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300 | Marcus writes: Although deep learning has advanced the ability of machines to recognize patterns in data, it has three major flaws. The patterns that it learns are, ironically, superficial not conceptual; the results it creates are hard to interpret; and the results are difficult to use in the context of other processes, such as memory and reasoning. As Harvard University computer scientist Les Valiant noted, "The central challenge is to unify the formulation of... learning and reasoning." | Sagan effect | 0.854266 |
301 | Digital genetic sequences may be analyzed using the tools of bioinformatics to attempt to determine its function. | Full gene sequence | 0.854214 |
302 | The Sylow theorems imply that for a prime number p {\displaystyle p} every Sylow p {\displaystyle p} -subgroup is of the same order, p n {\displaystyle p^{n}} . Conversely, if a subgroup has order p n {\displaystyle p^{n}} , then it is a Sylow p {\displaystyle p} -subgroup, and so is conjugate to every other Sylow p {\displaystyle p} -subgroup. Due to the maximality condition, if H {\displaystyle H} is any p {\displaystyle p} -subgroup of G {\displaystyle G} , then H {\displaystyle H} is a subgroup of a p {\displaystyle p} -subgroup of order p n {\displaystyle p^{n}} . A very important consequence of Theorem 2 is that the condition n p = 1 {\displaystyle n_{p}=1} is equivalent to saying that the Sylow p {\displaystyle p} -subgroup of G {\displaystyle G} is a normal subgroup. However, there are groups that have normal subgroups but no normal Sylow subgroups, such as S 4 {\displaystyle S_{4}} . | Sylow theorems | 0.854208 |
303 | As a consequence, determining whether it is possible to solve these problems quickly, called the P versus NP problem, is one of the fundamental unsolved problems in computer science today. While a method for computing the solutions to NP-complete problems quickly remains undiscovered, computer scientists and programmers still frequently encounter NP-complete problems. NP-complete problems are often addressed by using heuristic methods and approximation algorithms. | NP-complete problem | 0.854165 |
304 | The Volta potential (also called Volta potential difference, contact potential difference, outer potential difference, Δψ, or "delta psi") in electrochemistry, is the electrostatic potential difference between two metals (or one metal and one electrolyte) that are in contact and are in thermodynamic equilibrium. Specifically, it is the potential difference between a point close to the surface of the first metal and a point close to the surface of the second metal (or electrolyte).The Volta potential is named after Alessandro Volta. | Volta potential | 0.854113 |
305 | The program provides a platform for experiment selection, recommendation systems, and predictive modelling and is used in biomedicine, bioinformatics, genomic research, and teaching. In science, it is used as a platform for testing new machine learning algorithms and for implementing new techniques in genetics and bioinformatics. In education, it was used for teaching machine learning and data mining methods to students of biology, biomedicine, and informatics. | Orange (software) | 0.854101 |
306 | Thus some bioinformatics pipelines simply cut the end of the sequences at a defined threshold. Some sequencing technologies, like MiSeq, use paired-end sequencing during which sequencing is performed from both directions producing better quality. | Taxonomic resolution | 0.854079 |
307 | Every field of science has its own problems and needs efficient algorithms. Related problems in one field are often studied together. Some example classes are search algorithms, sorting algorithms, merge algorithms, numerical algorithms, graph algorithms, string algorithms, computational geometric algorithms, combinatorial algorithms, medical algorithms, machine learning, cryptography, data compression algorithms and parsing techniques. Fields tend to overlap with each other, and algorithm advances in one field may improve those of other, sometimes completely unrelated, fields. For example, dynamic programming was invented for optimization of resource consumption in industry but is now used in solving a broad range of problems in many fields. | Mathematical algorithm | 0.854051 |
308 | Uniform binary search is an optimization of the classic binary search algorithm invented by Donald Knuth and given in Knuth's The Art of Computer Programming. It uses a lookup table to update a single array index, rather than taking the midpoint of an upper and a lower bound on each iteration; therefore, it is optimized for architectures (such as Knuth's MIX) on which a table lookup is generally faster than an addition and a shift, and many searches will be performed on the same array, or on several arrays of the same length | Uniform binary search | 0.854039 |
309 | Suppose that there are three possible genotypes at some locus, and we refer to these as aa, Aa and AA. The distribution of genotype counts can be put in a 2 × 3 contingency table. For example, consider the following data, in which the genotype frequencies vary linearly in the cases and are constant in the controls: In genetics applications, the weights are selected according to the suspected mode of inheritance. For example, in order to test whether allele a is dominant over allele A, the choice t = (1, 1, 0) is locally optimal. | Cochran–Armitage test for trend | 0.854014 |
310 | Since kinetic energy is entirely a function of an object mass and velocity, the above result may be used with the parallel axis theorem to obtain the kinetic energy associated with simple rolling K rolling = K translation + K rotation {\displaystyle K_{\text{rolling}}=K_{\text{translation}}+K_{\text{rotation}}} | Rolling | 0.853974 |
311 | The general theory of abstract algebra allows an "addition" operation to be any associative and commutative operation on a set. Basic algebraic structures with such an addition operation include commutative monoids and abelian groups. | Addition of natural numbers | 0.853862 |
312 | objective function occurrence octree odd–even sort offline algorithm offset (computer science) omega omicron one-based indexing one-dimensional online algorithm open addressing optimal optimal cost optimal hashing optimal merge optimal mismatch optimal polygon triangulation problem optimal polyphase merge optimal polyphase merge sort optimal solution optimal triangulation problem optimal value optimization problem or oracle set oracle tape oracle Turing machine orders of approximation ordered array ordered binary decision diagram (OBDD) ordered linked list ordered tree order preserving hash order preserving minimal perfect hashing oriented acyclic graph oriented graph oriented tree orthogonal drawing orthogonal lists orthogonally convex rectilinear polygon oscillating merge sort out-branching out-degree overlapping subproblems | List of terms relating to algorithms and data structures | 0.853859 |
313 | In many applications of priority queues such as Dijkstra's algorithm, the minimum priorities form a monotonic sequence, allowing a monotone priority queue to be used. In these applications, for both the lazy and eager variations of the optimized structure, the sequential searches for non-empty buckets cover disjoint ranges of buckets. Because each bucket is in at most one of these ranges, their numbers of steps add to at most C. Therefore, in these applications, the total time for a sequence of n operations is O(n + C), rather than the slower O(nC) time bound that would result without this optimization. | Bucket queue | 0.85383 |
314 | In genetics, the breeding of pea plants allowed Gregor Mendel to derive the basic laws governing inheritance, and examination of chromosomes in maize allowed Barbara McClintock to demonstrate their connection to inherited traits. The plant Arabidopsis thaliana is used in laboratories as a model organism to understand how genes control the growth and development of plant structures. Space stations or space colonies may one day rely on plants for life support. | Human uses of living things | 0.853823 |
315 | Analysis of amplicons has been made possible by the development of amplification methods such as PCR, and increasingly by cheaper and more high-throughput technologies for DNA sequencing or next-generation sequencing, such as ion semiconductor sequencing, popularly referred to as the brand of the developer, Ion Torrent.DNA sequencing technologies such as next-generation sequencing have made it possible to study amplicons in genome biology and genetics, including cancer genetics research, phylogenetic research, and human genetics. For example, using the 16S rRNA gene, which is part of every bacterial and archaeal genome and is highly conserved, bacteria can be taxonomically classified by comparison of the amplicon sequence to known sequences. This works similarly in the fungal domain with the 18S rRNA gene as well as the ITS1 non-coding region.Irrespective of the approach used to amplify the amplicons, some technique must be used to quantitate the amplified product. Generally, these techniques incorporate a capture step and a detection step, although how these steps are incorporated depends on the individual assay. | Amplicon | 0.853812 |
316 | Finally, in the last period (1687-1689), the problem of measuring the probabilities is solved.Before the publication of his Ars Conjectandi, Bernoulli had produced a number of treatises related to probability: Parallelismus ratiocinii logici et algebraici, Basel, 1685. In the Journal des Sçavans 1685 (26.VIII), p. 314 there appear two problems concerning the probability each of two players may have of winning in a game of dice. | Ars Conjectandi | 0.853768 |
317 | Protein methylation is a type of post-translational modification featuring the addition of methyl groups to proteins. It can occur on the nitrogen-containing side-chains of arginine and lysine, but also at the amino- and carboxy-termini of a number of different proteins. In biology, methyltransferases catalyze the methylation process, activated primarily by S-adenosylmethionine. Protein methylation has been most studied in histones, where the transfer of methyl groups from S-adenosyl methionine is catalyzed by histone methyltransferases. Histones that are methylated on certain residues can act epigenetically to repress or activate gene expression. | Protein methylation | 0.853746 |
318 | Actin is used in scientific and technological laboratories as a track for molecular motors such as myosin (either in muscle tissue or outside it) and as a necessary component for cellular functioning. It can also be used as a diagnostic tool, as several of its anomalous variants are related to the appearance of specific pathologies. Nanotechnology. Actin-myosin systems act as molecular motors that permit the transport of vesicles and organelles throughout the cytoplasm. | F actin | 0.853712 |
319 | Although the exact electric potential at which this is set is dependent on the detector geometry, this high-voltage cathode typically produces a drift field of 500 V/cm across the detector.On the side opposite of the cathode plane is a set of anode wire planes set at potentials much higher (less negative) than that of the cathode. Each plane is separated from its neighbors by a small gap, usually on the order of 1 cm. A plane consists of many parallel conducting wires spaced by a few millimeters, and the angle at which the wires are oriented relative to the vertical varies from plane to plane. | Time-projection chamber | 0.853696 |
320 | Chemical synthesis of proteins is a valuable tool in chemical biology as it allows for the introduction of non-natural amino acids as well as residue specific incorporation of "posttranslational modifications" such as phosphorylation, glycosylation, acetylation, and even ubiquitination. These capabilities are valuable for chemical biologists as non-natural amino acids can be used to probe and alter the functionality of proteins, while post translational modifications are widely known to regulate the structure and activity of proteins. Although strictly biological techniques have been developed to achieve these ends, the chemical synthesis of peptides often has a lower technical and practical barrier to obtaining small amounts of the desired protein. In order to make protein-sized polypeptide chains via the small peptide fragments made by synthesis, chemical biologists use the process of native chemical ligation. | Chemical Biology | 0.853684 |
321 | Theorem:: 14, 15 Up to isomorphism, there are exactly three 2-dimensional unital algebras over the reals: the ordinary complex numbers, the split-complex numbers, and the dual numbers. In particular, every 2-dimensional unital algebra over the reals is associative and commutative. Proof: Since the algebra is 2-dimensional, we can pick a basis {1, u}. Since the algebra is closed under squaring, the non-real basis element u squares to a linear combination of 1 and u: u 2 = a 0 + a 1 u {\displaystyle u^{2}=a_{0}+a_{1}u} for some real numbers a0 and a1. | Hypercomplex number | 0.8536 |
322 | Norsteroids (nor-, L. norma, from "normal" in chemistry, indicating carbon removal) are a structural class of steroids that have had an atom or atoms (typically carbon) removed, biosynthetically or synthetically, from positions of branching off of rings or side chains (e.g., removal of methyl groups), or from within rings of the steroid ring system. For instance, 19-norsteroids (e.g., 19-norprogesterone) constitute an important class of natural and synthetic steroids derived by removal of the methyl group of the natural product progesterone; the equivalent change between testosterone and 19-nortestosterone (nandrolone) is illustrated below. | Norsteroid | 0.85358 |
323 | The water in Earth's atmosphere absorbs so strongly in this range that it renders the atmosphere in effect opaque. However, there are certain wavelength ranges ("windows") within the opaque range that allow partial transmission, and can be used for astronomy. The wavelength range from approximately 200 μm up to a few mm is often referred to as Submillimetre astronomy, reserving far infrared for wavelengths below 200 μm. | EM band | 0.853552 |
324 | The E matrix for the Ratio and Algebra hierarchy is shown below. If the cognitive model is true, then 58 unique item response patterns should be produced by examinees who write these cognitively-based items. A row of 0s is usually added to the E matrix which represents an examinee who has not mastered any attributes. To summarize, if the attribute pattern of the examinee contains the attributes required by the item, then the examinee is expected to answer the item correctly. However, if the examinee's attribute pattern is missing one or more of the cognitive attributes required by the item, the examinee is not expected to answer the item correctly. | Attribute hierarchy method | 0.853542 |
325 | During the lessons Four Team Selection Tests are held which are considered the four parts of the Selection Competition under 15.5 and are called Euclides. All the student have the same test. In each of the competition 5 students are eliminated. So after the 4th competition the six member of national team for Junior BMO and the four runners-up are selected. In every competition or test there are four problem usually covering geometry, number theory, algebra, and combinatorics (elementary level) and last four hours each. | Cyprus Mathematical Society | 0.853527 |
326 | The AMC 10 and AMC 12 are 25 question, 75-minute multiple choice competitions in secondary school mathematics containing problems which can be understood and solved with pre-calculus concepts. Calculators have not been allowed on the AMC 10/12 since 2008.High scores on the AMC 10 or 12 can qualify the participant for the American Invitational Mathematics Examination (AIME). On the AMC 10, the top 2.5% make it, typically around 100 to 115 points. On the AMC 12, the top 5% make it, typically around 85 to 95 points. | American Mathematics Competitions | 0.853524 |
327 | This includes further education about microbial, molecular and cell biology. Classes can include cell biology, virology, microbial and plant biology | Environmental engineering science | 0.853466 |
328 | Bressler's research program in skeletal muscle biophysics received support from the Medical Research Council of Canada and the Canadian Institutes for Health Research for 29 years. His research focuses on providing new information about the fundamental mechanisms for force production in skeletal muscle. Experiments are designed to test some fundamental assumptions of the cross-bridge model as well as the role of the protein troponin C (TnC) in the regulation of calcium sensitivity in striated muscle. Part of the research is designed to explore how the level of activation of skeletal muscle is controlled by the calcium binding properties of troponin C – the protein responsible for the initiation of muscle contraction. | Bernard H. Bressler | 0.853465 |
329 | Application: The 2-points–2-tangents property can be used for the construction of the tangent of a parabola at point P 2 {\displaystyle P_{2}} , if P 1 , P 2 {\displaystyle P_{1},P_{2}} and the tangent at P 1 {\displaystyle P_{1}} are given. Remark 1: The 2-points–2-tangents property of a parabola is an affine version of the 3-point degeneration of Pascal's theorem. Remark 2: The 2-points–2-tangents property should not be confused with the following property of a parabola, which also deals with 2 points and 2 tangents, but is not related to Pascal's theorem. | Parabola | 0.853447 |
330 | Using various modifiers, the activity of the enzyme can be regulated, enabling control of the biochemistry of the cell as a whole. The structure of proteins is traditionally described in a hierarchy of four levels. The primary structure of a protein consists of its linear sequence of amino acids; for instance, "alanine-glycine-tryptophan-serine-glutamate-asparagine-glycine-lysine-...". | Biochemical analysis | 0.853418 |
331 | As computing power has grown exponentially this approach to research, often referred to as in silico (as opposed to in vitro and in vivo), has amassed more attention, especially in the area of bioinformatics. More specifically, within bioinformatics, is the study of proteins or proteomics, which is the elucidation of their unknown structures and folding patterns. The general approach in the elucidation of protein structure has been to first purify a protein, crystallize it and then send X-rays through such a purified protein crystal to observe how these x-rays diffract into specific pattern—a process referred to as X-ray crystallography. However, many proteins, especially those embedded in cellular membranes, are nearly impossible to crystallize due to their hydrophobic nature. Although other techniques exists, such as ramachandran plotting and mass spectrometry, these alone generally do not lead to the full elucidation of protein structure or folding mechanisms. | Dry lab | 0.853399 |
332 | Comment: For any real symmetric matrix A, the eigendecomposition always exists and can be written as A = V D V T {\displaystyle A=VDV^{\mathsf {T}}} , where both D and V are real-valued. Comment: The eigendecomposition is useful for understanding the solution of a system of linear ordinary differential equations or linear difference equations. For example, the difference equation x t + 1 = A x t {\displaystyle x_{t+1}=Ax_{t}} starting from the initial condition x 0 = c {\displaystyle x_{0}=c} is solved by x t = A t c {\displaystyle x_{t}=A^{t}c} , which is equivalent to x t = V D t V − 1 c {\displaystyle x_{t}=VD^{t}V^{-1}c} , where V and D are the matrices formed from the eigenvectors and eigenvalues of A. Since D is diagonal, raising it to power D t {\displaystyle D^{t}} , just involves raising each element on the diagonal to the power t. This is much easier to do and understand than raising A to power t, since A is usually not diagonal. | Matrix factorization | 0.853357 |
333 | Chlamydomonas is used as a model organism for research on fundamental questions in cell and molecular biology such as: How do cells move? How do cells respond to light? How do cells recognize one another? How do cells generate regular, repeatable flagellar waveforms? | Chlamydomonas reinhardtii | 0.85335 |
334 | A ring is an algebraic structure with two operations, addition and multiplication, which are denoted as the usual operations on numbers. Under addition, a ring is an abelian group, which means that addition is commutative and associative; it has an identity, called the additive identity, and denoted 0; and every element x has an inverse, called its additive inverse and denoted −x. Because of commutativity, the concepts of left and right inverses are meaningless since they do not differ from inverses. Under multiplication, a ring is a monoid; this means that multiplication is associative and has an identity called the multiplicative identity and denoted 1. | I-semigroup | 0.85333 |
335 | Nevertheless, the set { 1 , i , j , k , − 1 , − i , − j , − k } {\displaystyle \{1,\,i,\,j,\,k,\,-\!1,\,-\!i,\,-\!j,\,-\!k\}} is closed under multiplication. It satisfies all the properties of an abstract group except the associativity property; being finite, it is a Latin square or quasigroup, a peripheral mathematical structure. Loss of the associativity property of multiplication as found in quasigroup theory is not consistent with linear algebra since all linear transformations compose in an associative manner. | Hyperbolic quaternion | 0.85331 |
336 | Finally, the inverse of a / b {\displaystyle a/b} is b / a {\displaystyle b/a} , therefore the axiom of the inverse element is satisfied. The rational numbers (including zero) also form a group under addition. Intertwining addition and multiplication operations yields more complicated structures called rings and – if division by other than zero is possible, such as in Q {\displaystyle \mathbb {Q} } – fields, which occupy a central position in abstract algebra. Group theoretic arguments therefore underlie parts of the theory of those entities. | Group axioms | 0.85328 |
337 | Lagrange's theorem states that for a finite group G and a subgroup H, = | G | | H | {\displaystyle ={|G| \over |H|}} where |G| and |H| denote the orders of G and H, respectively. In particular, the order of every subgroup of G (and the order of every element of G) must be a divisor of |G|.Right cosets are defined analogously: Ha = {ha: h in H}. They are also the equivalence classes for a suitable equivalence relation and their number is equal to . | Proper subgroup | 0.853266 |
338 | Classifier performance depends greatly on the characteristics of the data to be classified. There is no single classifier that works best on all given problems (a phenomenon that may be explained by the no-free-lunch theorem). Various empirical tests have been performed to compare classifier performance and to find the characteristics of data that determine classifier performance. Determining a suitable classifier for a given problem is however still more an art than a science. | Statistical classifier | 0.85324 |
339 | If the number of glass and batch components is not equal, if it is impossible to exactly obtain the desired glass composition using the selected batch ingredients, or if the matrix equation is not soluble for other reasons (i.e., the rows/columns are linearly dependent), the batch composition must be determined by optimization techniques. | Batch mixing | 0.853233 |
340 | In this equation, P is the (negative of the) field induced in the material when the "fixed" charges, the dipoles, shift in response to the total underlying field E, whereas D is the field due to the remaining charges, known as "free" charges.In general, P varies as a function of E depending on the medium, as described later in the article. In many problems, it is more convenient to work with D and the free charges than with E and the total charge.Therefore, a polarized medium, by way of Green's Theorem can be split into four components. The bound volumetric charge density: ρ b = − ∇ ⋅ P {\displaystyle \rho _{b}=-\nabla \cdot \mathbf {P} } The bound surface charge density: σ b = n ^ out ⋅ P {\displaystyle \sigma _{b}=\mathbf {\hat {n}} _{\text{out}}\cdot \mathbf {P} } The free volumetric charge density: ρ f = ∇ ⋅ D {\displaystyle \rho _{f}=\nabla \cdot \mathbf {D} } The free surface charge density: σ f = n ^ out ⋅ D {\displaystyle \sigma _{f}=\mathbf {\hat {n}} _{\text{out}}\cdot \mathbf {D} } | Bound charge | 0.853193 |
341 | 2002 – First virus produced 'from scratch', an artificial polio virus that paralyzes and kills mice. 2007 – Commercialization of Illumina Next generation Sequencing tools. This has become the most popular high-throughput sequencing system. 2012 – Use of CRISPR-Cas9 as a DNA-editing biotechnology tool. | Timeline of biology and organic chemistry | 0.853191 |
342 | A key question in molecular biology is how proteins evolve, i.e. how can mutations (or rather changes in amino acid sequence) lead to new structures and functions? Most amino acids in a protein can be changed without disrupting activity or function, as can be seen from numerous homologous proteins across species (as collected in specialized databases for protein families, e.g. PFAM). In order to prevent dramatic consequences of mutations, a gene may be duplicated before it can mutate freely. | Structural proteins | 0.853189 |
343 | In abstract algebra, a branch of mathematics, a monoid is a set equipped with an associative binary operation and an identity element. For example, the nonnegative integers with addition form a monoid, the identity element being 0. Monoids are semigroups with identity. Such algebraic structures occur in several branches of mathematics. | Monoid | 0.853186 |
344 | In vascular plant biology, electro-osmosis is also used as an alternative or supplemental explanation for the movement of polar liquids via the phloem that differs from the cohesion-tension theory supplied in the mass flow hypothesis and others, such as cytoplasmic streaming. Companion cells are involved in the "cyclic" withdrawal of ions (K+) from sieve tubes, and their secretion parallel to their position of withdrawal between sieve plates, resulting in polarisation of sieve plate elements alongside potential difference in pressure, and results in polar water molecules and other solutes present moved upward through the phloem.In 2003, St Petersburg University graduates applied direct electric current to 10 mm segments of mesocotyls of maize seedlings alongside one-year linden shoots; electrolyte solutions present in the tissues moved toward the cathode that was in place, suggesting that electro-osmosis might play a role in solution transport through conductive plant tissues. | Electro-osmosis | 0.853164 |
345 | These endosymbiotic cyanobacteria in eukaryotes then evolved and differentiated into specialized organelles such as chloroplasts, chromoplasts, etioplasts, and leucoplasts, collectively known as plastids. Cyanobacteria are the first organisms known to have produced oxygen. By producing and releasing oxygen as a byproduct of photosynthesis, cyanobacteria are thought to have converted the early oxygen-poor, reducing atmosphere into an oxidizing one, causing the Great Oxidation Event and the "rusting of the Earth", which dramatically changed the composition of life forms on Earth.The cyanobacteria Synechocystis and Cyanothece are important model organisms with potential applications in biotechnology for bioethanol production, food colorings, as a source of human and animal food, dietary supplements and raw materials. Cyanobacteria produce a range of toxins known as cyanotoxins that can pose a danger to humans and animals. | Blue-green bacteria | 0.853122 |
346 | If N ◃ G {\displaystyle N\triangleleft G} is a non-trivial normal subgroup of G {\displaystyle G} then I ∩ N ≠ { 1 } . {\displaystyle I\cap N\neq \left\{1\right\}.} Remark: The concept of an absolute presentation has been fruitful in fields such as algebraically closed groups and the Grigorchuk topology. In the literature, in a context where absolute presentations are being discussed, a presentation (in the usual sense of the word) is sometimes referred to as a relative presentation, which is an instance of a retronym. | Absolute presentation of a group | 0.853116 |
347 | Naegleria gruberi, freshwater non-pathogenic amoeboflagellate sometimes used in eukaryotic cell biology experiments. Emiliania huxleyi, unicellular marine coccolithophore alga, extensively studied as a model phytoplankton species. Thalassiosira pseudonana, unicellular marine diatom alga, extensively studied as a model marine diatom since its genome was published in 2004. | List of model organisms | 0.853109 |
348 | A polynomial equation, also called an algebraic equation, is an equation of the form For example, is a polynomial equation. When considering equations, the indeterminates (variables) of polynomials are also called unknowns, and the solutions are the possible values of the unknowns for which the equality is true (in general more than one solution may exist). A polynomial equation stands in contrast to a polynomial identity like (x + y)(x − y) = x2 − y2, where both expressions represent the same polynomial in different forms, and as a consequence any evaluation of both members gives a valid equality. In elementary algebra, methods such as the quadratic formula are taught for solving all first degree and second degree polynomial equations in one variable. | Polynomial curve | 0.853094 |
349 | These are plane algebraic curves. A point of the plane lies on an algebraic curve if its coordinates satisfy a given polynomial equation. | Computational algebraic geometry | 0.853035 |
350 | In mathematics, a constant term (sometimes referred to as a free term) is a term in an algebraic expression that does not contain any variables and therefore is constant. For example, in the quadratic polynomial x 2 + 2 x + 3 , {\displaystyle x^{2}+2x+3,\ } the 3 is a constant term.After like terms are combined, an algebraic expression will have at most one constant term. Thus, it is common to speak of the quadratic polynomial a x 2 + b x + c , {\displaystyle ax^{2}+bx+c,\ } where x {\displaystyle x} is the variable, as having a constant term of c . {\displaystyle c.} | Constant term | 0.853014 |
351 | Proof: can be done (like the properties above) for the unit parabola y = x 2 {\displaystyle y=x^{2}} . Application: This property can be used to determine the direction of the axis of a parabola, if two points and their tangents are given. An alternative way is to determine the midpoints of two parallel chords, see section on parallel chords. Remark: This property is an affine version of the theorem of two perspective triangles of a non-degenerate conic. | Parabolic curve | 0.853014 |
352 | and Alan Eustace 2003 (for 1993): Space Efficient Conservative Garbage Collection, Hans Boehm 2002 (for 1992): Lazy Code Motion, Jens Knoop, Oliver Rüthing, Bernhard Steffen 2001 (for 1991): A data locality optimizing algorithm, Michael E. Wolf and Monica S. Lam 2000 (for 1990): Profile guided code positioning, Karl Pettis and Robert C. Hansen | Programming Languages Software Award | 0.852986 |
353 | A corresponding optimization can be applied in applications where a bucket queue is used to find elements of maximum priority, but in this case it should maintain an index that upper-bounds the maximum priority, and the sequential search for a non-empty bucket should proceed downwards from this upper bound.Another optimization (already given by Dial 1969) can be used to save space when the priorities are monotonic and, throughout the course of an algorithm, always fall within a range of r values rather than extending over the whole range from 0 to C. In this case, one can index the array by the priorities modulo r rather than by their actual values. The search for the minimum priority element should always begin at the previous minimum, to avoid priorities that are higher than the minimum but have lower moduli. In particular, this idea can be applied in Dijkstra's algorithm on graphs whose edge lengths are integers in the range from 1 to r.Because creating a new bucket queue involves initializing an array of empty buckets, this initialization step takes time proportional to the number of priorities. A variation of the bucket queue described by Donald B. Johnson in 1981 instead stores only the non-empty buckets in a linked list, sorted by their priorities, and uses an auxiliary search tree to quickly find the position in this linked list for any new buckets. It takes time O(log log C) to initialize this variant structure, constant time to find an element with minimum or maximum priority, and time O(log log D) to insert or delete an element, where D is the difference between the nearest smaller and larger priorities to the priority of the inserted or deleted element. | Bucket queue | 0.852981 |
354 | Output: same as TDX but supplied to only a control transformer or another CDX.Torque receiver (TR) Input: Electrical angle position data from TX or TDX supplied to stator. Output: Rotor assumes position determined by electrical input supplied.Torque differential receiver (TDR) Input: electrical data supplied from two TX's, two TDX's or from one TX and one TDX (one connected to the rotor and one connected to the stator). Output: rotor assumes position equal to the algebraic sum or difference of two angular inputs.Control transformer (CT) Input: electrical data from CX or CDX applied to stator. | Synchro | 0.852979 |
355 | Next-generation sequencing technology is performed resulting in about 100 bp single-end reads. Raw sequence data are filtered and aligned to a reference genome using usually Burrows–Wheeler alignment tool (BWA) or Bowtie 2. The next step is to identify SNPs from aligned tags and score all discovered SNPs for various coverage, depth and genotypic statistics. | Genotyping by sequencing | 0.852948 |
356 | This provides a partial converse to Lagrange's theorem giving information about how many subgroups of a given order are contained in G. | Finite group | 0.852937 |
357 | Genomic rearrangements Molecular phylogenetics Metagenomics Next generation sequence data analysis Epigenomics Barcoding of species Population genetics Horizontal gene transfer Sero/genotyping of viruses Allergenicity prediction SNP discovery Recombination detection Viral Classification Archaea Taxonomic Identification | Alignment-free sequence analysis | 0.852922 |
358 | In very complex problems such as scheduling there is no known way to get to a final answer, so we resort to searching for it trying to find a "good" answer. Scheduling problems most often use heuristic algorithms to search for the optimal solution. Heuristic search methods suffer as the inputs become more complex and varied. This type of problem is known in computer science as an NP-Hard problem. | Genetic algorithm scheduling | 0.852873 |
359 | (F1) Electric Fields, Royal Institute of Technology, Sweden (F2) Magnetic Fields, Applied Physics Laboratory/Johns Hopkins University, United States (F3C) Cold Plasma, National Research Council of Canada, Canada (F3H) Particles; Hot Plasma, Swedish Institute of Space Physics, Kiruna, Sweden (F4) Waves, Swedish Institute of Space Physics, Uppsala, Sweden (F5) Auroral Imager, University of Calgary, Canada (F6) Electron Beam, Max-Planck Institute, Germany (F7) Particle Correlator, Max-Planck Institute, Germany | Freja (satellite) | 0.852854 |
360 | Inequality relationships similar to those defined above can also be defined for column vectors. If we let the vectors x , y ∈ R n {\displaystyle x,y\in \mathbb {R} ^{n}} (meaning that x = ( x 1 , x 2 , … , x n ) T {\displaystyle x=(x_{1},x_{2},\ldots ,x_{n})^{\mathsf {T}}} and y = ( y 1 , y 2 , … , y n ) T {\displaystyle y=(y_{1},y_{2},\ldots ,y_{n})^{\mathsf {T}}} , where x i {\displaystyle x_{i}} and y i {\displaystyle y_{i}} are real numbers for i = 1 , … , n {\displaystyle i=1,\ldots ,n} ), we can define the following relationships: x = y {\displaystyle x=y} , if x i = y i {\displaystyle x_{i}=y_{i}} for i = 1 , … , n {\displaystyle i=1,\ldots ,n} . x < y {\displaystyle x y {\displaystyle x>y} , x ≥ y {\displaystyle x\geq y} , and x ≧ y {\displaystyle x\geqq y} . This notation is consistent with that used by Matthias Ehrgott in Multicriteria Optimization (see References). | Algebraic inequality | 0.852847 |
361 | The minimal counterexample method has been much used in the classification of finite simple groups. The Feit–Thompson theorem, that finite simple groups that are not cyclic groups have even order, was based on the hypothesis of some, and therefore some minimal, simple group G of odd order. Every proper subgroup of G can be assumed a solvable group, meaning that much theory of such subgroups could be applied. Euclid's proof of the fundamental theorem of arithmetic is a simple proof which uses a minimal counterexample. == References == | Minimal counterexample | 0.852767 |
362 | The agent learns to choose responses that are classified as "good".Transfer learning is when the knowledge gained from one problem is applied to a new problem. Deep learning uses artificial neural networks for all of these types of learning. Computational learning theory can assess learners by computational complexity, by sample complexity (how much data is required), or by other notions of optimization. | Artificial Intelligence | 0.852743 |
363 | Paper 1: Pure Mathematics Paper 2: Content on Paper 1 plus Mechanics Paper 3: Content on Paper 1 plus Statistics | Advanced level mathematics | 0.852726 |
364 | The term best-case performance is used in computer science to describe an algorithm's behavior under optimal conditions. For example, the best case for a simple linear search on a list occurs when the desired element is the first element of the list. Development and choice of algorithms is rarely based on best-case performance: most academic and commercial enterprises are more interested in improving Average-case complexity and worst-case performance. Algorithms may also be trivially modified to have good best-case running time by hard-coding solutions to a finite set of inputs, making the measure almost meaningless. | Average case analysis | 0.852714 |
365 | In the other direction, there may exist many homomorphisms from a Boolean algebra B to 2. Any such homomorphism partitions B into those elements mapped to 1 and those to 0. | Boolean algebras canonically defined | 0.852702 |
366 | By Planck's law, as the temperature decreases, the peak of the black-body radiation curve moves to longer wavelengths, i.e. from the blue to the yellow. However, the blue light from a gas burner's premixed flame is primarily a product of molecular emission (Swan bands) rather than black-body radiation. Other factors, particularly the fuel chemistry and its propensity for forming soot, have an influence on luminosity. | Luminous flame | 0.852652 |
367 | Tasks tend to require analysis and more complex reasoning about quantities and data; statistics and chance; spatial relationships; and change, proportions and formulas. Tasks at this level may also require understanding arguments or communicating well-reasoned explanations for answers or choices.Level 5 – 376 – 500 Tasks at this level require the respondent to understand complex representations and abstract and formal mathematical and statistical ideas, possibly embedded in complex texts. Respondents may have to integrate multiple types of mathematical information where considerable translation or interpretation is required; draw inferences; develop or work with mathematical arguments or models; and justify, evaluate and critically reflect upon solutions or choices. | Programme for the International Assessment of Adult Competencies | 0.852625 |
368 | A4 is the smallest group demonstrating that the converse of Lagrange's theorem is not true in general: given a finite group G and a divisor d of |G|, there does not necessarily exist a subgroup of G with order d: the group G = A4, of order 12, has no subgroup of order 6. A subgroup of three elements (generated by a cyclic rotation of three objects) with any distinct nontrivial element generates the whole group. For all n > 4, An has no nontrivial (that is, proper) normal subgroups. Thus, An is a simple group for all n > 4. A5 is the smallest non-solvable group. | Alternating groups | 0.852611 |
369 | A very simple example of a useful variable change can be seen in the problem of finding the roots of the sixth-degree polynomial: x 6 − 9 x 3 + 8 = 0. {\displaystyle x^{6}-9x^{3}+8=0.} Sixth-degree polynomial equations are generally impossible to solve in terms of radicals (see Abel–Ruffini theorem). | Change of variables | 0.852606 |
370 | In other words, for each pair of points x and y, this expression calculates the energy related to the fact that the charge at x is attracted to or repelled from the charge at y. The factor of 1⁄2 corrects for double-counting the pairs of points. In quantum mechanics, it is also possible to calculate a charge density ρ, which is a function of x ∈ ℝ3. More specifically, ρ is defined as the expectation value of charge density at each point. | Lieb–Oxford inequality | 0.852554 |
371 | A variable-frequency drive (VFD, or adjustable-frequency drives, adjustable-speed drives), variable-speed drives, AC drives, micro drives, inverter drives, or drives) is a type of AC motor drive (system incorporating a motor) that controls speed and torque by varying the frequency of the input electricity. Depending on its topology, it controls the associated voltage or current variation.VFDs are used in applications ranging from small appliances to large compressors. Systems using VFDs can be more efficient than hydraulic systems, such as in systems with pumps and damper control for fans.Since the 1980s, power electronics technology has reduced VFD cost and size and has improved performance through advances in semiconductor switching devices, drive topologies, simulation and control techniques, and control hardware and software. VFDs include low- and medium-voltage AC-AC and DC-AC topologies. | Regenerative variable-frequency drives | 0.852547 |
372 | In contrast with protein studies, where a primary protein structure is unambiguously defined by the sequence of nucleotides (the genetic code), the glycobiology still cannot explain how a certain "message" is encoded using carbohydrates or how it is "read" and "translated" by other biological entities. An interdisciplinary effort, combining chemistry, biology, and biochemistry, studies glycan-protein interactions to see how different sequences of carbohydrates initiate different cellular responses. | Glycan-protein interactions | 0.852524 |
373 | (b) The size of the merged department of Neurosciences, Physiology and Pharmacology means less interaction between staff, and less collegiate spirit. (c) The changes created two extra levels of administration, so that now five levels existed between academics and the provost. Staff were told at the time that the new organisation would be rolled out to other Faculties across UCL, though this has not happened. | Department of Pharmacology, University College London | 0.852518 |
374 | Some additional order structures that are often specified via algebraic operations and defining identities are Heyting algebras and Boolean algebras,which both introduce a new operation ~ called negation. Both structures play a role in mathematical logic and especially Boolean algebras have major applications in computer science. | Order theory | 0.852508 |
375 | Organic Chemistry and Inorganic Chemistry questions in the theory are important for choosing the representatives. In the experiment, students solve one Organic Chemistry experiment and one Quantitative Chemistry experiment. Four students who got a high score represents South Korea in IChO. If all the four representatives are the same gender, the student who got a highest score between the other gender who ranked eighth or higher becomes the representative instead of the fourth student. | Korean Chemistry Olympiad | 0.852495 |
376 | The annual AP Chemistry examination, which is typically administered in May, is divided into two major sections (multiple-choice questions and free response essays). | AP Chemistry | 0.852487 |
377 | In general, in the presence of both a charge density ρ(r, t) and current density J(r, t), there will be both an electric and a magnetic field, and both will vary in time. They are determined by Maxwell's equations, a set of differential equations which directly relate E and B to ρ and J.Alternatively, one can describe the system in terms of its scalar and vector potentials V and A. A set of integral equations known as retarded potentials allow one to calculate V and A from ρ and J, and from there the electric and magnetic fields are determined via the relations E = − ∇ V − ∂ A ∂ t {\displaystyle \mathbf {E} =-{\boldsymbol {\nabla }}V-{\frac {\partial \mathbf {A} }{\partial t}}} B = ∇ × A . {\displaystyle \mathbf {B} ={\boldsymbol {\nabla }}\times \mathbf {A} .} At the end of the 19th century, the electromagnetic field was understood as a collection of two vector fields in space. Nowadays, one recognizes this as a single antisymmetric 2nd-rank tensor field in spacetime. | Classical field | 0.852485 |
378 | With the development of these three techniques, the field of structural biology expanded and also became a branch of molecular biology, biochemistry, and biophysics concerned with the molecular structure of biological macromolecules (especially proteins, made up of amino acids, RNA or DNA, made up of nucleotides, and membranes, made up of lipids), how they acquire the structures they have, and how alterations in their structures affect their function. This subject is of great interest to biologists because macromolecules carry out most of the functions of cells, and it is only by coiling into specific three-dimensional shapes that they are able to perform these functions. This architecture, the "tertiary structure" of molecules, depends in a complicated way on each molecule's basic composition, or "primary structure." | Structural biologist | 0.852465 |
379 | For detailed discussions of some solution methods see: Tschirnhaus transformation (general method, not guaranteed to succeed); Bezout method (general method, not guaranteed to succeed); Ferrari method (solutions for degree 4); Euler method (solutions for degree 4); Lagrange method (solutions for degree 4); Descartes method (solutions for degree 2 or 4);A quartic equation a x 4 + b x 3 + c x 2 + d x + e = 0 {\displaystyle ax^{4}+bx^{3}+cx^{2}+dx+e=0} with a ≠ 0 {\displaystyle a\neq 0} may be reduced to a quadratic equation by a change of variable provided it is either biquadratic (b = d = 0) or quasi-palindromic (e = a, d = b). Some cubic and quartic equations can be solved using trigonometry or hyperbolic functions. | Polynomial equation | 0.852459 |
380 | By exposing specific states to energizing collisions, new structures can be established and tracked through different conformational changes. Changes in conformation during the gas-phase data can then be mapped back to the original populations of structures. In this way, researchers can understand the possible pathways between structures.Understanding how protein folding occurs in three-dimensional molecules is one of biology's enduring problems. | David E. Clemmer | 0.852458 |
381 | The SAT Subject Test in Physics, Physics SAT II, or simply the Physics SAT, was a one-hour multiple choice test on physics administered by the College Board in the United States. A high school student generally chose to take the test to fulfill college entrance requirements for the schools at which the student was planning to apply. Until 1994, the SAT Subject Tests were known as Achievement Tests; until January 2005, they were known as SAT IIs; they are still well known by this name. The material tested on the Physics SAT was supposed to be equivalent to that taught in a junior- or senior-level high school physics class. | SAT Subject Test in Physics | 0.852442 |
382 | The test specifications for the Biology section changed in 2014. These changes reflected a shift on the way that Biology is taught in survey courses. This means that the questions now focus on "complex interactions within biological systems, rather than viewing biology in a reductionist manner". There are also changes to the Quantitative Reasoning section. | Dental Admission Test | 0.852426 |
383 | Supervised Machine Learning algorithms require large amounts of human-annotated data to be trained successfully. Machine learning researchers have hired Workers through Mechanical Turk to produce datasets such as SQuAD, a question answering dataset. | Amazon Mechanical Turk | 0.852401 |
384 | Calcium ions (Ca2+) contribute to the physiology and biochemistry of organisms' cells. They play an important role in signal transduction pathways, where they act as a second messenger, in neurotransmitter release from neurons, in contraction of all muscle cell types, and in fertilization. Many enzymes require calcium ions as a cofactor, including several of the coagulation factors. Extracellular calcium is also important for maintaining the potential difference across excitable cell membranes, as well as proper bone formation. | Calcium in biology | 0.852368 |
385 | The core problems in computational geometry may be classified in different ways, according to various criteria. The following general classes may be distinguished. | Computational Geometry | 0.852361 |
386 | They reduce the problem, so that it eventually fits in cache no matter how small the cache is, and end the recursion at some small size determined by the function-call overhead and similar cache-unrelated optimizations, and then use some cache-efficient access pattern to merge the results of these small, solved problems. Like external sorting in the external memory model, cache-oblivious sorting is possible in two variants: funnelsort, which resembles mergesort, and cache-oblivious distribution sort, which resembles quicksort. Like their external memory counterparts, both achieve a running time of O ( N B log M B N B ) {\displaystyle O\left({\tfrac {N}{B}}\log _{\tfrac {M}{B}}{\tfrac {N}{B}}\right)} , which matches a lower bound and is thus asymptotically optimal. | Cache-oblivious algorithm | 0.852356 |
387 | Given a subset X of an algebraic structure S, the closure of X is the smallest substructure of S that is closed under all operations of S. In the context of algebraic structures, this closure is generally called the substructure generated or spanned by X, and one says that X is a generating set of the substructure. For example, a group is a set with an associative operation, often called multiplication, with an identity element, such that every element has an inverse element. Here, the auxiliary operations are the nullary operation that results in the identity element and the unary operation of inversion. | Reflexive transitive closure | 0.852338 |
388 | In computer science, merge sort (also commonly spelled as mergesort) is an efficient, general-purpose, and comparison-based sorting algorithm. Most implementations produce a stable sort, which means that the relative order of equal elements is the same in the input and output. Merge sort is a divide-and-conquer algorithm that was invented by John von Neumann in 1945. A detailed description and analysis of bottom-up merge sort appeared in a report by Goldstine and von Neumann as early as 1948. | In-place merge sort | 0.852291 |
389 | On-line Questions are uploaded again after the Winter School. The leftovers of the Winter School and other people who didn't join the Winter School have to take this test to join the Summer School 2. Second grade students in the high school take this test. In this test, almost half of these questions will be related to Organic Chemistry. 20 well-ranked students can join the Winter School 2. | Korean Chemistry Olympiad | 0.852287 |
390 | Methods of studying a large genomic data include variant-calling, transcriptomic analysis, and variant interpretation. Genome informatics can analyze DNA sequence information and to predict protein sequence and structure. Genome informatics dealing with microbial and metagenomics, sequencing algorithms, variant discovery and genome assembly, evolution, complex traits and phylogenetics, personal and medical genomics, transcriptomics, genome structure and function. | Genome informatics | 0.852226 |
391 | Natural language processing algorithms personalized medicine for patients who suffer genetic diseases, by combining the extraction of clinical information and genomic data available from the patients. Institutes such as Health-funded Pharmacogenomics Research Network focus on finding breast cancer treatments.Precision medicine considers individual genomic variability, enabled by large-scale biological databases. Machine learning can be applied to perform the matching function between (groups of patients) and specific treatment modalities.Computational techniques are used to solve other problems, such as efficient primer design for PCR, biological-image analysis and back translation of proteins (which is, given the degeneration of the genetic code, a complex combinatorial problem). | Machine learning in bioinformatics | 0.852196 |
392 | {\displaystyle y^{2}+x^{2}=1.\,} This determines y, except only up to an overall sign; accordingly, it has two branches: y = ± 1 − x 2 . {\displaystyle y=\pm {\sqrt {1-x^{2}}}.\,} An algebraic function in m variables is similarly defined as a function y = f ( x 1 , … , x m ) {\displaystyle y=f(x_{1},\dots ,x_{m})} which solves a polynomial equation in m + 1 variables: p ( y , x 1 , x 2 , … , x m ) = 0. {\displaystyle p(y,x_{1},x_{2},\dots ,x_{m})=0.} | Algebraic function | 0.852148 |
393 | Although usually applied to time efficiency, an algorithm can be said to use asymptotically optimal space, random bits, number of processors, or any other resource commonly measured using big-O notation. Sometimes vague or implicit assumptions can make it unclear whether an algorithm is asymptotically optimal. For example, a lower bound theorem might assume a particular abstract machine model, as in the case of comparison sorts, or a particular organization of memory. By violating these assumptions, a new algorithm could potentially asymptotically outperform the lower bound and the "asymptotically optimal" algorithms. | Asymptotically optimal algorithm | 0.852146 |
394 | Examples and applications of groups abound. A starting point is the group Z {\displaystyle \mathbb {Z} } of integers with addition as group operation, introduced above. If instead of addition multiplication is considered, one obtains multiplicative groups. These groups are predecessors of important constructions in abstract algebra. | Group (mathematics) | 0.852124 |
395 | Given a polynomial equation or a system of polynomial equations it is often useful to compute or to bound the number of solutions without computing explicitly the solutions. In the case of a single equation, this problem is solved by the fundamental theorem of algebra, which asserts that the number of complex solutions is bounded by the degree of the polynomial, with equality, if the solutions are counted with their multiplicities. In the case of a system of n polynomial equations in n unknowns, the problem is solved by Bézout's theorem, which asserts that, if the number of complex solutions is finite, their number is bounded by the product of the degrees of the polynomials. Moreover, if the number of solutions at infinity is also finite, then the product of the degrees equals the number of solutions counted with multiplicities and including the solutions at infinity. | Multi-homogeneous polynomial | 0.852116 |
396 | The following conditions comprise the classification theorem for Min Ones problems. If setting all variables false satisfies all clauses, it is in PO. If each clause can be written as a CNF of Horn subclauses, it is in PO. If it is an instance of 2-X(N)OR-SAT, it is in PO. | Max/min CSP/Ones classification theorems | 0.852106 |
397 | Once we can see how a protein folds then we can see how it works as a catalyst, or in intracellular communication, e.g. neuroreceptor-neurotransmitter interaction. How certain compounds may be used to enhance or prevent the function of these proteins and how an elucidated protein overall plays a role in disease can also be much better understood.There are many other avenues of research in which the dry lab approach has been implemented. Other physical phenomena, such as sound, properties of newly discovered or hypothetical compounds and quantum mechanics models have recently received more attention in this area of approach. | Dry lab | 0.852084 |
398 | The Sun is classified as G2.The fact that the Harvard classification of a star indicated its surface or photospheric temperature (or more precisely, its effective temperature) was not fully understood until after its development, though by the time the first Hertzsprung–Russell diagram was formulated (by 1914), this was generally suspected to be true. In the 1920s, the Indian physicist Meghnad Saha derived a theory of ionization by extending well-known ideas in physical chemistry pertaining to the dissociation of molecules to the ionization of atoms. First he applied it to the solar chromosphere, then to stellar spectra.Harvard astronomer Cecilia Payne then demonstrated that the O-B-A-F-G-K-M spectral sequence is actually a sequence in temperature. Because the classification sequence predates our understanding that it is a temperature sequence, the placement of a spectrum into a given subtype, such as B3 or A7, depends upon (largely subjective) estimates of the strengths of absorption features in stellar spectra. As a result, these subtypes are not evenly divided into any sort of mathematically representable intervals. | Spectral type | 0.852083 |
399 | Third-generation sequencing (also known as long-read sequencing) is a class of DNA sequencing methods currently under active development.Third generation sequencing technologies have the capability to produce substantially longer reads than second generation sequencing, also known as next-generation sequencing. Such an advantage has critical implications for both genome science and the study of biology in general. However, third generation sequencing data have much higher error rates than previous technologies, which can complicate downstream genome assembly and analysis of the resulting data. These technologies are undergoing active development and it is expected that there will be improvements to the high error rates. For applications that are more tolerant to error rates, such as structural variant calling, third generation sequencing has been found to outperform existing methods, even at a low depth of sequencing coverage. | Long-read sequencing | 0.852059 |
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