# Browsing by Author "Yamazaki, Kazuo"

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Item Exploring social and economic predictors for U.S. Government elections(2021-08) Dassanayake, Isuru; Volchenkov, Dimitri; Swed, Ori; Ellingson, Leif; Wang, Chunmei; Yamazaki, KazuoShow more In democracy, elections are the way we settle our differences and redistribute power. It is the best assurance for avoiding the concentration of power by few and the shuffle of governments priorities. The main purpose of my research study is to develop a method to predict US government elections (US Presidential election, US Senate election and Election of US House of Representatives) outcome ahead of the time without using polling data. Thus, this study is focused on developing an alternative prediction tool that looks at the relations between a variety of variables and indicators that are associated with voting, among them historical, economic, and social indicators. On average when considering these different types of elections, the data available for each election are different. Therefore, it had to assume that for a given state voter turnout rate would be the same for each congressional district in that state. If those separate voter turnout data was available for the study, it would be greatly beneficial in predicting the House election. If the model incorporates demographic data such as, the population, education level, composition of ethnicity, income levels for a given state or better for a given congressional district, that will play a huge factor in predicting an outcome for an election. The mathematical model includes a novel competitive analysis involving the con- current use of Linear Discriminant Analysis (LDA), Support Vector Machine (SVM), and Long Short-Term Memory Neural Network (LSTM) learning models for each state individually, in search for the minimal forecasting error over the available elec- tion history and the economic factors. Drawing on advancements in mathematical modeling and artificial intelligence we were able to run thousands of simulations and generate predictions. Testing model, this tool was able to predict the outcome of 2020 Presidential, Senate and House Elections. The developed model was validated by using the past US Presidential elections, which yielded results with high accuracy rates. It was founded that the Voter turnout rates for elections has a significant impact on the outcome of an election. Therefore, according to different levels voter turnout rates several predictions were made for each type of election.Show more Item Global Regularity Aspects of Equations in Hydrodynamics(2023-08) Rahman, Mohammad Mahabubur; Yamazaki, Kazuo; Bornia, Giorgio; Gelca, Razvan; Hoang, LuanShow more The question of the global regularity of the two-dimensional magnetohydrodynamics system without viscous dissipation is currently unknown. A challenging problem concerning the global regularity of the two-and-a-half and three-dimensional Hall-magnetohydrodynamics system is still open. The global regularity of two-dimensional and three-dimensional Kuramoto–Sivashinsky equations are not solved as well. Chapter 2 explores some cancellations and bounds within the Hall term for both two-and-a-half dimensional and three-dimensional cases, as well as various regularity criteria. The two-a-half-dimensional Hall equation and Hall-magnetohydrodynamics system are also proved to be globally well-posed when magnetic dissipation is considered at the below-critical level in the horizontal direction and at the supercritical level in the vertical direction. The purpose of Chapter 3 is to introduce and prove some global regularity criteria on the Sobolev and Besov spaces in dimensions two and three. In Chapter 4, a two-and-a-half-dimensional magnetohydrodynamics system is presented, and its global well-posedness is demonstrated. Furthermore, a magnetohydrodynamics system without viscous dissipation is introduced, and a global regularity criterion is derived.Show more Item Improved uniform persistence for partially diffusive models of infectious diseases: cases of avian influenza and Ebola virus disease(2023) Covington, Ryan (TTU); Patton, Samuel (TTU); Walker, Elliott (TTU); Yamazaki, KazuoShow more Past works on partially diffusive models of diseases typically rely on a strong assumption regarding the initial data of their infection-related compartments in order to demonstrate uniform persistence in the case that the basic reproduction number R0 is above 1. Such a model for avian influenza was proposed, and its uniform persistence was proven for the case R0 > 1 when all of the infected bird population, recovered bird population and virus concentration in water do not initially vanish. Similarly, a work regarding a model of the Ebola virus disease required that the infected human population does not initially vanish to show an analogous result. We introduce a modification on the standard method of proving uniform persistence, extending both of these results by weakening their respective assumptions to requiring that only one (rather than all) infection-related compartment is initially non-vanishing. That is, we show that, given R0 > 1, if either the infected bird population or the viral concentration are initially nonzero anywhere in the case of avian influenza, or if any of the infected human population, viral concentration or population of deceased individuals who are under care are initially nonzero anywhere in the case of the Ebola virus disease, then their respective models predict uniform persistence. The difficulty which we overcome here is the lack of diffusion, and hence the inability to apply the minimum principle, in the equations of the avian influenza virus concentration in water and of the population of the individuals deceased due to the Ebola virus disease who are still in the process of caring.Show more Item Models of Chemotaxis Systems via Einstein’s and Probabilistic Frameworks and their Analysis(2023-08) Islam, Rahnuma; Hoang, Luan; Ibragimov, Akif; Peace, Angela; Yamazaki, KazuoShow more We study the movement of the living organism in a band form towards the presence of chemical substrates based on a system of partial differential evolution equations. We incorporate Einstein's method of Brownian motion to deduce Keler--Segel type chemotactic model exhibiting a traveling band. It is the first time that Einstein's method has been used to motivate equations describing the mutual interaction of the chemotactic system. We show that in the presence of limited and unlimited substrate traveling bands are achievable and it has been explained accordingly. We also establish the profiles of the traveling bands on the parameters of the system. Our method can also be used to derive a model for cellular aggregation of slime mold. The model describes the chemotaxis response of amoeba towards the chemical substrate named acrasin. It results in a new system of non-linear partial differential equations. The coefficients in this system have a clear biological interpretation. We study the stability of the constant steady states for the system. The linearized system about a constant steady state is obtained under the mixed Dirichlet and Neumann boundary conditions. We are able to find explicit conditions for linear instability. These instability conditions show that the large acrasin production and length of domain support the change of state. The linear stability is established with respect to the $L^2$-norm, $H^1$-norm, and $L^\infty$-norm under certain conditions. Such conditions reflect that a large value of diffusion of amoeba and chemotactic response is needed for stability. We derive the chemotaxis models using the probabilistic method. In addition to considering the chemotactic response and the random motion of bacteria, we also consider the formation of the crowd by bacteria via interactions within or between the community. On the one hand, we prove the non-existence of a traveling band solution satisfying certain conditions under some constraints. On the other hand, the existence of a traveling band solution is established in some situations.Show more Item Protecting data privacy with anonymity: Quantifying instinctive measures and intelligent effective search for optimal anonymized data(2022-05) Arca, Sevgi; Hewett, Rattikorn; Serwadda, Abdul; Dang, Tommy; Salman, Tara; Chen, Lin; Yamazaki, KazuoShow more Data privacy entails the ability for individuals to control their personal data. With advanced technology in this digital era, users can lose control of their personal data without knowing as their data can be tracked, stored, and shared across multiple parties. Protecting online data privacy is a daunting task. Current consent-based privacy policies tend to be too elaborate and difficult to apply effectively. There is a need for new approaches to protecting data privacy that go beyond user consent model. As more data are shared and publicly available, attackers can further infer confidential data from multiple query sources to commit malicious acts. This dissertation addresses the issues of how to better protect privacy of such published structured data, particularly, fundamental issues of anonymity quantification and practical issues on efficiency and optimality of automated anonymization. Anonymity is among the most widely used property for data privacy protection. It represents the state of indistinguishability. Thus, increasing users’ anonymity increases their indistinguishability that makes it harder for them to be re-identified. Anonymization ensures that each set of "critical" data values belongs to more than one individual so that the individual's identity can be protected. Many privacy-preserving approaches to anonymizing structured data involve transforming the original data into a more anonymous form (via generalization and suppression) while preserving the data integrity. Although techniques for anonymization have been studied extensively, to our surprise, most of them do not directly measure anonymity but use a measure specified to indirectly indicate the quality of anonymity (e.g., anonymity degree in k-anonymity). Most existing anonymity measures are indirect since they are based on entropy that estimates information loss, a partial consequence of anonymity. Anonymity measure is at the heart of anonymization and yet there is little research on quantifying a direct measure of anonymity. This dissertation models two direct anonymity measures: information-based and inference-based for the disclosure breach and re-identification attack, respectively. The unique aspect of the formulation is its instinctive articulation of opposing perspectives of victims (in concealing their identity) and attackers (in finding the disclosure or identity). Furthermore, unlike most other work, this study distinguishes the measure of an individual anonymity from that of the group. When dealing with large-scaled data, by using data distribution, this dissertation proposes measures of uniformity, variety, and diversity as anonymity indicators to quickly assess degrees of data privacy. On practical issues of anonymization, to improve efficiency, most general-purpose anonymization techniques aim to find "optimal" k-anonymization (or anonymized data satisfying k-anonymity requirements), e.g., by minimizing data distortion or the number of generalization steps. However, the problem of finding k-anonymization to maximize preserved information is NP-hard. This has led to greedy anonymization and special purpose techniques. Still, a common issue in anonymization is trade-offs between data privacy and informativeness. Generalization helps gain anonymity but can result in data that are not useful. Anonymization approaches are mostly designed to address specific goals (e.g., accurate classification, efficient algorithms) but none provides an integrated solution for efficiency, privacy, and preserved informativeness. This dissertation presents a general-purpose anonymization technique that applies generalization for securing privacy by satisfying user-specified anonymity requirements while optimizing information preservation. The proposed approach exploits the monotonicity property of generalization along with a heuristic search to efficiently find optimal generalized data that comply with the anonymity requirements. The approach is theoretically grounded as the search can be mapped to a well-known efficient optimal search in Artificial Intelligence. In addition, the approach can give the data quality for classification relatively well even though its intent is to keep the generalized data as close as possible to the original. Finally, this dissertation puts together a practical methodology for anonymity analytics and retention.Show more Item Random walk of Brownian motion in non-linear system(2020-05) Islam, Rahnuma; Ibraguimov, Akif; Hoang, Luan; Yamazaki, KazuoShow more We study the long-time asymptotics of prototypical non-linear diffusion equations. Specifically, we consider the case of a non-degenerate diffusivity function that is a (non-negative) polynomial of the dependent variable of the problem. We motivate these types of equations using Einstein's random walk paradigm, leading to a partial differential equation in non-divergence form. On the other hand, using conservation principles leads to a partial differential equation in divergence form. A transformation is derived to handle both cases. Then, a maximum principle (on both an unbounded and a bounded domain) is proved, in order to obtain bounds above and below for the time-evolution of the solution to the non-linear diffusion problem. Specifically, these bounds are based on the fundamental solution of the linear problem (the so-called Aranson's Green function). Having thus sandwiched the long-time asymptotics of solutions to the non-linear problems between two fundamental solutions of the linear problem, we prove that, unlike the case of degenerate diffusion, a non-degenerate diffusion equation's solution converges onto the linear diffusion solution at long times. Select numerical examples support the mathematical theorems and illustrate the convergence process. Our results have implications on how to interpret asymptotic scalings of potentially anomalous diffusion processes (such as in the flow of particulate materials) that have been discussed in the applied physics literature.Show more