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Mathematics

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2020

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Articles 481 - 509 of 509

Full-Text Articles in Physical Sciences and Mathematics

What's Your Sphericity Index? Rationalizing Surface Area And Volume, John A. Adam Jan 2020

What's Your Sphericity Index? Rationalizing Surface Area And Volume, John A. Adam

Mathematics & Statistics Faculty Publications

Virginia Standards of Learning include mathematical content related to the surface area and the volume of various geometric objects. In the seventh grade, “Students... solve problems involving volume and surface area” In the eighth grade, “Proportional reasoning is expounded upon as students solve a variety of problems. Students find the volume and surface area of more complex three dimensional figures”. In high school geometry, “The student... use[s] surface area and volume of three-dimensional objects to solve practical problems” (Virginia Department of Education, 2016). The challenge is to find scenarios that are engaging to students and keep them interested in the …

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Quantifying The Varying Predictive Value Of Physical Activity Measures Obtained From Wearable Accelerometers On All-Cause Mortality Over Short To Medium Time Horizons In Nhanes 2003-2006, Lucia Tabacu, Mark Ledbetter, Andrew Leroux, Ciprian Crainiceanu, Ekaterina Smirnova Jan 2020

Quantifying The Varying Predictive Value Of Physical Activity Measures Obtained From Wearable Accelerometers On All-Cause Mortality Over Short To Medium Time Horizons In Nhanes 2003-2006, Lucia Tabacu, Mark Ledbetter, Andrew Leroux, Ciprian Crainiceanu, Ekaterina Smirnova

Mathematics & Statistics Faculty Publications

Physical activity measures derived from wearable accelerometers have been shown to be highly predictive of all-cause mortality. Prediction models based on traditional risk factors and accelerometry-derived physical activity measures are developed for five time horizons. The data set contains 2978 study participants between 50 and 85 years old with an average of 13.08 years of follow-up in the NHANES 2003–2004 and 2005–2006. Univariate and multivariate logistic regression models were fit separately for five datasets for one- to five-year all-cause mortality as outcome (number of events 46, 94, 155, 218, and 297, respectively). In univariate models the total activity count (TAC) …

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Multiplicative Noise Removal: Nonlocal Low-Rank Model And It's Proximal Alternating Reweighted Minimization Algorithm, Xiaoxia Liu, Jian Lu, Lixin Shen, Chen Xu, Yuesheng Xu Jan 2020

Multiplicative Noise Removal: Nonlocal Low-Rank Model And It's Proximal Alternating Reweighted Minimization Algorithm, Xiaoxia Liu, Jian Lu, Lixin Shen, Chen Xu, Yuesheng Xu

Mathematics & Statistics Faculty Publications

The goal of this paper is to develop a novel numerical method for efficient multiplicative noise removal. The nonlocal self-similarity of natural images implies that the matrices formed by their nonlocal similar patches are low-rank. By exploiting this low-rank prior with application to multiplicative noise removal, we propose a nonlocal low-rank model for this task and develop a proximal alternating reweighted minimization (PARM) algorithm to solve the optimization problem resulting from the model. Specifically, we utilize a generalized nonconvex surrogate of the rank function to regularize the patch matrices and develop a new nonlocal low-rank model, which is a nonconvex …

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Stochastic Technique For Solutions Of Non-Linear Fin Equation Arising In Thermal Equilibrium Model, Iftikhar Ahmad, Hina Qureshi, Muhammad Bilal, Muhammad Usman Jan 2020

Stochastic Technique For Solutions Of Non-Linear Fin Equation Arising In Thermal Equilibrium Model, Iftikhar Ahmad, Hina Qureshi, Muhammad Bilal, Muhammad Usman

Mathematics Faculty Publications

In this study, a stochastic numerical technique is used to investigate the numerical solution of heat transfer temperature distribution system using feed forward artificial neural networks. Mathematical model of fin equation is formulated with the help of artificial neural networks. The effect of the heat on a rectangular fin with thermal conductivity and temperature de-pendent internal heat generation is calculated through neural networks optimization with optimizers like active set technique, interior point technique, pattern search, genetic algorithm and a hybrid approach of pattern search - interior point technique, genetic algorithm - active set technique, genetic algorithm - interior point technique, …

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A Robust Hyperviscosity Formulation For Stable Rbf-Fd Discretizations Of Advection-Diffusion-Reaction Equations On Manifolds, Varun Shankar, Grady B. Wright, Akil Narayan Jan 2020

A Robust Hyperviscosity Formulation For Stable Rbf-Fd Discretizations Of Advection-Diffusion-Reaction Equations On Manifolds, Varun Shankar, Grady B. Wright, Akil Narayan

Mathematics Faculty Publications and Presentations

We present a new hyperviscosity formulation for stabilizing radial basis function-finite difference (RBF-FD) discretizations of advection-diffusion-reaction equations on manifolds �� ⊂ ℝ3 of codimension 1. Our technique involves automatic addition of artificial hyperviscosity to damp out spurious modes in the differentiation matrices corresponding to surface gradients, in the process overcoming a technical limitation of a recently developed Euclidean formulation. Like the Euclidean formulation, the manifold formulation relies on von Neumann stability analysis performed on auxiliary differential operators that mimic the spurious solution growth induced by RBF-FD differentiation matrices. We demonstrate high-order convergence rates on problems involving surface advection and …

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On The Set Chromatic Number Of The Join And Comb Product Of Graphs, Bryan Ceasar L. Felipe, Agnes Garciano, Mark Anthony C. Tolentino Jan 2020

On The Set Chromatic Number Of The Join And Comb Product Of Graphs, Bryan Ceasar L. Felipe, Agnes Garciano, Mark Anthony C. Tolentino

Mathematics Faculty Publications

A vertex coloring c : V(G) → of a non-trivial connected graph G is called a set coloring if NC(u) ≠ NC(v) for any pair of adjacent vertices u and v. Here, NC(x) denotes the set of colors assigned to vertices adjacent to x. The set chromatic number of G, denoted by χs (G), is defined as the fewest number of colors needed to construct a set coloring of G. In this paper, we study the set chromatic number in relation to two graph operations: …

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On Eigenvalue Bounds For The Finite-State Birth-Death Process Intensity Matrix, R.R.P Tan, K Ikeda, Len Patrick Dominic M. Garces Jan 2020

On Eigenvalue Bounds For The Finite-State Birth-Death Process Intensity Matrix, R.R.P Tan, K Ikeda, Len Patrick Dominic M. Garces

Mathematics Faculty Publications

The paper sets forth a novel eigenvalue interlacing property across the finite-state birth-death process intensity matrix and two clearly identified submatrices as an extension of Cauchy’s interlace theorem for Hermitian matrix eigenvalues. A supplemental proof involving an examination of probabilities acquired from specific movements across states and a derivation of a form for the eigenpolynomial of the matrix through convolution and Laplace transform is then presented towards uncovering a similar characteristic for the general Markov chain transition rate matrix. Consequently, the proposition generates bounds for each eigenvalue of the original matrix, easing numerical computation. To conclude, the applicability of the …

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Orthogonal Groups In Characteristic 2 Acting On Polytopes Of High Rank, Peter A. Brooksbank, Dimitri Leemans, John T. Ferrara Jan 2020

Orthogonal Groups In Characteristic 2 Acting On Polytopes Of High Rank, Peter A. Brooksbank, Dimitri Leemans, John T. Ferrara

Faculty Journal Articles

No abstract provided.

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A Mass Conserving Mixed Stress Formulation For Stokes Flow With Weakly Imposed Stress Symmetry, Jay Gopalakrishnan, Philip L. Lederer, Joachim Schoeberl Jan 2020

A Mass Conserving Mixed Stress Formulation For Stokes Flow With Weakly Imposed Stress Symmetry, Jay Gopalakrishnan, Philip L. Lederer, Joachim Schoeberl

Mathematics and Statistics Faculty Publications and Presentations

We introduce a new discretization of a mixed formulation of the incompressible Stokes equations that includes symmetric viscous stresses. The method is built upon a mass conserving mixed formulation that we recently studied. The improvement in this work is a new method that directly approximates the viscous fluid stress $\sigma$, enforcing its symmetry weakly. The finite element space in which the stress is approximated consists of matrix-valued functions having continuous “normal-tangential” components across element interfaces. Stability is achieved by adding certain matrix bubbles that were introduced earlier in the literature on finite elements for linear elasticity. Like the earlier work, …

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Pseudo-Contractions, Rigidity, Fixed Points And Related Questions, Daniel Alpay, Vladimir Bolotnikov, David Shoikhet Jan 2020

Pseudo-Contractions, Rigidity, Fixed Points And Related Questions, Daniel Alpay, Vladimir Bolotnikov, David Shoikhet

Mathematics, Physics, and Computer Science Faculty Articles and Research

The class of holomorphic self-mappings of the open unit disk (which are contractions with respect to the Poincaré metric) admits a natural extension to the class of holomorphic pseudo-contractions. In this paper, we study various inequalities involving the values of derivatives of holomorphic pseudo-contractions at fixed points (particularly, at the Denjoy–Wolff fixed point).

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The Infinite Is The Chasm In Which Our Thoughts Are Lost: Reflections On Sophie Germain's Essays, Adam Glesser, Bogdan D. Suceavă, Mihaela Vajiac Jan 2020

The Infinite Is The Chasm In Which Our Thoughts Are Lost: Reflections On Sophie Germain's Essays, Adam Glesser, Bogdan D. Suceavă, Mihaela Vajiac

Mathematics, Physics, and Computer Science Faculty Articles and Research

"Sophie Germain (1776–1831) is quite well-known to the mathematical community for her contributions to number theory [17] and elasticity theory (e.g., see [2, 5]). On the other hand, there have been few attempts to understand Sophie Germain as an intellectual of her time, as an independent thinker outside of academia, and as a female mathematician in France, facing the prejudice of the time of the First Empire and of the Bourbon Restoration, while pursuing her thoughts and interests and writing on them. Sophie Germain had to face a double challenge: the mathematical difficulty of the problems she approached and the …

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Residual Control Chart For Binary Response With Multicollinearity Covariates By Neural Network Model, Jong-Min Kim, Ning Wang, Yumin Liu, Kayoung Park Jan 2020

Residual Control Chart For Binary Response With Multicollinearity Covariates By Neural Network Model, Jong-Min Kim, Ning Wang, Yumin Liu, Kayoung Park

Mathematics & Statistics Faculty Publications

Quality control studies have dealt with symmetrical data having the same shape with respect to left and right. In this research, we propose the residual (r) control chart for binary asymmetrical (non-symmetric) data with multicollinearity between input variables via combining principal component analysis (PCA), functional PCA (FPCA) and the generalized linear model with probit and logit link functions, and neural network regression model. The motivation in this research is that the proposed control chart method can deal with both high-dimensional correlated multivariate data and high frequency functional multivariate data by neural network model and FPCA. We show that the neural …

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On The Ranks Of String C-Group Representations For Symplectic And Orthogonal Groups, Peter A. Brooksbank Jan 2020

On The Ranks Of String C-Group Representations For Symplectic And Orthogonal Groups, Peter A. Brooksbank

Faculty Journal Articles

We determine the ranks of string C-group representations of 4-dimensional projective symplectic groups over a finite field, and comment on those of higher-dimensional symplectic and orthogonal groups.

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Exact Sequences Of Inner Automorphisms Of Tensors, Peter A. Brooksbank Jan 2020

Exact Sequences Of Inner Automorphisms Of Tensors, Peter A. Brooksbank

Faculty Journal Articles

We produce a long exact sequence whose terms are unit groups of associative algebras that behave as inner automorphisms of a given tensor. Our sequence generalizes known sequences for associative and non-associative algebras. In a manner similar to those, our sequence facilitates inductive reasoning about, and calculation of the groups of symmetries of a tensor. The new insights these methods afford can be applied to problems ranging from understanding algebraic structures to distinguishing entangled states in particle physics.

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Surviving Mathematics, Nathalie M. Luna Jan 2020

Surviving Mathematics, Nathalie M. Luna

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

In this essay written in an informal voice, the author shares the ups and downs of her experience in academia. She shares her motivation to study mathematics, her undergraduate experience in Puerto Rico, and her graduate experience in South Texas.

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Formation Of Escherichia Coli O157: H7 Persister Cells In The Lettuce Phyllosphere And Application Of Differential Equation Models To Predict Their Prevalence On Lettuce Plants In The Field, Daniel S. Munther, Michelle Q. Carter, Claude V. Aldric, Renata Ivanek, Maria T. Brandl Jan 2020

Formation Of Escherichia Coli O157: H7 Persister Cells In The Lettuce Phyllosphere And Application Of Differential Equation Models To Predict Their Prevalence On Lettuce Plants In The Field, Daniel S. Munther, Michelle Q. Carter, Claude V. Aldric, Renata Ivanek, Maria T. Brandl

Mathematics and Statistics Faculty Publications

American Society for Microbiology. Escherichia coli O157:H7 (EcO157) infections have been recurrently associated with produce. The physiological state of EcO157 cells surviving the many stresses encountered on plants is poorly understood. EcO157 populations on plants in the field generally follow a biphasic decay in which small subpopulations survive over longer periods of time. We hypothesized that these subpopulations include persister cells, known as cells in a transient dormant state that arise through phenotypic variation in a clonal population. Using three experimental regimes (with growing, stationary at carrying capacity, and decaying populations), we measured the persister cell fractions in culturable EcO157 …

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Role Of Hydrodynamic Interactions In Chemotaxis Of Bacterial Populations, Shawn D. Ryan Jan 2020

Role Of Hydrodynamic Interactions In Chemotaxis Of Bacterial Populations, Shawn D. Ryan

Mathematics and Statistics Faculty Publications

How bacteria sense local chemical gradients and decide to move has been a fascinating area of recent study. Chemotaxis of bacterial populations has been traditionally modeled using either individual-based models describing the motion of a single bacterium as a velocity jump process, or macroscopic PDE models that describe the evolution of the bacterial density. In these models, the hydrodynamic interaction between the bacteria is usually ignored. However, hydrodynamic interaction has been shown to induce collective bacterial motion and self-organization resulting in larger mesoscale structures. In this paper, the role of hydrodynamic interactions in bacterial chemotaxis is investigated by extending a …

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A Trace Bound For Integer-Diagonal Positive Semidefinite Matrices, Lon Mitchell Jan 2020

A Trace Bound For Integer-Diagonal Positive Semidefinite Matrices, Lon Mitchell

USF St. Petersburg campus Faculty Publications

We prove that an n-by-n complex positive semidefinite matrix of rank r whose graph is connected, whose diagonal entries are integers, and whose non-zero off-diagonal entries have modulus at least one, has trace at least n + r-1.

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On The Voronoi Conjecture For Combinatorially Voronoi Parallelohedra In Dimension 5, Mathieu Dutour Sikiric, Alexey Garber, Alexander Magazinov Jan 2020

On The Voronoi Conjecture For Combinatorially Voronoi Parallelohedra In Dimension 5, Mathieu Dutour Sikiric, Alexey Garber, Alexander Magazinov

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

In a recent paper, Garber, Gavrilyuk, and Magazinov [Discrete Comput. Geom., 53 (2015), pp. 245--260] proposed a sufficient combinatorial condition for a parallelohedron to be affinely Voronoi. We show that this condition holds for all 5-dimensional Voronoi parallelohedra. Consequently, the Voronoi conjecture in $\mathbb{R}^5$ holds if and only if every 5-dimensional parallelohedron is combinatorially Voronoi. Here, by saying that a parallelohedron $P$ is combinatorially Voronoi, we mean that $P$ is combinatorially equivalent to a Dirichlet--Voronoi polytope for some lattice $\Lambda$, and this combinatorial equivalence is naturally translated into equivalence of the tiling by copies of $P$ with …

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Topological Pressure And Fractal Dimensions Of Cookie-Cutter-Like Sets, Mrinal Kanti Roychowdhury Jan 2020

Topological Pressure And Fractal Dimensions Of Cookie-Cutter-Like Sets, Mrinal Kanti Roychowdhury

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

The cookie-cutter-like set is defined as the limit set of a sequence of classical cookie-cutter mappings. For this cookie-cutter set it is shown that the topological pressure function exists, and that the fractal dimensions such as the Hausdorff dimension, the packing dimension and the box-counting dimension are all equal to the unique zero h of the pressure function. Moreover, it is shown that the h-dimensional Hausdorff measure and the h-dimensional packing measure are finite and positive.

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Conformal Geometry Of Polygons, Michael Albert Jan 2020

Conformal Geometry Of Polygons, Michael Albert

WWU Honors College Senior Projects

Conformal maps are functions from subsets of the complex plane to the complex plane that locally preserve angles. Our goal is to understand conformal maps that pass to and from polygonal domains. In order to do so, we derive some of the basic theory of harmonic functions on simply connected domains. In particular, our goal with the first few sections is to prove the Schwarz Reflection principle. Using this, as well as other tools from complex analysis, we give an in-depth explanation of Tao’s proof of the Schwarz-Christoffel formula. This is a differential equation that allows one to compute a …

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Teacher Support Of Co- And Socially-Shared Regulation Of Learning In Middle School Mathematics Classrooms, Melissa Quackenbush, Linda Bol Jan 2020

Teacher Support Of Co- And Socially-Shared Regulation Of Learning In Middle School Mathematics Classrooms, Melissa Quackenbush, Linda Bol

Educational Leadership & Workforce Development Faculty Publications

Social influences on classroom learning have a long research tradition and are critical components of self-regulated learning theories. More recently, researchers have explored the social influences of self-regulated learning in cooperative learning contexts. In these settings, co-regulation of learning and socially-shared regulation of learning strategies have been aligned with self-regulated learning theory. However, without specific training or structure, teachers are not likely to explicitly integrate SRL strategies into their teaching. We use case studies to better understand how Zimmerman's theory of self-regulated learning (2008) and Hadwin's conceptual framework of socially-shared regulation of learning (2018) emerge from teachers' support of student-centered …

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Codes, Cryptography, And The Mceliece Cryptosystem, Bethany Matsick Jan 2020

Codes, Cryptography, And The Mceliece Cryptosystem, Bethany Matsick

Senior Honors Theses

Over the past several decades, technology has continued to develop at an incredible rate, and the importance of properly securing information has increased significantly. While a variety of encryption schemes currently exist for this purpose, a number of them rely on problems, such as integer factorization, that are not resistant to quantum algorithms. With the reality of quantum computers approaching, it is critical that a quantum-resistant method of protecting information is found. After developing the proper background, we evaluate the potential of the McEliece cryptosystem for use in the post-quantum era by examining families of algebraic geometry codes that allow …

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Teaching Introductory Statistics With Datacamp, Benjamin Baumer, Andrew P. Bray, Mine Çetinkaya-Rundel, Johanna S. Hardin Jan 2020

Teaching Introductory Statistics With Datacamp, Benjamin Baumer, Andrew P. Bray, Mine Çetinkaya-Rundel, Johanna S. Hardin

Statistical and Data Sciences: Faculty Publications

We designed a sequence of courses for the DataCamp online learning platform that approximates the content of a typical introductory statistics course. We discuss the design and implementation of these courses and illustrate how they can be successfully integrated into a brick-and-mortar class. We reflect on the process of creating content for online consumers, ruminate on the pedagogical considerations we faced, and describe an R package for statistical inference that became a by-product of this development process. We discuss the pros and cons of creating the course sequence and express our view that some aspects were particularly problematic. The issues …

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Testing Gene-Environment Interactions For Rare And/Or Common Variants In Sequencing Association Studies., Zihan Zhao, Jianjun Zhang, Qiuying Sha, Han Hao Jan 2020

Testing Gene-Environment Interactions For Rare And/Or Common Variants In Sequencing Association Studies., Zihan Zhao, Jianjun Zhang, Qiuying Sha, Han Hao

Michigan Tech Publications

The risk of many complex diseases is determined by a complex interplay of genetic and environmental factors. Advanced next generation sequencing technology makes identification of gene-environment (GE) interactions for both common and rare variants possible. However, most existing methods focus on testing the main effects of common and/or rare genetic variants. There are limited methods developed to test the effects of GE interactions for rare variants only or rare and common variants simultaneously. In this study, we develop novel approaches to test the effects of GE interactions of rare and/or common risk, and/or protective variants in sequencing association studies. We …

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Uniformly Resolvable Decompositions Of Kv In 1-Factors And 4-Stars, Melissa S. Keranen, Donald L. Kreher, Salvatore Milici, Antoinette Tripodi Jan 2020

Uniformly Resolvable Decompositions Of Kv In 1-Factors And 4-Stars, Melissa S. Keranen, Donald L. Kreher, Salvatore Milici, Antoinette Tripodi

Michigan Tech Publications

If X is a connected graph, then an X-factor of a larger graph is a spanning subgraph in which all of its components are isomorphic to X. A uniformly resolvable {X, Y }-decomposition of the complete graph Kv is an edge decomposition of Kv into exactly r X-factors and s Y -factors. In this article we determine necessary and sufficient conditions for when the complete graph Kv has a uniformly resolvable decompositions into 1-factors and K1,4-factors.

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The Tsukano Conjectures On Exponential Sums, Brad Isaacson Jan 2020

The Tsukano Conjectures On Exponential Sums, Brad Isaacson

Publications and Research

We prove three conjectures of Tsukano about exponential sums stated in his Master’s thesis written at Osaka University. These conjectures are variations of earlier conjectures made by Lee and Weintraub which were first proved by Ibukiyama and Saito.

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Graphs Admitting Only Constant Splines, Katie Anders, Alissa S. Crans, Briana Foster-Greenwood, Blake Mellor, Julianna Tymoczko Jan 2020

Graphs Admitting Only Constant Splines, Katie Anders, Alissa S. Crans, Briana Foster-Greenwood, Blake Mellor, Julianna Tymoczko

Mathematics Sciences: Faculty Publications

We study generalized graph splines, introduced by Gilbert, Tymoczko, and Viel (2016). For a large class of rings, we characterize the graphs that only admit constant splines. To do this, we prove that if a graph has a particular type of cutset (e.g., a bridge), then the space of splines naturally decomposes as a certain direct sum of submodules. As an application, we use these results to describe splines on a triangulation studied by Zhou and Lai, but over a different ring than they used.

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A Filtration On The Cohomology Rings Of Regular Nilpotent Hessenberg Varieties, Megumi Harada, Tatsuya Horiguchi, Satoshi Murai, Martha Precup, Julianna Tymoczko Jan 2020

A Filtration On The Cohomology Rings Of Regular Nilpotent Hessenberg Varieties, Megumi Harada, Tatsuya Horiguchi, Satoshi Murai, Martha Precup, Julianna Tymoczko

Mathematics Sciences: Faculty Publications

Let n be a positive integer. The main result of this manuscript is a construction of a filtration on the cohomology ring of a regular nilpotent Hessenberg variety in GL(n, C) / B such that its associated graded ring has graded pieces (i.e., homogeneous components) isomorphic to rings which are related to the cohomology rings of Hessenberg varieties in GL(n- 1 , C) / B, showing the inductive nature of these rings. In previous work, the first two authors, together with Abe and Masuda, gave an explicit presentation of these cohomology rings in terms of generators and relations. We introduce …

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