Physical Sciences and Mathematics Commons^™

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 …

Effective Wordle Heuristics, Ronald I. Greenberg

Computer Science: Faculty Publications and Other Works

While previous researchers have performed an exhaustive search to determine an optimal Wordle strategy, that computation is very time consuming and produced a strategy using words that are unfamiliar to most people. With Wordle solutions being gradually eliminated (with a new puzzle each day and no reuse), an improved strategy could be generated each day, but the computation time makes a daily exhaustive search impractical. This paper shows that simple heuristics allow for fast generation of effective strategies and that little is lost by guessing only words that are possible solution words rather than more obscure words.

Convex Ancient Solutions To Anisotropic Curve Shortening Flow, Benjamin Richards

Doctoral Dissertations

We construct ancient solutions to Anisotropic Curve Shortening Flow, including a
noncompact translator and compact solution that lives in a slab. We then show that
these are the unique ancient solutions that exist in a slab of a given width.

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 …

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

Dissertations and Doctoral Documents from 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 …

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

Dissertations and Doctoral Documents from 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

On Regularity Of Graph C*-Algebras, Gregory Joseph Faurot

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

We prove that for any countable directed graph E with Condition (K), the corresponding graph C*-algebra C*(E) has nuclear dimension at most two. We also prove that the nuclear dimension of certain extensions is at most one, which can be applied to certain graphs to achieve the optimal upper bound of one. Finally, we generalize some previous results for O_∞ -stability of graph algebras, and prove some partial results for Z-stability.

Advisor: Christopher Schafhauser

Gevrey Class Estimates Towards Null Controllability Of A Fluid Structure Interaction System, Dylan Mcknight

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

Fluid-Structure Interaction concerns the interaction of parabolic fluids and hyperbolic elastic structures via numerous mechanisms such as boundary coupling and pressure. These models find application in blood flow, fluid flow in the eye, and air flow over plane wings. Parabolic equations are well known for “infinite speed of propagation,” which manifests itself via a uniform bound on the resolvent of the infinitesimal generator of the associated strongly continuous semigroup. Qualitatively, a solution of a parabolic pde with rough initial data is immediately smooth for any positive time. A priori, it is not clear whether a fluid structure interaction inherits any …

On Neumann Boundary Conditions For Nonlocal Models With Finite Horizon, Scott Alex Hootman-Ng

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

Nonlocal models are have recently seen an explosive interest and development in the context of fracture mechanics, diffusion, image processing, population dynamics due to their ability to approximate differential-like operators with integral operators for inherently discontinuous solutions. Much of the work in the field focuses on how concepts from partial differential equations (PDEs) can be extended to the nonlocal domain. Boundary conditions for PDEs are crucial components for applications to physical problems, prescribing data on the domain boundary to capture the behavior of physical phenomena accurately with the underlying model. In this thesis we specifically examine a Neumann-type boundary condition …

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

Dissertations and Doctoral Documents from 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 …

Perturbations Of Representations Of Cartan Inclusions, Catherine Zimmitti

Dissertations and Doctoral Documents from 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, …

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

Dissertations and Doctoral Documents from 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 …

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 …

A Uniformly Most Powerful Test For The Mean Of A Beta Distribution, Richard Ntiamoah Kyei

Electronic Theses and Dissertations

The beta distribution is used in numerous real-world applications, including areas such as manufacturing (quality control) and analyzing patient outcomes in health care. It also plays a key role in statistical theory, including multivariate analysis of variance (MANOVA) and Bayesian statistics. It is a flexible distribution that can account for many different characteristics of real data. To our surprise, there has been very little work or discussion on performing statistical hypothesis testing for the mean when it is reasonable to assume that the population is beta distributed. Many analysts conduct traditional analyses using a t-test or nonparametric approach, try transformations, …

Robust Multivariate Estimation And Inference With The Minimum Density Power Divergence Estimator, Ebenezer Nkum

Open Access Theses & Dissertations

The estimation of the location vector and scatter matrix plays a crucial role in many multivariate statistical methods. However, the classical likelihood-based estimation is greatly influenced by outliers, potentially leading to unreliable decisions. Hence, a fundamental challenge in multivariate statistics is to develop robust alternatives that can maintain performancein the presence of outliers and deviations from the assumed data distribution. Unfortunately, methods with good global robustness often substantially sacrifice efficiency. To address this, we propose the adoption of Minimum Density Power Divergence (MDPD) estimation, a well-established robust technique known for its efficiency and statistical robustness to outliers and model violations. …

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 …

Data-Driven Model Reduction Strategies For Dynamical Systems, Talha Ahmed

Doctoral Dissertations

Many physically occurring phenomena are nonlinear in nature and can be understood through dynamical systems theory which describes how the state of the particular system evolves in time. However, it is generally cumbersome to analyze these processes in depth because of the nonlinearities in the mathematical model or large sets of equations. Model reduction strategies are employed for such nonlinear processes to reduce the model dimensionality and approximate the full model dynamics. In this study, we focus on data driven model reduction strategies for various biological systems where only observable data is available and illustrate their efficacy.

Our first work …

Contraction Rates For Mckean-Vlassov Stochastic Differential Equations, Dan Noelck

Theses and Dissertations

In response to the pressing need of modeling, analyzing and applying complex systems with inherent distribution- and memory-dependent dynamical behaviours, this dissertation investigates both distribution- and memory-dependent stochastic differential equations. Following the establishment of the well-posedness of these stochastic differential equations, this dissertation is focused on asymptotic properties of the underlying processes. Under suitable conditions on the coefficients of the stochastic differential equations, this dissertation derives explicit quantitative contraction rates for the convergence in Wasserstein distance for McKean-Vlasov stochastic differential equations (MVSDEs) and McKean-Vlasov functional stochastic differential equations (MVFSDEs). The obtained contraction results for MVSDEs are further utilized to demonstrate …

Cte Induced Premium Principles And Properties, Linjiao Wu

Theses and Dissertations

The traditional pricing approach in the insurance industry assumes independence among insureds, yet overlooks the complexities of interdependent risk profiles. This dissertation addresses this limitation by proposing a premium pricing model tailored for managing dependent risks, drawing inspiration from conditional tail expectation (CTE) theory. In our model, each individual insured's premium is contingent upon the collective loss surpassing a predefined threshold.

To validate the efficacy of our model, we introduce several key properties to ensure fairness and stability in premium determination among insured individuals, including diversification and monotonicity. Diversification ensures that adding one policyholder to the insured group does not …

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 …

The Geometry Of Ancient Solutions To Curvature Flows, Sathyanarayanan Rengaswami

Doctoral Dissertations

Following the tremendous success of the mean curvature flow, other variants such as the Gauss curvature flow, inverse mean curvature flow have been investigated in great detail, leading to interesting applications to other fields including partial differential equations, convex geometry etc. This calls for an investigation of curvature flow as a general phenomenon. While basic existence and uniqueness results, roundness estimates etc have been obtained, there isn't a substantial body of work that addresses the geometry of solutions of curvature flows and their relation to the choice of speed function used. It is therefore interesting to investigate curvature flows as …

First Diffusion Course: "The Structure Of Language As A Connection Between Artificial Intelligence, Information And Ethics", Dioneia Monte-Serrat

Journal of Humanistic Mathematics

From August 22nd to November 21st, the first Diffusion Course on “The structure of language as a connection between artificial intelligence, information and ethics” will take place on a Thursday of each month, in Ribeirao Preto, Brazil. You are cordially invited to sign up for in-person classes and join other researchers and students on this course.

7th International Conference On Creative Mathematical Sciences Communication (Cmsc`24), Frances A. Rosamond

Journal of Humanistic Mathematics

The 7th International Creative Mathematical Sciences Communication (CMSC) conference is scheduled for October 2024 in Trier, Germany. Initiated in Darwin, Australia in 2013, CMSC aims to explore novel methods of imparting computational thinking to diverse audiences including non-specialists, modern citizens, and children. Participants from around the world and from various and interdisciplinary disciplines such as science, education, dance, drama, and visual arts convene to exchange ideas, present experimental approaches, and collaborate on engaging children in the exploration of ongoing, unresolved research challenges.

Oh Statistics!, Heather L. Cook

Journal of Humanistic Mathematics

This poem was written about statistics and the usefulness thereof.

Discordium Mathematica - A Symphony In Aleph Minor, Vijay Fafat

Journal of Humanistic Mathematics

How did Mathematics arise? Who created it? Why is it subject to Godel’s Incompleteness Theorems? And what does all this have to do with Coleridge’s poem, “Kubla Khan”, and “The Person from Porlock”? Here is a complete mythology of Mathematics set in an epic poetry format, fusing thoughts and verses from Western religions and Eastern mysticism… Those with immense patience and careful reading shall reap the fruit… (best read on a large screen or in printed form)

Love Is No Mean Thing: A Larkin Logarithm, Michael P.H. Stanley Md

Journal of Humanistic Mathematics

This poem was recited at a marriage recently in Vermont. I met the groom in my freshman year. He was the first college friend I ever made, and he used to burst into the room like Cosmo Kramer and settle down in an easy-chair to think about math (my side of the dorm was quieter than his). I thought that was remarkable and delightful, and so, when the task came to write a matrimonial poem for him, I selected a mathematical conceit. The poem concludes with a mathematical paraphrasing of Philip Larkin's last line from Arundel Tomb.

Pi: A Perpetual Journey, Ravindra K. Bisht

Journal of Humanistic Mathematics

A brief history of the constant pi is presented with a poetic flavor.

Eighth Grade Algebra, Joseph Chaney

Journal of Humanistic Mathematics

This is a poem about the affirming power of algebra in the life of a teenager.

Prime Motivation Of Eratosthenes, Pamela L. King

Journal of Humanistic Mathematics

The sieve of Eratosthenes is used as a metaphor for the concept of people falling through the social safety net, and people who were once excluded, making efforts to increase inclusiveness.

Poems From The Series "At The Dimensional Border", Philip Fried

Journal of Humanistic Mathematics

Poems about the border between the second and third dimensions, on geometry and the human condition.