Applied Mathematics Commons^™

Compare And Contrast Maximum Likelihood Method And Inverse Probability Weighting Method In Missing Data Analysis, Scott Sun

Mathematical Sciences Technical Reports (MSTR)

Data can be lost for different reasons, but sometimes the missingness is a part of the data collection process. Unbiased and efficient estimation of the parameters governing the response mean model requires the missing data to be appropriately addressed. This paper compares and contrasts the Maximum Likelihood and Inverse Probability Weighting estimators in an Outcome-Dependendent Sampling design that deliberately generates incomplete observations. WE demonstrate the comparison through numerical simulations under varied conditions: different coefficient of determination, and whether or not the mean model is misspecified.

Access To Higher Education: Do Schools “Grant” Success?, Nathaniel Jones

Symposium of Student Scholars

University education can lead to upward income mobility for low-income students. Being exposed to other student’s life experiences that are different from their own may highlight activities and actions that they may want to consider aiding their success. According to the U.S. Bureau of Labor Statistics, the median weekly earnings in 2019 for all workers in the U.S. was $969. Of those, U.S. workers who held bachelor’s degrees earned $1,248. In 2016, the Brookings Institute found that Pell Grant recipients and first-generation student loan borrowers attended universities that had lower graduation rates and higher loan default rates in comparison to …

Environmental Impact On Competition In Ecological Communities, Isabel Ouko

Symposium of Student Scholars

We study the effects of environmental feedback on the ecological competition by analyzing the classic Lotka-Volterra model coupled with a simple model of the environment. In particular, we look for ways in which feedback between competing populations and the environment stabilizes or destabilizes coexistence between the species. To do so, we use a combination of mathematical analysis and computer software such as Matlab.

KEYWORDS; mathematical modeling, Lotka-Volterra, ecological competition, environmental feedback

Characterizing The Northern Hemisphere Circumpolar Vortex Through Space And Time, Nazla Bushra

LSU Doctoral Dissertations

This hemispheric-scale, steering atmospheric circulation represented by the circumpolar vortices (CPVs) are the middle- and upper-tropospheric wind belts circumnavigating the poles. Variability in the CPV area, shape, and position are important topics in geoenvironmental sciences because of the many links to environmental features. However, a means of characterizing the CPV has remained elusive. The goal of this research is to (i) identify the Northern Hemisphere CPV (NHCPV) and its morphometric characteristics, (ii) understand the daily characteristics of NHCPV area and circularity over time, (iii) identify and analyze spatiotemporal variability in the NHCPV’s centroid, and (iv) analyze how CPV features relate …

Computational Design Of Nonlinear Stress-Strain Of Isotropic Materials, Askhad M.Polatov, Akhmat M. Ikramov, Daniyarbek Razmukhamedov

Chemical Technology, Control and Management

The article deals with the problems of numerical modeling of nonlinear physical processes of the stress-strain state of structural elements. An elastoplastic medium of a homogeneous solid material is investigated. The results of computational experiments on the study of the process of physically nonlinear deformation of isotropic elements of three-dimensional structures with a system of one- and double-periodic spherical cavities under uniaxial compression are presented. The influence and mutual influence of stress concentrators in the form of spherical cavities, vertically located two cavities and a horizontally located system of two cavities on the deformation of the structure are investigated. Numerical …

Morgan- Voyce Approach For Solution Bratu Problems, Bushra Eesa Kashiem

Emirates Journal for Engineering Research

Bratu equations are substantial in electrostatic and plasma problem. The aim of this paper is design a morgan-voyce approach for solving bratu problem. We present a morgan-voyce polynomial along with significant properties; the effectiveness of the proposed algorithm is demonstrated by considering three numerical examples.

High-Order Flexible Multirate Integrators For Multiphysics Applications, Rujeko Chinomona

Mathematics Theses and Dissertations

Traditionally, time integration methods within multiphysics simulations have been chosen to cater to the most restrictive dynamics, sometimes at a great computational cost. Multirate integrators accurately and efficiently solve systems of ordinary differential equations that exhibit different time scales using two or more time steps. In this thesis, we explore three classes of time integrators that can be classified as one-step multi-stage multirate methods for which the slow dynamics are evolved using a traditional one step scheme and the fast dynamics are solved through a sequence of modified initial value problems. Practically, the fast dynamics are subcycled using a small …

A Survey On Long-Range Wide-Area Network Technology Optimizations, Felipe S. Dantas Silva, Emidio P. Neto, Helder Oliveira, Denis Rosário, Eduardo Cerqueira, Cristiano Both, Sherali Zeadally, Augusto V. Neto

Information Science Faculty Publications

Long-Range Wide-Area Network (LoRaWAN) enables flexible long-range service communications with low power consumption which is suitable for many IoT applications. The densification of LoRaWAN, which is needed to meet a wide range of IoT networking requirements, poses further challenges. For instance, the deployment of gateways and IoT devices are widely deployed in urban areas, which leads to interference caused by concurrent transmissions on the same channel. In this context, it is crucial to understand aspects such as the coexistence of IoT devices and applications, resource allocation, Media Access Control (MAC) layer, network planning, and mobility support, that directly affect LoRaWAN’s …

Higher Order Fourier Finite Element Methods For Hodge Laplacian Problems On Axisymmetric Domains, Nicole E. Stock

Senior Honors Projects, 2020-current

We construct efficient higher order Fourier finite element spaces to approximate the solution of Hodge Laplacian problems on axisymmetric domains. In [16], a new family of Fourier finite element spaces was constructed by using the lowest order finite element methods. These spaces were used to discretize Hodge Laplacian problems in [18]. In this research, we extend the results of [16,18] by constructing higher order Fourier finite element spaces. We demonstrate that these new higher order Fourier finite element methods provide improved computational efficiency as well as increased accuracy.

Sampling Compactness Scores To Detect Gerrymandering In Squaretopia, Joshua Mariz

Honors Thesis

In electoral politics, gerrymandering is the phenomenon of creating electoral district partitionings that are often not geographically compact for the unfair benefit of one political party over another. Researchers have proposed several methods to quantify compactness, but identifying gerrymandering using these measures is an open problem. We analyze the possible distributions of compactness scores by exploring “Squaretopia,” a square n x n grid that we must partition into n equally-sized contiguous districts that each contain n cells. However, even in this simplified model, the number of possible partitions of a Squaretopia of size n = 9 exceeds 700 trillion, rendering …

Research Focus: Pattern Recognition

In The Loop

A CDM health informatics team joins a global race to advance COVID-19 diagnostics through X-ray insights.

Application Of Randomness In Finance, Jose Sanchez, Daanial Ahmad, Satyanand Singh

Publications and Research

Brownian Motion which is also considered to be a Wiener process and can be thought of as a random walk. In our project we had briefly discussed the fluctuations of financial indices and related it to Brownian Motion and the modeling of Stock prices.

An Investigation Of The Effects Of Variable Magnetic Field Gradients On Soot And Co Emissions From Non-Premixed Hydrocarbon Flames, Edison Ekperechukwu Chukwuemeka

LSU Doctoral Dissertations

The interaction of the paramagnetic species in a combustion process with the mag- netic field placed in the vicinity of non-premixed flames affects the characteristics of the non-premixed flames - flame height and flame lift-off height. However, the effect of this magnetic interaction on the pollutants generated by the flame is unknown.

In general, pollutant formation is promoted in most combustion systems due to in- complete combustion of the hydrocarbon due to improper mixing. Since paramagnetic combustion species such as O2, O, OH, etc interacts with magnetic fields and possess a preferential motion direction, imposing magnetic field on non-premixed flames …

A Component-Wise Approach To Smooth Extension Embedding Methods, Vivian Montiforte

Dissertations

Krylov Subspace Spectral (KSS) Methods have demonstrated to be highly scalable methods for PDEs. However, a current limitation of these methods is the requirement of a rectangular or box-shaped domain. Smooth Extension Embedding Methods (SEEM) use fictitious domain methods to extend a general domain to a simple, rectangular or box-shaped domain. This dissertation describes how these methods can be combined to extend the applicability of KSS methods, while also providing a component-wise approach for solving the systems of equations produced with SEEM.

Efficient Denoising Of High Resolution Color Digital Images Utilizing Krylov Subspace Spectral Methods, Eva Lynn Greenman

Dissertations

The solution to a parabolic nonlinear diffusion equation using a Krylov Subspace Spectral method is applied to high resolution color digital images with parallel processing for efficient denoising. The evolution of digital image technology, processing power, and numerical methods must evolve to increase efficiency in order to meet current usage requirements. Much work has been done to perfect the edge detector in Perona-Malik equation variants, while minimizing the effects of artifacts. It is demonstrated that this implementation of a regularized partial differential equation model controls backward diffusion, achieves strong denoising, and minimizes blurring and other ancillary effects. By adaptively tuning …

How To Extend Interval Arithmetic So That Inverse And Division Are Always Defined, Tahea Hossain, Jonathan Rivera, Yash Sharma, Vladik Kreinovich

Departmental Technical Reports (CS)

In many real-life data processing situations, we only know the values of the inputs with interval uncertainty. In such situations, it is necessary to take this interval uncertainty into account when processing data. Most existing methods for dealing with interval uncertainty are based on interval arithmetic, i.e., on the formulas that describe the range of possible values of the result of an arithmetic operation when the inputs are known with interval uncertainty. For most arithmetic operations, this range is also an interval, but for division, the range is sometimes a disjoint union of two semi-infinite intervals. It is therefore desirable …

Optimal Control Of Algae Biofilm Growth In Wastewater Treatment Using Computational Mathematical Models, Gerald Benjamin Jones

Undergraduate Honors Capstone Projects

Microalgal biofilms are comprised of a syntrophic consortium of microalgae and other microorganisms embedded within an extracellular matrix. Despite significant processes in the application of microalgal biofilms in wastewater treatment, mechanistic understanding and optimization of microalgal biomass yield and productivity under environmental constraints is still lacking. This paper identifies theoretical insights on this challenging biological problem by leveraging novel mathematical and computational tools. In particular, through a computational mathematical model to advance the understanding of microalgal biofilm growth kinetics under environmental constraints through a systematic parameter study. Moreover, design of algae biofilm reactors for optimal biomass yield and productivity in …

Extinction Of Species Due To Deterministic And Stochastic Interactions In Food Webs, Claire M. Burke

Theses, Dissertations and Culminating Projects

Previous research on the extinctions that occur in niche model food webs with deterministic and stochastic dynamics has shown that the structure of the food web can play an important role in extinction cascades. In this thesis, other types of synthetic food web models are considered, namely the cascade and generalized cascade models, and the extinction cascades of these food webs are compared with previous findings on the extinction cascades from the niche model. It was found that there are many similarities in the results for all three models, which prompted a closer analysis using food webs with deterministic dynamics. …

Constructing Non-Proxy Small Test Modules For The Complete Intersection Property, Benjamin Briggs, Eloísa Grifo, Josh Pollitz

Department of Mathematics: Faculty Publications

A local ring R is regular if and only if every finitely generated R-module has finite projective dimension. Moreover, the residue field k is a test module: R is regular if and only if k has finite projective dimension. This characterization can be extended to the bounded derived category Df(R), which contains only small objects if and only if R is regular. Recent results of Pollitz, completing work initiated by Dwyer-Greenlees-Iyengar, yield an analogous characterization for complete intersections: R is a complete intersection if and only if every object in Df(R) is proxy small. In this paper, we study a …

Zeta Function Regularization And Its Relationship To Number Theory, Stephen Wang

Electronic Theses and Dissertations

While the "path integral" formulation of quantum mechanics is both highly intuitive and far reaching, the path integrals themselves often fail to converge in the usual sense. Richard Feynman developed regularization as a solution, such that regularized path integrals could be calculated and analyzed within a strictly physics context. Over the past 50 years, mathematicians and physicists have retroactively introduced schemes for achieving mathematical rigor in the study and application of regularized path integrals. One such scheme was introduced in 2007 by the mathematicians Klaus Kirsten and Paul Loya. In this thesis, we reproduce the Kirsten and Loya approach to …