Networks out of control
Welcome to the Master-level course Networks Out of Control (informally a.k.a. Models and Methods for Random Networks).
The goal of this class is to acquire mathematical tools and engineering insight about networks whose structure is random.
Many communication networks, such as the global Internet and its multiple interconnected autonomous domains, mobile ad hoc and embedded sensor networks, social networks, and peer-to-peer overlay networks, usually evade detailed engineering and exhaustive measurement to rely instead on principles of self-organization. This new world of massive scale, lack of central control, and randomness requires new theoretical tools to reason about networks and their behavior, as well as new approaches to engineer for and measure aggregate properties. Most of these tools are borrowed from other fields, such as random graph theory, statistical physics, nonlinear dynamical systems, random algorithms, developmental biology, and game theory.
This course will bring together elements of these theories and their application to "large-scale, self-organized or uncontrolled" networks. It will provide an introduction to and perspective on this emerging field, and an opportunity to track and discuss new developments. The course will balance mathematical rigor with practical lessons for engineering.
Projects, homework, exam
- The course will have a set of homework sets (one every two weeks); you may discuss the homework problems with other students but may not use online resources and must write up your solutions on your own.
- A term paper will be due at the end of the course in May. The project develops one topic of the course you are most interested in. The topic can be one proposed by you or by us. It can be more theoretically or more practically oriented. A short report has to be handed in, and a presentation in front of the class is done at the end of the semester. The report has to be turned in one weee presentation, and is maximum 4 pages (double column) long. We suggest to write the report in Latex with this template. If you want to use another text editor, try to use a template whose output is the closer possible to that of the given template.
- The final exam takes place on Monday 27.06.2016 from 08h15 until 11h15 (Room INJ218). The exam is open book, but only the official class notes and your own personal notes are allowed. In particular, no textbook, no article nor any other document are allowed. No homework or former exam, nor their solutions, are allowed. No computing device of any kind is allowed. You will be asked questions to show your level of understanding of the concepts and material covered in class, as well as exercises similar but different from those given as homework.
- Grade: 10% homework (between 4 and 6) + 40% term paper (project) + 50% final exam.
- The homeworks are individual, you may discuss some problems and approaches with your fellow students, but must complete the solutions for all problems by yourself.
Support documentsClass notes (See under weekly schedule)
- B. Bollobas, Random Graphs (2nd edition), Cambridge University Press, 2001.
- D. Easley, J. Kleinberg. Networks, Crowds, and Markets: Reasoning About a Highly Connected World, Cambridge University Press, 2010.
- R. Durrett, Random Graph Dynamics, Cambridge University Press, 2006.
- M. Jackson, Social and Economic Networks, Princeton University Press, 2008.
- G. Grimmett, Percolation (2nd edition), Springer, 1999.
- A. D. Barbour, L. Holst and S. Janson, Poisson Approximation, Oxford Science Publications, 1992.
- S. Janson, T. Luczak, A. Rucinski, Random Graphs, Wiley, 2000.
- R. Meester and R. Roy, Continuum Percolation, Cambridge University Press, 1996.