Author ORCID Identifier

Semester

Summer

Date of Graduation

2024

Document Type

Dissertation

Degree Type

PhD

College

Eberly College of Arts and Sciences

Department

Mathematics

Committee Chair

Ádám Halász

Committee Co-Chair

Srinjoy Das

Committee Member

Casian Pantea

Committee Member

Hong-Jian Lai

Committee Member

Ela Celikbas

Committee Member

Kenneth J. Ryan

Abstract

This dissertation discusses three instances of temporal prediction, applied to population dynamics and deep learning.

In population modeling, dynamic processes are frequently represented by systems of differential equations, allowing for the analysis of various phenomena. The first application explores modeling cloned hematopoiesis in chronic myeloid leukemia (CML) via a nonlinear system of differential equations. By tracking the evolution of different cell compartments, including cycling and quiescent stem cells, progenitor cells, differentiated cells, and terminally differentiated cells, the model captures the transition from normal hematopoiesis to the chronic and accelerated-acute phases of CML. Three distinct non-zero steady states are identified, representing different disease stages. We investigate the local stability of these steady states and provide a characterization of the hematopoietic states based on this analysis. Numerical simulations further illustrate these findings.

The second application features a different approach to population dynamics. In the context of infectious disease modeling, we extend the classic SIR model to predict future COVID-19 incidence. Utilizing the instantaneous reproduction number ($R_t$) estimated via Bayesian inference, short-term predictions of COVID-19 incidence in West Virginia, are made. Special attention is given to accounting for the influence of larger population centers on rural counties. A Markov Chain Monte Carlo (MCMC) algorithm is employed here for optimization in prediction.

The last part of the dissertation proposes a novel prediction framework for enhancing bandwidth reduction in motion transfer-enabled video applications. Employing neural networks and the First Order Motion Model (FOMM), dynamic objects are represented using learned keypoints organized in a time series. Prediction of keypoints is achieved using a Variational Recurrent Neural Network (VRNN). For real-time applications, our results show the effectiveness of our proposed architecture by enabling up to 2x additional bandwidth reduction over existing keypoint based video motion transfer frameworks without significantly compromising video quality.

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