Physical Sciences and Mathematics Commons^™

Constrained Quantization For Probability Distributions, Megha Pandey, Mrinal Kanti Roychowdhury

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

In this paper, for a Borel probability measure P on a Euclidean space Rk, we extend the definitions of nth unconstrained quantization error, unconstrained quantization dimension, and unconstrained quantization coefficient, which traditionally in the literature known as nth quantization error, quantization dimension, and quantization coefficient, to the definitions of nth constrained quantization error, constrained quantization dimension, and constrained quantization coefficient. The work in this paper extends the theory of quantization and opens a new area of research. In unconstrained quantization, the elements in an optimal set are the conditional expectations in their own Voronoi regions, and it is not true …

Flow Patterns For Newtonian And Non-Newtonian Fluids In A Cylindrical Pipe, Erick Sanchez, Dambaru Bhatta

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

A fully developed laminar steady flow of an incompressible, viscous fluid in a horizontal cylindrical pipe is considered here. Flow patterns for an incompressible, viscous fluid for both Newtonian and non-Newtonian fluids such as shear-thinning, shear-thickening and Bingham plastic fluids are analyzed in this study. Assuming that the flow is only due to the wall shear stress and the pressure drop, the velocity component in the axial direction for these cases is derived. Computational results of the velocity profiles for various cases are obtained using MATLAB and presented in graphical forms. It is observed that the velocity profile is parabolic …

Equity In Focus : Investigating Gender Disparities In Glioblastoma Via Propensity Score Matching, Solomon Eshun

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Gender disparities in health outcomes have garnered significant attention, prompting investigations into their underlying causes. Glioblastoma (GBM), a devastating and highly aggressive form of brain tumor, serves as a case for such inquiries. Despite the mounting evidence on gender disparities in GBM outcomes, investigations specific at the molecular level remain scarce and often limited by confounding biases in observational studies. In this study, I aimed to investigate the gender-related differences in GBM outcomes using propensity score matching (PSM) to control for potential confounding variables. The data used was accessed from the Cancer Genome Atlas (TCGA), encompassing factors such as gender, …

Intellibeehive: An Automated Honey Bee, Pollen, And Varroa Destructor Monitoring System, Christian I. Narcia-Macias, Joselito Guardado, Jocell Rodriguez, Joanne Rampersad, Erik Enriquez, Dong-Chul Kim

Computer Science Faculty Publications and Presentations

Utilizing computer vision and the latest technological advancements, in this study, we developed a honey bee monitoring system that aims to enhance our understanding of Colony Collapse Disorder, honey bee behavior, population decline, and overall hive health. The system is positioned at the hive entrance providing real-time data, enabling beekeepers to closely monitor the hive's activity and health through an account-based website. Using machine learning, our monitoring system can accurately track honey bees, monitor pollen-gathering activity, and detect Varroa mites, all without causing any disruption to the honey bees. Moreover, we have ensured that the development of this monitoring system …

Probabilistic Solutions Of Fractional Differential And Partial Differential Equations And Their Monte Carlo Simulations, Tamer Oraby, Erwin Suazo, Harrinson Arrubla

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

The work in this paper is four-fold. Firstly, we introduce an alternative approach to solve fractional ordinary differential equations as an expected value of a random time process. Using the latter, we present an interesting numerical approach based on Monte Carlo integration to simulate solutions of fractional ordinary and partial differential equations. Thirdly, we show that this approach allows us to find the fundamental solutions for fractional partial differential equations (PDEs), in which the fractional derivative in time is in the Caputo sense and the fractional in space one is in the Riesz–Feller sense. Lastly, using Riccati equation, we …

Long-Time Asymptotics Of A Complex Cubic Camassa-Holm Equation, Hongyi Zhang, Yufeng Zhang, Zhijun Qiao

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

n this paper, we study the Cauchy problem of the following complex cubic Camassa-Holm (ccCH) equation mt=bux+12[m(|u|2−|ux|2)]x−12m(uu¯x−uxu¯),m=u−uxx,

where b is an arbitrary real constant. %By applying ∂¯-steepest descent method, l Long-time asymptotics of the equation is obtained through the ∂¯-steepest descent method. Firstly, based on the spectral analysis of the Lax pair and scattering matrix, the solution of the equation is able to be constructed %can be expressed by %the solution of via solving the corresponding Riemann-Hilbert problem (RHP). Then, we present %obtain different long time asymptotic expansions of the solution u(y,t) in different space-time solitonic regions of ξ=y/t. The …

Classification On Boundary-Equilibria And Singular Continuums Of Continuous Piecewise Linear Systems, Hebai Chen, Zhaosheng Feng, Hao Yang, Linfeng Zhou

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

In this paper, we show that any switching hypersurface of n -dimensional continuous piecewise linear systems is an (n−1) -dimensional hyperplane. For two-dimensional continuous piecewise linear systems, we present local phase portraits and indices near the boundary equilibria (i.e. equilibria at the switching line) and singular continuum (i.e. continuum of nonisolated equilibria) between two parallel switching lines. The index of singular continuum is defined. Then we show that boundary-equilibria and singular continuums can appear with many parallel switching lines.

Circle Actions On Oriented 4-Manifolds, Donghoon Jang, Oleg R. Musin

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

In the present paper, we consider an action of the circle group on a compact oriented 4-manifold. We derive the Atiyah-Hirzebruch formula for the manifold, and associate a graph in terms of data on the fixed point set. We show in the case of isolated fixed points that if an abstract graph satisfies the Atiyah-Hirzebruch formula, then there exists a corresponding 4-dimensional oriented S1-manifold.

Rogue Peakon, Well-Posedness, Ill-Posedness And Blow-Up Phenomenon For An Integrable Camassa-Holm Type Equation, Mingxuan Zhu, Zhenteng Zeng, Zaihong Jiang, Baoqiang Xia, Zhijun Qiao

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

In this paper, we study an integrable Camassa-Holm (CH) type equation with quadratic nonlinearity. The CH type equation is shown integrable through a Lax pair, and particularly the equation is found to possess a new kind of peaked soliton (peakon) solution - called {\sf rogue peakon}, that is given in a rational form with some logarithmic function, but not a regular traveling wave. We also provide multi-rogue peakon solutions. Furthermore, we discuss the local well-posedness of the solution in the Besov space Bsp,r with 1≤p,r≤∞ , s>max{1+1/p,3/2} or B3/22,1 , and then prove the ill-posedness of the solution in …

Quantization Dimension For Inhomogeneous Bi-Lipschitz Ifs, Amit Priyadarshi, Mrinal Kanti Roychowdhury, Manuj Verma

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Let ν be a Borel probability measure on a d-dimensional Euclidean space Rd, d≥1, with a compact support, and let (p0,p1,p2,…,pN) be a probability vector with pj>0 for 1≤j≤N. Let {Sj:1≤j≤N} be a set of contractive mappings on Rd. Then, a Borel probability measure μ on Rd such that μ=∑Nj=1pjμ∘S−1j+p0ν is called an inhomogeneous measure, also known as a condensation measure on Rd. For a given r∈(0,+∞), the quantization dimension of order r, if it exists, denoted by Dr(μ), of a Borel probability measure μ on Rd represents the speed at which the nth quantization error of order r …

On The Total Perimeter Of Disjoint Convex Bodies, Arseniy Akopyan, Alexey Glazyrin

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

In this note we introduce a pseudometric on convex planar curves based on distances between normal lines and show its basic properties. Then we use this pseudometric to give a short proof of the theorem by Pinchasi that the sum of perimeters of k convex planar bodies with disjoint interiors contained in a convex body of perimeter p and diameter d is not greater than p+2(k−1)d.

Quantization For A Set Of Discrete Distributions On The Set Of Natural Numbers, Juan Gomez, Haily Martinez, Mrinal Kanti Roychowdhury, Alexis Salazar, Daniel J. Vallez

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

The quantization scheme in probability theory deals with finding a best approximation of a given probability distribution by a probability distribution that is supported on finitely many points. In this paper, first we state and prove a theorem, and then give a conjecture. We verify the conjecture by a few examples. Assuming that the conjecture is true, for a set of discrete distributions on the set of natural numbers we have calculated the optimal sets of n-means and the nth quantization errors for all positive integers n. In addition, the quantization dimension is also calculated.

Gwtc-2.1: Deep Extended Catalog Of Compact Binary Coalescences Observed By Ligo And Virgo During The First Half Of The Third Observing Run, R. Abbott, T. D. Abbott, F. Acernese, K. Ackley, Teviet Creighton, Mario C. Diaz, F. Llamas, Soma Mukherjee, Volker Quetschke, W. H. Wang

Physics and Astronomy Faculty Publications and Presentations

The second Gravitational-Wave Transient Catalog reported on 39 compact binary coalescences observed by the Advanced LIGO and Advanced Virgo detectors between 1 April 2019 15:00 UTC and 1 October 2019 15:00 UTC. We present GWTC-2.1, which reports on a deeper list of candidate events observed over the same period. We analyze the final version of the strain data over this period with improved calibration and better subtraction of excess noise, which has been publicly released. We employ three matched-filter search pipelines for candidate identification, and estimate the astrophysical probability for each candidate event. While GWTC-2 used a false alarm rate …

Brooks' Theorem For 2-Fold Coloring, Jacob A. White

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

The two-fold chromatic number of a graph is the minimum number of colors needed to ensure that there is a way to color the graph so that each vertex gets two distinct colors, and adjacent vertices have no colors in common. The Ore degree is the maximum sum of degrees of an edge in a graph. We prove that, for 2-connected graphs, the two-fold chromatic number is at most the Ore degree, unless G is a complete graph or an odd cycle.

Model-Based Cross-Correlation Search For Gravitational Waves From The Low-Mass X-Ray Binary Scorpius X-1 In Ligo O3 Data, R. Abbott, H. Abe, Fausto Acernese, Teviet Creighton, Mario C. Diaz, Francisco Llamas, Soma Mukherjee, Gaukhar Nurbek, Volker Quetschke, Wenhui Wang

Physics and Astronomy Faculty Publications and Presentations

We present the results of a model-based search for continuous gravitational waves from the low-mass X-ray binary Scorpius X-1 using LIGO detector data from the third observing run of Advanced LIGO and Advanced Virgo. This is a semicoherent search that uses details of the signal model to coherently combine data separated by less than a specified coherence time, which can be adjusted to balance sensitivity with computing cost. The search covered a range of gravitational-wave frequencies from 25 to 1600 Hz, as well as ranges in orbital speed, frequency, and phase determined from observational constraints. No significant detection candidates were …

Preferential Stiffness And The Crack-Tip Fields Of An Elastic Porous Solid Based On The Density-Dependent Moduli Model, Hyun C. Yoon, S. M. Mallikarjunaiah, Dambaru Bhatta

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

In this paper, we study the preferential stiffness and the crack-tip fields for an elastic porous solid of which material properties are dependent upon the density. Such a description is necessary to describe the failure that can be caused by damaged pores in many porous bodies such as ceramics, concrete and human bones. To that end, we revisit a new class of implicit constitutive relations under the assumption of small deformation. Although the constitutive relationship \textit{appears linear} in both the Cauchy stress and linearized strain, the governing equation bestowed from the balance of linear momentum results in a quasi-linear partial …

Predicting The Outcomes Of Internet-Based Cognitive Behavioral Therapy For Tinnitus: Applications Of Artificial Neural Network And Support Vector Machine, Hansapani Rodrigo, Eldré W. Beukes, Gerhard Andersson, Vinaya Manchaiah

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Purpose:

Internet-based cognitive behavioral therapy (ICBT) has been found to be effective for tinnitus management, although there is limited understanding about who will benefit the most from ICBT. Traditional statistical models have largely failed to identify the nonlinear associations and hence find strong predictors of success with ICBT. This study aimed at examining the use of an artificial neural network (ANN) and support vector machine (SVM) to identify variables associated with treatment success in ICBT for tinnitus.

Method:

The study involved a secondary analysis of data from 228 individuals who had completed ICBT in previous intervention studies. A 13-point reduction …

Stabilization Of Zero-Energy Skin Modes In Finite Non-Hermitian Lattices, Cem Yuce, Hamidreza Ramezani

Physics and Astronomy Faculty Publications and Presentations

The zero energy of a one-dimensional semi-infinite non-Hermitian lattice with nontrivial spectral topology may disappear when we introduce boundaries to the system. While the corresponding zero-energy state can be considered as a quasi-edge state for the finite lattice with a long survival time, any small disruption (noise) in the initial form of the quasi-edge state can significantly shorten the survival time. Here, by tailoring the couplings at one edge we form an exceptional point allowing for a topological phase transition and the stabilization of the quasi-edge state in a finite-size lattice with open edges. Such a small modification in the …

Local Well-Posedness Of The Cauchy Problem For A P -Adic Nagumo-Type Equation, L. F. Chacón-Cortés, C. A. Garcia-Bibiano, Wilson A. Zuniga-Galindo

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

We introduce a new family of p -adic nonlinear evolution equations. We establish the local well-posedness of the Cauchy problem for these equations in Sobolev-type spaces. For a certain subfamily, we show that the blow-up phenomenon occurs and provide numerical simulations showing this phenomenon.

Congruences For Consecutive Coefficients Of Gaussian Polynomials With Crank Statistics, Dennis Eichhorn, Lydia Engle, Brandt Kronholm

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

In this paper, we establish infinite families of congruences in consecutive arithmetic progressions modulo any odd prime ℓ for the function p ( n , m , N ) , which enumerates the partitions of n into at most m parts with no part larger than N . We also treat the function p ( n , m , ( a , b ] ) , which bounds the largest part above and below, and obtain similar infinite families of congruences.

For m ≤ 4 and ℓ = 3 , simple combinatorial statistics called "cranks" witness these congruences. We prove …

South Texas Wildlife Activity Across A Fragmented Landscape And Road Mitigation Corridor, Caitlin K. Brett

Theses and Dissertations

Wildlife crossing structures (WCS) and roadside fencing are commonly installed to mitigate habitat fragmentation, wildlife road mortalities, and other negative effects that roads can have on the surrounding landscape. Eight such WCS were constructed below Farm-to-Market (FM)106 in Cameron County, Texas, across a 16 km corridor transecting the Laguna Atascosa National Wildlife Refuge. These WCS, paired with adjacent roadside fencing, were intended to prevent road mortalities of the endangered ocelot (Leopardus pardalis) and to mitigate the barrier effect of FM106 on this and other meso-mammal species. This study will analyze camera trap data from roadside and habitat reference …

An Assessment Of Physical And Microbial Dynamic Properties Sensitive To Tillage Practices In Hidalgo Sandy Clay Loam Soils, Rocio N. Hernandez

Theses and Dissertations

Mechanized tillage is known to impact the dynamic physical, biological and chemical properties of a given soil, and as a result, can cause systematic harm to the soil’s function (Alam et al., 2014). The aim of this study is to assess how a series of land management tillage practices will impact dynamic physical and biological soil health parameters such as aggregation, carbon, respiration, and enzymatic activity (β-glucosidase). According to Acir et al (2020), the aforementioned soil parameters are both co-influenced and dependent, indicating a response to tillage is likely. A total of 198 samples of Hidalgo series soils were collected …

Glitch Estimation And Removal Using Adaptive Spline Fitting And Wavelet Shrinkage On The Gravitational Wave Data, Mohammad Abu Thaher Chowdhury

Theses and Dissertations

The false alarm rate and reduced sensitivity of searches for astrophysical signals are caused by transient signals of earthly origin, or "glitches," in gravitational wave strain data from groundbased detectors. The greater number of observable astrophysical signals will increase the likelihood of glitch overlaps and exacerbate their negative impact for future detectors with higher sensitivities. The wide morphological diversity and unpredictable waveforms of glitches, and with the vast majority of cases lacking supplemental data present the main obstacles to their mitigation. Thus, nonparametric glitch mitigation techniques are required, which should operate for a wide range of glitches and, in the …

Investigating The Relationship Between Dissolved Oxygen And Nitrate Concentration As A Proxy For Marine Ecosystem Health, Natalia M. Moore

Theses and Dissertations

Coastal environments such as seagrass meadows span a wide range of spatial scales and can experience disturbances that cause rapid shifts to ecosystem dynamics. Increased pressure to the coastal zone has highlighted the need for constant, real-time monitoring to monitor current ecosystem status. A custom, low cost, high resolution, in situ sensor network was designed and tested in the Lower Laguna Madre, Texas to characterize primary productivity in seagrass meadows through gradient patterns of dissolved oxygen concentration, with the purpose of determining whether seagrass or phytoplankton were the more dominant primary producer. There was a distinct vertical and horizontal gradient …

Dynamic Soil Properties In The Lower Rio Grande Valley: Understanding Responses Of Infiltration Rate, Bulk Density, Aggregate Stability To Different Tillage Practices, Temiloluwa Faith Awotoye

Theses and Dissertations

Dynamic Soil Properties (DSPs) are soil properties that change in response to both natural and human-caused interruptions and pressures such as agro-based and wildland management. These soil properties can transform for months or even years in response to the farm use and management procedures. This research project investigates the relationship between different dynamic soil physical properties and tillage practices in the Texas Hidalgo sandy clay loam benchmark soil series. Data analyses was done to compare the effect of tillage to these soil physical properties and build a discussion about relationships between on-farm practices to other aspects of farm viability. We …

Search For Gravitational Waves From Core Collapse Supernovae In Ligo's Observation Runs Using A Network Of Detectors, Shahrear Khan Faisal

Theses and Dissertations

Core-Collapse Supernova (CCSN) is one of the most anticipated sources of Gravitational Waves (GW) in the fourth observation run (O4) of LIGO and other network of GW detectors. A very low rate of galactic CCSN, coupled with the fact that the CCSN waveforms are unmodeled, make detection of these signals extremely challenging. Mukherjee et. al. have developed a new burst search pipeline, the Multi-Layer Signal Enhancement with cWB and CNN or MuLaSEcC, that integrates a non-parametric signal estimation and Machine Learning. MuLaSEcC operates on GW data from a network of detectors and enhances the detection probability while reducing the false …

Dft Investigation Of Lewis Acid Assisted C-Cn Bond Activation Of Benzonitrile With [Ni(Dmpe)] Fragment, Lubna Kader

Theses and Dissertations

There has been recent interest in the field of organometallics with C—C bond activation of organic substrates that are mediated by transition metal complexes. The bond activation of C—C bonds is important, not only in organic synthesis but also in industrial processes. However, the activation of these bonds remains difficult since they are thermodynamically more stable and sterically less available to activate than the activation of the C—H bond. Most of the successful C—C cleavage uses the relief of ring strain, achievement of aromaticity, or proximity, as the driving force for the reaction.3 Another strategy is the use of a …

Gmres Convergence Of Block Preconditioners For Nonsymmetric Matrices, Miguel A. Mascorro

Theses and Dissertations

GMRES is an iterative method for solving linear systems that minimizes the residual over the k-dimensional Krylov subspace at iteration k. Murphy, Golub and Wathen in [11] show that saddle point type matrices can be preconditioned so that GMRES converges in two or three steps. Ipsen in [10] extends this work to matrixes where the (2,2) block is nonzero. However, the three step convergence result no longer holds in this case. In this thesis we investigate how many more steps are needed for convergence as a function of the size of that (2,2) block.

Grapefruit Peel Biochar Applications For Immobilizing Copper And Lead In Soil, Michael Alfredo Navarro

Theses and Dissertations

This study investigated the efficacy of grapefruit peel (GP) derived biochar materials (two pyrolysis temperatures 450°C and 800°C) as a potential adsorbent to immobilize heavy metal (copper and lead) in a local sandy loam clay soil. A batch adsorption test with heavy metal concentrations at 50 mg L-1, and 100 mg L-1 revealed that soil itself had the highest immobilization percentage compared to the GP biochars. A soil column experiment was conducted to determine how much the GP biochar samples and the tested soil will exhibit adsorptive characteristics for heavy metals when 50 ml of 50 mg L-1 copper or …

Synthesis Of Bioactive Heterocycles, Shaila Akter Shetu

Theses and Dissertations

The Discovery of a variety of heterocyclic drugs for the treatment of cancer and other diseases (e.g, neglected tropical diseases) is a medical breakthrough and inspiring for the research community as a whole. A wide range of natural, semi-synthetic, and synthetic anticancer drugs are synthesized using various methods. Among them, β -lactams stand out as a novel class of antibiotics that has different types of biological as well as anti-cancer properties. β -lactam has become a premier and active research subject towards the development of revolutionary anti-cancer drugs. In recent years, a large amount of investigations have been done to …