Physical Sciences and Mathematics Commons^™

About Time: Visualizing Time At Burning Man, Gordon D. Hoople, Austin Choi-Fitzpatrick, Nathaniel Parde, Diane Hoffoss, Max Mellette, Rachel Nishimura, Virginia Gutman

The STEAM Journal

About Time was a 30 foot long, 3000 pound wooden sundial that went up in flames at Burning Man 2019. The piece reflected on the role time plays in our lives. We organize our lives around time—are enslaved to time—and yet we know so little about it. Physicists and philosophers continue to grapple with deep puzzles of time—Is time a fundamental quantity, independent of human actions or observations or is it an emergent property of our perception? This installation projected time using two sundials: a horizontal dial which swept time out across the desert floor and an …

Convex Relaxations Of A Continuum Aggregation Model, And Their Efficient Numerical Solution, Mahdi Bandegi

Dissertations

In this dissertation, the global minimization of a large deviations rate function (the Helmholtz free energy functional) for the Boltzmann distribution is discussed. The Helmholtz functional arises in large systems of interacting particles — which are widely used as models in computational chemistry and molecular dynamics. Global minimizers of the rate function (Helmholtz functional) characterize the asymptotics of the partition function and thereby determine many important physical properties such as self-assembly, or phase transitions. Finding and verifying local minima to the Helmholtz free energy functional is relatively straightforward. However, finding and verifying global minima is much more difficult since the …

Dimension Reduction Techniques For High Dimensional And Ultra-High Dimensional Data, Subha Datta

Dissertations

This dissertation introduces two statistical techniques to tackle high-dimensional data, which is very commonplace nowadays. It consists of two topics which are inter-related by a common link, dimension reduction.

The first topic is a recently introduced classification technique, the weighted principal support vector machine (WPSVM), which is incorporated into a spatial point process framework. The WPSVM possesses an additional parameter, a weight parameter, besides the regularization parameter. Most statistical techniques, including WPSVM, have an inherent assumption of independence, which means the data points are not connected with each other in any manner. But spatial data violates this assumption. Correlation between …

Connectivity Differences Between Gulf War Illness (Gwi) Phenotypes During A Test Of Attention, Tomas Clarke, Jessie Jamieson, Patrick Malone, Rakib U. Rayhan, Stuart Washington, John W. Vanmeter, James N. Baraniuk

Department of Mathematics: Faculty Publications

One quarter of veterans returning from the 1990–1991 Persian Gulf War have developed Gulf War Illness (GWI) with chronic pain, fatigue, cognitive and gastrointestinal dysfunction. Exertion leads to characteristic, delayed onset exacerbations that are not relieved by sleep. We have modeled exertional exhaustion by comparing magnetic resonance images from before and after submaximal exercise. One third of the 27 GWI participants had brain stem atrophy and developed postural tachycardia after exercise (START: Stress Test Activated Reversible Tachycardia). The remainder activated basal ganglia and anterior insulae during a cognitive task (STOPP: Stress Test Originated Phantom Perception). Here, the role of attention …

Eigenvalue Problems For An Elliptic Equation With Two Singular Coefficients, Asror M. Shokirov

Scientific Bulletin. Physical and Mathematical Research

For the elliptic type of differential equation with two singular coefficients, the quadratic values of the Dirixle and Dirixle-Neumann problems were found in the quarter in that work. The field and boundary conditions for solving these problems are described in the polar coordinate system. The result is a rectangle in the polar coordinate system. Then, we used the method of separating variables in the right rectangle, that is, divided the variables by the equation and divided the problem into two distinct values for ordinary differential equations. The first of the ordinary differential equations is the substitution of , where the …

The Task Of Prosecuting Simple Differential Games On The Rectangle, Azizhon O. Zunnunov

Scientific Bulletin. Physical and Mathematical Research

The theory of differential games is developed and resulted from modeling technical problems. Some of the problems in differential games theory can be described as controlling two moving objects, i.e. one of them is the follower that tries to catch the other object, and obviously the other object is the runner. The runner tries to run away from the follower. Most of the practical and theoretical IT problems, planning, technical and other challenges will be derived to the differential games theory for resolution. Thus researching this theory is one of most important topics currently. A lot of researchers contributed enormous …

Description Of 2-Local Two Sided Multiplication On An Algebra Of Matrices, Farhodjon N. Arzikulov, Kamola A. Solijanova

Scientific Bulletin. Physical and Mathematical Research

The present paper is devoted to 2-local derivation on associative and Jordan matrix rings. In 1997, P. Semrl introduced the notion of 2-local derivations and described 2-local derivations on the algebra ¬B(H) of all bounded linear operators on the infinite-dimensional separable Hilbert space H. A similar description for the finite-dimensional case appeared later in 2004. In the paper Y. Lin and T. Wong 2-local derivations have been described on matrix algebras over finite dimensional division rings. In 2012 Sh. Ayupov, K. Kudaybergenov suggested a new technique and have generalized the above mentioned results for abritrary Hilbert spaces. Namely they considered …

Isolated Point Theorems For Uniform Algebras On Smooth Manifolds, Swarup Ghosh

Faculty Articles & Research

In 1957, Andrew Gleason conjectured that if A is a uniform algebra on its maximal ideal space X and every point of X is a one-point Gleason part for A, then A must contain all continuous functions on X. Gleason’s conjecture was disproved by Brian Cole in 1968. In this paper, we establish a strengthened form of Gleason’s conjecture for uniform algebras generated by real-analytic functions on compact subsets of real-analytic three-dimensional manifolds-with-boundary.

Model Selection And Experimental Design Of Biological Networks With Algebraic Geometry, Anyu Zhang

Mathematics Theses and Dissertations

Model selection based on experimental data is an essential challenge in biological data science. In decades, the volume of biological data from varied sources, including laboratory experiments, field observations, and patient health records has seen an unprecedented increase. Mainly when collecting data is expensive or time-consuming, as it is often in the case with clinical trials and biomolecular experiments, the problem of selecting information-rich data becomes crucial for creating relevant models.

Motivated by certain geometric relationships between data, we partitioned input data sets, especially data sets that correspond to a unique basis, into equivalence classes with the same basis to …

A Qualitative Representation Of Spatial Scenes In R2 With Regions And Lines, Joshua Lewis

Electronic Theses and Dissertations

Regions and lines are common geographic abstractions for geographic objects. Collections of regions, lines, and other representations of spatial objects form a spatial scene, along with their relations. For instance, the states of Maine and New Hampshire can be represented by a pair of regions and related based on their topological properties. These two states are adjacent (i.e., they meet along their shared boundary), whereas Maine and Florida are not adjacent (i.e., they are disjoint).

A detailed model for qualitatively describing spatial scenes should capture the essential properties of a configuration such that a description of the represented objects …

Theory Of Lexicographic Differentiation In The Banach Space Setting, Jaeho Choi

Electronic Theses and Dissertations

Derivative information is useful for many problems found in science and engineering that require equation solving or optimization. Driven by its utility and mathematical curiosity, researchers over the years have developed a variety of generalized derivatives. In this thesis, we will first take a look at Clarke’s generalized derivative for locally Lipschitz continuous functions between Euclidean spaces, which roughly is the smallest convex set containing all nearby derivatives of a domain point of interest. Clarke’s generalized derivative in this setting possesses a strong theoretical and numerical toolkit, which is analogous to that of the classical derivative. It includes nonsmooth versions …

Individual Based Modeling And Analysis Of Pathogen Levels In Poultry Chilling Process, Zachary Mccarthy, Ben Smith, Aamir Fazil, Jianhong Wu, Shawn D. Ryan, Daniel Munther

Mathematics and Statistics Faculty Publications

Pathogen control during poultry processing critically depends on more enhanced insight into contamination dynamics. In this study we build an individual based model (IBM) of the chilling process. Quantifying the relationships between typical Canadian processing specifications, water chemistry dynamics and pathogen levels both in the chiller water and on individual carcasses, the IBM is shown to provide a useful tool for risk management as it can inform risk assessment models. We apply the IBM to Campylobacter spp. contamination on broiler carcasses, illustrating how free chlorine (FC) sanitization, organic load in the water, and pre-chill carcass pathogen levels affect pathogen levels …

Enriched Derivators, James Richardson

Electronic Thesis and Dissertation Repository

In homotopical algebra, the theory of derivators provides a convenient abstract setting for computing with homotopy limits and colimits. In enriched homotopy theory, the analogues of homotopy (co)limits are weighted homotopy (co)limits. In this thesis, we develop a theory of derivators and, more generally, prederivators enriched over a monoidal derivator E. In parallel to the unenriched case, these E-prederivators provide a framework for studying the constructions of enriched homotopy theory, in particular weighted homotopy (co)limits.

As a precursor to E-(pre)derivators, we study E-categories, which are categories enriched over a bicategory Prof(E) associated to E. We prove a number of fundamental …

Rearrangement Operations On Unrooted Phylogenetic Networks, Remie Janssen, Jonathan Klawitter

Theory and Applications of Graphs

Rearrangement operations transform a phylogenetic tree into another one and hence induce a metric on the space of phylogenetic trees. Popular operations for unrooted phylogenetic trees are NNI (nearest neighbour interchange), SPR (subtree prune and regraft), and TBR (tree bisection and reconnection). Recently, these operations have been extended to unrooted phylogenetic networks, which are generalisations of phylogenetic trees that can model reticulated evolutionary relationships. Here, we study global and local properties of spaces of phylogenetic networks under these three operations. In particular, we prove connectedness and asymptotic bounds on the diameters of spaces of different classes of phylogenetic networks, including …

Constructing Invariant Subspaces As Kernels Of Commuting Matrices, Carl C. Cowen, William Johnston, Rebecca G. Wahl

Scholarship and Professional Work - LAS

Given an n n matrix A over C and an invariant subspace N, a straightforward formula constructs an n n matrix N that commutes with A and has N = kerN. For Q a matrix putting A into Jordan canonical form, J = Q􀀀1AQ, we get N = Q􀀀1M where M= ker(M) is an invariant subspace for J with M commuting with J. In the formula J = PZT􀀀1Pt, the matrices Z and T are m m and P is an n m row selection matrix. If N is a marked subspace, m = n and Z is an n …

Cell Velocity Is Asymptotically Independent Of Force: A Differential Equation Model With Random Switching., J. C. Dallon, Emily J. Evans, Christopher P. Grant, William V. Smith

Faculty Publications

Numerical simulations suggest that average velocity of a biological cell depends largely on attachment dynamics and less on the forces exerted by the cell. We determine the relationship between two models of cell motion, one based on finite spring constants modeling attachment properties (a randomly switched differential equation) and a limiting case (a centroid model-a generalized random walk) where spring constants are infinite. We prove the main result of this paper, the Expected Velocity Relationship theorem. This result shows that the expected value of the difference between cell locations in the differential equation model at the initial time and at …

Arbitrary High Order Finite Difference Methods With Applications To Wave Propagation Modeled By Maxwell's Equations, Min Chen

UNLV Theses, Dissertations, Professional Papers, and Capstones

This dissertation investigates two different mathematical models based on the time-domain Maxwell's equations: the Drude model for metamaterials and an equivalent Berenger's perfectly matched layer (PML) model. We develop both an explicit high order finite difference scheme and a compact implicit scheme to solve both models. We develop a systematic technique to prove stability and error estimate for both schemes. Extensive numerical results supporting our analysis are presented. To our best knowledge, our convergence theory and stability results are novel and provide the first error estimate for the high-order finite difference methods for Maxwell's equations.

Characterizing Compact Game Trees, Andrew Dubose

UNLV Theses, Dissertations, Professional Papers, and Capstones

It is well-known that the body of a game tree of height less than or equal to ω is compact

if and only if the tree is finitely branching. In this thesis, we develop necessary and sufficient

conditions for the body of any game tree to be compact.

A Pedagogic Analysis Of Linear Algebra Courses, Andrew Taylor

Mathematics & Statistics ETDs

This project is concerned with investigating the question, "Do our applied linear algebra courses (at the University of New Mexico) adequately prepare STEM students for future work in their respective fields?" In order to explore this, surveys were issued to three groups (sections) of students (among two different instructors) at the conclusion of their applied linear algebra course, as well as STEM professors/instructors from a variety of STEM fields. Students were surveyed regarding their perceived mastery of given topics/ideas from the course and professors/instructors were surveyed about the level of mastery they felt was necessary (referred to as ``desired mastery") …

Efficient Smooth Non-Convex Stochastic Compositional Optimization Via Stochastic Recursive Gradient Descent, Wenqing Hu, Chris Junchi Li, Xiangru Lian, Ji Liu, Huizhuo Yuan

Mathematics and Statistics Faculty Research & Creative Works

Stochastic compositional optimization arises in many important machine learning applications. The objective function is the composition of two expectations of stochastic functions, and is more challenging to optimize than vanilla stochastic optimization problems. In this paper, we investigate the stochastic compositional optimization in the general smooth non-convex setting. We employ a recently developed idea of Stochastic Recursive Gradient Descent to design a novel algorithm named SARAH-Compositional, and prove a sharp Incremental First-order Oracle (IFO) complexity upper bound for stochastic compositional optimization: 𝒪((n + m)^1/2ε^-2) in the finite-sum case and 𝒪(ε^-3) in the online case. …

Normalized Multi-Bump Solutions For Saturable Schrödinger Equations, Xiaoming Wang, Zhi-Qiang Wang

Mathematics and Statistics Faculty Publications

In this paper, we are concerned with the existence of multi-bump solutions for a class of semiclassical saturable Schrödinger equations with an density function:

We prove that, with the density function being radially symmetric, for given integer k ≥ 2 there exist a family of non-radial, k-bump type normalized solutions (i.e., with the L² constraint) which concentrate at the global maximum points of density functions when ε → 0⁺. The proof is based on a variational method in particular on a convexity technique and the concentration-compactness method.

Albert Forms, Quaternions, Schubert Varieties & Embeddability, Jasmin Omanovic

Electronic Thesis and Dissertation Repository

The origin of embedding problems can be understood as an effort to find some minimal datum which describes certain algebraic or geometric objects. In the algebraic theory of quadratic forms, Pfister forms are studied for a litany of powerful properties and representations which make them particularly interesting to study in terms of embeddability. A generalization of these properties is captured by the study of central simple algebras carrying involutions, where we may characterize the involution by the existence of particular elements in the algebra. Extending this idea even further, embeddings are just flags in the Grassmannian, meaning that their study …

Implications Of The Modifiable Areal Unit Problem For Wildfire Analyses, Timothy P. Nagle-Mcnaughton, Xi Gong, Jose A. Constantine

Geography and Environmental Studies Faculty Publications

Wildfires pose a danger to both ecologies and communities. To this end, many large-scale analyses of wildfire patterns and behavior rely on the aggregation of point data to polygons, typically those based on distinct disparate ecological areas. However, the sizes, shapes, andorientations of the polygons to which data are aggregated are not neutral factors in the resulting analysis. The influence of the aggregation polygons on calculated results is known as the modifiable areal unit problem (MAUP), which is well-documented in the spatial statistics literature. Despite the documentation of the MAUP, relatively few wildfire studies consider the effects of the MAUP …

Reflection On Use Of The "Reacting To The Past" Pedagogy In A History Of Mathematics Course, Davida Fischman

Q2S Enhancing Pedagogy

This brief report provides a reflection on the use of the "Reacting to the Past" (RTTP) pedagogy in a History of Mathematics classroom. The conclusion is drawn that the RTTP pedagogy is very successful in engaging students in active learning, and appropriate games may be utilized to help students learn about the role of mathematics in historical developments as well as in society today.

Intermediate C∗-Algebras Of Cartan Embeddings, Jonathan H. Brown, Ruy Exel, Adam H. Fuller, David R. Pitts, Sarah A. Reznikoff

Department of Mathematics: Faculty Publications

Let A be a C*-algebra and let D be a Cartan subalgebra of A. We study the following question: if B is a C*-algebra such that D B A, is D a Cartan subalgebra of B? We give a positive answer in two cases: the case when there is a faithful conditional expectation from A onto B, and the case when A is nuclear and D is a C*-diagonal of A. In both cases there is a one-to-one correspondence between the intermediate C*-algebras B, and a class of open subgroupoids of the groupoid G, where ! G is the twist …

Eigenvalue Continuity And Gersgorin's Theorem, Chi-Kwong Li, Fuzhen Zhang

Mathematics Faculty Articles

Two types of eigenvalue continuity are commonly used in the literature. However, their meanings and the conditions under which continuities are used are not always stated clearly. This can lead to some confusion and needs to be addressed. In this note, the Geršgorin disk theorem is revisited and the issue concerning the proofs of the theorem by continuity is clarified.

Recent Experimental Findings Supporting Smarandache’S Hypothesis And Quantum Sorites Paradoxes And Subquantum Kinetic Model Of Electron, Victor Christianto, Robert N. Boyd, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Smarandache Hypothesis states that there is no speed limit of anything, including light and particles. While the idea is quite simple and based on known hypothesis of quantum mechanics, called Einstein-Podolski-Rosen paradox, in reality such a superluminal physics seems still hard to accept by majority of physicists. Here we review some experiments to support superluminal physics and also findings to explain Smarandache Quantum Paradoxes and Quantum Sorites Paradox. We also touch briefly on new experiment on magneton, supporting SubQuantum Kinetic Model of Electron.

Conclusion & Significance: Multiexperimental findings assessment allows one to verify conjectures by two of us (FS & …

Re-Reading Wilczek’S Remark On “Lost In Math”: The Perils Of Postempirical Science And Their Resolution, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Sabine Hossenfelder’s recent book “Lost in Math” has attracted numerous responses, including by notable physicists such as Frank Wilczek. In this article we focus on Wilczek’s remark on that book, in particular on the perils of postempirical science. We also discuss shortly multiverse hypothesis from philosophical perspective. In last section, we offer a resolution from the perspective of Neutrosophic Logic on this problem of classical tension between mathematics and experience approach to physics, which seems to cause the stagnation of modern physics.

Individual Based Model To Simulate The Evolution Of Insecticide Resistance, William B. Jamieson

Department of Mathematics: Dissertations, Theses, and Student Research

Insecticides play a critical role in agricultural productivity. However, insecticides impose selective pressures on insect populations, so the Darwinian principles of natural selection predict that resistance to the insecticide is likely to form in the insect populations. Insecticide resistance, in turn, severely reduces the utility of the insecticides being used. Thus there is a strong economic incentive to reduce the rate of resistance evolution. Moreover, resistance evolution represents an example of evolution under novel selective pressures, so its study contributes to the fundamental understanding of evolutionary theory.

Insecticide resistance often represents a complex interplay of multiple fitness trade-offs for individual …

Complex Powers Of I Satisfying The Continued Fraction Functional Equation Over The Gaussian Integers, Matthew Niemiro '20

Exemplary Student Work

We investigate and then state the conditions under which i^z satisfies the simple continued fraction functional equation for real and then complex z over the Gaussian integers.