Complexity and Emergence : Lake Como School of Advanced Studies, Italy, July 22–27, 2018

This book includes contributions about mathematics, physics, philosophy of science, economics and finance and resulted from the Summer School “Complexity and Emergence: Ideas, Methods, with a Special Attention to Economics and Finance” held in Lake Como School of Advanced Studies, on 22–27 July 2018. The aim of the book is to provide useful instruments from the theory of complex systems, both on the theoretical level and the methodological ones, profiting from knowledge and insights from leading experts of different communities. It moves from the volume editors' conviction that to achieve progress in understanding socio-economical as well as ecological problems of our complex word such preparation is needed, together with a critical reconsideration of our basic scientific and economical approach. The potential readers are primarily master and doctorate students of mathematics, information sciences, theoretical physics and economics, as well as research workers in those areas, who want to enlarge their spectrum of knowledge towards the area of complexity and emergence. Since ideas and methods of the theory of complex systems also apply to other areas (from engineering and architecture to biology and medicine, e.g.), students and research workers from those areas will also profit from this book. Preface to the Volume Advanced School on Complexity and Emergence: Ideas, Methods, with a Special Attention to Mathematics and Its Application to Economics and Finance Acknowledgments Contents A Topological and Dynamical Approach to the Study of Complex Living Systems 1 Introduction: Complex Structures in Physics 2 Topological Stability in Condensed Matter and Phase Transition 3 Epistemological Remarks on the Limits of the Hierarchical Paradigm of Science 4 The Spin-Like Representation of the KT Topological Phase Transition 5 The Effectiveness of the Concept of Winding 6 Topological Changes and Emergence of Physical Patterns 7 Complexity of Time and of the Universe 8 The Complexity and the Breaking-Symmetry Phenomenon 9 The Specificity of Biological Complexity, Emergence and Causation 10 Systems Biology and Complexity 11 Self-Organization and the Causal Role Played by Systemic Properties in Biology 12 Systems Biology, Reductionism and Emergence 13 Chaos, Fractality and Complexity 14 The Difference Between Self-Assembly and Self-Organization 15 Complexity of Biological Systems: The Genome as a Complex System 16 The Need for a Systems Biology Approach 17 The Complex Topology of Biological Structures: From Topoisomerases to Supercoiling 18 The Functional Role of Topological Plasticity 19 The Topological State of Supercoiling and Its Biological Functions 20 Conclusive Remarks References The Complexity Theory and Financial Systems Regulation 1 The Characteristics of Complex Systems 2 Complexity Theory and the Law: Complex Versus Complicated 3 Complexity Theory and Legal Thinking 4 Complexity Theory and the Financial System 5 Complexity Jurisprudence and Financial Systems Regulation 6 The Financial System Regulation and the Systemic Risk 7 Complex Systems Models and the Role of Fraud References The Emergence of the Order Parameter in the Interpolating Replica Trick for Disordered Statistical Mechanics Systems 1 Introduction 2 Replicas and the Auxiliary Function 3 Interpolating on the Number of Replicas 4 The Replica Trick in the Random Energy Model and the Emergence of the Universal Order Parameter 5 The Emergence of the Order Parameter and the Trial Function in the Sherrington-Kirkpatrick Model 6 Conclusion and Outlook References Information and Complexity, Or: Where Is the Information? 1 Introduction 2 Background: Principles of Information Theory 2.1 Shannon Information 2.2 Mutual and Conditional Information 2.3 Maximum Entropy 2.4 Kullback-Leibler Divergence 3 Complexity 3.1 Algorithmic Complexity 3.2 External and Internal Complexity 3.3 Optimization Principles 3.4 Correlations in Time Series 3.5 Complementarity 3.6 Hierarchical Models and Complexity Measures 3.7 Interactions Between Levels 4 Information Decomposition References Complex Systems: From the Presocratics to Pension Funds 1 Introduction 2 Presocratic Philosophy Revisited 2.1 Heraclitus and the Philosophy of Nature 2.2 Parmenides and the Modern Idea of Science 2.3 Democritus and Atomism 2.4 Markov Chains 3 Models and Causes 3.1 The Example of Feynman Diagrams 3.2 Aristotle on Causality 3.3 Aristotle's Causes in Modern Science 4 Mathematical Atomism 4.1 Logical and Mathematical Atoms 4.2 The Principle of Reason 4.3 Mathematics as a Dynamical System 5 Pension Schemes as Complex Systems 5.1 Defined Benefit Pension Funds 5.2 Wrong Way Risk 5.3 A Merton Model for Defaults 5.4 Quantitative Results 5.5 Financial Conclusions 5.6 Epistemological Lessons References From Complex Dynamics to the Architecture of the City 1 Introduction 2 Basic Classic Theories on Urban Systems 3 Cities: Design and Self-organization 4 The City Designed 5 The Spontaneous Self-organizing City 6 The Artificial Self-organized City 7 The Scientific and Architectonic Way of Knowledge 8 From Object to Patterns 9 Imitation and Time 10 Communication Is the Main Problem that a City Faces and Solves 11 From Communication to the Basic Center-Area Pattern 12 The Channeling of Movement and the Establishment of a Center 13 The Two Basic Patterns 14 The Self-similarity of the System of Patterns 15 The Spatial Organization of the System of Patterns 16 The Tracing of the Roads Network 17 The Topological Aspects of the Roads Network, and the Production of Urban Space 18 Final Remarks 19 Conclusions References Randomness, Emergence and Causation: A Historical Perspective of Simulation in the Social Sciences 1 Introduction 2 Experiments with Early Computers 2.1 ENIAC 2.2 Intermezzo 2.3 FERMIAC 2.4 MONIAC 3 System Dynamics 3.1 Intermezzo 4 Discrete-Event Simulation 5 Microsimulation 5.1 Microsimulation in Economics 5.2 Intermezzo 5.3 Early Simulation of Voting Behavior 6 Cellular Automata 6.1 Intermezzo 7 Agent-Based Models 7.1 A Menagerie of Names 8 Conclusions References