Information theory for complex systems

Elective in master programs

SEE Chalmers

Bachelor degree, including 30 credits mathematics, plus programming

The course introduces the students to important concepts in information theory that can be used to describe and characterise complex systems. The concepts are applied to a number of areas in complex systems: cellular automata, fractals, chemical self-organisation, and chaos. The main aim is to give students the knowledge and skills to apply information theory to a wide variety of different systems. The course also gives a presentation of the connections between information theory and physics, primarily statistical mechanics and thermodynamics.

Basic concepts of information theory
- Shannon entropy, relative information, complexity measures
Information theory for symbol sequences and lattice systems
- correlations and randomness in symbol sequences
Information theory and physics
- entropy in physics and its relation to randomness in information theory
Cellular automata
- order and disorder in the time evolution of various cellular automaton rules
Geometric information theory
- presentation of an information-theoretic framework for characterising patterns
Self-organising chemical systems
- flows of information in the process of pattern formation
Chaotic systems and information
- flows of information from micro to macro in chaotic systems

After successfully completing this course the 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 spatically extended systems like pictures
Explain how information is flowing in chemical self-organising systems exhibiting pattern formation

The course is based on a series of lectures, in total 30 hours, covering the topics listed above. Every week a set of home assignments are distributed. An optional mini project can also be done.

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

If a student who has been failed twice for the same examination element wishes to change examiner before the next examination session, such a request is to be granted unless there are specific reasons to the contrary (Chapter 6 Section 22 HF).

If a student has received a certificate of disability study support from the University of Gothenburg with a recommendation of adapted examination and/or adapted forms of assessment, an examiner may decide, if this is consistent with the course’s intended learning outcomes and provided that no unreasonable resources would be needed, to grant the student adapted examination and/or adapted forms of assessment.

If a course has been discontinued or undergone major changes, the student must be offered at least two examination sessions in addition to ordinary examination sessions. These sessions are to be spread over a period of at least one year but no more than two years after the course has been discontinued/changed. The same applies to placement and internship (VFU) except that this is restricted to only one further examination session.

If a student has been notified that they fulfil the requirements for being a student at Riksidrottsuniversitetet (RIU student), to combine elite sports activities with studies, the examiner is entitled to decide on adaptation of examinations if this is done in accordance with the Local rules regarding RIU students at the University of Gothenburg.

The results of and possible changes to the course will be shared with students who participated in the evaluation and students who are starting the course.