6,052 articles
Empirical interpolation method
The empirical interpolation method is a greedy numerical technique that approximates parametrized functions at automatically selected points, introduced in 2004 to restore the offline-online decomposition in reduced-basis solvers of parametrized partial differential equations.
Empirical likelihood
Empirical likelihood is a nonparametric statistical method that assigns probability weights to observed data points and maximizes the likelihood under constraints, yielding tests and confidence regions without parametric assumptions.
Empirical measure
An empirical measure is a random probability measure constructed from observed data by placing equal mass at each sampled point; in statistics it proxies the unknown underlying distribution.
Empirical mode decomposition
Empirical mode decomposition (EMD) is an adaptive signal-processing method that decomposes nonlinear, nonstationary time series into intrinsic mode functions; with the Hilbert transform it forms the Hilbert–Huang transform, developed at NASA in 1998.
Empirical orthogonal functions
Empirical orthogonal function (EOF) analysis decomposes a geophysical field, such as sea level pressure, into orthogonal spatial patterns paired with uncorrelated time series; it is also known as principal component analysis.
Empirical process
An empirical process is the centered, √n-scaled version of an empirical distribution function, G_n(x) = √n(F_n(x) − F(x)), underlying goodness-of-fit tests like Kolmogorov–Smirnov; Donsker's theorem shows it converges to a Brownian bridge.
Empty set
The empty set, or empty subset, is the unique set containing no elements, denoted ∅; it has cardinality zero and is a subset of every set.
Endomorphism
An endomorphism is a structure-preserving map from a mathematical object to itself, defined for groups, modules, rings, and vector spaces; in linear algebra it is a linear map from a space to itself.
Endomorphism ring
The endomorphism ring, also called the endomorphism algebra, is the ring formed by all homomorphisms from a mathematical object to itself, with composition of maps as multiplication.
Energy Information Administration
The U.S. Energy Information Administration (EIA), established in 1977, is the independent statistical agency of the Department of Energy, collecting and publishing energy data for the public.
Energy method
The energy method is a technique in the analysis of partial differential equations in which an estimate for a nonnegative quantity, called an energy, is derived from the equation itself.
Engineering fit
An engineering fit is the degree of tightness or looseness between two mating mechanical parts, such as a shaft in a hole, classified as clearance, transition, or interference.
English Longitudinal Study of Ageing
The English Longitudinal Study of Ageing (ELSA) is a panel study following a representative cohort of people in England aged 50 and over, first interviewed in 2002.
Enriched category
An enriched category is a category-like structure whose hom-sets are replaced by objects of a monoidal base category, yielding ordinary categories, metric spaces, and 2-categories as instances.
Ensemble empirical mode decomposition
Ensemble empirical mode decomposition (EEMD) is a noise-assisted signal-processing method introduced by Zhaohua Wu and Norden Huang in 2009 that cures EMD's mode mixing by averaging many noise-added runs.
Ensemble Kalman filter
The ensemble Kalman filter (EnKF) is a Monte Carlo implementation of the Kalman filter for high-dimensional, nonlinear state estimation, proposed by Geir Evensen in 1994 for ocean modeling.
Ensemble transform Kalman filter
The ensemble transform Kalman filter (ETKF) is a deterministic square-root Kalman filter, introduced in 2001, that assimilates observations into a forecast ensemble without perturbing observations.
Entire function
An entire function, also called an integral function, is a complex-valued function that is complex differentiable everywhere on the complex plane; polynomials, the exponential, sine, and cosine are entire.
Entropy (information theory)
Entropy, also called Shannon entropy, measures the average uncertainty of a random variable; Claude Shannon introduced it in 1948 as a lower bound on lossless compression.
Entropy balancing
Entropy balancing is a reweighting method for causal inference and survey statistics, introduced by Jens Hainmueller in 2012, that reweights controls to match treated-group covariate moments.
Entropy weight method
The entropy weight method is an objective weighting technique in multi-criteria decision analysis that derives criterion weights from Shannon entropy in the decision matrix, minimizing subjective judgment.
Entscheidungsproblem
The Entscheidungsproblem, also known as Church's theorem, is the problem of deciding validity in first-order logic, posed by Hilbert and Ackermann in 1928 and proved unsolvable by Church and Turing in 1936.
Enumeration
Enumeration is the branch of combinatorics concerned with counting the elements of finite sets, using tools such as generating functions, bijective proofs, and Pólya's theorem for counting under symmetry.
Enumeration algorithm
An enumeration algorithm lists every element of a finite solution set exactly once, without repetition, producing results as a stream that can be consumed as they appear.
Enumeration degree
An enumeration degree is an equivalence class of sets of natural numbers under enumeration reducibility, where one set is computed from positive information about another.
Enumerative combinatorics
Enumerative combinatorics is the branch of mathematics that counts the elements of finite sets, seeking exact formulas, recurrences, or asymptotics for counting functions, as in Cayley's tree formula.
Envelope (mathematics)
In geometry and calculus, an envelope is a curve tangent to every member of a one-parameter family of curves, extended to surfaces; Leibniz introduced the idea in 1694.
Envelope method (statistics)
The envelope method is a dimension-reduction technique in multivariate statistics that improves regression efficiency by separating relevant variation from immaterial variation, introduced by Cook, Li, and Chiaromonte in 2010.
Environmental Indicators
Environmental indicators: quantitative measures communicating environmental trends, structured by the PSR/DPSIR framework, used in OECD Core Set, EEA, SDG, and EPI monitoring systems.
Epimenides paradox
The Epimenides paradox, also called the Cretan paradox, is a self-reference puzzle from the saying "all Cretans are liars" by Epimenides of Crete, quoted at Titus 1:12.