Mathematics and statistics

Birth process

The birth process, or pure birth process, is a continuous-time Markov chain that only moves upward, counting births or arrivals; the Poisson process is a constant-rate special case.

Birth–death process

A birth–death process, also called a birth and death process, is a continuous-time Markov chain where a count changes only by single births or deaths.

Birthday problem

The birthday problem, often called the birthday paradox, asks how large a group must be before two people likely share a birthday; the answer is 23.

Bisection method

The bisection method is a simple, robust root-finding algorithm that repeatedly halves an interval where a continuous function changes sign, converging linearly on a root of f(x) = 0.

Bisimulation (bisimilarity) is a relation between the states of two transition systems guaranteeing behavioral indistinguishability, introduced for automata by David Park in 1981 and extended by Robin Milner to communicating processes.

Bit numbering

Bit numbering assigns index numbers to the individual bits of a value. Conventions include LSB 0, where 0 is least significant, and MSB 0, where 0 is most significant.

Bitwise operation

A bitwise operation, also known as a bit operation, acts on the individual bits of binary numerals rather than on the numbers those bits represent, using operators like AND, OR, XOR, and shifts.

Bitwise operations in C

Bitwise operations in C manipulate individual bits of integer values with operators such as AND, OR, XOR, complement, and shifts, letting C work close to the hardware.

Bivariate analysis

Bivariate analysis is the simultaneous statistical analysis of two variables to determine whether and how strongly they are related, using correlation, simple regression, or chi-square tests.

Oct 22, 2026

Bivariate bicycle code

The bivariate bicycle code is a quantum low-density parity-check code introduced by IBM researchers in 2024, whose gross code encodes 12 logical qubits into 144 data qubits.

Bivector

A bivector is an oriented quantity of grade 2 in exterior algebra, formed as the outer product of two vectors and representing an oriented plane segment.

Black box group

A black box group is a finite group whose elements are encoded by bit strings, with operations available only through oracles; it was introduced by Babai and Szemerédi in 1984.

Black widow optimization algorithm

The Black Widow Optimization Algorithm (BWO) is a population-based metaheuristic for continuous nonlinear optimization, introduced by Hayyolalam and Pourhaji Kazem in 2020 and defined by a cannibalism stage that culls poor solutions.

Black-winged kite algorithm

The black-winged kite algorithm (BKA) is a swarm-intelligence metaheuristic for numerical and engineering optimization, introduced by Jun Wang and colleagues in Artificial Intelligence Review in 2024.

Blackboard bold

Blackboard bold, also called double-struck or chalkboard bold, is a mathematical typeface with doubled strokes imitating bold, used chiefly for number systems like ℤ, ℝ, and ℂ.

Bland–Altman plot

The Bland–Altman plot, also called Tukey mean-difference plot, compares two measurement methods by plotting differences against averages, showing bias and the 95% limits of agreement.

Bloch–Kato conjecture

The Bloch–Kato conjecture, now the norm residue isomorphism theorem, identifies Milnor K-theory modulo ℓ with étale cohomology; proved by Rost, Voevodsky, and Weibel.

Bloch's higher Chow group

Bloch's higher Chow groups are invariants CH^p(X, n) of algebraic varieties, defined by Spencer Bloch in 1986, recovering the classical Chow groups at n = 0.

Block bootstrap

The block bootstrap is a resampling method for time-series data that resamples blocks of consecutive observations to preserve autocorrelation, proposed by Hans R. Künsch in 1989.

Block design

A block design, also called a balanced incomplete block design, is a system of subsets of a finite point set with prescribed equal frequencies, used in statistics and combinatorics.

Block graph

A block graph, also called a clique tree, is an undirected graph in which every block (maximal 2-connected component) is a clique, a class introduced by Frank Harary in 1963.

Block matrix

A block matrix, also called a partitioned matrix, is a matrix divided into smaller rectangular submatrices called blocks, allowing sums, products, and inverses to be computed block by block.

Blocking (statistics)

Blocking is an experimental design technique in statistics that groups experimental units into homogeneous blocks, randomizing treatments within each block to reduce error from nuisance factors.

Blocking flow

A blocking flow is a flow in a network that saturates at least one arc on every source-to-sink path, so no admissible path remains usable.

Blocking set

A blocking set in a finite projective or affine plane is a set of points that intersects every line, originating in Moses Richardson's 1955 work on games.

Blossom algorithm

The blossom algorithm, also called Edmonds's matching algorithm, is Jack Edmonds's 1965 algorithm that computes a maximum-cardinality matching in any undirected graph, even with odd cycles, in polynomial time.

Blow-up (mathematics)

A blow-up in algebraic geometry is a birational transformation that replaces a closed subscheme with the tangent directions out of it; by Hironaka's 1964 theorem, resolutions of singularities are built from sequences of blowups.

Blow-up lemma

The blow-up lemma, proved by Komlós, Sárközy, and Szemerédi and published in Combinatorica in 1997, states that regular pairs of vertices behave like complete bipartite graphs for embedding bounded-degree subgraphs.

Blum–Shub–Smale machine

The Blum–Shub–Smale machine (BSS machine) is a model of computation over the real numbers, treating each arithmetic operation as a single step, introduced by Blum, Shub, and Smale in 1989.