Note: This course is waved if students demonstrate familiarity with complex systems (e.g. M.S. in related field). It is taught every two years to guarantee sufficient quorum. It alternates with I585 which students can take instead of I601.

Motivation

Nature is complex. Biological, social, economic, technological and information systems are all composed of many interacting agents giving rise to macroscopic complex features. Complexity science is the novel interdisciplinary research ­field devoted to the understanding of the roots of complex phenomenology observable in nature, and to developing a common theoretical framework able to explain the astonishing similarity between complex real systems of so different origin.

Aims

This course aims at providing an introduction to complex systems and networks. The course will touch several topics of traditional and current research in complexity science. Students will learn mathematical and statistical concepts of the science of complexity, and, by being exposed to a great deal of real examples, they will learn how to measure and characterize complex features in natural systems. These notions and analytic tools are increasingly in demand to approach complex problems in many different disciplines including biology, data and sport analytics, social science, informatics, neuroscience, and economics.

This course is taught once every two years alternating with I709, to obtain a sufficient quorum of students. Majority of students from Complex Systems track, but students from other tracks and programs frequently take this seminar.

Motivation

A complex system is any system featuring a large number of interacting components (agents, processes, etc.) whose aggregate activity is nonlinear (not derivable from the summations of the activity of individual components) and typically exhibits hierarchical self-organization under selective pressures. This definition applies to systems from a wide array of scientific disciplines. Indeed, the sciences of complexity are necessarily based on interdisciplinary research. Almost all interesting processes in nature are highly cross linked. In many systems, however, we can distinguish a set of fundamental building blocks, which interact nonlinearly to form compound structures or functions with an identity that requires more explanatory devices than those used to explain the building blocks. This process of emergence of the need for new, complementary, modes of description is known as hierarchical self-organization, and systems that observe this characteristic are defined as complex. Examples of these systems are gene networks that direct developmental processes, immune networks that preserve the identity of organisms, social insect colonies, neural networks in the brain that produce intelligence and consciousness, ecological networks, social networks comprised of transportation, utilities, and telecommunication systems, as well as economies. The field of complex systems studies the general characteristics of all these systems. Its goal is to identify and model the laws and behaviors common to various classes of complex systems.

Aims

This seminar is designed to present and discuss the history, methodology and impact of complex systems; we cover key literature as well as recent advances in the field.

Evaluation

Students are expected to read and annotate the materials presented, as well as present several of the key readings. Students will also work on a term paper.

Syllabus

1. Part I: History of the Field
   1. Cybernetics and the Informational Turn
   2. Systems Science, Prediction, and Limits
   3. Self-Organizing Systems
   4. Second-Order Cybernetics
   5. Organization of Complex Systems
2. Part II: Current Research
   1. Towards a practice of Complex Systems
   2. Evolutionary Systems
   3. Information and Complexity
   4. Neo-Cybernetics themes

This course is taught once every two years alternating with I609, to obtain a sufficient quorum of students. Majority of students from Complex Systems track, but students from other tracks and programs frequently take this seminar.

Most Recent offering: https://yongyeol.com/courses/2013S-I709/

Motivation

Complex systems are the systems that contain many sub-parts that interact with each other. Thanks to the structure and dynamics of interactions, fascinating and unpredictable phenomena emerge. Many natural and artificial systems that fascinate us (e.g. cells, brains, societies) are complex systems. Because complex systems exist all over the places, the study of complex systems is inherently interdisciplinary. In this course, we will try to find the answers to the following questions: What are the complex systems around us? What characterizes the complex systems approach? What are the fundamentals of complex systems approach? How has it been applied to other fields? What are the frontiers of the research? We will explore fascinating papers ranging from the fundamental theory to the various applications, along with individual research project.

Aims

• To be able to think like a complex systems researcher.
• To be able to apply complex systems approaches to your research.
• To finish a small research project about complex systems.

Evaluation

Paper Review (20%): a short review of the papers is due by the midnight before the class

Paper Presentation: Assigned moderators make a brief (~ 5 minutes) presentation about the premises and the results of the paper.

Project proposal: A two to four page document that contains project title, motivation, relevant prior work, approach, plan, proposal presentation.

Proposal Presentation: 20 slides, 1–5 presentation.

Progress report: draft of the final paper, with preliminary results.

Final project paper (40%): full research paper (~10 pages) with all the details.

Final presentation (20%): 10 minute presentation.

Participation (20%)

Syllabus

1. Schooling Flocks and Crowds
2. Traffic and Panic
3. Collective Behavior and Social Segregation
4. Emergence of Network Communities
5. Threshold Model and Information Diffusion
6. Social Contagion and Virality
7. Economic Complexity
8. Networks of Genes, Proteins, Diseases, and Drugs
9. Evolution: Cost Optimization in Brain
10. Evolution of Cooperation
11. 1/f Noise and Music
12. Fractal
13. Self-Organized Criticality
14. Power-Law
15. Common Patterns of Nature
16. Allometric Scaling
17. Cities
18. Boolean Networks
19. Robustness of Regulatory Networks
20. Control
21. Homophily and Influence
22. Laws of Mobility
23. Virtual Worlds
24. Stochastic Resonance
25. Data

Readings From Spring 2013

Listed at: https://yongyeol.com/courses/2013S-I709/#schedule

Note: This course is waved if students demonstrate sufficient mathematical prior training (e.g. M.S. in related field). It is taught every two years to guarantee sufficient quorum.

Motivation

Complexity deals with the structural, behavioral, and organizational properties that emerge from the unsupervised local interactions of a multitude of elementary units. During this courses we will study the mathematical and computational techniques that have been developed to describe and understand such properties. In doing so we will always discuss the math/algorithmic side in the context of specific examples; We will touch upon a number of important and fascinating sub-areas: linearity and non-linearity, chaos, self-similarity, stochastic processes, self-organization and network theory.

Aims

To provide students with a technical (mathematical, computational) background to describe, model and reason in quantitative terms about Complex Systems.

Evaluation

Students are required to simulate a number of “model-system”. Some (minimal) programming skills are therefore required. Some college-level background in calculus, probability and linear algebra is also required. If these requirements are not met, a preliminary conversation with the instructor is appreciated.

Syllabus

Part 0: The Art of Modeling

• The role of abstraction
  •    Deterministic vs Random
  •    Microscopic vs Macroscopic
  •    Order and Disorder

Part 1.A: Deterministic systems with few degrees of freedom

Continuous dynamical systems
•    Linearization and stability
•    Phase space and qualitative analysis
•    Elements of bifurcation theory
The role of non-linearity
•    Recurrence equations
•    Bifurcation, period doubling – the case of the logistic map
•    Routes to chaos
•    Universality and the renormalization group

Part 1B: Randomness - the basic

• Poisson process
  •    Random walks
  •    Multiplicative processes
  •    Branching processes
  •    Markov processes

Part 2: From microscopic to macroscopic

• From random walk to the diffusion equation
  •    From Langevin to Fokker-Plank equation
  Collective Phenomena
  •    Cellular Automata.
  •    Mean field techniques, their limits and extensions.
  •    Precursor of organization: emergence of long-range interactions in space and time.
  •    Self-Organized Criticality.
  •    The emergence of structure and order.
  •    Information and Entropy.
  •    Beyond Gaussian statistics – power laws, their significance and possible causes.
  Networks
  •    Small-world and scale-free networks.
  •    Generative models.
  •    Processes on “non-uniform” networks (e.g. traffic, epidemics, search, failures).

Readings

1. N. Boccara, Modeling Complex Systems, Springer-Verlag, NY (2004).
   2.    Y. Bar-Yam.Dynamics of Complex Systems. Westview Press, Boulder, CO (2003). 
   3.    D. Sornette, Critical Phenomena in Natural Sciences. Springer-Verlag, Berlin, 2nd ed.(2003)
   4.    S. Boccaletti, V. Latora, Y. Morenod, M. Chavez and D.-U. Hwanga, Complex networks: Structure and dynamics, Physics Report, 424, 175-308 (2006)