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I am an applied mathematician interested in problems arising from biology, physics, computer science and engineering disciplines. To be more specific, I am interesed in limit theorems in probability theory and statistical inference with applications in chemical reaction networks, infectious disease epidemiology, communication networks.
A lot of what I work on has to do with large random graphs (networks). A convenient choice of a random graph is the configuration model, which allows prescribed degrees (the number of connections). You just pair the edges uniformly at random to generate the graph! I like to consider processes that run on the graph (e.g., spread of disease/virus, information) and ponder what would happen when the graph grows bigger and bigger. If I can figure out the limit, I like to use it to do statistical inference. Turns out Dynamic Survival Analysis (DSA) is a cool way to do that! Cool because it allows you to extract probability distributions out of dynamical systems and do parameter inference based on a random sample of observations!
Conctruction of a configuration model random graph.
Sequence of growing configuration model random graphs with a Poisson degree distribution.
Dynamic Survival Analysis allows parameter inference based on a random sample of observations! Check out a Python implementation here.