New Directions in Statistical Physics: Econophysics, Bioinformatics, and Pattern Recognition

Front Cover
Luc T. Wille
Springer Science & Business Media, Jan 14, 2004 - Science - 363 pages
Statistical physics addresses the study and understanding of systems with many degrees of freedom. As such it has a rich and varied history, with applications to thermodynamics, magnetic phase transitions, and order/disorder transformations, to name just a few. However, the tools of statistical physics can be profitably used to investigate any system with a large number of components. Thus, recent years have seen these methods applied in many unexpected directions, three of which are the main focus of this volume. These applications have been remarkably successful and have enriched the financial, biological, and engineering literature. Although reported in the physics literature, the results tend to be scattered and the underlying unity of the field overlooked. This book provides a unique insight into the latest breakthroughs in a consistent manner, at a level accessible to undergraduates, yet with enough attention to the theory and computation to satisfy the professional researcher.
 

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Contents

Predicting the Direction of a Time Series
3
2 Embedding in Direction Space
4
3 Predicting the Direction
7
4 Empirical Examples
11
5 Concluding Remarks
14
On the Variability of Timing in a Spatially Continuous System with Heterogeneous Connectivity
17
2 Spatiotemporal Dynamics and Integral Equations
18
A TwoPoint Connection
21
Sequence Alignment in Bioinformatics
193
11 The Holy Grail
194
12 Alignment Algorithms
195
13 Score Statistics
200
14 Substitution Scoring Matrices
201
2 Some Recent Developments
204
22 Hybrid Alignment
205
23 Open Problems
208

4 Variability of the Timing of Distant Sites
23
41 Homogeneous Connectivity Only
25
42 Homogeneous Connectivity and Projection from A to B
26
44 Heterogeneous Pathways Only
27
5 Conclusions
28
References
29
A FokkerPlanck Approach
31
2 FPT Distribution for Brownian Motion
32
3 FPT Distribution for Continuous Time Random Walks
38
4 Summary
45
First and LastPassage Algorithms in Diffusion Monte Carlo
47
2 The AngleAveraging Method
52
3 The SimulationTabulation ST Method
53
4 The FeynmanKac Method
56
5 Last Passage Methods for Diffusion Monte Carlo
58
6 Conclusions and Suggestions for Further Study
64
References
65
Complex Market Ecology Power Laws in Wealth Distribution and Market Returns
69
2 Crashes Booms and Cycles
71
3 Predation Competition and Symbiosis Between Trader Species
73
32 Three Investor Species
79
Realistic Dynamics of Market Returns
80
42 Excess Volatility
81
5 The Emergence of Paretos Law in LLS
82
6 Market Efficiency Pareto Law and Thermal Equilibrium
84
7 Leptokurtic Market Returns in LLS
86
8 Summary
89
Patterns Trends and Predictions in Stock Market Indices and Foreign Currency Exchange Rates
93
11 Tulipomania
95
12 Monopolymania
96
13 WallStreetmania
97
2 Econophysics of Stock Market Indices
98
21 Methodology and Data Analysis
101
22 Aftershock Patterns
104
3 Foreign Currency Exchange Rates
107
32 Data and Analysis
108
33 Probing the Local Correlations
110
4 Conclusions
112
Toward an Understanding of Financial Markets using Multiagent Games
115
3 Grand Canonical Minority Game
119
4 Next Timestep Prediction
121
5 Corridors for Future Price Movements
123
6 RealWorld Risk
124
7 Conclusion
126
References
127
Towards Understanding the Predictability of Stock Markets from the Perspective of Computational Complexity
129
2 A Basic Market Model
130
21 Defining the DSMC Model
131
22 Computer Simulation on the DSMC Model
133
3 A General Market Model
134
4 Predicting the Market
135
41 Markets as Systems of Linear Constraints
136
Many Traders but Few Strategies
138
Many Strategies
141
5 Future Research Directions
149
References
150
Patterns in Economic Phenomena
153
2 Classic Approaches to Finance Patterns
156
3 Patterns in Finance Fluctuations
157
4 Patterns Resembling Diffusion in a Tsunami Wave
161
5 Patterns Resembling Critical Point Phenomena
162
of Different Stocks
164
8 Universality of the Firm Growth Problem
165
9 TakeHome Message
166
References
167
New Algorithms and the Physics of Protein Folding
173
2 The GeneralizedEnsemble Approach
175
22 1kSampling
177
23 Simulated Tempering
178
25 Parallel Tempering
179
3 The Thermodynamics of Folding
180
32 Energy Landscape Analysis of Peptides
185
4 Structure Prediction of Proteins
188
5 Conclusion
190
References
211
A Computer Study
213
2 Brief Description of Human Immune System
214
3 The Dintzis Experimental Results and the Immunon Theory
217
5 Results
219
References
224
Proliferation and Competition in Discrete Biological Systems
225
2 Dynamics of Discrete Proliferating Agents
227
How Well Do Different Methods Deal with Discreteness?
229
4 Single S Analysis 10
230
5 RG Analysis 10
232
6 Mechanisms Limiting Population Growth
233
61 Local Competition
234
62 Global Competition
235
63 Emergence of Complexity
238
7 Discussion
239
71 Dimensionality
240
References
241
Privacy and Data Exchanges
243
2 A Lightning Review of Cryptographic Techniques
245
3 Secret Matching of Data Sets
246
4 Private Surveys in the Public Arena
247
5 Conclusion
250
Statistical Physics and the Clustering Problem
253
2 Hierarchical Clustering for Phylogeny Reconstruction
255
22 Distance Measures
257
23 Experiment
259
24 Discussion
260
3 The Autoencoder Frame
261
32 Deterministic Annealing
264
34 Resampling Technique for Unsupervised Estimation of the Number of Classes
266
35 Discussion
268
4 Conclusions
271
The Challenges of Clustering High Dimensional Data
273
2 Basic Concepts and Techniques of Cluster Analysis
274
22 What Cluster Analysis Is Not
275
24 The Proximity Matrix
276
27 Measures Indices of Similarity and Dissimilarity
279
28 Hierarchical and Partitional Clustering
281
KMeans
282
MIN MAX Group Average
283
3 The Curse of Dimensionality
284
4 Recent Work in Clustering High Dimensional Data
288
42 Grid Based Clustering Approaches
289
43 Noise Modeling in Wavelet Space
296
44 A ConceptBased Approach to Clustering High Dimensional Data
297
5 Conclusions
307
Some Statistical Physics Approaches for Trends and Predictions in Meteorology
313
11 Techniques of Time Series Analysis
315
3 Nonstationarity and Spectral Density
317
4 Roughness and Detrended Fluctuation Analysis
319
5 Time Dependence of the Correlations
322
6 Multiaffinity and Intermittency
324
7 Conclusions
326
Appendix
327
References
328
An Initial Look at AccelerationModulated Thermal Convection
331
2 Laboratory
334
22 Numerical Methods
336
3 Onset TimeDependence and Typical Patterns
337
32 Confirmation of TimeDependence
338
33 Harmonic Patterns at Onset
339
34 Harmonic Patterns away from Onset
340
35 Subharmonic Patterns at Onset
343
4 Direct HarmonicSubharmonic Transition
344
41 Transition from Pure Harmonics to Coexistence
345
42 Transition from Pure Subharmonics to Coexistence
347
5 Superlattices
349
52 Observations away from Bicriticality
351
53 Resonant Tetrads
352
54 Other Frequencies
354
6 Discussion
356
Index
359
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