Mathematics Commons^™

Circulant Matrices And Mathematical Juggling, Richard A. Brualdi, Michael W. Schroeder

Mathematics Faculty Research

Circulants form a well-studied and important class of matrices, and they arise in many algebraic and combinatorial contexts, in particular as multiplication tables of cyclic groups and as special classes of latin squares. There is also a known connection between circulants and mathematical juggling. The purpose of this note is to expound on this connection developing further some of its properties. We also formulate some problems and conjectures with some computational data supporting them.

Reconstructability And Dynamics Of Elementary Cellular Automata, Martin Zwick

Complex Systems Faculty Publications and Presentations

Reconstructability analysis (RA) is a method to determine whether a multivariate relation, defined set- or information-theoretically, is decomposable with or without loss into lower ordinality relations. Set-theoretic RA (SRA) is used to characterize the mappings of elementary cellular automata. The decomposition possible for each mapping w/o loss is a better predictor than the λ parameter (Walker & Ashby, Langton) of chaos, & non-decomposable mappings tend to produce chaos. SRA yields not only the simplest lossless structure but also a vector of losses for all structures, indexed by parameter τ. These losses are analogous to transmissions in information-theoretic RA (IRA). IRA …

Essays On Boundedly Rational Choice., Tanmoy Das Dr.

Doctoral Theses

Decision theory or the theory of choice is the analysis of individual behavior, typically in noninteractive situations. We can conceptualize two types of decision theory - normative and descriptive. A normative theory is concerned with identifying the best decision to make, modeling a decision maker who comports to certain ideals. A descriptive theory is a theory about how decisions are made. Such a theory is concerned with explaining observed behavior or predicting behavior under the assumption that the decision-maker or decision process follows some rules. The predictions about behavior that descriptive theory produces allow further tests of the assumed underlying, …

Modeling Reit Returns With Macroeconomic, Monetary Policy And Financial Variables In The Frameworks Of Structural Break And Regime-Switching Var: Evidence From The Usa And The Uk., Mahamitra Das Dr.

Doctoral Theses

This thesis is basically concerned with studying the various relationships involving REIT returns, inflation, monetary policy variables, and general equity market returns in the USA and the UK markets by considering modeling approaches which allow for either structural breaks or regime-switching behavior in the relationship. Although study of such relationships, especially the one involving inflation and REIT returns, have evoked significant interest amongst researchers, the number of such studies is still very few in number. Moreover, there is an element of ‘puzzle’ embedded in this relationship. Hence, it is imperative as well as interesting that further empirical investigations are done …

Integer-Antimagic Spectra Of Disjoint Unions Of Cycles, Wai Chee Shiu

Theory & Applications of Graphs

Let A be a non-trivial abelian group. A simple graph G = (V, E) is A-antimagic if there exists an edge labeling f: E(G) \to A \setminus \{0\} such that the induced vertex labeling f^+: V(G) \to A, defined by f^+(v) = \sum_{uv\in E(G)}f(uv), is injective. The integer-antimagic spectrum of a graph G is the set IAM(G) = \{k\;|\; G \textnormal{ is } \mathbb{Z}_k\textnormal{-antimagic and } k \geq 2\}. In this paper, we determine the integer-antimagic spectra of disjoint unions of cycles.

Persistence Equivalence Of Discrete Morse Functions On Trees, Yuqing Liu

Mathematics Summer Fellows

We introduce a new notion of equivalence of discrete Morse functions on graphs called persistence equivalence. Two functions are considered persistence equivalent if and only if they induce the same persistence diagram. We compare this notion of equivalence to other notions of equivalent discrete Morse functions. We then compute an upper bound for the number of persistence equivalent discrete Morse functions on a fixed graph and show that this upper bound is sharp in the case where our graph is a tree. We conclude with an example illustrating our construction.

Aluthge Transforms Of 2-Variable Weighted Shifts, Raul E. Curto, Jasang Yoon

School of Mathematical & Statistical Sciences Faculty Publications

We introduce two natural notions of multivariable Aluthge transforms (toral and spherical), and study their basic properties. In the case of 2-variable weighted shifts, we first prove that the toral Aluthge transform does not preserve (joint) hyponormality, in sharp contrast with the 1-variable case. Second, we identify a large class of 2-variable weighted shifts for which hyponormality is preserved under both transforms. Third, we consider whether these Aluthge transforms are norm-continuous. Fourth, we study how the Taylor and Taylor essential spectra of 2-variable weighted shifts behave under the toral and spherical Aluthge transforms; as a special case, we consider the …

An Efficient Algorithm To Test Forcibly-Connectedness Of Graphical Degree Sequences, Kai Wang

Theory & Applications of Graphs

We present an algorithm to test whether a given graphical degree sequence is forcibly connected or not and prove its correctness. We also outline the extensions of the algorithm to test whether a given graphical degree sequence is forcibly k-connected or not for every fixed k ≥ 2. We show through experimental evaluations that the algorithm is efficient on average, though its worst case run time is probably exponential. We also adapt Ruskey et al's classic algorithm to enumerate zero-free graphical degree sequences of length n and Barnes and Savage's classic algorithm to enumerate graphical partitions of even integer …

Cancerin: A Computational Pipeline To Infer Cancer-Associated Cerna Interaction Networks, Duc Do, Serdar Bozdag

Mathematics, Statistics and Computer Science Faculty Research and Publications

MicroRNAs (miRNAs) inhibit expression of target genes by binding to their RNA transcripts. It has been recently shown that RNA transcripts targeted by the same miRNA could “compete” for the miRNA molecules and thereby indirectly regulate each other. Experimental evidence has suggested that the aberration of such miRNA-mediated interaction between RNAs—called competing endogenous RNA (ceRNA) interaction—can play important roles in tumorigenesis. Given the difficulty of deciphering context-specific miRNA binding, and the existence of various gene regulatory factors such as DNA methylation and copy number alteration, inferring context-specific ceRNA interactions accurately is a computationally challenging task. Here we propose a computational …

Applying Computer Algebra Systems In Approximating The Trigonometric Functions, Le Phuong Quan, Thái Ahn Nhan

Mathematics and Computer Science

We propose numerical algorithms which can be integrated with modern computer algebra systems in a way that is easily implemented to approximate the sine and cosine functions with an arbitrary accuracy. Our approach is based on Taylor’s expansion about a point having a form of kp, k ∈ ℤ and p = π/2 , and being chosen such that it is closest to the argument. A full error analysis, which takes advantage of current computer algebra systems in approximating π with a very high accuracy, of our proposed methods is provided. A numerical integration application is performed to demonstrate the …

Finite Asymptotic Clusters Of Metric Spaces, Viktoriia Bilet, Oleksiy Dovgoshey

Theory & Applications of Graphs

Let (X, d) be an unbounded metric space and let \tilde r=(r_n)_{n\in\mathbb N} be a sequence of positive real numbers tending to infinity. A pretangent space \Omega_{\infty, \tilde r}^{X} to (X, d) at infinity is a limit of the rescaling sequence \left(X, \frac{1}{r_n}d\right). The set of all pretangent spaces \Omega_{\infty, \tilde r}^{X} is called an asymptotic cluster of pretangent spaces. Such a cluster can be considered as a weighted graph (G_{X, \tilde r}, \rho_{X}) whose maximal cliques coincide with \Omega_{\infty, \tilde r}^{X} and the weight \rho_{X} is defined by metrics on \Omega_{\infty, \tilde r}^{X}. We describe the structure …

Quantitative Literacy And Civic Virtue, William Briggs

Numeracy

Mathematics educators are occasionally called upon to justify the existence or the offering of quantitative literacy courses. This paper argues that effective quantitative literacy courses have different goals than algebra courses and are legitimate alternatives to algebra courses for non-STEM students. Furthermore, quantitative literacy courses affirm the historic relationship between citizenship and education. In today’s world of proliferating news sources, social media, and fake news, quantitative literacy has become an essential component of the long-held ideal of civic virtue.

Gain Control With A-Type Potassium Current: Ia As A Switch Between Divisive And Subtractive Inhibition, Joshua H. Goldwyn, B. R. Slabe, J. B. Travers, D. Terman

Mathematics & Statistics Faculty Works

Neurons process and convey information by transforming barrages of synaptic inputs into spiking activity. Synaptic inhibition typically suppresses the output firing activity of a neuron, and is commonly classified as having a subtractive or divisive effect on a neuron’s output firing activity. Subtractive inhibition can narrow the range of inputs that evoke spiking activity by eliminating responses to non-preferred inputs. Divisive inhibition is a form of gain control: it modifies firing rates while preserving the range of inputs that evoke firing activity. Since these two “modes” of inhibition have distinct impacts on neural coding, it is important to understand the …

The Archimedean Projection Property, Vincent Coll, Jeff Dodd, Michael Harrison

Research, Publications & Creative Work

Let H be a hypersurface in Rn and let π be an orthogonal projection in Rn restricted to H. We say that H satisfies the Archimedean projection property corresponding to π if there exists a constant C such that Vol(π−1(U)) = C ・ Vol(U) for every measurable U in the range of π. It is well-known that the (n − 1) dimensional sphere, as a hypersurface in Rn, satisfies the Archimedean projection property corresponding to any codimension 2 orthogonal projection in Rn, the range of any such projection being an (n − 2)-dimensional ball. Here we construct new hypersurfaces that …

Hamiltonian Structures And Riemann-Hilbert Problems Of Integrable Systems, Xiang Gu

USF Tampa Graduate Theses and Dissertations

We begin this dissertation by presenting a brief introduction to the theory of solitons and integrability (plus some classical methods applied in this field) in Chapter 1, mainly using the Korteweg-de Vries equation as a typical model. At the end of this Chapter a mathematical framework of notations and terminologies is established for the whole dissertation.

In Chapter 2, we first introduce two specific matrix spectral problems (with 3 potentials) associated with matrix Lie algebras $\mbox{sl}(2;\mathbb{R})$ and $\mbox{so}(3;\mathbb{R})$, respectively; and then we engender two soliton hierarchies. The computation and analysis of their Hamiltonian structures based on the trace identity affirms …

Generalizations Of Quandles And Their Cohomologies, Matthew J. Green

USF Tampa Graduate Theses and Dissertations

Quandles are distributive algebraic structures originally introduced independently by David Joyce and Sergei Matveev in 1979, motivated by the study of knots. In this dissertation, we discuss a number of generalizations of the notion of quandles. In the first part of this dissertation we discuss biquandles, in the context of augmented biquandles, a representation of biquandles in terms of actions of a set by an augmentation group. Using this representation we are able to develop a homology and cohomology theory for these structures.

We then introduce an n-ary generalization of the notion of quandles. We discuss a number of properties …

R Program For Estimation Of Group Efficiency And Finding Its Gradient. Stochastic Data Envelopment Analysis With A Perfect Object Approach, Alexander Vaninsky

Publications and Research

The data presented here are related to the research article “Energy-environmental efficiency and optimal restructuring of the global economy” (Vaninsky, 2018) [1]. This article describes how the world economy can be restructured to become more energy-environmental efficient, while still increasing its growth potential. It demonstrates how available energy-environmental and economic information may support policy-making decisions on the atmosphere preservation and climate change prevention. This Data article presents a computer program in R language together with examples of input and output files that serve as a means of implementation of the novel approach suggested in publication[1]. The computer program utilizes stochastic …

Nearness Without Distance, Nicholas A. Scoville

Topology

No abstract provided.

Determining The Determinant, Danny Otero

Linear Algebra

No abstract provided.

Music From Vibrating Wallpaper, Frank A. Farris

Mathematics and Computer Science

Wallpaper patterns have been shown to be decomposable into standing waves of plane vibrations [6]. Previously unexplored are the sounds that arise from these vibrations. The main result of this paper is that each wallpaper type (square, hexagonal, rectangular, generic) has its own distinctive family of pitches relative to a fundamental. We review the method to make wallpaper with wave functions and describe new musical scales for each type, including initial attempts to use the scales: a movie showing vibrations of wallpaper patterns with 3- and 6-fold symmetry inspired a new piece by American composer William Susman, commissioned by the …