Radial glial progenitors follow patterns of proliferation and differentiation to produce neurons and glia in the developing brain. The cells first undergo neurogenesis, producing neurons in a fairly deterministic manner, and then a portion of the cell population switches to producing glia. This neurogenesis-to-gliogenesis switch (NGS) and the patterns of cell division in gliogenesis are…

For models with high-dimensional input spaces, constructing accurate response surfaces can be prohibitively expensive. Additionally, the high-dimensionality of the parameter spaces can impact the computational cost of a parameter investigation. Using an active subspace construction, we can efficiently approximate complex models by constructing low-order response surfaces based on a smaller subspace of the high-dimensional parameter…

Nik Bravo: Title: Data-Driven Model Development and Feedback Control Design for PZT Bimorph Actuators Abstract: In the talk, we discuss the development of a high-fidelity and surrogate model for a PZT bimorph used as an actuator for micro-air vehicles including Robobee. The models must quantify the nonlinear, hysteretic, and rate-dependent behavior inherent to PZT in…

Borosilicate glass is the material predominately used for encasing carbon fiber (CF) microelectrodes for fast-scan cyclic voltammetry (FSCV) experiments. These capillaries insulate unexposed CF from the surrounding environment, while leaving a 150-200 um exposed CF tip in vivo that allows for electrochemical measurements of neurotransmitters. However, borosilicate glass commonly breaks during implantation; this can leave…

Poro-elastic and poro-visco-elastic models describe fluid flow through porous, deformable media. They are relevant in many applications in bioengineering and medicine, such as tissue perfusion and fluid flow inside cartilages and bones. In this talk, I will discuss the application of these models specifically to optical perfusion and its relation to glaucoma, as well as…

We address global sensitivity analysis for models with high-dimensional inputs and function-valued (functional) outputs. Variance-based global sensitivity approaches based on Sobol' indices have been proven useful in a wide range of outputs. However, Sobol' indices can be challenging to compute for computationally intensive models with a large number of parameters. We propose derivative based global…

We propose a Mixed Integer Partial Differential Equation Constrained Optimization (MIPDECO) formulation of the topological optimization for electromagnetic cloaking. Our formulation introduces binary variables to indicate the presence/absence of metamaterial at a given location within the cloaking device. The cloaking device is discretized on a 20x20 and 40x40 domain of squared material locations, and has two to…

The issue of parameter identifiability is a pervasive one in determining model parameters from data, specifically in trying to answer whether unique parameter estimation is possible for a given problem. Many related definitions of identifiability with subtle distinctions can be found in existing literature, and in this talk, we highlight some of the most utilized…

Accurate simulations of neutron transport within nuclear reactors are an important component in developing safe and efficient reactors and operation protocols. However, high-fidelity simulations of an entire core are often too costly for use in multi-query applications, such as multi-physics coupling, uncertainty quantification, or optimal experimental design. To facilitate efficient simulations, we utilize a simulation…

Variance-based global sensitivity analysis (GSA) provides useful measures, Sobol' indices, of how important individual input variables are to the output of a mathematical model. Traditional estimation of Sobol' indices by Monte Carlo methods can be unfeasible for models which are computationally expensive to evaluate. An appealing approach is to instead use a surrogate whose Sobol'…

We consider an optimal control problem subject to a poro-visco-elastic model with applications to fluid flows through biological tissues. Our goal is to optimize the fluid pressure and solid displacement using distributed or boundary control. We discuss an application of this problem to a tissue in the human eye. Previous literature on well- posedness of…

Many computational problems depend on solving systems of linear equations. The Conjugate Gradient method (CG) is a widely used iterative method that solves systems of linear equations. Early termination of CG sacrifices accuracy to save computational resources. The Bayesian Conjugate Gradient method (BayesCG) is a probabilistic generalization of CG that solves systems of linear equations…

Many inference problems relate to the dynamical system, x'=f(x). One primary problem in applications is that of system identification, i.e., how should the user accurately and efficiently identify the model f(x), including its functional family or parameter values, from discrete time-series data? One of the most successful algorithms to this end is the Sparse Identification of…

In a Take-Away Game on hypergraphs, two players take turns to remove the vertices and the hyperedges of the hypergraphs. In each turn, a player must remove either only one vertex or only one hyperedge. When a player chooses to remove one vertex, all of the hyperedges that contain the chosen vertex are also removed.…

A significant challenge in the development of drugs to treat central nervous system (CNS) disorders is to attain sufficient delivery of antibodies across blood-brain barriers (BBB). Since not all antibodies can pass through BBB, it is crucial to understand antibody exposure in the CNS quantitatively to construct drug characteristics and identify proper dosing regimens. We…

Variance-based global sensitivity analysis (GSA) can provide a wealth of information when applied to complex models. A well-known Achilles' heel of this approach is its computational cost which often renders it unfeasible in practice. An appealing alternative is to analyze instead the sensitivity of a surrogate model with the goal of lowering computational costs while…

Galerkin reduced-order models (ROMs) approximate computational fluid simulations by reducing snapshot data to a basis of proper orthogonal decomposition (POD) modes and solving for modal coefficients with ordinary differential equations. Galerkin ROMs reduce computational cost and can approximate flows with alternate Reynolds numbers, while parametric reduced order models allow adjustment of other system parameters. However,…

Given the inability to directly observe the conditions of a fault line, inversion of parameters describing them has been a subject of practical interest for the past couple of decades. To resolve this under a linear elasticity forward model, we consider Bayesian inference in the infinite dimensional setting given some surface displacement measurements, resulting in…

If you are interested in learning more about applied math research from your fellow students, or you want a friendly and constructive environment to practice presenting your own applied math research, AMGSS is for you! This is an informational and sign-up meeting, so come to learn more about AMGSS and/or to sign up to present…