Digital Commons Network^™

Randomized Algorithms For Resource Allocation In Device To Device Communication., Subhankar Ghosal Dr.

Doctoral Theses

In device to device (D2D) communication, two users residing in close proximity can directly communicate between them, through a common channel, without the need of a base station. A pair of D2D users forms a link and a channel needs to be allocated to it. The interference relationship among the active links at time t is modelled as an interference graph g(t). To establish interference-free communication, we have to assign a channel vector C(t) and a power vector corresponding to the active links such that the required signal to interference plus noise ratio (SINR) is satisfied for each link. Since …

Mitigation Impact Of Statewide Non-Pharmaceutical Policies On Covid-19: An Application Of Infectious Disease Transmission Model And Partially Observed Markov Process To New Mexico, Xingya Ma

Mathematics & Statistics ETDs

This thesis is an application of epidemiological models for infectious disease transmission and the use of partially observed Markov process (POMP) for model fitting. It focuses on COVID-19 pandemic in the state of New Mexico. The analysis covered March 2020 to June 2021. Daily data of COVID19 cases and deaths and a daily index of eleven statewide government non-pharmaceutical intervention (NPI) policies were collected from six public sources and were validated. These data were integrated through the Susceptible-Exposed-Infected-Removed (SEIR) model. Estimated daily transmission rates between the model compartments quantify the impact of the mitigation policies, and show that transmission rates …

Geometry And Dynamics Of Rolling Systems, Bowei Zhao

Arts & Sciences Electronic Theses and Dissertations

Billiard systems, broadly speaking, may be regarded as models of mechanical systems in which rigid parts interact through elastic impulsive collision forces. When it is desired or necessary to account for linear/angular momentum exchange in collisions involving a spherical body, a type of billiard system often referred to as no-slip has been used. Previous work indicated that no-slip billiards resemble non-holonomic systems, specifically, systems consisting of a ball rolling on surface. In prior research, such connections were only observed numerically and were restricted to very special surfaces. In this thesis, it is shown that no-slip billiard and rolling systems are …

Multi-Trace Matrix Models From Noncommutative Geometry, Hamed Hessam

Electronic Thesis and Dissertation Repository

Dirac ensembles are finite dimensional real spectral triples where the Dirac operator is allowed to vary within a suitable family of operators and is assumed to be random. The Dirac operator plays the role of a metric on a manifold in the noncommutative geometry context of spectral triples. Thus, integration over the set of Dirac operators within a Dirac ensemble, a crucial aspect of a theory of quantum gravity, is a noncommutative analog of integration over metrics.

Dirac ensembles are closely related to random matrix ensembles. In order to determine properties of specific Dirac ensembles, we use techniques from random …

A View Into Secondary Education Mathematics, Thomas Krieger Jr.

Honors Theses

Teaching methods, and the effects they can have on students, are important to consider for a classroom because when teaching you should allow for every student to have an opportunity. Every student should feel encouraged in the classroom, however not every method may allow for that. An important task for a teacher is to find out how to reach their students in their classroom; be it adapting methods or choosing when to implement one item over another. This task differs with every student that enters the classroom as no student is the same. Every students’ differences stem from their academic …

On The Spatial Modelling Of Biological Invasions, Tedi Ramaj

Electronic Thesis and Dissertation Repository

We investigate problems of biological spatial invasion through the use of spatial modelling. We begin by examining the spread of an invasive weed plant species through a forest by developing a system of partial differential equations (PDEs) involving an invasive weed and a competing native plant species. We find that extinction of the native plant species may be achieved by increasing the carrying capacity of the forest as well as the competition coefficient between the species. We also find that the boundary conditions exert long-term control on the biomass of the invasive weed and hence should be considered when implementing …

Irreducible Representations From Group Actions On Trees, Charlie Liou

Master's Theses

We study the representations of the symmetric group $S_n$ found by acting on

labeled graphs and trees with $n$ vertices. Our main results provide

combinatorial interpretations that give the number of times the irreducible

representations associated with the integer partitions $(n)$ and $(1^n)$ appear

in the representations. We describe a new sign

reversing involution with fixed points that provide a combinatorial

interpretation for the number of times the irreducible associated with the

integer partition $(n-1, 1)$ appears in the representations.

Classification Of Nuclear Pastas Through Alpha Shapes Model, Daniela Ramirez Chavez

Open Access Theses & Dissertations

The nuclear pasta is important because is an astromaterial with incredible strength that may be a source for gravitational waves, which observe from the rotation of neutron stars. The characterization of the pasta is vital because the nuclear phases have transport properties - compressibility, neutrino opacity, thermal conductivity, and electrical conductivity - associated with their shape for which neutron stars may be sensitive. These properties could interpret observations of supernova neutrinos, magnetic field decay, and crust cooling of accreting neutron stars. Here, we study the nuclear pasta using alpha shapes to achieve a phase characterization with the Minkowski functionals (area, …

Time Series Classification With Multistage Modeling Using Deep Learning, James Arthur

Open Access Theses & Dissertations

Time series classification (TSC) can be efficiently implemented with several techniques. Many techniques are based on analyzing 1-D signals in the time series data. In this work, we make an intrinsic analytical implementation of a new time series classification that involves a two-stage process. Firstly, by using Recurrence Plots (RP), we transform the time series into 2D images. The second stage consists in taking advantage of deep learn- ing models to perform our classification. The image illustration of time series introduces different feature types that are not available for all 1D signals, and therefore our classifi- cation problem is treated …

Meshfree Methods For Pdes On Surfaces, Andrew Michael Jones

Boise State University Theses and Dissertations

This dissertation focuses on meshfree methods for solving surface partial differential equations (PDEs). These PDEs arise in many areas of science and engineering where they are used to model phenomena ranging from atmospheric dynamics on earth to chemical signaling on cell membranes. Meshfree methods have been shown to be effective for solving surface PDEs and are attractive alternatives to mesh-based methods such as finite differences/elements since they do not require a mesh and can be used for surfaces represented only by a point cloud. The dissertation is subdivided into two papers and software.

In the first paper, we examine the …

Voting Rules And Properties, Zhuorong Mao

Undergraduate Honors Theses

This thesis composes of two chapters. Chapter one considers the higher order of Borda Rules (Bp) and the Perron Rule (P) as extensions of the classic Borda Rule. We study the properties of those vector-valued voting rules and compare them with Simple Majority Voting (SMV). Using simulation, we found that SMV can yield different results from B1, B2, and P even when it is transitive. We also give a new condition that forces SMV to be transitive, and then quantify the frequency of transitivity when it fails.

In chapter two, we study the `protocol paradox' of approval voting. In approval …

Financial Literacy Among Buffalo State College Undergraduate Students, Toni Martinucci

Public Administration Master’s Projects

Financial literacy can be complex and difficult for college students to comprehend. Many students struggle to afford college and are faced with large amounts of student loan debt. Financial awareness needs to be addressed early on for students to make informed decisions about college costs, student debt, and financial aid. However, financial aid applications, terms and conditions, and eligibility requirements are difficult for many students to comprehend on their own. The purpose of this study is to access financial literacy among undergraduate students at Buffalo State College. A quantitative approach is used in this study by implementing a web-based cross-sectional …

Cohen-Macaulay Type Of Weighted Path Ideals, Shuai Wei

All Dissertations

In this dissertation we give a combinatorial characterization of all the weighted $r$-path suspensions for which the $f$-weighted $r$-path ideal is Cohen-Macaulay. In particular, it is shown that the $f$-weighted $r$-path ideal of a weighted $r$-path suspension is Cohen-Macaulay if and only if it is unmixed. Type is an important invariant of a Cohen-Macaulay homogeneous ideal in a polynomial ring $R$ with coefficients in a field. We compute the type of $R/I$ when $I$ is any Cohen-Macaulay $f$-weighted $r$-path ideal of any weighted $r$-path suspension, for some chosen function $f$. In particular, this computes the type for all weighted trees …

Data Visualization, Dimensionality Reduction, And Data Alignment Via Manifold Learning, Andrés Felipe Duque Correa

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The high dimensionality of modern data introduces significant challenges in descriptive and exploratory data analysis. These challenges gave rise to extensive work on dimensionality reduction and manifold learning aiming to provide low dimensional representations that preserve or uncover intrinsic patterns and structures in the data. In this thesis, we expand the current literature in manifold learning developing two methods called DIG (Dynamical Information Geometry) and GRAE (Geometry Regularized Autoencoders). DIG is a method capable of finding low-dimensional representations of high-frequency multivariate time series data, especially suited for visualization. GRAE is a general framework which splices the well-established machinery from kernel …

Convexity Of Regularized Optimal Transport Dissimilarity Measures For Signed Signals, Christian P. Fowler

Mathematics & Statistics ETDs

Debiased Sinkhorn divergence (DS divergence) is a distance function of

regularized optimal transport that measures the dissimilarity between two

probability measures of optimal transport. This thesis analyzes the advantages of

using DS divergence when compared to the more computationally expensive

Wasserstein distance as well as the classical Euclidean norm. Specifically, theory

and numerical experiments are used to show that Debiased Sinkhorn divergence

has geometrically desirable properties such as maintained convexity after data

normalization. Data normalization is often needed to calculate Sinkhorn

divergence as well as Wasserstein distance, as these formulas only accept

probability distributions as inputs and do not directly …

Statistical Methods For Differential Gene Expression Analysis Under The Case-Cohort Design, Lidong Wang

Mathematics & Statistics ETDs

Differential gene expression analysis has the potential to discover candidate biomarkers, therapeutic targets, and gene signatures. How to save money when using an unaffordable sample is a practical question. The case-cohort (CCH) study design can blend the economy of case-control studies with the advantages of cohort studies. But it has not been seen in the medical research literature where high-throughput genomic data were involved.

A score test does not need to fit the Cox PH model iteratively; hence, it can save computing time and avoid potential convergence issues. We developed a score test under the CCH design to identify DEGs …

Functional Data Analysis Of Covid-19, Nichole L. Fluke

Mathematics & Statistics ETDs

This thesis deals with Functional Data Analysis (FDA) on COVID data. The Data involves counts for new COVID cases, hospitalized COVID patients, and new COVID deaths. The data used is for all the states and regions in the United States. The data starts in March 1^st, 2020 and goes through March 31^st, 2021. The FDA smooths the data and looks to see if there are similarities or differences between the states and regions in the data. The data also shows which states and regions stand out from the others and which ones are similar. Also shown …

Music Genre Classification By Convolutional Neural Networks, Usame Suud

Mathematics & Statistics ETDs

In today’s world, deep learning models are widely used in a variety of fields. Audio

applications include speech recognition, audio classification, and music information

retrieval. In this paper, we will focus on the classification of music genres using an

artificial neural network. The development of audio machine learning techniques has

created an independence from traditional, more time-consuming signal processing

techniques. Starting with raw audio data, we will gain an understanding of what

audio is and its digital representation. Then, the focus will be on obtaining frequency

information from audio signals through the use of spectrograms. Transforming the

spectrograms into the …

Fractal Like Snowflakes Generated By Non-Contractive Function Systems, William H. Kelly Iii

LSU Master's Theses

At the heart of this thesis is the examination of a non-contractive iterative function system T on the Hausdorff metric space of all compact subset of ℝ . Despite the absence of an 2 attracting fixed point, an examination reveals the appearance of fractal-like shapes (snowflakes) when applying the Barnsley’ random walk method to study the iterative sequence ��ⁿ(0) (�� ∈ ℕ) for �� = ��¹ ∪ ��² ∪ ��³, where ��₁(��) = ����, ��₂(��) = ���� + ��, and ��₃(��) = ���� - ��, and �� = …

On The Projections Of Commutative C*-Algebras, Alaa Ahmad Hamdan

Theses

Gelfand and Naimark proved that the Banach algebra of continuous complex-valued functions on a compact space Ω is the only example of commutative unital C*-algebras. We study the C*-algebra C(Ω) and its main elements, such as projections. Also, we discuss the mapping between projections, which preserves orthogonality (orthoisomorphism). A bijective θ between projections induces a bijective Θ between the Boolean algebra of clopen subsets of X. Then, we give main properties of such Θ. For a compact subset X of ℝ, we classify the projections of C(X) by introducing the similar relation on P(C(X)). We introduce an …

Manufacturability And Analysis Of Topologically Optimized Continuous Fiber Reinforced Composites, Jesus A. Ferrand

Doctoral Dissertations and Master's Theses

Researchers are unlocking the potential of Continuous Fiber Reinforced Composites for producing components with greater strength-to-weight ratios than state of the art metal alloys and unidirectional composites. The key is the emerging technology of topology optimization and advances in additive manufacturing. Topology optimization can fine tune component geometry and fiber placement all while satisfying stress constraints. However, the technology cannot yet robustly guarantee manufacturability. For this reason, substantial post-processing of an optimized design consisting of manual fiber replacement and subsequent Finite Element Analysis (FEA) is still required.

To automate this post-processing in two dimensions, two (2) algorithms were developed. The …

Valuation Of Options In A High Volatile Regime Switching Market, Tasnim Mazen Sharif Alhamad

Theses

Financial modeling by Stochastic Differential Equations-SDEs with regime-switching has been utilized to allow moving from one economic state to another. The aim of this thesis is to tackle the pricing of European options under a regime-switching model where the volatility is augmented. Regime-switching models are more realistic since they encompass the effect of an external event on the underlying asset prices. But they are challenging, considering in addition increased volatility in the model will for sure make the option pricing problem more complicated and its solution may not exist analytically. Numerical methods for finance could be very helpful in this …

Numerical Methods For Locating Zeros Of Polynomial Systems Using Resultant, Ayade Salah Abdelmalk

Theses

In this thesis, we modify two methods for locating zeros of polynomial systems which are one dimensional path following and Lanczos method. Both approaches are based on calculating the resultant matrix corresponding to each variable in the system. These methods are stable and preserving the spareness of these matrices. These methods are developed to avoid using the zeros of the multiresultant of each variable which are condition problems. Theoretical and numerical results will be given to show the efficiency of these methods. Finally, algorithms for the Mathematica codes are given.

Applications Of Statistical Physics To Ecology: Ising Models And Two-Cycle Coupled Oscillators, Vahini Reddy Nareddy

Doctoral Dissertations

Many ecological systems exhibit noisy period-2 oscillations and, when they are spatially extended, they undergo phase transition from synchrony to incoherence in the Ising universality class. Period-2 cycles have two possible phases of oscillations and can be represented as two states in the bistable systems. Understanding the dynamics of ecological systems by representing their oscillations as bistable states and developing dynamical models using the tools from statistical physics to predict their future states is the focus of this thesis. As the ecological oscillators with two-cycle behavior undergo phase transitions in the Ising universality class, many features of synchrony and equilibrium …

A Representation For Cmc 1 Surfaces In H^3 Using Two Pairs Of Spinors, Tetsuya Nakamura

Doctoral Dissertations

For Bryant's representation $\Phi\colon \widetilde{M} \rightarrow \SL_2(\C)$ of a constant mean curvature (CMC) $1$ surface $f\colon M\rightarrow \Hyp^3$ in the $3$-dimensional hyperbolic space $\Hyp^3$, we will give a formula expressed only by the global $\tbinom{P}{Q}$ and local $\tbinom{p}{q}$ spinors and their derivatives. We will see that this formula is derived from the Klein correspondence, understanding $\Phi$ as a null curve immersion into a $3$-dimensional quadric. We will show that, if $f$ is a CMC $1$ surface with smooth ends modeled on a compact Riemann surface, the linear change of $\tbinom{P}{Q}\oplus \tbinom{p}{-q}$ by some $\Sp(\C^4)$ matrices gives rise to a transformtion …

Combinatorial Algorithms For Graph Discovery And Experimental Design, Raghavendra K. Addanki

Doctoral Dissertations

In this thesis, we study the design and analysis of algorithms for discovering the structure and properties of an unknown graph, with applications in two different domains: causal inference and sublinear graph algorithms. In both these domains, graph discovery is possible using restricted forms of experiments, and our objective is to design low-cost experiments. First, we describe efficient experimental approaches to the causal discovery problem, which in its simplest form, asks us to identify the causal relations (edges of the unknown graph) between variables (vertices of the unknown graph) of a given system. For causal discovery, we study algorithms …

Accelerating Multiparametric Mri For Adaptive Radiotherapy, Shraddha Pandey

USF Tampa Graduate Theses and Dissertations

MR guided Radiotherapy (MRgRT) marks an important paradigm shift in the field of radiotherapy. Superior tissue contrast of MRI offers better visualization of the abnormal lesions, as a result precise radiation dose delivery is possible. In case of online treatment planning, MRgRT offers better control of intratumoral motion and quick adaptation to changes in the gross tumor volume. Nonetheless, the MRgRT process flow does suffer from some challenges that limit its clinical usability. The primary aspects of MRgRT workflow are MRI acquisition, tumor delineation, dose map prediction and administering treatment. It is estimated that the acquisition of MRI takes around …

A Cluster Structure On The Coordinate Ring Of Partial Flag Varieties, Fayadh Kadhem

LSU Doctoral Dissertations

The main goal of this dissertation is to show that the (multi-homogeneous) coordinate ring of a partial flag variety C[G/P_K^−] contains a cluster algebra for every semisimple complex algebraic group G. We use derivation properties and a canonical lifting map to prove that the cluster algebra structure A of the coordinate ring C[N_K] of a Schubert cell constructed by Goodearl and Yakimov can be lifted, in an explicit way, to a cluster structure \hat{A} living in the coordinate ring of the corresponding partial flag variety. Then we use a minimality condition to prove that the cluster algebra \hat{A} is equal …

Determining The Idealizers Of Principal Monomial Ideals Over A Rational Normal Curve, Perla A. Maldonado Cortez

Mathematics & Statistics ETDs

Given an ideal J generated by an element of the form sm1 tm2 , where
m1 ≥ 2 and m2 ≥ 0, we illustrate how to compute the idealizer I(J) over the ring
of the rational normal curve of degree n and we give a formula for it using the
graded pieces of the sets of differential operators.

Transcriptional Profile Of Cohesin Complex Mutations In The Background Of Npm1 And Runx1-Runx1t1 Aml, Jacob Tiegs

Master's Theses (2009 -)

Acute Myeloid Leukemia is a cancer of the blood, characterized by a heterogenous mixture of disease causing mutations. Mutations of the cohesin complex is a group of such mutations and occur alongside several other driving mutations in the development of Acute Myeloid Leukemia. This thesis specifically focuses on cohesin complex mutations in the context of concurrence with NPM1 mutation and the Core Binding Factor (CBF) mutation RUNX1-RUNX1T1 in three distinct components. The first two components involved Differential Expression Analysis (DEA) to identify significantly differentiated genes in each model, followed by Gene Set Enrichment Analysis (GSEA) to identify Gene Ontology (GO) …