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

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