A Topological Foundation for Self-Organization,

Abstract

It is shown that by the use of Information Theory, any metrizable topology may be metrized as an orthogonal Euclidean space (with a random Gaussian probability distribution) times a denumerable random cartesian product of irreducible (wrt direct product) denumerable groups. The necessary algorithm to accomplish this metrization from a statistical basis is presented. If such a basis is unavailable, a certain nilpotent projection operator has to be used instead, as is shown in detail in the companion paper. This operator possesses self-organizing features. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Nov 14, 1963
Accession Number
ADA037365

Entities

People

  • Romuald I. Scibor-marchocki

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Cartesian Coordinates
  • Coordinate Systems
  • Decomposition
  • Gaussian Distributions
  • Geometry
  • Information Theory
  • Mathematical Models
  • Mathematics
  • Measure Theory
  • New York
  • Probability
  • Probability Distributions
  • Real Numbers
  • Self Organizing Systems
  • Topology

Fields of Study

  • Mathematics

Readers

  • Graph Algorithms and Convex Optimization.
  • Mathematical Modeling and Probability Theory.
  • Systems Analysis and Design

Technology Areas

  • Space