Physical Sciences and Mathematics Commons^™

Corrigendum To “Applicability Of Reducing Valve Timing Overlap For Diesel Engines Under High Exhaust Back Pressure”

Journal of Marine Science and Technology

No abstract provided.

Moab Local Food Guide 2024, Roslynn Mccann, Shiree Duncan

All Current Publications

Thank you for picking up this Moab Utah Local Food Guide. Those growing and producing food within a 100 mile radius from Moab have been included in this guide to help YOU make locally sourced purchasing decisions!

Random Forests Regression For Soft Interval Data, Paul Gaona-Partida, Chih-Ching Yeh, Yan Sun, Adele Cutler

Mathematics and Statistics Faculty Publications

Analyzing soft interval data for uncertainty quantification has attracted much attention recently. Within this context, regression methods for interval data have been extensively studied. As most existing works focus on linear models, it is important to note that many problems in practice are nonlinear in nature and the development of nonlinear regression tools for interval data is crucial. This paper proposes an interval-valued random forests model that defines the splitting criterion of variance reduction based on an L₂ type metric in the space of compact intervals. The model simultaneously considers the centers and ranges of the interval data as …

An Investigation Of Students' Modes Of Thinking Concerning Linearity In Linear Algebra, Noa Levy

Honors Undergraduate Theses

The intent of this thesis is to investigate student approaches to linearity within a linear algebra context, focusing on definitional, computational, and theoretical skills. Linear algebra’s abstract nature constitutes a major challenge for a significant sector of STEM students, with the course often serving as undergraduates’ first encounter with mathematical proofs and extrapolations. The current student struggle is reflected through the prominent gap in knowledge derived from a lack of a concrete understanding of rudimentary concepts (like linearity), pivotal to student success. As such, this investigation aimed to bridge this gap by considering students’ modes of thinking regarding the elementary …

Critical Convergence: Mapping The Boundaries Of How Faculty Interrogate Whiteness In The Geoscience Educational Landscape, James E. Hobbs

Educational Leadership & Policy Studies Dissertations

This study examined the role of faculty members in interrogating whiteness within geoscience education. The dominant reliance on whiteness as the primary way of knowing in geoscience education has long perpetuated a singular perspective that serves as a mechanism for reinforcing existing power structures rooted in white supremacy. Drawing on tenets from Critical whiteness Studies, Curriculum Theory, and Transformative Learning Theory, this research investigated U.S. higher education faculty members' strategies and challenges in disrupting whiteness within the geoscience curriculum.

Through critical qualitative narrative inquiry, data were collected through semi-structured interviews with geoscience faculty members across multiple institutions across the United …

Tracking The Reaction Networks Of Criegee Intermediates Formed In The Ozone-Assisted Oxidation Reactions Of C5 Acyclic And Endocyclic Alkenes, Arden M. Floyd

Honors Undergraduate Theses

Uni- and bi-molecular reactions involving Criegee intermediates (CIs), characteristic to alkene-ozone reactions, play an important role in synthetic organic, atmospheric, and combustion chemistry. However, difficulty in detecting key intermediates has prevented a thorough understanding of the details of the ozonolysis mechanism. To gain new insights into how alkene structure affects the CI network, the ozone assisted oxidation reactions of trans-2-pentene and cyclopentene are investigated between 320 K and 760 K in an atmospheric pressure jet stirred reactor (JSR). Molecular-beam mass spectrometry in conjunction with single photon tunable synchrotron VUV radiation is used to identify elusive intermediates by means of …

Infusing Machine Learning And Computational Linguistics Into Clinical Notes, Funke V. Alabi, Onyeka Omose, Omotomilola Jegede

Mathematics & Statistics Faculty Publications

Entering free-form text notes into Electronic Health Records (EHR) systems takes a lot of time from clinicians. A large portion of this paper work is viewed as a burden, which cuts into the amount of time doctors spend with patients and increases the risk of burnout. We will see how machine learning and computational linguistics can be infused in the processing of taking clinical notes. We are presenting a new language modeling task that predicts the content of notes conditioned on historical data from a patient's medical record, such as patient demographics, lab results, medications, and previous notes, with the …

Inexact Fixed-Point Proximity Algorithm For The ℓ₀ Sparse Regularization Problem, Ronglong Fang, Yuesheng Xu, Mingsong Yan

Mathematics & Statistics Faculty Publications

We study inexact fixed-point proximity algorithms for solving a class of sparse regularization problems involving the ℓ₀ norm. Specifically, the ℓ₀ model has an objective function that is the sum of a convex fidelity term and a Moreau envelope of the ℓ₀ norm regularization term. Such an ℓ₀ model is non-convex. Existing exact algorithms for solving the problems require the availability of closed-form formulas for the proximity operator of convex functions involved in the objective function. When such formulas are not available, numerical computation of the proximity operator becomes inevitable. This leads to inexact iteration algorithms. We investigate in this …

A Novel K-Nearest Neighbors Method Based On Generalized Feature Optimization For Precipitation Forecasting, Sean Guidry Stanteen

Mathematics Dissertations

This study introduces a novel k-nearest neighbors (kNN) method of forecasting precipitation at weather-observing stations. The method identifies numerous monthly temporal patterns to produce precipitation forecasts for a specific month. Compared to climatological forecasts, which average the observed precipitation over the prior thirty years, and other existing contemporary iterations of kNN, the proposed novel kNN method produces more accurate forecasts on a consistent basis. Specifically, the novel kNN method produces improved root mean square errors (RMSE), mean relative errors, and Nash-Sutcliffe coefficients when compared to climatological and other kNN forecasts at five weather …

Point Modules And Line Modules Of Certain Quadratic Quantum Projective Spaces, Jose E. Lozano

Mathematics Dissertations

During the past 36 years, some research in noncommutative algebra has been driven by attempts to classify AS-regular algebras of global dimension four. Such algebras are often considered to be noncommutative analogues of polynomial rings. In the 1980s, Artin, Tate, and Van den Bergh introduced a projective scheme that parametrizes the point modules over a graded algebra generated by elements of degree one. In 2002, Shelton and Vancliff introduced the concept of line scheme, which is a projective scheme that parametrizes line modules.

This dissertation is in two parts. In the first part, we consider a 1-parameter family of quadratic …

Exploring The Role Of Undergraduate And Graduate Real Analysis Experiences In The Mathematical Trajectories Of Women Mathematicians From Historically Disenfranchised Groups, Te'a Riley

Mathematics Dissertations

This phenomenological study examines the role of undergraduate and graduate Real Analysis courses in shaping the mathematical trajectories of seven women Ph.D. mathematicians from groups historically disenfranchised in mathematics.Qualitative analysis of interviews explores various aspects of their development as mathematicians with a focus on their experiences in Real Analysis. This study applies Ryan & Deci’s (1985) Self-Determination Theory's Basic Psychological Need Theory and Critical Race Theory to analyze the trajectories of the participants. The research explores how the fulfillment of basic psychological needs in their Real Analysis courses may have influenced their academic and professional journeys. The basic psychological need …

Calculus Students’ Problem-Solving Strategies On Related Rates Of Change Problems Appearing In Online Versus Paper-And-Pencil Format, Tyson Bailey

Mathematics Dissertations

This study explores first-semester calculus students’ use of mathematical problem-solving strategies while working related rates of change problems in both an online homework format and a traditional pencil-paper format. We address two research questions: (1) How do students’ mathematical problem-solving strategies when working online homework on related rates of change problems compare with their problem-solving strategies when working paper-and-pencil homework related rates of change problems? (2) What influence does the ‘view an example’ feature in online homework have on a student’s problem-solving strategies when working an online RRC homework problem? Using scores on free-response midterm exam problems on related rates …

Batch Culture Models Of The Murine Gut Microbiome & The Impact Of Simple Dormancy On Dormancy-Capable Microorganisms Models, Ana C. Mendez

Mathematics Dissertations

The proposed mathematical biology research utilizes mathematical models to gain insight into biological systems. These systems of ordinary differential equations model diverse topics, ranging from gut microbiomes to harmful algal blooms. A complete stability analysis, supporting phase plane portraits, bifurcation diagrams, and numerical simulations will accompany the models presented. In Chapter 2, the murine gut microbiome is modeled to match laboratory experiments in the literature. In these experiments, mice eat plasmid-carrying “donor” bacteria and naturally carry plasmid-free “resident” bacteria in their gut. The models aim to capture the behavior of plasmids, donor bacteria, and resident bacteria. Chapter 3 explores dormancy …

The Direct And Inverse Scattering Problems For The Third-Order Operator, Ivan Toledo

Mathematics Dissertations

We consider the full-line direct and inverse scattering problems for the third-order ordinary differential equation containing two potentials decaying sufficiently fast at infinity. The direct scattering problem consists of the determination of the scattering data set when the two potentials are known. The scattering data set is made up of the corresponding scattering coefficients and the bound-state information. On the other hand, the inverse scattering problem involves the recovery of the two potentials when the scattering data set is available. We formulate the inverse scattering problem via a related Riemann--Hilbert problem on the complex plane. We describe the recovery of …

New Methods In Electrical Source Imaging Based On Eeg And Post-Mortem Pathology Data, Julio Cesar Enciso Alva

Mathematics Dissertations

A central task for Neuroscience is to determine the location of electrical activity of neural origin inside the brain. Electrical signals can be recorded at a high resolution in time but low resolution in space, thus making it difficult to locate their source unambiguously. Electrical Source Imaging (ESI) is a particular framework for neural electrical source location; it is possible by modeling any additional information we may have about the electrical sources. For instance, minimal-norm estimators assume that the most plausible estimation is that with a lower norm. However, these estimators possess a low resolution in space.

In this work, …

A New Mechanistic Model Of Brain Metabolism With Optimal Parametrization, Alice Lubbe

Mathematics Dissertations

Models of glucose metabolism in the brain often focus on chemical exchanges and reactions that occur as part of the tricarboxylic acid cycle (TCA cycle). Experiments involving nuclear magnetic resonance (NMR) spectroscopy to detect and measure carbon-labeled isotopomers of metabolites such as glutamate in vivo inform kinetic, mechanistic models used to study metabolic pathways. In the present work, a new model with two compartments, astrocytic and neuronal, is developed using known biochemical processes and fit to experimental data coming from fully labeled glucose infusions. A gradient descent method is introduced and employed to obtain optimal flux parameter values involved in …

Towards Energy-Efficient Edge Computing For Tiny Ai Applications, Vamsi Krishna Bhagavathula

Theses and Dissertations

As artificial intelligence (AI) applications become more common on the edge of networks, like Raspberry Pi servers, it is crucial to optimize their energy use. This research project investigates how AI algorithms affect energy efficiency and resource usage on Raspberry Pi servers. Two models were created: one predicts resource usage, and the other predicts power consumption of AI algorithms on Raspberry Pi. Several factors are considered like CPU and memory use, algorithm speed, dataset size, and types of algorithms and datasets. Using regression-based methods, we model how these factors affect energy use. By converting categorical factors into numerical ones, we …

Structure Of Fine Selmer Groups In Abelian P-Adic Lie Extensions, Debanjana Kundu, Filippo Alberto Edoardo Nuccio Mortarino Majno Di Capriglio, Sujatha Ramdorai

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

This paper studies fine Selmer groups of elliptic curves in abelian p -adic Lie extensions. A class of elliptic curves are provided where both the Selmer group and the fine Selmer group are trivial in the cyclotomic Z p -extension. The fine Selmer groups of elliptic curves with complex multiplication are shown to be pseudonull over the trivializing extension in some new cases. Finally, a relationship between the structure of the fine Selmer group for some CM elliptic curves and the Generalized Greenberg's Conjecture is clarified.

Deep Neural Networks: A Formulation Via Non-Archimedean Analysis, Wilson A. Zuniga-Galindo

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

We introduce a new class of deep neural networks (DNNs) with multilayered tree-like architectures. The architectures are codified using numbers from the ring of integers of non-Archimdean local fields. These rings have a natural hierarchical organization as infinite rooted trees. Natural morphisms on these rings allow us to construct finite multilayered architectures. The new DNNs are robust universal approximators of real-valued functions defined on the mentioned rings. We also show that the DNNs are robust universal approximators of real-valued square-integrable functions defined in the unit interval.

Conditional Quantization For Uniform Distributions On Line Segments And Regular Polygons, Pigar Biteng, Mathieu Caguiat, Tsianna Dominguez, Mrinal Kanti Roychowdhury

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Quantization for a Borel probability measure refers to the idea of estimating a given probability by a discrete probability with support containing a finite number of elements. If in the quantization some of the elements in the support are preselected, then the quantization is called a conditional quantization. In this paper, we have investigated the conditional quantization for the uniform distributions defined on the unit line segments and m-sided regular polygons, where m≥3, inscribed in a unit circle.

Integrable Semi-Discretization For A Modified Camassa-Holm Equation With Cubic Nonlinearity, Bao-Feng Feng, Heng-Chun Hu, Han-Han Sheng, Wei Yin, Guo-Fu Yu

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

In the present paper, an integrable semi-discretization of the modified Camassa-Holm (mCH) equation with cubic nonlinearity is presented. The key points of the construction are based on the discrete Kadomtsev-Petviashvili (KP) equation and appropriate definition of discrete reciprocal transformations. First, we demonstrate that these bilinear equations and their determinant solutions can be derived from the discrete KP equation through Miwa transformation and some reductions. Then, by scrutinizing the reduction process, we obtain a set of semi-discrete bilinear equations and their general soliton solutions in the Gram-type determinant form. Finally, we obtain an integrable semi-discrete analog of the mCH equation by …

Assessing Concepts, Procedures, And Cognitive Demand Of Chatgpt-Generated Mathematical Tasks, Bima Sapkota, Liza Bondurant

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

In November 2022, ChatGPT, an Artificial Intelligence (AI) large language model (LLM) capable of generating human-like responses, was launched. ChatGPT has a variety of promising applications in education, such as using it as thought-partner in generating curricular resources. However, scholars also recognize that the use of ChatGPT raises concerns, such as outputs that are inaccurate, nonsensical, or vague. We, two mathematics teacher educators, engaged in a collaborative self-study using qualitative descriptive approaches to investigate the procedures, concepts, and cognitive demand of ChatGPT-generated mathematical tasks focused on fraction multiplication using the area model approach. We found that the ChatGPT-generated tasks were …

Ivermectin, Colleen Aldous, Eleftherios Gkioulekas, Philip Oldfield

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

No abstract provided.

Brillouin Zones Of Integer Lattices And Their Perturbations, Herbert Edelsbrunner, Alexey Garber, Mohadese Ghafari, Teresa Heiss, Morteza Saghafian, Mathijs Wintraecken

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

For a locally finite set, 𝐴⊆ℝ𝑑 , the 𝑘 th Brillouin zone of 𝑎∈𝐴 is the region of points 𝑥∈ℝ𝑑 for which ‖𝑥−𝑎‖ is the 𝑘 th smallest among the Euclidean distances between 𝑥 and the points in 𝐴 . If 𝐴 is a lattice, the 𝑘 th Brillouin zones of the points in 𝐴 are translates of each other, and together they tile space. Depending on the value of 𝑘 , they express medium- or long-range order in the set. We study fundamental geometric and combinatorial properties of Brillouin zones, focusing on the integer lattice and its perturbations. Our …

Enhanced Resolution Method For Electromagnetic Vortex Imaging Based On Electromagnetic Information Theory, Da Liu, Hongyin Shi, Ting Yang, Zhijun Qiao

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

The electromagnetic vortex imaging possesses independent orbital angular momentum with orthogonal degrees of freedom (DoF), which implies the existence of enhanced information capacity. However, high-mode orbital angular momentum (OAM) beams have stringent generation conditions and inefficient information carrying capacity, which results in limited resolution. This paper proposes a method to combine the electromagnetic information theory (EIT) with the traditional electromagnetic vortex imaging technique, which allows one may obtain more target azimuth information. The DoF, as the main component of information, has been increased to achieve higher azimuth resolution. First, the propagation and imaging model for the electromagnetic vortex with statistical …

Optimizing Energy Consumption In Smart Homes Using Ga-Lstm, Akibor Junior Chukwuka, Bakare-Bolaji Moyosoreoluwa, Baboucarr Dibba

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

The need to optimize energy consumption arises from the inadequate energy supply many homes face. However, to optimize energy consumption in a home, one must be equipped with the knowledge of the energy consumption rate and energy supply rate in the home. This paper proposed the use of a Long Short-Term Memory (LSTM) model optimized by Genetic Algorithm (GA) to optimize the energy consumption in a smart home. The model was designed using 8 input variables, which were observed weather information of a given region over a span of 350 days. The data set was split into a training data …

Order-2 Delaunay Triangulations Optimize Angles, Herbert Edelsbrunner, Alexey Garber, Morteza Saghafian

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

The local angle property of the (order-1) Delaunay triangulations of a generic set in R2 asserts that the sum of two angles opposite a common edge is less than π. This paper extends this property to higher order and uses it to generalize two classic properties from order-1 to order-2: (1) among the complete level-2 hypertriangulations of a generic point set in R2, the order-2 Delaunay triangulation lexicographically maximizes the sorted angle vector; (2) among the maximal level-2 hypertriangulations of a generic point set in R2, the order-2 Delaunay triangulation is the only one that has the local angle property. …

Modeling The Effect Of Observational Social Learning On Parental Decision-Making For Childhood Vaccination And Diseases Spread Over Household Networks, Tamer Oraby, Andras Balogh

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

In this paper, we introduce a novel model for parental decision-making about vaccinations against a childhood disease that spreads through a contact network. This model considers a bilayer network comprising two overlapping networks, which are either Erdős–Rényi (random) networks or Barabási–Albert networks. The model also employs a Bayesian aggregation rule for observational social learning on a social network. This new model encompasses other decision models, such as voting and DeGroot models, as special cases. Using our model, we demonstrate how certain levels of social learning about vaccination preferences can converge opinions, influencing vaccine uptake and ultimately disease spread. In addition, …

Climate Risk, Insurance Retreat, And State Response, Mark P. Nevitt, Michael Pappas

Faculty Articles

Climate change is fundamentally destabilizing the private insurance industry, with many high-profile insurance companies exiting states in the face of catastrophic, climate-­induced risk. This rapid "insurance retreat" represents a major market signal in response to climate-exacerbated risks. Private businesses are making actuarial decisions, assessing that some locations are just too vulnerable to insure. At the same time, this insurance retreat also poses a policy challenge for states as they react to the mounting insurance gaps left by exiting private insurers.

This Article analyzes insurance retreat, its attendant policy challenges, and the lessons that can be drawn from state responses. It …

A Social-Ecological Approach To Evaluating Short-Term Water Leasing For Streamflow Conservation In Montana, Usa, Logan A. Brauer

Graduate Student Theses, Dissertations, & Professional Papers

Streams throughout Montana are increasingly caught between increasing temperatures, decreasing summer precipitation, and heavy water demand for irrigated agriculture. Amid rapidly growing urban populations and uncertain climatic futures, many watersheds in Montana may face water shortages that impact aquatic species and habitat in the upcoming years. Conservation efforts around the state are working to mitigate water stress in these streams especially during the late summer season, when streamflow is naturally lower, and/or in times of drought. One policy solution to address low flows is a concept known as temporary leasing or split season leasing programs (SSLP), whereby an entity (e.g., …