classes consisting of models of given maximal Kolmogorov complexity. The Kolmogorov structure function of an individual data string expresses the relation...

described by Kolmogorov's turbulence law Kolmogorov structure function Kolmogorov–Uspenskii machine model Kolmogorov's zero–one law Kolmogorov–Zurbenko filter...

mathematics, a topological space X is a T0 space or Kolmogorov space (named after Andrey Kolmogorov) if for every pair of distinct points of X, at least...

information theory (a subfield of computer science and mathematics), the Kolmogorov complexity of an object, such as a piece of text, is the length of a shortest...

statistic, although it is restricted to linear estimators. The Kolmogorov structure function deals with individual finite data; the related notion there...

approximation theory, the Kolmogorov–Arnold representation theorem (or superposition theorem) states that every multivariate continuous function f : [ 0 , 1 ] n...

after Andrey Kolmogorov and Nikolai Smirnov. The Kolmogorov–Smirnov statistic quantifies a distance between the empirical distribution function of the sample...

mathematics, a function space is a set of functions between two fixed sets. Often, the domain and/or codomain will have additional structure which is inherited...

In mathematical logic, the Brouwer–Heyting–Kolmogorov interpretation, or BHK interpretation, of intuitionistic logic was proposed by L. E. J. Brouwer and...

{F}}_{n}-F\|_{\infty }>z{\Big )}\leq 2e^{-2z^{2}}.} In fact, Kolmogorov has shown that if the cumulative distribution function F is continuous, then the expression n ‖ F...

distributions going back to the 1920s. In a 1932 paper, Kolmogorov derived a characteristic function for random variables associated with Lévy processes....

between algebraic structures is a function that is compatible with the operations of the structures. For all common algebraic structures, and, in particular...

theory, see interpretation (model theory). In database theory, structures with no functions are studied as models for relational databases, in the form of...

the "Kolmogorov −⁠5/3⁠ spectrum" is generally observed in turbulence. However, for high order structure functions, the difference with the Kolmogorov scaling...

Rissanen bases the mathematical underpinning of MDL on the Kolmogorov structure function. According to the MDL philosophy, Bayesian methods should be...

mathematics, the Kolmogorov extension theorem (also known as Kolmogorov existence theorem, the Kolmogorov consistency theorem or the Daniell-Kolmogorov theorem)...

pioneered theory and applications of Kolmogorov complexity. They co-authored the textbook An Introduction to Kolmogorov Complexity and Its Applications, parts...

Knuth–Morris–Pratt algorithm Königsberg bridges problem Kolmogorov complexity Kraft's inequality Kripke structure Kruskal's algorithm kth order Fibonacci numbers...

structures; continuous functions, which preserve topological structures; and differentiable functions, which preserve differential structures. In 1939, the French...

finitary functions on the natural numbers is uncountable so most are not computable. Concrete examples of such functions are Busy beaver, Kolmogorov complexity...

A trophic function was first introduced in the differential equations of the Kolmogorov predator–prey model. It generalizes the linear case of predator–prey...

result is equivalent to a Fourier transform of Kolmogorov's 1941 result for the turbulent structure function. The pressure fluctuations in a turbulent flow...

(1890): 16–18. Bibcode:1941DoSSR..32...16K. JSTOR 51981. Kolmogorov, A. N. (1941). "The local structure of turbulence in incompressible viscous fluid for very...

regular spaces and Tychonoff spaces are related through the notion of Kolmogorov equivalence. A topological space is Tychonoff if and only if it's both...

A likelihood function (often simply called the likelihood) measures how well a statistical model explains observed data by calculating the probability...

completely arbitrary function can be expanded in Fourier series, even if its Fourier coefficients are well-defined. For example, Kolmogorov (1922) constructed...

for "morphism" or "arrow", which is a structure-respecting function and thus may imply more structure than "function" does. For example, a morphism f : X...

World Scientific. ISBN 9789814366847. Kolmogorov, A. N.; Fomin, S. V. (1999) [1957]. Elements of the theory of functions and functional analysis. Mineola,...

formal system in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution. Untyped...

A bijection, bijective function, or one-to-one correspondence between two mathematical sets is a function such that each element of the second set (the...