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Dynamic Systems and Dynamic Classification Problems in Geophysical Applications [Kõva köide]

  • Formaat: Hardback, 259 pages, kõrgus x laius: 235x155 mm, kaal: 520 g, biography
  • Sari: Data and Knowledge in a Changing World (Closed)
  • Ilmumisaeg: 06-May-1998
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3540642382
  • ISBN-13: 9783540642381
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  • Formaat: Hardback, 259 pages, kõrgus x laius: 235x155 mm, kaal: 520 g, biography
  • Sari: Data and Knowledge in a Changing World (Closed)
  • Ilmumisaeg: 06-May-1998
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3540642382
  • ISBN-13: 9783540642381
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.
Acknowledgement XI
Introduction 1(4)
Chapter 1 Why the Techniques Developed in this Book are Important? (A Few Examples of Applications)
5(18)
Part I Foundations 23(20)
Chapter 2 Basic Mathematical Facts
23(20)
2.1 Elements of Set Theory
23(6)
2.1.1 Sets
23(4)
2.1.2 Functions
27(2)
2.2 Elements of Linear Algebra
29(3)
2.3 Elements of Boolean Algebra
32(5)
2.4 Metric spaces
37(6)
Part II Dynamic Pattern Recognition Problems and Control over Classification Reliabity 43(80)
Chapter 3 "Voting by a Set of Features" Algorithms
43(18)
3.1 Basic Definitions
43(2)
3.2 "Voting by Elementary Features" Algorithms
45(4)
3.3 Definition of Classes of Algorithms "Voting by a Set of Features" (VSF) and "Voting by Elementary Features" (VEF). Normal Weights
49(3)
3.4 Class of Algorithms "CORA-i"
52(2)
3.5 "Neighbours" as a VSF Algorithm
54(2)
3.6 "Threshold" Classification Algorithms
56(2)
3.7 "Bayes" as a VEF Algorithm
58(3)
Chapter 4 Dynamic and Limit Classification Problems
61(24)
4.1 Formulation of the Dynamic Recognition Problem
61(4)
4.2 Stability of Prediction in Dynamic Classification Problems
65(1)
4.3 Stability of Prediction, Algorithm VEF-0
66(3)
4.4 Stability Conditions in the Case of the Algorithm VEF-1
69(4)
4.5 Stability Zone for Prediction Obtained by the Algorithm VEF-2
73(4)
4.6 Stability Zone for Prediction Obtained by a VSF Algorithm
77(3)
4.7 Stability of Prediction in Case of Normal Weights
80(5)
Chapter 5 Dual Systems of Sets and Local Stability of Classification
85(12)
5.1 Dual Systems of Sets
85(2)
5.2 S-Theorems and S-Counter-examples
87(2)
5.3 Local Stability and Stabilizing Sets
89(4)
5.4 Local Stability and Cluster Analysis
93(4)
Chapter 6 Investigation of Earthquake-prone Areas as a Limit Pattern Recognition Problem
97(8)
6.1 Formalizing the Recognition of Strongly Earthquake-prone Areas
97(4)
6.2 Correspondance Between Prediction and Classification Problems
101(4)
Chapter 7 Control Experiments for Evaluating Classification Reliability
105(18)
7.1 Comparison of Quality Solutions for Real and Random Learning Materials
105(5)
7.2 Estimating the Probability of the Classification Error
110(3)
7.3 Estimation of Parameters of the Classification Problem using Estimation of Non-randomness and Reliability Functions
113(3)
7.4 Additional Arguments for Evaluating the Classification Reliability
116(7)
Part III Dynamic Systems 123(86)
Chapter 8 Basic Definitions and Facts
123(32)
8.1 Measure and Dimension
123(3)
8.1.1 Hausdorff measure
124(1)
8.1.2 Hausdorff dimension
125(1)
8.2 Discrete Dynamic Systems
126(1)
8.3 Continuous Dynamic Systems
127(1)
8.4 Representation and Study of Dynamic Systems
128(18)
8.4.1 Iterative scheme as a tool in dynamic system study
129(11)
8.4.2 Bifurcation
140(6)
8.5 Attraction and Repulsion Cycles
146(2)
8.5.1 Areas contraction and consequences
147(1)
8.6 Fractal Attractors, Basin of Attraction, Repellers
148(2)
8.7 Lyapunov Exponents
150(5)
Chapter 9 Geometry of Attractors
155(18)
9.1 Classical Examples of Strange Attractors
155(6)
9.1.1 The Lorenz attractor
155(3)
9.1.2 The Henon attractor
158(1)
9.1.3 Some other classical attractors
158(3)
9.2 Correlation Function Method
161(3)
9.3 What Time Delay?
164(8)
9.3.1 The mutual information criterion
165(1)
9.3.2 The minimum embedding dimension
165(2)
9.3.3 The Lyapunov exponents computation (Sano and Sawada Method)
167(3)
9.3.4 Calculation of Lyapunov exponents (the method of Wolf et al.)
170(2)
9.4 First Return Mapping
172(1)
Chapter 10 Bifurcation, Cascades and Chaos
173(16)
10.1 Floquet Matrix, Hopf Bifurcation
173(7)
10.1.1 Floquet matrix
174(2)
10.1.2 Hopf bifurcation
176(2)
10.1.3 Passing from torus I(2) to torus I(3). Ruelle-Takens theory
178(2)
10.2 Curry and Yorke Model and Route to Chaos
180(3)
10.3 Definition of Chaos
183(1)
10.4 Control of Chaos
183(6)
Chapter 11 Self Organisation
189(6)
11.1 The Evolving Sandpile Experiment
189(4)
11.2 General Aspects of Self-Organized Criticality
193(2)
Chapter 12 Multifractals
195(14)
12.1 Generalized Dimensions of Fractals and Strange Attractors
195(3)
12.2 Definitions and Properties
198(11)
12.2.1 A Simple Definition
198(1)
12.2.2 A Measure on the Middle Third Cantor Set
199(1)
12.2.3 Practical Methods of Constructing a Multifractal Spectrum
199(10)
Part IV Convex Programming and Systems of Rigid Blocks with Deformable Layers 209(16)
Chapter 13 Systems of Rigid Blocks with Thin Deformable Layers (SRBTDL)
209(6)
Chapter 14 System of Rigid and Deformable Blocks (SRDB)
215(10)
Part V Bibliography 225(18)
Part VI Index 243(8)
Colour Plates
251