Title: Uncovering potential interventions for pancreatic cancer patients via mathematical modeling

Abstract: While any cancer diagnosis is life-altering, pancreatic cancer is among the most discouraging to receive because of its extreme difficulty to overcome. Recent literature suggests that the surrounding environment of pancreatic cancer cells could play a key role in their therapeutic response. Thus, there is a growing need for the discovery of intervention strategies that can attack these cancer cells and the microenvironment that protects them. To address this problem, we have built a mathematical model to computationally predict patient outcomes and test discovered control targets. Using amenable control approaches, we were able discover novel control targets as well as validate previously known results. Further, we were able to predict a hierarchy of disease aggression based on which mutations were present, in the sense that some combinations may be more difficult to treat or that the patient might see a faster decline. This is a step forward in aiding the development of personalized medicine, as treatment protocols progress in becoming more patient-specific.

Title: Low-rank Structured Data Analysis

Abstract: In modern data analysis, the datasets are often represented by large-scale matrices or tensors (the generalization of matrices to higher dimensions). To have a better understanding of the data, an important step is to construct a low-dimensional/compressed representation of the data that may be better to analyze and interpret in light of a corpus of field-specific information. To implement the goal, a primary tool is the matrix/tensor decomposition. In this talk, I will talk about novel matrix/tensor decompositions, CUR decompositions, which are memory efficient and computationally cheap. Besides, I will also discuss how CUR decompositions are applied to develop efficient algorithms or models to robust decomposition and completions and show the efficiency of the algorithms on some real and synthetic datasets.

Title: Identification of control targets in Boolean networks via computational algebra.

Abstract: Many problems in systems biology have the goal of finding strategies to change an undesirable state of a biological system into another state through an intervention. The identification of such strategies is typically based on a mathematical model such as Boolean networks. In this talk we will see how to find node and edge interventions using computational algebra.

Title: Reliable computation of exterior eigenvalues through matrix functions

Abstract: Exterior eigenvalues of large sparse matrices are needed for

various applications, such as linear stability analysis. These

eigenvalues are difficult to compute efficiently and reliably if they

are much smaller than the dominant eigenvalues in modulus. Traditional

spectral transformations such as Cayley transform are far from reliable.

In this talk, we discuss a simple idea of spectral transformation based

on functions of matrices that maps the desired exterior eigenvalues to

dominant ones. Approximations of the action of matrix functions on

vectors is fundamental for this approach, which can be performed by

rational Krylov subspace methods (RKSM). Numerical experiments for

linear and nonlinear eigenvalue problems demonstrate the reliability of

this method.

Title: Geometry and Statistics: New Developments in Statistics on Manifolds

Abstract: With the increasing prevalence of modern complex data in non-Euclidean (e.g., manifold) forms, there is a growing need for developing models and theory for  inference of  non-Euclidean data. This talk first presents some recent advances in nonparametric inference on manifolds and other non-Euclidean spaces.   The initial focus is on nonparametric inference based on Fréchet means.  In particular, we present omnibus central limit theorems for Fréchet means for inference, which can be applied to general metric spaces including  stratified spaces, greatly expanding the current scope of inference.  A robust framework based on the classical idea of median-of-means is then proposed which yields  estimates with provable robustness and improved concentration. In addition to inferring i.i.d data, we also consider nonparametric regression problems where predictors or responses lie on manifolds. Various simulated or real data examples are considered

Title: A Feedback Control Architecture for Bioelectronic Devices with Applications to Wound Healing 

Abstract:  Bioelectronic devices can provide an interface for feedback control of biological processes in real-time based on sensor information tracking biological response. The main control challenges are guaranteeing system convergence in the presence of saturating inputs into the bioelectronic device and complexities from indirect control of biological systems. In this talk, we first derive a saturated-based robust sliding mode control design for a partially unknown nonlinear system with disturbance. Next, we develop a data informed model of a bioelectronic device for in silico simulations. Our controller is then applied to the model to demonstrate controlled pH of a target area. A modular control architecture is chosen to interface the bioelectronic device and controller with a bistable phenomenological model of wound healing to demonstrate closed-loop biological treatment. External pH is regulated by the bioelectronic device to accelerate wound healing, while avoiding chronic inflammation. 

Title: Evaluation of the United States COVID-19 vaccine allocation strategy

Abstract: Anticipating an initial shortage of vaccines for COVID-19, the Centers for Disease Control (CDC) in the United States developed priority vaccine allocations for specific demographic groups in the population. In this talk, I present our recent study that evaluates the performance of the CDC vaccine allocation strategy with respect to multiple potentially competing vaccination goals (minimizing mortality, cases, infections, and years of life lost (YLL)), under the same framework as the CDC allocation: four priority vaccination groups and population demographics stratified by age, comorbidities, occupation and living condition (congested or non-congested). We developed a compartmental disease model that incorporates key elements of the current pandemic including age-varying susceptibility to infection, age-varying clinical fraction, an active case-count dependent social distancing level, and time-varying infectivity (accounting for the emergence of more infectious virus strains). The CDC allocation strategy is compared to all other possibly optimal allocations that stagger vaccine roll-out in up to four phases (17.5 million strategies). The CDC allocation strategy performed well in all vaccination goals but never optimally.  Under the developed model, the CDC allocation deviated from the optimal allocations by small amounts, with 0.19\% more deaths, 4.0% more cases, 4.07% more infections, and 0.97% higher YLL, than the respective optimal strategies. The CDC decision to not prioritize the vaccination of individuals under the age of 16 was optimal, as was the prioritization of health-care workers and other essential workers over non-essential workers. Finally, a higher prioritization of individuals with comorbidities in all age groups improved outcomes compared to the CDC allocation. The developed approach can be used to inform the design of future mass vaccine rollouts in the United States, or adapted for use by other countries seeking to optimize the effectiveness of their vaccine allocation strategies.

Title: Global-in-time domain decomposition methods for the coupled Stokes and Darcy flows