Titlebook: Regular Structures; Lectures in Pattern Ulf Grenander Book 1981 Springer-Verlag New York Inc. 1981 Finite.Lattice.Logic.Mathematica.Muster

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Applied Mathematical Scienceshttp://image.papertrans.cn/r/image/825544.jpg

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https://doi.org/10.1007/978-1-4612-5905-3Finite; Lattice; Logic; Mathematica; Mustererkennung; Outlook; Structures; calculus; chaos; diagrams; form; min

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Patterns: From Chaos to Order,The search for regularity is a dominant theme in man’s attempt to understand the world around him. Any such attempt is based on an assumption, tacitly made or explicit, that phenomena in nature and in the man-made world are governed by laws that result in order and structure.

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A Pattern Formalism,We shall now examine the basic concepts and relations of pattern theory as expressed in a formalism whose terminology and notation will be discussed in this chapter.

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Algebra of Regular Structures,In Volume I we introduced the .: generators, configurations, and images, as well as .: similarities, combinatory relations, and deformations. We are now going to deepen our understanding of these concepts with the emphasis on their algebraic properties.

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Synthesis of Social Patterns of Domination,Sociology studies systems of interacting individuals or groups of individuals, and mathematical sociology creates the mathematical tools needed for such studies. We suggest that pattern theory — the mathematical theory of regular structures — can be used to create such tools.

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Urgency

Introduction,n theory rests. Chapter 3 is devoted to the algebraic study of regularity while Chapter 5 contains new results in metric pattern theory. Some brief remarks on topological image algebras can be found in Chapter 4.

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Taxonomic Patterns,ess or dissimilarity of specimens. In abstract terms if the specimens are represented as elements x of some space X, x € X, we look for a way of decomposing X into subsets X.; υ = 1,2,…; such that the elements in X. are quite different from those of X. when υ ≠ µ, see Notes A.