Mathematics and statistics

Strongly connected component

A strongly connected component (SCC) of a directed graph is a maximal set of vertices in which every vertex reaches every other, partitioning the graph into disjoint components.

Strongly regular graph

A strongly regular graph is a regular graph in which adjacent and non-adjacent vertex pairs have constant numbers of common neighbors, described by parameters (n, k, λ, μ).

Struck by Lightning (book)

Struck by Lightning: The Curious World of Probabilities is a popular science book about probability in everyday life by statistician Jeffrey S. Rosenthal, published in 2005.

A structural causal model (SCM) is a statistical framework that represents causal relationships among variables through structural equations and a directed graph, supporting interventions and counterfactuals.

Structural equation modeling

Structural equation modeling, also known as covariance structure modeling, is a family of statistical techniques combining factor analysis with regression to test relationships among observed variables and latent constructs.

Structural estimation (econometrics)

Structural estimation is a class of econometric methods that estimates the parameters of an explicitly specified economic model, such as a utility or cost function, to answer counterfactual policy questions.

Structural induction

Structural induction is a proof technique that establishes a property for all elements of an inductively defined data type, such as lists, trees, or formulae.

Structural properties of random variables

Structural properties of random variables are constraints on the joint law, such as independence, exchangeability, joint Gaussianity, and uncorrelatedness, which are not interchangeable and differ in strength.

Structural vector autoregression

A structural vector autoregression (SVAR) is an econometric time-series model combining a VAR with identifying restrictions, turning reduced-form residuals into interpretable structural shocks for causal macroeconomic estimates.

Structure (mathematical logic)

In mathematical logic, a structure, also called a model, is a set with relations and functions that interpret a formal language's symbols, making sentences true or false.

Structure set (surgery theory)

In surgery theory, a structure set is the set of manifolds homotopy equivalent to a given space, taken up to a bordism equivalence, and it classifies manifolds.

Structure theorem for finitely generated modules over a principal ideal domain

The structure theorem for finitely generated modules over a principal ideal domain classifies every such module as a product of cyclic modules, generalizing the classification of finitely generated abelian groups.

Student's t copula

The Student's t copula is a copula built from the multivariate t distribution, parameterized by a correlation matrix and degrees of freedom, with positive symmetric tail dependence.

Student's t-distribution

Student's t-distribution, also called Student t or Gosset's t, is a bell-shaped probability distribution with heavier tails than the normal, derived by William Gosset in 1908 under the pseudonym Student and used in t-tests.

Student's t-test

Student's t-test is a statistical hypothesis test that compares sample means using Student's t-distribution, introduced in 1908 by Guinness brewer William Gosset under the pen name "Student".

Sturges's rule

Sturges's rule is a formula, k = 1 + log2(n), for choosing the number of histogram bins from sample size alone, published by Herbert Sturges in 1926.

Sturm–Liouville theory

Sturm–Liouville theory is the branch of analysis studying second-order linear differential eigenvalue problems with boundary conditions; created by Sturm and Liouville in 1836–1837, it underlies Fourier series and eigenfunction expansions in mathematical physics.

Sturmian word

A Sturmian word, also known as a billiard sequence, is an infinite word over two letters with exactly n + 1 distinct subwords of each length n, the minimum for an aperiodic word.

Subconvexity problem

The subconvexity problem is the problem in analytic number theory of beating the convexity bound for L-functions by a power saving in the analytic conductor.

Subdirect product

A subdirect product is a subalgebra of a direct product of algebras that projects onto every factor, so each factor is a homomorphic image; introduced by Garrett Birkhoff in 1944, it underlies his subdirect representation theorem.

Subfactor

A subfactor is an inclusion of factors within von Neumann algebras, a theory initiated by Vaughan Jones in the early 1980s, whose Jones index takes quantized values.

Subgame perfect equilibrium

Subgame perfect equilibrium is a refinement of Nash equilibrium for sequential games, introduced by Reinhard Selten in 1965, requiring equilibrium in every subgame and ruling out non-credible threats.

Subgradient

A subgradient is a vector generalizing the gradient of a differentiable function to convex functions that may fail to be differentiable, defined by a supporting hyperplane to the graph.

Subgraph isomorphism

Subgraph isomorphism is the NP-complete computational problem of deciding whether a smaller pattern graph can be mapped into a larger host graph, used in cheminformatics, graph databases, and computer vision.

Subgroup

In group theory, a subgroup of a group G is a non-empty subset that forms a group under the same operation; its order divides |G| by Lagrange's theorem.

Submodular set function

A submodular set function assigns real numbers to subsets of a finite set with diminishing returns; its Lovász extension is convex, and it can be minimized in strongly polynomial time.

Subobject classifier

A subobject classifier is an object Ω in a category that classifies subobjects via pullbacks, generalizing characteristic functions of subsets; it is a defining axiom of a topos.

Subordinator (mathematics)

A subordinator is a nondecreasing Lévy process taking values in [0, ∞), serving as a random clock; Bochner introduced subordination in 1949, first applied in finance by Clark in 1973.

Subsequence

A subsequence of a sequence is a new sequence formed by deleting some terms and keeping the rest in their original order, so the indices must strictly increase.