We propose an entropy-based framework for uncertainty quantification in settings involving multiple, heterogeneous data sources. The central idea is to represent each empirical layer through an entropy-induced probability measure, allowing information to be shared and propagated across layers in a principled and consistent manner. This approach provides a natural mechanism for reconciling...
The challenge of developing predictive models for gene regulatory networks has motivated a multitude of approaches, ranging from the discrete to the continuous, the deterministic to the probabilistic. In many settings, however, available experimental data do not determine a unique model: time series or input-output data typically admit multiple network structures or dynamical rules that are...
In this talk, we examine switching behavior in stochastic reaction networks, where molecular copy numbers fluctuate between multiple distinct states. Such switching occurs when intrinsic noise drives transitions between multiple stable or quasi-stable states, rather than through deterministic oscillations. Stochastic switching has been observed in various biological phenomena, including gene...
Standard recommendations of 7โ9 hours of sleep do not reliably guarantee daytime alertness. Using wearable-derived sleep-wake data, we infer two latent physiological statesโhomeostatic sleep pressure and circadian phaseโvia a mathematical model, and generate personalized sleep-wake schedules aligned with each individual's circadian rhythm. In two prospective clinical trials, adherence to...
I will discuss the use of diffusion models for particle tracking microscopy images. The goal is to have a fully integrated generative model that connects stochastic models of particle motion to microscopy image data. Unfortunately, the observation likelihood function is too complex to explicitly model, and we do not know this function. Learning the likelihood function from a suitably large...
In this talk, I present a computational approach to precision oncology that combines mechanistic modeling with modern machine learning to build predictive digital twins; patient- and subgroup-specific models that forecast tumor progression and response to therapy. Our foundation is quantitative systems pharmacology (QSP) modeling, where tumorโimmune dynamics are represented as systems of...
Pain episodes are a defining feature of sickle cell disease and can lead to reduced quality of life. Statistical analyses by Valrie et al. (2021) examined interactions between physiological (like pain severity and sleep quality) and psychosocial variables (like positive and negative affect) in pediatric sickle cell patients. Clinical datasets can present challenges for continuous dynamical...
Optic glioma, a slow-growing tumor, is associated with Neurofibromatosis type 1 (NF1) mutations and increased midkine (MDK) production. A connection between asthma and optic glioma has previously been observed, but the mechanisms are unclear. To elucidate the role of asthma in the regulation of glioma formation, we investigated the role of T cells and the subsequent pathways in the regulation...
This minisymposium brings together members of the Mathematical Biosciences Institute (MBI) community to highlight the latest mathematical methods, models, and applications inspired by biological questions. The session showcases the breadth of mathematical biology, including stochastic and continuum models of molecular and cellular processes, network dynamics in infectious diseases and...
