Graduate Students Seminar

Speaker 1: Naghmeh Akhavan

Title

Multi-Phase-Field Modeling of Cell Migration

Abstract

The architecture of the Drosophila egg chamber plays a pivotal role in the migration of clustered cells. Within this microenvironment, the extracellular space poses geometric constraints, influencing the distribution of the chemoattractant concentration that is secreted by the oocyte. In our research, we are developing a model for clustered cell migration based on multi-phase-field modeling. This new nonlinear partial differential equations model framework takes into account the complexities of the multi-cellular system, incorporating factors such as cell-cell adhesion, cell-cell repulsion, and cell volume. Significantly, our approach allows the utilization of a single phase variable as well as allows us to efficiently represent the position of the cluster within the egg chamber.  Unlike more agent-based models, our phase-field approach offers a distinctive perspective. It provides a continuous and mathematically elegant representation of cell movements, granting us a different perspective on the mechanisms steering clustered cell migration. In this talk, we will discuss the model components and show some early results.

Speaker 2: Mouhamed Oloude

Title

Modelling Bivariate Survival Data using the Clayton Copula Function

Abstract

Analysis of time-to-event data arises in various fields, such as medical research, engineering, economics and public health. Examples of such events include time to disease progression or death, time to failure of a machine,  and time to re-occurrence of a particular disease. The statistical methodology requires special attention as not all individuals will experience the event during the period of study. In case of univariate time variables, several methods have been developed to provide estimates of the survival function.  Cases of multivariate survival times are of interest. The modeling of multivariate survival times using copula functions, with emphasis on the Clayton model will be addressed.