Applied Mathematics Commons^™

A Computational Investigation Of The Biophysical Mechanisms Underlying Thermotaxis In The Afd Neurons Of Caenorhabditis Elegans, Zachary Mobille

Theses and Dissertations

Thermotaxis in the nematode Caenorhabditis elegans (C. elegans) is studied at the cellular scale of the amphid finger-like ciliated (AFD) neurons, which have previously been shown to be essential for thermoreception. The voltage and calcium signals of AFD during temperature stimuli are described with ordinary differential equations. The primary calcium model is a modified version of that published by Kuramochi and Doi in 2017 to explain the calcium responses of the chemosensitive amphid single-ciliated right (ASER) neuron to fluctuations in extracellular salt concentration. To account for the effects of temperature, changes to the stimuli conditions under which inactivation takes place …

On The Bounded Negativity Conjecture And Singular Plane Curves, Alexandru Dimca, Brian Harbourne, Gabriel Sticlaru

Department of Mathematics: Faculty Publications

There are no known failures of Bounded Negativity in characteristic 0. In the light of recent work showing the Bounded Negativity Conjecture fails in positive characteristics for rational surfaces, we propose new characteristic free conjectures as a replacement. We also develop bounds on numerical characteristics of curves constraining their negativity. For example, we show that the H-constant of a rational curve C with at most 9 singular points satisfies H(C) > -2 regardless of the characteristic.

Undetermined Coefficients: A Fully Generalized Approach, Taylor Powell

Undergraduate Research Symposium

In this presentation, I outline the development of a fully-generalized solution of linear, non-homogeneous differential equations with constant coefficients and whose non-homogeneous function is any product of sinusoidal, exponential, and polynomial functions. This particular method does not require the reader to work with annihilator operators or additional related ODEs, and only requires an understanding of summation notation, matrix multiplication, and calculus. Additionally, this method provides a straightforward way to develop a program to implement the technique, and potentially reduces the time-complexity for solutions with comparisons to other methods.

Accelerated Gradient Descent Methods For The Uniaxially Constrained Landau-De Gennes Model, Edison E. Chukwuemeka

LSU Master's Theses

Liquid crystal models with the capability of capturing defects has been one of the main focus in modeling the behavior of such phase mathematically. A uni-axially constrained Landau-de Gennes one-constant model, which has this capability was modeled using three minimization schemes - standard gradient descent, Nesterov accelerated gradient descent, and heavy-ball accelerated gradient descent. The uni-axially constrained Landau-de Gennes energy is discretized using finite element method and the performance of the minimization schemes are measured using the classical gradient descent scheme as the baseline. The numerical experiments conducted indicated that the accelerated gradient descent schemes improved the convergence rate and …

A Quantitative Analysis On Bitmex Perpetual Inverse Futures Xbtusd Contract, Yue Wu

Undergraduate Economic Review

The perpetual inverse futures contract is a recent and most popularly traded cryptocurrency derivative over crypto derivatives exchanges. Exchanges implement a liquidation mechanism that terminates positions which no longer satisfy maintenance requirements. In this study, we use regression, stochastic calculus, and simulation methods to provide a quantitative description of the wealth/return process for holding an XBTUSD contract on BitMEX, examine the funding rate and index price properties, and relate liquidation to leverage as a stopping time problem. The results will help investors understand liquidation to optimize their trading strategy and researchers in studying the design of crypto derivatives.

Are Terrorist Networks Just Glorified Criminal Cells?, Elie Alhajjar, Ryan Fameli, Shane Warren

Northeast Journal of Complex Systems (NEJCS)

The notions of organized crime and terrorism have an old and rich history around the globe. Researchers and practitioners have been studying events and phenomena related to these notions for a long time. There are pointers in the literature in which it is misleading to see the unfair comparison between terrorist and criminal networks with the argument that all actors involved in these networks are simply evil individuals. In this paper, we conduct a systematic study of the operational structure of such networks from a network science perspective. We highlight some of the major differences between them and support our …

Stochastic Navier-Stokes Equations With Markov Switching, Po-Han Hsu

LSU Doctoral Dissertations

This dissertation is devoted to the study of three-dimensional (regularized) stochastic Navier-Stokes equations with Markov switching. A Markov chain is introduced into the noise term to capture the transitions from laminar to turbulent flow, and vice versa. The existence of the weak solution (in the sense of stochastic analysis) is shown by studying the martingale problem posed by it. This together with the pathwise uniqueness yields existence of the unique strong solution (in the sense of stochastic analysis). The existence and uniqueness of a stationary measure is established when the noise terms are additive and autonomous. Certain exit time estimates …

Modeling Of Covid-19 Utilizing Various Compartmental Models To Predict Infection Rates Throughout Michigan, Colleen M. Staniszewski

Honors Theses

Compartmental modeling is a method of employing math to create a visual representation of a disease interacting with a select population, typically used in epidemiology analyses. This project applies compartmental modeling equations to data collected on the various aspects of COVID-19 in Michigan. Comparing current data to past predictive models, as well as the visual representations that were developed through the various compartmental modeling methods, allows an assessment of the effects of the preventative measures taken by the state, the various rates at which the infection is able to spread, as well as the potential path and spread of the …

The Encyclopedia Of Neutrosophic Researchers - 4th Volume (2021), Florentin Smarandache, Maykel Leyva-Vazquez

Branch Mathematics and Statistics Faculty and Staff Publications

Este es el cuarto volumen de la Enciclopedia de Investigadores Neutróficos, editados a partir de materiales ofrecidos por los autores que respondieron a la invitación del editor. Los autores se enumeran alfabéticamente. La introducción contiene una breve historia de la neutrosófica, y en especial se su impacto en Latinoamérica junto con enlaces a los principales artículos y libros. Los conjuntos neutrosóficos, la lógica neutrosófica, la probabilidad neutrosófica, la estadística neutrosófica, el precálculo neutrosófico, el cálculo neutrosófico, la psicología neutrosófica, la sociología neutrosófica etc., están ganando una atención significativa en resolver muchos problemas de la vida real que implican incertidumbre, imprecisión, …

An Analysis Of The Effects Of Technology Readiness Levels On Cost Growth, Christopher R. Bissing

Theses and Dissertations

This research seeks to evaluate the effects of Technology Readiness Levels (TRL) on Cost Growth. It makes use of data from Technology Readiness Assessments (TRA) and Selected Acquisition Reports (SAR) to explore relationships between TRLs at Milestone B and cost growth in Major Defense Acquisition Programs (MDAP) and Major Automated Information Systems (MAIS). Programs using higher proportions of critical technologies rated below TRL 7 tend to experience greater cost growth than programs that use more mature technologies. Current DoD doctrine requires TRL 6 to enter Milestone B. The results of this research seek to evaluate the merit of this requirement. …

The Reemergence Of Eradicated Disease Due To Ecological Impact Of Climate Change, Claudia Kolakowski

Theses and Dissertations

Global warming is radically changing aspects of the Earth. As scientists continue to research the effects, the ramifications of melting permafrost is coming to light. We build off of a previously existing Anthrax model in the hopes to include climate change as a factor in Anthrax spread. Chapter II develops a simplified version of an Anthrax model. Parameters for the model are found by using previous research and eigenvalues are analyzed in order to find thresholds and equilibria. Chapter III consider the general solutions of the model through eigenvalues and eigenvectors. This model is then extended to include a parameter …

Adventures In The "Islands" - Enhancing Student Engagement In Teaching Statistics, Leszek Gawarecki

Mathematics Presentations And Conference Materials

The factors for enhancing student engagement frequently identified are active and problem-based learning as well as real-life experience relevant to students' interests. The importance of using real data in teaching statistics has been repeatedly emphasized and its importance is growing. However, data collection, as part of a student project, faces serious practical problems. It is time-consuming, may require access to equipment, or raise ethical issues.

The Pencil Code, A Modular Mpi Code For Partial Differential Equations And Particles: Multipurpose And Multiuser-Maintained, The Pencil Code Collaboration, Chao-Chin Yang

Physics & Astronomy Faculty Research

The Pencil Code is a highly modular physics-oriented simulation code that can be adapted to a wide range of applications. It is primarily designed to solve partial differential equations (PDEs) of compressible hydrodynamics and has lots of add-ons ranging from astrophysical magnetohydrodynamics (MHD) (A. Brandenburg & Dobler, 2010) to meteorological cloud microphysics (Li et al., 2017) and engineering applications in combustion (Babkovskaia et al., 2011). Nevertheless, the framework is general and can also be applied to situations not related to hydrodynamics or even PDEs, for example when just the message passing interface or input/output strategies of the code are to …

Sars-Cov-2 And Rohingya Refugee Camp, Bangladesh: Uncertainty And How The Government Took Over The Situation, Md. Md. Kamrujjaman, Md. Shahriar Mahmud, Shakil Ahmed, Md. Omar Qayum, Mohammad Morshad Alam, Md. Nazmul Hassan, Md. Rafiul Islam, Kaniz Fatema Nipa, Ummugul Bulut

Mathematics Faculty Publications (Archived)

Background: Bangladesh hosts more than 800,000 Rohingya refugees from Myanmar. The low health immunity, lifestyle, access to good healthcare services, and social-security cause this population to be at risk of far more direct effects of COVID-19 than the host population. Therefore, evidence-based forecasting of the COVID-19 burden is vital in this regard. In this study, we aimed to forecast the COVID-19 obligation among the Rohingya refugees of Bangladesh to keep up with the disease outbreak’s pace, health needs, and disaster preparedness. Methodology and Findings: To estimate the possible consequences of COVID-19 in the Rohingya camps of Bangladesh, we used a …

Symbolic Rees Algebras, Eloísa Grifo, Alexandra Seceleanu

Department of Mathematics: Faculty Publications

We survey old and new approaches to the study of symbolic powers of ideals. Our focus is on the symbolic Rees algebra of an ideal, viewed both as a tool to investigate its symbolic powers and as a source of challenging problems in its own right. We provide an invitation to this area of investigation by stating several open questions.

Long-Term Dynamics Of The Kidney Disease Epidemic Among Hiv-Infected Individuals, Heather Gudaz, Henry A. Ogu, Elissa J. Schwartz

Spora: A Journal of Biomathematics

One of many risks facing HIV+ individuals is the development of kidney dysfunction and end stage kidney disease (ESKD). A differential equation-based mathematical model was developed to assess the impact of antiretroviral therapy on the progression to kidney disease and on reducing mortality due to kidney failure. Analytical and numerical predictions of long-term HIV+ ESKD prevalence show that therapy can lead to either extremely low levels of disease prevalence or increased prevalence, depending on drug efficacy levels and mechanisms of action. Maintenance of HIV+ ESKD prevalence below one individual is possible with sufficient efficacy (e.g., 99%) against the progression from …

Principles For Determining The Motion Of Blood Through Arteries, Sylvio R. Bistafa

Euleriana

Translation of Principia pro motu sanguinis per arterias determinando (E855). This work of 1775 by L. Euler is considered to be the first mathematical treatment of circulatory physiology and hemodynamics.

Symbolic Rees Algebras, Eloísa Grifo, Alexandra Seceleanu

Department of Mathematics: Faculty Publications

We survey old and new approaches to the study of symbolic powers of ideals. Our focus is on the symbolic Rees algebra of an ideal, viewed both as a tool to investigate its symbolic powers and as a source of challenging problems in its own right. We provide an invitation to this area of investigation by stating several open questions.

Computational Modelling Enables Robust Multidimensional Nanoscopy, Matthew D. Lew

Electrical & Systems Engineering Publications and Presentations

The following sections are included:

• Present State of Computational Modelling in Fluorescence Nanoscopy

• Recent Contributions to Computational Modelling in Fluorescence Nanoscopy

• Outlook on Computational Modelling in Fluorescence Nanoscopy

• Acknowledgments

• References

Theory And Application Of Hypersoft Set, Florentin Smarandache, Muhammad Saeed, Muhammad Saqlain, Mohamed Abdel-Baset

Branch Mathematics and Statistics Faculty and Staff Publications

Aims and Scope Florentin Smarandache generalize the soft set to the hypersoft set by transforming the function �� into a multi-argument function. This extension reveals that the hypersoft set with neutrosophic, intuitionistic, and fuzzy set theory will be very helpful to construct a connection between alternatives and attributes. Also, the hypersoft set will reduce the complexity of the case study. The Book “Theory and Application of Hypersoft Set” focuses on theories, methods, algorithms for decision making and also applications involving neutrosophic, intuitionistic, and fuzzy information. Our goal is to develop a strong relationship with the MCDM solving techniques and to …