## New Directions in Statistical Physics: Econophysics, Bioinformatics, and Pattern RecognitionStatistical 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 |

356 | |

359 | |

### Other editions - View all

New Directions in Statistical Physics: Econophysics, Bioinformatics, and ... Luc T. Wille Limited preview - 2013 |

New Directions in Statistical Physics: Econophysics, Bioinformatics, and ... Luc T. Wille No preview available - 2010 |

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