Digital Commons Network^™

Optimal Selection Of Good Polynomials And Constructions Of Locally Recoverable Codes Via Galois Theory, Austin Dukes

USF Tampa Graduate Theses and Dissertations

To keep up with the ever-growing demand for reliable and efficient availability of data,locally recoverable codes (LRCs) have been the focus of much study due to their applications in cloud and distributed storage systems. A fundamental construction of LRCs was given in [36] based on polynomials which relied on the existence of r-good polynomials. In the same paper some constructions of good polynomials were given, but these constructions did not cover every configuration of parameters. Naturally this led to research into constructing good polynomials for what was not addressed in [36], but new ponderings were also posed, such as the …

Numerical Issues For A Non-Autonomous Logistic Model, Marina Mancuso, Kaitlyn M. Martinez, Carrie Manore, Fabio Milner

CODEE Journal

The user-friendly aspects of standardized, built-in numerical solvers in
computational software aid in the simulations of many problems solved using
differential equations. The tendency to trust output from built-in numerical
solvers may stem from their ease-of-use or the user’s unfamiliarity with the
inner workings of the numerical methods. Here, we show a case where the
most frequently used and trusted built-in numerical methods in Python’s
SciPy library produce incorrect, inconsistent, and even unstable approxima-
tions for a the non-autonomous logistic equation, which is used to model
biological phenomena across a variety of disciplines. Some of the most com-
monly used …

Supplementary Files For "Using Digitized Building And Weather Records To Improve The Accuracy Of Ground To Roof Snow Load Ratio Estimations", Gideon Parry, Brennan Bean

Browse all Datasets

Reliability targeted snow loads (RTLs) measure the weight in accumulated snow (i.e. snow load) that a roof is required to support to ensure the probability of failure is suf- ficiently low. This calculation has historically relied upon a probability distribution that characterizes the ratio between the annual maximum ground snow load to the annual max- imum roof snow load, a quantity referred to as Gr. The best available data for estimating Gr comes from Canadian case studies from the 1950s and 1960s. However, much of the data was never digitized, with only approximations of data being made available in scanned …

Cellular Automata Modeling Approach Of Addiction, Ruba Hameed

Thesis/ Dissertation Defenses

This thesis develops a mathematical model and cellular automata simulations to study the spread of drug addiction in populations, incorporating key factors like peer influence, substance availability, support networks, and awareness campaigns. The model describes transitions between non-use, experimental use, recreational use, and addiction states. Mathematical analysis establishes model properties, while an irregular graph cellular automata framework analyzes emerging spatial patterns and behaviors. Extensive scenario simulations explore peer influence, isolation, substance availability, support networks, and awareness campaign impacts, enabling visualization of model evolution over time and determining thresholds, tipping points, and intervention effectiveness. The findings provide an actionable understanding of …

Mixed Uncertainty Analysis On Pumping By Peristaltic Hearts Using Dempster-Shafer Theory, Yanyan He, Nicholas A. Battista, Lindsay D. Waldrop

Biology, Chemistry, and Environmental Sciences Faculty Articles and Research

In this paper, we introduce the numerical strategy for mixed uncertainty propagation based on probability and Dempster–Shafer theories, and apply it to the computational model of peristalsis in a heart-pumping system. Specifically, the stochastic uncertainty in the system is represented with random variables while epistemic uncertainty is represented using non-probabilistic uncertain variables with belief functions. The mixed uncertainty is propagated through the system, resulting in the uncertainty in the chosen quantities of interest (QoI, such as flow volume, cost of transport and work). With the introduced numerical method, the uncertainty in the statistics of QoIs will be represented using belief …

Combinatorial Problems On The Integers: Colorings, Games, And Permutations, Collier Gaiser

Electronic Theses and Dissertations

This dissertation consists of several combinatorial problems on the integers. These problems fit inside the areas of extremal combinatorics and enumerative combinatorics.

We first study monochromatic solutions to equations when integers are colored with finitely many colors in Chapter 2. By looking at subsets of {1, 2, . . . , n} whose least common multiple is small, we improved a result of Brown and Rödl on the smallest integer n such that every 2-coloring of {1, 2, . . . , n} has a monochromatic solution to equations with unit fractions. Using a recent result of Boza, …

Building Blocks For W-Algebras Of Classical Types, Vladimir Kovalchuk

Electronic Theses and Dissertations

The universal 2-parameter vertex algebra W_∞ of type W(2, 3, 4; . . . ) serves as a classifying object for vertex algebras of type W(2, 3, . . . ,N) for some N in the sense that under mild hypothesis, all such vertex algebras arise as quotients of W_∞. There is an ℕ X ℕ family of such 1-parameter vertex algebras known as Y-algebras. They were introduced by Gaiotto and Rapčák are expected to be building blocks for all W-algebras in type A, i.e, every W-(super) algebra in …

Circling The Square: Computing Radical Two, Isaiah Mellace, Joshua Kroeker

NEXUS: The Liberty Journal of Interdisciplinary Studies

Discoveries of equations for irrational numbers are not new. From Newton’s Method to Taylor Series,there are many ways to calculate the square root of two to arbitrary precision. The following method is similar in this way, but it is also a fascinating derivation from geometry that has applications to other irrationals. Additionally, the equation derived has some properties that may lead to fast computation. The first part of this paper is dedicated to deriving the equation, and the second is focused on computer science implementations and optimizations.

Mathematical Modeling Of An Epidemic In Scale-Free Network With Imperfect Vaccination, Heba Hameed

Thesis/ Dissertation Defenses

In light of the recent COVID-19 pandemic, the mathematical epidemiological model has proven to be essential for understanding the disease dynamic and finding the best control tool to help contain the disease and minimize its impact. This thesis investigates the dynamics of an infectious disease spread with latent infection and vaccination. The aim is to study this model's dynamic in a network that reflects the heterogeneity of the environment where the disease spreads. The vaccination is assumed to be not perfect, which means that vaccinated persons are likely to be infected and that the vaccinated person could lose their immunity, …

The Product Of Distributions And Stochastic Differential Equations Arising From Powers Of Infinite Dimensional Brownian Motions, Un Cig Ji, Hui-Hsiung Kuo, Hara-Yuko Mimachi, Kimiaki Saitô

Journal of Stochastic Analysis

No abstract provided.

Instructional Strategies That Support Student Achievement With The Eureka Algebra 1 Curriculum, Honnalora Hill

Walden Dissertations and Doctoral Studies

Numerous states use research-based mathematics curricula as a teaching tool to enhance mathematics performance outcomes on state assessment scores. Despite implementation of the Eureka curriculum, students at the study site were still struggling to master Algebra 1 skills sufficiently to pass the Louisiana state exam. The aim of this basic qualitative study was to explore strategies teachers employed while implementing the Eureka curriculum to increase student achievement. The study was guided by Vygotsky’s zone of proximal development (ZPD) theoretical framework and involved semi-structured interviews with 12 participants who had been teaching Algebra 1 with the Eureka curriculum for at least …

Instructional Strategies That Support Student Achievement With The Eureka Algebra 1 Curriculum, Honnalora Hill

Walden Dissertations and Doctoral Studies

Numerous states use research-based mathematics curricula as a teaching tool to enhance mathematics performance outcomes on state assessment scores. Despite implementation of the Eureka curriculum, students at the study site were still struggling to master Algebra 1 skills sufficiently to pass the Louisiana state exam. The aim of this basic qualitative study was to explore strategies teachers employed while implementing the Eureka curriculum to increase student achievement. The study was guided by Vygotsky’s zone of proximal development (ZPD) theoretical framework and involved semi-structured interviews with 12 participants who had been teaching Algebra 1 with the Eureka curriculum for at least …

Schur Analysis Over The Unit Spectral Ball, Daniel Alpay, Ilwoo Choo

Mathematics, Physics, and Computer Science Faculty Articles and Research

We begin a study of Schur analysis when the variable is now a matrix rather than a complex number. We define the corresponding Hardy space, Schur multipliers and their realizations, and interpolation. Possible applications of the present work include matrices of quaternions, matrices of split quaternions, and other algebras of hypercomplex numbers.

Nidus Idearum. Scilogs, Xiv: Superhyperalgebra, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this fourteenth book of scilogs – one may find topics on examples where neutrosophics works and others don’t, law of included infinitely-many-middles, decision making in games and real life through neutrosophic lens, sociology by neutrosophic methods, Smarandache multispace, algebraic structures using natural class of intervals, continuous linguistic set, cyclic neutrosophic graph, graph of neutrosophic triplet group , how to convert the crisp data to neutrosophic data, n-refined neutrosophic set ranking, adjoint of a square neutrosophic matrix, neutrosophic optimization, de-neutrosophication, the n-ary soft set relationship, hypersoft set, extending the hypergroupoid to the superhypergroupoid, alternative ranking, Dezert-Smarandache Theory (DSmT), reconciliation between …

`The Very Beautiful Principles Of Natural Philosophy': Michael Faraday, Paper Marbling And The Physics Of Natural Forms, Robert Pepperell

LASER Journal

In 1854, Michael Faraday wrote to thank the author who had sent him a book on the art of paper marbling. In the letter, Faraday referred to `the very beautiful principles of natural philosophy' involved in the process of dropping ink on thickened water. What are the `beautiful principles' that Faraday referred to, and how are they involved in the art of paper marbling? Here I consider some of the physical processes that occur in paper marbling and how the patterns that emerge represent `dissipative structures' that are governed by fundamental principles of nature, in particular the tendency for physical …

Are All Weakly Convex And Decomposable Polyhedral Surfaces Infinitesimally Rigid?, Jilly Kevo

Rose-Hulman Undergraduate Mathematics Journal

It is conjectured that all decomposable (that is, interior can be triangulated without adding new vertices) polyhedra with vertices in convex position are infinitesimally rigid and only recently has it been shown that this is indeed true under an additional assumption of codecomposability (that is, the interior of the difference between the convex hull and the polyhedron itself can be triangulated without adding new vertices). One major set of tools for studying infinitesimal rigidity happens to be the (negative) Hessian M_T of the discrete Hilbert-Einstein functional. Besides its theoretical importance, it provides the necessary machinery to tackle the problem …

Big Two And N-Card Poker Probabilities, Brian Wu, Chai Wah Wu

Communications on Number Theory and Combinatorial Theory

Between the poker hands of straight, flush, and full house, which hand is more common? In standard 5-card poker, the order from most common to least common is straight, flush, full house. The same order is true for 7-card poker such as Texas hold'em. However, is the same true for n-card poker for larger n? We study the probability of obtaining these various hands for n-card poker for various values of n≥5. In particular, we derive closed expressions for the probabilities of flush, straight and full house and show that the probability of a flush is less than a straight …

Khovanov Homology And Legendrian Simple Knots, Ryan J. Maguire

Dartmouth College Ph.D Dissertations

The Jones polynomial and Khovanov homology are powerful invariants in knot theory. Their computations are known to be NP-Hard and it can be quite a challenge to directly compute either of them for a general knot. We develop explicit algorithms for the Jones polynomial and discuss the implementation of an algorithm for Khovanov homology. Using this we tabulate the invariants for millions of knots, generate statistics on them, and formulate conjectures for Legendrian and transversely simple knots.

Penney’S Game For Permutations, Yixin Lin

Dartmouth College Ph.D Dissertations

We explore the permutation analog of Penney's game for coin flips. Two players, in order, each choose a permutation of length $k\ge3$. Then a sequence of independent random values from a continuous distribution is generated until the relative order of the last $k$ numbers matches one of the chosen permutations, declaring the player who selected that permutation as the winner.

We calculate the winning probabilities for all pairs of permutations of length $3$ and some pairs of length $4$, demonstrating the non-transitive property of this game, consistent with the original word version. Alternatively, we provide formulas for computing the winning …

On Pattern Avoidance And Dynamical Algebraic Combinatorics, Benjamin Adenbaum

Dartmouth College Ph.D Dissertations

Over the past decade since the term `dynamical algebraic combinatorics' was coined there has been a tremendous amount of activity in the field. Adding to that growing body of work this thesis hopes to be a step towards a broader study of pattern avoidance within dynamical algebraic combinatorics and helps initiate that by considering an action of rowmotion on 321-avoiding permutations. Additionally within we show the first known instance of piecewise-linear rowmotion periodicity for an infinite family of posets that does not follow from a more general birational result. Finally we show that the code of permutation restricted to permutations …

Bi-Harmonic Maps' Existence And P-Balanced Energy And Connections To Harmonic Maps, Lina Wu

Publications and Research

We discover a bi-harmonic map’ existence, its energy growth, and its connections to a harmonic map. First, we prove the existence of a nontrivial bi-harmonic map in a unit sphere. Second, we investigate the p-balanced energy growth of biharmonic maps. As the most important energy technical breakthroughs, we propose an innovative energy algorithm called p-balanced energy technique to break the constraints of the existing L^q-energy technique in detecting L^q-energy growth towards boundlessness. The disadvantage of the finite L^q -energy technique in the L ^q spaces is not effective in dealing with infinite L^q- energy in Non-L^q spaces. Third, we study …

Supplementary Files For: "Interactive Modeling Of Bear Lake Elevations In A Future Climate", Benjamin D. Shaw, Scout Jarman, Brennan Bean, Kevin R. Moon, Wei Zhang, Nathan Butler, Tommy Bolton, April Knight, Emeline Haroldsen, Abby Funk, Rebecca Higbee

Browse all Datasets

The water level, or elevation, of Bear Lake has a significant impact on agriculture, power, infrastructure, and recreation for communities around the lake. Climatological variables, such as precipitation, temperature, and snowfall, all have an impact on the elevation of Bear Lake. As the climate changes due to greenhouse gas emissions, the typical behaviors of these climate variables change, leading to new behaviors in Bear Lake elevation. Because of the importance of Bear Lake, it is vital to be able to model and understand how Bear Lake's elevation may change in the face of different climate scenarios and to gain further …

Topological Indices And Their Applications In Designing Drugs, Fedaa Ismail Abunawa

Thesis/ Dissertation Defenses

This research delves into the use of indices, in the field of drug design with a specific focus on anticancer medications. Topological indices, values derived from representations of chemical structures provide meaningful connections to the physical and chemical characteristics of molecules. These indices act as tools for predicting behavior playing a vital role in crafting therapeutic drugs. The study primarily delves into topological indices like the Sombor index, Randić index, and Atom Bond Connectivity (ABC) index. These indices are calculated for structures and their relationships with physical properties such as molar volume, refractive index, and flash point are explored using …

Oscillations In Neuronal Activity: A Neuron-Centered Spatiotemporal Model Of The Unfolded Protein Response In Prion Diseases, Elliot M. Miller, Tat Chung D. Chan, Carlos Montes-Matamoros, Omar Sharif, Laurent Pujo-Menjouet, Michael R. Lindstrom

School of Mathematical & Statistical Sciences Faculty Publications

Many neurodegenerative diseases (NDs) are characterized by the slow spatial spread of toxic protein species in the brain. The toxic proteins can induce neuronal stress, triggering the Unfolded Protein Response (UPR), which slows or stops protein translation and can indirectly reduce the toxic load. However, the UPR may also trigger processes leading to apoptotic cell death and the UPR is implicated in the progression of several NDs. In this paper, we develop a novel mathematical model to describe the spatiotemporal dynamics of the UPR mechanism for prion diseases. Our model is centered around a single neuron, with representative proteins P …

Yang-Baxter Equations, David Lovitz

Dissertations and Theses

Multiple equations in math, physics, quantum information, and elsewhere are referred to as "the" Yang-Baxter equation, in spite of being a broad family of equations. Most of the equations are nonlinear matrix equations, where the unknown variable is a matrix. This is the case for the so called braided, algebraic, and generalized forms of "the" equation, which are the primary focus of this dissertation. Finding solutions to the various forms of these equations has been the subject of much research. The equations in all their forms are largely considered intractable in high dimensions, and only in dimension 2 have the …

Statistics For Anticyclotomic Iwasawa Invariants Of Elliptic Curves, Jeffrey Hatley, Debanjana Kundu, Anwesh Ray

School of Mathematical & Statistical Sciences Faculty Publications

We study the average behaviour of the Iwasawa invariants for Selmer groups of elliptic curves, considered over anticyclotomic Zp -extensions in both the definite and indefinite settings. The results in this paper lie at the intersection of arithmetic statistics and Iwasawa theory.

How To Propagate Uncertainty Via Ai Algorithms, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Any data processing starts with measurement results. Measurement results are never absolutely accurate. Because of this measurement uncertainty, the results of processing measurement results are, in general, somewhat different from what we would have obtained if we knew the exact values of the measured quantities. To make a decision based on the result of data processing, we need to know how accurate is this result, i.e., we need to propagate the measurement uncertainty through the data processing algorithm. There are many techniques for uncertainty propagation. Usually, they involve applying the same data processing algorithm several times to appropriately modified data. …

Multivalued Variational Inequalities With Generalized Fractional Φ-Laplacians, Vy Khoi Le

Mathematics and Statistics Faculty Research & Creative Works

In this article, we examine variational inequalities of the form (Formula presented.), where (Formula presented.) is a generalized fractional (Formula presented.) -Laplace operator, K is a closed convex set in a fractional Musielak–Orlicz–Sobolev space, and (Formula presented.) is a multivalued integral operator. We consider a functional analytic framework for the above problem, including conditions on the multivalued lower order term (Formula presented.) such that the problem can be properly formulated in a fractional Musielak–Orlicz–Sobolev space, and the involved mappings have certain useful monotonicity–continuity properties. Furthermore, we investigate the existence of solutions contingent upon certain coercivity conditions.

For Discrete-Time Linear Dynamical Systems Under Interval Uncertainty, Predicting Two Moments Ahead Is Np-Hard, Luc Jaulin, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In the first approximation, when changes are small, most real-world systems are described by linear dynamical equations. If we know the initial state of the system, and we know its dynamics, then we can, in principle, predict the system's state many moments ahead. In practice, however, we usually know both the initial state and the coefficients of the system's dynamics with some uncertainty. Frequently, we encounter interval uncertainty, when for each parameter, we only know its range, but we have no information about the probability of different values from this range. In such situations, we want to know the range …

How To Make Ai More Reliable, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the reasons why the results of the current AI methods (especially deep-learning-based methods) are not absolutely reliable is that, in contrast to more traditional data processing techniques which are based on solid mathematical and statistical foundations, modern AI techniques use a lot of semi-heuristic methods. These methods have been, in many cases, empirically successful, but the absence of solid justification makes us less certain that these methods will work in other cases as well. To make AI more reliable, it is therefore necessary to provide mathematical foundations for the current semi-heuristic techniques. In this paper, we show that …