Dynamic networks and stochastic approximation: the fundamental role of mathematics
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Abstract
Models for networks that evolve and change over time are ubiquitous in a host of domains including modeling social networks, understanding the evolution of systems in proteomics, the study of the growth and spread of epidemics etc. While there has been tremendous advancement in the empirical exploration of these systems and the corresponding models for such systems, the goal of this talk is, through three different stories describe the importance of math in understanding the emergence of phenomenon in such systems.(i) Understanding the effect and detectability of change point in the evolution of the system dynamics. (ii) The disparity in the behavior of different centrality measures such as degree and page rank centrality for measuring popularity in settings where there are vertices of different types such as majorities and minorities as well as insight analyzing such problems give for at first sight unrelated issues such as sampling rare groups within the network. (iii) Understanding the effect of delay when new individuals entering the system only have a snapshot of the network at an earlier time point to make decisions on whom to connect. The main goal will to be convey unexpected findings in each of these three areas.
Prof. Shankar is a Professor in the Department of Statistics and Operations Research. He joined the department in July 2009 after completing a postdoc in the Mathematics Department, at the University of British Columbia, Vancouver. He did his Ph.D. in 2008 at the Department of Statistics, University of California, Berkeley under Professor David Aldous. He worked on stochastic processes, random networks including dynamics on network models and random graphs. He is interested in problems that have originated from some applied branch of science, to which probability can say something fruitful and non-trivial. He tries to find unifying mathematical principles which can be used to solve a variety of problems.