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Complexity Explained: A brief intro to complex systems
- 1. Complexity Explained A Brief Intro to Complex Systems HIROKI SAYAMA (BINGHAMTON UNIVERSITY & WASEDA UNIVERSITY) [email protected]
- 2. What Are Complex Systems? Networks of many components Typically involve nonlinear interactions among components Arise and evolve through self- organization Reside between regularity and randomness Show emergent structure/behavior
- 3. Examples of Complex Systems • Chemical networks • Gene networks • Organisms • Physiologies • Brains • Ecosystems • Economies • Organizations • Societies • Weather/climate • The Internet
- 4. * Diagram available from Wikipedia
- 5. Nonlinear Dynamics Iterative maps Chaos Bifurcation Population dynamics Stability analysis Phase space Time series analysis Ordinary differential equations Attractors Coupled map lattices Multistability
- 6. Systems Theory Autopoiesis Sense making Information theory Complexity measurement Feedbacks Homeostasis Cybernetics System dynamics Self-reference Entropy Goal-oriented/ guided behavior Computation theory
- 7. Game Theory Rational decision making Bounded rationality Prisoner’s dilemma (PD) Iterative PD n-person PD Evolutionary game theory Spatial/network game theory Irrational behavior Cooperation versus competition
- 8. Pattern Formation Cellular automata Spatial fractals Reaction-diffusion systems Spatial ecology Dissipative structures Partial differential equations Percolation Self-replication Spatial evolutionary biology Geomorphology
- 9. Evolution & Adaptation Evolutionary robotics Evolutionary computation Genetic algorithms/programming Machine learning Artificial neural networks Artificial intelligence Artificial life Evolvability Evo-Devo
- 10. Networks Scale-free networks Small-world networks Centrality Graph theory Dynamical networks Robustness/vulnerability Systems biology Adaptive networks Community identification Motifs Social network analysis Scaling
- 11. Collective Behavior Collective intelligence Swarm behavior Agent- based modeling Ant colony optimization Social dynamics Particle swarm optimization Phase transition Self-organized criticality Herd mentality Synchronization
- 13. Seven Essential Concepts 1. Interactions: Complex systems consist of many components interacting with each other and their environment in multiple ways. 2. Emergence: Properties of complex systems as a whole are very different, and often unexpected, from properties of their individual components. 3. Dynamics: Complex systems tend to change their states dynamically, often showing unpredictable long-term behavior. 4. Self-Organization: Complex systems may self-organize to produce non-trivial patterns spontaneously without a blueprint. 5. Adaptation: Complex systems may adapt and evolve. 6. Interdisciplinarity: Complexity science can be used to understand and manage a wide variety of systems in many domains. 7. Methods: Mathematical and computational methods are powerful tools to study complex systems.
- 14. complexityexplained.github.io Website design by Manlio & Dirk Special thanks for booklet design by Serafina Agnello (Translation projects also ongoing!!) Powered by complexity-explorables.org
- 15. Demos with PyCX • “Python-based CompleX systems simulations” • Online repository (http://github.com/hsayama/pycx) of sample codes of complex systems simulations written in plain Python
- 17. Example: Epidemic and Social Distancing • Well-known “Washington Post” SIR simulation model • Changing interactions drastically changes outcomes
- 19. Example: Simple Cellular Automata • Droplet rule • Game of Life
- 21. Example: Bifurcation and Chaos • Qualitative changes of system behavior caused by small quantitative changes of conditions • Long-term unpredictability of behavior of fully deterministic systems
- 23. Example: Diffusion-Limited Aggregation • Moving particles get fixed when they collide with other fixed ones • Fractal-like tree branches grow spontaneously • Branches “sense” and avoid each other
- 25. Example: Evolution of Virulence • Let the agents die! • Virulence of virus (death rate) spontaneously evolves to a moderate level • May explain why majority of people have mild or no symptoms (but are still infectious)
- 27. Example: Keller-Segel Model • Agents attracted to areas with high concentration of signal (cAMP or $$$) • Agents produce signal • Signal diffuses and evaporates naturally
- 29. Research Methods Computer simulations Agent-based models, system dynamics models, etc. Network modeling and analysis Dynamical network models, social network analysis, etc. Machine learning Evolutionary computation, neural networks, deep learning, etc.
- 31. Pattern Discovery Social media analysis, network analysis, etc. From statistical analysis to big data analytics Analyze large amounts of multidimensional data Reveal hidden non- trivial patterns Classify data into multiple distinct classes
- 32. Mechanistic Modeling Mathematical equations Computer simulations (agent-based modeling, etc.) Predict macroscopic unknown outcomes using microscopic known rules Explain macroscopic known facts using hypothetical microscopic unknown rules
- 33. Science Needs Both • Pattern discovery and mechanistic modeling are two essential aspects of a single scientific loop • Their right balance is the key to reaching deeper understanding of organizational structures and behaviors Pattern Discovery Mechanistic Modeling
- 34. For More Information • Free online textbook available from OpenSUNY Textbooks (Just Google “sayama textbook”) • Sayama, H. (2015) Introduction to the Modeling and Analysis of Complex Systems, Open SUNY Textbooks, Milne Library, State University of New York at Geneseo.
- 35. [Advertisement] Complex Systems Society (http://cssociety.org/) • International society for complex systems science • Conference on Complex Systems (CCS) • Local chapters in US Northeast, Italy
- 36. [Advertisement] Systems Science Program at Binghamton University • M.S., Ph.D., Certficate • 50 yrs. of history • Interdisciplinary, flexible curriculum • Open to all majors • Most courses available online