Digital Commons Network^™

Waves In Cosmological Background With Static Schwarzschild Radius In The Expanding Universe, Karen Yagdjian

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we prove the existence of global in time small data solutions of semilinear Klein–Gordon equations in space-time with a static Schwarzschild radius in the expanding universe.

On The Colorability Of The Sphere Complex, Bennett Haffner

Master's Theses

One of the most prominently studied groups in geometric group theory is the outer automorphism group of the free group Out(F). The sphere complex provides a topological model for Out(F). We demonstrate the chromatic number of the sphere complex is finite.

Examining The Lived Experiences Of Educators Using Different Levels Of Support For Teaching Math To Students With Learning Disabilities In Math Computation And Problem-Solving For Teachers At Public Cyber Charter High Schools In The Northeastern United States: A Transcendental Phenomenological Study, Leeann E. Mccullough

Doctoral Dissertations and Projects

The purpose of this transcendental phenomenological study was to describe the lived experiences of educators using different levels of support for teaching math to students with learning disabilities in math computation and problem-solving for teachers at public cyber charter high schools in the Northeastern United States. The theory guiding this study was Sweller’s cognitive load theory, as it explained the learning process of students with learning disabilities and how educators developed instructional methods that complement the learner’s needs. The central research question was, “What is the lived experience of 9-12th-grade mathematics teachers in supporting students with differing learning abilities in …

A Measure Of Interactive Complexity In Network Models, Will Deter

Northeast Journal of Complex Systems (NEJCS)

This work presents an innovative approach to understanding and measuring complexity in network models. We revisit several classic characterizations of complexity and propose a novel measure that represents complexity as an interactive process. This measure incorporates transfer entropy and Jensen-Shannon divergence to quantify both the information transfer within a system and the dynamism of its constituents’ state changes. To validate our measure, we apply it to several well-known simulation models implemented in Python, including: two models of residential segregation, Conway’s Game of Life, and the Susceptible-Infected-Susceptible (SIS) model. Our results reveal varied trajectories of complexity, demonstrating the efficacy and sensitivity …

Bootstrap Methods For Bias-Correcting Probability Distribution Parameters Characterizing Extreme Snow Accumulations, Kenneth Pomeyie, Brennan Bean

Mathematics and Statistics Student Research and Class Projects

Accurately quantifying the threat of collapse due to the weight of settled snow on the roof of a structure is crucial for ensuring structural safety. This quantification relies upon direct measurements of the snow water equivalent (SWE) of settled snow, though most weather stations in the United States only measure snow depth. The absence of direct load measurements necessitates the use of modeled estimates of SWE, which often results in the underestimation of the scale/variance parameter of the distribution of annual maximum SWE. This paper introduces a novel bias correction method that employs a bootstrap technique with regression-based models to …

A Measurement Of The Differential Drell-Yan Cross Section As A Function Of Invariant Mass In Proton–Proton Collisions At √ S = 13 Tev, William Robert Tabb

Dissertations and Doctoral Documents, University of Nebraska-Lincoln, 2023–

The Drell-Yan process, a crucial mechanism for producing lepton pairs in highenergy hadron collisions, serves as an essential probe for testing the Standard Model of particle physics. This dissertation presents a comprehensive measurement of the differential cross section with respect to the invariant mass of the lepton pairs, utilizing data collected by the CMS experiment at CERN from 2016 to 2018. Cross sections are essential for refining our understanding of parton distribution functions and the underlying quantum chromodynamics processes, thereby providing constraints on theoretical predictions. In this analysis, the cross sections are compared to theoretical models and simulations, offering new …

Hardy Spaces And Canonical Kernels On Quadric Cr Manifolds, Albert Boggess, Jennifer Brooks, Andrew Raich

Mathematical Sciences Faculty Publications and Presentations

R functions on an embedded quadric M always extend holomorphically to M + iΓ_M where Γ_M is the closure of the convex hull of the image of the Levi form. When Γ_M is a closed polygonal cone, we show that the Bergman kernel on the interior of M + iΓ_M is a derivative of the Szegö kernel. Moreover, we develop the L^p Hardy space theory which turns out to be particularly robust. We provide examples that show that it is unclear how to formulate a corresponding relationship between the Bergman and Szegö kernels …

What If The Resulting Interval Is Too Wide: From A Heuristic Fuzzy-Technique Idea To A Mathematically Justified Approach, Marc Fina, Vladik Kreinovich

Departmental Technical Reports (CS)

In engineering designs, we usually need to make sure that the values of some characteristics y do not exceed a certain threshold y0 – e.g., that the stress at each location does not exceed a certain critical value. Usually, we know how each of these characteristics y depends on the design parameters x1, . . . ,xn, i.e., we know the function y= f (x1, . . . ,xn). However, it is not enough to use the nominal values of the design parameters in our analysis, since the actual values are, in general, somewhat different from the nominal values. Often, …

Maximal Estimates For The ∂-Neumann Problem On Non-Pseudoconvex Domains, Phillip S. Harrington, Andrew Raich

Mathematical Sciences Faculty Publications and Presentations

It is well known that elliptic estimates fail for the ∂-Neumann problem. Instead, the best that one can hope for is that derivatives in every direction but one can be estimated by the associated Dirichlet form, and when this happens, we say that the ∂-Neumann problem satisfies maximal estimates. In the pseudoconvex case, a necessary and sufficient geometric condition for maximal estimates has been derived by Derridj (for (0, 1)-forms) and Ben Moussa (for (0, q)-forms when q ≥ 1). In this paper, we explore necessary conditions and sufficient conditions for maximal estimates in the non-pseudoconvex case. We also …

Mesenchymal Stem Cells In Autoimmune Disease: A Systematic Review And Meta-Analysis Of Pre-Clinical Studies, Hailey N. Swain, Parker D. Boyce, Bradley A. Bromet, Kaiden Barozinksy, Lacy Hance, Dakota Shields, Gayla R. Olbricht, Julie A. Semon

Mathematics and Statistics Faculty Research & Creative Works

Mesenchymal Stem Cells (MSCs) Are of Interest in the Clinic Because of their Immunomodulation Capabilities, Capacity to Act Upstream of Inflammation, and Ability to Sense Metabolic Environments. in Standard Physiologic Conditions, They Play a Role in Maintaining the Homeostasis of Tissues and Organs; However, there is Evidence that They Can Contribute to Some Autoimmune Diseases. Gaining a Deeper Understanding of the Factors that Transition MSCs from their Physiological Function to a Pathological Role in their Native Environment, and Elucidating Mechanisms that Reduce their Therapeutic Relevance in Regenerative Medicine, is Essential. We Conducted a Systematic Review and Meta-Analysis of Human MSCs …

Shapley Value Under Interval Uncertainty And Partial Information, Kittawit Autchariyapanikul, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In the 1950s, the future Nobelist Lloyd Shapley solved the problem of how to fairly divide the common gain. Namely, he showed that some reasonable requirements determine a unique division -- which is now known as the Shapley value. The main limitation of Shapley's solution is that it assumes that for each subgroup of the original group of participants, we know exactly how much this group could gain if it acted by itself, without involving others. In practice, we rarely know these exact values. At best, we know the bounds on each such value -- i.e., in other words, an …

Evolving Teacher Pedagogy Through Implementation Of Mathematical Modeling And Participation In Responsively Designed Professional Development, Geena Taite

Theses, Dissertations and Culminating Projects

Modeling with mathematics (MP4) is a mathematical practice standard that can be used to engage students in mathematical content standards as well as additional mathematical practice standards. Research has shown the benefits of mathematical modeling (e.g., Aguirre et al., 2019; Cirillo et al., 2016a), but also the challenges teachers can face implementing modeling (e.g., Asempapa & Sturgill, 2019; Manouchehri, 2017). This dissertation aimed to explore how mathematical modeling professional development was responsively designed and facilitated to support teachers’ pedagogical goals (RQ1). This dissertation also aimed to explore how my role as the designer and facilitator of professional development evolved (RQ2) …

Exploring Intraplate Seismicity In The Midwest, Alexa Fernández

Department of Earth and Atmospheric Sciences: Dissertations, Theses, and Student Research

Intraplate seismicity represents a notable occurrence within the stable North American Craton. This research explores the potential sources of stresses that could reactivate older faults and influence seismic activity within this region. Among these sources, the enduring impact of the last glacial period is considered, which includes continued glacial isostatic adjustments (GIA). During GIA the lithosphere rebounds due to the retreating ice, and the forebulge caused by far-field flexure in response to the glacial load, collapses. This results in significant faulting, fracturing, and seismic activity associated with the deglaciation phase. The adjustment of the lithosphere manifests as both near surface …

A Study On The Vanishing Of Ext, Andrew J. Soto Levins

Dissertations and Doctoral Documents, University of Nebraska-Lincoln, 2023–

This thesis has two goals. The first is to study an Ext analog of the rigidity of Tor, and the second is to study Auslander bounds.

In Chapter 2 we show that if R is an unramified hypersurface, if M and N are finitely generated R-modules, and if the nth Ext modules of M against N is zero for some n less than or equal to the grade of M, then the ith Ext module of M against N is zero for all i less than or equal to n. A corollary of this says that if …

Semigroup Well-Posedness And Finite Element Analysis Of A Biot-Stokes Interactive System, Sara Mcknight

Dissertations and Doctoral Documents, University of Nebraska-Lincoln, 2023–

The coupling of a porous medium modeled by the Biot equations and a fluid has many biological applications. There are numerous ways by which to model the fluid and to couple the porous medium with the fluid. This particular model couples the Biot equations to Stokes flow along the boundary, through the Beavers-Joseph-Saffman conditions. We address semigroup well-posedness of the system via an inf-sup approach, which along the way requires consideration of a related but uncoupled static Biot system. We also present the results of finite element analysis on both the uncoupled Biot system and the coupled system.

Advisor: Sara …

Virtual Unknotting Numbers For Families Of Virtual Torus Knots, Kaitlin R. Tademy

Dissertations and Doctoral Documents, University of Nebraska-Lincoln, 2023–

A virtual torus knot T(p,q,VC) sits in the intersection of the well-understood torus knot and the not-so-well-understood virtual knot, making it an intriguing object to study.

The unknotting number of a classical knot K is defined unambiguously. However, "the" unknotting number when K is a virtual knot is not as clear to define, since virtual knots have both classical and virtual crossings. We will define virtual unknotting number vu(K) as the minimum number of (classical) crossing changes required to unknot K. Under this definition of virtual unknotting, not all …

Spreads And Transversals And Their Connection To Geproci Sets, Allison Joan Ganger

Dissertations and Doctoral Documents, University of Nebraska-Lincoln, 2023–

Spreads of [set of prime numbers]³ over finite fields can yield geproci sets. We study the existence of transversals to such spreads, proving that spreads with two transversals exist for all finite fields, before further considering the groupoids coming from spreads when transversals do or do not exist. This is further considered for spreads of higher dimensional projective spaces. We also consider how certain spreads might generalize to characteristic zero and the connection to the previously known geproci sets coming from the root systems D₄ and F₄.

Advisor: Brian Harbourne

Perturbations Of Representations Of Cartan Inclusions, Catherine Zimmitti

Dissertations and Doctoral Documents, University of Nebraska-Lincoln, 2023–

A free semigroup algebra is the unital, weak operator topology closed algebra generated by a collection of Cuntz-Toeplitz isometries in B(H). Ken Davidson and David Pitts asked in [9] if a self-adjoint free semigroup algebra exists; Charles Read answered this question in [28] by constructing such an example, which Ken Davidson later simplified in [8]. The construction takes a standard representation of O₂ and multiplies it by a unitary operator in the diagonal MASA of the representation. This results in a new "perturbed" representation of O₂ generating a self-adjoint free semigroup algebra.

In this thesis, …

A Generalization Of The Graham-Pollak Tree Theorem To Even-Order Steiner Distance, Joshua N. Cooper, Gabrielle Tauscheck

Faculty Publications

Graham and Pollak showed in 1971 that the determinant of a tree’s distance matrix depends only on its number of vertices, and, in particular, it is always nonzero. The Steiner distance of a collection of 𝑘 vertices in a graph is the fewest number of edges in any connected subgraph containing those vertices; for 𝑘 =2 , this reduces to the ordinary definition of graphical distance. Here we show that the hyperdeterminant of the 𝑘 th order Steiner distance hypermatrix is always nonzero if 𝑘 is even, extending their result beyond 𝑘 =2 . Previously, the authors showed that the …

Numerical Simulation Of The Atmospheric Lamb Waves Generated By The Hunga Tonga-Hunga Ha'apai Eruption Using A Shallow Water Approximation, Augustus Tropea

Boise State University Theses and Dissertations

On January 15th, 2022 around 04:05 UTC the undersea volcano Hunga Tonga-Hunga Ha’apai located near the South Pacific island of Tonga violently erupted, and a large amount of energy was released into the atmosphere. The atmospheric disturbances generated by this event were detected by equipment all around the world. Analysis of this data revealed that some of these atmospheric disturbances were Lamb waves generated by the volcanic eruption. Previous works have successfully modeled these types of waves by using a shallow water approximation. Here we present results for the homogeneous shallow water equations at earth scale using high resolution finite …

Enumeration Of Level-K Hypertriangulations, Patrick J. Kaylor

Theses and Dissertations

Triangulations are a classical object in discrete and computational geometry that finds it uses in many other fields, including numerous applications. In this thesis we approach the question of enumerating all hypertriangulations of a point set, the family of tilings introduced by Olarte and Santos in 2022 as induced projections of hypersimplices. Unfortunately, the usual approach to enumeration of trinagulations using flips may not work for hypertriangulations as flip-connectivity is only conjectured for that family even in the two-dimensional case. As a result, we develop a DFS-based algorithm and present its Python implementation that enumerates all hypertriangulations of small point …

Making Sandwiches: A Novel Invariant In D-Module Theory, David Lieberman

Department of Mathematics: Dissertations, Theses, and Student Research

Say I hand you a shape, any shape. It could be a line, it could be a crinkled sheet, it could even be a the intersection of a cone with a 6-dimensional hypersurface embedded in a 7-dimensional space. Your job is to tell me about the pointy bits. This task is easier when you can draw the shape; you can you just point at them. When things get more complicated, we need a bigger hammer.

In a sense, that “bigger hammer” is what the ring of differential operators is to an algebraist. Then we will say some things and stuff …

Leveraging International Large-Scale Assessments: Insights From An Item-Writing Professional Development Program For High School Mathematics Teachers, Mark Lester B. Garcia, Catherine P. Vistro-Yu

Mathematics Faculty Publications

The Philippine Department of Education, despite seeing minimal improvements in the country’s score and rankings in the recent cycles of international large-scale assessments (ILSAs) such as TIMSS and PISA, maintained that it shall continue to participate in ILSAs to monitor the progress of educational effectiveness and benchmark with other countries by observing and adopting commendable practices. While legislators and other stakeholders push for increased financial resources in the education sector as part of the country’s preparations for upcoming ILSAs, one crucial aspect that is largely overlooked is teacher training. This paper presents a viable yet contentious way of upskilling teachers …

Missing Data Imputation With Longitudinal Data, Joseph Omar Alanis

Theses and Dissertations

In the repeated measures longitudinal datasets where missing data is a relatively common issue, we explored different imputation methods, including machine learning (ML) methods in order to examine potential efficiencies for using traditional versus newer computational methods. In order to accomplish said comparison, we used a Monte Carlo simulation experiment of a population of size N=70000 to mimic a clinical trial, with different scenarios of missing at random (MAR) data in the response variable. To compare the behavior of each method resulting from the difference between population and sample dataset, a real dataset was used from the Boston College on …

Recognizing Triangles Using Weighted Ehrhart Polynomials, Rafael Sarabia

Theses and Dissertations

Ehrhart theory is a classical topic for polygons or polytopes with vertices with integer coordinates. One of the main results of the theory claims that for every convex polygon P with integer vertices, the number of integer points in its nth dilation is a polynomial in n, the Ehrhart polynomial of P. This property can be extended if for a polynomial weight w(x, y), we sum values of w(x, y) over all points with integer coordinates in the nth dilation of P. The resulted polynomial is called the weighted Ehrhart polynomial of P associated with the weight w. In this …

Cohen-Macaulay Type Of Open Neighborhood Ideals Of Unmixed Trees, Jounglag Lim

All Theses

Given a tree T and a field k, we define the open neighborhood ideal N(T) of T in k[V] to be the ideal generated by the open neighborhoods of all vertices in the graph. If T is unmixed with respect to the total domination problem, then it is known that N(T) is Cohen-Macaulay. Our goal is to compute the (Cohen-Macaulay) type of k[V]/N(T) using graph theoretical properties of T. We achieve this by using homological algebra and properties of monomial ideals. Along the way, we also provide a different characterization of unmixed trees and a generalization of the total dominating …

A Survey On Homomorphic Encryption Based On The Learning With Rounding Problem, Jose Manuel Montoya

Boise State University Theses and Dissertations

Much of modern day cryptography deals with the notion of security and efficiency. The main concern with any cryptosystem deals with the practicality of being able to implement any encryption algorithm over large data sets. In this paper, we will look at the various properties of the Learning With Rounding problem (LWR) which comes from the Learning With Errors problem (LWE) first introduced by Oded Regev. We will also present the topic of Homomorphic Encryption (HE) as well as its three variants: Partially Homomorphic Encryption (PHE), Somewhat Homomorphic Encryption (SHE), and Fully Homomorphic Encryption (FHE). This paper also highlights SABER, …

Probabilistic Frames And Concepts From Optimal Transport, Dongwei Chen

All Dissertations

As the generalization of frames in the Euclidean space $\mathbb{R}^n$, a probabilistic frame is a probability measure on $\mathbb{R}^n$ that has a finite second moment and whose support spans $\mathbb{R}^n$. The p-Wasserstein distance with $p \geq 1$ from optimal transport is often used to compare probabilistic frames. It is particularly useful to compare frames of various cardinalities in the context of probabilistic frames. We show that the 2-Wasserstein distance appears naturally in the fundamental objects of frame theory and draws consequences leading to a geometric viewpoint of probabilistic frames.

We convert the classic lower bound estimates of 2-Wasserstein distance \cite{Gelbrich90, …

Relating Elasticity And Other Multiplicative Properties Among Orders In Number Fields And Related Rings, Grant Moles

All Dissertations

This dissertation will explore factorization within orders in a number ring. By far the most well-understood of these orders are rings of algebraic integers. We will begin by examining how certain types of subrings may relate to the larger rings in which they are contained. We will then apply this knowledge, along with additional techniques, to determine how the elasticity in an order relates to the elasticity of the full ring of algebraic integers. Using many of the same strategies, we will develop a corresponding result in the rings of formal power series. Finally, we will explore a number of …

Gan With Skip Patch Discriminator For Biological Electron Microscopy Image Generation, Nishith Ranjon Roy

Graduate Theses and Dissertations

GAN models have been successfully used for image generation in various sections such as real-life objects like human faces, cars, animal faces, landscapes, etc. This work focuses on biological electron microscopy (EM) image generation. Unlike other real-life objects, biological EM images are obtained through electron microscopy techniques to study biological specimens. Electron microscopy offers high resolution and magnification capabilities, making it a powerful tool for visualizing biological structures at the nanoscale. However, using GAN models for biological EM image generation poses challenges due to the complex and unique arrangements of biological structures and the sparse and asymmetrical patterns in EM …