Two Seminars on Wed, Sept 11:10am --12noon

Center for Mathematical Sciences, Room 813

Title: Intracellular transport in fungi: insight from mathematical modelling

Speaker:Congping Lin (University of Exeter, UK)

Abstract: Intracellular transport is a fundamental process for cellular function and survival, and regulates the spatial distribution of vesicles. An important type of motion inside living cells is directed transport, which is usually generated by the action of molecular motors, converting the chemical free energy of ATP (adenosine triphosphate) into kinetic energy along cytoskeletal filaments. Using live cell imaging data of the phytopathogenic fungus Ustilago maydis enables us to develop accurate quantitatively-valid models for motor and organelle transport. In this talk, I will talk about our study on modelling the long-distance bidirectional transport of dynein motors and their cargos in the Ustilago hyphal cell. For instance, for the dynein motor transport, concerning the volume exclusion in the interaction between motors, we employed an interacting random walk model - the asymmetric simple exclusion process (ASEP). This modelling revealed a new insight in the mechanism controling the accumulation of dynein motors near the hyphal toip, that is the combination of stochastic motor activity and deterministic capture and release. With this success, we are able to develop a comprehensive and predictable model for the cargo transport by incorporating complicated cytoskeleton network, and to address a number of (biological) questions on the transport in the entire fungal cell.

Title: Ergodic optimization of prevalent super-continuous functions

Speaker:Yiwei Zhang (Pontifical Catholic University of Chile, Chile)

Abstract: Ergodic optimization is the process of finding invariant probability measures that maximizes the integrals of a given function. This topic is naturally motivated by the studies in controlling chaos and bifurcation to riddled basins of chaotic attraction. In this talk, we will particularly concentrate on the long-standing periodic optimization problem in this area. To be more precise, given a dynamical system, we say that a performance function has property P if its time averages along orbits are maximized at a periodic orbit. It is conjectured by several authors that for sufficiently hyperbolic dynamical systems, property P should be typical among sufficiently regular performance functions. In contrast to the literatures by considering typicality in the topological sense, we first address this problem using a probabilistic notion of typicality that is suitable to infinite dimension: the concept of

prevalence as introduced by Hunt, Sauer, and Yorke. For the one-sided shift on two symbols, we prove that property P is prevalent in spaces of functions with a strong modulus of regularity. Our proof uses Haar wavelets to approximate the ergodic optimization problem by a finite-dimensional one, which can be conveniently restated as a maximum cycle mean

problem (a fundamental problem in combinatorial optimization) on a de Bruijin graph.