Mathematics and statistics

Heptagram

Heptagram (Heptagramm, heptagramme, heptagrama): a regular seven-pointed star polygon, {7/2} or great heptagram {7/3}, formed from a heptagon's diagonals; density 2, apex angles 540°/7 and 180°/7, not compass-and-straightedge constructible.

Heritability estimation

Heritability estimation is a family of statistical methods in genetics that quantify the proportion of variation in a trait attributable to genetic differences, using twin or genomic data.

Hermann Minkowski

Hermann Minkowski (1864–1909) was a German mathematician who created the geometry of numbers and gave special relativity its four-dimensional spacetime formulation, now called Minkowski space.

Hermite distribution

The Hermite distribution is a two-parameter discrete probability distribution for overdispersed or multimodal count data, introduced by C. D. Kemp and Adrienne W. Kemp in 1965.

Hermite interpolation

Hermite interpolation is a polynomial interpolation method matching function values and derivatives at nodes; matching values and first derivatives at n nodes gives a unique polynomial of degree at most 2n − 1.

Hermite normal form

The Hermite normal form (HNF) is a unique canonical echelon-like form of an integer matrix, reached by multiplying by a matrix of determinant ±1 while preserving the generated lattice.

Hermite polynomials

Hermite polynomials, also called the probabilists' Hermite polynomials in one of two conventions, are classical orthogonal polynomials on the real line with a Gaussian weight, central to the quantum harmonic oscillator.

Hermitian adjoint

The Hermitian adjoint, also called the Hermitian conjugate, is the unique operator A† with ⟨Au, v⟩ = ⟨u, A†v⟩, generalizing the conjugate transpose of a matrix.

Hermitian matrix

A Hermitian matrix, also called a self-adjoint matrix, is a complex square matrix that equals its own conjugate transpose; its eigenvalues are always real, and it is unitarily diagonalizable.

Hermitian metric

A Hermitian metric is a smoothly varying, positive-definite Hermitian inner product on the holomorphic tangent bundle of a complex manifold, the analog of a Riemannian metric.

Heron's formula

Heron's formula, also called Hero's formula, gives the area of a triangle from its three side lengths alone, without heights or angles, in Heron's Metrica of about AD 60.

Herringbone pattern

The herringbone pattern is a zigzag arrangement of rectangular pieces, such as tiles or bricks, laid at right angles with their ends meeting the sides of the next.

Hessian matrix

The Hessian matrix, or Hesse matrix, is the square matrix of a function's second-order partial derivatives, used to classify critical points as minima, maxima, or saddle points.

Heston model

The Heston model is a stochastic volatility model in mathematical finance in which an asset's variance is itself random and mean-reverting, introduced by Steven Heston in 1993.

Heun function

The Heun function solves Heun's equation, the most general second-order differential equation with four regular singular points, proposed by Karl Heun in 1889 as a generalization of the hypergeometric equation.

Heuristic

A heuristic, also called a heuristic technique, is a problem-solving or decision-making method that finds adequate answers quickly without guaranteeing an optimal solution, used where exact methods are too slow or unavailable.

Hewitt–Savage zero–one law

The Hewitt–Savage zero–one law is a probability theorem stating that any event invariant under finite permutations of i.i.d. random variables has probability 0 or 1.

Hexadecimal

Hexadecimal, also known as base 16 or hex, is a numeral system using sixteen digits, 0–9 and A–F, serving in computing as a compact shorthand for binary.

Hexagon

A hexagon is a polygon with six straight sides and six angles, regular when all sides and angles are equal, with interior angles of 120°.

Hexagram

A hexagram is a six-pointed star figure, most familiarly the compound of two equilateral triangles known as the Star of David and Seal of Solomon.

Heyting algebra

A Heyting algebra, also called a pseudo-Boolean algebra, is a bounded lattice with an implication operation, serving as the algebraic semantics of intuitionistic logic as Boolean algebras do for classical logic.

Hidden Markov model

A hidden Markov model (HMM), also called a hidden Markov chain, is a statistical model for sequential data where hidden states follow a Markov chain and each emits observations.

Hidden semi-Markov model

A hidden semi-Markov model (HSMM), also called an explicit duration HMM, is a statistical model extending the hidden Markov model by letting hidden states persist for explicitly modeled random durations.

Hierarchical Bayesian analysis

Hierarchical Bayesian analysis is a statistical modeling approach in which parameters have priors structured in multiple levels, partially pooling information across groups during Bayesian inference.

Hierarchical Dirichlet process

The hierarchical Dirichlet process (HDP) is a Bayesian nonparametric prior introduced by Teh, Jordan, Beal, and Blei in 2006, letting related groups share mixture components.

Hierarchy

In mathematics, a hierarchy classifies objects by definitional complexity; in combinatorics, it is a family of subsets in which any two are disjoint or nested.

Hierarchy of evidence

The hierarchy of evidence, or levels of evidence, ranks study designs by susceptibility to bias, with systematic reviews and meta-analyses of randomized trials at the top.

Higgs bundle

A Higgs bundle is a pair consisting of a holomorphic vector bundle and a Higgs field over a Riemann surface, introduced by Nigel Hitchin in 1987.

High availability

High availability (HA) is a property of a computer system that keeps a service usable through component interruptions, using redundancy, replication, and automatic failover to keep downtime small.