All articles starting with S

Stochastic computing

Stochastic computing is a computation paradigm that represents numbers as probabilities of 1s in random bit streams, letting simple logic gates multiply and add, suited to low-power hardware.

Stochastic control

Stochastic control is the branch of control theory and applied probability that finds optimal decision rules for random dynamical systems, minimizing expected cost or maximizing reward.

Stochastic cooling

Stochastic cooling is a beam-cooling technique invented by Simon van der Meer at CERN around 1970 that reduces the energy spread of particle beams in storage rings.

Stochastic density functional theory

Stochastic density functional theory, or sDFT, is a form of Kohn-Sham DFT that estimates the electron density statistically from random orbitals rather than computing every occupied orbital explicitly.

Stochastic differential equation

A stochastic differential equation (SDE) is a differential equation containing a stochastic process, typically a drift term plus noise driven by Brownian motion, used in finance, biology, and physics.

Stochastic dominance

Stochastic dominance is a statistical method for ranking risky prospects by comparing their cumulative distribution functions, without assuming a specific utility function; first-order dominance requires only increasing preferences.

Stochastic filtering

Stochastic filtering is a class of methods in probability and signal processing that estimate the hidden state of a dynamical system from noisy observations, updating the estimate recursively.

Stochastic frontier analysis

Stochastic frontier analysis (SFA) is an econometric method, proposed in 1977, that estimates production or cost frontiers and splits each firm's deviation into inefficiency and random noise.

Stochastic frontier model

The stochastic frontier model is an econometric regression model proposed in 1977 that estimates production or cost frontiers, separating random statistical noise from technical inefficiency.

Stochastic gradient descent

Stochastic gradient descent (SGD), also called incremental gradient descent, is an iterative optimization algorithm that updates model parameters using a gradient estimated from a random subset of training data.

Stochastic gravitational-wave background

The stochastic gravitational-wave background (SGWB, often GWB) is a random gravitational-wave signal from many weak, unresolved sources, with pulsar timing arrays reporting evidence in 2023.

Stochastic gravity

Stochastic gravity is the extension of semiclassical gravity that adds stress-energy fluctuations as metric noise via the Einstein–Langevin equation, developed mainly in the 1990s by Enric Verdaguer and Bei-Lok Hu.

Stochastic GW

Stochastic GW (sGW), introduced by Daniel Neuhauser and colleagues in 2014, is a computational chemistry method using stochastic orbitals to reduce GW's scaling from fourth order to near-linear.

Stochastic heat engine

A stochastic heat engine is a microscopic device that converts heat into work using a few strongly fluctuating degrees of freedom, so its output is random.

Stochastic heat equation

The stochastic heat equation is a stochastic partial differential equation adding random noise to the classical heat equation; it is a prototypical SPDE studied across dimensions.

Stochastic integral

A stochastic integral is an integral with respect to a random process such as Brownian motion, introduced by Kiyosi Itô in 1944 as the basis of stochastic calculus.

Stochastic magnetic tunnel junction

A stochastic magnetic tunnel junction is a magnetic tunnel junction that switches randomly between two resistance states with tunable probability, used as a true random-number generator and probabilistic bit.

Stochastic matrix

A stochastic matrix, also called a Markov matrix or transition probability matrix, is a square matrix whose rows or columns sum to 1, so each is a probability distribution.

Stochastic maximum principle

The stochastic maximum principle states necessary conditions for optimality of controls of systems governed by stochastic differential equations, generalizing Pontryagin's deterministic maximum principle to the stochastic setting.

Stochastic mechanics

Stochastic mechanics is a formulation of nonrelativistic quantum mechanics in which each particle follows a real, randomly fluctuating trajectory, formulated by Edward Nelson in 1966.

Stochastic model predictive control

Stochastic model predictive control (SMPC) is a family of model predictive control strategies for systems with stochastic uncertainty, using chance constraints that must hold only with a prescribed probability.

Stochastic neighbor embedding

Stochastic neighbor embedding (SNE) is a nonlinear probabilistic method for dimension reduction, introduced by Geoffrey Hinton and Sam Roweis at NIPS in 2002; its 2008 variant t-SNE is much more widely used.

Stochastic neural network

A stochastic neural network is a neural network in which units, weights, or connections are random variables, serving generative modeling, uncertainty estimation, and regularization; examples include Boltzmann machines and variational autoencoders.

Stochastic optical reconstruction microscopy

Stochastic optical reconstruction microscopy (STORM) is a fluorescence microscopy technique that bypasses the diffraction limit, introduced in 2006 by Xiaowei Zhuang's group at Harvard University.

Stochastic orders of dependence

Stochastic orders of dependence are mathematical orderings that rank probability distributions by dependence strength, with the concordance ordering, formalized by Harry Joe in 1990, as the central example.

Stochastic partial differential equation

A stochastic partial differential equation (SPDE) is a PDE perturbed by random forcing or coefficients, describing systems driven by noise, from growing interfaces and turbulent fluids to climate models.

Stochastic process

A stochastic process, also called a random process, is a family of random variables indexed by time that describes a system evolving under random influences.

Stochastic programming

Stochastic programming is a mathematical optimization framework for decision-making under uncertainty, optimizing an expected outcome or risk measure when some model parameters are random variables with known probability distributions.

Stochastic Schrödinger equation

A stochastic Schrödinger equation (SSE) describes a pure quantum state evolving stochastically, with the average over trajectories reproducing a Lindblad master equation; it arose in the early 1990s.