Mathematical Biology

Reconstruction of stochastic differential equations characterizing noisy single-cell molecular dynamics In the talk, I shall introduce our recent work on developing machine-learning-based methods for reconstructing noisy single-cell molecular dynamics as stochastic differential equations, which aims to quantify intrinsic fluctuations in the stochastic process characterizing cellular dynamics. I will then discuss how to apply my methods …

Parabolic System of Aggregation Formation in Bacterial Colonies The goal of this talk is to study a fourth-order nonlinear parabolic system with dispersion for describing bacterial aggregation. Analytical solution of traveling wave is found by taking into account the dispersion coefficient. Numerically, we demonstrate that the initial concentration of bacteria in the form of a …

Cancer Detection via Electrical Impedance Tomography and Optimal Control of Elliptic PDEs A new mathematical framework utilizing the theory of Partial Differential Equations(PDE), inverse problems and optimal control of systems with distributed parameters for the detection of the cancerous tumor growth in the human body is developed. The Inverse Electrical Impedance Tomography (EIT) problem on …

Continuous culture models of microbial kinetics In this talk, I will start with a bit of history of mathematical models of microbial kinetics in both batch and continuous cultures, briefly discuss the principle of competitive exclusion, and then concentrate on the models that incorporate the bacterial aggregation in various forms such as the flocculation and …

Insights into oscillatory neural dynamics using a phase-amplitude framework Model reduction techniques can provide useful insight into the dynamics behaviour of high dimensional oscillatory systems such as networks of neurons or neural field models. However, the utility of the classical technique of phase reduction is limited by the assumption that the local dynamics for each …