Simplicity of Complexity in Economic and Social Systems : Proceedings of the 54th Winter School of Theoretical Physics, Lądek Zdrój, Poland, February 18–24th 2018

This book presents the Proceedings of the __54th Winter School of Theoretical Physics on Simplicity of Complexity in Economic and Social Systems__, held in Lądek Zdrój, Poland, from 18 to 24 February 2018. The purpose of the book is to introduce the new interdisciplinary research that links statistical physics, and particular attention is given to link physics of complex systems, with financial analysis and sociology. The main tools used in these areas are numerical simulation of agents behavior and the interpretation of results with the help of complexity methods, therefore a background in statistical physics and in physics of phase transition is necessary to take the first steps towards these research fields called econophysics and sociophysics. In this perspective, the book is intended to graduated students and young researchers who want to begin the study of this established new area, which connects physicists, economists, sociologists and IT professionals, to better understand complexity phenomena existing not only in physics but also in complex systems being seemingly far from traditional view at physics. Preface 6 Contents 8 Contributors 9 1 Simple Approaches on How to Discover Promising Strategies for Efficient Enterprise Performance, at Time of Crisis in the Case of SMEs: Voronoi Clustering and Outlier Effects Perspective 11 Introduction 12 Data 13 Discussion 17 A Brief Description of the Voronoi Tessellation 21 Voronoi Correlations Approach 21 Voronoi Clustering Approach 22 Evidence from Outliers Approach 27 Conclusions 28 References 28 2 Enhancing Maximum Likelihood Estimation of Infection Source Localization 31 Introduction 32 Pinto-Thiran-Vetterli Algorithm 33 Gradient Maximum Likelihood Algorithm 36 Independent Paths 41 Multiple Correlated Paths 44 Equiprobable Paths (EPP) 46 Equiprobable Links (EPL) 47 EPP/EPL Results 47 Conclusions 49 References 50 3 Power-Law Cross-Correlations: Issues, Solutions and Future Challenges 52 Introduction 52 From Long-Range Dependence to Power-Law Cross-Correlations 53 The Issues with Power-Law Cross-Correlations 55 All in Vain? 57 Scale-Specific Correlations and Regressions 58 Power-Law Coherency 59 Discussion 60 References 61 4 Multi-phase Long-Term Autocorrelated Diffusion: Stationary Continuous-Time Weierstrass Walk Versus Flight 64 Historical Sketch and Inspirations 64 Initial Remarks 64 Elements of Lévy Random Motion 66 Stationary Continuous-Time Weierstrass Walk Versus Flight: Definitions 67 Useful Relations Between Single-Step Moments 70 Main Subject 72 Propagator 72 General Stationary Situation 72 Stationary Propagator and Even Moments: General Representation 73 Mean-Square Displacement and Autocorrelation Function in a Closed Form 75 Classification of the CTRW Diffusion Phases 76 Excess Kurtosis 78 Comparison with Stationary Continuous-Time Weierstrass Flight 79 Further Extension of the CTWW Diffusion Phase Diagram 81 Concluding Remarks 83 Appendix 1: Expansions of Propagator 84 Exact Stationary CTWW and CTWF Propagators 85 Auxiliary Calculations 89 The Key Marginal Equalities 90 Appendix 2: Basic Distributions and Means 91 Basic Distributions 91 Marginal Distributions 93 Non-factorial Spatial-Temporal Cross-Moments 94 References 95 5 A Brief Introduction to DFA-Based Multiscale Analysis 98 Introduction 98 Fractal Structures 100 Fractal Functions 101 Analysis of Time Series with the DFA Methodology 103 Multifractality of the Time Series 105 Estimation of Multifractality with the MFDFA 107 Multifractal Cross-Correlation Analysis 109 Summary 113 References 113 6 Complex Dynamics of Economic Models with Time Delay 116 Introduction 116 Complexity in Nonlinear Dynamics of Economic Models 116 Oscillations in Economic Models 119 Functional Differential Equations 120 Business Cycle Model with Delay 121 The Kaldor–Kalecki Model 121 The Kaldor–Kalecki Model in Small Time Lag Approximation 125 The Kaldor–Kalecki Model as a System with Self-sustaining Oscillations 130 The Kaldor–Kalecki Growth Model 132 Conclusion 136 References 138 Front Matter ....Pages i-x Simple Approaches on How to Discover Promising Strategies for Efficient Enterprise Performance, at Time of Crisis in the Case of SMEs: Voronoi Clustering and Outlier Effects Perspective (Marcel Ausloos, Francesca Bartolacci, Nicola G. Castellano, Roy Cerqueti)....Pages 1-20 Enhancing Maximum Likelihood Estimation of Infection Source Localization (Robert Paluch, Łukasz Gajewski, Krzysztof Suchecki, Bolesław Szymański, Janusz A. Hołyst)....Pages 21-41 Power-Law Cross-Correlations: Issues, Solutions and Future Challenges (Ladislav Kristoufek)....Pages 43-54 Multi-phase Long-Term Autocorrelated Diffusion: Stationary Continuous-Time Weierstrass Walk Versus Flight (Tomasz Gubiec, Jarosław Klamut, Ryszard Kutner)....Pages 55-88 A Brief Introduction to DFA-Based Multiscale Analysis (Paweł Oświȩcimka)....Pages 89-106 Complex Dynamics of Economic Models with Time Delay (Marek Szydłowski, Adam Krawiec)....Pages 107-130