Speaker: Dr. Peter Kim (Sydney). Link: http://www.maths.usyd.edu.au/u/pkim/ Time: Friday, Oct. 28, 2--3PM, 2011 Room: RC-4082, East Wing of the Red Centre Building, UNSW Lunch: meet around 12:30 for lunch by the fig tree outside East Wing of the Red Centre Building ------------------------------------------------------- Title: Bridging Agent-Based Models and PDEs: a Model of Cell Differentiation Abstract: different modelling frameworks have been applied to cell differentiation, including partial differential equations (PDEs) and agent-based models (ABMs). ABMs simulate individual cell behaviour, while PDEs model spatial dynamics at a population level. Also, ABMs directly capture randomness and variability, but PDEs are faster to evaluate numerically and more conducive to mathematical analysis. Because of the advantages of each modeling strategy, it is valuable to form bridges between them. To begin building this connection, we present an ABM of blood cell differentiation proposed by Roeder et al. (Nat Med 2006) and formulate a PDE model that reproduces the behavior of the ABM. We then show how to obtain the PDE model by translating the ABM to a system of difference equations that suggests a numerical scheme for a PDE system. We discuss how this approach of introducing an intermediate system of difference equations could provide a method for constructing analogous PDE systems from other ABMs. ------------------------------------------------------- One choice of commuting from Sydney: meet at Carslaw 620 around 12 and we share taxi to UNSW. The round trip is covered by department colloquium fund.