Mathematics and statistics

Universal quantification

Universal quantification, marked by the universal quantifier ∀, is the logical operation asserting a formula holds of every object in a domain, one of the two standard quantifiers of predicate logic.

Universal Turing machine

A universal Turing machine is a Turing machine that can simulate any other Turing machine given its encoding and input, described by Alan Turing in 1936.

Unramified extension

An unramified extension is a field extension in which no prime of the base field acquires ramification, meaning the ramification index is 1 and residue fields extend separably.

Untouchable number

An untouchable number, also called a nonaliquot number, is a positive integer that cannot be written as the sum of the proper divisors of any integer.

Unum computing

Unum computing is an approach to computer arithmetic based on the unum number format proposed by John L. Gustafson in 2013, later evolving into the posit.

UPGMA (unweighted pair group method with arithmetic mean) is an agglomerative average-linkage clustering algorithm that builds a rooted ultrametric tree from a distance matrix, widely used in phylogenetics.

Upper and lower bounds

An upper bound of a set is a value at least as large as every member, and a lower bound is one at least as small.

Upper bound theorem

The upper bound theorem, or upper bound conjecture, states that among convex polytopes with n vertices in d dimensions, the cyclic polytope has the most faces.

Utah teapot

The Utah teapot, or Newell teapot, is a standard 3D test model in computer graphics, created in 1975 by Martin Newell at the University of Utah.

Vacuous truth

Vacuous truth, or a vacuously true statement, is a statement true only because its subject class is empty, like a conditional with a false antecedent in classical logic.

Valuation ring

A valuation ring is an integral domain in which, for every pair of elements, one divides the other; it carries a valuation and is a local ring.

Valuative criterion

The valuative criterion is a test for separatedness and properness of a morphism of schemes, asking when maps from the generic point of a valuation ring extend.

Vampire number

A vampire number is a composite number whose digits can be split into two factors using the same digits, like 1260 = 21 × 60, named by Clifford Pickover in 1994.

Van der Pol oscillator

The van der Pol oscillator is a self-sustaining oscillator governed by a second-order differential equation with nonlinear damping, first published by the Dutch physicist Balthasar van der Pol in 1926.

Van der Waerden's theorem

Van der Waerden's theorem, a Ramsey theory result conjectured by Baudet and proved in 1927, states that any coloring of a long enough interval of integers contains a monochromatic arithmetic progression.

Vandermonde matrix

The Vandermonde matrix is a matrix of successive powers of fixed nodes, with determinant equal to the product of all pairwise node differences, used mainly for polynomial interpolation.

Vandermonde's identity

Vandermonde's identity, also called the Vandermonde convolution, is a binomial-coefficient identity stating that choosing k items from two disjoint sets can be counted by splitting the choice between the sets.

Vanishing point

A vanishing point, also called an accidental point, is the point in a perspective image where receding parallel lines appear to converge, central to linear perspective.

Variable (mathematics)

A variable in mathematics is a letter or symbol that represents a number whose value may change, unlike a constant; variables are the basic building blocks of algebra.

Variable elimination

Variable elimination (VE) is an exact inference algorithm for graphical models such as Bayesian networks, computing marginals and conditionals efficiently when the graph has low treewidth.

Variable importance in projection

Variable importance in projection (VIP) is a score from a partial least squares regression model that measures each predictor's contribution, used for variable selection in chemometrics.

Variable neighborhood search

Variable neighborhood search is a metaheuristic optimization method that changes neighborhoods within local search to escape local optima, formalized by Mladenović and Hansen in 1997.

Variable screening (statistics)

Variable screening is a fast statistical model-building step that ranks a large set of candidate predictors by marginal correlation and retains a smaller subset before formal variable selection.

Variance

Variance is a measure of dispersion: the expected squared distance of a random variable's values from its mean, a term introduced by R. A. Fisher in 1918.

Variance gamma process

The variance gamma process, also called Laplace motion, is a Lévy stochastic process that models asset prices, proposed by Dilip Madan and Eugene Seneta in 1990.

Variance inflation factor

The variance inflation factor (VIF) is a diagnostic statistic in regression analysis that measures how much multicollinearity among independent variables inflates the variance of an estimated regression coefficient.

Variance-based sensitivity analysis

Variance-based sensitivity analysis is a family of statistical methods that quantifies how uncertainty in each input of a mathematical model contributes to output variance, yielding Sobol' indices.

Variation of parameters

Variation of parameters is a method for solving nonhomogeneous linear differential equations, replacing the constants in the homogeneous solution with functions chosen to satisfy the full equation.