6,052 articles
Three utilities problem
The three utilities problem, also known as water, gas, and electricity, is a mathematical puzzle asking to connect three houses to three utilities without crossing lines, and it has no solution.
Three-dimensional space
Three-dimensional space is the space of everyday physical experience, in which every point is specified by three coordinates (x, y, z) along perpendicular axes, denoted mathematically as R³.
Threshold autoregressive model
The threshold autoregressive (TAR) model is a nonlinear time series model in which autoregressive coefficients switch between regimes according to whether a lagged value exceeds a threshold.
Threshold function (graph theory)
A threshold function in random graph theory is a function p0(n) marking where a graph property switches from almost surely absent to almost surely present in G(n,p).
Threshold graph
A threshold graph is a graph whose independent sets are exactly the vertex sets with total weight at most some threshold, defined by Chvátal and Hammer in 1977.
Threshold model
The threshold model is a statistical model in which the relationship between variables changes when an observed variable crosses a threshold, creating two or more linear regimes.
Thue–Morse sequence
The Thue–Morse sequence, also called the Prouhet–Thue–Morse sequence or parity sequence, is an infinite binary sequence whose nth term is the parity of the number of 1s in the binary expansion of n.
Thue–Siegel–Roth theorem
The Thue–Siegel–Roth theorem, also called Roth's theorem, is a result in Diophantine approximation stating that irrational algebraic numbers cannot be approximated by rationals faster than order 1/q².
tidyverse
The tidyverse is an opinionated collection of R packages for data science sharing a common design philosophy and grammar, including ggplot2, dplyr, and tidyr, maintained by Hadley Wickham.
Tight frame
A tight frame is a collection of vectors in a Hilbert space with a constant bound A such that every vector has a simple reconstruction formula.
Tightness of measures
Tightness of measures, or tightness of a measure, is the property that a family of probability measures puts mass at least 1 − ε on one compact set for every ε > 0.
Tiling problem
The tiling problem, also called the domino problem, asks whether a given finite set of Wang tiles can cover the infinite plane; it is undecidable.
Time formatting and storage bugs
Time formatting and storage bugs are software defects in how dates and times are represented, stored, or formatted, firing on a calendar date to produce wrong dates.
Time series
A time series, also called a time sequence, is a sequence of measurements of a variable taken at regular time intervals, such as monthly rainfall or daily stock prices.
Time series clustering
Time series clustering is an unsupervised method that partitions time series into clusters of similar temporal patterns, using distances such as dynamic time warping (DTW).
Time series decomposition
Time series decomposition is a statistical method that separates an observed series into trend, seasonal, and remainder components, combined additively or multiplicatively; it underlies seasonal adjustment and forecasting.
Time series regression
Time series regression is a statistical method for modeling relationships between variables observed over time, with errors that are dependent across periods, requiring corrections to ordinary least squares.
Time stepping
Time stepping, also called the time-stepping method, is a numerical technique that advances solutions of time-dependent differential equations step by step, the standard way to solve initial value problems for ODEs.
Time-lagged independent component analysis
Time-lagged independent component analysis (tICA, also called time-structure-based independent component analysis) is a linear dimensionality reduction method that, unlike PCA, finds coordinates with maximal time-autocorrelation and serves mainly to build Markov state models.
Time-scale calculus
Time-scale calculus is a mathematical framework unifying continuous and discrete analysis, introduced by Stefan Hilger in 1988, studying dynamic equations on closed subsets of the real line.
Time-varying parameter vector autoregression
A time-varying parameter vector autoregression (TVP-VAR) is a multivariate time-series model whose coefficients, and often error variances, evolve over time, used to study how economic relationships change across decades.
Timed automaton
A timed automaton (plural: timed automata) is a finite automaton extended with real-valued clocks that can be reset and compared against constants, introduced by Rajeev Alur and David L. Dill.
Tit for tat
Tit for tat is an iterated Prisoner's Dilemma strategy that cooperates first and then mirrors the opponent's previous move; Anatol Rapoport's entry won Robert Axelrod's 1980 computer tournaments.
TLA+
TLA+ is a formal specification language, created by Leslie Lamport, based on set theory and the Temporal Logic of Actions, used for designing and verifying concurrent and distributed systems.
TODIM method
TODIM (TOmada de Decisão Interativa e Multicritério) is a multi-criteria decision-making method, proposed in the early 1990s, that ranks alternatives by gains and losses relative to a reference point.
Toeplitz matrix
A Toeplitz matrix is a matrix whose entries are constant along each descending diagonal, named after the German mathematician Otto Toeplitz, who studied such matrices in 1911.
Tomita–Takesaki theory
Tomita–Takesaki theory, also known as Tomita's theorem, associates to a von Neumann algebra a modular operator and conjugation, and is central to operator algebra theory and quantum field theory.
Tomographic reconstruction
Tomographic reconstruction is the family of computational methods that turn projection measurements, line integrals through an object from many angles, into cross-sectional images, the core of CT, PET, and MRI.
Topological combinatorics
Topological combinatorics is a branch of mathematics applying topological methods, chiefly the Borsuk–Ulam theorem, to problems in combinatorics, dating from Lovász's 1978 proof of the Kneser conjecture.
Topological cyclic homology
Topological cyclic homology (TC) is a spectrum-valued invariant of rings, introduced in 1993 by Bökstedt, Hsiang, and Madsen as a computable approximation to algebraic K-theory via the cyclotomic trace.