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

Abstract: In many engineering and biological applications (e.g., groundwater flow problems, flows in vuggy porous media, industrial filtrations, biofluid-organ interaction and cardiovascular flows), the Stokes-Darcy system is used to model the interaction of fluid flow with porous media flow, where the Stokes equations represent an incompressible fluid, and the Darcy equations represent a flow through a porous medium. The time scales in the Stokes and Darcy regions could be largely different, thus it is inefficient to use the same time step throughout the entire spatial domain.

In this talk, we present decoupling iterative algorithms based on domain decomposition for the time-dependent Stokes-Darcy model, in which different time step sizes can be used in the flow region and in the porous medium. The coupled system is formulated as a space-time interface problem based on either physical interface conditions or equivalent Robin-Robin interface conditions. Such an interface problem is solved iteratively by a Krylov subspace method (e.g., GMRES) which involves at each iteration parallel solution of time-dependent Stokes and Darcy problems. Consequently, local discretizations in both space and time can be used to efficiently handle multiphysics systems with discontinuous parameters. Numerical experiments with nonconforming time grids are considered to illustrate the performance of the proposed methods.

Title: A New Block Preconditioner for Implicit Runge-Kutta Methods for Parabolic PDE Problems

Abstract: Explicit time integrators for parabolic PDE are subject to a restrictive timestep limit, so A-stable integrators are essential. It is well known that although there are no A-stable explicit linear multistep methods and implicit multistep methods cannot be A-stable beyond order two, there exist A-stable and L-stable implicit Runge-Kutta (IRK) methods at all orders. IRK methods offer an appealing combination of stability and high order; however, these methods are not widely used for PDE because they lead to large, strongly coupled linear systems. An s-stage IRK system has s-times as many degrees of freedom as the systems resulting from backward Euler or implicit trapezoidal rule discretization applied to the same equation set. In this talk, I will introduce a new block preconditioner for IRK methods, based on a block LDU factorization with algebraic multigrid subsolves for scalability. I will demonstrate the effectiveness of this preconditioner on two test problems, a 2-D heat equation and a model advection-difusion problem. I compare this preconditioner in condition number and eigenvalue distribution, and in numerical experiments with other preconditioners currently in the literature. Experiments are run using IRK methods with two to seven stages. We find that the new preconditioner outperforms the others, with the improvement becoming more pronounced as spatial discretization is refined and as temporal order is increased.

Title: Data-driven hierarchical kernel matrix methods

Abstract: The explosion of datasets from diverse applications and the increasing computational power of computer hardware call for the need of scalable algorithms and software. In this talk, I will focus on the computational bottlenecks associated with fully populated kernel matrices that are ubiquitous in machine learning as well as scientific simulations. Those dense matrices usually induce large computation costs that scale quadratically or cubically with problem size. The complexity can be significantly reduced by exploiting the hierarchical rank structure inside the kernel matrices. Representing a kernel matrix in an appropriate hierarchical format enables (nearly) optimal storage and computations. I will demonstrate the newly developed data-driven techniques for hierarchical representations and compare their performance with state-of-the-art methods/software on several real-world applications.

Title: Modeling and topological methods to better understand pattern formation in fish

Abstract: Many natural and social phenomena involve individual agents coming together to create group dynamics, whether the agents are drivers in a traffic jam, voters in an election, or locusts in a swarm. Self-organization also occurs at much smaller scales in biology, though, and here I will focus on elucidating how brightly colored cells interact to form skin patterns in zebrafish. Wild-type zebrafish are named for their dark and light stripes, but mutant zebrafish feature variable skin patterns, including spots and labyrinth curves. All these patterns form as the fish grow due to the interactions of tens of thousands of pigment cells. This leads to the question: how do cell interactions change to create mutant patterns? The longterm motivation for my work is to help shed light on this question and better link genes, cell behavior, and visible animal characteristics. Toward this goal, we combine different modeling approaches (including agent-based and continuum) to simulate pattern formation and make experimentally testable predictions. In this talk, I will overview our models and highlight how topological data analysis can be used to quantitatively describe self-organization in silico and in vivo.

Title: A Self-consistent-field Iteration for Orthogonal Canonical Correlation Analysis
Abstract: We propose an efficient algorithm for solving orthogonal canonical correlation analysis (OCCA) in the form of trace-fractional structure and orthogonal linear projections. Even though orthogonality has been widely used and proved to be a useful criterion for visualization, pattern recognition and feature extraction, existing methods for solving OCCA problem are either numerically unstable by relying on a deflation scheme, or less efficient by directly using generic optimization methods. In this paper, we propose an alternating numerical scheme whose core is the sub-maximization problem in the trace-fractional form with an orthogonality constraint. A customized self-consistent-field (SCF) iteration for this sub-maximization problem is devised. It is proved that the SCF iteration is globally convergent to a KKT point and that the alternating numerical scheme always converges. We further formulate a new trace-fractional maximization problem for orthogonal multiset CCA and propose an efficient algorithm with an either Jacobi-style or Gauss-Seidel-style updating scheme based on the SCF iteration. Extensive experiments are conducted to evaluate the proposed algorithms against existing methods, including real-world applications of multi-label classification and multi-view feature extraction. Experimental results show that our methods not only perform competitively to or better than the existing methods but also are more efficient.