id int32 0 100k | text stringlengths 21 3.54k | source stringlengths 1 124 | similarity float32 0.78 0.88 |
|---|---|---|---|
17,900 | Not every cylindric algebra has a representation as a cylindric set algebra. It is easier to connect the semantics of first-order predicate logic with cylindric set algebra. (For more details, see § Further reading.) | Cylindric algebra | 0.812611 |
17,901 | A cylindric set algebra of dimension α {\displaystyle \alpha } is an algebraic structure ( A , ∪ , ∩ , − , ∅ , X α , c κ , d κ λ ) κ , λ < α {\displaystyle (A,\cup ,\cap ,-,\emptyset ,X^{\alpha },c_{\kappa },d_{\kappa \lambda })_{\kappa ,\lambda <\alpha }} such that ⟨ X α , A ⟩ {\displaystyle \langle X^{\alpha },A\rang... | Cylindric algebra | 0.812611 |
17,902 | Cylindric algebras have been generalized to the case of many-sorted logic (Caleiro and Gonçalves 2006), which allows for a better modeling of the duality between first-order formulas and terms. | Cylindric algebra | 0.812611 |
17,903 | In mathematics, the notion of cylindric algebra, invented by Alfred Tarski, arises naturally in the algebraization of first-order logic with equality. This is comparable to the role Boolean algebras play for propositional logic. Cylindric algebras are Boolean algebras equipped with additional cylindrification operation... | Cylindric algebra | 0.812611 |
17,904 | Johannes Kepler (1571–1630) was the first to closely integrate the predictive geometrical astronomy, which had been dominant from Ptolemy in the 2nd century to Copernicus, with physical concepts to produce a New Astronomy, Based upon Causes, or Celestial Physics in 1609. His work led to the modern laws of planetary orb... | Celestial Mechanics | 0.812611 |
17,905 | The problem has been mitigated in some cases by adding a latency term to the instruments – for example, to cause the climb rate indication to not only reflect the current climb rate, but also be sensitive to the rate of change of the climb rate. The physics of flight make such oscillations more probable for pilots than... | Pilot induced oscillation | 0.812608 |
17,906 | Spherical Neutral Detector (SND) is a detector for particle physics experiments, successor of the Neutral Detector (ND), created by the team of physicists in the Budker Institute of Nuclear Physics (BINP), Novosibirsk, Russia. There are three major periods in evolution of the SND experiment; from 1995 to 2000 - data co... | SND Experiment | 0.812607 |
17,907 | Previous experiment with ND (predecessor of SND) has shown that the e+e− annihilation in the final states with neutral particles in the energy range 2E=0.4-1.4 GeV is mediated by the processes which need to be studied in more details. In particular, quark structure of the light scalar mesons can be studied in electric-... | SND Experiment | 0.812607 |
17,908 | However, this method is not yet as effective as chemical synthesis, and is not commercially available.With advances in artificial DNA synthesis, the possibility of DNA data storage is being explored. With its ultrahigh storage density and long-term stability, synthetic DNA is an interesting option to store large amount... | DNA synthesis | 0.812607 |
17,909 | The process has been automated since the late 1970s and can be used to form desired genetic sequences as well as for other uses in medicine and molecular biology. However, creating sequences chemically is impractical beyond 200-300 bases, and is an environmentally hazardous process. These oligos, of around 200 bases, c... | DNA synthesis | 0.812607 |
17,910 | The Whitney graph isomorphism theorem provides a converse to this for all but one pair of graphs. In the context of complex network theory, the line graph of a random network preserves many of the properties of the network such as the small-world property (the existence of short paths between all pairs of vertices) and... | Derived graph | 0.812605 |
17,911 | Rearranging the first equation, we obtain the Helmholtz equation: Likewise, after making the substitution ω = kc, where k is the wave number, and ω is the angular frequency (assuming a monochromatic field), the second equation becomes We now have Helmholtz's equation for the spatial variable r and a second-order ordina... | Helmholtz equation | 0.812603 |
17,912 | The Helmholtz equation often arises in the study of physical problems involving partial differential equations (PDEs) in both space and time. The Helmholtz equation, which represents a time-independent form of the wave equation, results from applying the technique of separation of variables to reduce the complexity of ... | Helmholtz equation | 0.812603 |
17,913 | CDFD started its operations at the Centre for Cellular and Molecular Biology, a Council of Scientific and Industrial Research organisation, and was housed in an interim building in Nacharam from early 1999 to December 2008. In 2009, it was moved to a sprawling new building in Gandipet locality at the outskirts of Hyder... | Centre for DNA Fingerprinting and Diagnostics | 0.812599 |
17,914 | CDFD was conceptualised by then CCMB director Lalji Singh. It evolved into its current form of a modern institution encompassing both basic and applied research in diverse areas of modern biology under its founder director, Seyed E. Hasnain (former vice-chancellor of the University of Hyderabad), who pursued this aim a... | Centre for DNA Fingerprinting and Diagnostics | 0.812599 |
17,915 | The CDFD and the U.S. Federal Bureau of Investigation signed a memorandum of understanding in 2014 for the acquisition of CODIS.CDFD receives funding from other agencies like the Wellcome Trust on specific collaborative projects. The centre is recognised by the University of Hyderabad and Manipal University for pursuin... | Centre for DNA Fingerprinting and Diagnostics | 0.812599 |
17,916 | The Centre for DNA Fingerprinting and Diagnostics (CDFD) is an Indian biotechnology research centre, located in Hyderabad, India, operated by the Department of Biotechnology, Ministry of Science and Technology, Government of India. CDFD is a Sun Microsystems centre of excellence in medical bio-informatics, supported wi... | Centre for DNA Fingerprinting and Diagnostics | 0.812599 |
17,917 | Since the additions, subtractions, and digit shifts (multiplications by powers of B) in Karatsuba's basic step take time proportional to n, their cost becomes negligible as n increases. More precisely, if T(n) denotes the total number of elementary operations that the algorithm performs when multiplying two n-digit num... | Karatsuba algorithm | 0.812596 |
17,918 | Rao, J. N. K. and C. F. J. Wu (1985). Inference from stratified samples: Second-order analysis of three methods for nonlinear statistics. Journal of the American Statistical Association, 80 (391), 620-630. | Balanced repeated replication | 0.812594 |
17,919 | Let a be the value of our statistic as calculated from the full sample; let ai (i = 1,...,n) be the corresponding statistics calculated for the half-samples. (n is the number of half-samples.) Then our estimate for the sampling variance of the statistic is the average of (ai − a)2. This is (at least in the ideal case) ... | Balanced repeated replication | 0.812594 |
17,920 | (1990). Fay's method for variance estimation. Journal of Official Statistics, 6 (3), 223-239. | Balanced repeated replication | 0.812594 |
17,921 | Inference from stratified samples: Properties of the linearization, jackknife and balanced repeated replication methods. The Annals of Statistics, 9 (5), 1010-1019. Judkins, D. R. | Balanced repeated replication | 0.812594 |
17,922 | Results from quantum chemistry suggest that a higher exponent than 12 has to be used, i.e. a steeper potential. Furthermore, the Lennard-Jones potential has a limited flexibility, i.e. only the two model parameters ε {\displaystyle \varepsilon } and σ {\displaystyle \sigma } can be used for the fitting to describe a re... | Lennard-Jones potential | 0.812591 |
17,923 | The Lennard-Jones potential gives a good description of molecular interactions in fluid phases, whereas molecular interactions in solid phases are only roughly well described. This is mainly due to the fact that multi-body interactions play a significant role in solid phases, which are not comprised in the Lennard-Jone... | Lennard-Jones potential | 0.812591 |
17,924 | Following Newton's mechanics, the actual force F {\displaystyle F} between two interacting particles is simply obtained by negating and differentiating the Lennard-Jones potential with respect to r {\displaystyle r} , i.e. F = − d V / d r {\displaystyle F=-\mathrm {d} V/\mathrm {d} r} . Depending on the distance betwee... | Lennard-Jones potential | 0.812591 |
17,925 | These differences in combination with differences in the treatment of the long-range interactions (see below) can influence computed thermophysical properties.Since the Lennard-Jonesium is the archetype for the modeling of simple yet realistic intermolecular interactions, a large number of thermophysical properties wer... | Lennard-Jones potential | 0.812591 |
17,926 | Thermophysical properties of the Lennard-Jones substance, i.e. particles interacting with the Lennard-Jones potential can be obtained using statistical mechanics. Some properties can be computed analytically, i.e. with machine precision, whereas most properties can only be obtained by performing molecular simulations. ... | Lennard-Jones potential | 0.812591 |
17,927 | A large number of equations of state (EOS) for the Lennard-Jones potential/ substance have been proposed since its characterization and evaluation became available with the first computer simulations. Due to the fundamental importance of the Lennard-Jones potential, most currently available molecular-based EOS are buil... | Lennard-Jones potential | 0.812591 |
17,928 | The database and knowledge for the Lennard-Jones solid is significantly poorer than for the fluid phases, which is mainly due to the fact that the Lennard-Jones potential is less frequently used in applications for the modeling of solid substances. It was realized early that the interactions in solid phases should not ... | Lennard-Jones potential | 0.812591 |
17,929 | Although most consider the French physicist Nicolas Sadi Carnot to be the first true thermodynamicist, the term thermodynamics itself wasn't coined until 1849 by Lord Kelvin in his publication An Account of Carnot's Theory of the Motive Power of Heat.The first thermodynamic textbook was written in 1859 by William Ranki... | Thermodynamicist | 0.812589 |
17,930 | In thermodynamics, a thermodynamicist is someone who studies thermodynamic processes and phenomena, i.e. the physics that deal with mechanical action and relations of heat. Among the well-known number of famous thermodynamicists, include Sadi Carnot, Rudolf Clausius, Willard Gibbs, Hermann von Helmholtz, and Max Planck... | Thermodynamicist | 0.812589 |
17,931 | For very small magnetic Reynolds numbers, the diffusive term overcomes the convective term. For example, in an electrically resistive fluid with large values of η {\displaystyle \eta } , the magnetic field is diffused away very fast, and the Alfvén's Theorem cannot be applied. This means magnetic energy is dissipated t... | Induction equation | 0.812588 |
17,932 | More generally, the equation for the perfectly-conducting limit applies in regions of large spatial scale rather than infinite electric conductivity, (i.e., η → 0 {\displaystyle \eta \to 0} ), as this also makes the magnetic Reynolds number very large such that the diffusion term can be neglected. This limit is called ... | Induction equation | 0.812588 |
17,933 | In magnetohydrodynamics, the induction equation is a partial differential equation that relates the magnetic field and velocity of an electrically conductive fluid such as a plasma. It can be derived from Maxwell's equations and Ohm's law, and plays a major role in plasma physics and astrophysics, especially in dynamo ... | Induction equation | 0.812588 |
17,934 | This effect is only explainable if light can behave as a stream of particles and it convinced the physics community of the existence of Einstein's light-particle. Lastly, in 1926, one year before the theory of quantum mechanics was published, Gilbert N. Lewis introduced the term "photon", which soon became the name for... | Messenger particle | 0.812588 |
17,935 | EM-Bokashi, invented and marketed by Higa, uses commercial EM to ferment organic kitchen waste. Treatments with EM-Bokashi show no effects on soil microbiology or as bio-fertilizer which are caused by the EM microorganisms. Observed effects relate to the effect of the nutrition rich compost carrier substrate of the EM-... | Effective microorganism | 0.812585 |
17,936 | The resulting effects on crop growth depend nonspecifically upon multiple factors, including effects of the introduced EM nutrient solution with microorganisms, effects of the naturally microorganism-rich bio-organic fraction in the soil, and indirect effects of microbially-synthesized metabolites (e.g., phytohormones ... | Effective microorganism | 0.812585 |
17,937 | in computer science from Columbia University's School of Engineering and Applied Science and a Ph.D. in computer science from Carnegie Mellon University. His 1990 thesis was titled A Practical Approach to Replication of Abstract Data Objects and was nominated for the ACM Distinguished Doctoral Dissertation Award.Bloch ... | Effective Java | 0.812585 |
17,938 | Prolate spheroidal coordinates are a three-dimensional orthogonal coordinate system that results from rotating the two-dimensional elliptic coordinate system about the focal axis of the ellipse, i.e., the symmetry axis on which the foci are located. Rotation about the other axis produces oblate spheroidal coordinates. ... | Prolate spheroidal coordinates | 0.812584 |
17,939 | Similar to Korn and Korn (1961), but uses colatitude θ = 90° - ν instead of latitude ν. Moon PH, Spencer DE (1988). "Prolate Spheroidal Coordinates (η, θ, ψ)". Field Theory Handbook, Including Coordinate Systems, Differential Equations, and Their Solutions (corrected 2nd ed., 3rd print ed.). | Prolate spheroidal coordinates | 0.812584 |
17,940 | Linear regression plays an important role in the subfield of artificial intelligence known as machine learning. The linear regression algorithm is one of the fundamental supervised machine-learning algorithms due to its relative simplicity and well-known properties. | Line regression | 0.812584 |
17,941 | Morse PM, Feshbach H (1953). Methods of Theoretical Physics, Part I. New York: McGraw-Hill. p. 661. | Prolate spheroidal coordinates | 0.812584 |
17,942 | The following are some of the important topics in mathematical statistics: | Mathematical Statistics | 0.812581 |
17,943 | Statistical inference is the process of drawing conclusions from data that are subject to random variation, for example, observational errors or sampling variation. Initial requirements of such a system of procedures for inference and induction are that the system should produce reasonable answers when applied to well-... | Mathematical Statistics | 0.812581 |
17,944 | Data analysis is divided into: descriptive statistics – the part of statistics that describes data, i.e. summarises the data and their typical properties. inferential statistics – the part of statistics that draws conclusions from data (using some model for the data): For example, inferential statistics involves select... | Mathematical Statistics | 0.812581 |
17,945 | Statistical data collection is concerned with the planning of studies, especially with the design of randomized experiments and with the planning of surveys using random sampling. The initial analysis of the data often follows the study protocol specified prior to the study being conducted. The data from a study can al... | Mathematical Statistics | 0.812581 |
17,946 | Mathematical statistics is a key subset of the discipline of statistics. Statistical theorists study and improve statistical procedures with mathematics, and statistical research often raises mathematical questions. Mathematicians and statisticians like Gauss, Laplace, and C. S. Peirce used decision theory with probabi... | Mathematical Statistics | 0.812581 |
17,947 | In statistics, regression analysis is a statistical process for estimating the relationships among variables. It includes many ways for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables. More specifically, regression analys... | Mathematical Statistics | 0.812581 |
17,948 | Nonparametric statistics are values calculated from data in a way that is not based on parameterized families of probability distributions. They include both descriptive and inferential statistics. The typical parameters are the mean, variance, etc. Unlike parametric statistics, nonparametric statistics make no assumpt... | Mathematical Statistics | 0.812581 |
17,949 | Mathematical statistics is the application of probability theory, a branch of mathematics, to statistics, as opposed to techniques for collecting statistical data. Specific mathematical techniques which are used for this include mathematical analysis, linear algebra, stochastic analysis, differential equations, and mea... | Mathematical Statistics | 0.812581 |
17,950 | In statistics, naive Bayes classifiers are a family of simple "probabilistic classifiers" based on applying Bayes' theorem with strong (naive) independence assumptions between the features (see Bayes classifier). They are among the simplest Bayesian network models, but coupled with kernel density estimation, they can a... | Naive Bayes classifier | 0.812574 |
17,951 | It is easy to design a cooling system for almost any equipment if there is unlimited space, power and budget. However, the majority of equipment will have a rigid specification that leaves a limited margin for error. There is a constant pressure to reduce power requirements, system weight and cost parts, without compro... | Thermal management of electronic devices and systems | 0.812572 |
17,952 | All the environmental advantages of semi-closed gas turbine cycles as to an absence of NOx and the release of non-diluted (in N2) CO2 in the flue gas stay the same. An effect of integration becomes apparent with the following clarification. Assigning the efficiency of syngas production in the integrated cycle a value e... | Combined cycle | 0.812569 |
17,953 | It is not exhaustive: C# allows generics directly for primitive types. Java, instead, allows the use of boxed types as type parameters (e.g., List instead of List ). This comes at a cost since all such values need to be boxed/unboxed when used, and they all need to be heap-allocated. However, a generic type can be spec... | Comparison of C Sharp and Java | 0.812568 |
17,954 | Java (the programming language) is designed to execute on the Java platform via the Java Runtime Environment (JRE). The Java platform includes the Java virtual machine (JVM) and a common set of libraries. The JRE was originally designed to support interpreted execution with final compiling as an option. Most JRE enviro... | Comparison of C Sharp and Java | 0.812568 |
17,955 | The book carries the subtitle "A text-book for the use of students of mathematics and physics. Founded upon the lectures of J. Willard Gibbs, Ph.D., LL.D." The first chapter covers vectors in three spatial dimensions, the concept of a (real) scalar, and the product of a scalar with a vector. The second chapter introduc... | Vector Analysis | 0.812567 |
17,956 | Vector Analysis is a textbook by Edwin Bidwell Wilson, first published in 1901 and based on the lectures that Josiah Willard Gibbs had delivered on the subject at Yale University. The book did much to standardize the notation and vocabulary of three-dimensional linear algebra and vector calculus, as used by physicists ... | Vector Analysis | 0.812567 |
17,957 | These are extended to a scalar triple product and a quadruple product. Pages 77–81 cover the essentials of spherical trigonometry, a topic of considerable interest at the time because of its use in celestial navigation. The third chapter introduces the vector calculus notation based on the del operator. | Vector Analysis | 0.812567 |
17,958 | This is a list of number theory topics. See also: List of recreational number theory topics Topics in cryptography | List of number theory topics | 0.812567 |
17,959 | Davenport–Schmidt theorem Irrational number Square root of two Quadratic irrational Integer square root Algebraic number Pisot–Vijayaraghavan number Salem number Transcendental number e (mathematical constant) pi, list of topics related to pi Squaring the circle Proof that e is irrational Lindemann–Weierstrass theorem ... | List of number theory topics | 0.812567 |
17,960 | Covering system Small set (combinatorics) Erdős–Ginzburg–Ziv theorem Polynomial method Van der Waerden's theorem Szemerédi's theorem Collatz conjecture Gilbreath's conjecture Erdős–Graham conjecture Znám's problem | List of number theory topics | 0.812567 |
17,961 | Pythagorean triple Pell's equation Elliptic curve Nagell–Lutz theorem Mordell–Weil theorem Mazur's torsion theorem Congruent number Arithmetic of abelian varieties Elliptic divisibility sequences Mordell curve Fermat's Last Theorem Mordell conjecture Euler's sum of powers conjecture abc Conjecture Catalan's conjecture ... | List of number theory topics | 0.812567 |
17,962 | Note: Computational number theory is also known as algorithmic number theory. Residue number system Cunningham project Quadratic residuosity problem | List of number theory topics | 0.812567 |
17,963 | Montgomery reduction Modular exponentiation Linear congruence theorem Method of successive substitution Chinese remainder theorem Fermat's little theorem Proofs of Fermat's little theorem Fermat quotient Euler's totient function Noncototient Nontotient Euler's theorem Wilson's theorem Primitive root modulo n Multiplica... | List of number theory topics | 0.812567 |
17,964 | Unimodular lattice Fermat's theorem on sums of two squares Proofs of Fermat's theorem on sums of two squares | List of number theory topics | 0.812567 |
17,965 | Twin prime Brun's constant Cousin prime Prime triplet Prime quadruplet Sexy prime Sophie Germain prime Cunningham chain Goldbach's conjecture Goldbach's weak conjecture Second Hardy–Littlewood conjecture Hardy–Littlewood circle method Schinzel's hypothesis H Bateman–Horn conjecture Waring's problem Brahmagupta–Fibonacc... | List of number theory topics | 0.812567 |
17,966 | Composite number Highly composite number Even and odd numbers Parity Divisor, aliquot part Greatest common divisor Least common multiple Euclidean algorithm Coprime Euclid's lemma Bézout's identity, Bézout's lemma Extended Euclidean algorithm Table of divisors Prime number, prime power Bonse's inequality Prime factor T... | List of number theory topics | 0.812567 |
17,967 | See list of algebraic number theory topics | List of number theory topics | 0.812567 |
17,968 | Riemann zeta function Basel problem on ζ(2) Hurwitz zeta function Bernoulli number Agoh–Giuga conjecture Von Staudt–Clausen theorem Dirichlet series Euler product Prime number theorem Prime-counting function Meissel–Lehmer algorithm Offset logarithmic integral Legendre's constant Skewes' number Bertrand's postulate Pro... | List of number theory topics | 0.812567 |
17,969 | Multiplicative function Additive function Dirichlet convolution Erdős–Kac theorem Möbius function Möbius inversion formula Divisor function Liouville function Partition function (number theory) Integer partition Bell numbers Landau's function Pentagonal number theorem Bell series Lambert series | List of number theory topics | 0.812567 |
17,970 | In particle physics, wave mechanics and optics, momentum transfer is the amount of momentum that one particle gives to another particle. It is also called the scattering vector as it describes the transfer of wavevector in wave mechanics. In the simplest example of scattering of two colliding particles with initial mom... | Momentum transfer | 0.812564 |
17,971 | Since 2012 there has been a push from the cellular and computational neuroscience community to come up with a universal classification of neurons that will apply to all neurons in the brain as well as across species. This is done by considering the three essential qualities of all neurons: electrophysiology, morphology... | Nerve cells | 0.812561 |
17,972 | The neuron's place as the primary functional unit of the nervous system was first recognized in the late 19th century through the work of the Spanish anatomist Santiago Ramón y Cajal.To make the structure of individual neurons visible, Ramón y Cajal improved a silver staining process that had been developed by Camillo ... | Nerve cells | 0.812561 |
17,973 | Mechanica (Latin: Mechanica sive motus scientia analytice exposita; 1736) is a two-volume work published by mathematician Leonhard Euler which describes analytically the mathematics governing movement. Euler both developed the techniques of analysis and applied them to numerous problems in mechanics, notably in later p... | Mechanica | 0.812559 |
17,974 | The data may have been used in published texts and statistics elsewhere, and the data could already be promoted in the media or bring in useful personal contacts. Secondary data generally have a pre-established degree of validity and reliability which need not be re-examined by the researcher who is re-using such data.... | Secondary Data | 0.812551 |
17,975 | Secondary data can be obtained from many sources: censuses and government departments like housing, social security, electoral statistics, tax records internet searches and libraries GPS and remote sensing km progress reports journals, newspapers and magazines | Secondary Data | 0.812551 |
17,976 | (In multiplying measures, some of which are infinite, we define the product to be zero if any factor is zero.) In fact, when the spaces are σ {\displaystyle \sigma } -finite, the product measure is uniquely defined, and for every measurable set E, ( μ 1 × μ 2 ) ( E ) = ∫ X 2 μ 1 ( E y ) d μ 2 ( y ) = ∫ X 1 μ 2 ( E x ) ... | Product measure | 0.81255 |
17,977 | Given two measure spaces, there is always a unique maximal product measure μmax on their product, with the property that if μmax(A) is finite for some measurable set A, then μmax(A) = μ(A) for any product measure μ. In particular its value on any measurable set is at least that of any other product measure. This is the... | Product measure | 0.812549 |
17,978 | {\displaystyle B_{2}\in \Sigma _{2}.} This sigma algebra is called the tensor-product σ-algebra on the product space. A product measure μ 1 × μ 2 {\displaystyle \mu _{1}\times \mu _{2}} (also denoted by μ 1 ⊗ μ 2 {\displaystyle \mu _{1}\otimes \mu _{2}} by many authors) is defined to be a measure on the measurable spac... | Product measure | 0.812549 |
17,979 | In mathematics, given two measurable spaces and measures on them, one can obtain a product measurable space and a product measure on that space. Conceptually, this is similar to defining the Cartesian product of sets and the product topology of two topological spaces, except that there can be many natural choices for t... | Product measure | 0.812549 |
17,980 | There are multiple ways to deal with underfitting: Increase the complexity of the model: If the model is too simple, it may be necessary to increase its complexity by adding more features, increasing the number of parameters, or using a more flexible model. However, this should be done carefully to avoid overfitting. U... | Underfitting | 0.812547 |
17,981 | At the other extreme are models that can be reproduced only by exactly duplicating the original modeler's entire setup, making reuse or scientific reproduction difficult. It may be possible to reconstruct details of individual training instances from an overfitted machine learning model's training set. This may be unde... | Underfitting | 0.812547 |
17,982 | Underfitting is the inverse of overfitting, meaning that the statistical model or machine learning algorithm is too simplistic to accurately capture the patterns in the data. A sign of underfitting is that there is a high bias and low variance detected in the current model or algorithm used (the inverse of overfitting:... | Underfitting | 0.812547 |
17,983 | In statistics, an inference is drawn from a statistical model, which has been selected via some procedure. Burnham & Anderson, in their much-cited text on model selection, argue that to avoid overfitting, we should adhere to the "Principle of Parsimony". The authors also state the following. : 32–33 Overfitted models …... | Underfitting | 0.812547 |
17,984 | Spinors are sections of our bundle Λ ∗ T , {\displaystyle \mathbf {\Lambda } ^{*}\mathbf {T} ,} and generators of the Clifford algebra are the fibers of our other bundle ( T ⊕ T ∗ ) ⊗ C . {\displaystyle (\mathbf {T} \oplus \mathbf {T} ^{*})\otimes \mathbb {C} .} Therefore, a given pure spinor is annihilated by a half-d... | Generalized complex structures | 0.812546 |
17,985 | Thus sections of the bundle ( T ⊕ T ∗ ) ⊗ C {\displaystyle (\mathbf {T} \oplus \mathbf {T} ^{*})\otimes \mathbb {C} } act on differential forms. This action is a representation of the action of the Clifford algebra on spinors. A spinor is said to be a pure spinor if it is annihilated by half of a set of a set of genera... | Generalized complex structures | 0.812546 |
17,986 | In materials science, shear modulus or modulus of rigidity, denoted by G, or sometimes S or μ, is a measure of the elastic shear stiffness of a material and is defined as the ratio of shear stress to the shear strain: G = d e f τ x y γ x y = F / A Δ x / l = F l A Δ x {\displaystyle G\ {\stackrel {\mathrm {def} }{=}}\ {... | Modulus of rigidity | 0.812545 |
17,987 | In the context of chemistry, energy is an attribute of a substance as a consequence of its atomic, molecular, or aggregate structure. Since a chemical transformation is accompanied by a change in one or more of these kinds of structure, it is usually accompanied by a decrease, and sometimes an increase, of the total en... | Energy (physics) | 0.812544 |
17,988 | In quantum mechanics, energy is defined in terms of the energy operator (Hamiltonian) as a time derivative of the wave function. The Schrödinger equation equates the energy operator to the full energy of a particle or a system. Its results can be considered as a definition of measurement of energy in quantum mechanics.... | Energy (physics) | 0.812544 |
17,989 | All living organisms constantly take in and release energy. Due to mass–energy equivalence, any object that has mass when stationary (called rest mass) also has an equivalent amount of energy whose form is called rest energy, and any additional energy (of any form) acquired by the object above that rest energy will inc... | Energy (physics) | 0.812544 |
17,990 | In physics, energy (from Ancient Greek ἐνέργεια (enérgeia) 'activity') is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat and light. Energy is a conserved quantity—the law of conservation of energy states that energy can be... | Energy (physics) | 0.812544 |
17,991 | Li and Lin have used the Babel function to aid in creating effective dictionaries for Machine Learning applications. | Babel function | 0.812543 |
17,992 | The binomial theorem is closely related to the probability mass function of the negative binomial distribution. The probability of a (countable) collection of independent Bernoulli trials { X t } t ∈ S {\displaystyle \{X_{t}\}_{t\in S}} with probability of success p ∈ {\displaystyle p\in } all not happening is P ( ⋂ t... | Multi-binomial theorem | 0.812541 |
17,993 | Induction yields another proof of the binomial theorem. When n = 0, both sides equal 1, since x0 = 1 and ( 0 0 ) = 1. {\displaystyle {\tbinom {0}{0}}=1.} Now suppose that the equality holds for a given n; we will prove it for n + 1. | Multi-binomial theorem | 0.812541 |
17,994 | If n {\displaystyle n} and d {\displaystyle d} are both large, ( n + d d ) {\displaystyle {\tbinom {n+d}{d}}} grows exponentially.PIT concerns whether a polynomial is identical to the zero polynomial, rather than whether the function implemented by the polynomial always evaluates to zero in the given domain. For exampl... | Polynomial identity testing | 0.812534 |
17,995 | As with any polynomial identity testing question, it can be trivially transformed into the question "Is a certain polynomial equal to 0? "; in this case we can ask "Does ( x + y ) ( x − y ) − ( x 2 − y 2 ) = 0 {\displaystyle (x+y)(x-y)-(x^{2}-y^{2})=0} "? If we are given the polynomial as an algebraic expression (rathe... | Polynomial identity testing | 0.812534 |
17,996 | In mathematics, polynomial identity testing (PIT) is the problem of efficiently determining whether two multivariate polynomials are identical. More formally, a PIT algorithm is given an arithmetic circuit that computes a polynomial p in a field, and decides whether p is the zero polynomial. Determining the computation... | Polynomial identity testing | 0.812534 |
17,997 | The Parker Solar Probe concept originates in the 1958 report by the Fields and Particles Group (Committee 8 of the National Academy of Sciences' Space Science Board) which proposed several space missions including "a solar probe to pass inside the orbit of Mercury to study the particles and fields in the vicinity of th... | Parker Solar Probe | 0.812531 |
17,998 | Johns Hopkins University Applied Physics Laboratory designed and built the spacecraft, which was launched on 12 August 2018. It became the first NASA spacecraft named after a living person, honoring physicist Eugene Newman Parker, professor emeritus at the University of Chicago.A memory card containing the names of ove... | Parker Solar Probe | 0.812531 |
17,999 | Floral biology is an area of ecological research that studies the evolutionary factors that have moulded the structures, behaviour and physiological aspects involved in the flowering of plants. The field is broad and interdisciplinary and involves research requiring expertise from multiple disciplines that can include ... | Floral biology | 0.81253 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.