6,052 articles
Datalog
Datalog is a declarative logic-based query and rule language that allows recursive queries over relational data, developed in the early 1980s and now used in program analysis, security, and graph databases.
Datasaurus dozen
The Datasaurus dozen is a set of 13 datasets with nearly identical summary statistics but completely different scatterplots, created in 2017 by Justin Matejka and George Fitzmaurice of Autodesk Research.
Daubechies wavelet
A Daubechies wavelet is a compactly supported, orthonormal wavelet from a family constructed by Ingrid Daubechies in 1988, notable for combining orthogonality, compact support, and high smoothness.
Davis–Putnam algorithm
The Davis–Putnam algorithm, introduced by Martin Davis and Hilary Putnam in 1960, is a complete decision procedure for propositional satisfiability that eliminates one variable at a time by resolution.
DC programming
DC programming is an optimization framework for minimizing a function expressed as a difference of two convex functions, applied to nonconvex problems in machine learning and finance.
De Bruijn graph
A de Bruijn graph is a directed graph whose vertices are strings and whose edges are k-length strings linking a prefix to its overlapping suffix, central to short-read genome assembly.
De Bruijn sequence
A de Bruijn sequence, or Ouroborean ring, is a cyclic sequence in which every possible length-n string over an alphabet occurs exactly once as a consecutive block.
De Casteljau's algorithm
De Casteljau's algorithm, developed by Paul de Casteljau at Citroën in 1963, evaluates a point on a Bézier curve from its control points by repeated linear interpolation.
De Finetti's theorem
De Finetti's theorem, also called de Finetti's representation theorem, is a result in probability theory: every infinite exchangeable sequence is a mixture of i.i.d. sequences.
De Giorgi–Nash–Moser theorem
The De Giorgi–Nash–Moser theorem is a result in PDE regularity theory: weak solutions of divergence-form equations with rough coefficients are Hölder continuous, proved by De Giorgi, Nash, and Moser in 1957–1960.
De Moivre–Laplace theorem
The de Moivre–Laplace theorem, a special case of the central limit theorem, states that a binomial distribution converges to the normal distribution as the number of trials grows.
De Moivre's formula
De Moivre's formula, also called De Moivre's theorem, states that (cos θ + i sin θ)^n = cos(nθ) + i sin(nθ) for any integer n.
De Morgan's laws
De Morgan's laws, also called De Morgan's theorem, are a pair of rules stating that the negation of AND is the OR of negations, and vice versa.
de Rham cohomology
De Rham cohomology assigns real vector spaces to a smooth manifold by taking closed differential forms modulo exact ones; Georges de Rham pioneered the approach in 1931.
Decagon
A decagon is a polygon with 10 sides and 10 vertices, from the Greek for ten corners; the regular decagon has equal sides and 144° interior angles.
Decidability (logic)
Decidability in logic is the property of a formal system, theory, or class of questions for which an algorithm answers every instance with a yes or a no.
Decidability of first-order theories
Decidability of first-order theories asks which first-order theories have an algorithm deciding whether any sentence follows from them; Presburger arithmetic is decidable, first-order validity is not.
Decimal
The decimal, or base-10, numeral system is the everyday number system whose digits 0 through 9 take place values in powers of ten, separated by a decimal point.
Decision curve analysis
Decision curve analysis is a statistical method for evaluating clinical prediction models by their net benefit across threshold probabilities, introduced by Andrew Vickers and Elena Elkin in 2006.
Decision problem
Decision problem: yes/no computational task over inputs (Entscheidungsproblem, German for decision problem). Central to computability and complexity theory; halting problem and first-order validity are undecidable (Church, Turing 1936).
Decision problems for formal languages
Decision problems for formal languages ask whether emptiness, membership, and equivalence are decidable: all are decidable for regular languages, but equivalence and inclusion are undecidable for context-free grammars.
Declustering (statistics)
Declustering is a family of spatial statistics methods that reweight or subsample clustered data so estimates are less biased by preferential sampling, where some areas are oversampled.
Decomposition theorem
The decomposition theorem is a 1981 result in algebraic geometry, proved by Beilinson, Bernstein, Deligne, and Gabber, stating that derived direct images of intersection cohomology complexes split into direct sums.
Dedekind cut
A Dedekind cut, also called a Dedekind section, is a partition of the rational numbers into two sets marking a real number, devised by Richard Dedekind in 1858.
Dedekind domain
A Dedekind domain, also called a Dedekind ring, is a Noetherian, integrally closed ring, named for Richard Dedekind, in which every nonzero ideal factors uniquely into prime ideals.
Dedekind zeta function
The Dedekind zeta function ζK(s) of a number field K is the analytic function summed over its integral ideals, generalizing the Riemann zeta function, the case K = Q.
Deduction theorem
The deduction theorem is a metatheorem of logic stating that if ψ is derivable from Γ plus assumption φ, then φ → ψ is derivable from Γ alone.
Deep inference
Deep inference is a proof-theoretic methodology in which inference rules apply at any depth inside logical expressions, not just at the root of a formula.
Defects per million opportunities
Defects per million opportunities (DPMO) is a Six Sigma measure: defects divided by opportunities for defects, multiplied by one million, standardized at Motorola in 1986.
Definable set
A definable set is a subset of a structure's universe picked out exactly by a first-order formula, and is a basic object of study in model theory.