preference in 60 percent of the cases. It can be concluded that humans prefer well-ordered structures in visual processing tasks, most likely because of a positive processing bias for symmetry, which Orangutans did not show in this task, and that, in humans, an aesthetic preference does not necessarily accompany the fixation preference.
Differences in the Visual Perception of Symmetric Patterns in Orangutans (Pongo pygmaeus abelii) and Two Human Cultural Groups: A Comparative Eye-Tracking Study
Mühlenbeck, Cordelia; Liebal, Katja; Pritsch, Carla; Jacobsen, Thomas
Symmetric structures are of importance in relation to aesthetic preference. To investigate whether the preference for symmetric patterns is unique to humans, independent of their cultural background, we compared two human populations with distinct cultural backgrounds (Namibian hunter-gatherers and German town dwellers) with one species of non-human great apes (Orangutans) in their viewing behavior regarding symmetric and asymmetric patterns in two levels of complexity. In addition, the human participants were asked to give their aesthetic evaluation of a subset of the presented patterns. The results showed that humans of both cultural groups fixated on symmetric patterns for a longer period of time, regardless of the pattern's complexity. On the contrary, Orangutans did not clearly differentiate between symmetric and asymmetric patterns, but were much faster in processing the presented stimuli and scanned the complete screen, while both human groups rested on the symmetric pattern after a short scanning time. The aesthetic evaluation test revealed that the fixation preference for symmetric patterns did not match with the aesthetic evaluation in the Hai//om group, whereas in the German group aesthetic evaluation was in accordance with the fixation preference in 60 percent of the cases. It can be concluded that humans prefer well-ordered structures in visual processing tasks, most likely because of a positive processing bias for symmetry, which Orangutans did not show in this task, and that, in humans, an aesthetic preference does not necessarily accompany the fixation preference. PMID:27065184
Symmetric weak ternary quantum homomorphic encryption schemes
NASA Astrophysics Data System (ADS)
Wang, Yuqi; She, Kun; Luo, Qingbin; Yang, Fan; Zhao, Chao
Based on a ternary quantum logic circuit, four symmetric weak ternary quantum homomorphic encryption (QHE) schemes were proposed. First, for a one-qutrit rotation gate, a QHE scheme was constructed. Second, in view of the synthesis of a general 3 × 3 unitary transformation, another one-qutrit QHE scheme was proposed. Third, according to the one-qutrit scheme, the two-qutrit QHE scheme about generalized controlled X (GCX(m,n)) gate was constructed and further generalized to the n-qutrit unitary matrix case. Finally, the security of these schemes was analyzed in two respects. It can be concluded that the attacker can correctly guess the encryption key with a maximum probability pk = 1/33n, thus it can better protect the privacy of users' data. Moreover, these schemes can be well integrated into the future quantum remote server architecture, and thus the computational security of the users' private quantum information can be well protected in a distributed computing environment.
Spherically symmetric conformal gravity and ''gravitational bubbles''
Berezin, V.A.; Dokuchaev, V.I.; Eroshenko, Yu.N. E-mail: firstname.lastname@example.com
The general structure of the spherically symmetric solutions in the Weyl conformal gravity is described. The corresponding Bach equations are derived for the special type of metrics, which can be considered as the representative of the general class. The complete set of the pure vacuum solutions is found. It consists of two classes. The first one contains the solutions with constant two-dimensional curvature scalar of our specific metrics, and the representatives are the famous Robertson-Walker metrics. One of them we called the ''gravitational bubbles'', which is compact and with zero Weyl tensor. Thus, we obtained the pure vacuum curved space-times (without any material sources, including the cosmological constant) what is absolutely impossible in General Relativity. Such a phenomenon makes it easier to create the universe from ''nothing''. The second class consists of the solutions with varying curvature scalar. We found its representative as the one-parameter family. It appears that it can be conformally covered by the thee-parameter Mannheim-Kazanas solution. We also investigated the general structure of the energy-momentum tensor in the spherical conformal gravity and constructed the vectorial equation that reveals clearly some features of non-vacuum solutions. Two of them are explicitly written, namely, the metrics à la Vaidya, and the electrovacuum space-time metrics.
Coscheduling Technique for Symmetric Multiprocessor Clusters
Yoo, A B; Jette, M A
Coscheduling is essential for obtaining good performance in a time-shared symmetric multiprocessor (SMP) cluster environment. However, the most common technique, gang scheduling, has limitations such as poor scalability and vulnerability to faults mainly due to explicit synchronization between its components. A decentralized approach called dynamic coscheduling (DCS) has been shown to be effective for network of workstations (NOW), but this technique is not suitable for the workloads on a very large SMP-cluster with thousands of processors. Furthermore, its implementation can be prohibitively expensive for such a large-scale machine. IN this paper, they propose a novel coscheduling technique based on the DCS approach which can achieve coscheduling on very large SMP-clusters in a scalable, efficient, and cost-effective way. In the proposed technique, each local scheduler achieves coscheduling based upon message traffic between the components of parallel jobs. Message trapping is carried out at the user-level, eliminating the need for unsupported hardware or device-level programming. A sending process attaches its status to outgoing messages so local schedulers on remote nodes can make more intelligent scheduling decisions. Once scheduled, processes are guaranteed some minimum period of time to execute. This provides an opportunity to synchronize the parallel job's components across all nodes and achieve good program performance. The results from a performance study reveal that the proposed technique is a promising approach that can reduce response time significantly over uncoordinated time-sharing and batch scheduling.
PELDOR in rotationally symmetric homo-oligomers
NASA Astrophysics Data System (ADS)
Giannoulis, Angeliki; Ward, Richard; Branigan, Emma; Naismith, James H.; Bode, Bela E.
Nanometre distance measurements by pulsed electron-electron double resonance (PELDOR) spectroscopy have become an increasingly important tool in structural biology. The theoretical underpinning of the experiment is well defined for systems containing two nitroxide spin-labels (spin pairs); however, recently experiments have been reported on homo-oligomeric membrane proteins consisting of up to eight spin-labelled monomers. We have explored the theory behind these systems by examining model systems based on multiple spins arranged in rotationally symmetric polygons. The results demonstrate that with a rising number of spins within the test molecule, increasingly strong distortions appear in distance distributions obtained from an analysis based on the simple spin pair approach. These distortions are significant over a range of system sizes and remain so even when random errors are introduced into the symmetry of the model. We present an alternative approach to the extraction of distances on such systems based on a minimisation that properly treats multi-spin correlations. We demonstrate the utility of this approach on a spin-labelled mutant of the heptameric Mechanosensitive Channel of Small Conductance of E. coli.
Spherically symmetric conformal gravity and ``gravitational bubbles''
NASA Astrophysics Data System (ADS)
Berezin, V. A.; Dokuchaev, V. I.; Eroshenko, Yu. N.
The general structure of the spherically symmetric solutions in the Weyl conformal gravity is described. The corresponding Bach equations are derived for the special type of metrics, which can be considered as the representative of the general class. The complete set of the pure vacuum solutions is found. It consists of two classes. The first one contains the solutions with constant two-dimensional curvature scalar of our specific metrics, and the representatives are the famous Robertson-Walker metrics. One of them we called the ``gravitational bubbles'', which is compact and with zero Weyl tensor. Thus, we obtained the pure vacuum curved space-times (without any material sources, including the cosmological constant) what is absolutely impossible in General Relativity. Such a phenomenon makes it easier to create the universe from ``nothing''. The second class consists of the solutions with varying curvature scalar. We found its representative as the one-parameter family. It appears that it can be conformally covered by the thee-parameter Mannheim-Kazanas solution. We also investigated the general structure of the energy-momentum tensor in the spherical conformal gravity and constructed the vectorial equation that reveals clearly some features of non-vacuum solutions. Two of them are explicitly written, namely, the metrics à la Vaidya, and the electrovacuum space-time metrics.
Plasma Control in Symmetric Mirror Machines
NASA Astrophysics Data System (ADS)
Horton, W.; Rowan, W. L.; Alvarado, Igor; Fu, X. R.; Beklemishev, A. D.
Plasma confinement in the symmetric rotating mirror plasma at the Budker Institute shows enhanced confinement with high electron temperatures with end plates biasing. Improved confinement is achieved by biasing end plate cells in the expansion tanks so as to achieve an inward pointing radial electric field. The negative potential well produces vortex plasma rotation similar to that in the negative potential well of Ohmic heated tokamaks. This plasma state has similarity with the lower turbulence level regimes documented in the Helimak where negative biasing of the end plates produces an inward radial electric field. To understand this vortex confinement we carry out 3D simulations with nonlinear partial differential equations for the electric potential and density in plasmas with an axially localized region of unfavorable and favorable magnetic curvature. The simulations show that the plasma density rapidly adjusts to be higher in the region of favorable curvature regions and remains relatively well confined while rapidly rotating. The results support the concept of using plasma-biasing electrodes in large expander tanks to achieve enhanced mirror plasma confinement. Supported by US-DoE grant to UT, LANL and the Budker Institute for Nuclear Physics.
Solitons in PT-symmetric periodic systems with the logarithmically saturable nonlinearity
Zhan, Kaiyun; Tian, Hao; Li, Xin; Xu, Xianfeng; Jiao, Zhiyong; Jia, Yulei
We report on the formation and stability of induced solitons in parity-time (PT) symmetric periodic systems with the logarithmically saturable nonlinearity. Both on-site and off-site lattice solitons exist for the self-focusing nonlinearity. The most intriguing result is that the above solitons can also be realized inside the several higher-order bands of the band structure, due to the change of nonlinear type with the soliton power. Stability analysis shows that on-site solitons are linearly stably, and off-site solitons are unstable in their existence domain. PMID:27596716
Molecular-dynamic investigation of the interaction of vacancies with symmetrical tilt grain boundaries in aluminum
NASA Astrophysics Data System (ADS)
Weckman, A. V.; Demyanov, B. F.; Dragunov, A. S.
The molecular-dynamic method has been used to study the interaction of lattice vacancies with symmetrical grain boundaries (GBs) in aluminum. The fraction of trapped vacancies has been found to depend linearly on the distance to the GB plane. The average velocity of the vacancy migration toward the boundary decreases exponentially with an increase in the distance between the GB plane and vacancy. The radius of the region of trapping of a vacancy by the boundary is limited to two to three lattice parameters and grows with an increase in temperature. Four types of boundaries, which are characterized by different capability for the trapping of vacancies, have been determined.
The dynamics of a symmetric coupling of three modified quadratic maps
NASA Astrophysics Data System (ADS)
Paulo, C. Rech
We investigate the dynamical behavior of a symmetric linear coupling of three quadratic maps with exponential terms, and identify various interesting features as a function of two control parameters. In particular, we investigate the emergence of quasiperiodic states arising from Naimark—Sacker bifurcations of stable period-1, period-2, and period-3 orbits. We also investigate the multistability in the same coupling. Lyapunov exponents, parameter planes, phase space portraits, and bifurcation diagrams are used to investigate transitions from periodic to quasiperiodic states, from quasiperiodic to mode-locked states and to chaotic states, and from chaotic to hyperchaotic states.
Five dimensional spherically symmetric cosmological model in Brans-Dicke theory of gravitation
NASA Astrophysics Data System (ADS)
Rao, V. U. M.; Jaysudha, V.
In this paper, we consider the spherically symmetric space-time in five dimensions in Brans-Dicke (Phys. Rev. 124:925, 1961) theory of gravitation in the presence of perfect fluid distribution. A determinate solution of the highly non-linear field equations is presented using (i) relation between metric potentials and (ii) an equation of state which represents disordered radiation in five dimensional universe. The solution obtained describes five dimensional radiating model in Brans-Dicke theory. Some physical and kinematical properties of the model are also discussed.
Five dimensional spherically symmetric minimally interacting holographic dark energy model in Brans-Dicke theory
NASA Astrophysics Data System (ADS)
Reddy, D. R. K.; Raju, P.; Sobhanbabu, K.
Five dimensional spherically symmetric space-time filled with two minimally interacting fields; matter and holographic dark energy components is investigated in a scalar tensor theory of gravitation proposed by Brans and Dicke (Phys. Rev. 124:925, 1961). To obtain a determinate solution of the highly non-linear field equations we have used (i) a relation between metric potentials and (ii) an equation of state which represents disordered radiation in five dimensional universe. The solution obtained represents a minimally interacting and radiating holographic dark energy model in five dimensional universe. Some physical and Kinematical properties of the model are, also, studied.
Solitons stabilization in PT symmetric potentials through modulation the shape of imaginary component
NASA Astrophysics Data System (ADS)
Huang, Chunfu; Zeng, Jiale
Stability and dynamics of PT symmetric fundamental bright solitons supported by localized potentials in a focusing Kerr medium are investigated numerically. How the shape and magnitude of the imaginary component affect soliton stability is addressed when fixed real part of the potentials. The unbroken PT symmetry in linear case and stable region in nonlinear case are discussed. Numerical simulations proved that solitons can propagate stably when the loss or gain distribution become narrower. So we can stabilize the solitons through modulation the shape of imaginary component, and can use the method for solitons formation and control in other nonlinear media with PT potentials.
Symmetric interactions and interference between pitch and timbre.
Allen, Emily J; Oxenham, Andrew J
Variations in the spectral shape of harmonic tone complexes are perceived as timbre changes and can lead to poorer fundamental frequency (F0) or pitch discrimination. Less is known about the effects of F0 variations on spectral shape discrimination. The aims of the study were to determine whether the interactions between pitch and timbre are symmetric, and to test whether musical training affects listeners' ability to ignore variations in irrelevant perceptual dimensions. Difference limens (DLs) for F0 were measured with and without random, concurrent, variations in spectral centroid, and vice versa. Additionally, sensitivity was measured as the target parameter and the interfering parameter varied by the same amount, in terms of individual DLs. Results showed significant and similar interference between pitch (F0) and timbre (spectral centroid) dimensions, with upward spectral motion often confused for upward F0 motion, and vice versa. Musicians had better F0DLs than non-musicians on average, but similar spectral centroid DLs. Both groups showed similar interference effects, in terms of decreased sensitivity, in both dimensions. Results reveal symmetry in the interference effects between pitch and timbre, once differences in sensitivity between dimensions and subjects are controlled. Musical training does not reliably help to overcome these effects.
Ballooning Stability of the Compact Quasiaxially Symmetric Stellarator
M.H. Redi; J. Canik; R.L. Dewar; J.L. Johnson; S. Klasky; W.A. Cooper; W. Kerbichler
The magnetohydrodynamic (MHD) ballooning stability of a compact, quasiaxially symmetric stellarator (QAS), expected to achieve good stability and particle confinement is examined with a method that can lead to estimates of global stability. Making use of fully 3D, ideal-MHD stability codes, the QAS beta is predicted to be limited above 4% by ballooning and high-n kink modes. Here MHD stability is analyzed through the calculation and examination of the ballooning mode eigenvalue isosurfaces in the 3-space [s, alpha, theta(subscript ''k'')]; s is the edge normalized toroidal flux, alpha is the field line variable, and theta(subscript ''k'') is the perpendicular wave vector or ballooning parameter. Broken symmetry, i.e., deviations from axisymmetry, in the stellarator magnetic field geometry causes localization of the ballooning mode eigenfunction, with new types of nonsymmetric, eigenvalue isosurfaces in both the stable and unstable spectrum. The isosurfaces around the most unstable points i n parameter space (well above marginal) are topologically spherical. In such cases, attempts to use ray tracing to construct global ballooning modes lead to a k-space runaway. Introduction of a reflecting cutoff in k(perpendicular) to model numerical truncation or finite Larmor radius (FLR) yields chaotic ray paths ergodically filling the allowed phase space, indicating that the global spectrum must be described using the language of quantum chaos theory. However, the isosurface for marginal stability in the cases studied are found to have a more complex topology, making estimation of FLR stabilization more difficult.
Controlling of blow-up responses by nonlinear PT -symmetric coupling
NASA Astrophysics Data System (ADS)
Karthiga, S.; Chandrasekar, V. K.; Senthilvelan, M.; Lakshmanan, M.
We investigate the dynamics of a coupled waveguide system with competing linear and nonlinear loss-gain profiles which can facilitate power saturation. We show the usefulness of the model in achieving unidirectional beam propagation. In this regard, the considered type of coupled waveguide system has two drawbacks: (i) difficulty in achieving perfect isolation of light in a waveguide and (ii) existence of blow-up-type behavior for certain input power situations. We here show a nonlinear PT -symmetric coupling that helps to overcome these two drawbacks. Such a nonlinear coupling has close connection with the phenomenon of stimulated Raman scattering. In particular, we have elucidated the role of this nonlinear coupling using an integrable PT -symmetric situation. In particular, using the integrals of motion, we have reduced this coupled waveguide problem to the problem of dynamics of a particle in a potential. With the latter picture, we have clearly illustrated the role of the considered nonlinear coupling. The above PT -symmetric case corresponds to a limiting form of a general equation describing the phenomenon of stimulated Raman scattering. We also point out the ability to transport light unidirectionally even in this general case.
SL(2,R) duality-symmetric action for electromagnetic theory with electric and magnetic sources
Lee, Choonkyu; Min, Hyunsoo
For the SL(2,R) duality-invariant generalization of Maxwell electrodynamics in the presence of both electric and magnetic sources, we formulate a local, manifestly duality-symmetric, Zwanziger-type action by introducing a pair of four-potentials A{sup μ} and B{sup μ} in a judicious way. On the two potentials A{sup μ} and B{sup μ} the SL(2,R) duality transformation acts in a simple linear manner. In quantum theory including charged source fields, this action can be recast as a SL(2,Z)-invariant action. Also given is a Zwanziger-type action for SL(2,R) duality-invariant Born–Infeld electrodynamics which can be important for D-brane dynamics in string theory. -- Highlights: •We formulate a local, manifestly duality-symmetric, Zwanziger-type action. •Maxwell electrodynamics is generalized to include dilaton and axion fields. •SL(2,R) symmetry is manifest. •We formulate a local, manifestly duality-symmetric, nonlinear Born–Infeld action with SL(2,R) symmetry.
Numerical experiments with a symmetric high-resolution shock-capturing scheme
NASA Technical Reports Server (NTRS)
Yee, H. C.
Characteristic-based explicit and implicit total variation diminishing (TVD) schemes for the two-dimensional compressible Euler equations have recently been developed. This is a generalization of recent work of Roe and Davis to a wider class of symmetric (non-upwind) TVD schemes other than Lax-Wendroff. The Roe and Davis schemes can be viewed as a subset of the class of explicit methods. The main properties of the present class of schemes are that they can be implicit, and, when steady-state calculations are sought, the numerical solution is independent of the time step. In a recent paper, a comparison of a linearized form of the present implicit symmetric TVD scheme with an implicit upwind TVD scheme originally developed by Harten and modified by Yee was given. Results favored the symmetric method. It was found that the latter is just as accurate as the upwind method while requiring less computational effort. Currently, more numerical experiments are being conducted on time-accurate calculations and on the effect of grid topology, numerical boundary condition procedures, and different flow conditions on the behavior of the method for steady-state applications. The purpose here is to report experiences with this type of scheme and give guidelines for its use.
Solid-Phase Synthesis of Triostin A Using a Symmetrical Bis(diphenylmethyl) Linker System.
Sable, Ganesh A; Lim, Dongyeol
Triostin A is a symmetric bicyclic depsipeptide with very potent antitumoral activity because of its bisintercalation into DNA. In this study, we report a new synthetic strategy that exploits a structural symmetry of triostin A. First, we prepared a novel symmetric linker molecule that is labile under mildly acidic conditions and suitable for a solid-phase synthesis procedure. Two Cys units were attached to a linker-resin conjugate via their free thiol groups, and double deprotection and double coupling reactions were then applied to synthesize linear tetradepsipeptides. Subsequently, the key biscyclization of the tetradepsipeptides was performed on the resin, and the resulting cyclic octapeptide was detached from the linker-resin conjugate to give a peptide with two free thiols. Finally, triostin A was obtained by oxidizing the free thiols in solution to produce a disulfide. The yield was improved through exploration of two different solid-phase synthetic approaches under similar strategy. Mainly, this strategy was developed to enable the ease and rapid preparation of libraries of symmetric bicyclic depsipeptides. It also addresses several synthetic problems with our synthesis, including diketopiperazine (DKP) formation, poor cyclization yields and preparation of noncommercial N-methyl amino acids in good yields.
The lack of large compact symmetric objects
NASA Astrophysics Data System (ADS)
Augusto, P.
In recent years, `baby' (< 103 yr) and `young' (103-105 yr) radio galaxies have been found and classified, although their numbers are still small (tens). Also, they have many different names, depending on the type of survey and scientific context in which they were found: compact steep spectrum sources (CSS), giga-Hertz peaked spectrum sources (GPS) and compact-medium symmetric objects (C-MSO). The latter have the radio galaxy structure more obvious and correspond to the `babies' (CSOs; < 1 kpc) and `young' (MSOs; 1-15 kpc) radio galaxies. The log-size distribution of CSOs shows a sharp drop at 0.3 kpc. This trend continues through flat-spectrum MSOs (over the full 1-15 kpc size range). In order to find out if this lack of large CSOs and flat-spectrum MSOs is due to poor sampling (lack of surveys that probe efficiently the 0.3-15 kpc size range) and/or has physical meaning (e.g. if the lobes of CSOs expand as they grow and age, they might become CSSs, `disappearing' from the flat-spectrum MSO statistics), we have built a sample of 157 flat-spectrum radio sources with structure on ˜0.3-15 kpc scales. We are using new, archived and published data to produce and inspect hundreds of multi-frequency multi-instrument maps and models. We have already found 13 new secure CSO/MSOs. We expect to uncover ˜30-40 new CSOs and MSOs, most on the 0.3-15 kpc size range, when our project is complete.
Recent advances in symmetric and network dynamics
NASA Astrophysics Data System (ADS)
Golubitsky, Martin; Stewart, Ian
We summarize some of the main results discovered over the past three decades concerning symmetric dynamical systems and networks of dynamical systems, with a focus on pattern formation. In both of these contexts, extra constraints on the dynamical system are imposed, and the generic phenomena can change. The main areas discussed are time-periodic states, mode interactions, and non-compact symmetry groups such as the Euclidean group. We consider both dynamics and bifurcations. We summarize applications of these ideas to pattern formation in a variety of physical and biological systems, and explain how the methods were motivated by transferring to new contexts René Thom's general viewpoint, one version of which became known as "catastrophe theory." We emphasize the role of symmetry-breaking in the creation of patterns. Topics include equivariant Hopf bifurcation, which gives conditions for a periodic state to bifurcate from an equilibrium, and the H/K theorem, which classifies the pairs of setwise and pointwise symmetries of periodic states in equivariant dynamics. We discuss mode interactions, which organize multiple bifurcations into a single degenerate bifurcation, and systems with non-compact symmetry groups, where new technical issues arise. We transfer many of the ideas to the context of networks of coupled dynamical systems, and interpret synchrony and phase relations in network dynamics as a type of pattern, in which space is discretized into finitely many nodes, while time remains continuous. We also describe a variety of applications including animal locomotion, Couette-Taylor flow, flames, the Belousov-Zhabotinskii reaction, binocular rivalry, and a nonlinear filter based on anomalous growth rates for the amplitude of periodic oscillations in a feed-forward network.
NASA Astrophysics Data System (ADS)
Bender, Carl M.
In this talk we propose to broaden the conventional notion of quantum mechanics. In conventional quantum mechanics one imposes the condition H†=H, where † represents complex conjugation and matrix transpose, to ensure that the Hamiltonian has a real spectrum. Replacing this mathematical condition by the weaker and more physical requirement H‡=H, where ‡=PT represents combined parity reflection and time reversal, one obtains new infinite classes of complex Hamiltonians whose spectra are also real and positive. These PT-symmetric theories may be viewed as analytic continuations of conventional theories from real to complex phase space. This talk describes the unusual classical and quantum properties of PT-symmetric quantum mechanical and quantum field theoretic models.
NASA Astrophysics Data System (ADS)
Bender, Carl M.
This talk proposes a generalization of conventional quantum mechanics. In conventional quantum mechanics one imposes the condition H †=H , where † represents complex conjugation and matrix transpose, to ensure that the Hamiltonian has a real spectrum. By replacing this mathematical condition with the weaker and more physical requirement H ‡=H , where ‡= PT represents combined parity reflection and time reversal, one obtains new infinite classes of complex Hamiltonians whose spectra are also real and positive. These PT-symmetric theories may be viewed as analytic continuations of conventional theories from real to complex-phase space. This talk describes the unusual classical and quantum properties of PT-symmetric quantum-mechanical and quantum-field-theoretic models.
The classification of quantum symmetric-key encryption protocols
NASA Astrophysics Data System (ADS)
Xiang, Chong; Yang, Li; Peng, Yong; Chen, Dongqing
The classification of quantum symmetric-key encryption protocol is presented. According to five elements of a quantum symmetric-key encryption protocol: plaintext, ciphertext, key, encryption algorithm and decryption algorithm, there are 32 different kinds of them. Among them, 5 kinds of protocols have already been constructed and studied, and 21 kinds of them are proved to be impossible to construct, the last 6 kinds of them are not yet presented effectively. That means the research on quantum symmetric-key encryption protocol only needs to consider with 5 kinds of them nowadays.
(M-theory-)Killing spinors on symmetric spaces
Hustler, Noel; Lischewski, Andree
We show how the theory of invariant principal bundle connections for reductive homogeneous spaces can be applied to determine the holonomy of generalised Killing spinor covariant derivatives of the form D = ∇ + Ω in a purely algebraic and algorithmic way, where Ω : TM → Λ{sup ∗}(TM) is a left-invariant homomorphism. Specialising this to the case of symmetric M-theory backgrounds (i.e., (M, g, F) with (M, g) an eleven-dimensional Lorentzian (locally) symmetric space and F an invariant closed 4-form), we derive several criteria for such a background to preserve some supersymmetry and consequently find all supersymmetric symmetric M-theory backgrounds.
Microfabricated linear Paul-Straubel ion trap
Mangan, Michael A [Albuquerque, NM; Blain, Matthew G [Albuquerque, NM; Tigges, Chris P [Albuquerque, NM; Linker, Kevin L [Albuquerque, NM
An array of microfabricated linear Paul-Straubel ion traps can be used for mass spectrometric applications. Each ion trap comprises two parallel inner RF electrodes and two parallel outer DC control electrodes symmetric about a central trap axis and suspended over an opening in a substrate. Neighboring ion traps in the array can share a common outer DC control electrode. The ions confined transversely by an RF quadrupole electric field potential well on the ion trap axis. The array can trap a wide array of ions.