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 …
Mathematical modeling of CD8 T cell search for malaria infection in the liver Malaria, a disease caused by parasites of the Plasmodium genus, begins when Plasmodium-infected mosquitoes inject malaria sporozoites while searching for blood. Sporozoites migrate from the skin via blood to the liver, infect hepatocytes, and form liver stages. In mice, sufficient numbers of …
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 …
Bistability between acute and chronic states in a Model of Hepatitis B Virus Dynamics Understanding the mechanisms responsible for different clinical outcomes following hepatitis B infection requires a systems investigation of dynamical interactions between the virus and the immune system. To help elucidate mechanisms of protection and those responsible from transition from acute to chronic …
Could malaria mosquitoes be controlled by periodic release of transgenic mosquitocidal Metarhizium pingshaense? A mathematical modeling approach Malaria remains one of the world's deadliest vector-borne diseases, with WHO reporting 249 million cases and 608,000 deaths across 85 countries in 2022 alone. Widespread insecticide-based interventions have significantly reduced malaria burden, but these gains are now threatened by …
Extreme first passage times for populations of identical rare events A collection of identical and independent rare event first passage times is considered. The problem of finding the fastest out of N such events to occur is called an extreme first passage time. The rare event times are singular and limit to infinity as a …
A connubio of Machine Learning and PDEs for Scientific Discovery in the Biological Sciences In this talk, I will describe some problems at the intersection of data science and applied mathematics with particular focus on questions emerging in the study of the neuro-musculo-skeletal-environmental system. Many aspects of this system can be studied with (potentially different) …
Are differences between Parkinson’s patients and healthy subjects like other brain diseases? The dynamical state of cortical neural activity constrains the complexity of functions it can perform. A marginally stable dynamical state - called criticality - is thought to be beneficial for brain functions that require multiple time scales, broad dynamic range, and large information …
Bistable Dynamics of Perceiving Ambiguous Stimuli When experiencing an ambiguous sensory stimulus (e.g., the vase-faces image), subjects may report random alternations (time scale, seconds) between the possible interpretations. I will describe dynamical models with multiple time scales for neuronal populations that compete (fast time scale) through mutual inhibition for dominance - showing alternations (slow time …