Complex Systems

Recommended Prerequisites

Introduction to Artificial intelligence, Calculus, Linear Algebra, Programming.

Teaching Methods

Lectures: theories and methods used in heuristic problem solving. Students solve in practical classes computer problems of medium complexity and by means of simulations using particular frameworks. This is a group work done under the supervision of the professor. Written synthesis of a recent research work, experimental work involving computer simulations, done individually and includes a written report and an oral presentation.

Learning Outcomes

This course aims to study complex systems, whether physical, biological, cognitive, or social. We will focus on the essential concepts, models, and tools for understanding these systems. We begin with a theoretical discussion on concepts such as system, complexity, self-organization, emergence, information, computation, and evolution. Next, we address model classes for analyzing complex systems, including Dynamical Systems, Network Science, and Agent-Based Modeling, concluding with practical case studies. By the end, students should be able to (1) understand and analyze the dynamics of complex systems, (2) apply appropriate modeling approaches, (3) create and test models, and (4) select suitable tools for analyzing and deriving insights from these systems.

Work Placement(s)

No

Syllabus

1. Concepts (system, complex system, complex adaptive system, dynamic system, complexity and diversity, information, computation, evolution and models).

2. Dynamical Systems

2.1- Concepts

2.2- Discrete Systems

2.3- Continuous Systems

2.4- Chaos and Fractals

3. Network Science

3.1- Graphs and Networks

3.2- Topologic Aspects and Dynamics of Networks

3.3- Random Graphs

3.4- Graph Neural Networks

3.5- Applications

4. Agent-Based Modeling

4.1- Motivations and Concepts

4.2- Components of an AMB: agents, environments, interactions

4.3- Design of an AMB

4.4- Analysis and Validation of an AMB

4.5- Cellular Automata

5. Case Studies: comparative study.

Head Lecturer(s)

Tiago Rodrigues Baptista

Assessment Methods

Assessment
Synthesis work: 10.0%
Project: 30.0%
Exam: 60.0%

Bibliography

1. Hiroki Sayama, Introduction to the modeling and analysis of complex systems, Binghamton University, SUNNY, 2015.

2. Steven Strogatz, Nonlinear Dynamics and chaos, Perseus Books Publishing, 1994.

3. Frank Giordano, William Fox, Steven Horton, A First course in Mathematical Modeling ( 5th Edition), Brooks/Cole, 2014.

4. Uri Wilenski and William Rand, An introduction to agent-based modeling, MIT Press, 2015.

5. Filippo Menczer, Santo Fortunato, Clayton A. Davis, A first course in network science, Cambridge University Press, 2020.

6. Albert-Laszlo Barabasi, Network Science, Cambridge University Press, 2016.

7. Guido Caldarelli, Alessandro Chessa, Data Science and Complex Networks, Oxford University Press, 2018.

8. David Feldman, Chaos and Dynamical  Systems, Princeto University Press, 2019.

9. Lingfei Wu, Peng Cui, Jian Pei, Liang Zhao , Introduction to the modeling and analysis of complex system,, Springer, 2022.