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13,300 | To avoid the potential problems associated with the mathematical definition, Dana Scott originally defined the let expression from lambda calculus. This may be considered as the bottom up, or constructive, definition of the let expression, in contrast to the top down, or axiomatic mathematical definition. The simple, n... | Let expression | 0.816355 |
13,301 | The expression L {\displaystyle L} means substitute every occurrence of G in L by S and return the expression. The definition used is extended to cover the substitution of expressions, from the definition given on the Lambda calculus page. The matching of expressions should compare expressions for alpha equivalence (r... | Let expression | 0.816355 |
13,302 | It is not sufficient for the form to represent only the set of values. Each value must have a condition that determines when the expression takes the value. The resulting construct is a set of pairs of conditions and values, called a "value set". See narrowing of algebraic value sets. | Let expression | 0.816355 |
13,303 | f ( x x ) ) {\displaystyle \lambda f. (\lambda x.x\ x)\ (\lambda x.f\ (x\ x))} This is possibly the simplest implementation of a fixed point combinator in lambda calculus. However one beta reduction gives the more symmetrical form of Curry's Y combinator. | Let expression | 0.816355 |
13,304 | In computer science, a "let" expression associates a function definition with a restricted scope. The "let" expression may also be defined in mathematics, where it associates a Boolean condition with a restricted scope. The "let" expression may be considered as a lambda abstraction applied to a value. Within mathematic... | Let expression | 0.816355 |
13,305 | Dana Scott's LCF language was a stage in the evolution of lambda calculus into modern functional languages. This language introduced the let expression, which has appeared in most functional languages since that time. The languages Scheme, ML, and more recently Haskell have inherited let expressions from LCF. Stateful ... | Let expression | 0.816355 |
13,306 | The Eta reduction gives a rule for describing lambda abstractions. This rule along with the two laws derived above define the relationship between lambda calculus and let expressions. | Let expression | 0.816355 |
13,307 | Another split example is given for a normal subgroup A with E set to the semidirect product A ⋊ G {\displaystyle A\rtimes G} . More serious examples are found in the theory of projective representations, in cases where the projective representation cannot be lifted to an ordinary linear representation. In the case of f... | Group extension | 0.816355 |
13,308 | These generators are in the center of e; by Noether's theorem, generators of symmetry groups correspond to conserved quantities, referred to as charges. The basic examples of central extensions as covering groups are: the spin groups, which double cover the special orthogonal groups, which (in even dimension) doubly co... | Group extension | 0.816355 |
13,309 | For example, when G∗ is the universal cover of G, the kernel of π is the fundamental group of G, which is known to be abelian (see H-space). Conversely, given a Lie group G and a discrete central subgroup Z, the quotient G/Z is a Lie group and G is a covering space of it. More generally, when the groups A, E and G occu... | Group extension | 0.816355 |
13,310 | In Lie group theory, central extensions arise in connection with algebraic topology. Roughly speaking, central extensions of Lie groups by discrete groups are the same as covering groups. More precisely, a connected covering space G∗ of a connected Lie group G is naturally a central extension of G, in such a way that t... | Group extension | 0.816355 |
13,311 | Mechatronics students take courses in various fields: Engineering Mathematics Mechanical engineering Electronics engineering Electrical engineering Materials science and engineering Computer engineering Computer aided and integrated manufacturing systems Computer-aided design Electronic design automation Computer Scien... | Mechatronic engineering | 0.816353 |
13,312 | Avionics is also considered a variant of mechatronics as it combines several fields such as electronics and telecom with Aerospace engineering. It is the subdiscipline of mechatronics engineering and aerospace engineering which is engineering branch focusing on electronics systems of aircraft. The word avionics is a bl... | Mechatronic engineering | 0.816353 |
13,313 | Telecommunications engineering deals with the transmission of information across a medium. Electronics engineering is related to computer engineering and electrical engineering. | Mechatronic engineering | 0.816353 |
13,314 | The branch of industrial engineer includes the design of machinery, assembly and process lines of various manufacturing industries. This branch can be said somewhat similar to automation and robotics. Mechatronics engineers who works as industrial engineers design and develop infrastructure of a manufacturing plant. Al... | Mechatronic engineering | 0.816353 |
13,315 | A large number of factories especially in automobile factories, robots are founds in assembly lines where they perform the job of drilling, installation and fitting. Programming skills are necessary for specialization in robotics. Knowledge of programming language —ROBOTC is important for functioning robots. An industr... | Mechatronic engineering | 0.816353 |
13,316 | Robotics is one of the newest emerging subfield of mechatronics. It is the study of robots that how they are manufactured and operated. Since 2000, this branch of mechatronics is attracting a number of aspirants. Robotics is interrelated with automation because here also not much human intervention is required. | Mechatronic engineering | 0.816353 |
13,317 | Machine vision Automation and robotics Servo-mechanics Sensing and control systems Automotive engineering, automotive equipment in the design of subsystems such as anti-lock braking systems Building automation / Home automation Computer-machine controls, such as computer driven machines like CNC milling machines, CNC w... | Mechatronic engineering | 0.816353 |
13,318 | The journal was created in response to the machine learning explosion of the 2010s. It launched in January 2019, and its opening was met with controversy and boycotts within the machine learning research community due to opposition to Nature publishing the journal as closed access. To address this issue, now Nature Mac... | Nature Machine Intelligence | 0.816352 |
13,319 | According to the Journal Citation Reports, the journal has a 2021 impact factor of 25.898, ranking it 1st out of 144 journals in the category "Computer Science, Artificial intelligence" and first out of 113 journals in the category "Computer Science, Interdisciplinary Applications". | Nature Machine Intelligence | 0.816352 |
13,320 | Nature Machine Intelligence is a monthly peer-reviewed scientific journal published by Nature Portfolio covering machine learning and artificial intelligence. The editor-in-chief is Liesbeth Venema. | Nature Machine Intelligence | 0.816352 |
13,321 | An RNN using LSTM units can be trained in a supervised fashion on a set of training sequences, using an optimization algorithm like gradient descent combined with backpropagation through time to compute the gradients needed during the optimization process, in order to change each weight of the LSTM network in proportio... | Long short term memory | 0.81635 |
13,322 | This has become the most cited neural network of the 21st century.2016: Google started using an LSTM to suggest messages in the Allo conversation app. In the same year, Google released the Google Neural Machine Translation system for Google Translate which used LSTMs to reduce translation errors by 60%.Apple announced ... | Long short term memory | 0.81635 |
13,323 | This was the first time an RNN won international competitions.2009: Justin Bayer et al. introduced neural architecture search for LSTM.2013: Alex Graves, Abdel-rahman Mohamed, and Geoffrey Hinton used LSTM networks as a major component of a network that achieved a record 17.7% phoneme error rate on the classic TIMIT na... | Long short term memory | 0.81635 |
13,324 | CTC-trained LSTM led to breakthroughs in speech recognition.Mayer et al. trained LSTM to control robots.2007: Wierstra, Foerster, Peters, and Schmidhuber trained LSTM by policy gradients for reinforcement learning without a teacher.Hochreiter, Heuesel, and Obermayr applied LSTM to protein homology detection the field o... | Long short term memory | 0.81635 |
13,325 | Long short-term memory (LSTM) network is a recurrent neural network (RNN), aimed to deal with the vanishing gradient problem present in traditional RNNs. Its relative insensitivity to gap length is its advantage over other RNNs, hidden Markov models and other sequence learning methods. It aims to provide a short-term m... | Long short term memory | 0.81635 |
13,326 | In other words, the network effectively learns which information might be needed later on in a sequence and when that information is no longer needed. For instance, in the context of natural language processing, the network can learn grammatical dependencies. An LSTM might process the sentence "Dave, as a result of his... | Long short term memory | 0.81635 |
13,327 | In theory, classic (or "vanilla") RNNs can keep track of arbitrary long-term dependencies in the input sequences. The problem with vanilla RNNs is computational (or practical) in nature: when training a vanilla RNN using back-propagation, the long-term gradients which are back-propagated can "vanish" (that is, they can... | Long short term memory | 0.81635 |
13,328 | The Hadwiger conjecture, that k-chromatic graphs necessarily contain k-vertex complete graphs as minors, has also been studied from the point of view of odd minors.A different parity-based extension of the notion of graph minors is the concept of a bipartite minor, which produces a bipartite graph whenever the starting... | Graph minor | 0.816346 |
13,329 | These graphs are forbidden minors for F: a graph belongs to F if and only if it does not contain as a minor any graph in X. That is, every minor-closed family F can be characterized as the family of X-minor-free graphs for some finite set X of forbidden minors. The best-known example of a characterization of this type ... | Graph minor | 0.816346 |
13,330 | Combinatorial principles Trial and error, brute-force search, bogosort, British Museum algorithm Pigeonhole principle Method of distinguished element Mathematical induction Recurrence relation, telescoping series Generating functions as an application of formal power series Cyclic sieving Schrödinger method Exponential... | Outline of combinatorics | 0.816336 |
13,331 | Data structure Data type Abstract data type Algebraic data type Composite type Array Associative array Deque List Linked list Queue Priority queue Skip list Stack Tree data structure Automatic garbage collection | Outline of combinatorics | 0.816336 |
13,332 | Advances in Combinatorics Annals of Combinatorics Ars Combinatoria Australasian Journal of Combinatorics Bulletin of the Institute of Combinatorics and Its Applications Combinatorica Combinatorics, Probability and Computing Computational Complexity Designs, Codes and Cryptography Discrete Analysis Discrete and Computat... | Outline of combinatorics | 0.816336 |
13,333 | Coding theory Combinatorial optimization Combinatorics and dynamical systems Combinatorics and physics Discrete geometry Finite geometry Phylogenetics | Outline of combinatorics | 0.816336 |
13,334 | Algebraic combinatorics Analytic combinatorics Arithmetic combinatorics Combinatorics on words Combinatorial design theory Enumerative combinatorics Extremal combinatorics Geometric combinatorics Graph theory Infinitary combinatorics Matroid theory Order theory Partition theory Probabilistic combinatorics Topological c... | Outline of combinatorics | 0.816336 |
13,335 | Matroid Greedoid Ramsey theory Van der Waerden's theorem Hales–Jewett theorem Umbral calculus, binomial type polynomial sequences Combinatorial species | Outline of combinatorics | 0.816336 |
13,336 | A multilayer perceptron (MLP) is a misnomer for a modern feedforward artificial neural network, consisting of fully connected neurons with a nonlinear kind of activation function, organized in at least three layers, notable for being able to distinguish data that is not linearly separable. It is a misnomer because the ... | Multilayer perceptron | 0.816335 |
13,337 | been introduced.In 2021, a very simple NN architecture combining two deep MLPs with skip connections and layer normalizations was designed and called MLP-Mixer; its realizations featuring 19 to 431 millions of parameters were shown to be comparable to vision transformers of similar size on ImageNet and similar image cl... | Multilayer perceptron | 0.816335 |
13,338 | In 1958, a layered network of perceptrons, consisting of an input layer, a hidden layer with randomized weights that did not learn, and an output layer with learning connections, was introduced already by Frank Rosenblatt in his book Perceptron. This extreme learning machine was not yet a deep learning network.In 1965,... | Multilayer perceptron | 0.816335 |
13,339 | Here y i {\displaystyle y_{i}} is the output of the i {\displaystyle i} th node (neuron) and v i {\displaystyle v_{i}} is the weighted sum of the input connections. Alternative activation functions have been proposed, including the rectifier and softplus functions. More specialized activation functions include radial b... | Multilayer perceptron | 0.816335 |
13,340 | If a multilayer perceptron has a linear activation function in all neurons, that is, a linear function that maps the weighted inputs to the output of each neuron, then linear algebra shows that any number of layers can be reduced to a two-layer input-output model. In MLPs some neurons use a nonlinear activation functio... | Multilayer perceptron | 0.816335 |
13,341 | The dramatic, rhythmic twisting that resulted in the 1940 collapse of "Galloping Gertie", the original Tacoma Narrows Bridge, is sometimes characterized in physics textbooks as a classic example of resonance. The catastrophic vibrations that destroyed the bridge were due to an oscillation caused by interactions between... | Mechanical resonance | 0.816331 |
13,342 | Powders are a special class of granular material due to their small particle size, which makes them more cohesive and more easily suspended in a gas. The soldier/physicist Brigadier Ralph Alger Bagnold was an early pioneer of the physics of granular matter and whose book The Physics of Blown Sand and Desert Dunes remai... | Granular Material | 0.816331 |
13,343 | A granular material is a conglomeration of discrete solid, macroscopic particles characterized by a loss of energy whenever the particles interact (the most common example would be friction when grains collide). The constituents that compose granular material are large enough such that they are not subject to thermal m... | Granular Material | 0.816331 |
13,344 | In parallel computing, the Geometric Arithmetic Parallel Processor (GAPP), invented by Polish mathematician Włodzimierz Holsztyński in 1981, was patented by Martin Marietta and is now owned by Silicon Optix, Inc. The GAPP's network topology is a mesh-connected array of single-bit SIMD processing elements (PEs), where e... | Geometric Arithmetic Parallel Processor | 0.816326 |
13,345 | In mathematics and physics, the diamagnetic inequality relates the Sobolev norm of the absolute value of a section of a line bundle to its covariant derivative. The diamagnetic inequality has an important physical interpretation, that a charged particle in a magnetic field has more energy in its ground state than it wo... | Diamagnetic inequality | 0.816319 |
13,346 | The LINPACK benchmark report appeared first in 1979 as an appendix to the LINPACK user's manual.LINPACK was designed to help users estimate the time required by their systems to solve a problem using the LINPACK package, by extrapolating the performance results obtained by 23 different computers solving a matrix proble... | LINPACK benchmarks | 0.816315 |
13,347 | The performance of a computer is a complex issue that depends on many interconnected variables. The performance measured by the LINPACK benchmark consists of the number of 64-bit floating-point operations, generally additions and multiplications, a computer can perform per second, also known as FLOPS. However, a comput... | LINPACK benchmarks | 0.816315 |
13,348 | Unlike the above solution concepts, no player's strategy is strictly dominated beginning at any information set even if it is off the equilibrium path. Thus in PBE, players cannot threaten to play strategies that are strictly dominated beginning at any information set off the equilibrium path. The Bayesian in the name ... | Equilibrium concept | 0.816315 |
13,349 | The operator is required to amputate a cockroach's antennae, use sandpaper to wear down the shell, insert a wire into the thorax, and then glue the electrodes and circuit board onto the insect's back. A mobile phone app can then be used to control it via Bluetooth. It has been suggested that the use of such a device ma... | Animal test | 0.816311 |
13,350 | Working memory capacity is correlated with learning outcomes in literacy and numeracy. Initial evidence for this relation comes from the correlation between working-memory capacity and reading comprehension, as first observed by Daneman and Carpenter (1980) and confirmed in a later meta-analytic review of several studi... | Working Memory | 0.81631 |
13,351 | Studies in the Neo-Piagetian tradition have added to this picture by analyzing the complexity of cognitive tasks in terms of the number of items or relations that have to be considered simultaneously for a solution. Across a broad range of tasks, children manage task versions of the same level of complexity at about th... | Working Memory | 0.81631 |
13,352 | Working memory is a cognitive system with a limited capacity that can hold information temporarily. It is important for reasoning and the guidance of decision-making and behavior. Working memory is often used synonymously with short-term memory, but some theorists consider the two forms of memory distinct, assuming tha... | Working Memory | 0.81631 |
13,353 | In theoretical computer science, almost wide probabilistic polynomial-time (AWPP) is a complexity class contained in PP defined via GapP functions. The class often arises in the context of quantum computing. AWPP contains the complexity class BQP (bounded-error quantum polynomial time), which contains the decision prob... | Almost Wide Probabilistic Polynomial-Time | 0.81631 |
13,354 | Let ( Ω , A , P ) {\displaystyle (\Omega ,{\mathcal {A}},\mathbb {P} )} be a probability space. Recall that the conditional probability of an A ∈ A {\displaystyle A\in {\mathcal {A}}} given B ∈ A {\displaystyle B\in {\mathcal {A}}} is defined as P ( A ∣ B ) := { P ( A ∩ B ) P ( B ) , P ( B ) > 0 , 0 P ( B ) = 0. {\disp... | Chain rule (probability) | 0.816305 |
13,355 | In probability theory, the chain rule (also called the general product rule) describes how to calculate the probability of the intersection of, not necessarily independent, events or the joint distribution of random variables respectively, using conditional probabilities. The rule is notably used in the context of disc... | Chain rule (probability) | 0.816305 |
13,356 | It is these infinitesimal transformations that generate a Lie algebra that is used to describe a Lie group of any dimension. The action of a one-parameter group on a set is known as a flow. A smooth vector field on a manifold, at a point, induces a local flow - a one parameter group of local diffeomorphisms, sending po... | 1-parameter group | 0.816298 |
13,357 | In the case at hand, heating acetate (1) with chloranil gives the conjugated dienone (2), and reaction of that compound with methylmagnesium bromide in the presence of cuprous chloride leads to addition of the methyl group to position 7 at the end of the conjugated system (3). The stereochemistry of the product again i... | Mibolerone | 0.816297 |
13,358 | A 2D lattice is a regular array of isolated points where if any one point is chosen as the Cartesian origin (0, 0), then all the other points are at (x, y) where x and y range over all positive and negative integers. A lattice triangle is any triangle drawn within a 2D lattice such that all vertices lie on lattice poin... | Rational triangle | 0.816293 |
13,359 | The institute opened in July 2000 in space in the Virginia Tech Corporate Research Center; it was hosted briefly in Building XI, then Building X, until it moved to Building XV in 2002, which was designed to host the institute. In January 2005, it moved into a new building on the main Virginia Tech's campus, called "Bio... | Biocomplexity Institute of Virginia Tech | 0.81629 |
13,360 | The Biocomplexity Institute of Virginia Tech (formerly the Virginia Bioinformatics Institute) is a research organization specializing in bioinformatics, computational biology, and systems biology. The institute has more than 250 personnel, including over 50 tenured and research faculty. Research at the institute involv... | Biocomplexity Institute of Virginia Tech | 0.81629 |
13,361 | It developed COPASI (Complex Pathway Simulator), an open-source software package that allows users with limited experience in mathematics to construct models and simulations of biochemical networks. It also developed GenoCAD, a web-based Computer Assisted Design environment for synthetic biology. The Medical Informatic... | Biocomplexity Institute of Virginia Tech | 0.81629 |
13,362 | The Cyberinfrastructure Division develops methods, infrastructure, and resources primarily for infectious disease research. The “Pathosystems Resource Integration Center - Bioinformatics Resource Center for Bacterial Diseases” aims to integrate information on pathogens, provide resources and tools to analyze genomic, p... | Biocomplexity Institute of Virginia Tech | 0.81629 |
13,363 | K–12 programs include "Kids' Tech University," (an educational research program for sparking interest in science, technology, engineering, and mathematics disciplines), the Climate Change Student Summit for teachers and students, and high school summer internships. Undergraduate Programs include Research Experiences fo... | Biocomplexity Institute of Virginia Tech | 0.81629 |
13,364 | According to the Hodge theorem, h 0 , 1 = h 1 , 0 {\displaystyle h^{0,1}=h^{1,0}} . Consequently h 0 , 1 = h 1 ( X ) / 2 = g {\displaystyle h^{0,1}=h^{1}(X)/2=g} , where g is the usual (topological) meaning of genus of a surface, so the definitions are compatible. When X is a compact Kähler manifold, applying hp,q = hq... | Arithmetic genus | 0.816287 |
13,365 | In mathematics, the arithmetic genus of an algebraic variety is one of a few possible generalizations of the genus of an algebraic curve or Riemann surface. | Arithmetic genus | 0.816287 |
13,366 | The Mathematical Experience (1981) is a book by Philip J. Davis and Reuben Hersh that discusses the practice of modern mathematics from a historical and philosophical perspective. The book discusses the psychology of mathematicians, and gives examples of famous proofs and outstanding problems. It goes on to speculate a... | The Mathematical Experience | 0.816286 |
13,367 | At the same time, in geometry and computer graphics there are a number of concepts to replace the notion of the "interior" for closed non-simple curves; see, e.g., "flood fill" and "winding number". In "mild" cases of self-intersection, with degenerate vertices when three consecutive points are allowed be on the same s... | Curve orientation | 0.816286 |
13,368 | In trigonometry, the unit circle is traditionally oriented counterclockwise. The concept of orientation of a curve is just a particular case of the notion of orientation of a manifold (that is, besides orientation of a curve one may also speak of orientation of a surface, hypersurface, etc.). Orientation of a curve is ... | Curve orientation | 0.816286 |
13,369 | This definition relies on the fact that every simple closed curve admits a well-defined interior, which follows from the Jordan curve theorem. The inner loop of a beltway road in a country where people drive on the right side of the road is an example of a negatively oriented (clockwise) curve. | Curve orientation | 0.816286 |
13,370 | Woodland Park High School chemistry teachers Jonathan Bergmann and Aaron Sams began practicing flipped teaching at the high school level when, in 2007, they recorded their lectures and posted them online to accommodate students who missed their classes. They note that one person cannot be credited with having invented ... | Flipped classroom | 0.816285 |
13,371 | He found that his approach, which moved information transfer out of the classroom and information assimilation into the classroom, allowed him to coach students in their learning instead of lecture.Lage, Platt and Treglia published a paper entitled "Inverting the Classroom: A Gateway to Creating an Inclusive Learning E... | Flipped classroom | 0.816285 |
13,372 | Along with practice problems, labs were also completed during regular class time, and workshops about choosing the appropriate approach, order and technique were implemented. Study materials for tests were administered through the videos to prepare students for assessments. In the chemistry setting, only certain topics... | Flipped classroom | 0.816285 |
13,373 | In other classrooms, students have also been encouraged by their professors to attend other public lectures to gain more information. Chemistry: In a chemistry class in Glenview, IL, pre-lecture materials were distributed through Moodle and YouTube. In class, students independently completed problems while the professo... | Flipped classroom | 0.816285 |
13,374 | Some classes included software that combined all of the resources accessible by students for the material that was assigned outside of the class period. The software also included small tests to assess a student's understanding of video material. Physics: In one instance, the flipped classroom technique was implemented... | Flipped classroom | 0.816285 |
13,375 | In the language of Heisenberg's matrix mechanics, the hydrogen atom was first solved by Wolfgang Pauli using a rotational symmetry in four dimensions generated by the angular momentum and the Laplace–Runge–Lenz vector. By extending the symmetry group O(4) to the dynamical group O(4,2), the entire spectrum and all tran... | Atomic hydrogen | 0.816281 |
13,376 | Reciprocal length or inverse length is a quantity or measurement used in several branches of science and mathematics. As the reciprocal of length, common units used for this measurement include the reciprocal metre or inverse metre (symbol: m−1), the reciprocal centimetre or inverse centimetre (symbol: cm−1). Quantitie... | Reciprocal meter | 0.816277 |
13,377 | A conceptual graph (CG) is a notation for logic based on the existential graphs of Charles Sanders Peirce and the semantic networks of artificial intelligence. In the first published paper on conceptual graphs, John F. Sowa used them to represent the conceptual schemas used in database systems. His first book applied t... | Diagrammatic Reasoning | 0.81627 |
13,378 | Diagrammatic reasoning is reasoning by means of visual representations. The study of diagrammatic reasoning is about the understanding of concepts and ideas, visualized with the use of diagrams and imagery instead of by linguistic or algebraic means. | Diagrammatic Reasoning | 0.81627 |
13,379 | Characteristica universalis, commonly interpreted as universal characteristic, or universal character in English, is a universal and formal language imagined by the German philosopher Gottfried Leibniz able to express mathematical, scientific, and metaphysical concepts. Leibniz thus hoped to create a language usable wi... | Diagrammatic Reasoning | 0.81627 |
13,380 | The semantics are: The blank page denotes Truth; Letters, phrases, subgraphs, and entire graphs may be True or False; To enclose a subgraph with a cut is equivalent to logical negation or Boolean complementation. Hence an empty cut denotes False; All subgraphs within a given cut are tacitly conjoined.Hence the alpha gr... | Diagrammatic Reasoning | 0.81627 |
13,381 | An existential graph is a type of diagrammatic or visual notation for logical expressions, proposed by Charles Sanders Peirce, who wrote his first paper on graphical logic in 1882 and continued to develop the method until his death in 1914. Peirce proposed three systems of existential graphs: alpha – isomorphic to sent... | Diagrammatic Reasoning | 0.81627 |
13,382 | The mathematical equation for such algorithms is presented in US patent 9269353: R M M ( t o k e n N ) = P M M ( t o k e n N ) × 1 2 d ( ∑ i = − d d ( ( P M M ( t o k e n N − 1 ) × P F ( t o k e n N , t o k e n N − 1 ) ) i ) {\displaystyle {RMM(token_{N})}={PMM(token_{N})}\times {\frac {1}{2d}}\left(\sum _{i=-d}^{d}{((... | Natural Language Processing | 0.81627 |
13,383 | As an example, George Lakoff offers a methodology to build natural language processing (NLP) algorithms through the perspective of cognitive science, along with the findings of cognitive linguistics, with two defining aspects: Apply the theory of conceptual metaphor, explained by Lakoff as "the understanding of one ide... | Natural Language Processing | 0.81627 |
13,384 | Memory allocation is a process that determines which specific synapses and neurons in a neural network will store a given memory. Although multiple neurons can receive a stimulus, only a subset of the neurons will induce the necessary plasticity for memory encoding. The selection of this subset of neurons is termed neu... | Neuronal memory allocation | 0.816267 |
13,385 | In organic chemistry, the Schmidt reaction is an organic reaction in which an azide reacts with a carbonyl derivative, usually an aldehyde, ketone, or carboxylic acid, under acidic conditions to give an amine or amide, with expulsion of nitrogen. It is named after Karl Friedrich Schmidt (1887–1971), who first reported ... | Schmidt reaction | 0.816266 |
13,386 | This volume attempts to formulate certain patterns of plausible reasoning. The relations of these patterns with the calculus of probability are also investigated. Their relation to mathematical invention and instruction are also discussed. The following are some of the patterns of plausible inference discussed by Polya... | Plausible reasoning | 0.816265 |
13,387 | If the graph is a metric space then there is an efficient approximation algorithm that finds a Hamiltonian cycle with maximum edge weight being no more than twice the optimum. This result follows by Fleischner's theorem, that the square of a 2-vertex-connected graph always contains a Hamiltonian cycle. It is easy to fi... | Bottleneck traveling salesman problem | 0.816258 |
13,388 | The Bottleneck traveling salesman problem (bottleneck TSP) is a problem in discrete or combinatorial optimization. The problem is to find the Hamiltonian cycle (visiting each node exactly once) in a weighted graph which minimizes the weight of the highest-weight edge of the cycle. It was first formulated by Gilmore & G... | Bottleneck traveling salesman problem | 0.816258 |
13,389 | A simple example of an algebraic function is given by the left side of the unit circle equation: x 2 + y 2 − 1 = 0 . {\displaystyle x^{2}+y^{2}-1=0\,.} Solving for y gives an explicit solution: y = ± 1 − x 2 . | Implicit equation | 0.816254 |
13,390 | An algebraic function is a function that satisfies a polynomial equation whose coefficients are themselves polynomials. For example, an algebraic function in one variable x gives a solution for y of an equation a n ( x ) y n + a n − 1 ( x ) y n − 1 + ⋯ + a 0 ( x ) = 0 , {\displaystyle a_{n}(x)y^{n}+a_{n-1}(x)y^{n-1}+\c... | Implicit equation | 0.816254 |
13,391 | Often in economic theory, some function such as a utility function or a profit function is to be maximized with respect to a choice vector x even though the objective function has not been restricted to any specific functional form. The implicit function theorem guarantees that the first-order conditions of the optimiz... | Implicit equation | 0.816254 |
13,392 | Historically, ideas from linear programming have inspired many of the central concepts of optimization theory, such as duality, decomposition, and the importance of convexity and its generalizations. Likewise, linear programming was heavily used in the early formation of microeconomics, and it is currently utilized in ... | LP problem | 0.816247 |
13,393 | Linear programming is a widely used field of optimization for several reasons. Many practical problems in operations research can be expressed as linear programming problems. Certain special cases of linear programming, such as network flow problems and multicommodity flow problems, are considered important enough to h... | LP problem | 0.816247 |
13,394 | Let G and H be groups, let P = G × H, and consider the following two subsets of P: G′ = { (g, 1): g ∈ G } and H′ = { (1, h): h ∈ H }.Both of these are in fact subgroups of P, the first being isomorphic to G, and the second being isomorphic to H. If we identify these with G and H, respectively, then we can think of the ... | Direct product (group theory) | 0.816243 |
13,395 | In mathematics, specifically in group theory, the direct product is an operation that takes two groups G and H and constructs a new group, usually denoted G × H. This operation is the group-theoretic analogue of the Cartesian product of sets and is one of several important notions of direct product in mathematics. In t... | Direct product (group theory) | 0.816243 |
13,396 | The algebraic structure of G × H can be used to give a presentation for the direct product in terms of the presentations of G and H. Specifically, suppose that G = ⟨ S G ∣ R G ⟩ {\displaystyle G=\langle S_{G}\mid R_{G}\rangle \ \ } and H = ⟨ S H ∣ R H ⟩ , {\displaystyle \ \ H=\langle S_{H}\mid R_{H}\rangle ,} where S G... | Direct product (group theory) | 0.816243 |
13,397 | MUltiple Sequence Comparison by Log-Expectation (MUSCLE) is computer software for multiple sequence alignment of protein and nucleotide sequences. It is licensed as public domain. The method was published by Robert C. Edgar in two papers in 2004. The first paper, published in Nucleic Acids Research, introduced the sequ... | Multiple Sequence Comparison by Log-Expectation | 0.816243 |
13,398 | MUSCLE is integrated into DNASTAR's Lasergene software, Geneious, and MacVector and is available in Sequencher, MEGA, and UGENE as a plug-in. MUSCLE is also available as a web service via the European Molecular Biology Laboratory (EMBL)-European Bioinformatics Institute (EBI). As of September 2016, the two papers descr... | Multiple Sequence Comparison by Log-Expectation | 0.816243 |
13,399 | In computer science, a 4D vector is a 4-component vector data type. Uses include homogeneous coordinates for 3-dimensional space in computer graphics, and red green blue alpha (RGBA) values for bitmap images with a color and alpha channel (as such they are widely used in computer graphics). They may also represent quat... | 4D vector | 0.816241 |
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