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Dynamic Systems and Dynamic Classification Problems in Geophysical Applications

  • Book
  • © 1998

Overview

Authors:
  1. Jacques Octave Dubois

    1. Institut de Physique du Globe de Paris, Paris Cedex 05, France

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    You can also search for this author in PubMed   Google Scholar

  2. Alexei Gvishiani

    1. Centre of Geophysical Data Studies and Telematics Applications, Moscow, Russian Federation

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Data and Knowledge in a Changing World (DATAKNOWL)

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Table of contents (15 chapters)

  1. Front Matter

    Pages I-XII
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  2. Introduction

    1. Introduction

      • Jacques Octave Dubois, Alexei Gvishiani
      Pages 1-4

  3. Why the Techniques Developed in this Book are Important? (A Few Examples of Applications)

    1. Why the Techniques Developed in this Book are Important? (A Few Examples of Applications)

      • Jacques Octave Dubois, Alexei Gvishiani
      Pages 5-20

  4. Foundations

    1. Front Matter

      Pages 21-22
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    2. Basic Mathematical Facts

      • Jacques Octave Dubois, Alexei Gvishiani
      Pages 23-40

  5. Dynamic Pattern Recognition Problems and Control over Classification Reliability

    1. Front Matter

      Pages 41-42
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    2. “Voting by a Set of Features” Algorithms

      • Jacques Octave Dubois, Alexei Gvishiani
      Pages 43-60

    3. Dynamic and Limit Classification Problems

      • Jacques Octave Dubois, Alexei Gvishiani
      Pages 61-84

    4. Dual Systems of Sets and Local Stability of Classification

      • Jacques Octave Dubois, Alexei Gvishiani
      Pages 85-96

    5. Investigation of Earthquake-prone Areas as a Limit Pattern Recognition Problem

      • Jacques Octave Dubois, Alexei Gvishiani
      Pages 97-104

    6. Control Experiments for Evaluating Classification Reliability

      • Jacques Octave Dubois, Alexei Gvishiani
      Pages 105-120

  6. Dynamic Systems

    1. Front Matter

      Pages 121-122
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    2. Basic Definitions and Facts

      • Jacques Octave Dubois, Alexei Gvishiani
      Pages 123-154

    3. Geometry of Attractors

      • Jacques Octave Dubois, Alexei Gvishiani
      Pages 155-172

    4. Bifurcation, Cascades and Chaos

      • Jacques Octave Dubois, Alexei Gvishiani
      Pages 173-188

    5. Self Organisation

      • Jacques Octave Dubois, Alexei Gvishiani
      Pages 189-194

    6. Multifractals

      • Jacques Octave Dubois, Alexei Gvishiani
      Pages 195-206

  7. Convex Programming and Systems of Rigid Blocks with Deformable Layers

    1. Front Matter

      Pages 207-208
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    2. Systems of Rigid Blocks with Thin Deformable Layers (SRBTDL)

      • Jacques Octave Dubois, Alexei Gvishiani
      Pages 209-214

    3. System of Rigid and Deformable Blocks (SRDB)

      • Jacques Octave Dubois, Alexei Gvishiani
      Pages 215-224
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Keywords

About this book

This book is the latest volume in the series entitled " Data and Knowledge in a Changing World ", published by the Committee on Data for Science and Technology (CODATA) of the International Council of Scientific Unions (Icsu). This series was established to collect together, from many diverse fields, the wealth of information pertaining t.o the intelligent exploitation of data in the conduct of science and technology. This volume is the first in a two-volume series that will discuss techniques for the analysis of natural dynamic systems, and their applications to a variety of geophysical problems. The present volume lays out the theoretical foun­ dations for these techniques. The second volume will use these techniques in applications to fields such as seismology, geodynamics, geoelectricity, ge­ omagnetism, aeromagnetics, topography and bathymetry. The book consists of two parts, which describe two complementary ap­ proaches to the analysis of natural systems. The first, written by A. Gvishi­ ani, deals with dynamic pattern recognition. It lays out the mathematical VI Foreword theory and the formalized algorithms that. forms the basis for the classifi­ cation of vector objects and the use of this classification in the study of dynamical systems, with particular emphasis on the prediction of system behavior in space and time. It discusses the construction of classification schemes, and the evaluation of their stability and reliability.

Authors and Affiliations

  • Institut de Physique du Globe de Paris, Paris Cedex 05, France

    Jacques Octave Dubois

  • Centre of Geophysical Data Studies and Telematics Applications, Moscow, Russian Federation

    Alexei Gvishiani

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