Dynamic Systems and Dynamic Classification Problems in Geophysical Applications

ISBN-13: 9783642499531 / Angielski / Miękka / 2012 / 259 str.

Jacques Octave DuBois; Alexei Gvishiani

Opis

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.

Spis treści

Why the Techniques Developed in this Book are Important? (A Few Examples of Applications).- Part I: Foundations.Basic Mathematical Facts.- Part II: Dynamic Pattern Recognition Problems and Control over Classification Reliability. 'Voting by a Set of Features' Algorithms.- Dynamic and Limit Classification Problems.- Dual Systems of Sets and Local Stability of Classification.- Investigation of Earthquake-prone Areas as a Limit Pattern Recognition Problem.- Control Experiments of Evaluating Classification Reliability.- Part III: Dynamic Systems. Basic Definitions and Facts.- Geometry of Attractors.- Bifurcation, Cascades and Chaos.- Self Organisation.- Multifractals.- Part IV: Convex Programming and Systems of Rigid Blocks with Deformable Layers. Systems of Rigid Blocks with Thin Deformable Layers (SRBTDL).- System of Rigid and Deformable Blocks (SRDB).-Part V: Bibliography.- Part VI: Index.

Blurb

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.