An introductory lecture on complex systems at NERCCS 2020 Pre-Conference School (April 1, 2020)

1. Complexity Explained
A Brief Intro to Complex Systems
HIROKI SAYAMA (BINGHAMTON UNIVERSITY & WASEDA UNIVERSITY)
SAYAMA@BINGHAMTON.EDU

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

12. “Complexity Explained”
Outreach Project

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.

30. Research Approaches
PATTERN
DISCOVERY
MECHANISTIC
MODELING

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.,
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• 50 yrs. of history
• Interdisciplinary,
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37. Thank You
@hirokisayama