Theses and Dissertations from UMD
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Item Dynamics, Networks, and Information: Methods for Nonlinear Interactions in Biological Systems(2021) Milzman, Jesse; Levy, Doron; Lyzinski, Vince; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)In this dissertation, we investigate complex, non-linear interactions in biological systems.This work is presented as two independent projects. The mathematics and biology in each differ, yet there is a unity in that both frameworks are interested in biological responses that cannot be reduced to linear causal chains, nor can they be expressed as an accumulation of binary interactions. In the first part of this dissertation, we use mathematical modeling to study tumor-immune dynamics at the cellular scale.Recent work suggests that LSD1 inhibition reduces tumor growth, increases T cell tumor infiltration, and complements PD1/PDL1 checkpoint inhibitor therapy. In order to elucidate the immunogenic effects of LSD1 inhibition, we create a delay differential equation model of tumor growth under the influence of the adaptive immune response in order to investigate the anti-tumor cytotoxicity of LSD1-mediated T cell dynamics. We fit our model to the B16 mouse model data from Sheng et al. [DOI:10.1016/j.cell.2018.05.052] Our results suggest that the immunogenic effect of LSD1 inhibition accelerates anti-tumor cytoxicity. However, cytotoxicity does not seem to account for the slower growth observed in LSD1 inhibited tumors, despite evidence suggesting immune-mediation of this effect. In the second part, we consider the partial information decomposition (PID) of response information within networks of interacting nodes, inspired by biomolecular networks.We specifically study the potential of PID synergy as a tool for network inference and edge nomination. We conduct both numeric and analytic investigations of the $\Imin$ and $\Ipm$ PIDs, from [arXiv:1004.2515] and [DOI:10.3390/e20040297], respectively. We find that the $I_\text{PM}$ synergy suffers from issues of non-specificity, while $I_{\text{min}}$ synergy is specific but somewhat insensitive. In the course of our work, we extend the $I_\text{PM}$ and $I_{\text{min}}$ PIDs to continuous variables for a general class of noise-free trivariate systems. The $I_\text{PM}$ PID does not respect conditional independence, while$I_{\text{min}}$ does, as demonstrated through asymptotic analysis of linear and non-linear interaction kernels. The technical results of this chapter relate the analytic and information-theoretic properties of our interactions, by expressing the continuous PID of noise-free interactions in terms of the partial derivatives of the interaction kernel.Item Emergent behaviors in adaptive dynamical networks with applications to biological and social systems(2021) Alexander, Brandon Marc; Girvan, Michelle; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)In this thesis, we consider three network-based systems, focusing on emergent behaviors resulting from adaptive dynamical features. In our first investigation, we create a model for gene regulatory networks in which the network topology evolves over time to avoid instability of the regulatory dynamics. We consider and compare different rules of competitive edge addition that use topological and dynamical information from the network to determine how new network links are added. We find that aiming to keep connected components small is more effective at preventing widespread network failure than limiting the connections of genes with high sensitivity (i.e., potential for high variability across conditions). Finally, we compare our results to real data from several species and find a trend toward disassortativity over evolutionary time that is similar to our model for structure-based selection. In our second investigation, we introduce a bidirectional coupling between a phase synchronization model and a cascade model to produce our `sync-contagion' model. The sync-contagion model is well-suited to describe a system in which a contagious signal alerts individuals to realign their orientations, where `orientation' can be in the literal sense (such as a school of fish escaping the threat of a predator) or a more abstract sense (such as a `political orientation' that changes in response to a hot topic). We find that success in realigning the population towards some desired target orientation depends on the relative strengths of contagion spread and synchronization coupling. In our third and final investigation, we attempt to forecast the complex infection dynamics of the COVID-19 pandemic through a data-driven reservoir computing approach. We focus our attention on forecasting case numbers in the United States at the national and state levels. Despite producing adequate short-term predictions, we find that a simple reservoir computing approach does not perform significantly better than a linear extrapolation. The biggest challenge is the lack of data quantity normally required for machine learning success. We discuss methods to augment our limited data, such as through a `library-based' method or a hybrid modeling approach.Item SUBJECT-SPECIFIC MULTICHANNEL BLIND SYSTEM IDENTIFICATION OF HUMAN ARTERIAL TREE VIA CUFF OSCILLATION MEASUREMENTS(2016) Lee, Jongchan; Hahn, Jin-Oh; Mechanical Engineering; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)We developed and evaluated a mathematical model-based method to monitor cardiovascular health and estimate risk predictors from two peripheral cuff oscillation measurements. The model structure was established by studying tube-load models individually augmented with a gain, Voigt model, and standard linear solid model to best capture the relationship between carotid tonometry and cuff waveforms at the upper arm and ankle. The arm-cuff interface was better modeled with increasing viscoelasticity but not as much for the ankle-cuff interface. Next, model-estimated ankle blood pressure waveforms were used to formulate a matrix equation for estimating wave reflection. Subsequently derived risk predictors were adequately correlated with those from reference methods. Finally, subject-specific central blood pressure waveforms were estimated from two cuff oscillation signals via multichannel blind system identification. The model estimated central arterial blood pressure waveforms with good accuracy with a median RMSE of 3.08 mmHg and IQR of 1.71 mmHg.Item Mathematical and Molecular Studies of Feline Erythro- and Lymphopoiesis(2005-08-11) Ewen, Bren S; Song, Wenxia; Pontzer, Carol M; Molecular and Cell Biology; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Feline leukemia virus, strain KT, is a retrovirus that causes a fatal erythroid aplasia. The fatal loss of erythrocytes is due to the interaction of this virus with the BFU-E stage of feline erythropoietic development. This virus is comparable to the human HTLV retrovirus. Through the development of a computer mathematical model, we demonstrate the disease process and show that infection of the BFU-E leads to a characteristic fatal erythroid aplasia in cats. Fetal feline lymphohematopoietic stem cells, before a certain point in gestation, lack genotypically unique class I major histocompatibility cell-surface antigens (FLA). The elucidation of a gestational time point when FLA appear on the surface of cells within the fetal liver will provide knowledge of when hematopoietic stem cells may be at maximal utility for gene therapy of feline hematopoietic disease, specifically FIV. Here we show that this time point occurs around day 40 in fetal feline gestation.Item MODELING AND OPTIMIZATION OF TRANSMISSION NETWORKS(2005-04-19) Frommer, Ian; Hunt, Brian; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)This dissertation focuses on transmission networks. These networks play an important role in communication (including data and voice), energy transmission (such as gas, electrical, and oil), and micro-electronics among other areas. In this dissertation, we consider two different problems associated with transmission networks: the dynamics on a data communication network and the optimal design of a general transmission network located on a non-uniform landscape. The first two parts of this dissertation develop and apply mathematical models of congested Internet connections and describe possible extensions to network traffic state estimation and network security. The third part looks at an optimal network design problem through a variation on the Euclidean Steiner tree problem, a well-known network optimization problem.Item The Non-Linear Transmission Dynamics of HIV/AIDS(2004-11-10) Rapatski, Brandy Lynn; Yorke, James A; Suppe, Frederick; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)How infectious a person is when infected with HIV depends upon what stage of the disease the person is in. We use three stages which we call primary, asymptomatic and symptomatic. It is important to have a systematic method for computing all three infectivities so that the measurements are comparable. Using robust modeling we provide high-resolution estimates of semen infectivity by HIV disease stage. We find that the infectivity of the symptomatic stage is far higher, hence more potent, than the values that prior studies have used when modeling HIV transmission dynamics. The stage infectivity rates for semen are 0.024, 0.002, 0.299 for primary, asymptomatic and symptomatic (late-stage) respectively. Implications of our infectivity estimates and modeling for understanding heterosexual epidemics such as the Sub-Saharan African one are explored. Most models are compartment models that are based on the number of new infections per unit time. We create a new risk-based model that focuses on a susceptible person's risk of becoming infected if he has a single contact with an infected individual.