6 EC
Semester 2, period 5
5284THCS6Y
The course introduces students to the theory of complex systems with a main focus on critical phenomena. We will discuss the following topics: from microscopic to macroscopic description of complex systems, emergence, phase transitions, critical phenomena, universality, scale invariance, mean-field theory, renormalisation, and self-organized criticality. The course will focus mainly on equilibrium phase transitions, but will also touch upon phase transitions in dynamical systems.
We will work with simple models of complex systems, such as percolation and epidemic models, the Ising model, the linear voter model, Metropolis and Glauber dynamics, the TASEP model (a simple traffic model), the sandpile model, simple models of collective behavior, etc. Numerical simulations of the studied models will be briefly discussed in class, but not implemented. The course will be illustrated with examples of complex systems taken from various fields of science (e.g., physics, neuroscience, social sciences, animal collective behavior, earth science). Contemporary research directions will be explored through the review of recent papers, as well as with a few invited guest lecturers throughout the course.
The course and the assignments will be mainly theoretical (problems with analytical answers, open answers). Assignments can involve implementing simple numerical simulations. For this reason, it is recommended to have basic programming skills prior to taking this class.
Website Complexity Explorables, which as a large collection of interactive simulations of complex systems.
The course material (slides, tutorials, assignments, and references) will be published every week on Canvas, in the "module" section of the course.
Lectures will give you general concepts and tools. During practical sessions, exercises will help you practices the mathematical tools see in class, and help you .
Activity | Hours | |
Hoorcollege | 28 | |
Werkcollege | 28 | |
Self study | 112 | |
Total | 168 | (6 EC x 28 uur) |
This programme does not have requirements concerning attendance (Ter part B).
| Item and weight | Details |
|
Final grade | |
|
0.15 (15%) Final Quiz grade | |
|
0.25 (25%) Homework H1 | |
|
0.6 (60%) Final Exam | NAP if missing |
Assessment: 1 homework assignment; 1 group project; 3 regular quizzes; 1 final exam.
Quizzes: There will be 3 quizzes spread out over the 7 weeks. Only your two best scores will be taken into account for your final quiz grade. This grade will count for 15% of your final grade.
Homework assignment and group project: There will be one homework assignment during the first part of the course, and one group project during the second part of the course. The result from these two assignments will count for 25% of your final grade.
Final exam: there will be a final written exam, which will count for 60% of your final grade.
Note: The quizzes will regularly assess your general understanding of the concepts seen during the lectures and the tutorials, while the homework and the final exam will assess your understanding of the technical and mathematical tools seen in class. Finally, the group project aim at pushing you to use/apply these tools and concepts to analyze a research paper on complex systems not studied in class.
Quizzes: There will be a quiz every two weeks about the content of the course of the last two weeks (+ two questions taken from the previous quiz). The three quizzes will take place on canvas. You will have directly access to your grade just after you have taken the quiz. There will be a few minutes in class to reflect back on the quiz just after the quiz has been taken place.
Homework assignment: You will be asked to submit your homework assignment on canvas, and will receive your grade directly on canvas. Please feel free to then check your result and ask us in class if you have any questions about your grading.
Final Exam: There will be a general announcement on canvas once the grade from your final exam is available (about a week after the exam), with a time and location on campus for you to come and consult the copy of your exam and ask any questions you may have regarding your final grade. Please don't hesitate to contact me if the time happens not to work for you due to overlap with another course.
Quizzes: will be taken individually in class directly on canvas. You will have to log in with your own student account on canvas. You will need to bring in your own laptop or tablet to take the quiz. Each quiz takes less than 15min, and the result will be directly available afterwards. Quizzes are graded.
Homework assignment: The homework assignment will take place over the first part of the course. The exact deadline of the assignment will be discussed in class. Your assignment must be submitted on canvas before the decided deadline. You can work through the solutions of the homework in group. However you will have to hand in your own written solutions to the homework, and we ask you to write these solutions on your own. Writing the answers of the homework on your own will help you prepare for the final exam. This homework is graded.
Final exam: will take place during week 8 and will be individual. It is a written exam. More details will be provided during the two weeks preceding the exam.
Tutorial exercises: Each module will have its own set of exercises, which will not be graded. Exercises will be discussed in class during tutorials. Students are expected to finish the exercises at home (we advise you to work in group). Written corrections for each set of exercises will be provided once all the exercises of the module have been discussed in class. Students are encouraged to check their answers to the exercises, and to discuss them in group, or in class if there is anything they haven't understood in the correction. Working through these exercises is a very good preparation for the final exam.
The 'Regulations governing fraud and plagiarism for UvA students' applies to this course. This will be monitored carefully. Upon suspicion of fraud or plagiarism the Examinations Board of the programme will be informed. For the 'Regulations governing fraud and plagiarism for UvA students' see: www.student.uva.nl
| Modules | Subject, Lectures | Examples, Tools and applications |
| 0 | Introduction to the theory of complex systems | The basic: Markov Processes and Poisson processes, application to the TASEP model |
| 1 | Emergent phenomena | Ex. Brownian motion & Lévy flights. Tools: studying Discrete and Continuous time Markov chain. Application to Random walks |
| 2 | Phase transition and critical phenomena | Practicing Markov chain with the Metropolis algorithm. Tools: Master equation, Detailed Balance. |
| 3 | From micro to macro: theory and examples | Example of the Ising model |
| 4 | Universality | Example of Percolation problem, epidemic models |
| 5 | The mean-field approximation and Landau theory | Application to the Ising model, the TASEP |
| 6 | Out-of-equilibrium phase transition | Application to the voter model |
| 7 | Scaling invariance and renormalisation | Application to data from... |
| 8 | Examples of complex systems: self-organized criticality and collective behavior | Vicsek model, Kuramoto model, |
| 8 | Exam |
If you have any questions, you can contact me or the TA, preferably through Canvas' messaging system.