1. Hiroki Sayama sayama@binghamton.edu
NECSI Summer School 2008 Week 2: Complex Systems Modeling and Networks Fundamentals of Modeling
Hiroki Sayama

2. Introduction

3. Examples of complex systems
Chemical networks
Gene networks
Organisms
Physiologies
Brains
Ecosystems
Economies
Societies
Internet

4. Several characteristics of complex systems
Networks of many components
Nonlinear interactions
Self-organization
Structure/behavior that is neither regular nor random
Emergent behavior

5. Topics to be covered Fundamentals of Modeling Non-Spatial Models
Cellular Automata
Agent-Based Models
Network Models

6. Course format Each module (~3 hrs.) includes
Basic concepts of model framework
Walkthrough of sample codes
Coding exercises
Application and discussion
Free Q&As and discussion at the end of each day

7. Course emphasis
Emphasis will be on the process of model development itself
Examples are no more than to show how to implement various models
Feel free to share your thought with class whenever you come up with interesting modeling ideas
The whole class will work together to develop and/or evaluate your model

8. Online resource
All the course slides and sample codes are (or will be) available at:
Login name: necsi
Password: com3sysB

9. Models in Science and Engineering

10. Science finds these kinds of laws (and engineering uses them)
F = m a
F = G m1 m2 / r2
P V = n R T
V = I R
E = m c2
Conservation of energy, momentum and angular momentum
etc…

11. Cycle of scientific efforts
Observe Nature
Develop a hypothesis that explains the observations
Make some predictions using your hypothesis
Carry out experiments to see if the predictions are correct
If correct, your hypothesis is proven
If not, you have to develop another hypothesis ?

12. Let’s do some logic A phenomenon P is observed
You come up with hypothesis H that explains P (i.e., H  P)
You predict another phenomenon Q using hypothesis H (i.e., H  Q)
You conduct experiments to see Q
What if “Q” is actually observed?
What if “not Q” is observed?

13. Easy to disprove, hard to prove
If “not Q” is observed, H is easily disproved
(H  Q)  (not Q  not H) (contraposition)
If “Q” is observed, we are not yet sure whether H is by itself right or not
Maybe H would need additional condition K we were not aware in experiments to cause Q (limitation of applicability)
Maybe another hypothesis R could also explain P and Q (possibility of alternative hypothesis)

14. Fallacy of “scientific truth”
People often say “This is scientifically proven”, but strictly speaking -- there is NO way to scientifically “prove” anything about real Nature
All laws are at best “well-tested hypotheses” valid within limited conditions
Room for other possible explanations always remain
No guarantee for their universal, permanent truth

15. So, they are all “models”!!
F = m a
F = G m1 m2 / r2
P V = n R T
V = I R
E = m c2
Conservation of energy, momentum and angular momentum
etc…
Valid only in Newtonian mechanics
Applicable to ideal cases only
Seems to be valid always, but there may be some other ways to explain our universe…

16. “Model”
A simplified representation of a system (either conceptual, verbal, diagrammatic, physical or formal)
You are always creating a model in your mind when you try to understand the external world
Worldviews, religions, cultures
Natural/social sciences

17. Models in science
Science is an endless effort to create “models” of Nature
What you’ve learned as “scientific truth” are actually the collection of “models” that have survived many attempts to disprove them so far
Modeling is the one and only rational approach to the unreachable reality

18. Models in engineering
Engineering is to control Nature to make something happen in it
The real Nature is unreachable though
 What we can actually control are “models” of Nature
Models are a logical construction; you can have a full control over them
Engineering is an endless effort to control Nature by creating and controlling its models

19. Think about…
A couple of models you have learned that are extensively used in today’s scientific/engineering fields
How were they developed?
What made them more useful than earlier models?
How could they possibly be wrong?

20. How to Create a Model?

21. Two ways of modeling Descriptive modeling Rule-based modeling
Tries to specify the system’s actual (or past) states
Images, miniatures, biographies
Rule-based modeling
Tries to extrapolate the system’s possible (or future) states
Theories, principles, equations
© Toyo Precision Parts Co., Ltd.
© Gramercy

22. Keep in mind: Models should be
Simple
Occam’s razor: Makes short descriptions
Correct
Produces predictions in good agreement with reality
Robust
Produces strong conclusions that can hold with various assumptions; broadens applicability

23. Cycle of modeling efforts
Observe the system of interest
Reflect on possible rules that might cause the system’s characteristics
Derive predictions from those rules and compare them with the reality
Repeat the above to modify the rules until you get satisfied
(This is exactly what scientists have been doing)

24. Problems in modeling Observe the system of interest
Reflect on possible rules that might cause the system’s characteristics
Derive predictions from those rules and compare them with the reality
Repeat the above to modify the rules until you get satisfied
This is so deeply interwoven with our everyday cognitive processes
Heavily depends on one’s past experience and knowledge
Hard to teach or learn…

25. Exercise Create a mathematical model of the following behavior:
Some quantity
Time

26. Exercise Create a mathematical model of the following behavior:
Some quantity
Time

27. Exercise Create a mathematical model of the following behavior:
Some quantity
Time

28. Exercise Create a mathematical model of the following behavior:
Some quantity
Time

29. Creating a model of complex systems
Define the key questions and choose the right scale of modeling
Identify structure (parts and their connections) of the system
Define possible states for each part
Describe how the state of each part changes over time through interactions with other parts

30. Exercise
Create a conceptual model for each of the following systems by describing which scale you look at, what are their parts, what states they can take, how the parts are connected, and how the states change through interactions between parts

31. Epistemological challenges in modeling complex systems
Many degrees of freedom
Parallelism
Non-linearity
Sensitivity to initial conditions
Pattern formation
Difficult to handle with traditional “reductionism” approaches

32. Epistemological challenges in modeling complex systems
Behavior of complex systems often contradict our everyday experiences
It is very hard to come up with underlying microscale rules that could explain those macroscale outcomes
One needs to get “experienced” and “familiar” with them to develop a better model of complex systems

33. Computer simulation
Reconstruct your model in full detail in a computer, and let it actually show (rather than predict) its behavior
Powerful tool for studying large, discrete, and/or inhomogeneous systems, through interactive and intuitive “experiences” of various possible model dynamics
Virtually no better tools available for general complex systems studies

34. Various tools for simulation
General programming languages
C, C++, Java, Python, etc.
Free simulation software packages
StarLogo, NetLogo, Swarm, etc.
Commercially available applications
MATLAB, Mathematica, MS Excel, etc.

35. How to Evaluate a Model?

36. Simplicity Is your model simple enough?
Are you getting more “outputs” from the model than “inputs” you gave to the model?
Can’t you reduce some of the parameters/variables from the model?

37. Correctness Does your model produce “correct” results?
Accurate predictions may not be practical for complex systems behaviors
Correctness may be “conceptual” or “quantitative”
Is the simulation free from mistakes?
Do different implementations produce the same results?

38. Robustness Are the results similar even if you slightly change:
Initial conditions
Parameter values
Model assumptions
To confirm the robustness, conduct:
Systematic experiments testing the variations listed above
Independent model development and their comparison within group

39. However… There is no single scale for evaluating the values of models
Similar to worldviews, religions, etc.
Ultimately, models are evaluated socially
E.g. # of users, papers
You should advocate your model if you believe it is better than others