6,052 articles
Binary arithmetic
Binary arithmetic is arithmetic in base 2 using only the digits 0 and 1, the arithmetic of electronic computers, first described by Leibniz around 1679.
Binary decision diagram
A binary decision diagram (BDD) is a rooted directed acyclic graph that represents a Boolean function compactly; Bryant's 1986 ordered form made it canonical and useful in formal verification.
Binary Golay code
The binary Golay code is a perfect error-correcting code of length 23 that corrects any three bit errors, published by Marcel Golay in 1949 and used on NASA's Voyager missions.
Binary logarithm
The binary logarithm, also called log2 or the base-2 logarithm, is the logarithm to base 2, the exponent y such that 2 to the power y equals x.
Binary matroid
A binary matroid is a matroid representable over the two-element field GF(2). Tutte proved in 1958 that these are exactly the matroids with no U2,4-minor.
Binary number
A binary number, also called a base-2 number, is written using only the digits 0 and 1, and digital computers use it to store and manipulate all data.
Binary operation
A binary operation, also called a binary operator or dyadic operation, is a function combining two elements of a set to yield an element of the same set.
Binary relation
A binary relation, also known as a dyadic or two-place relation, is a set of ordered pairs recording which elements of one set relate to which elements of another.
Binary-coded decimal
Binary-coded decimal (BCD) is a way of representing decimal digits in digital systems, storing each digit 0 through 9 in its own 4-bit group of bits.
Binet's formula
Binet's formula is a closed-form expression computing the nth Fibonacci number directly from the golden ratio, published by Jacques Binet in 1843 though Euler had it in 1765.
Binomial coefficient
The binomial coefficient, or choose function, counts the ways to choose k objects from n distinct objects without order, and gives the coefficients in the expansion of (a+b)^n.
Binomial distribution
The binomial distribution, also called the binomial probability distribution, is a discrete probability distribution that gives the probability of exactly x successes in n independent trials with constant success probability p.
Binomial proportion confidence interval
A binomial proportion confidence interval estimates a binomial success probability from trials and successes; common formulas include the Wald, Wilson score, Clopper-Pearson, and Agresti-Coull intervals.
Binomial regression
Binomial regression, also called the binomial regression model, is a generalized linear model for binary outcomes or success counts, estimating how predictors change the probability of success.
Binomial series
The binomial series, also known as Newton's binomial series, is the power series for (1+z)^α, converging for |z| < 1 and probably first stated by Newton in 1664–1665.
Binomial test
The binomial test is an exact statistical test of a Bernoulli success probability: it computes how improbable an observed success count would be under a specified value.
Binomial theorem
The binomial theorem, or binomial formula, expands powers of a sum using binomial coefficients from Pascal's triangle; first attributed to al-Karaji around 1029 and extended to fractional powers by Newton.
Binomial transform
The binomial transform is a sequence transformation of number theory and combinatorics mapping a(n) to b(n) = sum k(n,k) a(k), invertible with alternating signs, shifting Bell numbers.
Bioanalytical method validation
Bioanalytical method validation is the process of proving that a method measuring drugs, metabolites, or biomarkers in biological matrices is accurate, precise, and reliable enough to support regulatory decisions.
Bioequivalence
Bioequivalence is the demonstration that two drug products with the same active ingredient are absorbed at the same rate and extent, the basis for approving generics.
Biological network inference
Biological network inference is the reconstruction of a biological system's interaction structure, usually a gene regulatory network, from high-throughput data using methods like Bayesian networks and deep learning.
Biometrika
Biometrika is a quarterly peer-reviewed journal of statistical theory and method, founded in 1901 by Weldon, Galton, and Karl Pearson and published by Oxford University Press.
Biorthogonal wavelet
A biorthogonal wavelet is a wavelet paired with a dual basis, one used for analysis and one for synthesis, enabling symmetric, linear-phase compactly supported wavelets.
Biostatistics
Biostatistics, also called biometrics or biometry, is the science of collecting and analyzing biological and health data statistically, used to estimate disease frequency, search for causes, and design clinical trials.
Bipartite graph
A bipartite graph is a graph whose vertices split into two sets with every edge joining the sets, equivalent to having no odd cycle; used in matching and assignment problems.
Biplot
A biplot is a graphical method in multivariate statistics that displays the observations and variables of a data matrix in one plot, introduced by K. R. Gabriel in 1971.
Biquaternion
A biquaternion is a quaternion whose four coefficients are complex rather than real numbers, introduced by Hamilton by 1850 and generalized by Clifford in 1871, used in physics.
Birational geometry
Birational geometry, also known as birational algebraic geometry, is the branch of algebraic geometry that studies varieties up to birational equivalence, meaning rational maps invertible on dense open subsets.
Birch and Swinnerton-Dyer conjecture
The Birch and Swinnerton-Dyer conjecture, a Clay Millennium Prize Problem in number theory, states that an elliptic curve's L-function vanishes at s = 1 to order equal to its rank of rational points.
Birkhoff polytope
The Birkhoff polytope, also called the assignment polytope, is the convex polytope of n×n doubly stochastic matrices, whose vertices are the n! permutation matrices by the Birkhoff–von Neumann theorem.