This work presents multiscale modeling of blood flow and polymer suspensions which requires the use of heterogeneous modeling approaches. A hybrid method based on coupling …
In this thesis, we give a review of modern blind, semi-blind, and informed source separation techniques. Specifically, the details of independent component analysis are derived, …
Background: People who inject drugs (PWID) are at high-risk for acquiring HIV in the rural United States. In 2015, Scott County, Indiana experienced the largest …
Hidden Markov models are used in countless signal processing problems, and the associated nonlinear filtering algorithms are used to obtain posterior distributions for the hidden …
Consider a (possibly non-Markovian) interacting particle system (IPS) indexed by the nodes of a (possibly random) locally finite graph whose vertices and edges are equipped …
Solitary waves are localized disturbances that maintain their shape as they propagate at a constant velocity. They have applications in diverse fields such as fluid …
Many nonparametric Bayesian models can be viewed as an infinite-dimensional limit of a family of finite-dimensional models. However, another way to construct a flexible Bayesian …
In this thesis, we study optimization algorithms for evaluating solutions to certain high dimension (multi-time) Hamilton-Jacobi Partial Differential equations arising from optimal control. There are …
In recent years, there has been great interest in fluid-structure interaction (FSI) problems due to their relevance in structural engineering and biomedical applications. However, several …
This dissertation presents two topics on numerical solutions solving hyperbolic equations from both theoretical and practical points of view. In the first part, we introduce …
In this thesis, we aim to improve the accuracy and efficiency in uncertainty quantification (UQ) of stochastic partial differential equations (SPDEs) driven by Levy jump …
Neutrally buoyant, non-Brownian particles in a low Reynolds number pressure-driven flow display an irreversible net particle migration towards the center of the channel, resulting in …
In this thesis, we examine hybrid numerical models of calcium-induced calcium release using deterministic PDEs for the diffusion of cytosolic calcium and a stochastic process …
Monte Carlo methods are arguably among the most general purpose numerical tools currently available. There is a relatively long history of the use of large …
Oscillons are spatially localized, time-periodic structures that have been observed in many natural processes, often under temporally periodic forcing. Near Hopf bifurcations, such systems can …
Hamilton-Jacobi PDEs and optimal control problems are widely used in many practical problems in control engineering, physics, financial mathematics, and machine learning. For instance, controlling …
This thesis project examines a novel method of geoengineering, a means to ameliorate the effects of anthropogenic climate change. As discussed in the first chapter …
T cells recognize antigens via T cell receptors (TCR), initiating an intracellular signal transduction cascade. Tyrosine is one of the main amino acids that is …
T cells recognize antigens via T cell receptors (TCR), initiating an intracellular signal transduction cascade. Tyrosine is one of the main amino acids that is …