Dynamic Systems and Dynamic Classification Problems in Geophysical Applications

✍ Scribed by Prof. Dr. Jacques Octave Dubois, Prof. Dr. Alexei Gvishiani (auth.)

Publisher: Springer-Verlag Berlin Heidelberg
Year: 1998
Tongue: English
Leaves: 269
Series: Data and Knowledge in a Changing World
Edition: 1
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

The book contains two main parts dealing both with nonlinear approaches in the study of complex natural systems. In its first part it introduces a new construction of pattern recognition problems applicable to a wide range of geophysical and environmental objects. The classification in such problems depends on time which allows one to formulate the condition of stability of final classifications for verification of its reliability. A new wide set of pattern recognition algorithms with learning ("Voting by Set of Features") is introduced. Theoretical and algorithmical parts are illustrated by some examples of applications to natural hazard assessment.
In the second part of the book, an alternative approach to the geophysical applications is given in terms of dynamic systems and corresponding tools. Dynamic systems studies are useful to understand nonlinear time series. Self Organized Criticality and multifractal analysis are powerful new keys for understanding many natural phenomena. All these methods are of great interest in any long data file processing.

✦ Table of Contents

Front Matter....Pages I-XII
Introduction....Pages 1-4
Why the Techniques Developed in this Book are Important? (A Few Examples of Applications)....Pages 5-20
Front Matter....Pages 21-22
Basic Mathematical Facts....Pages 23-40
Front Matter....Pages 41-42
“Voting by a Set of Features” Algorithms....Pages 43-60
Dynamic and Limit Classification Problems....Pages 61-84
Dual Systems of Sets and Local Stability of Classification....Pages 85-96
Investigation of Earthquake-prone Areas as a Limit Pattern Recognition Problem....Pages 97-104
Control Experiments for Evaluating Classification Reliability....Pages 105-120
Front Matter....Pages 121-122
Basic Definitions and Facts....Pages 123-154
Geometry of Attractors....Pages 155-172
Bifurcation, Cascades and Chaos....Pages 173-188
Self Organisation....Pages 189-194
Multifractals....Pages 195-206
Front Matter....Pages 207-208
Systems of Rigid Blocks with Thin Deformable Layers (SRBTDL)....Pages 209-214
System of Rigid and Deformable Blocks (SRDB)....Pages 215-224
Back Matter....Pages 225-259

✦ Subjects

Environmental Monitoring/Analysis; Geographical Information Systems/Cartography; Earth Sciences, general

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