Course: An introduction to manifold learning and to asymmetric simple exclusion process (Khanh Dao Duc, Nathanael Hoze)

The emergence of high dimensional biological data from sequencing or imaging techniques requires methods for visualization and reconstruction. We shall introduce most widely used approaches in manifold learning (LLE, t-SNE, Isomap) and, in the context of the workshop and biological applications, focus more on diffusion maps and their application in single cell data and cryo EM.

Asymmetric Simple Exclusion Processes (ASEP) form a classical family of stochastic models for transport phenomena in a non-equilibrium particle system. Although they have been widely studied for the past thirty years, they are still of large interest, notably for their relationship to the KPZ universality class. Interestingly, they have also been used to model several processes in biology related to transport and gene expression, and recent methods in imaging and sequencing have led to new applications and methods to analyze the ASEP. To understand these advances, the introductory course on the ASEP will cover classical analytical methods from probability, statistical physics, PDE and combinatory (Bethe and matrix Ansatz, mean field approaches, hydrodynamic limit, analysis of phase diagram...).