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31,100 | The Synchronization Module and Intelligent Tools comprise the major processing power of the e-maintenance machine network and provide optimization, prediction, clustering, classification, bench-marking and so on. The results from this module can then be synchronized and shared with the e-business system on for decision... | Machine to Machine | 0.804655 |
31,101 | The symbol Qe is often used throughout literature to denote radiant energy ("e" for "energetic", to avoid confusion with photometric quantities). In branches of physics other than radiometry, electromagnetic energy is referred to using E or W. The term is used particularly when electromagnetic radiation is emitted by a... | Light energy | 0.80465 |
31,102 | In physics, and in particular as measured by radiometry, radiant energy is the energy of electromagnetic and gravitational radiation. As energy, its SI unit is the joule (J). The quantity of radiant energy may be calculated by integrating radiant flux (or power) with respect to time. | Light energy | 0.80465 |
31,103 | IEEE Spectrum – the flagship publication of the Institute of Electrical and Electronics Engineers (IEEE), explores the development, applications and implications of new technologies, and provides a forum for understanding, discussion and leadership in these areas. IEEE Transactions on Information Theory – peer-reviewed... | Outline of automation | 0.804649 |
31,104 | Cybernetics – the interdisciplinary study of the structure of regulatory systems. Cognitive science – interdisciplinary scientific study of the mind and its processes. It examines what cognition is, what it does and how it works. Robotics – the branch of technology that deals with the design, construction, operation, s... | Outline of automation | 0.804649 |
31,105 | Control system – a device, or set of devices to manage, command, direct or regulate the behavior of other devices or systems. Industrial control system (ICS) – encompasses several types of control systems used in industrial production, including supervisory control and data acquisition (SCADA) systems, distributed cont... | Outline of automation | 0.804649 |
31,106 | Artificial neural network (ANN) – mathematical model or computational model that is inspired by the structure or functional aspects of biological neural networks. Human machine interface (HMI) – operator level local control panel that monitors field devices Laboratory information management system (LIMS) – software pac... | Outline of automation | 0.804649 |
31,107 | Artificial intelligence – the intelligence of machines and the branch of computer science that aims to create it. Friendly artificial intelligence – an artificial intelligence that has a positive rather than negative effect on humanity, and the field of knowledge required to build such an artificial intelligence. | Outline of automation | 0.804649 |
31,108 | Machine to Machine – OLE for process control (OPC) – Process control – a statistics and engineering discipline that deals with architectures, mechanisms and algorithms for maintaining the output of a specific process within a desired range. Run Book Automation (RBA) – Robot – a mechanical or virtual intelligent agent t... | Outline of automation | 0.804649 |
31,109 | James S. Albus – a US government engineer and a prolific pioneering inventor of intelligent systems, automation and robotics. Also wrote extensively on the impact of automation on jobs, incomes, well-being and prosperity | Outline of automation | 0.804649 |
31,110 | Quantapoint was founded as K2T, Inc (or K2T) in Pittsburgh, Pennsylvania in 1991 by Eric Hoffman, Pradeep Khosla, Takeo Kanade and other Carnegie Mellon University faculty members. K2T focused on creating custom robotics and 3D range-finding imaging systems to help them navigate complex environments. The most notable a... | Quantapoint | 0.804649 |
31,111 | The cohomology groups Hn(G, M) of finite groups G are all torsion for all n≥1. Indeed, by Maschke's theorem the category of representations of a finite group is semi-simple over any field of characteristic zero (or more generally, any field whose characteristic does not divide the order of the group), hence, viewing gr... | Group cohomology | 0.804644 |
31,112 | The techniques of group cohomology can also be extended to the case that instead of a G-module, G acts on a nonabelian G-group; in effect, a generalization of a module to non-Abelian coefficients. These algebraic ideas are closely related to topological ideas. The group cohomology of a discrete group G is the singular ... | Group cohomology | 0.804644 |
31,113 | Group cohomology plays a role in the investigation of fixed points of a group action in a module or space and the quotient module or space with respect to a group action. Group cohomology is used in the fields of abstract algebra, homological algebra, algebraic topology and algebraic number theory, as well as in applic... | Group cohomology | 0.804644 |
31,114 | In mathematics (more specifically, in homological algebra), group cohomology is a set of mathematical tools used to study groups using cohomology theory, a technique from algebraic topology. Analogous to group representations, group cohomology looks at the group actions of a group G in an associated G-module M to eluci... | Group cohomology | 0.804644 |
31,115 | For instance, the Pythagorean theorem has been illustrated with shear mapping as well as the related geometric mean theorem. An algorithm due to Alan W. Paeth uses a sequence of three shear mappings (horizontal, vertical, then horizontal again) to rotate a digital image by an arbitrary angle. | Shear mapping | 0.804637 |
31,116 | A shear mapping is the main difference between the upright and slanted (or italic) styles of letters. The same definition is used in three-dimensional geometry, except that the distance is measured from a fixed plane. A three-dimensional shearing transformation preserves the volume of solid figures, but changes areas o... | Shear mapping | 0.804637 |
31,117 | In plane geometry, a shear mapping is a linear map that displaces each point in a fixed direction, by an amount proportional to its signed distance from the line that is parallel to that direction and goes through the origin. This type of mapping is also called shear transformation, transvection, or just shearing. An e... | Shear mapping | 0.804637 |
31,118 | Negation introduction is a rule of inference, or transformation rule, in the field of propositional calculus. Negation introduction states that if a given antecedent implies both the consequent and its complement, then the antecedent is a contradiction. | Negation introduction | 0.804633 |
31,119 | In chemistry, recrystallization: 127–132 is a procedure for purifying compounds. The most typical situation is that a desired "compound A" is contaminated by a small amount of "impurity B". There are various methods of purification that may be attempted (see Separation process), recrystallization being one of them. The... | Recrystallization (chemistry) | 0.804628 |
31,120 | In chemistry, recrystallization is a technique used to purify chemicals. By dissolving a mixture of a compound and impurities in an appropriate solvent, either the desired compound or impurities can be removed from the solution, leaving the other behind. It is named for the crystals often formed when the compound preci... | Recrystallization (chemistry) | 0.804628 |
31,121 | Laurence M. Harwood; Christopher J. Moody; Jonathan M. Percy (1999). Experimental organic chemistry: standard and microscaling. ISBN 9780632048199. John Leonard; B. Lygo; Garry Procter (2 June 1994). Advanced practical organic chemistry. ISBN 9780748740710. | Recrystallization (chemistry) | 0.804628 |
31,122 | 1. First postulate (principle of relativity) The laws of physics take the same form in all inertial frames of reference.2. Second postulate (invariance of c) As measured in any inertial frame of reference, light is always propagated in empty space with a definite velocity c that is independent of the state of motion of... | Postulates of special relativity | 0.804627 |
31,123 | The term neopolarogram refers to mathematical derivatives of polarograms or cyclic voltammograms that in effect deconvolute diffusion and electrochemical kinetics. This is achieved by analog or digital implementations of fractional calculus. The implementation of fractional derivative calculations by means of numerical... | Neopolarogram | 0.804627 |
31,124 | The G1 algorithm produces a numerical derivative that has the shape of a bell curve, this derivative obeys to certain laws, for example the G1 derivative of a cyclic voltammogram is mirrored at the abscissa as long as the electrochemical reaction is diffusion controlled, the planar diffusion approximation can be applie... | Neopolarogram | 0.804626 |
31,125 | In combinatorial game theory, and particularly in the theory of impartial games in misère play, an indistinguishability quotient is a commutative monoid that generalizes and localizes the Sprague–Grundy theorem for a specific game's rule set. In the specific case of misere-play impartial games, such commutative monoids... | Indistinguishability quotient | 0.804626 |
31,126 | The totality of all the congruence classes form the indistinguishability quotient. If A {\displaystyle A} is played as a normal-play (last-playing winning) impartial game, then the congruence classes of A {\displaystyle A} are in one-to-one correspondence with the nim values that occur in the play of the game (themselv... | Indistinguishability quotient | 0.804626 |
31,127 | Bayesian Data Analysis – Data used in the book are provided on-line (archive link) by Andrew Gelman, one of the book's authors. The Bupa liver data – Used in several papers in the machine learning (data mining) literature. Anscombe's quartet – Small data set illustrating the importance of graphing the data to avoid sta... | Data sets | 0.804625 |
31,128 | Several classic data sets have been used extensively in the statistical literature: Iris flower data set – Multivariate data set introduced by Ronald Fisher (1936). Provided online by University of California-Irvine Machine Learning Repository. MNIST database – Images of handwritten digits commonly used to test classif... | Data sets | 0.804625 |
31,129 | Missing values may exist, which must be indicated somehow. In statistics, data sets usually come from actual observations obtained by sampling a statistical population, and each row corresponds to the observations on one element of that population. Data sets may further be generated by algorithms for the purpose of tes... | Data sets | 0.804625 |
31,130 | M.Tinkham (2004). Introduction to Superconductivity. Dover Books on Physics (2nd ed.). Dover. ISBN 0-486-43503-2. | Coleman–Weinberg potential | 0.804622 |
31,131 | In statistics and in particular in regression analysis, a design matrix, also known as model matrix or regressor matrix and often denoted by X, is a matrix of values of explanatory variables of a set of objects. Each row represents an individual object, with the successive columns corresponding to the variables and the... | Data matrix (statistics) | 0.804622 |
31,132 | In this case the equation above is reduced to: One distinguishes the following cases: Point a is an ordinary point when functions p1(x) and p0(x) are analytic at x = a. Point a is a regular singular point if p1(x) has a pole up to order 1 at x = a and p0 has a pole of order up to 2 at x = a. Otherwise point a is an irr... | Fuchsian equation | 0.804621 |
31,133 | An often used approximation of relative permeability is the Corey correlation which is a power law in saturation. The Corey correlations of the relative permeability for oil and water are then K r o w ( S w ) = K r o t ( 1 − S w n ) N o {\displaystyle K_{\mathit {row}}(S_{w})=K{_{\mathit {rot}}}(1-S_{\mathit {wn}})^{N_... | Relative permeability | 0.804621 |
31,134 | The endpoint parameters K r o t {\displaystyle K_{\mathit {rot}}} and K r w r {\displaystyle K_{\mathit {rwr}}} (which is a simplification of K r w o r {\displaystyle K_{\mathit {rwor}}} ) are physical properties that are obtained either before or together with the optimization of shape parameters present in the shape ... | Relative permeability | 0.804621 |
31,135 | Note that the polytopic observer or other components can be generated in similar way, such as these vertexes are also generated from S {\displaystyle {\mathcal {S}}} . Convex hull manipulation based optimization The polytopic representation of a given qLPV model is not invariant. I.e. a given S ( p ( t ) ) {\displaysty... | TP model transformation in control theories | 0.80462 |
31,136 | Of any treatises containing neither, Hume orders, "Commit it then to the flames, for it can contain nothing but sophistry and illusion".Thus awakened from "dogmatic slumber", Immanuel Kant quested to answer Hume's challenge—but by explaining how metaphysics is possible. Eventually, in his 1781 work, Kant crossed the ti... | Observational statement | 0.804619 |
31,137 | Yet Kurt Gödel's incompleteness theorem showed this impossible except in trivial cases, and Alfred Tarski's undefinability theorem shattered all hopes of reducing mathematics to logic. Thus, a universal language failed to stem from Carnap's 1934 work Logische Syntax der Sprache (Logical Syntax of Language). Still, some... | Observational statement | 0.804619 |
31,138 | Gottlob Frege began the program of reducing mathematics to logic, continued it with Bertrand Russell, but lost interest in this logicism, and Russell continued it with Alfred North Whitehead in their Principia Mathematica, inspiring some of the more mathematical logical positivists, such as Hans Hahn and Rudolf Carnap.... | Observational statement | 0.804619 |
31,139 | Via Bertrand Russell's logicism, reducing mathematics to logic, physics' mathematical formulas would be converted to symbolic logic. Via Russell's logical atomism, ordinary language would break into discrete units of meaning. Rational reconstruction, then, would convert ordinary statements into standardized equivalents... | Observational statement | 0.804619 |
31,140 | In particular, this leads to quantum numbers that take values in discrete sets of integers or half-integers; although they could approach infinity in some cases. This distinguishes quantum mechanics from classical mechanics where the values that characterize the system such as mass, charge, or momentum, all range conti... | Additive quantum number | 0.804618 |
31,141 | In quantum physics and chemistry, quantum numbers describe values of conserved quantities in the dynamics of a quantum system. Quantum numbers correspond to eigenvalues of operators that commute with the Hamiltonian—quantities that can be known with precision at the same time as the system's energy—and their correspond... | Additive quantum number | 0.804618 |
31,142 | In a different usage to the above definition, a polynomial of degree 1 is said to be linear, because the graph of a function of that form is a straight line.Over the reals, a simple example of a linear equation is given by: y = m x + b {\displaystyle y=mx+b\ } where m is often called the slope or gradient, and b the y-... | Linearity | 0.804614 |
31,143 | In Boolean algebra, a linear function is a function f {\displaystyle f} for which there exist a 0 , a 1 , … , a n ∈ { 0 , 1 } {\displaystyle a_{0},a_{1},\ldots ,a_{n}\in \{0,1\}} such that f ( b 1 , … , b n ) = a 0 ⊕ ( a 1 ∧ b 1 ) ⊕ ⋯ ⊕ ( a n ∧ b n ) {\displaystyle f(b_{1},\ldots ,b_{n})=a_{0}\oplus (a_{1}\land b_{1})\... | Linearity | 0.804614 |
31,144 | In physics, linearity is a property of the differential equations governing many systems; for instance, the Maxwell equations or the diffusion equation.Linearity of a homogenous differential equation means that if two functions f and g are solutions of the equation, then any linear combination af + bg is, too. In instr... | Linearity | 0.804614 |
31,145 | Examples in physics include the linear relationship of voltage and current in an electrical conductor (Ohm's law), and the relationship of mass and weight. By contrast, more complicated relationships, such as between velocity and kinetic energy, are nonlinear. Generalized for functions in more than one dimension, linea... | Linearity | 0.804614 |
31,146 | Motorcycle testing and measurement includes a range of more than two dozen statistics giving the specifications of the motorcycle, and the actual performance, expressed by such things as the output of the engine, and the top speed or acceleration of the motorcycle. Most parameters are uncontroversial and claims made by... | Motorcycle testing and measurement | 0.804613 |
31,147 | The dataset contains a set of 150 records under five attributes: sepal length, sepal width, petal length, petal width and species.The iris data set is widely used as a beginner's dataset for machine learning purposes. The dataset is included in R base and Python in the machine learning library scikit-learn, so that use... | Iris flower data set | 0.804612 |
31,148 | Four features were measured from each sample: the length and the width of the sepals and petals, in centimeters. Based on the combination of these four features, Fisher developed a linear discriminant model to distinguish the species from each other. Fisher's paper was published in the Annals of Eugenics (today the Ann... | Iris flower data set | 0.804612 |
31,149 | Originally used as an example data set on which Fisher's linear discriminant analysis was applied, it became a typical test case for many statistical classification techniques in machine learning such as support vector machines.The use of this data set in cluster analysis however is not common, since the data set only ... | Iris flower data set | 0.804612 |
31,150 | In statistics, robust measures of scale are methods that quantify the statistical dispersion in a sample of numerical data while resisting outliers. The most common such robust statistics are the interquartile range (IQR) and the median absolute deviation (MAD). These are contrasted with conventional or non-robust meas... | Robust measures of scale | 0.804611 |
31,151 | The actual Forth process of compiling itself is a combination of a Forth being a self-hosting extensible programming language and sometimes cross compilation, long established terminology in computer science. Metacompilers are a general compiler writing system. | Compiler-compiler | 0.804611 |
31,152 | Many advocates of the language Forth call the process of creating a new implementation of Forth a meta-compilation and that it constitutes a metacompiler. The Forth definition of metacompiler is: "A metacompiler is a compiler which processes its own source code, resulting in an executable version of itself. "This Forth... | Compiler-compiler | 0.804611 |
31,153 | In computer science, the prefix meta is commonly used to mean about (its own category). For example, metadata are data that describe other data. A language that is used to describe other languages is a metalanguage. Meta may also mean on a higher level of abstraction. | Compiler-compiler | 0.804611 |
31,154 | A decadal survey is a 10-year plan outlining scientific missions and goals created by the United States National Academies. It is a summary of input from scientists in the United States and beyond. Examples include: Astronomy and Astrophysics Decadal Survey Solar and Space Physics Decadal Survey Planetary Science Decad... | Decadal survey | 0.804611 |
31,155 | In this question, however, we are merely asking about intellectual habits based on human reason, those discovered by the process of reasoning, which are deduced from what is evident to us. For it is in this sense that Aristotle calls metaphysics ‘theology’ and ‘the divine science’. Accordingly, metaphysics differs fro... | Secondary Causation | 0.804606 |
31,156 | The assignment of intrinsic qualities to objects which can mutate and evolve of their own accord without divine intervention was a crucial step in the transformation of the rational logic of the Greeks into the scientific method in the Western Tradition of the late Middle Ages. Because man could thus observe and charac... | Secondary Causation | 0.804606 |
31,157 | In power engineering, the voltage between two phases in a three-phase system equals 3 {\textstyle {\sqrt {3}}} times the line to neutral voltage. This is because any two phases are 120° apart, and two points on a circle 120 degrees apart are separated by 3 {\textstyle {\sqrt {3}}} times the radius (see geometry example... | Theodorus' constant | 0.804606 |
31,158 | Many phenomena in astrophysics are attributed to particle beams of various kinds. Solar Type III radio bursts, the most common impulsive radio signatures from the Sun, are used by scientists as a tool to better understand solar accelerated electron beams. | Particle beam | 0.804604 |
31,159 | Fatty acids and fatty acid derivatives are another group of carboxylic acids that play a significant role in biology. These contain long hydrocarbon chains and a carboxylic acid group on one end. The cell membrane of nearly all organisms is primarily made up of a phospholipid bilayer, a micelle of hydrophobic fatty aci... | Tetraprotic acid | 0.804603 |
31,160 | In machine learning and data mining, a string kernel is a kernel function that operates on strings, i.e. finite sequences of symbols that need not be of the same length. String kernels can be intuitively understood as functions measuring the similarity of pairs of strings: the more similar two strings a and b are, the ... | String kernel | 0.804603 |
31,161 | A kernel on a domain D {\displaystyle D} is a function K: D × D → R {\displaystyle K:D\times D\rightarrow \mathbb {R} } satisfying some conditions (being symmetric in the arguments, continuous and positive semidefinite in a certain sense). Mercer's theorem asserts that K {\displaystyle K} can then be expressed as K ( x... | String kernel | 0.804603 |
31,162 | Since several well-proven data clustering, classification and information retrieval methods (for example support vector machines) are designed to work on vectors (i.e. data are elements of a vector space), using a string kernel allows the extension of these methods to handle sequence data. The string kernel method is t... | String kernel | 0.804603 |
31,163 | Grid energy storage is a collection of methods used for energy storage on a large scale within an electrical power grid. Common examples of energy storage are the rechargeable battery, which stores chemical energy readily convertible to electricity to operate a mobile phone; the hydroelectric dam, which stores energy i... | Electricity storage | 0.804603 |
31,164 | Liquid hydrocarbon fuels are the most commonly used forms of energy storage for use in transportation, followed by a growing use of Battery Electric Vehicles and Hybrid Electric Vehicles. Other energy carriers such as hydrogen can be used to avoid producing greenhouse gases. Public transport systems like trams and trol... | Electricity storage | 0.804603 |
31,165 | Shortly after making his famous "God does not play dice" comment, Einstein attempted to formulate a deterministic counter proposal to quantum mechanics, presenting a paper at a meeting of the Academy of Sciences in Berlin, on 5 May 1927, titled "Bestimmt Schrödinger's Wellenmechanik die Bewegung eines Systems vollständ... | Hidden-variable theory | 0.804592 |
31,166 | Realistic interpretations (which were already incorporated, to an extent, into the physics of Feynman), on the other hand, assume that particles have certain trajectories. Under such view, these trajectories will almost always be continuous, which follows both from the finitude of the perceived speed of light ("leaps" ... | Hidden-variable theory | 0.804592 |
31,167 | The designation of variables as underlying "hidden" variables depends on the level of physical description (so, for example, "if a gas is described in terms of temperature, pressure, and volume, then the velocities of the individual atoms in the gas would be hidden variables"). Physicists supporting De Broglie–Bohm the... | Hidden-variable theory | 0.804592 |
31,168 | Per its mathematical formulation, quantum mechanics is non-deterministic, meaning that it generally does not predict the outcome of any measurement with certainty. Instead, it indicates what the probabilities of the outcomes are, with the indeterminism of observable quantities constrained by the uncertainty principle. ... | Hidden-variable theory | 0.804592 |
31,169 | Syneresis (also spelled 'synæresis' or 'synaeresis'), in chemistry, is the extraction or expulsion of a liquid from a gel, such as when serum drains from a contracting clot of blood. Another example of syneresis is the collection of whey on the surface of yogurt. Syneresis can also be observed when the amount of diluen... | Syneresis (chemistry) | 0.804591 |
31,170 | In probability and statistics, a probability mass function is a function that gives the probability that a discrete random variable is exactly equal to some value. Sometimes it is also known as the discrete probability density function. The probability mass function is often the primary means of defining a discrete pro... | Probability mass function | 0.804588 |
31,171 | A probability mass function of a discrete random variable X {\displaystyle X} can be seen as a special case of two more general measure theoretic constructions: the distribution of X {\displaystyle X} and the probability density function of X {\displaystyle X} with respect to the counting measure. We make this more pre... | Probability mass function | 0.804588 |
31,172 | However, their irregular pattern still retains an integrity that can be explained as reciprocal errors created by prehistoric surveyors using a cord (equal to the radius of each circuit) passed around the stone monument (the presence of the stones would have prevented an accurate circle from being scribed from the geom... | Y and Z Holes | 0.804586 |
31,173 | In the tenth year, courses focused on geometry through algebraic uses. The eleventh year focused on a continuation of more advanced algebra topics. These topics were more advanced than those discussed in the ninth grade. However, if the student took an advanced algebra class during the ninth year, then he took two of t... | National Council of Teachers of Mathematics | 0.804584 |
31,174 | Those who have a greater desire to study math would go on one track, studying algebra. Those who did not have a large interest in math would go another route, studying general mathematics, which eliminated the problem of students being held back. Finally, grades 10-12 built math maturity. | National Council of Teachers of Mathematics | 0.804584 |
31,175 | The army credited poor performance of males during the war to the men forgetting math concepts; it was recommended that reinforcing past concepts learned would solve this problem. The report lists the organization of the topics that should be taught in these years. "(1) number and computation; (2) the geometry of every... | National Council of Teachers of Mathematics | 0.804584 |
31,176 | The report outlined three strategies that helped math educators emphasize the everyday usage of algebra. First, teachers focused on the meanings behind concepts. Before, teachers were expected to use either the Drill or the Meaning Theory. | National Council of Teachers of Mathematics | 0.804584 |
31,177 | In 1944, NCTM created a postwar plan to help World War II have a lasting effect on math education. Grades 1-6 were considered crucial years to build the foundations of math concepts with the main focus on algebra. In the war years, algebra had one understood purpose: to help the military and industries with the war eff... | National Council of Teachers of Mathematics | 0.804584 |
31,178 | The controversy surrounding the 1989 standards paved the way for revised standards which sought more clarity and balance. In 2000, NCTM used a consensus process involving mathematicians, teachers, and educational researchers to revise its standards with the release of the Principles and Standards for School Mathematics... | National Council of Teachers of Mathematics | 0.804584 |
31,179 | Although the standards were the consensus of those teaching mathematics in the context of real life, they also became a lightning rod of criticism as "math wars" erupted in some communities that were opposed to some of the more radical changes to mathematics instruction such as Mathland's Fantasy Lunch and what some du... | National Council of Teachers of Mathematics | 0.804584 |
31,180 | The controversial 1989 NCTM Standards called for more emphasis on conceptual understanding and problem solving informed by a constructivist understanding of how children learn. The increased emphasis on concepts required decreased emphasis on direct instruction of facts and algorithms. This decrease of traditional rote... | National Council of Teachers of Mathematics | 0.804584 |
31,181 | Watson called this problem "the mysteries of life" in his letter to Crick. Soviet-American physicist George Gamow then at the George Washington University gave the first possible scheme for protein synthesis from DNA. In early 1954, he spent several days at Woods Hole on Cape Cod with Crick, Watson and Sydney Brenner, ... | RNA Tie Club | 0.804583 |
31,182 | Francis Crick proposed the "adaptor hypothesis" (the name given by Brenner) suggesting that some molecule ferried the amino acids around, and put them in the correct order corresponding to the nucleic acid sequence. The hypothesis contradicted Gamow's direct DNA template hypothesis positing that DNA could not synthesis... | RNA Tie Club | 0.804583 |
31,183 | Sydney Brenner proposed the concept of a codon, the idea that three non-overlapping nucleotides could code for one amino acid. His proof involved statistics and experimental evidence from amino acid protein sequences. | RNA Tie Club | 0.804583 |
31,184 | In mathematics, an exact differential equation or total differential equation is a certain kind of ordinary differential equation which is widely used in Physics and engineering. | Exact differential equation | 0.804583 |
31,185 | Vectors have many uses in physics and other sciences. | Antiparallel vectors | 0.804579 |
31,186 | A vector may also be multiplied, or re-scaled, by a real number r. In the context of conventional vector algebra, these real numbers are often called scalars (from scale) to distinguish them from vectors. The operation of multiplying a vector by a scalar is called scalar multiplication. The resulting vector is Intuitiv... | Antiparallel vectors | 0.804579 |
31,187 | In physics, as well as mathematics, a vector is often identified with a tuple of components, or list of numbers, that act as scalar coefficients for a set of basis vectors. When the basis is transformed, for example by rotation or stretching, then the components of any vector in terms of that basis also transform in an... | Antiparallel vectors | 0.804579 |
31,188 | In molecular biology, DNA replication is the biological process of producing two identical replicas of DNA from one original DNA molecule. DNA replication occurs in all living organisms acting as the most essential part of biological inheritance. This is essential for cell division during growth and repair of damaged t... | Replication Fork | 0.804577 |
31,189 | The Hodge numbers of any K3 surface are listed in the Hodge diamond: One way to show this is to calculate the Jacobian ideal of a specific K3 surface, and then using a variation of Hodge structure on the moduli of algebraic K3 surfaces to show that all such K3 surfaces have the same Hodge numbers. A more low-brow calcu... | K3 surface | 0.804576 |
31,190 | Any two complex analytic K3 surfaces are diffeomorphic as smooth 4-manifolds, by Kunihiko Kodaira. Every complex analytic K3 surface has a Kähler metric, by Yum-Tong Siu. (Analogously, but much easier: every algebraic K3 surface over a field is projective.) By Shing-Tung Yau's solution to the Calabi conjecture, it foll... | K3 surface | 0.804576 |
31,191 | A remarkable feature of algebraic K3 surfaces is that the Picard lattice determines many geometric properties of the surface, including the convex cone of ample divisors (up to automorphisms of the Picard lattice). The ample cone is determined by the Picard lattice as follows. By the Hodge index theorem, the intersecti... | K3 surface | 0.804576 |
31,192 | However, a concrete version of this idea is the fact that any two complex algebraic K3 surfaces are deformation-equivalent through algebraic K3 surfaces.More generally, a quasi-polarized K3 surface of genus g means a projective K3 surface with a primitive nef and big line bundle L such that c 1 ( L ) 2 = 2 g − 2 {\disp... | K3 surface | 0.804576 |
31,193 | A polarized K3 surface X of genus g is defined to be a projective K3 surface together with an ample line bundle L such that L is primitive (that is, not 2 or more times another line bundle) and c 1 ( L ) 2 = 2 g − 2 {\displaystyle c_{1}(L)^{2}=2g-2} . This is also called a polarized K3 surface of degree 2g−2.Under thes... | K3 surface | 0.804576 |
31,194 | K3 surfaces can be considered the simplest algebraic varieties whose structure does not reduce to curves or abelian varieties, and yet where a substantial understanding is possible. A complex K3 surface has real dimension 4, and it plays an important role in the study of smooth 4-manifolds. K3 surfaces have been applie... | K3 surface | 0.804576 |
31,195 | Together with two-dimensional compact complex tori, K3 surfaces are the Calabi–Yau manifolds (and also the hyperkähler manifolds) of dimension two. As such, they are at the center of the classification of algebraic surfaces, between the positively curved del Pezzo surfaces (which are easy to classify) and the negativel... | K3 surface | 0.804576 |
31,196 | In mathematics, a complex analytic K3 surface is a compact connected complex manifold of dimension 2 with а trivial canonical bundle and irregularity zero. An (algebraic) K3 surface over any field means a smooth proper geometrically connected algebraic surface that satisfies the same conditions. In the Enriques–Kodaira... | K3 surface | 0.804576 |
31,197 | Ganchev and Dredze showed that in text classification applications with random hash functions and several tens of thousands of columns in the output vectors, feature hashing need not have an adverse effect on classification performance, even without the signed hash function.Weinberger et al. (2009) applied their versio... | Feature hashing | 0.804574 |
31,198 | We want to say something about the geometric property of ϕ {\displaystyle \phi } , but T {\displaystyle T} , by itself, is just a set of tokens, we cannot impose a geometric structure on it except the discrete topology, which is generated by the discrete metric. To make it nicer, we lift it to T → R T {\displaystyle T\... | Feature hashing | 0.804574 |
31,199 | Feature hashing generally suffers from hash collision, which means that there exist pairs of different tokens with the same hash: t ≠ t ′ , ϕ ( t ) = ϕ ( t ′ ) = v {\displaystyle t\neq t',\phi (t)=\phi (t')=v} . A machine learning model trained on feature-hashed words would then have difficulty distinguishing t {\displ... | Feature hashing | 0.804574 |
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