# Course syllabus

## Course-PM

TIF150 / FIM780 Information theory for complex systems lp3 VT21 (7.5 hp)

Course is offered by the department of Space, Earth and Environment

### Contact details

- Kristian Lindgren (lecturer, examiner). Email: kristian.lindgren@chalmers.se
- Ankit Vikrant (some lectures, examples classes, projects). Email: ankitv@chalmers.se

### Course overview

The course provides an understanding of fundamental concepts used to describe complex systems, in particular dynamical systems such as chaotic low-dimensional systems, self-organizing systems, and simple spatially extended systems such as cellular automata. Many of the concepts are based in information theory.

- Basic concepts of information theory: Shannon entropy, complexity measures.
- Information theory and statistical mechanics.
- Geometric information theory -- randomness and complexity in spatially extended systems.
- Information flow. The relation between microscopic and macroscopic levels.
- Statistical models, in particular hidden Markov models.
- Cellular automata.
- Applications in nonlinear dynamics, computational biology, chemical self-organizing systems, and statistical mechanics.

### Schedule

Further details are given TIF150 Lecture plan 2021.pdf

### Course literature

**The lectures will follow the presentation in:**

K. Lindgren InformationTheoryOfComplexSystems.pdf

An information perspective on complexity in dynamicla systems, physics and chemistry. (Chalmers, 2014.)

**If you want to learn more:**

T. M. Cover and J. A. Thomas, Elements of information theory (Wiley, 1991).

See also: David MacKay, Information theory, Inference and Learning (2003).

### Problem sessions and solutions

**Preliminary list of problems to be solved**

- 22 January: 2.2, 2.4, 2.6, 2.8, 2.9, 2.16
- 29 January: 3.2, 3.3, 3.5, 3.7, 3.8 (possibly leaving one or two for the next session)
- 12 and 16 February: 4.1, 4.2, 4.4, 4.5, 4.6, 4.7, 4.8, 4.9
- 23 February: 5.1, 5.2, 5.3, 5.4, 5.6, 5.8
- 4 March: 8.1, 8.2, 8.7
- 12 March: solving an old exam (which one to be determined)

### Homework

Five optional homework problems are given below. Each one gives up to two (2) extra points for the exam. Late submissions will normally not be graded. Hand-written solutions are fine, but please take care to make them legible.

**Hand in your solutions in one of these ways:**

- on paper at the lecture
- by email as a PDF file named yourcid.pdf (e.g., rasmuse.pdf) to Ankit (address: ankitv@chalmers.se)

**The deadlines are:**

- Homework 1: Friday 29 January 2021, 13.15
- Homework 2: Friday 12 February 2021, 13.15
- Homework 3: Tuesday 23 February 2021, 15.15
- Homework 4: Thursday 4 March 2021 15.15
- Homework 5: Friday 12 March 2021 15.15

### Projects

Optional project work can be done in groups of 1-3 students. The project work is awarded up to 10 extra points for the exam. Further instructions are given in this file: InformationTheoryProject_2021.pdf

Exam, grading

The exam is given on March 19, 14:00-18:00. Since the exam most likely shall be conducted remotely, the exact details will be shared with the students well in time.

The course is graded based on the exam score including extra points from homework (max 10 points) and projects (max 10 points). The exam gives up to 50p. Grade limits (Chalmers/ECTS): 25p for 3/E, 28p for 3/D, 34p for 4/C, 38p for 4/B, 42p for 5/A. To pass, a minimum of 20p on the written exam is required, regardless of additional points.

### Learning objectives and syllabus

**After successfully completing this course students will be able to:**

- Define and use the basic concepts of information theory: Shannon entropy, relative entropy, complexity measures based on these
- Use information theory to characterise both cellular automata and low-dimensional chaos
- Understand the connection between information theory and statistical mechanics
- Use geometric information theory to characterise patterns in spatially extended systems like pictures
- Explain how information is flowing in chemical self-orginising systems exhibiting pattern formation

Link to the syllabus on Studieportalen (Chalmers).

Link to syllabus Gothenburg University.

### Examination form

The examination will be based on a final written exam, with the possibility of extra points from homework assignments and the optional mini project.