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Section: Research Program

Inverse problems

When studying biological populations (usually cells or big molecules) using PDE models, identification of the functions and parameters that govern the dynamics of a model may be achieved to a certain extent by statistics performed on individuals to reconstruct the probability distribution of their relevant characteristics in the population they constitute, but quantitative observations at the individual level (e.g., fluorescence in single cells  [60] or size/age tracking  [87]) require sophisticated techniques and are most often difficult to obtain. Relying on the accuracy of a PDE model to describe the population dynamics, inverse problem methods offer a tractable alternative in model identification, and they are presently an active theme of research in MAMBA. Following previous studies  [68], [69], some combining statistical and deterministic approaches  [67] with application to raw experimental data  [66], we plan to develop our methods to new structured-population models (or stochastic fragmentation processes as in  [66]), useful for other types of data or populations (e.g. size/age tracking, polymer length distribution, fluorescence in single cells).