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10,200 | In chemistry, molecular orbital theory (MO theory or MOT) is a method for describing the electronic structure of molecules using quantum mechanics. It was proposed early in the 20th century. In molecular orbital theory, electrons in a molecule are not assigned to individual chemical bonds between atoms, but are treated... | Molecular Orbital Theory | 0.819241 |
10,201 | This method of quantifying orbital contribution as a linear combination of atomic orbitals is used in computational chemistry. An additional unitary transformation can be applied on the system to accelerate the convergence in some computational schemes. | Molecular Orbital Theory | 0.819241 |
10,202 | In the LCAO method, each molecule has a set of molecular orbitals. It is assumed that the molecular orbital wave function ψj can be written as a simple weighted sum of the n constituent atomic orbitals χi, according to the following equation: One may determine cij coefficients numerically by substituting this equation ... | Molecular Orbital Theory | 0.819241 |
10,203 | This rigorous approach is known as the Hartree–Fock method for molecules although it had its origins in calculations on atoms. In calculations on molecules, the molecular orbitals are expanded in terms of an atomic orbital basis set, leading to the Roothaan equations. This led to the development of many ab initio quant... | Molecular Orbital Theory | 0.819241 |
10,204 | Infrared spectroscopy exploits the fact that molecules absorb frequencies that are characteristic of their structure. These absorptions occur at resonant frequencies, i.e. the frequency of the absorbed radiation matches the vibrational frequency. The energies are affected by the shape of the molecular potential energy ... | Infra-red spectroscopy | 0.819238 |
10,205 | Thorne & Hawking argued that since general relativity made it impossible for black holes to radiate, and lose information, the mass-energy and information carried by Hawking radiation must be "new", and must not originate from inside the black hole event horizon. Since this contradicted the idea under quantum mechanics... | Thorne–Hawking–Preskill bet | 0.819238 |
10,206 | The Thorne–Hawking–Preskill bet was a public bet on the outcome of the black hole information paradox made in 1997 by physics theorists Kip Thorne and Stephen Hawking on the one side, and John Preskill on the other, according to the document they signed 6 February 1997, as shown in Hawking's The Universe in a Nutshell. | Thorne–Hawking–Preskill bet | 0.819238 |
10,207 | In the most extreme view, as expressed by Ian Barbour in '’Technology, Environment, and Human Values'’, technology assessment is "a one-sided apology for contemporary technology by people with a stake in its continuation. "Overall, technology assessment is a very broad field which reaches beyond just technology and ind... | Technology Assessment | 0.819232 |
10,208 | In ring theory, a branch of abstract algebra, a ring homomorphism is a structure-preserving function between two rings. More explicitly, if R and S are rings, then a ring homomorphism is a function f: R → S such that f is: addition preserving: f ( a + b ) = f ( a ) + f ( b ) {\displaystyle f(a+b)=f(a)+f(b)} for all a a... | Rng homomorphism | 0.819224 |
10,209 | Nearest neighbor search (NNS), as a form of proximity search, is the optimization problem of finding the point in a given set that is closest (or most similar) to a given point. Closeness is typically expressed in terms of a dissimilarity function: the less similar the objects, the larger the function values. Formally,... | Nearest neighbor distance ratio | 0.819223 |
10,210 | According to the Erdős–Pósa theorem, the size of a minimum feedback vertex set is within a logarithmic factor of the maximum number of vertex-disjoint cycles in the given graph. | Feedback vertex set | 0.819218 |
10,211 | The corresponding NP optimization problem of finding the size of a minimum feedback vertex set can be solved in time O(1.7347n), where n is the number of vertices in the graph. This algorithm actually computes a maximum induced forest, and when such a forest is obtained, its complement is a minimum feedback vertex set.... | Feedback vertex set | 0.819218 |
10,212 | In the mathematical discipline of graph theory, a feedback vertex set (FVS) of a graph is a set of vertices whose removal leaves a graph without cycles ("removal" means deleting the vertex and all edges adjacent to it). Equivalently, each FVS contains at least one vertex of any cycle in the graph. The feedback vertex s... | Feedback vertex set | 0.819218 |
10,213 | ), Handbook of Combinatorial Optimization, Supplement vol. A (PDF), Kluwer Academic Publishers, pp. 209–259 Garey, Michael R.; Johnson, David S. | Feedback vertex set | 0.819218 |
10,214 | The distinction of DAEs to ODEs becomes apparent if some of the dependent variables occur without their derivatives. The vector of dependent variables may then be written as pair ( x , y ) {\displaystyle (x,y)} and the system of differential equations of the DAE appears in the form F ( x ˙ , x , y , t ) = 0 {\displayst... | Differential-algebraic system of equations | 0.819215 |
10,215 | DAE of the form x ˙ = f ( x , y , t ) , 0 = g ( x , y , t ) . {\displaystyle {\begin{aligned}{\dot {x}}&=f(x,y,t),\\0&=g(x,y,t).\end{aligned}}} are called semi-explicit. The index-1 property requires that g is solvable for y. In other words, the differentiation index is 1 if by differentiation of the algebraic equation... | Differential-algebraic system of equations | 0.819214 |
10,216 | Safari (web browser) – SAIL – Script kiddie – Scripting language – SCSI – Second-generation programming language – Secure Sockets Layer – sed – Self (or SELF) – Semaphore (programming) – Sequential access – SETL – Shareware – Shell script – Shellcode – SIMD – Simula – Sircam – Slide rule – SLIP – SLR parser – Smalltalk... | Index of computing articles | 0.81921 |
10,217 | Originally, the word computing was synonymous with counting and calculating, and the science and technology of mathematical calculations. Today, "computing" means using computers and other computing machines. It includes their operation and usage, the electrical processes carried out within the computing hardware itsel... | Index of computing articles | 0.81921 |
10,218 | LALR parser – Lambda calculus – Lasso – LaTeX – Leet – Legal aspects of computing – Lex – LibreOffice – Limbo – Linked list – Linux – Lisp – List of IBM products – List of Intel microprocessors – List of programming languages – List of operating systems – List of Soviet computer systems – LL parser – Logic programming ... | Index of computing articles | 0.81921 |
10,219 | G4 – G5 – GEM – General Algebraic Modeling System – Genie – GNU – GNU Bison – Gnutella – Graphical user interface – Graphics Device Interface – Greibach normal form – G.hn | Index of computing articles | 0.81921 |
10,220 | C++ – C# – C – Cache – Canonical LR parser – Cat (Unix) – CD-ROM – Central processing unit – Chimera – Chomsky normal form – CIH virus – Classic Mac OS – COBOL – Cocoa (software) – Code and fix – Code Red worm – ColdFusion – Colouring algorithm – COMAL – Comm (Unix) – Command line interface – Command line interpreter –... | Index of computing articles | 0.81921 |
10,221 | R (programming language) – RAM (random-access memory) – RAM drive – Random access – Rascal – Ratfor – RCA 1802 – Read-only memory (ROM) – REBOL – Recovery-oriented computing – Recursive descent parser – Recursion (computer science) – Recursive set – Recursively enumerable language – Recursively enumerable set – Referen... | Index of computing articles | 0.81921 |
10,222 | Emission of radiation is typically described using semi-classical quantum mechanics: the particle's energy levels and spacings are determined from quantum mechanics, and light is treated as an oscillating electric field that can drive a transition if it is in resonance with the system's natural frequency. The quantum m... | Molecular band emission | 0.81921 |
10,223 | In physics, emission is the process by which a higher energy quantum mechanical state of a particle becomes converted to a lower one through the emission of a photon, resulting in the production of light. The frequency of light emitted is a function of the energy of the transition. Since energy must be conserved, the e... | Molecular band emission | 0.81921 |
10,224 | In their previous work on a square lattice of frustrated magnets, they observed both ice-like short-range correlations and the absence of long-range correlations, just like in the spin ice at low temperature. These results solidify the uncharted ground on which the real physics of frustration can be visualized and mode... | Geometric frustration | 0.819205 |
10,225 | Geometry in Condensed Matter Physics. Singapore: World Scientific. ISBN 9789810200893. | Geometric frustration | 0.819205 |
10,226 | Self-verifying theories are consistent first-order systems of arithmetic, much weaker than Peano arithmetic, that are capable of proving their own consistency. Dan Willard was the first to investigate their properties, and he has described a family of such systems. According to Gödel's incompleteness theorem, these sys... | Self-verifying theories | 0.819205 |
10,227 | Weighing of gases using scales was not possible until the invention of the vacuum pump in the 17th century. Once understood, the conservation of mass was of great importance in progressing from alchemy to modern chemistry. Once early chemists realized that chemical substances never disappeared but were only transformed... | Conservation of matter | 0.819197 |
10,228 | In relativity theory, so long as any type of energy is retained within a system, this energy exhibits mass. Also, mass must be differentiated from matter, since matter may not be perfectly conserved in isolated systems, even though mass is always conserved in such systems. However, matter is so nearly conserved in chem... | Conservation of matter | 0.819197 |
10,229 | These systems are often governed by nonlinear differential equations. The mathematical techniques which have been developed to handle them are more rigorous and much less general, often applying only to narrow categories of systems. These include limit cycle theory, Poincaré maps, Lyapunov stability theory, and describ... | Nonlinear Control | 0.819197 |
10,230 | They are governed by linear differential equations. A major subclass is systems which in addition have parameters which do not change with time, called linear time invariant (LTI) systems. | Nonlinear Control | 0.819197 |
10,231 | The term "t-statistic" is abbreviated from "hypothesis test statistic". In statistics, the t-distribution was first derived as a posterior distribution in 1876 by Helmert and Lüroth. The t-distribution also appeared in a more general form as Pearson Type IV distribution in Karl Pearson's 1895 paper. However, the T-Dist... | Student's t-statistic | 0.819195 |
10,232 | Most frequently, t statistics are used in Student's t-tests, a form of statistical hypothesis testing, and in the computation of certain confidence intervals. The key property of the t statistic is that it is a pivotal quantity – while defined in terms of the sample mean, its sampling distribution does not depend on th... | Student's t-statistic | 0.819195 |
10,233 | ( β ^ ) {\displaystyle \operatorname {s.e.} ({\hat {\beta }})} is the standard error of the estimator β ^ {\displaystyle {\hat {\beta }}} for β. By default, statistical packages report t-statistic with β0 = 0 (these t-statistics are used to test the significance of corresponding regressor). However, when t-statistic ... | Student's t-statistic | 0.819195 |
10,234 | In statistics, the t-statistic is the ratio of the departure of the estimated value of a parameter from its hypothesized value to its standard error. It is used in hypothesis testing via Student's t-test. The t-statistic is used in a t-test to determine whether to support or reject the null hypothesis. | Student's t-statistic | 0.819195 |
10,235 | Signaling games describe situations where one player has information the other player does not have. These situations of asymmetric information are very common in economics and behavioral biology. | Signaling games | 0.819195 |
10,236 | The definition of a doubling measure may seem arbitrary, or purely of geometric interest. However, many results from classical harmonic analysis and computational geometry extend to the setting of metric spaces with doubling measures. == References == | Doubling space | 0.819187 |
10,237 | The NM-method or Naszodi–Mendonca method is the operation that can be applied in statistics, econometrics, economics, sociology, and demography to construct counterfactual contingency tables. The method finds the matrix X {\displaystyle X} ( X ∈ R n × m {\displaystyle X\in \mathbb {R} ^{n\times m}} ) which is "closest"... | NM-method | 0.819186 |
10,238 | It can be used to quantify certain ceteris paribus effects. More precisely, to quantify on a cardinal scale the difference between the directly unobservable degree of marital sorting in Zimbabwe and Yemen, or in Generation Z and Generation Y with a counterfactual decomposition. For the decomposition, the counterfactual... | NM-method | 0.819186 |
10,239 | Preservation breeding can take the following forms: Selective breeding of rare breeds and rare pedigrees, particularly monitoring breeding genetics in small populations to ensure diversity is maintained as much as possible; Rare breeds that suffer life-threatening genetic deficiencies can be intentionally cross-bred wi... | Preservation breeding | 0.819185 |
10,240 | The term preservation breeding was first used by notable American Kennel Club Judges Douglas Johnson and Bill Shelton in breeder seminars for dog breeders in the early 2000s. The preservation of dog breeds and the conservancy of canine genetics started gaining more traction in the mid-2010s. | Preservation breeding | 0.819185 |
10,241 | The basic unit of ABPP is the probe, which typically consists of two elements: a reactive group (RG, sometimes called a "warhead") and a tag. Additionally, some probes may contain a binding group which enhances selectivity. The reactive group usually contains a specially designed electrophile that becomes covalently-li... | Activity-based proteomics | 0.819178 |
10,242 | Substrate stiffness should ideally be in the myogenic range, which has been shown to be 10-15 kPa.Functional analysis of a tissue engineered muscle construct is important to illustrate its potential to help regenerate muscle. A variety of assays are generally used to evaluate a tissue engineered muscle construct includ... | Muscle tissue engineering | 0.819177 |
10,243 | In mathematics, an algebraic representation of a group G on a k-algebra A is a linear representation π: G → G L ( A ) {\displaystyle \pi :G\to GL(A)} such that, for each g in G, π ( g ) {\displaystyle \pi (g)} is an algebra automorphism. Equipped with such a representation, the algebra A is then called a G-algebra. For... | Algebraic representation | 0.81916 |
10,244 | What stopping rule minimizes the expected rank of the selected observation, and what is its corresponding value?The general solution to this full-information expected rank problem is unknown. The major difficulty is that the problem is fully history-dependent, that is, the optimal rule depends at every stage on all pre... | Robbins' problem (of optimal stopping) | 0.819158 |
10,245 | In probability theory, Robbins' problem of optimal stopping, named after Herbert Robbins, is sometimes referred to as the fourth secretary problem or the problem of minimizing the expected rank with full information.Let X1, ... , Xn be independent, identically distributed random variables, uniform on . We observe the X... | Robbins' problem (of optimal stopping) | 0.819158 |
10,246 | Every nontrivial proper rotation in 3 dimensions fixes a unique 1-dimensional linear subspace of R 3 {\displaystyle \mathbb {R} ^{3}} which is called the axis of rotation (this is Euler's rotation theorem). Each such rotation acts as an ordinary 2-dimensional rotation in the plane orthogonal to this axis. Since every 2... | Set of 3D rotations | 0.819153 |
10,247 | The same argument can be performed in general, and it shows that the fundamental group of SO(3) is the cyclic group of order 2 (a fundamental group with two elements). In physics applications, the non-triviality (more than one element) of the fundamental group allows for the existence of objects known as spinors, and i... | Set of 3D rotations | 0.819153 |
10,248 | The group SO(3) can therefore be identified with the group of these matrices under matrix multiplication. These matrices are known as "special orthogonal matrices", explaining the notation SO(3). The group SO(3) is used to describe the possible rotational symmetries of an object, as well as the possible orientations of... | Set of 3D rotations | 0.819153 |
10,249 | In mechanics and geometry, the 3D rotation group, often denoted SO(3), is the group of all rotations about the origin of three-dimensional Euclidean space R 3 {\displaystyle \mathbb {R} ^{3}} under the operation of composition.By definition, a rotation about the origin is a transformation that preserves the origin, Euc... | Set of 3D rotations | 0.819153 |
10,250 | Julia has the package HypothesisTests.jl with the function ExactOneSampleKSTest(x::AbstractVector{<:Real}, d::UnivariateDistribution). StatsDirect (StatsDirect Ltd, Manchester, UK) implements all common variants. Stata (Stata Corporation, College Station, TX) implements the test in ksmirnov (Kolmogorov–Smirnov equality... | Kolmogorov–Smirnov test | 0.819153 |
10,251 | The R package "KSgeneral" computes the KS test statistics and its p-values under arbitrary, possibly discrete, mixed or continuous null distribution. R's statistics base-package implements the test as ks.test {stats} in its "stats" package. SAS implements the test in its PROC NPAR1WAY procedure. | Kolmogorov–Smirnov test | 0.819153 |
10,252 | The Kolmogorov–Smirnov test is implemented in many software programs. Most of these implement both the one and two sampled test. Mathematica has KolmogorovSmirnovTest. MATLAB's Statistics Toolbox has kstest and kstest2 for one-sample and two-sample Kolmogorov–Smirnov tests, respectively. | Kolmogorov–Smirnov test | 0.819153 |
10,253 | In statistics, the Kolmogorov–Smirnov test (K–S test or KS test) is a nonparametric test of the equality of continuous (or discontinuous, see Section 2.2), one-dimensional probability distributions that can be used to compare a sample with a reference probability distribution (one-sample K–S test), or to compare two sa... | Kolmogorov–Smirnov test | 0.819153 |
10,254 | In abstract algebra, a branch of mathematics, the algebraic structure group with operators or Ω-group can be viewed as a group with a set Ω that operates on the elements of the group in a special way. Groups with operators were extensively studied by Emmy Noether and her school in the 1920s. She employed the concept in... | Group with operators | 0.819152 |
10,255 | The Jordan–Hölder theorem also holds in the context of operator groups. The requirement that a group have a composition series is analogous to that of compactness in topology, and can sometimes be too strong a requirement. It is natural to talk about "compactness relative to a set", i.e. talk about composition series w... | Group with operators | 0.819152 |
10,256 | In algebra, a cyclic division algebra is one of the basic examples of a division algebra over a field, and plays a key role in the theory of central simple algebras. | Cyclic algebra | 0.819147 |
10,257 | Let A be a finite-dimensional central simple algebra over a field F. Then A is said to be cyclic if it contains a strictly maximal subfield E such that E/F is a cyclic field extension (i.e., the Galois group is a cyclic group). | Cyclic algebra | 0.819147 |
10,258 | In computational number theory and computational algebra, Pollard's kangaroo algorithm (also Pollard's lambda algorithm, see Naming below) is an algorithm for solving the discrete logarithm problem. The algorithm was introduced in 1978 by the number theorist John M. Pollard, in the same paper as his better-known Pollar... | Pollard's kangaroo algorithm | 0.819147 |
10,259 | Pollard gives the time complexity of the algorithm as O ( b − a ) {\displaystyle O({\sqrt {b-a}})} , using a probabilistic argument based on the assumption that f {\displaystyle f} acts pseudorandomly. Since a , b {\displaystyle a,b} can be represented using O ( log b ) {\displaystyle O(\log b)} bits, this is exponen... | Pollard's kangaroo algorithm | 0.819147 |
10,260 | So "A or B" is implied.) Generally, the Inductive step will consist of a lengthy but simple case-by-case analysis of all the rules of inference, showing that each "preserves" semantic implication. By the definition of provability, there are no sentences provable other than by being a member of G, an axiom, or following... | Classical propositional logic | 0.819145 |
10,261 | . , ϕ n , χ ⊢ ψ {\displaystyle \phi _{1},\ ...,\ \phi _{n},\ \chi \vdash \psi } by means of modus ponens, Q.E.D.The converse of DT has powerful implications: it can be used to convert an axiom into an inference rule. For example, by axiom AND-1 we have, ⊢ ϕ ∧ χ → ϕ , {\displaystyle \vdash \phi \wedge \chi \to \phi ,} w... | Classical propositional logic | 0.819145 |
10,262 | In this sense, DT corresponds to the natural conditional proof inference rule which is part of the first version of propositional calculus introduced in this article. The converse of DT is also valid: If the sequence ϕ 1 , ϕ 2 , . . | Classical propositional logic | 0.819145 |
10,263 | , ϕ n ⊢ χ → ψ {\displaystyle \phi _{1},\ \phi _{2},\ ...,\ \phi _{n}\vdash \chi \to \psi } .This deduction theorem (DT) is not itself formulated with propositional calculus: it is not a theorem of propositional calculus, but a theorem about propositional calculus. In this sense, it is a meta-theorem, comparable to theo... | Classical propositional logic | 0.819145 |
10,264 | Let a demonstration be represented by a sequence, with hypotheses to the left of the turnstile and the conclusion to the right of the turnstile. Then the deduction theorem can be stated as follows: If the sequence ϕ 1 , ϕ 2 , . . . | Classical propositional logic | 0.819145 |
10,265 | One notable difference between propositional calculus and predicate calculus is that satisfiability of a propositional formula is decidable. Deciding satisfiability of propositional logic formulas is an NP-complete problem. However, practical methods exist (e.g., DPLL algorithm, 1962; Chaff algorithm, 2001) that are ve... | Classical propositional logic | 0.819144 |
10,266 | Examples of discrete items are the cloud structures, the distant red harbor cranes, power line poles, wooden railroad ties, the diagonal lines in the road, and the cross walk across the rails.The counting of the ties leads to the idea of iteration in computer programming and, more generally, to discrete mathematics, th... | Math walk | 0.81914 |
10,267 | A math walk, or math trail, is a type of themed walk in the US, where direct experience is translated into the language of mathematics or abstract mathematical sciences such as information science, computer science, decision science, or probability and statistics. Some sources specify how to create a math walk whereas ... | Math walk | 0.81914 |
10,268 | Any such map can be extended to a field homomorphism Q(S) → Q(S) which is not surjective. Such a field homomorphism can in turn be extended to the algebraic closure C, and the resulting field homomorphisms C → C are not surjective. The transcendence degree can give an intuitive understanding of the size of a field. For... | Transcendence degree | 0.819117 |
10,269 | Transcendence bases are a useful tool to prove various existence statements about field homomorphisms. Here is an example: Given an algebraically closed field L, a subfield K and a field automorphism f of K, there exists a field automorphism of L which extends f (i.e. whose restriction to K is f). For the proof, one st... | Transcendence degree | 0.819117 |
10,270 | If M / L and L / K are field extensions, then trdeg(M / K) = trdeg(M / L) + trdeg(L / K)This is proven by showing that a transcendence basis of M / K can be obtained by taking the union of a transcendence basis of M / L and one of L / K. If the set S is algebraically independent over K, then the field K(S) is isomorphi... | Transcendence degree | 0.819117 |
10,271 | (Since Q is countable, the field Q(S) will have the same cardinality as S for any infinite set S, and any algebraic extension of Q(S) will have the same cardinality again.) The transcendence degree of Q(e, π) over Q is either 1 or 2; the precise answer is unknown because it is not known whether e and π are algebraicall... | Transcendence degree | 0.819117 |
10,272 | An extension is algebraic if and only if its transcendence degree is 0; the empty set serves as a transcendence basis here. The field of rational functions in n variables K(x1,...,xn) (i.e. the field of fractions of the polynomial ring K) is a purely transcendental extension with transcendence degree n over K; we can f... | Transcendence degree | 0.819117 |
10,273 | Let A ⊂ B {\displaystyle A\subset B} be integral domains. If Q ( A ) {\displaystyle Q(A)} and Q ( B ) {\displaystyle Q(B)} denote the fields of fractions of A an B, then the transcendence degree of B over A is defined as the transcendence degree of the field extension Q ( B ) / Q ( A ) . {\displaystyle Q(B)/Q(A).} The ... | Transcendence degree | 0.819117 |
10,274 | In particular, all transcendence bases of a field extension have the same cardinality, called the transcendence degree of the extension. Thus, a field extension is a transcendental extension if and only if its transcendence degree is positive. Transcendental extensions are widely used in algebraic geometry. For example... | Transcendence degree | 0.819117 |
10,275 | A transcendence basis of a field extension L / K {\displaystyle L/K} (or a transcendence basis of L {\displaystyle L} over K {\displaystyle K} ) is a maximal algebraically independent subset of L {\displaystyle L} over K . {\displaystyle K.} Transcendence bases share many properties with bases of vector spaces. | Transcendence degree | 0.819117 |
10,276 | In mathematics, a transcendental extension L / K {\displaystyle L/K} is a field extension such that there exists an element in the field L {\displaystyle L} that is transcendental over the field K {\displaystyle K} ; that is, an element that is not a root of any univariate polynomial with coefficients in K {\displaysty... | Transcendence degree | 0.819117 |
10,277 | The non-relativistic Hamiltonian for a quantized charged particle of mass m in a classical electromagnetic field is (in cgs units) where A is the three-vector potential and φ is the scalar potential. This form of the Hamiltonian, as well as the Schrödinger equation Hψ = iħ∂ψ/∂t, the Maxwell equations and the Lorentz fo... | Commutation relations | 0.819114 |
10,278 | In quantum mechanics, the canonical commutation relation is the fundamental relation between canonical conjugate quantities (quantities which are related by definition such that one is the Fourier transform of another). For example, between the position operator x and momentum operator px in the x direction of a point ... | Commutation relations | 0.819114 |
10,279 | According to the correspondence principle, in certain limits the quantum equations of states must approach Hamilton's equations of motion. The latter state the following relation between the generalized coordinate q (e.g. position) and the generalized momentum p: In quantum mechanics the Hamiltonian H ^ {\displaystyle ... | Commutation relations | 0.819114 |
10,280 | It is often desirable to consider curves in the projective space. An algebraic curve in the projective plane or plane projective curve is the set of the points in a projective plane whose projective coordinates are zeros of a homogeneous polynomial in three variables P(x, y, z). Every affine algebraic curve of equation... | Plane projective curve | 0.819112 |
10,281 | The scope of classical control theory is limited to single-input and single-output (SISO) system design, except when analyzing for disturbance rejection using a second input. The system analysis is carried out in the time domain using differential equations, in the complex-s domain with the Laplace transform, or in the... | Closed- loop | 0.819111 |
10,282 | A control system must always have some robustness property. A robust controller is such that its properties do not change much if applied to a system slightly different from the mathematical one used for its synthesis. This requirement is important, as no real physical system truly behaves like the series of differenti... | Closed- loop | 0.819111 |
10,283 | A hierarchical control system is a type of control system in which a set of devices and governing software is arranged in a hierarchical tree. When the links in the tree are implemented by a computer network, then that hierarchical control system is also a form of networked control system. Intelligent control uses vari... | Closed- loop | 0.819111 |
10,284 | The Compton wavelength expresses a fundamental limitation on measuring the position of a particle, taking into account quantum mechanics and special relativity.This limitation depends on the mass m of the particle. To see how, note that we can measure the position of a particle by bouncing light off it – but measuring ... | Compton wavelength | 0.819107 |
10,285 | To detect such deception, researchers aim to create techniques and tools to inspect AI models and to understand the inner workings of black-box models such as neural networks. Additionally, researchers propose to solve the problem of systems disabling their off-switches by making AI agents uncertain about the objective... | AI control problem | 0.819105 |
10,286 | Leading AI labs such as OpenAI and DeepMind have stated their aim to develop artificial general intelligence (AGI), a hypothesized AI system that matches or outperforms humans in a broad range of cognitive tasks. Researchers who scale modern neural networks observe that they indeed develop increasingly general and unan... | AI control problem | 0.819105 |
10,287 | A learning augmented algorithm is said to be consistent if the algorithm can be proven to have a good performance when it is provided with an accurate prediction. Usually, this is quantified by giving a bound on the performance that depends on the error in the prediction. Robustnesss. An algorithm is called robust if i... | Learning augmented algorithm | 0.8191 |
10,288 | Motl writes a science and politics blog called "The Reference Frame: Supersymmetric world from a conservative viewpoint", in which he expresses his scientific and right-wing political opinions, including invective as well as personal insults. The blog has been described by George Musser as an "over-the-top" defense of ... | The Reference Frame | 0.819096 |
10,289 | As Lipton states:This alone could be important and often is a great reason for finding such algorithms. For example, if tomorrow there were a discovery that showed there is a factoring algorithm with a huge but provably polynomial time bound, that would change our beliefs about factoring. The algorithm might never be u... | Galactic algorithm | 0.819094 |
10,290 | Simulated annealing, when used with a logarithmic cooling schedule, has been proven to find the global optimum of any optimization problem. However, such a cooling schedule results in entirely impractical runtimes, and is never used. However, knowing this ideal algorithm exists has led to practical variants that are ab... | Galactic algorithm | 0.819094 |
10,291 | Even if they are never used in practice, galactic algorithms may still contribute to computer science: An algorithm, even if impractical, may show new techniques that may eventually be used to create practical algorithms. Available computational power may catch up to the crossover point, so that a previously impractica... | Galactic algorithm | 0.819094 |
10,292 | In mathematics, a graph polynomial is a graph invariant whose values are polynomials. Invariants of this type are studied in algebraic graph theory. Important graph polynomials include: The characteristic polynomial, based on the graph's adjacency matrix. | Graph polynomial | 0.819093 |
10,293 | A query plan (or query execution plan) is a sequence of steps used to access data in a SQL relational database management system. This is a specific case of the relational model concept of access plans. Since SQL is declarative, there are typically many alternative ways to execute a given query, with widely varying per... | Query plan | 0.819092 |
10,294 | For CBO to be used, all the tables referenced by the query must be analyzed. To analyze a table, a DBA can launch code from the DBMS_STATS package. Other tools for query optimization include: SQL Trace Oracle Trace and TKPROF Microsoft SMS (SQL) Execution Plan Tableau Performance Recording (all DB) == References == | Query plan | 0.819092 |
10,295 | Some databases - like Oracle - provide a plan table for query tuning. This plan table will return the cost and time for executing a query. Oracle offers two optimization approaches: CBO or Cost Based Optimization RBO or Rule Based OptimizationRBO is slowly being deprecated. | Query plan | 0.819092 |
10,296 | A given database management system may offer one or more mechanisms for returning the plan for a given query. Some packages feature tools which will generate a graphical representation of a query plan. Other tools allow a special mode to be set on the connection to cause the DBMS to return a textual description of the ... | Query plan | 0.819092 |
10,297 | Multivesicular Release (MVR) is the phenomenon by which individual chemical synapses, forming the junction between neurons, is mediated by multiple releasable vesicles of neurotransmitter. In neuroscience, whether one or many vesicles are released per action potential depends on the synapse and has been shown to be mor... | Multivesicular release | 0.819089 |
10,298 | In molecular biology, molecular chaperones are proteins that assist the conformational folding or unfolding of large proteins or macromolecular protein complexes. There are a number of classes of molecular chaperones, all of which function to assist large proteins in proper protein folding during or after synthesis, an... | Chaperone proteins | 0.819087 |
10,299 | Type theories, in general, do not have axioms and are defined by their rules of inference. Classical Set theory and logic have the law of excluded middle. That is, every theorem is true or false. | Propositional equality | 0.819087 |
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