Seminar: Wasiur KhudaBukhsh - Multi-Scale Dynamics of Stochastic Biological Systems Through the Lens of Survival Dynamical Systems (SDS)

Wasiur KhudaBukhsh (October 29, 2019)

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Abstract

Stochastic methods are becoming increasingly popular in biological sciences because of their ability to account for intrinsic fluctuations and uncertainty in occurrences or (experimental) outcomes. In this talk, we shall particularly focus on stochastic methods to analyse the multi-scale aspect of many biological systems. We use the term “scale” in a broad sense. It could refer to the size of the population, the abundance/volume, the time scale, the granularity or the amount of aggregation in the data collection procedure etc. We shall consider several examples from epidemiology, biochemical reaction networks to illustrate this multi-scale feature.

Given a biological system that operates over multiple scales, it is often not clear how to describe the dynamics in one scale in terms of that in another scale. Survival Dynamical System (SDS) is a way to bridge this apparent gap. An SDS, derived from the macro-scale dynamics, describes probability distributions (via survival functions) of individual trajectories at a micro scale. This SDS interpretation not only intertwines multiple scales but also allows us to employ tools from survival analysis to address various issues with data collection and statistical inference. In particular, this approach yields a new statistical inference method, which is computationally advantageous.