E2 334, Spring 2019
Topics in Computation over Networks
Lectures
- 03 Jan 2019: Lecture-01 Random Variables and Entropy
- 08 Jan 2019: Lecture-02 Joint Entropy and Mutual Information
- 10 Jan 2019: Lecture-03 Data Processing
- 12 Jan 2019: Lecture-04 Data Compression and Transmission
- 15 Jan 2019: Lecture-05 The Boltzmann Distribution
- 17 Jan 2019: Lecture-06 The Fluctuation-Dissipation Theorem
- 21 Jan 2019: Lecture-07 The Thermodynamic Limit
- 25 Jan 2019: Lecture-08 Ising Model: One-dimensional case
- 29 Jan 2019: Lecture-09 Curie-Weiss Model
- 31 Jan 2019: Lecture-10 Independent random variables
- 05 Feb 2019: Lecture-11 Correlated random variables
- 07 Feb 2019: Lecture-12 The Gartner-Ellis theorem
- 12 Feb 2019: Lecture-13 The Monte Carlo method
- 14 Feb 2019: Lecture-14 Total variation distance
- 19 Feb 2019: Lecture-15 Distance from stationarity
- 21 Feb 2019: Lecture-16 Mixing times
Homework
Grading Policy
Scribe : 50
Project: 50
Course Syllabus
Content will be a subset of the following topics:
- Statistical physics:
- Boltzmann distributions, Thermodynamic potentials and limit, Ferromagnets and Ising models
- Probability:
- Stochastic ordering, large deviations, Gibbs free energy, Monte Carlo method, simulated annealing
- Independence:
- Random energy model, random code ensemble, number partitioning, replica theory
- Graph models:
- Random factor graphs, Random K-SAT, LDPC codes
- Phase transitions:
- Erdos Renyi random graph
- Short-range correlations:
- Belief propagation, Ising models on random graphs
- Long range correlations:
- Cavity method
Course Description
A large number of local microscopic interactions can lead to many interesting macroscopic physical phenomena.
These effects have been observed in physical systems, and statistical physics presents models that can describe such effects.
In this course, we will learn the techniques from statistical physics to describe complex network behaviors.
Prerequisite
First graduate course in probability from any engineering or math department.
Familiarity with information and coding theory is desired, though not necessary to attend the course.
GitHub/Slack Information
Slack
Students can signup for course slack using their iisc.ac.in email at Slack signup.
Add yourself to #statphy-2019.
GitHub
All the students in the class have read/write access to Stastistical-Physics public repository on GitHub.
Please follow the guidelines in the sample lecture.
The source file for the sample lecture is in the repository.
It is recommended you save it with another name in your local repository for creating a new lecture.
A good book for Git is here and a simple tutorial here.
Instructor
Parimal Parag
Office: EC 2.17
Hours: By appointment.
Time and Location
Classroom: EC 1.07, Main ECE Building
Hours: Tue/Thu 08:30-10:00am.
References
- Factor Graphs and the Sum-Product Algorithm, Frank Kschischang, Brendan J. Frey, Hans-Andrea Leliger. IEEE Transactions on Information Theory. Vol. 47, no. 2, 2001.
- The Generalized Distributive Law, S.M. Aji, R.J. McEliece. IEEE Transactions on Information Theory. Vol. 46, no. 2, pp. 325–343, 2000.
Textbooks
- Information, Physics, and Computation, Mezard, Montanari, 2009.
- Random graphs and complex networks, Remco van der Hofstad, 2018.