Applied Mathematics Commons^™

Modeling Self-Diffusiophoretic Janus Particles In Fluid, Kausik Das

HMC Senior Theses

We explore spherical Janus particles in which a chemical reaction occurs on one face, depleting a substrate in the suspending fluid, while no reaction occurs on the other face. The steady state concentration field is governed by Laplace’s equation with mixed boundary conditions. We use the collocation method to obtain numerical solutions to the equation in spherical coordinates. The asymmetry of the reaction gives rise to a slip velocity that causes the particle to move spontaneously in the fluid through a process known as self-diffusiophoresis. Using the Lorentz reciprocal theorem, we obtain the swimming velocity of the particle. We extend …

Multilayer Network Model Of Gender Bias And Homophily In Hierarchical Structures, Emerson Mcmullen

HMC Senior Theses

Although women have made progress in entering positions in academia and
industry, they are still underrepresented at the highest levels of leadership.
Two factors that may contribute to this leaky pipeline are gender bias,
the tendency to treat individuals differently based on the person’s gender
identity, and homophily, the tendency of people to want to be around those
who are similar to themselves. Here, we present a multilayer network model
of gender representation in professional hierarchies that incorporates these
two factors. This model builds on previous work by Clifton et al. (2019), but
the multilayer network framework allows us to …

Graph-Based Acoustic Clustering And Classification, Justin Youngho Sunu

CGU Theses & Dissertations

The rapid growth of audio data collection in various domains necessitates advanced techniquesfor efficient analysis and classification. This dissertation proposes new approaches for categorizing acoustic data, using both unsupervised and semi-supervised learning methods. Starting with raw audio, we preprocess the signal to segment it into time windows, each of which we consider as an independent data point. We use the short-time Fourier transform to describe the signal in a given time window as a set of Fourier coefficients. We interpret the resulting frequency signature as a high-dimensional feature description of each data point. We then develop a graph-based approach for …

Application Of The Two-Variable Model To Simulate A Multisensory Reaction-Time Task, Rebecca Brady, John Butler

Academic Posters Collection

To navigate the world in an efficient manner, the brain seamlessly integrates signals received across multiple sensory modalities. Behavioral studies have suggested that multisensory processing is a winner-take-all sensory response mechanism to some optimal combination of sensory signals. In addition, multiple sensory cues are not always beneficial with some studies showing maladaptive multisensory processing as an identifier of older adults prone to falls from age matched healthy controls.

A stalwart of modelling sensory decision-making is the work by (Wong &Wang, 2006) but to date almost all of this research has been focused on unisensory tasks. We extend the reduced two-variable …

An Adaptive Algorithm For `The Secretary Problem': Alternate Proof Of The Divergence Of A Maximizer Sequence, Andrew Benfante, Xiang Xu

OUR Journal: ODU Undergraduate Research Journal

This paper presents an alternate proof of the divergence of the unique maximizer sequence {𝑥∗ 𝑛} of a function sequence {𝐹𝑛(𝑥)} that is derived from an adaptive algorithm based on the now classic optimal stopping problem, known by many names but here ‘the secretary problem’. The alternate proof uses a result established by Nguyen, Xu, and Zhao (n.d.) regarding the uniqueness of maximizer points of a generalized function sequence {𝑆𝜇,𝜎 𝑛 } and relies on the strict monotonicity of 𝐹𝑛(𝑥) as 𝑛 increases in order to show divergence of {𝑥∗ 𝑛}. Towards this, limits of the exponentiated Gaussian CDF are …

Evaluating A Temperature-Dependent Mosquito Population Model, Morgan H. Jackson, Elizabet L. Estallo, Cheng Ly, Michael A. Robert

Graduate Research Posters

Dengue Virus causes over 390 million infections and around 40,000 deaths each year. This virus is primarily transmitted by the mosquito Aedes aegypti. The life cycle of these mosquitos is significantly impacted by temperature, however, temperature is often neglected in mechanistic models. Predictive models of mosquito populations thus require the inclusion of temperature and are valuable for helping medical officials plan for the impact of outbreaks. Using mosquito and climate data collected in Córdoba, Argentina from 2010-2013, we developed a non-autonomous ordinary differential equations model that includes temperature dependent parameters associated with mosquito life history. We performed local sensitivity …

The Power Of Supercomputing Applied To Fractal Image Generation, Charlin Me Duff

Mathematics Senior Capstones

This project looks into how parallelism benefits the runtime of generating large fractal images. First, it explains what the Julia and Mandelbrot Sets are, who discovered them, and how they are calculated. Following that is an introduction to supercomputers, parallel computing, and Cal Poly Humboldt’s very own supercomputer. Once groundwork is laid, I explain my process of adapting a fractal image generation program from serial computing to different levels of parallelism. After that, is an analysis of the effects of levels of parallelism on the runtime of large fractal image generation. This paper concludes with a reflection on the project …

The Application Of Statistical Modeling To Identify Genetic Associations With Mild Traumatic Brain Injury Outcomes, Caroline Schott

Masters Theses

"Traumatic brain injury (TBI) is a growing health concern, with millions of TBI diagnoses in the United States each year. The vast majority of TBI diagnoses are mild traumatic brain injuries (mTBI), which can be challenging to manage due to variation in symptoms and outcomes. Most individuals with mTBI successfully recover quickly, but a small subset has a delayed recovery. Although the factors that contribute to this variation in recovery are not clearly understood, it is possible that genetic differences may play a role. Very few studies have investigated the association between single nucleotide polymorphisms (SNPs) with mTBI outcomes and …

Meta-Analysis Of Mesenchymal Stem Cell Gene Expression Data From Obese And Non-Obese Patients, Dakota William Shields

Masters Theses

"The prevalence of gene expression microarray datasets in public repositories gives opportunity to analyze biologically interesting datasets without running the laboratory aspect in house. Such experimentation is expensive in terms of finances, time, and expertise, which often results in low numbers of replicates. Meta-analysis techniques attempt to overcome issues due to few biological or technical replicates by combining separate experiments together to increase statistical power. Proper statistical considerations help to offset issues like simultaneous testing of thousands of genes, unintended hybridization, and other noises.

Microarrays contain light intensities from tens of thousands of hybridized probes giving a measure of gene …

Quantum Computing And Its Applications In Healthcare, Vu Giang

OUR Journal: ODU Undergraduate Research Journal

This paper serves as a review of the state of quantum computing and its application in healthcare. The various avenues for how quantum computing can be applied to healthcare is discussed here along with the conversation about the limitations of the technology. With more and more efforts put into the development of these computers, its future is promising with the endeavors of furthering healthcare and various other industries.

Graphs Without A 2c3-Minor And Bicircular Matroids Without A U3,6-Minor, Daniel Slilaty

Mathematics and Statistics Faculty Publications

In this note we characterize all graphs without a 2C3-minor. A consequence of this result is a characterization of the bicircular matroids with no U3,6-minor.

Optimal Agricultural Land Use: An Efficient Neutrosophic Linear Programming Method, Maisam Jdid, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The increase in the size of the problems facing humans, their overlap, the division of labor, the multiplicity of departments, as well as the diversity of products and commodities, led to the complexity of business and the emergence of many administrative and production problems. It was necessary to search for appropriate methods to confront these problems. The science of operations research, with its diverse methods, provided the optimal solutions. It addresses many problems and helps in making scientific and thoughtful decisions to carry out the work in the best way within the available capabilities. Operations research is one of the …

A Mathematical Modeling Technique To Understand The Role Of Decoy Receptors In Ligand‑Receptor Interaction, Subrata Dey, Aditi Ghosh, Malay Banerjee

Faculty Publications

The ligand‑receptor interaction is fundamental to many cellular processes in eukaryotic cells such as cell migration, proliferation, adhesion, signaling and so on. Cell migration is a central process in the development of organisms. Receptor induced chemo‑tactic sensitivity plays an important role in cell migration. However, recently some receptors identified as decoy receptors, obstruct some mechanisms of certain regular receptors. DcR3 is one such important decoy receptor, generally found in glioma cell, RCC cell and many various malignant cells which obstruct some mechanism including apoptosis cell‑signaling, cell inflammation, cell migration. The goal of our work is to mathematically formulate ligand‑receptor interaction …

Counting Spanning Trees On Triangular Lattices, Angie Wang

CMC Senior Theses

This thesis focuses on finding spanning tree counts for triangular lattices and other planar graphs comprised of triangular faces. This topic has applications in redistricting: many proposed algorithmic methods for detecting gerrymandering involve spanning trees, and graphs representing states/regions are often triangulated. First, we present and prove Kirchhoff’s Matrix Tree Theorem, a well known formula for computing the number of spanning trees of a multigraph. Then, we use combinatorial methods to find spanning tree counts for chains of triangles and 3 × n triangular lattices (some limiting formulas exist, but they rely on higher level mathematics). For a chain of …

Foundations Of Wave Phenomena: Complete Version, Charles G. Torre

Foundations of Wave Phenomena

This is the complete version of Foundations of Wave Phenomena. Version 8.3.1.

Please click here to explore the components of this work.

Modeling The Spread Of Covid-19 In Spatio-Temporal Context, S.H. Sathish Indika, Norou Diawara, Hueiwang Anna Jeng, Bridget D. Giles, Dilini S.K. Gamage

Mathematics & Statistics Faculty Publications

This study aims to use data provided by the Virginia Department of Public Health to illustrate the changes in trends of the total cases in COVID-19 since they were first recorded in the state. Each of the 93 counties in the state has its COVID-19 dashboard to help inform decision makers and the public of spatial and temporal counts of total cases. Our analysis shows the differences in the relative spread between the counties and compares the evolution in time using Bayesian conditional autoregressive framework. The models are built under the Markov Chain Monte Carlo method and Moran spatial correlations. …

Solitons And Their Applications In Physics, B. A. Yount

EWU Masters Thesis Collection

No abstract provided.

A Hierarchical Approach To Improve The Ant Colony Optimization Algorithm, Bryan J. Fischer

EWU Masters Thesis Collection

The ant colony optimization algorithm (ACO) is a fast heuristic-based method for finding favorable solutions to the traveling salesman problem (TSP). When the data set reaches larger values however, the ACO runtime increases dramatically. As a result, clustering nodes into groups is an effective way to reduce the size of the problem while leveraging the advantages of the ACO algorithm. The method for recombining groups of nodes is explored by treating the graph as a hierarchy of clusters, and modifying the original ACO heuristic to operate on a hypergraph. This method of using hierarchical clustering is significantly faster than the …

Novel Architectures And Optimization Algorithms For Training Neural Networks And Applications, Vasily I. Zadorozhnyy

Theses and Dissertations--Mathematics

The two main areas of Deep Learning are Unsupervised and Supervised Learning. Unsupervised Learning studies a class of data processing problems in which only descriptions of objects are known, without label information. Generative Adversarial Networks (GANs) have become among the most widely used unsupervised neural net models. GAN combines two neural nets, generative and discriminative, that work simultaneously. We introduce a new family of discriminator loss functions that adopts a weighted sum of real and fake parts, which we call adaptive weighted loss functions. Using the gradient information, we can adaptively choose weights to train a discriminator in the direction …

Impact Of Spallation And Internal Radiation On Fibrous Ablative Materials, Raghava Sai Chaitanya Davuluri

Theses and Dissertations--Mechanical and Aerospace Engineering

Space vehicles are equipped with Thermal Protection Systems (TPS) that encounter high heat rates and protect the payload while entering a planetary atmosphere. For most missions that interest NASA, ablative materials are used as TPS. These materials undergo several mass and energy transfer mechanisms to absorb intense heat. The size and construction of the TPS are based on the composition of the planetary atmosphere and the impact of various ablative mechanisms on the flow field and the material. Therefore, it is essential to quantify the rates of different ablative phenomena to model TPS accurately. In this work, the impact of …

Beginner's Analysis Of Financial Stochastic Process Models, David Garcia

HMC Senior Theses

This thesis explores the use of geometric Brownian motion (GBM) as a financial model for predicting stock prices. The model is first introduced and its assumptions and limitations are discussed. Then, it is shown how to simulate GBM in order to predict stock price values. The performance of the GBM model is then evaluated in two different periods of time to determine whether it's accuracy has changed before and after March 23, 2020.

The Lagrangian Formulation For Wave Motion With A Shear Current And Surface Tension, Conor Curtin, Rossen Ivanov

Articles

The Lagrangian formulation for the irrotational wave motion is straightforward and follows from a Lagrangian functional which is the difference between the kinetic and the potential energy of the system. In the case of fluid with constant vorticity, which arises for example when a shear current is present, the separation of the energy into kinetic and potential is not at all obvious and neither is the Lagrangian formulation of the problem. Nevertheless, we use the known Hamiltonian formulation of the problem in this case to obtain the Lagrangian density function, and utilising the Euler-Lagrange equations we proceed to derive some …

Bifurcation Levels Of The Integral Manifolds Of The Newtonian N-Body Problem, Hannah G. Havel

CURE Proceedings

The N-body problem, first proposed by Isaac Newton, is a field of study in mathematics and physics that involves predicting the motion of particles moving under their mutual gravitational attraction. It has significance to many areas of science, including physics and computer science, and is crucial in understanding how the universe works. In fact, it was a primary motivation for Newton's development of calculus. An important application of the N-body problem is within celestial mechanics and involves how planets and other celestial bodies move with mutual gravitational attraction. It is important in developing how satellites behave in space using complicated …

Dynamic Function Learning Through Control Of Ensemble Systems, Wei Zhang, Vignesh Narayanan, Jr-Shin Li

Publications

Learning tasks involving function approximation are preva- lent in numerous domains of science and engineering. The underlying idea is to design a learning algorithm that gener- ates a sequence of functions converging to the desired target function with arbitrary accuracy by using the available data samples. In this paper, we present a novel interpretation of iterative function learning through the lens of ensemble dy- namical systems, with an emphasis on establishing the equiv- alence between convergence of function learning algorithms and asymptotic behavior of ensemble systems. In particular, given a set of observation data in a function learning task, we …

Odd Solutions To Systems Of Inequalities Coming From Regular Chain Groups, Daniel Slilaty

Mathematics and Statistics Faculty Publications

Hoffman’s theorem on feasible circulations and Ghouila-Houry’s theorem on feasible tensions are classical results of graph theory. Camion generalized these results to systems of inequalities over regular chain groups. An analogue of Camion’s result is proved in which solutions can be forced to be odd valued. The obtained result also generalizes the results of Pretzel and Youngs as well as Slilaty. It is also shown how Ghouila-Houry’s result can be used to give a new proof of the graph- coloring theorem of Minty and Vitaver.

Measuring Racial Segregation In Los Angeles County Using Random Walks, Zarina Kismet Dhillon

CMC Senior Theses

As of now there is no universal quantitative measure used to evaluate racial segregation in different regions. This paper begins by providing a history of segregation, with an emphasis on the impact of redlining in the early 20th century. We move to its effect on the current population distribution in Los Angeles, California, and then provide an overview of the mathematical concepts that have been used in previous measurements of segregation. We then introduce a method that we believe encompasses the most representative aspects of preceding work, proposed by Sousa and Nicosia in their work on quantifying ethnic segregation in …

Using Modflow To Assess Groundwater Storage Enhancement Via A Floodplain Infiltration Basin, Lindsay Henning

All Master's Theses

Delaying groundwater discharge into rivers until it is critically needed during baseflow conditions provides promise for lowering elevated stream temperatures and improving habitat for aquatic species. Increasing groundwater storage may accomplish this in locations where excess spring runoff can be captured and allowed to infiltrate into the subsurface for later beneficial use, a process known as Managed Aquifer Recharge (MAR). Here, MAR via an infiltration basin is considered at a site along the Teanaway River in central Washington State. The effects of simulated ephemeral ponds of sizes varying from 554 m³ to 2430 m³ (0.449 acre-feet to 1.97 …

Clusters, Curves, And Centroids: Stellar Flare Morphology In The Ultraviolet, Vera Berger

Pomona Senior Theses

With a novel sample of 495 high-cadence light curves for stellar flares in the near-ultraviolet, I explore similarity measures, clustering algorithms, averaging methods, and curve fitting techniques for time series. This work seeks to provide insight into whether stellar flares are similar across stars, if we can identify physically meaningful patterns in their light curves, and how to construct a comprehensive model for flares. I construct the first empirical template for flare light curves in the ultraviolet, and compute ``average elements" of flares displaying complex features such as quasi-periodic oscillations and multipeak structures. Developing accurate models for flares in the …

Models For Decision-Making - Second Edition, Steven Cosares, Fred Rispoli

Open Educational Resources

Decision-Making often refers to a multi-stage process that starts with some form of introspection or reflection about a situation in which a person or group of people find themselves. These ruminations usually lead to series of questions that need to be answered, or to a set of data that needs to be collected and analyzed, or to some calculations that need to be performed before someone can be in a position to make informed decisions and take appropriate actions.

We provide some simple examples of Quantitative Models, which are often found in a decision-making situation. We focus on the use …

Addressing The Opioid Crisis In The United States And Modeling Its Proposed Interventions, Liza Eubanks

Honors Program Theses

A novel application of compartmental modeling is used to quantitatively study the impact of call centers on influencing an individual’s mindset as they begin or attempt to recover from opioid addiction. The opioid epidemic in the United States has affected millions of Americans, especially in West Virginia. This project studies the effectiveness of call centers in increasing the rate of recovery from opioid abuse. An active response is characterized by an open mindset and acceptance of help from others, while a passive response is defined by a closed mindset and an unwillingness to believe in the real possibility of recovery. …