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 …
Modeling insights into subcellular cytoskeleton organization with external size changes Actin is one of the most abundant proteins in eukaryotic cells and a fundamental component of the cytoskeleton, playing a critical role in maintaining cell structure and enabling motility. A compelling preliminary experimental observation underpins our work: in micropatterned epithelial cells of increasing sizes, the …
Mathematical modelling of malaria: Population-scale dynamics, vaccination, and evolution Malaria transmission and persistence depend critically on the interaction between parasite dynamics, human immunity, and epidemiological feedbacks. I will review recent work with collaborators developing and analysing structured PDE models spanning both population and within-host scales. At the population level, we couple vector–host epidemiology with the …
Mechanistic Insights Into Parkinson’s Disease and Sex Differences in Liver Oxidative Stress In volume transmission, or neuromodulation, neurons communicate not through direct, one-to-one synaptic connections, but by releasing neurotransmitters broadly into the extracellular space from numerous varicosities. This type of signaling is particularly relevant for serotonin and dopamine neurons, which project from the dorsal raphe …
Engineering ovarian cancer solutions using evolutionary medicine, math modeling, and big data Ovarian cancer is the most lethal gynecologic cancer despite the progress we’ve made in personalized medicine; there has only been modest survival gains for ovarian cancer patients with over 80% of patients experiencing recurrent disease. Furthermore, many current clinical trials often fail to …
Adaptive Dynamics on High-Dimensional Optimization Random Landscapes What do spin glasses (a subfield of high-dimensional probability and statistical physics), evolutionary biology, and artificial intelligence (AI) have in common? All involve optimization on rugged landscapes where metastable states pose significant challenges to the search for optima. In this talk, I will discuss an example of such …
Do higher-order interactions promote coexistence in diverse ecological communities? From the human microbiome to the Amazon rainforest, diverse ecological communities are widespread in the natural world, but we do not know how this diversity is maintained by the interactions between species. A central assumption in most ecological models is that the interactions in a community …
Network Architecture Dictates Dynamics: Operating Principles of Interconnected Feedback Loops in Cell Fate Transitions Interconnected feedback loops are prevalent in cell fate transitions, yet their operating principles remain largely unexplored. In this talk, we will examine high-dimensional feedback loops (HDFLs) organized into serial, hub, and cyclic network architectures. We will see that network architecture dictates …