MA/MS Theses - DO NOT EDIThttp://hdl.handle.net/10106/117592024-03-28T23:45:02Z2024-03-28T23:45:02ZDECOUPLING-BASED APPROACH TO CENTRALITY DETECTION IN HETEROGENEOUS MULTILAYER NETWORKShttp://hdl.handle.net/10106/300392022-03-02T17:09:30Z2021-08-13T00:00:00ZDECOUPLING-BASED APPROACH TO CENTRALITY DETECTION IN HETEROGENEOUS MULTILAYER NETWORKS
Graph analysis is one of the techniques widely used for data analysis. It is used extensively on single graphs. Its ability to capture entities and relationships makes it an attractive data model. Search on graphs, such as finding triangles, cliques, shortest paths, etc., and aggregate analysis, such as communities, substructure, or centrality measures have well-defined algorithms for single graphs. The centrality measure, which is the focus of this thesis, identifies the most important nodes in a graph or network. While there are many centrality measures, the most commonly used ones are degree and betweenness centrality. Algorithms for analyzing these measures are numerous for single graphs.
In addition to graphs, multilayer networks (MLNs) are being used to model complex data sets. MLNs consist of several layers, each being a graph. If there are different types of entities in each layer and inter-layer edges are present, then the network is an example of a Heterogeneous Multilayer Network (HeMLN). Due to the lack of algorithms for HeMLNs, they are currently analyzed using aggregation of HeMLN layers including inter-layer edges into a single graph. An alternative projection-based approach is also used to analyze HeMLNs by transforming it into a single graph.
A decoupling-based framework has been proposed to avoid aggregation or projection and still obtain accurate results. This approach analyses the layers independently and composes the partial results to obtain results for a HeMLN. These algorithms have been shown to produce accurate results and are also efficient. Another advantage of this approach is that the layers can be analyzed in parallel. The composition algorithm produces the results of the entire HeMLN. To the best of our knowledge, there are no algorithms that compute centrality measures directly on HeMLNs. This thesis focuses on developing decoupling-based algorithms for degree and betweenness centrality measures for HeMLNs.
The challenge is to minimize the amount of information retained from each layer for use during composition to maximize accuracy. Also, keep the algorithm more efficient than its single graph counterpart, which is considered as the ground truth. This thesis proposes different heuristics and compares the results with the ground truth and naive algorithm. The proposed heuristics consistently improve the accuracy as compared to the naive algorithm while taking less time than the single graph approach.
Finally, the algorithms proposed in the thesis are tested against both real-world and synthetic data sets with different graph characteristics. This is important to demonstrate the efficacy of heuristics on an arbitrary graph. The results obtained are analyzed in detail to empirically establish the heuristic performance in terms of accuracy, time, and space complexity.
2021-08-13T00:00:00ZOptimal Control Methods for Chagas Diseasehttp://hdl.handle.net/10106/277762022-03-17T16:45:44Z2018-12-10T00:00:00ZOptimal Control Methods for Chagas Disease
Chagas disease is the world's most neglected tropical disease. Having a lack of cure makes the primary focus on the disease preventing it and controlling it. This study takes into account three different control measures: bed nets, low-volume insecticide spraying, and improving housing conditions, analyzes their cost effectiveness compared to each other, and determines which combination of the three control measures prevents the most T. cruzi infections in a rural Latin American village over a decade.
It was shown that there is a a hierarchical importance in the control measures when preventing the spread of Chagas disease. In order of highest effectiveness, they are bed nets, low-volume insecticide spraying, and improving overall housing conditions. It was found that the most cost-effective scenario occurs when full coverage for bed nets and low-volume insecticide spraying is obtained, followed by devoting the remaining portion of the budget towards improving overall housing conditions. It was shown that if at least 36.30 USD per month is devoted to bed nets, then R₀ < 1.
2018-12-10T00:00:00ZA Mathematical Model of Hepatitis C Virus Infection Incorporating Immune Responses and Cell Proliferationhttp://hdl.handle.net/10106/269612023-07-18T15:20:12Z2017-08-03T00:00:00ZA Mathematical Model of Hepatitis C Virus Infection Incorporating Immune Responses and Cell Proliferation
This thesis introduces a mathematical model of differential equations for the chronic hepatitis C virus (HCV) infection, which is a contagious disease that infects the liver cells. Firstly, we present the early mathematical models for the basic dynamics of virus infection that developed and analyzed to understand the dynamics of human immunodeficiency virus (HIV), hepatitis B virus (HBV), and some other viruses. Next, we present the extended model of the basic HCV virus dynamics that incorporate the effectiveness of a treatment. After that, the mathematical model that includes proliferation terms for both infected and uninfected hepatocytes is discussed. Lastly, the mathematical model that is considering the interaction between HCV virus and immune responses in a host is introduced.
In this thesis, we formulate an ordinary differential equations (ODE) model to describe the interactions between the hepatitis C (HCV) virus and the immune system in a human body under treatment, taking into consideration the proliferation for both infected and uninfected hepatocytes. Analysis of the model reveals the existence of multiple equilibrium states: the disease-free steady state in which no virus is present, an infected state with no immune responses, an infected steady state with immune responses in which virus and infected cells are present, an infected steady state with dominant CTLs responses in which no antibody (B-cell) is present, an infected steady state with dominant antibody responses in which no CTLs is present, and an infected steady state with coexistence responses in which all are present. Finally, we run simulations and compare our model to other models in the literature. In addition, several different scenarios were numerically simulated to demonstrate the practical applications of the mathematical model.
2017-08-03T00:00:00ZA SNAPSHOT OF THE ALIGNMENT OF UNIVERSITY STUDENTS’ MATHEMATICAL PROBLEM SOLVING PRACTICES TO A LIKERT SCALE ASSESSMENT OF MATHEMATICAL PROBLEM SOLVINGhttp://hdl.handle.net/10106/268422023-07-17T20:00:05Z2017-05-22T00:00:00ZA SNAPSHOT OF THE ALIGNMENT OF UNIVERSITY STUDENTS’ MATHEMATICAL PROBLEM SOLVING PRACTICES TO A LIKERT SCALE ASSESSMENT OF MATHEMATICAL PROBLEM SOLVING
This study investigates the alignment of students' actual problem-solving practices and compares them to the outcomes on a Likert scale mathematical problem solving (MPS) assessment. The Likert scale survey items developed by the Mathematical Problem Solving Item Development Project (MPSI) to gather information on undergraduate's MPS in five domains: sense-making, representing/connecting, reviewing, justifying, and challenge (Epperson, Rhoads, and Campbell, 2016).
This snapshot investigation analyzes two individual undergraduate student interviews to characterize the students' MPS practices. Data analysis suggests a promising alignment between the MPSI survey results and students' actual practices. The analysis also establishes preliminary reliability of the MPSI survey items and their links to the MPS domains from observations and responses during the student interviews.
In addition, the relationship between the undergraduate students' subject-matter domain knowledge in algebra, their MPS behaviors, and their responses on the MPSI survey items is explored to determine what effects subject-matter domain knowledge may have on the MPSI survey results.
2017-05-22T00:00:00Z