Extracting knowledge from time series: an introduction to nonlinear empirical modeling
Gespeichert in:
Hauptverfasser: | , |
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Format: | Buch |
Sprache: | English |
Veröffentlicht: |
Berlin [u.a.]
Springer
2010
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Schriftenreihe: | Springer series in synergetics
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Schlagworte: | |
Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
Beschreibung: | XXI, 405 S. Ill., graph. Darst. |
ISBN: | 9783642126000 |
Internformat
MARC
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100 | 1 | |a Bezručko, Boris P. |e Verfasser |4 aut | |
245 | 1 | 0 | |a Extracting knowledge from time series |b an introduction to nonlinear empirical modeling |c Boris P. Bezruchko ; Dmitry A. Smirnov |
264 | 1 | |a Berlin [u.a.] |b Springer |c 2010 | |
300 | |a XXI, 405 S. |b Ill., graph. Darst. | ||
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700 | 1 | |a Smirnov, Dmitrij A. |e Verfasser |4 aut | |
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Datensatz im Suchindex
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adam_text |
CONTENTS PART I MODELS AND FORECAST 1 THE CONCEPT OF MODEL. WHAT IS
REMARKABLE IN MATHEMATICAL MODELS 3 1 . 1 WHAT IS CALLED "MODEL" AND
"MODELLING" 3 1.2 SCIENCE, SCIENTIFIC KNOWLEDGE, SYSTEMATISATION OF
SCIENTIFIC MODELS 6 1.3 DELUSION AND INTUITION: RESCUE VIA MATHEMATICS
10 1.4 HOW MANY MODELS FOR A SINGLE OBJECT CAN EXIST? 14 1.5 HOW THE
MODELS ARE BORN 16 1.6 STRUCTURAL SCHEME OF MATHEMATICAL MODELLING
PROCEDURE 17 1.7 CONCLUSIONS FROM HISTORICAL PRACTICE OF MODELLING:
INDICATIVE DESTINY OF MECHANICS MODELS 19 REFERENCES 23 2 TWO APPROACHES
TO MODELLING AND FORECAST 25 2. 1 BASIC CONCEPTS AND PECULIARITIES OF
DYNAMICAL MODELLING 26 2.1.1 DEFINITION OF DYNAMICAL SYSTEM 26 2.1.2
NON-RIGOROUS EXAMPLE: VARIABLES AND PARAMETERS 28 2.1.3 PHASE SPACE.
CONSERVATIVE AND DISSIPATIVE SYSTEMS. ATTRACTORS, MULTISTABILITY, BASINS
OF ATTRACTION 31 2.1.4 CHARACTERISTICS OF ATTRACTORS 35 2.1.5 PARAMETER
SPACE, BIFURCATIONS, COMBINED SPACES, BIFURCATION DIAGRAMS 40 2.2
FOUNDATIONS TO CLAIM A PROCESS "RANDOM" 42 2.2.1 SET-THEORETIC APPROACH
42 2.2.2 SIGNS OF RANDOMNESS TRADITIONAL FOR PHYSICISTS 52 2.2.3
ALGORITHMIC APPROACH 53 2.2.4 RANDOMNESS AS UNPREDICTABILITY 54 2.3
CONCEPTION OF PARTIAL DETERMINANCY 55 2. BIBLIOGRAFISCHE INFORMATIONEN
HTTP://D-NB.INFO/1002586674 DIGITALISIERT DURCH TVI CONTENTS 2.4.2
PREDICTABILITY AND LYAPUNOV EXPONENT: THE CASE OF INFINITESIMAL
PERTURBATIONS 57 2.5 SCALE OF CONSIDERATION INFLUENCES CLASSIFICATION OF
A PROCESS (COMPLEX DETERMINISTIC DYNAMICS VERSUS RANDOMNESS) 61 2.6
"COIN FLIP" EXAMPLE 64 REFERENCES 68 3 DYNAMICAL (DETERMINISTIC) MODELS
OF EVOLUTION 71 3.1 TERMINOLOGY 71 3.1.1 OPERATOR, MAP, EQUATION,
EVOLUTION OPERATOR 71 3.1.2 FUNCTIONS, CONTINUOUS AND DISCRETE TIME 72
3.1.3 DISCRETE MAP, ITERATE 73 3.1.4 FLOWS AND CASCADES, POINCARE
SECTION AND POINCARE MAP. 73 3.1.5 ILLUSTRATIVE EXAMPLE 73 3.2
SYSTEMATISATION OF MODEL EQUATIONS 75 3.3 EXPLICIT FUNCTIONAL
DEPENDENCIES 79 3.4 LINEARITY AND NON-LINEARITY 81 3.4.1 LINEARITY AND
NON-LINEARITY OF FUNCTIONS AND EQUATIONS . 81 3.4.2 THE NATURE OF
NON-LINEARITY 82 3.4.3 ILLUSTRATION WITH PENDULUMS 83 3.5 MODELS IN THE
FORM OF ORDINARY DIFFERENTIAL EQUATIONS 85 3.5.1 KINDS OF SOLUTIONS 85
3.5.2 OSCILLATORS, A POPULAR CLASS OF MODEL EQUATIONS 88 3.5.3 "STANDARD
FORM" OF ORDINARY DIFFERENTIAL EQUATIONS 92 3.6 MODELS IN THE FORM OF
DISCRETE MAPS 93 3.6.1 INTRODUCTION 93 3.6.2 EXEMPLARY NON-LINEAR MAPS
94 3.6.3 ROLE OF DISCRETE MODELS 99 3.7 MODELS OF SPATIALLY EXTENDED
SYSTEMS 105 3.7.1 COUPLED MAP LATTICES 105 3.7.2 CELLULAR AUTOMATA 110
3.7.3 NETWORKS WITH COMPLEX TOPOLOGY 112 3.7.4 DELAY DIFFERENTIAL
EQUATIONS 113 3.7. CONTENTS 4.1.2 CHARACTERISTICS OF RANDOM PROCESS 129
4.1.3 STATIONARITY AND ERGODICITY OF RANDOM PROCESSES 130 4.1.4
STATISTICAL ESTIMATES OF RANDOM PROCESS CHARACTERISTICS . 131 4.2 BASIC
MODELS OF RANDOM PROCESSES 131 4.3 EVOLUTIONARY EQUATIONS FOR
PROBABILITY DISTRIBUTION LAWS 134 4.4 AUTOREGRESSION AND MOVING AVERAGE
PROCESSES 135 4.5 STOCHASTIC DIFFERENTIAL EQUATIONS AND WHITE NOISE 138
4.5.1 THE CONCEPT OF STOCHASTIC DIFFERENTIAL EQUATION 138 4.5.2
NUMERICAL INTEGRATION OF STOCHASTIC DIFFERENTIAL EQUATIONS 141 4.5.3
CONSTRUCTIVE ROLE OF NOISE 143 REFERENCES 146 PART II MODELLING FROM
TIME SERIES 5 PROBLEM POSING IN MODELLING FROM DATA SERIES 151 5.1
SCHEME OF MODEL CONSTRUCTION PROCEDURE 151 5.2 SYSTEMATISATION IN
RESPECT OF A PRIORI INFORMATION 153 5.3 SPECIFIC FEATURES OF EMPIRICAL
MODELLING PROBLEMS 154 5.3.1 DIRECT AND INVERSE PROBLEMS 154 5.3.2
WELL-POSED AND ILL-POSED PROBLEMS 155 5.3.3 ILL-CONDITIONED PROBLEMS 157
REFERENCES 157 6 DATA SERIES AS A SOURCE FOR MODELLING 159 6. 1
OBSERVABLE AND MODEL QUANTITIES 159 6.1.1 OBSERVATIONS AND MEASUREMENTS
159 6.1.2 HOW TO INCREASE OR REDUCE A NUMBER OF CHARACTERISING
QUANTITIES 163 6.2 ANALOGUE-TO-DIGITAL CONVERTERS 164 6.3 TIME SERIES
166 6.3.1 TERMS 166 6.3.2 EXAMPLES 167 6. XVIII CONTENTS 7.1.1
ESTIMATION TECHNIQUES 203 7.1.2 COMPARISON OF TECHNIQUES 207 7.2
APPROXIMATION 212 7.2.1 PROBLEM FORMULATION AND TERMS 212 7.2.2
PARAMETER ESTIMATION 214 7.2.3 MODEL SIZE SELECTION, OVERFITTING AND
OCKHAM'S RAZOR .215 7.2.4 SELECTING THE CLASS OF APPROXIMATING
FUNCTIONS 220 7.3 MODEL VALIDATION 222 7.3.1 INDEPENDENCE OF RESIDUALS
223 7.3.2 NORMALITY OF RESIDUALS 223 7.4 EXAMPLES OF MODEL APPLICATIONS
225 7.4.1 FORECAST 225 7.4.2 NUMERICAL DIFFERENTIATION 227 REFERENCES
230 8 MODEL EQUATIONS: PARAMETER ESTIMATION 233 8. 1 PARAMETER
ESTIMATORS AND THEIR ACCURACY 235 8.1.1 DYNAMICAL NOISE 235 8.1.2
MEASUREMENT NOISE 236 8.2 HIDDEN VARIABLES 239 8.2.1 MEASUREMENT NOISE
240 8.2.2 DYNAMICAL AND MEASUREMENT NOISE 244 8.3 WHAT ONE CAN LEARN
FROM MODELLING SUCCESSES AND FAILURES 248 8.3.1 AN EXAMPLE FROM CELL
BIOLOGY 249 8.3.2 CONCLUDING REMARKS 252 REFERENCES 252 9 MODEL
EQUATIONS: RESTORATION OF EQUIVALENT CHARACTERISTICS 255 9. 1
RESTORATION PROCEDURE AND PECULIARITIES OF THE PROBLEM 256 9.1.1
DISCRETE MAPS 256 9.1.2 ORDINARY DIFFERENTIAL EQUATIONS 257 9.1.3
STOCHASTIC DIFFERENTIAL EQUATIONS 258 9.2 MODEL STRUCTURE OPTIMISATION
260 9.3 EQUIVALENT CHARACTERISTICS FOR TWO REAL-WORLD OSCILLATORS 262
9.3. CONTENTS XIX 10.1.1 TAKENS' THEOREMS 277 10.1.2 PRACTICAL
RECONSTRUCTION ALGORITHMS 284 10.2 MULTIVARIABLE FUNCTION APPROXIMATION
290 10.2.1 MODEL MAPS 290 10.2.2 MODEL DIFFERENTIAL EQUATIONS 299 10.3
FORECAST WITH VARIOUS MODELS 300 10.3.1 TECHNIQUES WHICH ARE NOT BASED
ON NON-LINEAR DYNAMICS IDEAS 300 10.3.2 ITERATIVE, DIRECT AND COMBINED
PREDICTORS 301 10.3.3 DIFFERENT KINDS OF MODEL MAPS 302 10.3.4 MODEL
MAPS VERSUS MODEL ODES 303 10.4 MODEL VALIDATION 304 REFERENCES 305 11
PRACTICAL APPLICATIONS OF EMPIRICAL MODELLING 309 11.1 SEGMENTATION OF
NON-STATIONARY TIME SERIES 310 11.2 CONFIDENTIAL INFORMATION
TRANSMISSION 312 11.3 OTHER APPLICATIONS 314 REFERENCES 317 12
IDENTIFICATION OF DIRECTIONAL COUPLINGS 319 12.1 GRANGER CAUSALITY 319
12.2 PHASE DYNAMICS MODELLING 322 12.3 BRAIN - LIMB COUPLINGS IN
PARKINSONIAN RESTING TREMOR 326 12.4 COUPLINGS BETWEEN BRAIN AREAS IN
EPILEPTIC RATS 329 12.5 EL NINO - SOUTHERN OSCILLATION AND NORTH
ATLANTIC OSCILLATION 333 12.5.1 PHASE DYNAMICS MODELLING 333 12.5.2
GRANGER CAUSALITY ANALYSIS 335 12.6 CAUSES OF GLOBAL WARMING 337 12.6.1
UNIVARIATE MODELS OF THE GST VARIATIONS 338 12.6.2 GST MODELS INCLUDING
SOLAR ACTIVITY 341 12.6.3 GST MODELS INCLUDING VOLCANIC ACTIVITY 343
12.6.4 GST MODELS INCLUDING CO2 CONCENTRATION 343 REFERENCE XX CONTENTS
13.2.2 DATA ACQUISITION AND PRELIMINARY PROCESSING 364 13.2.3 SELECTION
OF THE MODEL EQUATION STRUCTURE 367 13.2.4 MODEL FITTING, VALIDATION AND
USAGE 368 13.2.5 VALIDATION OF TIME DELAY ESTIMATION 371 13.3
EL-NINO/SOUTHERN OSCILLATION AND INDIAN MONSOON 375 13.3.1 OBJECT
DESCRIPTION 375 13.3.2 DATA ACQUISITION AND PRELIMINARY PROCESSING 376
13.3.3 SELECTION OF THE MODEL EQUATION STRUCTURE 378 13.3.4 MODEL
FITTING, VALIDATION AND USAGE 379 13.4 CONCLUSIONS 386 REFERENCES 386
SUMMARY AND OUTLOOK 389 LIST OF MATHEMATICAL MODELS 395 LIST OF
REAL-WORLD EXAMPLES 399 INDEX 401 |
any_adam_object | 1 |
author | Bezručko, Boris P. Smirnov, Dmitrij A. |
author_facet | Bezručko, Boris P. Smirnov, Dmitrij A. |
author_role | aut aut |
author_sort | Bezručko, Boris P. |
author_variant | b p b bp bpb d a s da das |
building | Verbundindex |
bvnumber | BV036715025 |
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dewey-full | 519.55 511.8 |
dewey-hundreds | 500 - Natural sciences and mathematics |
dewey-ones | 519 - Probabilities and applied mathematics 511 - General principles of mathematics |
dewey-raw | 519.55 511.8 |
dewey-search | 519.55 511.8 |
dewey-sort | 3519.55 |
dewey-tens | 510 - Mathematics |
discipline | Informatik Bauingenieurwesen Mathematik Wirtschaftswissenschaften |
format | Book |
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institution | BVB |
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language | English |
oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020633024 |
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spelling | Bezručko, Boris P. Verfasser aut Extracting knowledge from time series an introduction to nonlinear empirical modeling Boris P. Bezruchko ; Dmitry A. Smirnov Berlin [u.a.] Springer 2010 XXI, 405 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Springer series in synergetics Nichtlineares dynamisches System (DE-588)4126142-2 gnd rswk-swf Zeitreihenanalyse (DE-588)4067486-1 gnd rswk-swf Mathematische Modellierung (DE-588)7651795-0 gnd rswk-swf Nichtlineares dynamisches System (DE-588)4126142-2 s Mathematische Modellierung (DE-588)7651795-0 s Zeitreihenanalyse (DE-588)4067486-1 s DE-188 Smirnov, Dmitrij A. Verfasser aut Erscheint auch als Online-Ausgabe 978-3-642-12601-7 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=3478426&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020633024&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
spellingShingle | Bezručko, Boris P. Smirnov, Dmitrij A. Extracting knowledge from time series an introduction to nonlinear empirical modeling Nichtlineares dynamisches System (DE-588)4126142-2 gnd Zeitreihenanalyse (DE-588)4067486-1 gnd Mathematische Modellierung (DE-588)7651795-0 gnd |
subject_GND | (DE-588)4126142-2 (DE-588)4067486-1 (DE-588)7651795-0 |
title | Extracting knowledge from time series an introduction to nonlinear empirical modeling |
title_auth | Extracting knowledge from time series an introduction to nonlinear empirical modeling |
title_exact_search | Extracting knowledge from time series an introduction to nonlinear empirical modeling |
title_full | Extracting knowledge from time series an introduction to nonlinear empirical modeling Boris P. Bezruchko ; Dmitry A. Smirnov |
title_fullStr | Extracting knowledge from time series an introduction to nonlinear empirical modeling Boris P. Bezruchko ; Dmitry A. Smirnov |
title_full_unstemmed | Extracting knowledge from time series an introduction to nonlinear empirical modeling Boris P. Bezruchko ; Dmitry A. Smirnov |
title_short | Extracting knowledge from time series |
title_sort | extracting knowledge from time series an introduction to nonlinear empirical modeling |
title_sub | an introduction to nonlinear empirical modeling |
topic | Nichtlineares dynamisches System (DE-588)4126142-2 gnd Zeitreihenanalyse (DE-588)4067486-1 gnd Mathematische Modellierung (DE-588)7651795-0 gnd |
topic_facet | Nichtlineares dynamisches System Zeitreihenanalyse Mathematische Modellierung |
url | http://deposit.dnb.de/cgi-bin/dokserv?id=3478426&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020633024&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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