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Center for Nonlinear Studies |
Part 3: The main goal of this series of talks is to introduce the audience to some current problems of network theory. In the first talk we discuss how these problems arise from practical research. We identify five main topics. Then we will study in detail several notions related to degree sequences, and discuss some classical, fundamental results. In the second talk we will discuss further some existence and listing problems. Then we will introduce sampling problems in connection with degree sequence realizations. After a short survey of samplings based on the configuration model and an importance sampling approach, we will turn to the Markov Chain Monte Carlo (MCMC) method and will discuss some known results and methods. In the last talk we discuss MCMC decompositions in general and a new decomposition technique for degree sequences, then we will apply it to construct degree sequence classes with fast mixing swap-based Markov chain-sampling processes.
Host: Nathan Lemons