Mathematics and statistics

Solid torus

A solid torus is the three-dimensional shape of a doughnut, the product of a circle with a disk, and a basic building block of three-manifold topology.

Solomonoff's theory of inductive inference

Solomonoff's theory of inductive inference, also called Solomonoff induction, is a mathematical framework for sequence prediction presented by Ray J. Solomonoff in 1964 that initiated algorithmic information theory.

Solvable group

A solvable group, also called a soluble group, is a group built up from abelian groups by a finite chain of extensions, central to Galois theory.

Somers' D

Somers' D, also called Somers' delta, is an asymmetric measure of association between two ordinal variables, treating one as predictor and one as outcome, introduced by Robert H. Somers in 1962.

Sophie Germain

Sophie Germain, born Marie-Sophie Germain, was a self-taught French mathematician who proved the first general results toward Fermat's Last Theorem and won the Paris Academy's 1816 grand prize.

Soul theorem

The soul theorem is a 1972 result of Cheeger and Gromoll: every complete non-compact Riemannian manifold of non-negative curvature is diffeomorphic to the normal bundle of a compact soul.

Soundness

Soundness (logical soundness) is the property of a proof system that proves only what is semantically valid: derivable conclusions hold in every model of the premises.

Soundness and completeness

Soundness and completeness are the properties linking a formal proof system to its semantics: what is provable is valid, and what is valid is provable.

Oct 21, 2026

SOUNDS study

SOUNDS (NCT04661631, Surgery and Lung Ultrasound in COVID-19 Infection) was a Colombian diagnostic accuracy study of lung ultrasound screening for SARS-CoV-2 in 203 urgent surgery patients; sensitivity 52.9%, specificity 91% at score >8, judged not useful for screening.

Space-time clustering

Space-time clustering is a family of statistical tests, such as the Knox test, that detect whether events like disease cases cluster in both space and time.

Space-time white noise

Space-time white noise is a Gaussian random field with independent values at every point of time and space, the standard forcing term for stochastic partial differential equations.

Spacetime algebra

Spacetime algebra (STA) is the Clifford algebra of Minkowski spacetime, introduced by David Hestenes in 1966 to unify spinors, tensors, and Lorentz transformations in one coordinate-free structure.

Spanning tree

A spanning tree of a connected graph is a subgraph including every vertex that is itself a tree, connected and acyclic, and every connected graph has at least one.

Sparse approximation

Sparse approximation is the task of representing a signal as a combination of a small number of elements from a larger dictionary, underlying compression, denoising, and inverse-problem regularization.

Sparse canonical correlation analysis

Sparse canonical correlation analysis (sparse CCA) is a multivariate statistical method finding sparse, maximally correlated linear combinations of two variable sets, enabling feature selection in high-dimensional paired data.

Sparse estimation (statistics)

Sparse estimation is a class of statistical methods that fit high-dimensional models by penalizing coefficients so many are exactly zero, as in Robert Tibshirani's 1996 lasso.

Sparse Fourier transform

A sparse Fourier transform (SFT) is an algorithm that computes a k-sparse approximation of the discrete Fourier transform faster than the fast Fourier transform for frequency-sparse signals.

Sparse grid

A sparse grid is a numerical construction that represents high-dimensional functions on a subset of a full tensor-product grid, using the Smolyak algorithm, enabling quadrature, interpolation, and surrogate modeling in tens of dimensions.

Sparse matrix

A sparse matrix, also known as a sparse array, is a matrix in which most entries are zero; exploiting sparsity makes solving systems with millions of unknowns practical.

Sparse PCA

Sparse PCA is a dimension-reduction method that performs principal component analysis under sparsity constraints, so each component combines only a few of the original variables.

Sparse principal component analysis

Sparse principal component analysis (sparse PCA) is a statistical method that makes PCA components depend on only a few variables, trading some explained variance for interpretability.

Sparse regression

Sparse regression fits a linear model while forcing most coefficients to be exactly zero, delivering both prediction and variable selection on high-dimensional data where ordinary least squares fails.

Sparsification (graph theory)

Graph sparsification replaces a dense weighted graph with a sparse subgraph that preserves every cut value or the Laplacian quadratic form within a small factor.

Sparsity matroid

A sparsity matroid, also called a count matroid, is a matroid defined on the edge set of a graph, where edges are independent exactly when every vertex subset spans at most k|V| − ℓ of them.

Spatial analysis

Spatial analysis, also called spatial data analysis, examines the locations, patterns, and relationships of features in geographic data; its statistics incorporate space directly, unlike traditional statistics.

Oct 10, 2026

Spatial autocorrelation

Spatial autocorrelation is the positive or negative correlation of a variable with itself across geographic space, so similar values cluster on a map; it is measured by Moran's I and matters for regional economic data.

Spatial autoregressive model

The spatial autoregressive (SAR) model is a regression model where each location's outcome depends partly on neighboring outcomes through a spatial weights matrix, used for property values.

Spatial clustering

Spatial clustering is a family of data-analysis methods that groups observations so points close together in geographic location, and often similar in attributes, fall into the same cluster.

Spatial Durbin model

The spatial Durbin model (SDM) is a spatial econometric regression in which the outcome depends on neighbors' outcomes and neighbors' covariates, nesting the SAR, SLX, and SEM models.