Physical Sciences and Mathematics Commons^™

Conditional Constrained And Unconstrained Quantization For A Uniform Distribution On A Hexagon, Christina Hamilton

Theses and Dissertations

In this thesis, we have considered a uniform distribution on a regular hexagon and the set of all its six vertices as a conditional set. For the uniform distribution under the conditional set first, for all positive integers n ≥ 6, we obtain the conditional optimal sets of n-points and the nth conditional quantization errors, and then we calculate the conditional quantization dimension and the conditional quantization coefficient in the unconstrained scenario. Then, for the uniform distribution on the hexagon taking the same conditional set, we investigate the conditional constrained optimal sets of n-points and the conditional constrained quantization errors …

A Multivariate Analysis Of The Gravitational Wave Signal Landscape From Core Collapse Supernovae, Raul Alberto Espinosa Perez

Theses and Dissertations

Core collapse supernovae (CCSN) are highly anticipated sources of gravitational waves (GW) during the on-going fourth observation run (O4) of GW detectors like LIGO and the future observation runs. The GW signal from the CCSN cannot be modeled mathematically. Several groups around the world have engaged in simulation of the predicted GW signals from CCSN sources. These simulations are carried out in supercomputers, and they incorporate general relativity, hydrodynamics, neutrino physics, mass and angular momentum of the stellar progenitor and nuclear equations of state (EoS). The output consists of simulated signals with varying duration, peak frequency, GW energy and time-frequency …

Bayesian Estimation Of Reproduction Numbers From Distributions Of Outbreaks Sizes: Branching Process Approach, Alberta Araba Johnson

Theses and Dissertations

The Generalized Poisson distribution is useful in modeling epidemiological processes as a branching stochastic processes problem. Our goal is to construct accurate and reliable estimators for the reproduction number (R0) (i.e., the number of secondary infections), particularly in the context of disease outbreaks modeled by a Galton-Watson process. Towards this goal, we construct the classical Bayes estimator, the Maximum Likelihood estimator, and the Empirical Bayes (EB) estimator under the Square Error Loss function in Chapter II. We prove that the Empirical Bayes estimator is asymptotically optimal and estimate the rate of convergence. We then proceed to monotonize the Empirical Bayes …

Mitigation Methods For Instrumental Artifacts In Gravitational Wave Data, Raghav Girgaonkar

Theses and Dissertations

Strain data from ground-based gravitational wave detectors are regularly affected by instrumental artifacts known as glitches. Such glitches form the background of false alarms in the detection of gravitational waves from compact binary coalescences, in-turn reducing search sensitivity. If left unaccounted, these glitches along with other non-stationarity may also contribute towards a corrupted representation of the statistical properties of detector noise, subsequently affecting parameter estimation for detected gravitational wave candidates. Therefore, effective data analysis methods to veto glitches and identify non-stationarities in detector data are crucial to enhancing the sensitivity of a gravitational wave search. In this thesis, we …

Conditional Quantization For Uniform Distributions On Line Segments And Regular Polygons, Tsianna Danielle Dominguez

Theses and Dissertations

Quantization for a Borel probability measure refers to the idea of estimating a given probability by a discrete probability with support containing a finite number of elements. If in the quantization some of the elements in the support are preselected, then the quantization is called a conditional quantization. In this thesis, we have investigated the conditional quantization for the uniform distributions defined on the unit line segments and m-sided regular polygons, where m ≥ 3, inscribed in a unit circle.

Variational Bias Sampling For Collaborative Filtering Recommender Systems, Prisca Stephens

Theses and Dissertations

Advancements in digitalization has yielded enormous growth of data on online platforms, overwhelming users with multitude of options to choose from. Recommender systems narrow down these options to a few relevant ones thereby facilitating the decision-making processes for users. This study presents a framework for integrating variational bias sampling into model-based collaborative filtering techniques for recommender systems. Variational bias sampling is a novel and unique way to account for random factors that affect explicit ratings in collaborative filtering recommender systems. A Gaussian distribution is used to model all the possible random factors that could affect ratings. Sampling user and item …

A Study Of Quantitative Reasoning Instructors’ Choices And Motivations When Teaching Quantitative Reasoning For The First Time, Trish Ann Harding

Theses and Dissertations

This qualitative study delves into the instructional decision-making processes of post-secondary instructors teaching quantitative reasoning (QR) courses for the first time. The study aims to address the gap in understanding how first-time QR instructors navigate the complexities of curriculum design and pedagogical strategies, and how these experiences contribute to their professional development. The research questions center on identifying the instructional decisions made by these instructors, exploring the factors influencing their decision-making, and understanding the impact of exercising agency has on their professional development. Through in-depth exploration, this study seeks to shed light on the challenges and opportunities faced by first-time …

How Mathematics Instructors Foster The Development Of Black Students' Mathematics Identity In Undergraduate Active Learning Mathematics Courses, Ashly J. Olusanya

Theses and Dissertations

Black students must overcome unique challenges to succeed in mathematics. Educators are tasked with identifying equitable teaching practices to support these students. Active learning (AL) is a teaching pedagogy that engages students in rigorous mathematical activities and encourages student participation. This research study will explore the professors’ beliefs about how students learn mathematics and why they use active learning in their collegiate mathematics courses. The study explores the connections between these beliefs and their reported use of instructional practices. The study also identifies the instructors’ beliefs about developing students’ mathematics identities, particularly their Black …

A Study On A Vector Complex Modified Korteweg-De Vries Equation, Changyan Shi

Theses and Dissertations

In this thesis, we systematically study a vector complex modified Kordeweg-de Vries equation by combining Hirota's bilinear method and the the Kadomtsev–Petviashvili (KP) reduction method. This vector nonlinear equation is a multi-component generalization of the well-known modified Kordeweg-de Vries (mKdV) equation and can be reduced to the known Hirota equation, Sasa-Satsuma (SS) equation, Sasa-Satsuma-mKdV equation as well as coupled Sasa-Satsuma equation. First, we bilinearize the vector complex mKdV equation under both the zero and nonzero boundary conditions by introducing auxiliary tau functions. Then, starting from two sets of bilinear equations of multi-component KP hierarchy and single-component KP-Toda …

Soil Carbon Sequestration Efforts In Arid And Semi-Arid Climates Under Conservation Agriculture And Reforestation, Samantha Lynn Colunga

Theses and Dissertations

Soil organic carbon (SOC) plays a vital role in the global carbon cycle and aids in climate change mitigation. However, deforestation and intensive agricultural practices threaten topsoil and carbon (C) pools through soil disturbances releasing vast amounts of carbon dioxide (CO2) by enhancing the decomposition of organic materials. Degraded soils typically lack stable aggregates, nutrient and water retention, and overall low fertility. In arid and semi-arid regions, soils are in an even more dire situation, as low precipitation and high temperatures slow down the accumulation of SOC. This thesis has two objectives: 1) to evaluate whether conservation tillage practices increase …

Ramanujan Type Congruences For Quotients Of Klein Forms, Timothy Huber, Nathaniel Mayes, Jeffery Opoku, Dongxi Ye

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

In this work, Ramanujan type congruences modulo powers of primes p≥5 are derived for a general class of products that are modular forms of level p. These products are constructed in terms of Klein forms and subsume generating functions for t-core partitions known to satisfy Ramanujan type congruences for p=5,7,11. The vectors of exponents corresponding to products that are modular forms for Γ1(p) are subsets of bounded polytopes with explicit parameterizations. This allows for the derivation of a complete list of products that are modular forms for Γ1(p) of weights 1≤k≤5 for primes 5≤p≤19 and whose Fourier coefficients …

Local Existence Of Solutions To A Nonlinear Autonomous Pde Model For Population Dynamics With Nonlocal Transport And Competition, Michael R. Lindstrom

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Highlights

• Partial differential equation models are ubiquitous in applied sciences.

• A partial differential equation based in ecology is studied for solution existence.

• Energy methods and convergence analysis lead to local classical solutions.

Abstract

In this paper, we prove that a particular nondegenerate, nonlinear, autonomous parabolic partial differential equation with nonlocal mass transfer admits the local existence of classical solutions. The equation was developed to qualitatively describe temporal changes in population densities over space through accounting for location desirability and fast, long-range travel. Beginning with sufficiently regular initial conditions, through smoothing the PDE and employing energy arguments, we obtain a sequence …

Remnant Polarization And Structural Arrangement In P(Vdf-Trfe) Electrospun Fiber Meshes Affect Osteogenic Differentiation Of Human Mesenchymal Stromal Cells, Bahareh Azimi, Massimiliano Labardi, Mohammad Sajad Sorayani Bafqi, Teresa Macchi, Claudio Ricci, Veronica Carnicelli, Lorenzo Scarpelli, Istiak Hussain, Francesca Matino, Mohammed Uddin

Physics and Astronomy Faculty Publications and Presentations

Highlights

• The type of solvent had noticeable effects on morphology and piezoelectric properties of P(VDF-TrFE) electrospun fibers.

• Using MEK as a solvent and specific environmental conditions led to the obtainment of surface nanopores.

• Uniaxially aligned fibers exhibited higher β phase and mechanical properties than random ones.

• Randomly oriented fibers had higher remnant piezoelectric properties (Vout, d31 piezoelectric coefficient) than aligned ones.

• Human mesenchymal stem cells cultured on randomly oriented fibers showed an accelerated osteogenic differentiation.

Abstract

Many tissues and cells are influenced by mechano-electric stimulation, thus the application of piezoelectric materials has recently received considerable attention in tissue engineering. …

Weighted Ehrhart Theory: Extending Stanley's Nonnegativity Theorem, Esme Bajo, Robert Davis, Jesús A. De Loera, Alexey Garber, Sofía Garzón Mora, Katharina Jochemko, Josephine Yu

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

We generalize R. P. Stanley's celebrated theorem that the h∗-polynomial of the Ehrhart series of a rational polytope has nonnegative coefficients and is monotone under containment of polytopes. We show that these results continue to hold for weighted Ehrhart series where lattice points are counted with polynomial weights, as long as the weights are homogeneous polynomials decomposable as sums of products of linear forms that are nonnegative on the polytope. We also show nonnegativity of the h∗-polynomial as a real-valued function for a larger family of weights.

We generalize R. P. Stanley's celebrated theorem that the h ⁎ -polynomial of …

Statistics For Iwasawa Invariants Of Elliptic Curves, Ii, Debanjana Kundu, Anwesh Ray

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

We study the average behavior of the Iwasawa invariants for Selmer groups of elliptic curves. These results lie at the intersection of arithmetic statistics and Iwasawa theory. We obtain lower bounds for the density of rational elliptic curves with prescribed Iwasawa invariants.

A Search For Intermediate-Mass Black Holes In Compact Stellar Systems Through Optical Emissions From Tidal Disruption Events, Richard T. Pomeroy, Mark A. Norris

Physics and Astronomy Faculty Publications and Presentations

Intermediate-mass black holes (IMBH) are expected to exist in globular clusters (GCs) and compact stellar systems (CSS) in general, but none have been conclusively detected. Tidal disruption events (TDEs), where a star is tidally disrupted by the gravitational field of a black hole, have been observed to occur around the supermassive black holes (SMBH) found at the centres of galaxies, and should also arise around IMBHs, especially in the dense stellar cores of CSS's. However, to date none have been observed in such environments. Using data from the Zwicky Transient Facility (ZTF) we search for TDEs associated with CSS, but …

Search For Extreme Mass Ratio Inspirals Using Particle Swarm Optimization And Reduced Dimensionality Likelihoods, Xiao-Bo Zou, Soumya Mohanty, Hong-Gang Luo, Yu-Xiao Liu

Physics and Astronomy Faculty Publications and Presentations

Extreme-mass-ratio inspirals (EMRIs) are significant observational targets for spaceborne gravitational wave detectors, namely, LISA, Taiji, and Tianqin, which involve the inspiral of stellar-mass compact objects into massive black holes (MBHs) with a mass range of approximately 104 ∼107𝑀⊙ . EMRIs are estimated to produce long-lived gravitational wave signals with more than 105 cycles before plunge, making them an ideal laboratory for exploring the strong-gravity properties of the spacetimes around the MBHs, stellar dynamics in galactic nuclei, and properties of the MBHs itself. However, the complexity of the waveform model, which involves the superposition of multiple harmonics, as well as the …

Study Of Hybrid Nanofluid Flow In A Stationary Cone-Disk System With Temperature-Dependent Fluid Properties, A. S. John, Mahanthesh Basavarajappa, G. Lorenzini

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Cone-disk systems find frequent use such as conical diffusers, medical devices, various rheometric, and viscosimetry applications. In this study, we investigate the three-dimensional flow of a water-based Ag-MgO hybrid nanofluid in a static cone-disk system while considering temperature-dependent fluid properties. How the variable fluid properties affect the dynamics and heat transfer features is studied by Reynolds’s linearized model for variable viscosity and Chiam’s model for variable thermal conductivity. The single-phase nanofluid model is utilized to describe convective heat transfer in hybrid nanofluids, incorporating the experimental data. This model is developed as a coupled system of convective-diffusion equations, encompassing the conservation …

Reevaluating The Origin Of Detectable Cataclysmic Variables In Globular Clusters: Testing The Importance Of Dynamics, Liliana Rivera Sandoval, Diogo Belloni, Miriam Ramos Arevalo

Physics and Astronomy Faculty Publications and Presentations

Based on the current detectable cataclysmic variable (CV) population in Galactic globular clusters (GCs), we show that there is not a clear relation between the number of sources per unit of mass and the stellar encounter rate, the cluster mass, or the cluster central density. If any, only in the case of core-collapsed GCs could there be an anticorrelation with the stellar encounter rate. Our findings contrast with previous studies where clear positive correlations were identified. Our results suggest that correlations between faint X-ray sources, from which often conclusions for the CV population are drawn, and the GC parameters considered …

Normalized Ground State Of A Mixed Dispersion Nonlinear Schrodinger Equation With Combined Power-Type Nonlinearities, Zhouji Ma, Xiaojun Chang, Zhaosheng Feng

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

We study the existence of normalized ground state solutions to a mixed dispersion fourth-order nonlinear Schrodinger equation with combined power-type nonlinearities. By analyzing the subadditivity of the ground state energy with respect to the prescribed mass, we employ a constrained minimization method to establish the existence of ground state that corresponds to a local minimum of the associated functional. Under certain conditions, by studying the monotonicity of ground state energy as the mass varies, we apply the constrained minimization arguments on the Nehari-Pohozaev manifold to prove the existence of normalized ground state solutions.

A Joint Fermi-Gbm And Swift-Bat Analysis Of Gravitational-Wave Candidates From The Third Gravitational-Wave Observing Run, C. Fletcher, J. Wood, R. Hamburg, Michael G. Benjamin, Teviet Creighton, Mario C. Diaz, Francisco Llamas, Soma Mukherjee, Gaukhar Nurbek, Volker Quetschke, Wenhui Wang

Physics and Astronomy Faculty Publications and Presentations

We present Fermi Gamma-ray Burst Monitor (Fermi-GBM) and Swift Burst Alert Telescope (Swift-BAT) searches for gamma-ray/X-ray counterparts to gravitational-wave (GW) candidate events identified during the third observing run of the Advanced LIGO and Advanced Virgo detectors. Using Fermi-GBM onboard triggers and subthreshold gamma-ray burst (GRB) candidates found in the Fermi-GBM ground analyses, the Targeted Search and the Untargeted Search, we investigate whether there are any coincident GRBs associated with the GWs. We also search the Swift-BAT rate data around the GW times to determine whether a GRB counterpart is present. No counterparts are found. Using both the Fermi-GBM Targeted Search …

The Invariantring Package For Macaulay2, Luigi Ferraro, Federico Galetto, Francesca Gandini, Hang Huang, Matthew Mastroeni, Xianglong Ni

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

We describe a significant update to the existing InvariantRing package for Macaulay2. In addition to expanding and improving the methods of the existing package for actions of finite groups, the updated package adds functionality for computing invariants of diagonal actions of tori and finite abelian groups, as well as invariants of arbitrary linearly reductive group actions. The implementation of the package has been completely overhauled with the aim of serving as a unified resource for invariant theory computations in Macaulay2.

New Ways To Improve Dispersibility Of Nanotubes: Approaching From The Formation Of Silicon Nanoparticles By High Energy Reactive Ball Milling (Herbm) In Polar Solvents, Julie P. Vanegas, Yolanda V. Gutierrez, Joaquin Rivera, Juan García Jr.

Research Symposium

Background: This research aims to synthesize stable silicon nanoparticles using different molar ratios of N-Cyclohexyl-2-pyrrolidone (CHP) and Silicon to demonstrate if there is any significance towards the production of effective nanotubes. To determine this, the synthesized nanoparticles will be characterized by scanning electron microscopy (SEM), UV visible absorption spectroscopy, and photoluminescence spectroscopy (PL).

Methods: 50 Mg of silicon wafer are added with differing ratios of ligand (CHP), 5mL of water, and 3 steel iron balls into a ball milling vial. Vials are then placed into a ball milling apparatus for 7 cycles or 3.5 hours. Once the cycles are complete, …

Mechanistic Investigation Of C—C Bond Activation Of Phosphaalkynes With Pt(0) Complexes, Roberto M. Escobar, Abdurrahman C. Ateşin, Christian Müller, William D. Jones, Tülay Ateşin

Research Symposium

Carbon–carbon (C–C) bond activation has gained increased attention as a direct method for the synthesis of pharmaceuticals. Due to the thermodynamic stability and kinetic inaccessibility of the C–C bonds, however, activation of C–C bonds by homogeneous transition-metal catalysts under mild homogeneous conditions is still a challenge. Most of the systems in which the activation occurs either have aromatization or relief of ring strain as the primary driving force. The activation of unstrained C–C bonds of phosphaalkynes does not have this advantage. This study employs Density Functional Theory (DFT) calculations to elucidate Pt(0)-mediated C–CP bond activation mechanisms in phosphaalkynes. Investigating the …

La1-Xsrxcoo3 Perovskite Nanomaterial: Synthesis, Characterization, And Its Biomedical Application, Adhira Tippur, Anyet Shohag, Luke Franco, Ahmed Touhami, Swati Mohan, Mohammed Uddin

Research Symposium

Early cancer detection is paramount for effective treatment and potential cures. This research explores the application of perovskite materials, specifically Sr2+-doped Lanthanum Cobaltite (La1-xSrxCoO3) nanomaterials, in cancer detection, with a focus on rats as an experimental model. The ferroelectric nature of these materials, synthesized through a combination of sol-gel and molten-salt processes, was examined at varying Sr2+ doping levels (1-20 wt%). Rigorous characterization, employing X-ray diffraction and scanning electron microscopy, confirmed the uniform morphology of nano cubes, laying the foundation for subsequent investigations. The magnetic properties of the perovskite nanoparticles were probed, suggesting their potential as a diagnostic tool for …

Ex-Vivo Hippocampus Segmentation Using Diffusion-Weighted Mri, Haoteng Tang, Siyuan Dai, Eric M. Zou, Guodong Liu, Ryan Ahearn, Ryan Krafty, Michel Modo, Liang Zhan

Computer Science Faculty Publications and Presentations

The hippocampus is a crucial brain structure involved in memory formation, spatial navigation, emotional regulation, and learning. An accurate MRI image segmentation of the human hippocampus plays an important role in multiple neuro-imaging research and clinical practice, such as diagnosing neurological diseases and guiding surgical interventions. While most hippocampus segmentation studies focus on using T1-weighted or T2-weighted MRI scans, we explore the use of diffusion-weighted MRI (dMRI), which offers unique insights into the microstructural properties of the hippocampus. Particularly, we utilize various anisotropy measures derived from diffusion MRI (dMRI), including fractional anisotropy, mean diffusivity, axial diffusivity, and radial diffusivity, for …

Assessing Gait Metrics For Early Parkinson's Disease Prediction: A Preliminary Analysis Of Underfit Models, Daniel Salinas, Gerardo Medellin, Katherine Bolado, Tomas Gomez, Kelsey Potter-Baker, Nawaz Khan Abdul Hack, Ramu Vadukapuram

Research Symposium

Background: Parkinson's Disease (PD) is characterized by both motor and non-motor symptoms, and its diagnosis primarily relies on clinical presentation. There is a growing need for diagnostic tools to identify the early signs of PD, particularly the initial motor impairments often manifested as gait abnormalities. Here we seek to present preliminary findings to address this need. Our study focuses on using Machine Learning techniques (ML) to predict the PD clinical stage most efficiently and accurately. Specifically, we have sought to evaluate how spatiotemporal characteristics and other locomotor performance variables obtained on a walkway system can be utilized to identify the …

Assessment Of Mucin 13 (Muc13) As An Imaging Target For Guiding Colorectal Cancer Treatment: A Pathway Towards Theranostic Development, Ryan P. Coll, Aiko Yamaguchi, Jianbo Wang, Xiaoxia Wen, Denise Hernandez, Subhash C. Chauhan, H. Charles Manning

Research Symposium

Background: A theranostic strategy combining diagnostic imaging and targeted therapy in a single regimen is proposed for improved management and treatment of colorectal cancer (CRC). Increased specificity in detection by the noninvasive imaging technique positron emission tomography (PET) can be achieved by radiolabeling antibodies (Abs) designed to target tumor-associated antigens with increased expression post-translational modifications present in cancer cells. In this study, an Ab designed to target the transmembrane glycoprotein mucin 13 (MUC13) was radiolabeled with the positron-emitting radionuclide zirconium-89 (⁸⁹Zr) for PET imaging of a xenograft mouse model of CRC. Specified uptake of this radioimmunoconjugate was observed …

Adsorption Of Crystal Violet Dye From Synthetic Wastewater By Ball-Milled Royal Palm Leaf Sheath, Neloy Sen, Nawrin Rahman Shefa, Kismot Reza, Sk Md Ali Zaker Shawon, Md. Wasikur Rahman

Physics and Astronomy Faculty Publications and Presentations

The current study shows that using a batch approach to remove crystal violet dye from synthetic wastewater is feasible when using royal palm leaf sheath powder as an adsorbent. In order to investigate the effects of many parameters, including starting concentration, pH effect, dye concentration, adsorbent dose, contact time, and temperature, experiments were carried out under various operating conditions. Maximum removal was obtained at pH 6 and at a concentration of 100 ppm, which are considered as ideal values. The influence of pH and dye concentration was shown to be substantial. Langmuir, Freundlich, and Temkin isotherm models were fitted to …

Possible Role Of Correlation Coefficients And Network Analysis Of Multiple Intracellular Proteins In Blood Cells Of Patients With Bipolar Disorder In Studying The Mechanism Of Lithium Responsiveness: A Proof-Concept Study, Keming Gao, Marzieh Ayati, Nicholas M. Kaye, Mehmet Koyutürk, Joseph R. Calabrese, Eric Christian, Hillard M. Lazarus, David Kaplan

Computer Science Faculty Publications and Presentations

Background: The mechanism of lithium treatment responsiveness in bipolar disorder (BD) remains unclear. The aim of this study was to explore the utility of correlation coefficients and protein-to-protein interaction (PPI) network analyses of intracellular proteins in monocytes and CD4+ lymphocytes of patients with BD in studying the potential mechanism of lithium treatment responsiveness. Methods: Patients with bipolar I or II disorder who were diagnosed with the MINI for DSM-5 and at any phase of the illness with at least mild symptom severity and received lithium (serum level ≥ 0.6 mEq/L) for 16 weeks were divided into two groups, responders (≥50% …