Complex Networked Systems – Group Discussions

Upcoming Topics

  • Non-Convex Optimization

  • Large Deviations

  • Heavy-Traffic Analysis

Ongoing Topic

  • Game Theory

Past Topics

  • Advanced Optimization Theory and Methods

    • Nesterov's “Introductory lectures on convex optimization”
      Sep 29:

      • Reading: Prof. Eryilmaz's lecture notes: Lecture 16,17,18.

      • Reading: Nesterov - Section 1.2.3, Section 1.3.1

      • Exercise: Prove theorem B1, B2 from Lecture 17, Page 3.

      • Exercise: Prove the implications of strong convexity in Lecture 18, Page 1.

    • “Gradient-Based Algorithms with Applications to Signal Recovery Problems” by Beck and Teboulle

  • Reversibility
    Resource: Frank Kelly's book on Reversibility

  • Mixing Time of Markov Chains Resources:

I did a little experiment on the first example we discussed today (n binary bits, doing nothing with prob p, and flip a uniformly selected bit with prob 1-p) in MATLAB. I calculated theoretically the total variation distance starting from one state when n=10, and plotted in the above figure. Agreeing with our intuition, the mixing time for larger p (i.e., larger prob of doing nothing) is longer.