Other Physical Sciences and Mathematics Commons^™

Multiscale Modelling Of Brain Networks And The Analysis Of Dynamic Processes In Neurodegenerative Disorders, Hina Shaheen

Theses and Dissertations (Comprehensive)

The complex nature of the human brain, with its intricate organic structure and multiscale spatio-temporal characteristics ranging from synapses to the entire brain, presents a major obstacle in brain modelling. Capturing this complexity poses a significant challenge for researchers. The complex interplay of coupled multiphysics and biochemical activities within this intricate system shapes the brain's capacity, functioning within a structure-function relationship that necessitates a specific mathematical framework. Advanced mathematical modelling approaches that incorporate the coupling of brain networks and the analysis of dynamic processes are essential for advancing therapeutic strategies aimed at treating neurodegenerative diseases (NDDs), which afflict millions of …

Convolution And Autoencoders Applied To Nonlinear Differential Equations, Noah Borquaye

Electronic Theses and Dissertations

Autoencoders, a type of artificial neural network, have gained recognition by researchers in various fields, especially machine learning due to their vast applications in data representations from inputs. Recently researchers have explored the possibility to extend the application of autoencoders to solve nonlinear differential equations. Algorithms and methods employed in an autoencoder framework include sparse identification of nonlinear dynamics (SINDy), dynamic mode decomposition (DMD), Koopman operator theory and singular value decomposition (SVD). These approaches use matrix multiplication to represent linear transformation. However, machine learning algorithms often use convolution to represent linear transformations. In our work, we modify these approaches to …

Random Variable Spaces: Mathematical Properties And An Extension To Programming Computable Functions, Mohammed Kurd-Misto

Computational and Data Sciences (PhD) Dissertations

This dissertation aims to extend the boundaries of Programming Computable Functions (PCF) by introducing a novel collection of categories referred to as Random Variable Spaces. Originating as a generalization of Quasi-Borel Spaces, Random Variable Spaces are rigorously defined as categories where objects are sets paired with a collection of random variables from an underlying measurable space. These spaces offer a theoretical foundation for extending PCF to natively handle stochastic elements.

The dissertation is structured into seven chapters that provide a multi-disciplinary background, from PCF and Measure Theory to Category Theory with special attention to Monads and the Giry Monad. The …

Translation Speed Influence On Tropical Cyclone Storm Tide And Surge Generation Along The Gulf Of Mexico Coast, Samantha L. Camarda

LSU Master's Theses

This research examines tropical cyclone translation speed as a factor in storm tide and surge height upon landfall on the United States Gulf Coast. Understanding the effect of translation speed on peak storm tide/surge height is needed to better prepare for and predict future damage from tropical cyclone events. Tropical cyclone data are taken from hourly interpolated best-track HURDAT2 data from 1970–2021. This study uses the HURDAT2 hourly interpolated observation data points (24-hours) pre-landfall to landfall. Translation speed is calculated based on the distance traversed between hourly points. Peak storm tide and storm surge data are taken from SURGEDAT from …

Helices In Fluids And Applications To Modeling In Biology, Eva M. Strawbridge

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Reducing Uncertainty In Sea-Level Rise Prediction: A Spatial-Variability-Aware Approach, Subhankar Ghosh, Shuai An, Arun Sharma, Jayant Gupta, Shashi Shekhar, Aneesh Subramanian

I-GUIDE Forum

Given multi-model ensemble climate projections, the goal is to accurately and reliably predict future sea-level rise while lowering the uncertainty. This problem is important because sea-level rise affects millions of people in coastal communities and beyond due to climate change's impacts on polar ice sheets and the ocean. This problem is challenging due to spatial variability and unknowns such as possible tipping points (e.g., collapse of Greenland or West Antarctic ice-shelf), climate feedback loops (e.g., clouds, permafrost thawing), future policy decisions, and human actions. Most existing climate modeling approaches use the same set of weights globally, during either regression or …

Longitudinal Case-Control Study Of Mammographic Breast Tissue Subtypes, Kendra Batchelder

Electronic Theses and Dissertations

Breast density is a known risk factor for breast cancer. However, there has been limited research on potential subtypes of mammographic dense breast tissue to identify areas of active dense tissue that is structurally reorganizing and links to cancer dynamics, versus areas of passive dense tissue which remains organized. We hypothesize that the amounts of subtypes of mammographic dense tissue and the associated rate of change through time could provide insights into breast cancer risk. A retrospective study was conducted to investigate breast cancer using longitudinal screening mammograms and accompanying pathology reports collected in 2015. Patients were matched by age …

Bite-Sized Quantitative Reasoning Essays: A Review Of Numbers Don’T Lie: 71 Stories To Help Us Understand The Modern World (2020), By Vaclav Smil, Samuel L. Tunstall

Numeracy

In Numbers Don’t Lie: 71 Stories to Help Us Understand the Modern World (2020), Vaclav Smil draws on his interdisciplinary background in science, public policy, and history to provide readers with 71 short essays that help us better understand aspects of the world–including its people, environment, energy consumption, and present crises (among other things). In most of his essays, Smil utilizes both data and reasoning with data to shed light on diverse topics, with issues ranging from happiness rankings and vaccine payoffs to chicken production and diesel engines. Though the book arguably has some flaws, its easy-to-digest essays–many of which …

One Formula For Non-Prime Numbers: Motivations And Characteristics, Mahmoud Mansour, Kamal Hassan Prof.

Basic Science Engineering

Primes are essential for computer encryption and cryptography, as they are fundamental units of whole numbers and are of the highest importance due to their mathematical qualities. However, identifying a pattern of primes is not easy. Thinking in a different way may get benefits, by considering the opposite side of the problem which means focusing on non-prime numbers. Recently, researchers introduced, the pattern of non-primes in two maximal sets while in this paper, non-primes are presented in one formula. Getting one-way formula for non-primes may pave the way for further applications based on the idea of primes.

Understanding The Beauty Of Mathematics By Composing Claude Debussy's Syrinx Into Mathematical Equations, Mackenzi Mehlberg

Honors Projects

Mesmerizing melodies and narrative storytelling are exemplified in Claude Debussy's Syrinx. As a well-known piece of solo flute literature, it is considered beautiful. Conversely, mathematics is seen as logical, and by implication not beautiful. Using Fourier Analysis, Syrinx can be represented in a different context: a series of mathematical equations. These mathematical equations can then be played as a different interpretation of Syrinx. With this interpretation, we see that mathematics is beautiful.

A Confluence Of Cultural And Water History With The Seli’Š Ksanka Qlispe’ Dam Formerly Named The Kerr Dam, Allisen A. Hansen

2023 Symposium

The Seli’š Ksanka Qlispe’ Dam (SKC Dam), formerly known as the Kerr Dam is the first Native American tribally owned dam in the United States. Located on the Confederated Salish and Kootenai Tribes(CSKT) of the Flathead Reservation, on the Flathead River in Montana, the dam was once considered the blight of the Whiteman’s landgrab and genocide of culture and language. Now it is a source of hope to the tribe to help its members and improve its future. Completed in 1938, it is one of two dams on the Flathead River, just south of the Flathead Lake. By following the …

Understanding The Impacts Of Topobathymetric Data On Storm Surge Model Predictions, Sydni Crain

Master's Theses

The topobathymetric characteristics of a region are regularly altered by natural and anthropogenic causes. This directly impacts the resulting storm surge during a hurricane. The primary goal of this research was to gain a better understanding of the impact that topography and bathymetry have on storm surge models, particularly the Advanced Circulation (ADCIRC) Model. Hurricane Zeta (2020) and Hurricane Ida (2021) were chosen as case studies; therefore, the Gulf of Mexico (GOM) was chosen as the study site. This research was completed by comparing ADCIRC storm surge results which were based on older, lower-resolution data with results derived from more …

Development And Applications Of Similarity Measures For Spatial-Temporal Event And Setting Sequences, Fuyu Xu

Electronic Theses and Dissertations

Similarity or distance measures between data objects are applied frequently in many fields or domains such as geography, environmental science, biology, economics, computer science, linguistics, logic, business analytics, and statistics, among others. One area where similarity measures are particularly important is in the analysis of spatiotemporal event sequences and associated environs or settings. This dissertation focuses on developing a framework of modeling, representation, and new similarity measure construction for sequences of spatiotemporal events and corresponding settings, which can be applied to different event data types and used in different areas of data science. The first core part of this dissertation …

Multiparametric Continuous And Mixed-Integer Nonlinear Optimization With Parameters In General Locations, Andrew Pangia

All Dissertations

Convex programming has been a research topic for a long time, both theoretically and algorithmically. Frequently, these programs lack complete data or contain rapidly shifting data. In response, we consider solving parametric programs, which allow for fast evaluation of the optimal solutions once the data is known. It has been established that, when the objective and constraint functions are convex in both variables and parameters, the optimal solutions can be estimated via linear interpolation. Many applications of parametric optimization violate the necessary convexity assumption. However, the linear interpolation is still useful; as such, we extend this interpolation to more general …

Soil Health And Remediation For Urban Gardens In Utah, Melissa Chilinski

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Urban environments are at an increased risk of soil contamination and poor soil health due to anthropogenic causes. As healthy farmland is developed, new urban farmers and gardeners are often left growing food on unwanted land with unknown histories of previous use. Varied research and methods for obtaining healthy soils can cause new growers to make decisions that negatively impact soil health and fertility, or on the other hand, conflicting information can cause individuals to become unnecessarily fearful of common soil contaminants and their effect on human health. Common soil contaminants, like trace metals (often referred to as heavy metals) …

Impact Of Cover Crop Species Diversity On Soil Nutrient Availability And Crop Productivity, Amanda Kramer

Masters Theses

Cover crops provide multiple environmental benefits that improve both soil and water quality; however, farmers only utilize them on approximately 5% of harvested U.S. cropland. Low adoption rates are attributed to yield impact concerns, seed and planting costs, and lack of advocacy. This study, which began in October 2019, assessed the effects of nitrogen rate and cover crop diversity on weed biomass, soil coverage, in-situ residue decomposition, soil nitrogen and phosphorus availability, and cash crop yield to better understand the costs and benefits of cover crop adoption at two locations in Tennessee (Milan and Spring Hill). Treatments were replicated 4 …

The Magnetic Field Of Protostar-Disk-Outflow Systems, Mahmoud Sharkawi

Electronic Thesis and Dissertation Repository

Recent observations of protostellar cores reveal complex magnetic field configurations that are distorted in the innermost disk region. Unlike the prestellar phase, where the magnetic field geometry is simpler with an hourglass configuration, magnetic fields in the protostellar phase are sculpted by the formation of outflows and rapid rotation. This gives rise to a significant azimuthal (or toroidal) component that has not yet been analytically modelled in the literature. Moreover, the onset of outflows, which act as angular momentum transport mechanisms, have received considerable attention in the past few decades. Two mechanisms: 1) the driving by the gradient of a …

Using Integral Projection Models To Explore Management Strategies For Silver Carp (Hypophthalmichthys Molitrix), Cameron Coles, Elizabeth Balas, James Peirce, Greg Sandland, Richard Erickson

Spora: A Journal of Biomathematics

Silver carp (Hypophthalmichthys molitrix) are planktivorous fish that were originally introduced to the United States for use in fish production ponds and have since escaped these enclosures and are invading the Mississippi River Basin. The silver carp invasion of the Illinois River has a myriad of negative effects on native ecosystems. In this paper, we introduce key dependencies that are likely important in the population dynamics of silver carp: length-dependent egg production and density-dependent growth. Using movement data between two adjacent pools of the Illinois River, we conduct numerical simulations to explore the theoretical effect of harvesting and …

Viscous Thin-Film Models Of Nanoscale Self-Organization Under Ion Bombardment, Tyler Evans

Mathematics Theses and Dissertations

For decades, it has been observed that broad-beam irradiation of semiconductor surfaces can lead to spontaneous self-organization into highly regular patterns, sometimes at length scales of only a few nanometers. Initial theory was largely based on erosion and redistribution of material occurring on fast time scales, which are able to produce good agreement with certain aspects of surface evolution. However, further experimental and theoretical work eventually led to the realization that numerous effects are active in the irradiated target, including stresses associated with ion-implantation and the accumulation of damage leading to the development of a disordered, amorphous layer atop the …

The Use Of Probability In Quantum Mechanics To Calculate Measurement Outcomes, Hannah E. Collins

CAFE Symposium 2023

The concept of probability can help measure some of the possible outcomes of different experiments in the field of quantum mechanics. Those experiments include Thomas Young's double slit experiment, the Schrödinger equation, the wave function, and the Born Rule, which all make use of probability to predict the placement of certain subatomic particles including photons of light, in the experiments. In this project, the manner in which probability does this is explored in depth.