Mathematics and statistics

Sierpiński curve

The Sierpiński curve is a space-filling curve introduced by the Polish mathematician Wacław Sierpiński in 1912, a closed path passing through every interior point of a square.

Sierpiński set

A Sierpiński set is an uncountable set of real numbers meeting every Lebesgue measure zero set in only countably many points, first shown to exist under CH in 1924.

Sierpiński triangle

The Sierpiński triangle, also called the Sierpiński gasket or Sierpiński sieve, is a self-similar fractal formed by repeatedly removing central triangles, described by Wacław Sierpiński in 1915.

Sieve methods (combinatorics)

Sieve methods are combinatorial counting techniques, rooted in the inclusion–exclusion principle, that strike out unwanted objects to control the explosion of terms, from Eratosthenes to Brun.

Sieve of Atkin

The Sieve of Atkin, or Atkin sieve, is an algorithm by Atkin and Bernstein, introduced in 2004, that generates all primes up to N in sublinear time.

Sieve of Eratosthenes

The Sieve of Eratosthenes is an ancient algorithm for finding all primes up to a limit by crossing out multiples, attributed to Eratosthenes of Cyrene around 200 BC.

Sigmoid function

The sigmoid function, also called the logistic function or squashing function, is an S-shaped curve mapping real numbers into (0, 1), used in logistic regression and neural networks.

Sign function

The sign function, also called the signum function and written sgn x, is the function that equals 1, 0, or −1 according to whether x is positive, zero, or negative.

Sign test

The sign test is a nonparametric statistical test presented by Dixon and Mood in 1946, testing paired differences or a single sample's median using only the signs of the differences.

Signal temporal logic

Signal temporal logic (STL) is a temporal logic for specifying and monitoring properties of real-valued, dense-time signals in cyber-physical systems, analog circuits, and systems biology.

Signaling game

A signaling game is a game-theoretic model in which an informed sender conveys private information to a receiver through signals, used in economics, biology, and machine learning.

Signature (logic)

In mathematical logic, a signature, also called a vocabulary or language, is the collection of constant, function, and relation symbols, with their arities, for building first-order formulas.

Signed distance function

A signed distance function (SDF) returns, for each point in space, the distance to the nearest surface of a shape, negative inside and positive outside by convention.

Signed number representations, also known as signed integer representations, are conventions for encoding positive and negative integers as binary bits, with two's complement dominating modern hardware.

Signed zero

Signed zero is the property of floating-point systems, notably IEEE 754, of representing zero as +0 and −0, which compare equal but behave differently in division.

Significance analysis of microarrays

Significance analysis of microarrays (SAM) is a permutation-based statistical method introduced by Tusher, Tibshirani, and Chu in 2001 that identifies differentially expressed genes in microarray experiments while estimating the false discovery rate.

Significance arithmetic

Significance arithmetic is a form of computer arithmetic for approximate quantities that propagates errors through each operation and reports only reliable digits; it underlies Mathematica's arbitrary-precision arithmetic.

Significance of numbers in Judaism

The significance of numbers in Judaism covers symbolic numbers like seven, twelve, and 40, plus gematria, which gives Hebrew letters numerical values, making 18 the value of chai, or life.

Silver ratio

The silver ratio, also called the silver mean, is the irrational number 1 + √2 (about 2.414), the second metallic mean after the golden ratio.

Similarity (geometry)

Similarity in geometry is the relation between figures with the same shape but not necessarily the same size: corresponding angles are equal and corresponding sides are in constant ratio.

Similarity solution

A similarity solution is a partial differential equation solution that keeps its shape under rescaling of variables, reducing the PDE to an ordinary differential equation, as in the Blasius boundary layer.

Simple group

A simple group is a nontrivial group whose only normal subgroups are the identity and itself, playing the role in group theory that primes play in arithmetic.

Simple linear regression

Simple linear regression, or simple regression, is a statistical method that models one response variable as a straight-line function of one explanatory variable, fitted by least squares.

Simple module

A simple module, also called an irreducible module, is a nonzero module over a ring whose only submodules are zero and itself, corresponding to irreducible representations.

Simple random sample

A simple random sample is a sample drawn so that every subset of units has the same chance of selection, the baseline probability sampling design in statistics.

Simple set (computability theory)

A simple set, introduced by Emil Post in 1944, is a recursively enumerable set of natural numbers whose complement is infinite but contains no infinite recursively enumerable subset.

Simple theory (model theory)

In model theory, a simple theory is a complete first-order theory in which no formula has the tree property. Introduced by Shelah, the class properly contains the stable theories.

Simplex

A simplex, plural simplexes or simplices, is the simplest convex polytope of a given dimension, the convex hull of k + 1 points: point, segment, triangle, tetrahedron, and beyond.

Simplex lattice design

A simplex lattice design is a design of experiments for mixture problems, varying component proportions over a simplex to fit a response surface from few runs.