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9,800 | TensorFlow is an open source software library powered by Google Brain that allows anyone to utilize machine learning by providing the tools to train one's own neural network. The tool has been used by farmers to reduce the amount of manual labor required to sort their yield, by training it with a data set of human-sort... | Google Brain | 0.819759 |
9,801 | The 1-center problem, also known as minimax problem or minmax location problem, is a classical combinatorial optimization problem in operations research of facilities location type. In its most general case the problem is stated as follows: given a set of n demand points, a space of feasible locations of a facility and... | 1-center problem | 0.819754 |
9,802 | See for example Cartan's theorems A and B, relating to sheaf cohomology. In the GAGA set of analogies, Stein manifolds correspond to affine varieties.Stein manifolds are in some sense dual to the elliptic manifolds in complex analysis which admit "many" holomorphic functions from the complex numbers into themselves. It... | Several complex variables | 0.819752 |
9,803 | Every Stein manifold of (complex) dimension n has the homotopy type of an n-dimensional CW-Complex. In one complex dimension the Stein condition can be simplified: a connected Riemann surface is a Stein manifold if and only if it is not compact. This can be proved using a version of the Runge theorem for Riemann surfac... | Several complex variables | 0.819752 |
9,804 | The standard complex space C n {\displaystyle \mathbb {C} ^{n}} is a Stein manifold. Every domain of holomorphy in C n {\displaystyle \mathbb {C} ^{n}} is a Stein manifold. It can be shown quite easily that every closed complex submanifold of a Stein manifold is a Stein manifold, too. The embedding theorem for Stein ma... | Several complex variables | 0.819752 |
9,805 | From the establishment of the inverse function theorem, the following mapping can be defined. For the domain U, V of the n-dimensional complex space C n {\displaystyle \mathbb {C} ^{n}} , the bijective holomorphic function ϕ: U → V {\displaystyle \phi :U\to V} and the inverse mapping ϕ − 1: V → U {\displaystyle \phi ^{... | Several complex variables | 0.819752 |
9,806 | Broadly, the GAGA principle says that the geometry of projective complex analytic spaces (or manifolds) is equivalent to the geometry of projective complex varieties. The combination of analytic and algebraic methods for complex projective varieties lead to areas such as Hodge theory. Also, the deformation theory of co... | Several complex variables | 0.819752 |
9,807 | Then combined with Kodaira's result, a compact Kähler manifold M embeds as an algebraic variety. This gives an example of a complex manifold with enough meromorphic functions. Similarities in the Levi problems on the complex projective space C P n {\displaystyle \mathbb {CP} ^{n}} , have been proved in some patterns, f... | Several complex variables | 0.819752 |
9,808 | The Kodaira vanishing theorem (1954) and its generalization Nakano vanishing theorem etc. gives the condition, when the sheaf cohomology group vanishing, and the condition is to satisfy a kind of positivity. As an example given by this theorem, Kodaira embedding theorem says that a compact Kähler manifold M, with a Hod... | Several complex variables | 0.819752 |
9,809 | Cartan–Serre proved the following property: the cohomology group is finite-dimensional for a coherent sheaf on a compact complex manifold M. Riemann–Roch on a Riemann surface for a vector bundle was proved by Weil in 1938.Hirzebruch generalized the theorem to compact complex manifolds in 1994 and Grothendieck generaliz... | Several complex variables | 0.819752 |
9,810 | However, there is a Siegel result that gives the necessary conditions for compact complex manifolds to be algebraic. The generalization of the Riemann-Roch theorem to several complex variables was first extended to compact analytic surfaces by Kodaira, Kodaira also extended the theorem to three-dimensional, and n-dimen... | Several complex variables | 0.819752 |
9,811 | ), but it is not easy to verify which compact complex analytic spaces are algebraizable. In fact, Hopf found a class of compact complex manifolds without nonconstant meromorphic functions. | Several complex variables | 0.819752 |
9,812 | Meromorphic function in one-variable complex function were studied in a compact (closed) Riemann surface, because since the Riemann-Roch theorem (Riemann's inequality) holds for compact Riemann surfaces (Therefore the theory of compact Riemann surface can be regarded as the theory of (smooth (non-singular) projective) ... | Several complex variables | 0.819752 |
9,813 | The classical candidates are the Hilbert modular forms and Siegel modular forms. These days these are associated to algebraic groups (respectively the Weil restriction from a totally real number field of GL(2), and the symplectic group), for which it happens that automorphic representations can be derived from analytic... | Several complex variables | 0.819752 |
9,814 | The celebrated paper GAGA of Serre pinned down the crossover point from géometrie analytique to géometrie algébrique. C. L. Siegel was heard to complain that the new theory of functions of several complex variables had few functions in it, meaning that the special function side of the theory was subordinated to sheaves... | Several complex variables | 0.819752 |
9,815 | In fact it was the need to put (in particular) the work of Oka on a clearer basis that led quickly to the consistent use of sheaves for the formulation of the theory (with major repercussions for algebraic geometry, in particular from Grauert's work). From this point onwards there was a foundational theory, which could... | Several complex variables | 0.819752 |
9,816 | This means that the residue calculus will have to take a very different character. After 1945 important work in France, in the seminar of Henri Cartan, and Germany with Hans Grauert and Reinhold Remmert, quickly changed the picture of the theory. A number of issues were clarified, in particular that of analytic continu... | Several complex variables | 0.819752 |
9,817 | Many examples of such functions were familiar in nineteenth-century mathematics; abelian functions, theta functions, and some hypergeometric series, and also, as an example of an inverse problem; the Jacobi inversion problem. Naturally also same function of one variable that depends on some complex parameter is a candi... | Several complex variables | 0.819752 |
9,818 | Let K be the sheaf of meromorphic functions and O the sheaf of holomorphic functions on M. If the next map is surjective, Cousin first problem can be solved. H 0 ( M , K ) → ϕ H 0 ( M , K / O ) . {\displaystyle H^{0}(M,\mathbf {K} ){\xrightarrow {\phi }}H^{0}(M,\mathbf {K} /\mathbf {O} ).} By the long exact cohomology ... | Several complex variables | 0.819752 |
9,819 | Baker and co-workers justified statistical PMFs from a Bayesian point of view and used these insights in the construction of the coarse grained ROSETTA energy function. According to Bayesian probability calculus, the conditional probability P ( X ∣ A ) {\displaystyle P(X\mid A)} of a structure X {\displaystyle X} , giv... | Statistical potential | 0.81975 |
9,820 | Expressions that resemble statistical PMFs naturally result from the application of probability theory to solve a fundamental problem that arises in protein structure prediction: how to improve an imperfect probability distribution Q ( X ) {\displaystyle Q(X)} over a first variable X {\displaystyle X} using a probabili... | Statistical potential | 0.819749 |
9,821 | Possible features to which a pseudo-energy can be assigned include: interatomic distances, torsion angles, solvent exposure, or hydrogen bond geometry.The classic application is, however, based on pairwise amino acid contacts or distances, thus producing statistical interatomic potentials. For pairwise amino acid conta... | Statistical potential | 0.819749 |
9,822 | In the mid-2000s, authors started to combine multiple statistical potentials, derived from different structural features, into composite scores. For that purpose, they used machine learning techniques, such as support vector machines (SVMs). Probabilistic neural networks (PNNs) have also been applied for the training o... | Statistical potential | 0.819749 |
9,823 | The two-particle potential of mean force W ( r ) {\displaystyle W(r)} is related to g ( r ) {\displaystyle g(r)} by: W ( r ) = − k T log g ( r ) = − k T log P ( r ) Q R ( r ) {\displaystyle W(r)=-kT\log g(r)=-kT\log {\frac {P(r)}{Q_{R}(r)}}} According to the reversible work theorem, the two-particle potential of me... | Statistical potential | 0.819749 |
9,824 | In response to the issue regarding the physical validity, the first justification of statistical PMFs was attempted by Sippl. It was based on an analogy with the statistical physics of liquids. For liquids, the potential of mean force is related to the radial distribution function g ( r ) {\displaystyle g(r)} , which i... | Statistical potential | 0.819749 |
9,825 | of particles with collective long range interaction. 1939 – Nikolay Krylov and Nikolay Bogolyubov give the first consistent microscopic derivation of the Fokker–Planck equation in the single scheme of classical and quantum mechanics 1942 – Joseph L. Doob states his theorem on Gauss–Markov processes 1944 – Lars Onsager ... | Timeline of thermodynamics | 0.819746 |
9,826 | 1900 – Max Planck suggests that light may be emitted in discrete frequencies, giving his law of black-body radiation 1905 – Albert Einstein, in the first of his miracle year papers, argues that the reality of quanta would explain the photoelectric effect 1905 – Einstein mathematically analyzes Brownian motion as a resu... | Timeline of thermodynamics | 0.819746 |
9,827 | Species sorting is a mechanism in the metacommunity framework of ecology whereby species distributions and abundances can be related to the environmental or biotic conditions in a particular habitat. The species sorting paradigm describes a system of habitat patches with different environmental conditions that organism... | Species sorting | 0.819744 |
9,828 | The distance between the surfaces at the point of closest approach varies between a few micrometers to a few nanometers depending on the apparatus. When the two curved cylinders have the same radius of curvature, R, this so-called 'crossed cylinders' geometry is mathematically equivalent to the interaction between a fl... | Surface force apparatus | 0.819744 |
9,829 | The geometry is published by the institution proposing the model. Beside the model itself, a standard model support, such as a sting, to be used with the model, is usually defined. An actual model is built to a size suitable for the size of a specific wind tunnel test section, in particular taking care that the frontal... | Standard wind tunnel models | 0.819744 |
9,830 | For dynamic tests, the often-used standard models are: SDM (Standard dynamic model, a generic fighter-like airplane shape somewhat similar to F-16)), BFM (Basic finner model, a generic conical-cylindrical missile with four fins at the rear end) and MBFM (Modified basic finner model). A number of other standard models e... | Standard wind tunnel models | 0.819744 |
9,831 | In 499 CE Aryabhata, used this illustrated method in the Aryabhatiya (section 2.6).Although simple, this formula is only useful if the height can be readily found, which is not always the case. For example, the land surveyor of a triangular field might find it relatively easy to measure the length of each side, but rel... | Area of a triangle | 0.819738 |
9,832 | In geometry, calculating the area of a triangle is an elementary problem encountered often in many different situations. The best known and simplest formula is T = b h / 2 , {\displaystyle T=bh/2,} where b is the length of the base of the triangle, and h is the height or altitude of the triangle. The term "base" denote... | Area of a triangle | 0.819738 |
9,833 | Heron of Alexandria found what is known as Heron's formula for the area of a triangle in terms of its sides, and a proof can be found in his book, Metrica, written around 60 CE. It has been suggested that Archimedes knew the formula over two centuries earlier, and since Metrica is a collection of the mathematical knowl... | Area of a triangle | 0.819738 |
9,834 | The area within any closed curve, such as a triangle, is given by the line integral around the curve of the algebraic or signed distance of a point on the curve from an arbitrary oriented straight line L. Points to the right of L as oriented are taken to be at negative distance from L, while the weight for the integral... | Area of a triangle | 0.819738 |
9,835 | See Pick's theorem for a technique for finding the area of any arbitrary lattice polygon (one drawn on a grid with vertically and horizontally adjacent lattice points at equal distances, and with vertices on lattice points). The theorem states: T = I + 1 2 B − 1 {\displaystyle T=I+{\tfrac {1}{2}}B-1} where I {\displays... | Area of a triangle | 0.819738 |
9,836 | Some logic can be written without branches or with fewer branches. It is often possible to use bitwise operations, conditional moves or other predication instead of branches. In fact, branch-free code is a must for cryptography due to timing attacks. | Branch-free code | 0.819737 |
9,837 | {\displaystyle x|(y\mid (x\mid z))=((z\mid y)\mid y)\mid x.} In 1973, Padmanabhan and Quackenbush demonstrated a method that, in principle, would yield a 1-basis for Boolean algebra. | Minimal axioms for Boolean algebra | 0.819735 |
9,838 | The conjecture was eventually proved in 1996 with the aid of theorem-proving software. This proof established that the Robbins axiom, together with associativity and commutativity, form a 3-basis for Boolean algebra. The existence of a 2-basis was established in 1967 by Carew Arthur Meredith: ¬ ( ¬ x ∨ y ) ∨ x = x , {\... | Minimal axioms for Boolean algebra | 0.819735 |
9,839 | McCune et al. also found a longer single axiom for Boolean algebra based on disjunction and negation.In 1933, Edward Vermilye Huntington identified the axiom ¬ ( ¬ x ∨ y ) ∨ ¬ ( ¬ x ∨ ¬ y ) = x {\displaystyle {\neg ({\neg x}\lor {y})}\lor {\neg ({\neg x}\lor {\neg y})}=x} as being equivalent to Boolean algebra, when co... | Minimal axioms for Boolean algebra | 0.819735 |
9,840 | In mathematical logic, minimal axioms for Boolean algebra are assumptions which are equivalent to the axioms of Boolean algebra (or propositional calculus), chosen to be as short as possible. For example, if one chooses to take commutativity for granted, an axiom with six NAND operations and three variables is equivale... | Minimal axioms for Boolean algebra | 0.819735 |
9,841 | Expanding the right-hand-side using the product rule from differential calculus, this becomes α = 1 r d v ⊥ d t − v ⊥ r 2 d r d t . {\displaystyle \alpha ={\frac {1}{r}}{\frac {dv_{\perp }}{dt}}-{\frac {v_{\perp }}{r^{2}}}{\frac {dr}{dt}}.} In the special case where the particle undergoes circular motion about the orig... | Angular acceleration | 0.819726 |
9,842 | In physics, angular acceleration (symbol α, alpha) is the time rate of change of angular velocity. Following the two types of angular velocity, spin angular velocity and orbital angular velocity, the respective types of angular acceleration are: spin angular acceleration, involving a rigid body about an axis of rotatio... | Angular acceleration | 0.819726 |
9,843 | MathSciNet contains information on over 3 million articles and over eight hundred thousand authors indexed from 1800 mathematical journals, many of them abstracted "cover-to-cover". A portion of those journals (about 450 in 2012) are designated as "Reference List Journals"; for MathSciNet entries of papers from these j... | MathSciNet | 0.81972 |
9,844 | The following projects contributed to D4Science development: BlueBRIDGE (2015-2018), EGI-Engage (2015-2017), ENVRIplus (2015-2019), Parthenos (2015-2019), SoBigData (2015-2019), AGINFRAplus (2017-2019), PerformFish (2017-2022), ARIADNEplus (2019-2022), EOSC-Pillar (2019-2022), DESIRA (2019-2023), RISIS2 (2019-2022), So... | D4Science | 0.819717 |
9,845 | One of its key objectives was to test theories of the early Universe and the origin of cosmic structure. The mission provided significant insights into the composition and evolution of the Universe, shedding light on the fundamental physics that governs the cosmos. Planck was initially called COBRAS/SAMBA, which stands... | Planck Telescope | 0.819709 |
9,846 | Now, condition 2 is violated: the states (s1,s1) and (s1,s2) may be (d,r)-close, but g(s1,s1) = 0 while g(s1,s2) > 0. so the above theorem cannot be applied. Indeed, the problem does not have an FPTAS unless P=NP, since an FPTAS could be used to decide in polytime whether the optimal value is 0.2. | Fully polynomial-time approximation scheme | 0.819706 |
9,847 | Here are some examples of extremely-benevolent problems, that have an FPTAS by the above theorem.1. Multiway number partitioning (equivalently, Identical-machines scheduling) with the goal of minimizing the largest sum is extremely-benevolent. Here, we have a = 1 (the inputs are integers) and b = the number of bins (wh... | Fully polynomial-time approximation scheme | 0.819706 |
9,848 | So the theorem cannot be used. Indeed, this problem does not have an FPTAS unless P=NP. The same is true for the two-dimensional knapsack problem. | Fully polynomial-time approximation scheme | 0.819706 |
9,849 | Here are some examples of benevolent problems, that have an FPTAS by the above theorem.1. The 0-1 knapsack problem is benevolent. Here, we have a=2: each input is a 2-vector (weight, value). There is a DP with b=2: each state encodes (current weight, current value). | Fully polynomial-time approximation scheme | 0.819706 |
9,850 | A fully polynomial-time approximation scheme (FPTAS) is an algorithm for finding approximate solutions to function problems, especially optimization problems. An FPTAS takes as input an instance of the problem and a parameter ε > 0. It returns as output a value is at least 1 − ϵ {\displaystyle 1-\epsilon } times the co... | Fully polynomial-time approximation scheme | 0.819706 |
9,851 | A central problem in algorithmic graph theory is the shortest path problem. Hereby, the problem of finding the shortest path between every pair of nodes is known as all-pair-shortest-paths (APSP) problem. As sequential algorithms for this problem often yield long runtimes, parallelization has shown to be beneficial in ... | Parallel all-pairs shortest path algorithm | 0.8197 |
9,852 | He received his PhD in 1982 from Yale University's Department of Molecular Biophysics and Biochemistry, where he conducted research on X-ray scattering and protein structure. Pickover graduated first in his class from Franklin and Marshall College, after completing the four-year undergraduate program in three years.Pic... | Wonders of Numbers | 0.819696 |
9,853 | Starting in 2008, Pickover's books began to focus on the history of science and mathematics, with such titles as Archimedes to Hawking, as well as The Math Book, The Physics Book, and The Medical Book—a trilogy of more than 1,500 pages that presents various historical milestones, breakthroughs, and curiosities. | Wonders of Numbers | 0.819696 |
9,854 | Pickover stalks are certain kinds of details that are empirically found in the Mandelbrot set in the study of fractal geometry. In the 1980s, Pickover proposed that experimental mathematicians and computer artists examine the behavior of orbit trajectories for the Mandelbrot set in order to study how closely the orbits... | Wonders of Numbers | 0.819696 |
9,855 | In molecular biology, foldases are a particular kind of molecular chaperones that assist the non-covalent folding of proteins in an ATP-dependent manner. Examples of foldase systems are the GroEL/GroES and the DnaK/DnaJ/GrpE system. | Foldase | 0.81969 |
9,856 | Routh's theorem - Many problems involving triangles with cevians will ask for areas, and mass points does not provide a method for calculating areas. However, Routh's theorem, which goes hand in hand with mass points, uses ratios of lengths to calculate the ratio of areas between a triangle and a triangle formed by thr... | Mass point geometry | 0.819688 |
9,857 | Mass point geometry, colloquially known as mass points, is a problem-solving technique in geometry which applies the physical principle of the center of mass to geometry problems involving triangles and intersecting cevians. All problems that can be solved using mass point geometry can also be solved using either simil... | Mass point geometry | 0.819688 |
9,858 | Thereby, checking whether such an equation has a solution can be done on all the completions of K {\displaystyle K} , which is often easier, since analytic methods (classical analytic tools such as intermediate value theorem at the archimedean places and p-adic analysis at the nonarchimedean places) can be used. This i... | Algebraic number field | 0.819681 |
9,859 | In fact, unramified morphisms of schemes in algebraic geometry are a direct generalization of unramified extensions of number fields. Ramification is a purely local property, i.e., depends only on the completions around the primes p and qi. The inertia group measures the difference between the local Galois groups at so... | Algebraic number field | 0.819681 |
9,860 | This ideal may or may not be a prime ideal, but, according to the Lasker–Noether theorem (see above), always is given by pO K {\displaystyle K} = q1e1 q2e2 ⋯ qmemwith uniquely determined prime ideals qi of O K {\displaystyle {\mathcal {O}}_{K}} and numbers (called ramification indices) ei. Whenever one ramification ind... | Algebraic number field | 0.819681 |
9,861 | This is an example of a branched covering of Riemann surfaces. This intuition also serves to define ramification in algebraic number theory. Given a (necessarily finite) extension of number fields K / L {\displaystyle K/L} , a prime ideal p of O L {\displaystyle {\mathcal {O}}_{L}} generates the ideal pOK of O K {\disp... | Algebraic number field | 0.819681 |
9,862 | Blended artificial intelligence (Blended AI) refers to the blending of different artificial intelligence techniques or approaches to achieve more robust and effective solutions. It involves integrating multiple AI models, algorithms, and/or technologies to leverage their respective strengths and compensate for their we... | Blended artificial intelligence | 0.81968 |
9,863 | In the context of machine learning, blended AI can involve using different types of models, such as generative AI, decision trees, neural networks, and support vector machines. By combining their results, predictions are more accurate and reliable. This blending of models can be done through techniques like ensemble le... | Blended artificial intelligence | 0.81968 |
9,864 | Commercial implementations range from consumer devices such as the Sony Eyetoy or games such as Dance Dance Revolution to more esoteric and pragmatic uses including machine vision utilized in the automation of quality inspection along a factory assembly line. Exergaming, such as Nintendo's Wii Fit, can be considered a ... | Physical computing | 0.819679 |
9,865 | Physical computing involves interactive systems that can sense and respond to the world around them. While this definition is broad enough to encompass systems such as smart automotive traffic control systems or factory automation processes, it is not commonly used to describe them. In a broader sense, physical computi... | Physical computing | 0.819679 |
9,866 | The field of complex numbers is quadratically closed; more generally, any algebraically closed field is quadratically closed. The field of real numbers is not quadratically closed as it does not contain a square root of −1. The union of the finite fields F 5 2 n {\displaystyle \mathbb {F} _{5^{2^{n}}}} for n ≥ 0 is qua... | Quadratically closed field | 0.819667 |
9,867 | A quadratic closure of a field F is a quadratically closed field containing F which embeds in any quadratically closed field containing F. A quadratic closure for any given F may be constructed as a subfield of the algebraic closure Falg of F, as the union of all iterated quadratic extensions of F in Falg. | Quadratically closed field | 0.819667 |
9,868 | Let E/F be a finite extension where E is quadratically closed. Either −1 is a square in F and F is quadratically closed, or −1 is not a square in F and F is Euclidean. This "going-down theorem" may be deduced from the Diller–Dress theorem. | Quadratically closed field | 0.819667 |
9,869 | Furthermore, where psychometrics investigates the stochastic dependence structure between variables as observed in the population, mathematical psychology almost exclusively focuses on the modeling of data obtained from experimental paradigms and is therefore even more closely related to experimental psychology, cognit... | Mathematical Psychology | 0.819664 |
9,870 | Mathematical psychology is an approach to psychological research that is based on mathematical modeling of perceptual, thought, cognitive and motor processes, and on the establishment of law-like rules that relate quantifiable stimulus characteristics with quantifiable behavior (in practice often constituted by task pe... | Mathematical Psychology | 0.819664 |
9,871 | But the emergence of English psychology is because of Francis Galton, who interested in individual differences between humans on psychological variables. The math in English psychology is mainly statistics and the work and methods of Galton is the foundation of psychometrics. Galton introduced bivariate normal distribu... | Mathematical Psychology | 0.819664 |
9,872 | They thereby established the fields of experimental psychology in general, and that of psychophysics in particular. Researchers in astronomy in the 19th century were mapping distances between stars by denoting the exact time of a star's passing of a cross-hair on a telescope. For lack of the automatic registration inst... | Mathematical Psychology | 0.819664 |
9,873 | The research developments in Germany and England in the 19th century made psychology a new academic subject. Since the German approach emphasized experiments in the investigation of the psychological processes that all humans share and the English approach was in the measurement of individual differences, the applicati... | Mathematical Psychology | 0.819664 |
9,874 | Petersburg Paradox in decision making, Daniel Bernoulli gave a solution and Laplace proposed a modification to the solution later on. In 1763, Bayes published the paper "An Essay towards solving a Problem in the Doctrine of Chances", which is the milestone of Bayesian statistics. Robert Hooke worked on modeling human m... | Mathematical Psychology | 0.819664 |
9,875 | Choice and decision making theory are rooted in the development of probability theory. In the mid 1600s, Blaise Pascal considered situations in gambling and further extended to Pascal's wager. In the 18th century, Nicolas Bernoulli proposed the St. | Mathematical Psychology | 0.819664 |
9,876 | Accumulator models Diffusion models Neural network/connectionist models Race models Random walk models Renewal models | Mathematical Psychology | 0.819664 |
9,877 | In the summer of 1963 the need was felt for a journal for theoretical and mathematical studies in all areas in psychology, excluding work that was mainly factor analytical. An initiative led by R. C. Atkinson, R. R. Bush, W. K. Estes, R. D. Luce, and P. Suppes resulted in the appearance of the first issue of the Journa... | Mathematical Psychology | 0.819664 |
9,878 | Allen Newell and Herbert Simon proposed the model of human solving problems. The development in artificial intelligence and human computer interface are active areas in both computer science and psychology. Before the 1950s, psychometricians emphasized the structure of measurement error and the development of high-powe... | Mathematical Psychology | 0.819664 |
9,879 | R. Duncan Luce and Howard Raiffa contributed to the choice and decision making area. The area of language and thinking comes into the spotlight with the development of computer science and linguistics, especially information theory and computation theory. Chomsky proposed the model of linguistics and computational hier... | Mathematical Psychology | 0.819664 |
9,880 | One development is the stimulus sampling theory by Williams K. Estes, the other is linear operator models by Robert R. Bush, and Frederick Mosteller. Signal processing and detection theory are broadly used in perception, psychophysics and nonsensory area of cognition. Von Neumann's book The Theory of Games and Economic... | Mathematical Psychology | 0.819664 |
9,881 | Formal theories were mostly absent (except for vision and hearing). During the war, developments in engineering, mathematical logic and computability theory, computer science and mathematics, and the military need to understand human performance and limitations, brought together experimental psychologists, mathematicia... | Mathematical Psychology | 0.819664 |
9,882 | However, the trees produced by the method are only rooted if the substitution model is irreversible, which is not generally true of biological systems. The search for the maximum-likelihood tree also includes a branch length optimization component that is difficult to improve upon algorithmically; general global optimi... | Computational phylogenetics | 0.819659 |
9,883 | Bayesian inference can be used to produce phylogenetic trees in a manner closely related to the maximum likelihood methods. Bayesian methods assume a prior probability distribution of the possible trees, which may simply be the probability of any one tree among all the possible trees that could be generated from the da... | Computational phylogenetics | 0.819659 |
9,884 | The branch and bound algorithm is a general method used to increase the efficiency of searches for near-optimal solutions of NP-hard problems first applied to phylogenetics in the early 1980s. Branch and bound is particularly well suited to phylogenetic tree construction because it inherently requires dividing a proble... | Computational phylogenetics | 0.819659 |
9,885 | The basic problem in morphological phylogenetics is the assembly of a matrix representing a mapping from each of the taxa being compared to representative measurements for each of the phenotypic characteristics being used as a classifier. The types of phenotypic data used to construct this matrix depend on the taxa bei... | Computational phylogenetics | 0.819659 |
9,886 | By contrast, unrooted trees plot the distances and relationships between input sequences without making assumptions regarding their descent. An unrooted tree can always be produced from a rooted tree, but a root cannot usually be placed on an unrooted tree without additional data on divergence rates, such as the assump... | Computational phylogenetics | 0.819659 |
9,887 | Phylogenetic trees generated by computational phylogenetics can be either rooted or unrooted depending on the input data and the algorithm used. A rooted tree is a directed graph that explicitly identifies a most recent common ancestor (MRCA), usually an imputed sequence that is not represented in the input. Genetic di... | Computational phylogenetics | 0.819659 |
9,888 | Owing to the development of advanced sequencing techniques in molecular biology, it has become feasible to gather large amounts of data (DNA or amino acid sequences) to infer phylogenetic hypotheses. For example, it is not rare to find studies with character matrices based on whole mitochondrial genomes (~16,000 nucleo... | Computational phylogenetics | 0.819659 |
9,889 | Nodes with support lower than 70% are typically considered unresolved. Jackknifing in phylogenetics is a similar procedure, except the columns of the matrix are sampled without replacement. Pseudoreplicates are generated by randomly subsampling the data—for example, a "10% jackknife" would involve randomly sampling 10%... | Computational phylogenetics | 0.819659 |
9,890 | In phylogenetics, bootstrapping is conducted using the columns of the character matrix. Each pseudoreplicate contains the same number of species (rows) and characters (columns) randomly sampled from the original matrix, with replacement. A phylogeny is reconstructed from each pseudoreplicate, with the same methods used... | Computational phylogenetics | 0.819659 |
9,891 | In statistics, the bootstrap is a method for inferring the variability of data that has an unknown distribution using pseudoreplications of the original data. For example, given a set of 100 data points, a pseudoreplicate is a data set of the same size (100 points) randomly sampled from the original data, with replacem... | Computational phylogenetics | 0.819659 |
9,892 | In some areas of geometry and topology the term cylinder refers to what has been called a cylindrical surface. A cylinder is defined as a surface consisting of all the points on all the lines which are parallel to a given line and which pass through a fixed plane curve in a plane not parallel to the given line. Such cy... | Circular cylinder | 0.819658 |
9,893 | "Normed Algebra". Encyclopaedia of Mathematics. Retrieved 20 May 2018. | Normed algebra | 0.819653 |
9,894 | In mathematics, a normed algebra A is an algebra over a field which has a sub-multiplicative norm: ∀ x , y ∈ A ‖ x y ‖ ≤ ‖ x ‖ ‖ y ‖ . {\displaystyle \forall x,y\in A\qquad \|xy\|\leq \|x\|\|y\|.} Some authors require it to have a multiplicative identity 1A such that ║1A║ = 1. | Normed algebra | 0.819653 |
9,895 | The boundary vector field (BVF) is an external force for parametric active contours (i.e. Snakes). In the fields of computer vision and image processing, parametric active contours are widely used for segmentation and object extraction. The active contours move progressively towards its target based on the external for... | Boundary vector field | 0.819651 |
9,896 | Large Scale Biology Corporation (LSBC) (bankrupt) – used Tobacco mosaic virus to develop reagents and patient-specific vaccines for Non-Hodgkin's lymphoma, Papillomavirus vaccine, parvovirus vaccine, alpha galactosidase for Fabry disease, lysosomal acid lipase, aprotinin, interferon Alpha 2a and 2b, G-CSF, and Hepatiti... | Molecular farming | 0.819649 |
9,897 | Was in process of launching trypsin product in 2002 when later that year its field test crops contaminated conventional crops. Unable to pay the $3 million cost of the cleanup, it was purchased by International Oilseed Distributors in 2003 International Oilseed Distributors is controlled by Harry H. Stine, who owns one... | Molecular farming | 0.819649 |
9,898 | Pharming – C1 inhibitor, human collagen 1, fibrinogen (with American Red Cross), and lactoferrin in cow milk The intellectual property behind the fibrinogen project was acquired from PPL Therapeutics when PPL went bankrupt in 2004. Phyton Biotech uses plant cell culture systems to manufacture active pharmaceutical ingr... | Molecular farming | 0.819649 |
9,899 | Genzyme – antithrombin III in goat milk GTC Biotherapeutics – ATryn (recombinant human antithrombin) in goat milk Icon Genetics produces therapeutics in transiently infected Nicotiana benthamiana (relative of tobacco) plants in greenhouses in Halle, Germany or in fields. First product is a vaccine for a cancer, non-Hod... | Molecular farming | 0.819649 |
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