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Gaussian (software)
Gaussian is a commercial software package for electronic structure modeling and computational chemistry, first released in 1970 by John Pople's Nobel-recognized group and still among the field's most widely used codes.
Gaussian accelerated molecular dynamics
Gaussian accelerated molecular dynamics (GaMD) is an enhanced sampling method for molecular dynamics simulations, introduced by Yinglong Miao and J. Andrew McCammon as a fix to accelerated MD's reweighting problem.
Gaussian approximation (density evolution)
The Gaussian approximation is a one-dimensional simplification of density evolution, assuming decoder messages follow Gaussian distributions; introduced for LDPC codes by Chung, Richardson, and Urbanke in 2001.
Gaussian approximation potential
The Gaussian approximation potential (GAP) is a machine learning method, and code, that uses Gaussian process regression to reproduce density-functional-theory energies and forces at far lower computational cost.
Gaussian basis set
A Gaussian basis set is a collection of Gaussian-type functions centered on a molecule's atoms whose combinations represent molecular orbitals in quantum chemical calculations, proposed by S. F. Boys in 1950.
Gaussian beam
A Gaussian beam is a beam of light with a Gaussian transverse intensity profile and a waist where wavefronts are flat, the fundamental TEM00 mode of a laser resonator.
Gaussian binomial coefficient
The Gaussian binomial coefficient, or q-binomial coefficient, is a polynomial in q that counts the k-dimensional subspaces of an n-dimensional vector space over a finite field of q elements.
Gaussian copula
The Gaussian copula is a probability model that couples random variables by multivariate normal dependence while their margins stay arbitrary; it was widely used to price structured credit before the 2008 financial crisis.
Gaussian curvature
Gaussian curvature is the product of the two principal curvatures of a surface at a point. Gauss introduced it in 1827, proving it is measurable from within the surface.
Gaussian elimination
Gaussian elimination, also known as row reduction, is an algorithm that solves systems of linear equations by reducing a matrix to upper triangular form and applying back substitution.
Gaussian free field
The Gaussian free field is a centered Gaussian random field with covariance given by the Laplacian's Green function, described as a higher-dimensional analog of Brownian motion.
Gaussian function
The Gaussian function, also known as the Gaussian curve, is a function whose graph is a symmetric bell-shaped curve that falls off rapidly, named after Carl Friedrich Gauss.
Gaussian graphical model
A Gaussian graphical model, or covariance selection model, is a probabilistic graphical model for Gaussian variables whose graph edges correspond to nonzero entries of the inverse covariance matrix.
Gaussian integer
A Gaussian integer, also known as a complex integer, is a complex number a + bi where a and b are ordinary integers, named for Carl Friedrich Gauss.
Gaussian integral
The Gaussian integral, also known as the Euler-Poisson integral, is the integral of the Gaussian function over the whole real line, equal to the square root of pi.
Gaussian isoperimetric inequality
The Gaussian isoperimetric inequality, proven independently by Sudakov and Tsirelson and by Borell in the 1970s, states that half-spaces minimize Gaussian perimeter among sets of given measure, implying Gaussian concentration.
Gaussian Markov process
A Gaussian Markov process is a stochastic process that is both Gaussian and Markov, so its future depends only on its present value; examples include Brownian motion and the Ornstein–Uhlenbeck process.
Gaussian measure
A Gaussian measure is a probability measure on an infinite-dimensional space, such as a Banach or Hilbert space, where every continuous linear functional is a Gaussian random variable.
Gaussian mixture model
A Gaussian mixture model is a probabilistic model representing data as a weighted sum of Gaussian distributions, used for soft clustering and fitted with the EM algorithm.
Gaussian orthogonal ensemble
The Gaussian orthogonal ensemble (GOE) is a probability distribution on real symmetric matrices whose law is invariant under conjugation by orthogonal matrices, introduced by Eugene Wigner for nuclear level statistics.
Gaussian prime
A Gaussian prime is a Gaussian integer like 1 + i or 3 that cannot be factored except by units, classified by Carl Friedrich Gauss in 1832.
Gaussian process
A Gaussian process, also called a Gaussian stochastic process, is a stochastic process where every finite subset of variables has a joint multivariate Gaussian distribution.
Gaussian process regression
Gaussian process regression, developed in geostatistics as kriging, is a Bayesian method that places a Gaussian process prior over functions and predicts with calibrated uncertainty.
Gaussian random field
A Gaussian random field is a collection of random variables over space where every finite set follows a normal distribution, the standard model of spatial uncertainty.
Gaussian Schell model
The Gaussian Schell model is a statistical model of partially coherent light beams in which intensity and spatial coherence follow Gaussian functions, used in free-space optical communication.
Gaussian simulation
Gaussian simulation is a computational method that generates samples from Gaussian distributions, multivariate normal vectors, and Gaussian process realizations, typically by transforming independent standard normal draws to match a required mean and covariance.
Gaussian state
A Gaussian state is a quantum state of bosonic modes, such as light, whose Wigner function is Gaussian; examples include vacuum, coherent, squeezed, and thermal states.
Gaussian surface
A Gaussian surface is any closed, real or imaginary surface in space through which the electric flux is evaluated when applying Gauss's law; only charge inside counts.
Gaussian symplectic ensemble
The Gaussian symplectic ensemble (GSE) is a random matrix ensemble introduced by Freeman Dyson in 1962 for quantum systems with time-reversal invariance but no rotational symmetry.
Gaussian units
Gaussian units are a system of metric electrical and magnetic units built on the centimeter, gram, and second, with charge defined directly from Coulomb's law.