A multi-scale approach for modeling cell dynamics The characterization of biological phenomena related to cell evolution and their interactions with the microenvironment often involves processes occurring across a range of spatial and temporal scales. As a result, mathematical models designed to describe cell dynamics must capture this inherent multi-scale complexity. In this seminar, we introduce …
How cells stay together; a mechanism for maintenance of a robust cluster explored by local and nonlocal continuum models Formation of organs and specialized tissues in embryonic development requires migration of cells to specific targets. In some instances, such cells migrate as a robust cluster. We here explore a recent local approximation of nonlocal continuum …
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 …
