Question: What is the form of the Lagrangian that describes the interaction between the kaon field and the vector meson φµ, and how does it contribute to the kaon propagator at the one-loop level?

Answer: The Lagrangian that describes the interaction between the kaon field and the vector meson φµ is given by \( L = \frac{g}{\sqrt{2}} \phi_\mu \bar{K} \partial^\mu K \). At the one-loop level, this interaction contributes to the kaon propagator through the one-meson exchange diagram (c), which is part of the one-loop kaon polarization. The one-loop kaon polarization can be decomposed into contributions from different diagrams, including the baryonic tadpoles (a), kaon tadpoles mediated by scalar mesons (b), and the one-meson exchange (c).


Question: What is the significance of the angle ρ in the expression for the geometric correction factor cq, and how does it affect the value of cq?

Answer: The angle ρ is the angle between the vertical and the major principal direction of the stress tensor. The value of cq depends on ρ, with a value of 1 for smooth cones (when ρ = 120º) and larger values for rough cones (ρ > 120º). Therefore, the value of cq not only depends on soil properties but also on those of the soil-cone interface.


Question: What are the specific values for the ODDS-TEXT and ODDS-VIS explanations when ϵ is set to 0.5 in the workplace evaluation scenario?

Answer: When ϵ is set to 0.5, the values for the ODDS-TEXT and ODDS-VIS explanations are x = 39 and y = 61, where x represents the number of potential DP outputs that lead the manager to believe the employee responded dtrue if they do not participate/respond dfalse, and y represents the number of potential DP outputs that lead the manager to believe the employee responded dtrue if they participate/respond dtrue.


Question: How does the performance of TDM vary with different values of T and K in the MCAR, MAR, MNARL, and MNARQ settings?

Answer: Figure 12 shows the RMSE for TDM with different values of T and K in the MCAR, MAR, MNARL, and MNARQ settings. The configurations include TDM (T=1,K=2), TDM (T=2,K=2), TDM (T=3,K=2), TDM (T=4,K=2), TDM (T=2,K=1), TDM (T=2,K=3), and TDM (T=2,K=4).


Question: How do the values of P6,1(s) and P6,5(s) relate to the values of P3,1(s) and P3,2(s)?

Answer: P6,1(s) equals P3,1(s), and P6,5(s) equals P3,2(s) − 1/2s.


Question: How does Sraffa's approach to economic analysis differ from Ricardo's in terms of the reproduction of the economic system and the concept of returns?

Answer: Sraffa's approach focuses on determining equilibrium prices and distribution for given quantities and techniques, without addressing the reproduction of the economic system or changes in output and production proportions. In contrast, Ricardo's analysis is embedded in a larger framework of the reproduction of the whole economic system, where the determination of profits is a precondition for analyzing capital accumulation and the evolution of the production system. Sraffa rejects any assumption about returns, as it implies a comparison between different production systems, which is not possible without an invariable standard. Ricardo, however, considers the concept of returns essential for analyzing reproduction, though his approach differs from the neo-classical one.


Question: How does the 8:3 resonance scenario differ from the 5:2 resonance scenario in terms of the moons' eccentricity and inclination evolution?

Answer: In the 8:3 resonance scenario, the moons leave the resonance in about 15 Myr, and both during and immediately after the resonance, the moons' orbits in the simulation are consistent with the observed system. In contrast, in the 5:2 resonance scenario, Namaka’s eccentricity and inclination are well short of the observed values as the moons cross the resonance.


Question: What is the definition of a cusped Cayley graph in the context of a relatively hyperbolic group, and how is it constructed?

Answer: The cusped Cayley graph X(G, P, S) is a quotient of the disjoint union of the Cayley graph of G with respect to a compatible generating set S and for each i a combinatorial horoball over Pi for every coset of Pi. The horoballs are attached to the Cayley graph so that every vertex gp in the Cayley graph is identified with (p, 0) in the combinatorial horoball over Pi associated with gPi.


Question: What are the specific parameter ranges used in the cMSSM scan, and how do they affect the LSP properties?

Answer: The cMSSM parameter ranges used in the scan are: scalar mass (0.1 < m0 < 6 TeV), gaugino mass (0.1 < m1/2 < 6 TeV), trilinear coupling (−12 < A0 < 12), ratio of Higgs doublet VEVs (1 < tan β < 60), and the sign of the µ parameter (µ > 0). These parameters are set at the GUT scale. In the cMSSM, the LSP is usually bino-like, and a wino-like LSP is not possible due to the assumption of gaugino mass unification. A higgsino-like LSP is possible only if m0 ≫ m1/2, and co-annihilation with ˜t1 is impossible in this framework.


Question: How does the angular distribution of the emitted photon change with the distance between atoms in the photon generation scheme?

Answer: For kLa = 0.25, the atoms are so close together that the atomic excitation (spin wave) acts as a single degree of freedom that couples to the radiation field, resulting in an almost spherical intensity profile which is modulated by the dipole radiation pattern. In the intermediate case kLa = 1.36, the coupling to the radiation field is still dominated by collective effects, and the photon emission is strongly peaked along a polar direction.


Question: What are the limitations of the physics-focused model presented in Section 2.2, and how does the piecewise affine (PWA) model in Section 2.3 address these limitations?

Answer: The physics-focused model in Section 2.2 does not explicitly model the deposited fluid volume, focusing instead on the volumetric flow rate of fluid out of the nozzle. This is because past works considered droplet volume ill-defined until the jet breaks, at which point the droplet volume was considered constant. The PWA model in Section 2.3 addresses this limitation by defining the droplet volume as a dynamical state variable that can evolve over time, presenting a new division of the ejection process into partial processes to facilitate droplet volume modeling, and proposing and experimentally validating a mapping between nozzle flow rate and deposited droplet volume.


Question: How do the differences in the linear overdensity parameter δc and the virial overdensity ∆V evolve with redshift for the non-minimally coupled models compared to the ΛCDM model?

Answer: Differences in δc are very small, much below 1% at z = 0, while at high redshifts, all models converge to the Einstein-de Sitter (EdS) result. Models with a lower (higher) growth factor have a smaller (larger) δc. The NMC1 model is virtually indistinguishable from the ΛCDM model, while the largest differences appear for models with negative coupling (NMC2). Model MCH2 shows lower values for δc with respect to the ΛCDM model even at high redshifts. For the virial overdensity ∆V, the differences are also presented in the lower panel of Fig. 6.


Question: What RHEED and AFM results are presented for the In2Se3 layer formed on the InP(111)B substrate?

Answer: RHEED images show the InP(111)B surface at different temperatures, including the deoxidized surface with the newly formed In2Se3 layer after annealing at 505 °C for 5 minutes. The AFM image of the sample shows a smooth, atomically flat In2Se3 layer with a roughness of Rq=0.4 nm.


Question: What are the main drawbacks of existing role mining algorithms that aim to minimize deviation or the number of roles?

Answer: The main drawbacks are that the discovered roles are often artificial and unintuitive for administrators, making them difficult to interpret as functional roles. This limits the acceptance of the new RBAC configuration among employees and makes it difficult to maintain. Additionally, optimizing roles to fit existing authorizations closely can lead to the migration of erroneous user-permission assignments to the new RBAC system.


Question: How does the IFC renormalization method compare to the DFT+fitting method in terms of accuracy and computational efficiency for optimizing the thermal expansion and pyroelectricity of wurtzite GaN and ZnO?

Answer: The IFC renormalization method shows good agreement with the DFT+fitting method, especially for gallium nitride. The fitting error in the IFC calculation is lower in GaN (0.7696%) than in ZnO (2.1930%). The DFT+fitting method, however, can be inefficient for multi-parameter cases and can lead to unphysical fluctuations in the pyroelectricity calculations, presumably due to the less accurate fitting with a fourth-order polynomial of the atomic displacement compared to fitting with an equation of state for the thermal expansion coefficient.


Question: What are the specific signal strengths for the γγ channel as reported by CMS and ATLAS, and how do they compare to the SM expectation?

Answer: CMS reports a signal strength of 0.468 ± 0.396 for the γγ channel, while ATLAS reports 1.62 ± 0.411. Both values are relative to the standard model Higgs boson.


Question: How is the path of the charge described mathematically as it leaves the solenoid, and what are the key equations involved?

Answer: The path of the charge as it leaves the solenoid is described by the equation of a straight line given by \( z(x) = g(x_2) + a(x - x_2) \). The slope \( a \) at the point \( (x_2, g(x_2)) \) where the charge leaves the solenoid is given by \( a = -rac{(x_2 - (x_1 + r))}{(g(x_2) - f(x_1))} \). The coordinates of the point where the charge leaves the solenoid are \( (x_2, g(x_2)) \), and the circular path within the solenoid is described by \( g(x_2) = f(x_1) \sqrt{r^2 - (x_2 - (x_1 + r))^2} \).


Question: What is the specific example provided to illustrate the commutor for the two-dimensional irreducible representation V of Uq(sl2)?

Answer: The commutor for the two-dimensional irreducible representation V of Uq(sl2) is given by the matrix σV V =        1 0 0 0 0 1−q2 1+q2 2q 1+q2 0 0 2q 1+q2 −1+q2 1+q2 0 0 0 0 1        with respect to the standard (lexicographically ordered) basis for V ⊗ V. The denominators of the rational functions appearing in σV V are nonzero for all real q.


Question: What are the specific stable matchings M1 and M2 under the given preferences, and how do they affect the optimal regret for p1 and u2?

Answer: The two stable matchings under the given preferences are M1 and M2. M1 is defined as: p2 for u1, p1 for u2, p3 for u3, u2 for p1, u1 for p2, and u3 for p3. M2 is defined as: p2 for u1, p3 for u2, p1 for u3, u3 for p1, u1 for p2, and u2 for p3. The optimal regret for p1 grows linearly in T if T(M(· ; νt) = M2) grows linearly in T, and the optimal regret for u2 grows linearly in T if T(M(· ; νt) = M1) grows linearly in T.


Question: What is the specific form of the bilinear form B#_M and the linear form L#_M in the variational problem for the viscoelastic generalized membrane shell?

Answer: The bilinear form B#_M and the linear form L#_M are defined as follows: B#_M(ξ(t), η) = ∫_ω aαβστγστ(ξ(t))γαβ(η)√ady + ∫_ω bαβστγστ(˙ξ(t))γαβ(η)√ady - ∫_0^t e^(-k(t-s)) ∫_ω cαβστγστ(ξ(s))γαβ(η)√adyds, and L#_M(η)(t) = ∫_ω ϕαβ(t)γαβ(η)√ady, where k = (λ + 2µ) / (θ + ρ), and ϕαβ(t) = ∫_(-1)^1 (F αβ(t) - (θ / (θ + ρ))F 33(t)aαβ + (θΛ / (θ + ρ)) ∫_0^t e^(-k(t-s))F 33(s)dsaαβ) dx3.


Question: How does the property of short, monotone maps relate to the order on PX being closed and transitive?

Answer: The short, monotone maps are precisely those which satisfy f(x) − f(y) ≤ dL(x, y) for all x and y. Since dL is lower-semicontinuous and satisfies the triangle inequality, we can apply Kantorovich duality to show that the order on PX is closed and transitive. Antisymmetry will be proven in Corollary 4.3.2.


Question: What is the definition of an eigenfamily for a Riemannian manifold, and how does it relate to the functions φi and ψk mentioned in the proof?

Answer: An eigenfamily for a Riemannian manifold (M, g) is a set E = {φi : M → C | i ∈ I} of complex-valued functions such that there exist complex numbers λ, µ ∈ C such that for all φ, ψ ∈ E, τ(φ) = λφ and κ(φ, ψ) = µφψ. In the context of the proof, the sets E1 = {φi | i = 1, 2, ..., n} and E2 = {ψk | k = 1, 2, ..., n} are eigenfamilies, and it is shown that κ(φi, ψk) = 0, which implies that they are orthogonal.


Question: How does the paper describe the construction of the weights for the irreversible cycles in the Glauber dynamics?

Answer: The weights associated to the irreversible cycles are set as ρ(C) := e−H∗ec τew+ if C ∈C+e, and ρ(C) := e−H∗ec τew− if C ∈C−e, where w+ and w− are non-negative functions such that D(w±) ∩{0, 1} = ∅.


Question: What are the specific Neumann problems that the functions u2 and u3 solve in the asymptotic analysis of the Hele-Shaw problem?

Answer:
The functions u2 and u3 solve the following Neumann problems:
\ u2:
\ -∂²u2/∂ξ₂²(y₁, ξ₂, t) = ∂²w₀/∂y₁²(y₁, t), ξ₂ ∈ (0, S(y₁, t)),
\ ∂u₂/∂ξ₂(y₁, S(y₁, t), t) = ∂S/∂y₁ ∂w₀/∂y₁ - γ ∂S/∂t,
\ ∂u₂/∂ξ₂(y₁, 0, t) = -χ₁(y₁) ϕ₂(y₁, t),
\ u3:
\ -∂²u₃/∂ξ₂²(y₁, ξ₂, t) = ∂²w₁/∂y₁²(y₁, t), ξ₂ ∈ (0, S(y₁, t)),
\ ∂u₃/∂ξ₂(y₁, S(y₁, t), t) = ∂S/∂y₁ ∂w₁/∂y₁,
\ ∂u₃/∂ξ₂(y₁, 0, t) = 0.


Question: How is the light travel time difference calculated for the geodesic-defined interferometer, and what specific code is used to determine the travel time for one interferometer arm?

Answer: The light travel time differences δτrθ, δτrφ, and δτθφ are calculated by determining the difference in proper time τ between the beam-splitter and the mirrors. The code to determine the light travel time for one interferometer arm is as follows: geodesic outward_ray = connecting_null_geodesic(beam_splitter_origin, mirror_worldline, L)->second; point reflection = outward_ray(1); double light_travel_time = connecting_null_geodesic(reflection, beam_splitter_worldline, 2 * L)->first; The third argument to connecting_null_geodesic is an initial guess for the parameter value of the curve at which the null geodesic will intersect, chosen to be L for the outgoing ray and 2L for the ingoing ray, corresponding to the exact points of intersection in flat space.


Question: What is the relationship between a strongly ss-injective module and the extension of R-homomorphisms from small submodules?

Answer: A module M is strongly ss-injective if and only if every R-homomorphism α : A → M, where A is a small submodule of N and α(A) is a semisimple submodule in M, extends to an R-homomorphism from N to M.


Question: How does the iterative algorithm for optimizing the density profile converge, and what factors influence its performance?

Answer: The iterative algorithm converges almost monotonously to about 0.06 after the first 6 iterations and then stays approximately constant. Increasing the value of K0 speeds up the convergence, but too large values of K0 lead to strong local variations in the measured images. The number of averaged images (Na) also affects the convergence, with both Fm and Nd decreasing with Na, while F remains constant. The main limitation is the number of iterations used in the experiment (∼15), and further reducing the figure of merit F to ∼0.02 would require prohibitively long experimental times.


Question: How are the transition functions for the fiber bundle π : E → B defined in the case when the fiber is D = {(z, w) ∈ C* × C : |zp||w| < 1}, p ≥ 2?

Answer: The transition functions for the fiber bundle π : E → B in this case are of the form τα,β(b, z, w) = (b, za1/pα,β(b, zpwq), eiθα,β(b)wa−1/qα,β(b, zpwq)), for some aα,β ∈ O∗((Ωα ∩ Ωβ) × D) and θα,β(b) ∈ R.


Question: What is the behavior of the space-dependent term \( u_x(γ(α, t), t) \) as \( η \) approaches \( η^* \) for \( (λ, κ) \in (-\infty, -1] 	imes \mathbb{R}^- \)?

Answer: The space-dependent term \( u_x(γ(α, t), t) \) approaches \(-\infty\) as \( η \) approaches \( η^* \) for \( (λ, κ) \in (-\infty, -1] 	imes \mathbb{R}^- \).


Question: How is the Fourier transform of Slm(t, r) derived and what is the integral expression for it?

Answer: The Fourier transform of Slm(t, r) is derived by expressing eSlmk(ω, r) in terms of Slm(t, r) and substituting the result into (5.97). The final expression is given by Slm(ω, r) = ∑_{k=-∞}^{∞} δ(ω - ωmk) Ωr / 2π ∫_0^P ei(ωmk t′ - mφ′) f lm(r) (˙r′)^n δ(r - r′) dt′, where n = 0, 1, 2.


Question: How are the Gamow eigensolutions for resonance and anti-resonance poles defined in terms of the wave number and what are their normalization factors?

Answer: The nth Gamow eigensolution for the resonance pole is given by u(r; zn) = u(r; kn) = Nn { 1/J3(kn) sin(knr) for 0 < r < a, J1(kn)/J3(kn) eiQnr + J2(kn)/J3(kn) e−iQnr for a < r < b, eiknr for b < r < ∞ }, where Nn is a normalization factor, Nn^2 = i res [S(k)]k=kn. The nth Gamow eigensolution for the anti-resonance pole is given by u(r; z*n) = u(r; −k*n) = Mn { 1/J3(−k*n) sin(−k*n r) for 0 < r < a, J1(−k*n)/J3(−k*n) e−iQ*n r + J2(−k*n)/J3(−k*n) eiQ*n r for a < r < b, e−ik*n r for b < r < ∞ }, where Mn is a normalization factor, M2n = i res [S(k)]k=−k*n = (N2n)*.


Question: What is the significance of the openness of the nondegeneracy property of semi-Riemannian submanifolds in the context of GECs?

Answer: The openness of the nondegeneracy property of semi-Riemannian submanifolds is significant because it ensures that the subset AgA,ν,P, which consists of metrics g in AgA,ν such that g is nondegenerate on P, is open in AgA,ν. This property is crucial for endowing P with a product metric and is a more general result that will be applied in the context of GECs.


Question: What are the implications of the condition e2(M) ≠ 0 in the context of the equivalence of statements 1., 2., and 3. when r = 2?

Answer: The condition depth grM(M) > 0 implies fM1 = M1, hence Pj≥1 vj(eM) = 1 and e2(M) ≠ 0. This completes the proof of the equivalence of 1., 2., and 3. in the case r = 2.


Question: What specific improvements were achieved in the E-mode MOSFET design using Si+ implantation for the source and drain regions?

Answer: Si+ implantation was used to form a source and drain, a self-aligned gate, and a thin channel (22 nm). A record value of the maximum transconductance of 35 mS/mm was obtained. The Rc value was 1.5 Ω ×mm.


Question: How does SynST differ from the latent Transformer in terms of the sequence it generates and the subsequent decoding process?

Answer: SynST first autoregressively predicts a sequence of target syntactic chunks, and then non-autoregressively generates all target tokens conditioned on the predicted parse. In contrast, the latent Transformer autoregressively generates a short sequence of discrete latent variables before non-autoregressively producing all target tokens conditioned on the generated latent sequence.


Question: What are the specific equations that describe the tortuosity factor for nanocomposite films containing graphene layers, and how do they differ based on the dispersion of the graphene layers?

Answer: For a nanocomposite film containing a random array of circular graphene layers, the tortuosity factor is given by: τ = 4 [1 + x + 0.1245x^2 / (2 + x)]^2, where x = (πD^2 / 2W) ln(D / 2W) ϕ. For a nanocomposite film containing a random dispersion of non-overlapping circular graphene layers, the tortuosity factor is: τ = exp[(D / 3.47W ϕ)^0.71]. The modified form of the original polynomial equation, accounting for the decrease in solubility, is: τ = 1 − ϕ + 4 [1 + x + 0.1245x^2 / (2 + x)]^2, where x = (πD^2 / 2W) ln(D / 2W) ϕ. The exponential function τ = 1 + 0.71D / 3.47W ϕ was proposed by Gusev and Lusti and later modified by Picard et al. to account for solubility effects.


Question: What are the key findings regarding the bending loss and crosstalk in the high-permittivity waveguide solution?

Answer: The bending loss is dominated by mode conversion, and the extremely high dielectric constant achieves good confinement, making the increase in confinement for higher frequencies irrelevant. The crosstalk behavior is excellent, with more than 55 dB of loss over the entire spectrum, making the solution attractive from a signal integrity perspective.


Question: What are the specific dI/dV spectra and their fitting parameters for the dark row-1, and how do they compare to the bright row-I studied in the main text?

Answer: The dI/dV spectra for the dark row-1 are shown in Fig. S5(a) with an energy range from +16 mV to -16 mV. The fitting parameters for the spectra are:  = 8.7 meV, q = 20 for #1;  = 9.6 meV, q = -40 for #5;  = 9.9 meV, q = -15 for #7. These spectra were acquired at 0.4 K with a magnetic field of 0.5 T applied to suppress superconductivity. The bright row-I, studied in the main text, is indicated by the red arrow in the corresponding topographic image.


Question: What is the proposed explanation for the absence of the anomaly at TF2 in the ρ(T) and M(T) curves for x=0.55?

Answer: The absence of the anomaly at TF2 for x=0.55 is attributed to the competition between the CO2/3 and CO1/2 states, which leads to disordered arrangements of Li+ and Co3+/Co4+ even after slow cooling. This disorder can result in either Li ions not undergoing the transition at TF2 or the Co3+/Co4+ arrangement remaining disordered across TF2.


Question: How does the evolution of fNL in the N-axion model compare to the axion-quartic model discussed in the query text, particularly in the non-slow-roll regime?

Answer: In the N-axion model, the evolution of fNL approaches its asymptotic limit later in the evolution, and the slow-roll phase ends when ϵ = 1. The evolution near and after this point is not reliable and requires numerical calculation. In contrast, the axion-quartic model shows that the analytic results remain applicable even when slow-roll begins to break, with the analytic spectral index ns = 0.964 being within 1% of the non-slow-roll value.


Question: How does the performance of PointNet degrade when classifying arbitrarily rotated objects with sparse points, and what specific conditions were tested?

Answer: PointNet's performance degrades significantly when classifying arbitrarily rotated objects with sparse points. The conditions tested included: a) Point clouds with no rotation, b) Only rotated around the z-axis, and c) Arbitrary SO(3) rotations. The results show that PointNet performs well with dense point clouds under all rotational conditions, but performance decays as rotation is applied, especially under arbitrary SO(3) rotations. The accuracy drop from no rotation to arbitrary SO(3) rotation is 9.43% for 1024 points, 14.88% for 256 points, 25.80% for 64 points, and 41.12% for 16 points.


Question: What are the specific percentage differences in the leader's profit between the reference case and the optimized case for the instances with zero inconvenience and high DG?

Answer: For the instance with zero inconvenience, the percentage difference is 4.63%, and for the instance with high DG, the percentage difference is -1.62%.


Question: How does the proof of the equivalence between c(˙es′pq)(P) and c∗(˙es′pq)(P) utilize the maximal operator Mt and the Feﬀerman-Stein vector valued inequality?

Answer: Using the maximal operator Mt (0 < t ≤ 1) and the Feﬀerman-Stein vector valued inequality, the proof shows that c∗( ˙f s′pq)(P) = ||{∑i≥j (2is′ ∑l(R)=2−i |c∗(R)|χR)q}1/q||Lp(P) ≤ C||{∑i≥j (2is′ ∑l(R)=2−i ∑l(R′)=2−i |c(R′)|(1 + 2i|xR −xR′|)−LχR)q}1/q||Lp(P) ≤ C||{∑i≥j (2is′ ∑l(R)=2−i Mt(∑l(R′)=2−i |c(R′)|χR′)χR)q}1/q||Lp(P) ≤ C||{∑i≥j (∑l(R′)=2−i 2is′|c(R′)|χR′)q}1/q||Lp(P) = Cc( ˙f s′pq)(P) if 0 < t < min(p, q), L > n/t, and 0 < p < ∞, 0 < q ≤∞.


Question: How does the effectiveness of social distancing at different compliance levels (70%, 80%, and 90%) impact the disease control during the suppression period?

Answer: Strong compliance with social distancing (at 80% and above) effectively controls the disease during the suppression period, while lower levels of compliance (at 70% or less) do not succeed for any duration of the suppression. The duration of each social distancing strategy is set to 91 days (13 weeks), and the traces include incidence, prevalence, cumulative incidence, and the daily growth rate of cumulative incidence, shown as average (solid) and 95% confidence interval (shaded) profiles over 20 runs.


Question: What is the initialization process for the streaming algorithm for computing edit distance, and how does it handle the main loop over blocks of size O(k)?

Answer: The initialization process for the streaming algorithm involves initializing each list Li (for i = 0, ..., k) to be empty and setting D(d, h) = null and C(d, h) = 0 for all integers d, h such that |d| ≤ h ≤ k. The function Update(0, 0, 0) is then invoked. The main loop runs over blocks of size O(k), where for each block j, the algorithm processes substrings x′ and y′, builds a generalized suffix tree for the concatenation of x′ and y′, and processes each list Li within the current block. During this process, it evaluates queries using the suffix tree and updates the lists and scores accordingly.


Question: How were the mean blocking temperatures (TB) and effective magnetic anisotropy (Keff) determined for the synthesized nanoparticles, and what is the significance of the high irreversibility temperature observed in the curves?

Answer: The mean blocking temperatures (TB) were obtained from the MZFC(T) and MFC(T) measurements, and the effective magnetic anisotropy (Keff) was calculated through the definition of blocking temperature in Néel's model by matching the diameter distribution from TEM results and the f(TB) distribution obtained from magnetic measurements. The high irreversibility temperature observed in all curves, except for sample x = 0.19, indicates the contribution of nanoparticles with large anisotropy but not so relevant in population.


Question: How does the Stieltjes transform relate to the empirical spectral measure in the context of random matrix theory, and why is it important for the analysis in this paper?

Answer: The Stieltjes transform of the empirical spectral measure, gˆµ(z), is defined as 1/n tr R(z), where R(z) is the resolvent of the matrix S. The almost sure convergence of gˆµ(z) to a deterministic Stieltjes transform g(z) is equivalent to the weak convergence of the underlying probability measures. This relationship is crucial for the analysis in this paper because it allows the authors to estimate quantities involving 1/n tr R(z), making the resolvent approach a natural choice for characterizing the spectral behavior of large symmetric random matrices.


Question: What are the two main reasons the authors believe predictive models can be used to perform slightly superhuman tasks?

Answer: First, the prediction orthogonality thesis suggests that predictors can be effectively steered towards different optimization targets. Second, there is substantially more hope of being able to inner align models to prediction objectives due to the simplicity of such objectives.


Question: What is the cohomological consequence of the basic lemma for affine varieties, and how does it relate to the Andreotti-Frankel theorem?

Answer: The cohomological version of the Andreotti-Frankel theorem for affine varieties is an immediate consequence of the basic lemma. If X is affine of dimension n, the basic lemma deduces an increasing sequence of Zariski closed sets Xi of dimension at most i such that Hj(Xi, Xi−1) = 0 whenever j ≠ i. Consequently, the j-th cohomology of the complex D•, where Di = Hi(Xi, Xi−1), coincides with the j-th cohomology of X, which therefore vanishes whenever j > n.


Question: What is the expression for the density of P x with respect to Rx in terms of ζx, and how is it derived?

Answer: The density of P x with respect to Rx is given by dP x / dRx = 1{ dP x / dRx > 0} exp(∫_0^1 ⟨ζx_t, dP x_m Xt⟩ - 1/2 ∫_0^1 ∥ζx_s∥^2 ds). The proof involves a change of measure formula for stopped processes, using stopping times to localize the semi-martingale, and a uniqueness property of the reflected Brownian motion.


Question: What is the form of the controllability matrix for a second order continuous-time linear state-space system, and how is it derived from the given relations?

Answer: The controllability matrix for a second order continuous-time linear state-space system has the Kalman criterion form [B, AB, A^2B, ..., A^(n-1)B]. This is derived by substituting the relations M_0 = B, M_1 = AB, ..., M_(n-1) = A^(n-1)B into the controllability matrix [M_0, M_1, ..., M_(n-1)].


Question: What is the observed behavior of the Hall resistivity in the bilayers with small m, and how does it differ from the conventional Hall effect?

Answer: In the bilayers with small m, the Hall resistivity shows an unconventional behavior below 60 K, characterized by a non-monotonic hump structure between 0.8 and 2.1 T at 5 K. This hump structure is attributed to the topological Hall effect, which cannot be explained by the magnetization (M-H) curve alone.


Question: How does the jet multiplicity distribution differ between signal and background events in the single lepton analysis for a sgluon mass of 400 GeV?

Answer: In the single lepton analysis for a sgluon mass of 400 GeV, the signal events show a higher multiplicity of hard jets compared to the background events. Specifically, the signal distributions for the tjtj, tjtt, and tttt channels are represented by plain, strong dashed, and light dashed lines, respectively, while the background is dominated by t¯t and W-boson plus jets contributions.


Question: How does the Raman efficiency of the Γ-point phonon mode in graphene change in the presence of a strong magnetic field, and what are the selection rules for the strongest mode?

Answer: In strong magnetic fields, the Raman spectra of graphene acquire a pronounced structure with peaks corresponding to inter-Landau-level transitions. The selection rules for the strongest mode preserve the Landau level number n: n−→n+. The quantum efficiency of a single peak in this process is I1 ∼ (v^2 c^2 e^2 / λB πΩ)^2 ∼ 10^-12 per incoming photon for Ω ∼ 1 eV photons in a magnetic field B ∼ 10 T. The theoretical prediction for the intensity of the phonon-induced G peak is IG ∼ 10^-11, which is close in order of magnitude to the intensity of a single n−→n+ peak.


Question: What are the dimensionless expressions for the energy density, charge density, and pressure, and how are they related to the local chemical potential and the dimensionless mass squared?

Answer: The dimensionless expressions are ˆρ = ˆβ ∫_h/√f^ˆm ϵ^2 √(ϵ^2 − ˆm^2) dϵ, ˆσ = ˆβ ∫_h/√f^ˆm ϵ √(ϵ^2 − ˆm^2) dϵ, and −ˆp = ˆρ − h √f ˆσ. These expressions are related to the local chemical potential µ_loc = A_t / (L √f) = e / (κ h √f) and the dimensionless mass squared ˆm^2 = κ^2 / (e^2 m^2).


Question: What is the asymptotic behavior of the mean square displacement (MSD) of a tagged particle in single file diffusion for large times, and how is it derived?

Answer: For large times, the asymptotic behavior of the mean square displacement (MSD) of a tagged particle in single file diffusion is given by the equation ∆2x = 2a2(1 − c) / c * (Γt / π)^(1/2), where a is the lattice spacing, c is the homogeneous concentration per site, and Γ is the transition rate of a particle to an empty neighboring site. This result was demonstrated by Richards [2].


Question: How does the performance of CCC-Q compare to other classifiers as ρ increases from 1 to 10?

Answer: When ρ = 1, CCC-Q significantly outperformed the other competitors. As ρ grew up to 10, the performance of classifiers was generally improved, though PLCC and PCC still output pretty high misclassification rates.


Question: What is the form of the lower bound in the elliptic Lehmer conjecture for points satisfying an elliptic mod m condition?

Answer: The lower bound in the elliptic Lehmer conjecture for points Q ∈ E(¯K) satisfying an elliptic mod m condition is of the form CE/K,ǫ log m.


Question: What are the potential issues and solutions for updating set values in the concurrent setting, and how do they affect the work bound?

Answer: In the concurrent setting, updating the value in the new root during a link requires a DCAS or a more-complicated implementation using CAS. Using DCAS invalidates the analysis, as it can lead to overall work Ω(np) due to contention. This problem can be overcome by relaxing the linearization requirement, such as linking roots in pairs, which reduces contention and may suffice in many applications, even though it violates linearization.


Question: How is the R-operator represented in a coherent space and what is the relationship between the R- and S-matrices in this representation?

Answer: The R-operator has a simple form in a coherent space representation defined by formulas (2.21-2.3). Using a coherent state basis (2.21) for spaces V1, V3, and an anti-coherent basis (2.23) for V2, along with relations (2.27, 2.28), the connection between the R- and S-matrices is given by R = e−¯ψirijψj = e−¯ηiSijηj, where ηi = ψi and ¯ηi = Cij ¯ψj.


Question: How do the clustering results of the proposed method compare to other methods on the MNIST dataset in terms of ACC, NMI, and ARI?

Answer: The proposed method achieves ACC of 95.0%, NMI of 93.4%, and ARI of 91.5% on the MNIST dataset, outperforming other methods such as K-means, FCM, ECM-NSGA-II, ECM-MOEA/D, MFS-FCM, DI-FCM, RL-FCM, and FDPC.


Question: What are the isomorphisms Φ0 to Φ5 that relate the Chow groups of U and R, and how are they defined?

Answer: The isomorphisms Φ0 to Φ5 are defined as follows: Φ0 := h5 ◦(pU)∗, Φ1 := (h5 ◦(pU)∗, h4 ◦(pU)∗), Φ2 := (h5 ◦(pU)∗, h4 ◦(pU)∗, h3 ◦(pU)∗, (b · h) ◦(pU)∗), Φ3 := (h5 ◦(pU)∗, h4 ◦(pU)∗, h3 ◦(pU)∗, (b · h) ◦(pU)∗, h2 ◦(pU)∗, b ◦(pU)∗), Φ4 := (h4 ◦(pU)∗, h3 ◦(pU)∗, (b · h) ◦(pU)∗, h2 ◦(pU)∗, b ◦(pU)∗, h ◦(pU)∗), Φ5 := (h3 ◦(pU)∗, (b · h) ◦(pU)∗, h2 ◦(pU)∗, b ◦(pU)∗, h ◦(pU)∗, (pU)∗). These isomorphisms relate the Chow groups of U and R.


Question: What is the nature of the fixed points in the large N limit of Chern-Simons-gauged critical fermions and regular scalars?

Answer: In the strict large N limit, these 'quasi-bosonic' theories appear as fixed lines parameterized by x6, the coefficient of a sextic term in the potential. While x6 is an exactly marginal deformation at leading order in large N, it develops a non-trivial β function at first subleading order in 1/N. The beta function is a cubic polynomial in x6 at this order in 1/N, and it is conjectured that flows governed by this leading large N beta function have three fixed points for x6 at every non-zero value of the 't Hooft coupling, implying the existence of three distinct regular bosonic and three distinct dual critical fermionic conformal fixed points at every value of the 't Hooft coupling.


Question: What is the unique solution for the mass parameter m2 of the Wilson-Fisher fixed point, and how is it determined?

Answer: The unique solution for the mass parameter m2 of the Wilson-Fisher fixed point is m2 = −0.388 346 718 912 782 · · ·. This value is determined by solving the transcendental equation H(m2) = −1, where H(x) = 1/2 * x / (1 + x) + 3/4 * √(−x) * ln((1 − √(−x)) / (1 + √(−x))).


Question: How does the Fisher-Gnedenko-Tippet theorem apply to the distribution of the largest micro-crack in the wire, and what are the possible universal distributions?

Answer: The Fisher-Gnedenko-Tippet theorem ensures that the distribution of the largest micro-crack, FN(z), converges to one of three universal distributions: Weibull, Fréchet, or Gumbel. The convergence to one of these distributions depends on the asymptotic properties of the distribution of micro-cracks, P(n).


Question: What are the current experimental bounds on the neutron and mercury EDMs, and how do they relate to the quark EDMs and CEDMs?

Answer: The current experimental bounds on the neutron EDM (dn) and mercury EDM (dHg) imply bounds on the quark EDMs and CEDMs through the following relations: dHg ≃ 7 × 10−3e [˜du(ˆµh) − ˜dd(ˆµh)] + 10−2de, and dn ≃ (1.4 ± 0.6) [dd(ˆµh) − 0.25du(ˆµh)] + (1.1 ± 0.5)e [˜dd(ˆµh) + 0.5 ˜du(ˆµh)], where the quark (C)EDMs are evaluated at the hadronic scale ˆµh ≃ 1 GeV.


Question: ¿Cuáles son las dificultades principales para determinar la distribución asintótica nula de Rn,w(ˆθn) y Sn,w(ˆθn)?

Answer: Las principales dificultades son: 1) Determinar los conjuntos {λRj}j≥1 y {λSj}j≥1, ya que calcular los autovalores de un operador no es una tarea simple. 2) Obtener las expresiones de hR(x, y; θ) y hS(x, y; θ), que dependen de la función ℓ, la cual generalmente no tiene una expresión sencilla.


Question: What is the phase noise behavior of the comb spacing in the free-running condition, and how does it change when phase-locked to a high-performance microwave synthesizer?

Answer: In the free-running condition, the phase noise of the comb spacing shows a ݂ିଷ.ହ dependence on the offset frequency, indicating it is dominated by a mixture of technical noise such as frequency flicker and random walk. When phase-locked to a high-performance microwave synthesizer, the close-to-carrier phase noise can reach -70 dBc/Hz at 10 Hz with a ݂ିଵ.ହ dependence on the offset frequency, limited by the noise of the microwave synthesizer.


Question: How does the transmission spectrum change when considering only the dayside atmospheric properties compared to the nightside?

Answer: When considering only the dayside atmospheric properties, the transmission spectrum shows an offset (increase) in the transit depth of between 25 - 50 ppm, which is unlikely to be detectable through the instrument noise. This increase is due to higher cloud particle number densities on the dayside, leading to increased optical depths.


Question: What are the main components of the WASA detector and what are their roles in the experiment?

Answer: The WASA detector consists of two main parts: the Forward Detector (FD) and the Central Detector (CD). The Forward Detector is optimized for tagging the recoil particles, while the Central Detector is optimized for registering the meson decay products.


Question: How are the floating-point approximations of binomial coefficients and numbers (2k −1)s computed in the context of generating labeled DAGs?

Answer: The floating-point approximations with 2 log n bits for the exponent and 1 + log(3n3/ε) bits for the mantissa are obtained by setting the exponent to the length of the exact number and filling in the mantissa with the first 1 + log(3n3/ε) bits of the exact number. The number 2k(n−k−s) can be represented exactly by setting the exponent to k(n −k −s) + 1, the first bit of the mantissa to 1, and the remaining bits to 0.


Question: What is the form of the effective pair potential derived from the coarse-grained model, and how does it relate to the DLVO theory?

Answer:
The effective pair potential derived from the coarse-grained model is a screened-Coulomb (Yukawa) potential given by \( v_{	ext{eff}}(r) = Z^2 \lambda_B \left( rac{e^{\kappa a}}{1 + \kappa a}
ight)^2 rac{e^{-\kappa r}}{r} \) for \( r > 2a \). This form is the basis of the classic Derjaguin-Landau-Verwey-Overbeek (DLVO) theory of charged colloids, which was first derived within a Debye-Hückel approximation, but without the associated volume energy and without excluded-volume corrections.


Question: How does the synchrotron radiation emission frequency relate to the electron's Lorentz factor and the magnetic field strength?

Answer: The emission frequency of synchrotron radiation is given by ∆f ∗≫f = 2πwB; γ ≫1, where γ is the Lorentz factor of the electron and B is the magnetic field strength. This relationship explains why synchrotron radiation can be detected across a wide range of frequencies, from high frequencies like X-rays to low frequencies like radio waves, in the afterglows of GRBs.


Question: What is the specific example of a set that is porous with respect to the CC distance but not porous at the point 0 with respect to the Euclidean distance?

Answer: The set Pc is porous with respect to the CC distance, but not porous at the point 0 with respect to the Euclidean distance.


Question: What are the specific conditions and transformations required to ensure (‡) holds for subcases (a) and (b) in H11 and H12?

Answer: For subcase (a), where η(X) = c sn and si /= tiη holds for some 1 ≤ i ≤ n, (‡) can be ensured by transforming the store with H11 and a particular value of i such that si /= tiη holds, taking Y' = Zn, defining η' as the valuation that satisfies η'(Zj) = sj for all 1 ≤ j ≤ n and η'(Y) = η(Y) for any other variable Y, and proving η' ∈ WT SolH((Zi /= ti, Π)σ1 2 σσ1). For subcase (b), where η(X) = d sm and d ∈ DCm belongs to the same datatype as c but d ≠ c, (‡) can be ensured by transforming the store with H12 and the particular data constructor d ∈ DCm for which η(X) = d sm, taking Y' = Zm, defining η' as the valuation that satisfies η'(Zj) = sj for all 1 ≤ j ≤ m and η'(Y) = η(Y) for any other variable Y, and proving η' ∈ WT SolH(Πσ1 2 σσ1).


Question: What are the specific conditions that a pseudo-term must satisfy to meet the Bang condition, and what are the implications of violating these conditions?

Answer: A pseudo-term t satisfies the Bang condition if for any bang subterm u of t: (i) u contains at most one occurrence of a free variable x!C, and it has a bang type !C; (ii) for any subterm v of u such that v ≠ u and v ≠ x, s(doors(u, v)) ≥ 1. Violating these conditions can rule out canonical morphisms for monoidalness, such as !A⊗!B−◦!(A ⊗B) and §A−◦!A, which are not valid in LAL. For example, the pseudo-term λx!(A⊸B).λy!B⊸C.λz!A.(y)§((¯§x)¯§z) contains more than one free variable in the bang subterm §((¯§x)¯§z), and the pseudo-term λx§A.λy!A⊸B.(y)§(¯§x) has a free variable x with a linear type, both violating the Bang condition (i).


Question: How does the DDWD algorithm perform when tested with synthetic signals composed of different wavelets, and what does this indicate about its robustness?

Answer: The DDWD algorithm is highly accurate and robust when tested with synthetic signals composed of different wavelets, such as Meyer, fk6, and db2 wavelets. It accurately recovers the underlying wavelets across a wide range of the variance penalty parameter 𝜆2, with 𝛼(𝑏1,𝑏2) ≳ 0.95 for stages 1 through 14. This indicates that DDWD is reliable and can effectively uncover the wavelet shapes from synthetic datasets, even when the energy distribution and mean of the wavelets vary.


Question: How does the uniqueness of the identification of sections γ1 and γ2 with a given section γ support the construction of connections on V E?

Answer: The uniqueness of the identification of sections γ1 and γ2 with a given section γ ensures that the construction of connections on V E is well-defined and globally consistent. Specifically, since there is only one pair of sections γ1, γ2 that can be associated with a given section γ, this identification is unique, allowing us to lift connections on E to connections on V E via the formula ∇V E,Xγ := vlγ1∇Xγ2.


Question: What are the geodesic equations used to study the timelike geodesic in M2, and how do they relate to the proper time and the van Vleck determinant discussed in the query text?

Answer:
The geodesic equations in M2 are given by:
¨t + A′/A ˙r∗˙t = 0,
¨r∗+ A′/A ˙r∗^2 − A′/(2A^2) ϵ = 0,
with the first integral −A(˙t^2 − ˙r∗^2) = ϵ, where ϵ = 0, −1, +1 for null, timelike, and spacelike geodesics, respectively. The conserved quantity A˙t = E, where E is constant along the geodesic, corresponds to the Killing vector ∂/∂t in M2. For timelike geodesics (ϵ = −1), the equation (3.10) reduces to (dr∗/dt)^2 = 1 + ϵ A/E^2, which helps in determining the proper time and the van Vleck determinant along the geodesic.


Question: What methods are used to determine the pT-dependent corrections for residual differences within |η| < 1.3 at 30 < pT < 800 GeV?

Answer: The pT-dependent corrections for residual differences within |η| < 1.3 at 30 < pT < 800 GeV are measured combining photon+jet, Z(→µµ)+jet, and Z(→ee)+jet events. The pT dependence at pT > 800 GeV is directly constrained with multijet events.


Question: What are the key technical challenges and potential solutions for obtaining accurate CSI in THz RIS systems?

Answer: Obtaining accurate CSI for multiple RISs is a key challenge due to the estimation of multiple channels simultaneously, the large number of metasurfaces with non-linear hardware characteristics, and the highly-varying THz channel. One potential solution is to exploit the sparse nature of the channel and extract features from the geometric configuration of the network to learn more accurate CSI. Data-driven and proactive predictive methods can also bypass the highly-varying THz channel and infer accurate CSI within the coherence time of THz and the stringent E2E latency requirements of 6G applications.


Question: How does the proof of Theorem 2.5 establish the injectivity of the map ι∗: π0( bU(A)) →π0( bU(M2(A)))?

Answer: The proof of Theorem 2.5 establishes the injectivity of the map ι∗ by showing that if a ∈ bU(A) such that ι(a) ∼ 0 in bU(M2(A)), then a ∼ 0 in bU(A). Specifically, for any x ∈ X, ιx(a(x)) ∼ 0 in bU(M2(A(x))). Since A(x) is K-stable, a(x) ∼ 0 in bU(A(x)). By Lemma 2.4, there is a closed neighbourhood Yx of x such that πYx(a) ∼ 0 in bU(A(Yx)). Since X is compact and zero-dimensional, disjoint open sets {Yx1, Yx2, ..., Yxn} can be chosen to cover X. By Lemma 1.8, A is isomorphic to the direct sum of A(Yxi) for 1 ≤ i ≤ n. Since πYxi(a) ∼ 0 for each 1 ≤ i ≤ n, it follows that a ∼ 0, thus proving the injectivity of ι∗.


Question: What are the constraints on the coefficients C(3,33)φq and C(1,33)φq from precision electroweak observables, and how are they related in the context of the bLbLZ coupling?

Answer: The coefficients C(3,33)φq and C(1,33)φq are constrained by precision electroweak observables to be C(3,33)φq + C(1,33)φq = 0.016 ± 0.021 (with Λ ≡ 1 TeV). To simplify the analysis, it is assumed that C(3,33)φq = −C(1,33)φq ≡ Cφq.


Question: How does the global monopole parameter η influence the critical behavior and microscopic structure of the charged AdS black hole in both extended and alternate phase spaces?

Answer: The global monopole parameter η acts as a hindrance for critical behavior in both extended and alternate phase spaces. The Ruppeiner invariant scalar, which describes the microscopic structure of the black hole, behaves differently in these two spaces. The monopole parameter influences the microscopic structure, which in turn affects the critical behavior, with the effect being significant at the maximal strength of the monopole parameter.


Question: What are the predicted deviations in the CP asymmetries of Bs →φφ and Bs →φη′ decays due to the gluino-sbottom-quark interaction?

Answer: The CP asymmetries of the Bs →φφ and Bs →φη′ decays could be largely deviated from the SM predictions such as −0.1 ≲Sφφ ≲0.2 and −0.1 ≲Sφη′ ≲0.2.


Question: What is the relationship between the leakage current and the FWHM of the alpha-energy peaks at temperatures above 300 °C?

Answer: Above 300 °C, the leakage current was 10-6 A, and the increase in leakage current exceeded the FWHM at room temperature, causing the FWHM to increase exponentially with temperature.


Question: How does the quantum-inspired classical algorithm compare to the uniform sampler in terms of success probability for finding the maximum weighted clique?

Answer: The quantum-inspired classical sampler performs better than the uniform sampler, which has frequently been used as a benchmark, especially after implementing additional heuristic procedures such as shrinking and searching.


Question: What are the specific aspect ratios of TWA structures in the core of the duct and in the channel at Reτ = 180 and Reτ = 360, and how do they compare to the aspect ratios reported by Lozano-Durán et al. (2012)?

Answer: The aspect ratio of TWA structures in the core of the duct and in the channel is approximately αxy ≃3.1 and αxy ≃2.8 for Reτ = 180 and Reτ = 360, respectively, which are in good agreement with that reported for the same structures by Lozano-Durán et al. (2012) in channel flow at much higher Reynolds number (αxy ≃3).


Question: What are the additional symmetries that appear in the near horizon region of non-extremal black holes when considering time-dependent boundary conditions?

Answer: By considering a more general set of boundary conditions that admit time dependence, the asymptotic isometries in the near horizon region of non-extremal black holes are further enhanced, leading to the appearance of a new set of supertranslations. In four dimensions, this results in an infinite-dimensional algebra of charges that includes the Virasoro algebra.


Question: What is the condition on the nilpotency of the attractor flow generator k that ensures the function u scales correctly as r goes to zero?

Answer: The condition is that k must be nilpotent, with k3 = 0. This ensures that u scales as r2 as r goes to zero, which is necessary for extremal black hole solutions with a near horizon AdS2 × S2 geometry.


Question: How does the non-parametric method using Principal Component Analysis (PCA) help in identifying dark energy evolution, and what are the implications of the results obtained with the addition of BAO data?

Answer: The non-parametric method using PCA helps in identifying dark energy evolution by expressing the dark energy density as a sum of a constant term and an additional term constructed from the non-constant density contribution. This formulation ensures that all parameters have uncorrelated errors, and a non-constant amplitude of these modes would indicate dark energy evolution. The addition of BAO data results in constraints on the non-constant modes that are slightly shifted from zero, with the second principal component not being consistent with zero at 1σ. This suggests a possible deviation in the dark energy equation of state from -1, though it could also be due to unknown systematic effects.


Question: What is the framework U and how does it ensure universal truthfulness in the context of multi-unit auctions?

Answer: Framework U distinguishes two cases: either there is a dominant bidder such that allocating all items to him is a good approximation to the revenue, or there is no such bidder. In the first case, all items are assigned to a bidder. In the second case, a fixed-price auction is performed. In a first phase, bidders are partitioned randomly into three sets. One set is used to gather statistics in phase II, which allows setting a reserve price in the second-price auction of phase III. If the reserve price is not met, the items are sold in the fixed-price auction in phase IV. The mechanism is universally truthful because it ensures that players maximize their utility by reporting their true valuations for any fixed outcome of the random choices made by the mechanism. This is shown to be true for each of the three partitions: STAT, SECOND-PRICE, and FIXED.


Question: How does the conference's acceptance policy affect the acceptance rate, and what role does author self-selection play in this process?

Answer: A strict acceptance policy may lead to a lot of self-selection on the part of the authors, which can result in a higher acceptance rate. This is because authors who believe their papers are of lower quality may choose not to submit, leading to a pool of higher-quality submissions.


Question: What are the advantages of using GEMs over Micromegas and MWPCs in the harsh environment of the detector?

Answer: GEMs may be operated more stable compared to Micromegas and MWPCs in the harsh environment with particle fluxes of the order of MHz/cm². Additionally, the low particle energy requires minimizing the radiation thickness to avoid significant resolution reduction due to multiple scattering, which favors GEMs as it is easier to equip them with a thin readout.


Question: What is the relationship between the velocity dispersion and cloud size in three-dimensional space, and how does it compare to the two-dimensional counterpart?

Answer: The relationship between the velocity dispersion (σv) and cloud size (Rcl) in three-dimensional space is given by σv = (1.19 ± 0.04) km s−1(Rcl/10 pc)0.37±0.02 for Rcl > 1.6 pc. This relation is consistent with its two-dimensional counterpart, apart from the lower normalization due to the fact that Rcl > Re on average.


Question: What are the key methods proposed for estimating the graphon function f in the context of exchangeable networks, and how do they address the identifiability issue?

Answer: Wolfe and Olhede (arXiv:1309.5936) and Choi & Wolfe (2014) proposed estimating f up to a measure-preserving transformation σ via step-function approximations based on fitting the stochastic block model with a larger number of blocks K. This approximation does not assume that the network itself follows the block model, and some theoretical guarantees have been obtained under more general models. Olhede & Wolfe (2014) proposed to approximate the graphon with so-called network histograms, that is, stochastic block models with many blocks of equal size, akin to histogram bins. Another method to compute a network histogram was proposed by Amini & Levina (2017), as an application of their semi-definite programming approach to fitting block models with equal size blocks. Gao et al. (2015) established the minimax error rate for estimating P and proposed a least squares type estimator to achieve this rate, which obtains the estimated probability P by averaging the adjacency matrix elements within a given block partition. A similar estimator was proposed in Choi (2017), applicable also to non-smooth graphons. However, these methods are in principle computationally infeasible since they require an exhaustive enumeration of all possible block partitions. Cai et al. (arXiv:1412.2129) proposed an iterative algorithm to fit a stochastic blockmodel and approximate the graphon, but its error rate is unknown for general graphons.


Question: What are the discrepancies between the SND and BaBar measurements of the e+e−→ωη cross section, and what is the significance of these discrepancies?

Answer: There is a significant discrepancy between the SND and BaBar measurements of the e+e−→ωη cross section, particularly above 1.6 GeV. The SND results have better accuracy and disagree with the BaBar data in this energy range. The SND measurements are the most precise to date, and the discrepancy is evident in Fig. 34(a).


Question: How does the introduction of a thin layer of dark matter affect the black hole shadow in the context of the proposed model?

Answer: The introduction of a thin layer of dark matter surrounding the black hole at a given radial coordinate is used to illustrate that interesting features of the black hole shadow can be understood in a simplified approach. This thin layer, while exaggerated compared to realistic dark matter halos, helps maintain mathematical simplicity and provides a transparent interpretation of the relevant physics content. The main advantage is that the discontinuity introduced by this thin layer simplifies the mathematical treatment and interpretation of the black hole shadow, especially in scenarios where the Maxwell construction cannot be established.


Question: What is the 'constrained parameter goodness-of-fit' test, and how is it used to assess the compatibility of multiple data sets in the context of dark matter models?

Answer: The 'constrained parameter goodness-of-fit' test is an extension of the parameter goodness-of-fit test that quantifies the compatibility of various data sets for a given dark matter particle candidate, assuming the halo function ˜η(vmin) passes through a particular point (v∗, ˜η∗). By calculating the p-values for each (v∗, ˜η∗) throughout the vmin −˜η plane, one can construct plausibility regions, such that for any halo function not entirely contained within the plausibility region, the data are incompatible at the chosen level, e.g., p < 10%.


Question: What are the key observations from the estimated consideration set model regarding the number of unique customer types and the average size of consideration sets?

Answer: The number of unique customer types (i.e., |C|) under the estimated model varies from 36 to 108 across all product categories, indicating sparsity in the number of customer types. The weighted average size of the consideration sets ranges between 1.3 and 2.8 across all product categories, despite some categories having as many as 18-21 products, suggesting that a typical customer considers a relatively small number of products.


Question: What is the mathematical formulation of the equilibrium configurations of the MEMS device described in the paper?

Answer: Equilibrium configurations of the MEMS device are weak solutions u ∈ H2_D(D) to the fourth-order obstacle problem β∂4_xu − (τ + α∥∂xu∥2_L2(D))∂2_xu + ∂I_¯S0(u) ∋ −g(u) in D, where H2_D(D) := {v ∈ H2(D) : v(±L) = ∂xv(±L) = 0}, and ∂I_¯S0(u) denotes the subdifferential in H2_D(D) of the indicator function I_¯S0 of the closed convex subset ¯S0 := {v ∈ H2_D(D) : v ≥ −H in D} of H2_D(D).


Question: How does the presence of a primordial magnetic field (PMF) affect the rates of weak reactions and the cosmic expansion rate during big bang nucleosynthesis (BBN)?

Answer: The presence of a primordial magnetic field (PMF) directly affects the rates of weak reactions and also the cosmic expansion rate through the PMF energy density. The boost of cosmic expansion by the PMF energy density is the dominant effect, while the change in weak reaction rates is subdominant.


Question: What are the specific entries of the matrix B for the type C and type D cases when cℓ+1 = 1 and cℓ+1 = 2, respectively?

Answer: For the type C case when cℓ+1 = 1, the nontrivial entries with index ℓ are Bℓ,ℓ−1 = Bℓ−1,ℓ = t3(s2_1 − s−2_1), and Bℓ,ℓ = −t3(s2_1 − s−2_1)(s1s−1_2 + s−1_1 s2). For the type D case when cℓ+1 = 2, the nonzero entries involving index ℓ are Bℓ,ℓ−2 = Bℓ−2,ℓ = t1t3, and Bℓ,ℓ = −t1t3(s2 + s−1_2).


Question: What conditions lead to the formation of multiple small-scale vortices instead of a single large-scale vortex at the outer edge of the dead zone?

Answer: Multiple small-scale vortices ensue for the case of less coupled dust, while a single large-scale vortex develops if the dust content of the disc is well coupled to the gas.


Question: How is the breakdown flow identified in the data processing steps?

Answer: The breakdown flow is identified by finding the first minute with speed below 40 km/h. The TF intensity in the three-minute interval directly preceding this minute is considered the breakdown flow, unless the data suggests that the queue already started building in the previous minute, in which case the breakdown flow interval is shifted one extra minute back.


Question: How does the assumption in the nonparametric additive model compare to the standard restricted eigenvalue (RE) condition for high-dimensional linear models?

Answer: The nonparametric additive model uses a condition similar to the RE condition, but with modifications due to the use of neural networks for approximating component functions. Specifically, the condition is: ∑_{j∈S} ∥fj − f0,j∥²_n ≲ ∥ˆf − f0∥²_n for all f = ∑_j fj that satisfies ∑_{j∈Sc} ∥fj∥_n ≲ ∑_{j∈S} ∥fj − f0,j∥_n. The key difference is the inclusion of approximation error terms s1ρ²_n,1 + s2ρ²_n,2 and s1λ²_n,1 + s2λ²_n,2 on the right-hand side of the condition.


Question: What is the contribution of sterile neutrinos to the neutrinoless double beta decay amplitude, and how does it affect the half-life of the decay?

Answer: The sterile neutrinos contribute to the neutrinoless double beta decay amplitude through the effective mass parameter mee_S, which is given by the sum of (VνS_ei)^2 * |p|^2 / ˆmSi. The half-life of the decay is inversely proportional to the square of the effective mass (meff), which includes contributions from light neutrinos (mee_ν), sterile neutrinos (mee_S), and heavy RH neutrinos (mee_N). The first (second) generation sterile neutrino saturates the current experimental bounds at ˆmS1 ∼1 (ˆmS2 ∼2−3) GeV, and for larger values of these mass eigenvalues, the predicted half-life increases but asymptotically approaches the horizontal lines as in the case of QD mass hierarchy of light neutrinos when other contributions are neglected.


Question: What is the new location of the sight line after the laser adjustment, and how does it compare to the reference line on the measuring sheet?

Answer: The new location of the sight line was measured to be 105 cm from the reference line on the sheet.


Question: How does the update rule for stochastic gradient descent (SGD) differ from the general update rule for stochastic mirror descent (SMD) in terms of the gradient and potential function?

Answer: In SGD, the update rule is θi = θi−1 − ηi∇fpθi−1, ζi), where the parameter is updated directly by moving in the direction of the negative gradient. In SMD, the update rule is ∇ψ(θi) = ∇ψ(θi−1) − ηi∇fpθi−1, ζi), where the update is performed in the 'mirrored' domain determined by the potential function ψ(·). The gradient ∇ψ(·) defines an invertible map, ensuring a unique θi at each iteration.


Question: What is the definition of the stack Coh^sp_{O, ext}^C(Y) and what are the associated stack functions introduced in this context?

Answer: Coh^sp_{O, ext}^C(Y) is the stack defined by the fiber product Coh^sp_{O, ext}^C(Y) → SP(Y) → Coh^ext_C(Y) → Coh^≤1(Y), where SP(Y) denotes the moduli space of Pandharipande-Thomas stable pairs on Y. The associated stack functions are 1SPC := h Coh^sp_{O, ext}^C(Y) → Coh^≤1(Y) i and 1 f-SPC := h f-SP C(Y) → Coh^≤1(Y) i, where the moduli stack f-SP C(Y) has been introduced in §5.2.


Question: What is the impact of adding random noise with a mean distance of 15 pixels on the quality of synthetic images compared to other methods?

Answer: Adding random noise with a mean distance of 15 pixels yields the highest similarity comparison of the synthetic images to real images, as evaluated using Frechet Distance (FD) based on InceptionV3 and ResNet50. This method is closer to the result based on a single-cell structure than synthetic images generated by polygon-based masks by a factor of 1.76.


Question: What is the impact of quantum particle production effects on the structure of sudden singularities, and how do these effects vary with different regularization procedures?

Answer: The generic sudden singularity is T-weak and K-weak, suggesting that quantum particle production effects are not expected to modify these singularity structures. However, some studies confirm this, while quantum modifications can occur for particular regularization procedures.


Question: What are the key challenges in preparing the perovskite SrCoO3-δ phase, and how were these challenges addressed in the current study?

Answer: The preparation of the perovskite SrCoO3-δ phase has typically required a two-step processing of the brownmillerite SrCoO2.5 phase, which can lead to micro-cracks, grain boundaries, and impurity phases. Additionally, the gas-phase oxidation process required a long annealing time (t ≥ 10 hours) and high oxygen pressure. In this study, these challenges were addressed by using pulsed laser epitaxy (PLE) with a mixed gas of ozone and oxygen, allowing for the direct epitaxy of high-quality SrCoO3-δ thin films without post-growth oxidation.


Question: How does the magnetic field angle affect the frequency and intensity of the most intense mode in the FMR spectra?

Answer: At an applied-field angle of θ = 0°, the most intense mode shows a monotonous increase in frequency as the magnitude of the external field increases, produced by the islands aligned along the signal line (horizontal islands). At θ = 75°, the most intense mode is lowered in frequency and is mostly flat, with ∂f/∂H ≈ 0 in the investigated field range. This behavior is fundamentally different from what is observed at 0°, where the slope of the most intense curve ∂f/∂H monotonically decreases as the field is swept from negative to positive fields until the horizontal islands switch at around +80 mT.


Question: What are the explicit forms of the transformed potential terms Xn and Yn in the context of the Darboux transformation applied to the Dirac equation?

Answer: The transformed potential term Xn is given by Xn(x) = −2 f(x) −m′(x) −V ′(x) / (m(x) −V (x)) + d/dx log[ˆWvn−1(x) / Wvn−1(x)]. The term Yn can be found in (19), and it involves a complex expression with terms related to m(x), V(x), and f(x).


Question: What does the relationship between the amplitude of radial velocity variations and surface gravity suggest about the origin of these variations in K giant stars?

Answer: The amplitude of the radial velocity increases with decreasing surface gravity, suggesting an intrinsic mechanism for these long period radial velocity variations, as it takes longer to decrease the velocity of a moving parcel in lower surface gravity.


Question: What are the limitations of standard particle filters when used for parameter estimation in an augmented state-space?

Answer: Standard particle filters working on an augmented state-space do not necessarily converge in general because the resulting systems are non-ergodic.


Question: What are the conditions under which stable bound sliding states occur for the swimmer near a planar wall, and how do these states relate to the mobility dipole and chemical solute consumption?

Answer: Stable bound sliding states occur for 0 < ∆µ/µ0 < 1, where swimmers stay at a fixed height and orientation relative to the wall. The re-orientation of the mobility dipole (µ1) is proportional to the net consumption or production of the chemical solutes (α0).


Question: How does the proof establish that the harmonic map h has the required residue at the pole, especially when the transverse measure is zero?

Answer: When the transverse measure is zero, we are in the case of a closed center at the pole, and the only parameter to determine is R. The diameter in T of the image of a lift of An under the model map ˜mR,± π/2 is Ln, which is related to the modulus of the annulus by Ln = Rmod(An). Since mod(An) →∞ as n →∞, by Lemma 5.8, diam(ehn( eAn)) / mod(An) = Ln + O(1) / mod(An) → R as n →∞, which specifies R uniquely. Hence, the map h has the required residue at the pole, concluding the proof of (b).


Question: What are the specific results comparing the standard POD method, residual-based adaptive POD, and the two-grid based adaptive POD method for different values of ϵ?

Answer: For ϵ = 0.5, the average errors are 0.193343 for POD, 0.151803 for Residual-APOD with η0 = 5 × 10^-3, 0.001166 for Residual-APOD with η0 = 5 × 10^-4, and 0.001129 for TG-APOD with η0 = 5 × 10^-3. For ϵ = 0.1, the average errors are 0.559466 for POD, 0.167838 for Residual-APOD with η0 = 5 × 10^-3, 0.012444 for Residual-APOD with η0 = 8 × 10^-4, and 0.004524 for TG-APOD with η0 = 5 × 10^-3. For ϵ = 0.05, the average errors are 0.805803 for POD, 0.251224 for Residual-APOD with η0 = 5 × 10^-3, 0.020072 for Residual-APOD with η0 = 1 × 10^-3, and 0.008663 for TG-APOD with η0 = 5 × 10^-3. For ϵ = 0.01, the average errors are 0.771091 for POD, 0.250940 for Residual-APOD with η0 = 2 × 10^-2, 0.051444 for Residual-APOD with η0 = 5 × 10^-3, and 0.010969 for TG-APOD with η0 = 5 × 10^-3.


Question: What conditions must be satisfied for the Hausdorff dimension of the intersection of a transformed set and a self-similar set to be less than the Hausdorff dimension of the original set?

Answer: The conditions are: (1) F and E must satisfy the conditions of Theorem 1.2, (2) there must exist a map φ ∈ Φ with contraction ratio α such that log α / log β is irrational, where β is the uniform contraction ratio of maps in Ψ.


Question: What condition must be satisfied for the divergent term in λ21 to vanish in the case of point interactions of a δ′-type?

Answer: The divergent term in λ21 vanishes if the equation κ1 tan(κ1d1) + κ2 tan(κ2d2) = 0 takes place.


Question: What is the recommended approach for selecting the vector 𝑢 to build 𝑣𝑘+1 in the context of the lemma discussed?

Answer: One should choose the vector 𝑢 in a low-dimensional subspace of K𝑘 such that the sketched projection of 𝐴𝑢 onto K𝑘 also lies in a low-dimensional subspace of K𝑘, and ensure access to bases of these low-dimensional subspaces at each iteration.


Question: What method is used to determine the number of accreted and in-situ globular clusters in M31 based on their orbital orientation?

Answer: The method assumes that all clusters that formed in-situ have retained orbits that are co-rotating with the rotation of M31, and the accreted population consists of an equal number of co-rotating and counter-rotating clusters. The number of in-situ clusters is calculated as A - B, and the number of accreted clusters is 2B, where A is the number of co-rotating clusters and B is the number of counter-rotating clusters.


Question: What are the specific gauge conditions and transformations that are applied to the electromagnetic potential in the far past, and how do they relate to the radiation gauge?

Answer: In the far past, the gauge condition r2γz¯z∇µAµ(z, ¯z, r, −∞) = 0 is applied, which is part of the radiation gauge. This condition leaves a residual v-independent gauge symmetry. The residual gauge transformations are given by 2∂z∂¯zˆε + γz¯z∂r(r2∂rˆε) = 0 = ∂vˆε, allowing local transformations ˆε = ε(z) + ¯ε(¯z) and δεAz = ∂zε for holomorphic ε. These transformations are the electromagnetic analog of the local conformal transformations in the extended BMS group and create zero-momentum 'boundary photons'.


Question: What are the convergence rates established for the regularized solution under the given conditions in the conclusion?

Answer: For β(δ) ∼ δ^(1/2s), the convergence rate is O(√δ) as δ → 0 for the error ‖f† − fδβ(δ),2‖, and O(δ) as δ → 0 for the error ‖g − F(fδβ(δ),2)‖H.


Question: What are the specific material properties used in the most detailed breast model, and how do they compare to the simplified models?

Answer: The most detailed model differentiated the left and right breast properties, with Eright_breast = 0.3 kPa, Eleft_breast = 0.2 kPa, Eskin = 4 kPa, Efascia = 120 kPa, Eligaments = 120 kPa, and Emuscle = 10 kPa. Simplified models, on the other hand, used a single material to model the whole breast behavior, with properties ranging on average from 0.25 to 0.3 kPa.


Question: How does the concept of curvature in submodular functions help in strengthening approximation bounds for submodular optimization problems?

Answer: The curvature of a submodular function measures its deviation from linearity and can be used to strengthen approximation bounds for various submodular optimization problems. This is because the curvature provides a way to quantify how close the function is to being linear, which can be leveraged to derive tighter bounds on the performance of optimization algorithms.


Question: How does the MCTS algorithm in SubgraphX guide the exploration of subgraphs and what are the key variables it uses?

Answer: In SubgraphX, the MCTS algorithm guides subgraph explorations by building a search tree where the root is the input graph and each node corresponds to a connected subgraph. The edges represent node-pruning actions. The MCTS records four key variables for each node and action pair (Ni, aj): C(Ni, aj) for the number of counts, W(Ni, aj) for the total reward, Q(Ni, aj) for the averaged reward, and R(Ni, aj) for the immediate reward, which measures the importance of the subgraph Gj obtained by action aj from Gi.


Question: How does the application of the PMC procedure improve the pQCD prediction for the b quark forward-backward asymmetry A0,bFB?

Answer: The application of the PMC procedure eliminates the renormalization scale uncertainty and greatly improves the convergence of the pQCD series by eliminating renormalon divergences. The PMC-improved result for the bare b quark forward-backward asymmetry is A0,bFB = 0.1004±0.0016, which reduces the tension between the experimental determination and the respective SM fit to 2.1σ.


Question: How do the mean absolute errors for the Correspondence Tracker compare to the Lucas-Kanade Tracker in terms of speed impact?

Answer: For the Correspondence Tracker, the mean absolute errors increase with speed in both the horizontal and vertical coordinates, as shown in the right column plots of Figure 91. In contrast, for the Lucas-Kanade Tracker, mean tracking errors are not much affected by speed, as indicated by the overlapping lines in the left column plots of Figure 87.


Question: How does the pinning strength affect inter-islet synchronization in the network 121212 under different external glucose inputs?

Answer: At a lower pinning strength, network 121212 generates different degrees of inter-islet synchronization for different external glucose inputs, I. The mean glucose concentration, G, is independent of the pinning strength, but glucose fluctuations are highly correlated with inter-islet synchronization.


Question: What conditions must be satisfied for a projective variety X to be projectively equivalent to a scroll over a curve according to Theorem 1.4?

Answer: According to Theorem 1.4, if X satisfies Condition (E1), then for a general point x ∈ X, the subvariety Dx(X) is an (n − 1)-dimensional linear space passing through x. Consequently, X is projectively equivalent to a scroll over a curve.


Question: What is the specific form of z(k) that ensures (err) is nonpositive, and what is the resulting step size limitation?

Answer: The specific form of z(k) that ensures (err) is nonpositive is z(k) := (˜h + 1)/(2˜h + 1) x(k) + ˜h/(2˜h + 1) v(k). The resulting step size limitation is ˜h ≤ √(β + γ) / (√(α + γ) − √(β + γ)).


Question: How does the proof of Proposition 2 demonstrate that the S-polynomial reduces to 0 modulo (MG+)?

Answer: The proof of Proposition 2 shows that for every neighbor-pair mj1, mj2 ∈N such that 1 · mj1 = xℓ· mj2, the S-polynomial (Y (mj1) + τ(mj1)) −xℓ· (Y (mj2) + τ(mj2)) reduces to 0. This is because mj1 ∈N \ LM implies Y (mj1) = 0 and xℓ· Y (mj2) →0, so the result follows immediately from Lemma 9.


Question: What are the specific models and equations used to study the motion of a single nonequilibrium oscillator exposed to a temperature gradient?

Answer: Two models were used: one with a single Nosé-Hoover thermostat variable ζ, described by the equations { ˙q = p ; ˙p = −q −ζp ; ˙ζ = p2 −T(q) }, and another with two control variables, ζ and ξ, described by the equations { ˙q = p ; ˙p = −q −ζp −ξp3 ; ˙ζ = p2 −T(q) ; ˙ξ = p4 −3p2 }. The temperature gradient T(q) is given by T(q) ≡1 + ǫ tanh(q).


Question: How does the mode-coupling theory (MCT) perform in predicting the yield stress for different types of glasses, and what are the limitations?

Answer: For hard sphere glasses, MCT correctly predicts the emergence of solid behavior with entropic origin, with a yield stress and shear modulus proportional to kBT. However, it overestimates the degree of localization of particles near the jamming transition. For soft glasses and metallic glasses, MCT predicts a yield stress proportional to kBT, which is incorrect as solidity is the result of direct interparticle forces, scaling as ǫ/a³. MCT provides limited insight into solid phases, and its predictions become unreliable below a temperature scale Tq, where the static structure is dominated by quenched disorder.


Question: How does the calculation of transmission and reflection coefficients through a magnetic breakdown junction contribute to understanding the Onsager phase of de Haas-van Alphen oscillations?

Answer: The calculation of transmission and reflection coefficients through a magnetic breakdown junction helps determine the Onsager phase of de Haas-van Alphen oscillations. This is achieved by addressing the phase divergence of the S-matrix describing wave function transmission through suitable asymptotic analysis. The amplitude of the wave function is then calculated using approximate and exact models of connected Fermi surfaces, yielding the field-dependent phase offset relevant to de Haas-van Alphen oscillations for Fermi surfaces with magnetic breakdown.


Question: How does the FANCI wavefunction ensure size-consistency in the context of non-interacting subsystems A and B?

Answer: The FANCI wavefunction ensures size-consistency by requiring that the weight function f be multiplicatively separable, i.e., fAB = fAfB, and that the Slater determinants and parameters must be divisible into two disjoint parts, {mA, mB} and {⃗PA, ⃗PB}, respectively. This allows the wavefunction to be written as a product of the subsystem wavefunctions, |ΨAB⟩ = |ΨA⟩|ΨB⟩.


Question: How does the mechanism M = ([0, 1/2], 0) impact the profits of firms A and B when consumers are uniformly distributed?

Answer: Under the mechanism M = ([0, 1/2], 0), the profits for firm A are πA = t/4, and the profits for firm B are πB = v/2 - t/8, which is greater than 7t/8 when v > 2t. Thus, total profits are at least 9t/8.


Question: How is the harmonic extension of a function defined on V0 to Vm+1 related to the energy minimization problem on the Sierpinski Gasket?

Answer: The harmonic extension of a function u defined on V0 to Vm+1, denoted ˆu, is the unique extension that minimizes the energy Em+1 with the relation E0(u) = (5/3)^m Em+1(ˆu).


Question: What new collective mode is observed in the system, and how is it influenced by the lattice diffraction orders?

Answer: A new collective mode is observed, which arises from the coupling between the excitons mediated by the lattice diffraction orders. This mode can be actively tuned via electrical gating.


Question: How does the total islet number affect the fluctuation of glucose regulation and the initial condition dependence of the nonlinear dynamics?

Answer: As the total islet number (N) increases, the fluctuation of glucose regulation decreases (Fig. S7). Additionally, the initial condition dependence of the nonlinear dynamics is largely suppressed in the large N limit.


Question: What are the specific constraints on the signal strength of the Higgs boson in the NMSSM model, and how do they compare to the SM Higgs boson?

Answer: The signal strength of the Higgs boson in the NMSSM model is required to be within the 1σ range measured at the LHC for the most constraining channels. Specifically, the requirements are: 0.81 < RZZ < 1.32, 0.74 < RWW < 1.40, 0 < Rb¯b < 1.10, and 0.27 < Rττ < 1.15. For the diphoton channel, the range is 1.40 < Rγγ < 1.99, which is discussed separately. Here, R is defined as the ratio of the production cross section and branching fraction of the NMSSM Higgs to the SM Higgs.


Question: How does the mean field potential relate to the interaction energy in the context of the nonlinear Fokker-Planck equation?

Answer: The mean field potential Vi is a function of the number of particles in the site, ni, and in equilibrium, it satisfies the relation neq,i ∝ exp{−β[V (neq,i) + Ui]}, where Ui is an external potential. The interaction energy of a configuration of ni particles is given by a function Φ(ni), and the mean field potential is derived from this interaction energy to satisfy Boltzmann statistics in equilibrium.


Question: How does MUSBO address the challenges of distributional shift and out-of-distribution actions in the deployment-constrained setting?

Answer: MUSBO addresses these challenges by sampling fictitious rollouts from the learned model and performing policy updates weighted with an uncertainty regularized coefficient. This coefficient quantifies the amount of uncertainty for each state-action pair within the fictitious rollouts and the data. In areas of low confidence or low data support, MUSBO takes a pessimistic point of view and discounts the update by the uncertainty regularized coefficient when the policy bootstraps into out-of-distribution states and actions regions.


Question: How does the spin-twisting itinerant motion of Bloch electrons influence the quantized cyclotron motion in the absence of an external magnetic field?

Answer: The quantized cyclotron motion occurs even without an external magnetic field due to the existence of Aﬁc arising from the spin-twisting itinerant motion of electrons.


Question: How was the place of residence for each user determined using mobile phone data, and what was the accuracy of this method compared to census data?

Answer: The presumed residence of each user was computed as the most visited Voronoi cell between 08:00PM and 06:00AM during workdays and the entire day on Sundays and holidays. Users had to be regularly detected in this cell (at least five times) and the number of visits at the most frequented cell had to be greater than the number of visits at the second most frequented cell. The final dataset contained 350,685 mobile phone users. The identification of users' place of residence was evaluated using data from the IBGE 2010 census, and a good match was observed with a Pearson correlation coefficient of 0.9.


Question: What evidence suggests that the B1 bubble is interacting with the 20/50 MC, and what are the estimated kinetic parameters of the B1?

Answer: The B1 bubble interacts with the 20/50 MC as these clouds curve around the entire southern part of the shell in the b − v diagrams. The B1 has higher CS(J = 2 −1)/CS(J = 1 −0) line ratios (∼3) than the ambient 20/50 MC by a factor of 2, suggesting low-level emission of B1 is shocked. The kinetic energy of the northern HG-feature, which is part of B1, is estimated to be ∼10^49 erg with an H2 mass of ∼1000 M⊙, and the expansion time of the B1 is ∼3 × 10^5 years with an expansion velocity of 40 km s−1 and a size of 13 pc.


Question: What are the degrees of freedom defined for the function u in the discrete gradgrad complex, and how do they compare to the degrees of freedom for σxx and σxy in the discrete elasticity complex?

Answer: The degrees of freedom for the function u in the discrete gradgrad complex include: 1. The moments of u and its normal derivatives on each edge e, 2. The moments of u and its normal derivatives on each face F, and 3. The moments of u inside the element T. These degrees of freedom are defined for p ∈Qk−4(x), p ∈Qk−4,k−4(y, z), and p ∈Qk−4,k−4,k−4(x, y, z) respectively. In comparison, the degrees of freedom for σxx and σxy in the discrete elasticity complex are defined for different polynomial spaces and involve moments on faces, edges, and inside the element, but with different polynomial degrees and integrals.


Question: How is the integral in Eq. (20) calculated for a theoretically given two-mode state, and what is the role of the Wigner function in this process?

Answer: To decide whether a theoretically given two-mode state ̺AB contains nonzero quantum discord, one first obtains its Wigner function based on the definition, and then calculates the integral in Eq. (20) using the obtained Wigner function. After that, one can easily check whether the integral result Qr is equal to zero or not.


Question: What is the relationship between the axis of the NMO-velocity cylinder and the zero-offset ray in homogeneous anisotropic media?

Answer: The axis of the NMO-velocity cylinder in homogeneous anisotropic media is parallel to the zero-offset ray. This is because the eigenvector e corresponding to the zero eigenvalue of the matrix Uhom is parallel to the group-velocity vector g at the CMP location, which points in the direction of the zero-offset ray.


Question: What are the specific mass ranges for the charged Higgs boson H± that are expected to be discovered if the Scenario 2 interpretation of the ATLAS and CMS excesses is confirmed?

Answer: If the Scenario 2 interpretation of the ATLAS and CMS excesses is confirmed, then one should expect to discover a charged Higgs boson either in the mass range of [220, 320] GeV or in the range of [570, 670] GeV.


Question: What are the maximal dimensions of the filtered simplicial complexes used by the TDABC classifiers for the Moon and Swissroll datasets?

Answer: For the Moon dataset, the maximal dimension q = 3, and for the Swissroll dataset, the maximal dimension q = 6.


Question: How is the energy price dynamically adjusted to reflect the congestion level in the proposed ATDM strategy?

Answer: The energy price is dynamically adjusted using the formula p(k) := c1 d(k) + c2uPEV(k) − c3 ∑_{ℓ=2}^N ∆ℓ(k), where c1, c2, c3 > 0 are scaling parameters tuned by the Highway Operator (HO). The term ∆ℓ(k) represents the increase in travel time in cell ℓ due to congestion, and the price is inversely proportional to the congestion level. The HO also computes an estimated price ˆp(t) for future time intervals, which is broadcast to PEVs to help them make informed decisions.


Question: How is the population on different lattice sites detected, and what is the sequence used for this detection?

Answer: To detect the population on different sites, the short lattice is first ramped up to freeze all tunneling dynamics and preserve the atom population on each lattice site. Then, atoms located on odd sites are transferred non-adiabatically to the third energy level in the system by increasing the energy offset between neighboring sites. Ramping down the short lattice adiabatically preserves the population in the different Bloch bands, which are detected by a following band-mapping sequence.


Question: What are the key properties of the focusing and accelerating fields in the blowout regime, and how do they differ from the linear regime?

Answer: In the blowout regime, the focusing field for a relativistic charged particle traveling at c accelerating in the blowout region is given by W⊥= Er −Bθ = r², where r is the distance to the axis, Er is the radial electric field, and Bθ is the azimuthal magnetic field. This field is always focusing for electrons and leads to transverse harmonic oscillations (betatron oscillations), which are crucial for preserving beam emittance. In contrast, in the linear regime, the focusing fields are non-linear with high-order contributions in powers of r, leading to anharmonic oscillations and higher final bunch emittances. The accelerating field in the blowout regime is given by Eaccel = ξ/2, which determines the maximum energy of a witness electron bunch.


Question: What does the study conclude about the role of fitness cost in reverting antibiotic resistance to susceptibility?

Answer: The study concludes that fitness cost may have a limited role in reverting resistance to susceptibility, as the average population fitness in various stages of gain-loss-re-gain of resistant traits with or without fitness cost incurred is not statistically significant.


Question: What is the formal definition of classical independence in probability theory, and how is it related to conditional probability?

Answer: In a probability space (Ω,F,P), events A ∈ F and B ∈ F are classically independent if P(A ∩ B) = P(A)P(B). If P(B) > 0, this condition can be equivalently expressed as P(A|B) = P(A) using the definition of conditional probability.


Question: What factors are investigated in the study to understand their influence on altcoin prices, and what method is used for this analysis?

Answer: The study investigates the factors influencing altcoin prices from a causal analysis perspective using Bayesian networks. The factors include the nature of interactions between five leading altcoins, traditional financial assets such as gold, oil, and S&P 500, and social media. The causal networks are built from historic price data of these assets, social media data, and price data of altcoins.


Question: What is the key observation that led to the development of probabilistic generating circuits (PGCs) and how do they differ from existing tractable probabilistic models?

Answer: The key observation is that marginal probabilities (including likelihoods) for a probability distribution can be computed by evaluating its generating polynomial in a particular way. PGCs represent probability generating polynomials compactly as directed acyclic graphs, and they are strictly more expressive efficient than decomposable probabilistic circuits (PCs), in particular, sum-product networks, and determinantal point processes (DPPs) while supporting tractable marginal inference.


Question: How does the Map of Hate constructed using task-specific embeddings differ from the one using general-purpose embeddings, and what does this indicate about the effectiveness of domain adaptation?

Answer: When using general-purpose embeddings, the tweets belonging to different classes do not appear distinguishably separated, whereas they appear clustered when using task-specific embeddings. This highlights the impact of performing domain adaptation for textual embedding, as it improves the model's ability to distinguish between different classes of tweets.


Question: How do the performance metrics of the disaggregated and aggregated models compare to Rajs estimator in terms of RRMSE, RAE, RB, RW, and coverage?

Answer: The disaggregated model has an RRMSE of 0.845, RAE of 0.580, RB of 0.448, RW of 2.362, and a coverage of 99.2%. The aggregated model has an RRMSE of 0.987, RAE of 0.780, RB of 0.687, RW of 2.359, and a coverage of 49.4%. Rajs estimator has an RRMSE of 1.018, RAE of 1.018, RB of 0.967, RW of 4.222, and a coverage of 99.0%.


Question: What are the potential QFV final states with significant rates at LHC (14 TeV) due to the large branching ratio of the QFV decay ˜u2 →˜u1h0?

Answer: The potential QFV final states with significant rates at LHC (14 TeV) include pp →˜g˜gX →t + h0 + 3 jets + ET/ + X and pp →˜g˜gX →tt (or ¯t¯t) + h0 + 2 jets + ET/ + X.


Question: How does HierNMF2 compare to other clustering methods in terms of cluster quality on the Reuters, 20Newsgroups (level 2), Cora, and NIPS datasets?

Answer: HierNMF2 is a very competitive method, achieving comparable NMI scores with other state-of-the-art clustering methods on the Reuters, 20Newsgroups (level 2), Cora, and NIPS datasets. The NMI scores for HierNMF2 are generally high and competitive across all datasets, as shown in Figure 4.


Question: How does the inclusion of black holes as seeds of inhomogeneity affect the nucleation rates of true vacuum bubbles, and what is the significance of this for the Higgs vacuum?

Answer: The inclusion of black holes as seeds of inhomogeneity leads to enhanced decay rates, which can significantly increase the probability of vacuum decay, potentially affecting the lifetime of the Higgs vacuum.


Question: What are the future experimental goals for distinguishing between the normal and inverted neutrino mass hierarchies?

Answer: Next-generation long-baseline neutrino experiments have, as one of their goals, the use of matter effects to distinguish between the normal and inverted hierarchies.


Question: How does the number of applicable eigenvectors for network component analysis depend on the measurement time τ?

Answer: The number of applicable eigenvectors from the ordered orthogonal basis of eigenvectors, [ f1, . . . fN ], depends on the measurement time τ. The longer the time of measurements τ, the fewer eigenvectors are needed for network component analysis. Specifically, while observing the network close to an equilibrium state during short time, we detect flows resulting from a large number of transient processes evolving toward the stationary distribution and being characterized by the relaxation times ∝λ−1_k. In contrast, measuring the flows in sufficiently long time τ reveals just n different eigenmodes.


Question: How does changing the initialization scheme affect the rank-preserving quality of batch normalization in VGG19 on the CIFAR-10 dataset?

Answer: Changing the initialization from the standard PyTorch way (Wl,i,j ∼ uniform [−1/√dl, 1/√dl]) to a uniform distribution with the same variance but no mean deduction (Wl,i,j ∼ uniform [0, +2/√dl]) significantly reduces the rank-preserving quality of batch normalization, leading to much slower learning behavior. This is evident in the rank of the last hidden layer, which is much lower for the network with the modified initialization.


Question: What are the specific modules and their functions in the Dynamic Kernel Scheduler (DKS) architecture that support the FFT solver in OPAL?

Answer: The DKS architecture includes CUDA FFT-Poisson, OpenCL FFT-Poisson, and MIC FFT-Poisson modules. These modules handle the FFT solver offloads for OPAL, providing functions for the FFT solver on CUDA, OpenCL, and MIC devices, respectively.


Question: What is the relationship between the moduli space of stable quotients and the Gromov-Witten theory of the Grassmannian?

Answer: The moduli space of stable quotients is proven to carry a canonical 2-term obstruction theory and thus a virtual class. The resulting system of descendent invariants is proven to equal the Gromov-Witten theory of the Grassmannian in all genera.


Question: How does the EPRL-FK ansatz relate the matrix elements of the boost generators to the rotation generators in the context of the simplicity constraints?

Answer: The EPRL-FK ansatz chooses the maximal value for the label of the SL(2, C) irrep, ne = je. This leads to a unique solution for ρe as a function of the spin je: ρe(je) = βe(je + 1). This results in the proportionality coefficient β(ne,ρe)je = βe, leading to the equality ⟨ϕ| ⃗K(L)e | ˜ϕ⟩ = βe ⟨ϕ| ⃗J(L)e | ˜ϕ⟩, which is the (linear) simplicity constraint imposed in the EPRL-FK spinfoam model with Immirzi parameter βe.


Question: What are the results of the fit to the pion mass, pion decay constant, and dilaton mass for the 5 different fermion masses, and how does omitting the highest-mass ensemble affect these results?

Answer: The fit to Eq. (2.13) for the 5 different fermion masses (ami ∈ {0.00125, 0.00222, 0.005, 0.0075, 0.00889}) results in χ2/dof = 11.9/10 and a p-value of 0.29. The parameters obtained are γ* = 0.933(19), log d0 = 1.938(60), d1 = 0.250(26), log d2 = -16.68(94), and d3 = 2.83(31). When the highest-mass ensemble (am = 0.00889) is omitted, the results are χ2/dof = 2.9/7 and a p-value of 0.89, with parameters γ* = 0.936(19), log d0 = 1.931(61), d1 = 0.232(23), log d2 = -16.14(85), and d3 = 3.03(32).


Question: What are the key findings from the computational experiments regarding the trade-off between stability requirements and the maximum number of transplants?

Answer: The computational experiments show that with increasing instance size, the trade-off between stability requirements and the maximum number of transplants decreases. For instances with more than 50 nodes, core allocations impact the reduction of transplants by less than 3%, decreasing to 1% for the largest instance. Additionally, when the objective is to maximize the number of transplants, the 'unstability' of the solutions, measured by the number of weakly blocking cycles, barely depends on the length of the exchanges. Maximizing total weight instead of the number of transplants leads to solutions where patients' preferences matter more.


Question: What was the impact of reordering the sentences to a canonical structure on the predictability of rare words in the newswire domain?

Answer: In the experiment, 11 noncanonical sentences from the VIT treebank taken from the newswire domain were chosen and their syntactic structure was turned into canonical order to check the relevance of the unusual syntactic constructions. BERT was run with both non-canonical and canonical versions to verify the import of syntactic structure.


Question: What are the advantages of using nanoscale LiMn2O4 over its bulk counterpart as a cathode material in Li-ion batteries?

Answer: Nanoscale LiMn2O4 offers shorter Li+-ion path diffusion length due to its decreased particle size and increased surface area, which increases the electrolyte/electrode interface area. This leads to better cathode performance compared to its bulk counterpart.


Question: How does the Born Oppenheimer Approximation (BOA) differ from Space Adiabatic Perturbation Theory (SAPT) in the context of quantum cosmology?

Answer: The Born Oppenheimer Approximation (BOA) is a leading-order approximation where the fast degrees of freedom (electrons) are considered to adiabatically adapt to the slow degrees of freedom (nuclei) without much disturbance. In BOA, the leading order neglects the modifications that the nuclear part of the Hamiltonian has on the eigenstates of the electrons. However, when trying to incorporate backreaction effects beyond the leading order, one faces an infinite set of coupled equations. Space Adiabatic Perturbation Theory (SAPT) provides a systematic perturbative approach to decouple this infinite set of equations. SAPT constructs the projection onto the corresponding subspace, the unitary rotation between the subspace and the undisturbed one, and the effective slow Hamiltonian acting on that subspace, allowing for a more precise treatment of backreaction effects.


Question: What are the specific isomorphism results for graded twistings of function algebras on finite groups discussed in the paper?

Answer: The paper provides isomorphism results for Hopf algebras that are obtained as graded twistings of function algebras on finite groups by cocentral actions of cyclic groups. Specifically, the results cover: (1) O(SLn(Fq)) by Zm, where q is a power of a prime number, m = GCD(n, q −1) is prime and (n, q) ̸∈{(2, 9), (3, 4)}; (2) O(fAn) by Z2, where fAn is the unique Schur cover of the alternating group An, with n ̸= 6; (3) O(fSn) by Z2, where fSn is any of the two Schur covers of the symmetric group Sn, with n ̸= 6.


Question: What is the proof strategy for Theorem 3 when considering the single-labelled transition as an input?

Answer: The proof strategy for Theorem 3 when considering the single-labelled transition as an input involves induction on n. For n > 0, it is shown that there exist p : fii · (⃗L), λ, and P ′ such that P p:fii·(⃗L) −−−−−→ λ P ′, but (P ′, |P ′| × |Q′|, Q′) /∈≈n−1 for all Q′ such that Q q:fii·( ⃗H) =====⇒ σ,σ1,σ′ Q′. Since the LLTS is image-finite, the set of such Q′ is finite. Using the induction hypothesis, for each j ∈ J, P | (M + g(0) · (∗)) | D /•≈ Q′ | (M + g(0) · (∗)) | D. Fresh co-symbols d, c′, and cj (j ∈ J) are introduced, and processes D, M, and N are defined to interact and generate internal reductions. The contradiction is derived by assuming A ≈ B, leading to the conclusion that B′ must be of a specific form, and the inductive hypothesis is then applied to P ′, Qj, and Mj.


Question: What are the typical values of the neutrino mixing angles predicted by the model, and how do they compare with the experimental data?

Answer: The typical values of the neutrino mixing angles predicted by the model are sin2 θ12 ∼ 0.36, sin2 θ13 ∼ 4.8 × 10−6, and sin2 θ23 ∼ 0.48. These values are consistent with the experimental data within the 3σ range: sin2 θ12 = 0.25 ∼ 0.37, sin2 θ13 ≤ 0.056, and sin2 θ23 = 0.36 ∼ 0.67.