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Pattern theory, formulated by Ulf Grenander, is a mathematical formalism to describe knowledge of the world as patterns.It differs from other approaches to artificial intelligence in that it does not begin by prescribing algorithms and machinery to recognize and classify patterns; rather, it prescribes a vocabulary to articulate and recast the pattern concepts in precise language.
Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions.German mathematician Carl Friedrich Gauss (1777–1855) said, "Mathematics is the queen of the sciences—and number theory is the queen of mathematics."
In mathematical knot theory, 7 4 is the name of a 7-crossing knot which can be visually depicted in a highly-symmetric form, ... The 7 4 knot is a Lissajous knot, ...
Once a Gödel numbering for a formal theory is established, each inference rule of the theory can be expressed as a function on the natural numbers. If f is the Gödel mapping and r is an inference rule, then there should be some arithmetical function g r of natural numbers such that if formula C is derived from formulas A and B through an ...
Cover's theorem is a statement in computational learning theory and is one of the primary theoretical motivations for the use of non-linear kernel methods in machine learning applications. It is so termed after the information theorist Thomas M. Cover who stated it in 1965, referring to it as counting function theorem .
In coding theory, Hamming(7,4) is a linear error-correcting code that encodes four bits of data into seven bits by adding three parity bits. It is a member of a larger family of Hamming codes , but the term Hamming code often refers to this specific code that Richard W. Hamming introduced in 1950.
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In number theory the standard unqualified use of the term continued fraction refers to the special case where all numerators are 1, and is treated in the article Simple continued fraction. The present article treats the case where numerators and denominators are sequences { a i } , { b i } {\displaystyle \{a_{i}\},\{b_{i}\}} of constants or ...