Perfect Matchings Of Trimmed Aztec Rectangles,
2017
University of Nebraska - Lincoln
Perfect Matchings Of Trimmed Aztec Rectangles, Tri Lai
Department of Mathematics: Faculty Publications
We consider several new families of subgraphs of the square grid whose matchings are enumerated by powers of several small prime numbers: 2, 3, 5, and 11. Our graphs are obtained by trimming two opposite corners of an Aztec rectangle. The result yields a proof of a conjecture posed by Ciucu. In addition, we reveal a hidden connection between our graphs and the hexagonal dungeons introduced by Blum.
Matching And Independence Complexes Related To Small Grids,
2017
University of Kentucky
Matching And Independence Complexes Related To Small Grids, Benjamin Braun, Wesley K. Hough
Mathematics Faculty Publications
The topology of the matching complex for the 2 x n grid graph is mysterious. We describe a discrete Morse matching for a family of independence complexes Ind(Δmn) that include these matching complexes. Using this matching, we determine the dimensions of the chain spaces for the resulting Morse complexes and derive bounds on the location of non-trivial homology groups for certain Ind(Δmn). Furthermore, we determine the Euler characteristic of Ind(Δmn) and prove that several homology groups of Ind(Δmn) are non-zero.
Dodrant-Homomorphic Encryption For Cloud Databases Using Table Lookup,
2017
Marquette University
Dodrant-Homomorphic Encryption For Cloud Databases Using Table Lookup, Thomas Schwarz
Mathematics, Statistics and Computer Science Faculty Research and Publications
Users of large commercial databases increasingly want to outsource their database operations to a cloud service providers, but guaranteeing the privacy of data in an outsourced database has become the major obstacle to this move. Encrypting all data solves the privacy issue, but makes many operations on the data impossible in the cloud, unless the service provider has the capacity to decrypt data temporarily. Homomorphic encryption would solve this issue, but despite great and on-going progress, it is still far from being operationally feasible. In 2015, we presented what we now call dodrant-homomorphic encryption, a method that encrypts numeric values …
Method Of Lines Transpose: Energy Gradient Flows Using Direct Operator Inversion For Phase-Field Models,
2017
Kettering University
Method Of Lines Transpose: Energy Gradient Flows Using Direct Operator Inversion For Phase-Field Models, Matthew Causley, Hana Cho, Andrew Christlieb
Mathematics Publications
In this work, we develop an $\mathcal{O}(N)$ implicit real space method in 1D and 2D for the Cahn--Hilliard (CH) and vector Cahn--Hilliard (VCH) equations, based on the method of lines transpose (MOL$^{T}$) formulation. This formulation results in a semidiscrete time stepping algorithm, which we prove is gradient stable in the $H^{-1}$ norm. The spatial discretization follows from dimensional splitting and an $\mathcal{O}(N)$ matrix-free solver, which applies fast convolution to the modified Helmholtz equation. We propose a novel factorization technique, in which fourth-order spatial derivatives are incorporated into the solver. The splitting error is included in the nonlinear fixed point iteration, …
Thermodynamics Of Concentrated Solid Solution Alloys,
2017
National Energy Transportation Laboratory
Thermodynamics Of Concentrated Solid Solution Alloys, Michael C. Gao, Chuan Zhang, Pan Gao, Fan Zhang, Lizhi Ouyang, Michael Widom, Jeffrey A. Hawk
Mathematical Sciences Faculty Research
This paper reviews the three main approaches for predicting the formation of concentrated solid solution alloys (CSSA) and for modeling their thermodynamic properties, in particular, utilizing the methodologies of empirical thermo-physical parameters, CALPHAD method, and first-principles calculations combined with hybrid Monte Carlo/Molecular Dynamics (MC/MD) simulations. In order to speed up CSSA development, a variety of empirical parameters based on Hume-Rothery rules have been developed. Herein, these parameters have been systematically and critically evaluated for their efficiency in predicting solid solution formation. The phase stability of representative CSSA systems is then illustrated from the perspectives of phase diagrams and nucleation driving …
Using Multivariate Statistical Techniques To Aid In A Sports Index Construction,
2017
ESPN Stats & Information Group
Using Multivariate Statistical Techniques To Aid In A Sports Index Construction, Tiffany Kelly
Mathematics Colloquium Series
Within a quantitative career, you are/will soon be challenged to create an overall value to explain a situational status. For example, socio-economic status, well-being, and in this specific example, happiness among sports fans. This talk seeks to discuss my previous work developed out from student research performed at NSU in its application to my first project for ESPN Sports Analytics, the College Football Fan Happiness Index (http://es.pn/2vmParA) . I will dive into the multivariate statistical techniques of principal component analysis and hierarchal clustering to create this happiness index from a slew of variables.
A Bivariate Hypothesis Testing Approach For Mapping The Trait-Influential Gene,
2017
Brigham Young University-Idaho
A Bivariate Hypothesis Testing Approach For Mapping The Trait-Influential Gene, Garrett Saunders, Matthew D. Meng, John R. Stevens
Mathematics and Statistics Faculty Publications
The linkage disequilibrium (LD) based quantitative trait loci (QTL) model involves two indispensable hypothesis tests: the test of whether or not a QTL exists, and the test of the LD strength between the QTaL and the observed marker. The advantage of this two-test framework is to test whether there is an influential QTL around the observed marker instead of just having a QTL by random chance. There exist unsolved, open statistical questions about the inaccurate asymptotic distributions of the test statistics. We propose a bivariate null kernel (BNK) hypothesis testing method, which characterizes the joint distribution of the two test …
Distributive Residuated Frames And Generalized Bunched Implication Algebras,
2017
University of Denver
Distributive Residuated Frames And Generalized Bunched Implication Algebras, Nikolaos Galatos, Peter Jipsen
Mathematics, Physics, and Computer Science Faculty Articles and Research
We show that all extensions of the (non-associative) Gentzen system for distributive full Lambek calculus by simple structural rules have the cut elimination property. Also, extensions by such rules that do not increase complexity have the finite model property, hence many subvarieties of the variety of distributive residuated lattices have decidable equational theories. For some other extensions, we prove the finite embeddability property, which implies the decidability of the universal theory, and we show that our results also apply to generalized bunched implication algebras. Our analysis is conducted in the general setting of residuated frames.
An Extended Formulation Of The Convex Recoloring Problem On A Phylogenetic Tree,
2017
Illinois State University
An Extended Formulation Of The Convex Recoloring Problem On A Phylogenetic Tree, Sangho Shim
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Modeling Bacillus Anthracis Infection In Vitro,
2017
University of St Francis
Modeling Bacillus Anthracis Infection In Vitro, Maria Macias-Bedolla, Yareley Gonzalez
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Distributed Evolution Of Spiking Neuron Models On Apache Mahout For Time Series Analysis,
2017
Cylance, Inc.
Distributed Evolution Of Spiking Neuron Models On Apache Mahout For Time Series Analysis, Andrew Palumbo
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Repeat And Return Patterns In Double Occurrence Words,
2017
University of South Florida
Repeat And Return Patterns In Double Occurrence Words, Lukas Nabergall
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
An Improved Pairwise- Approximation Technique For Studying The Dynamics Of A Probabilistic, Two- State Lattice Model Of Intracellular Cardiac Calcium,
2017
Loyola Marymount University
An Improved Pairwise- Approximation Technique For Studying The Dynamics Of A Probabilistic, Two- State Lattice Model Of Intracellular Cardiac Calcium, Robert J. Rovetti
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Mathematical Modeling Of Inhibitory Effects On Chemically Coupled Neurons,
2017
Illinois State University
Mathematical Modeling Of Inhibitory Effects On Chemically Coupled Neurons, Nathhaniel Harraman, Epaminondas Rosa
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Temperature Effects On Neuronal Tonic-To-Bursting Transitions,
2017
Illinois State University
Temperature Effects On Neuronal Tonic-To-Bursting Transitions, Manuela Burek, Epaminondas Rosa
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
A Brief History Of Neuroscience,
2017
Illinois State University
A Brief History Of Neuroscience, Zachary Mobille, Epaminondas Rosa
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Numerical Methods Of Miscible Displacements In Porous Media,
2017
Michigan Technological University
Numerical Methods Of Miscible Displacements In Porous Media, Yang Yang
TechTalks
For miscible displacements in porous media, the volume fraction of the concentration is between 0 and 1. The main idea of my current work is to numerically preserve the two bound and keep the high-order accuracy. Then the numerical scheme is stable. The idea can be applied to other similar areas such as seawater intrusion, and contaminant transportation, etc.
Equivariant Iterated Loop Space Theory And Permutative G–Categories,
2017
University of Kentucky
Equivariant Iterated Loop Space Theory And Permutative G–Categories, Bertrand J. Guillou, J. Peter May
Mathematics Faculty Publications
We set up operadic foundations for equivariant iterated loop space theory. We start by building up from a discussion of the approximation theorem and recognition principle for V–fold loop G–spaces to several avatars of a recognition principle for infinite loop G–spaces. We then explain what genuine permutative G–categories are and, more generally, what E∞–G–categories are, giving examples showing how they arise. As an application, we prove the equivariant Barratt–Priddy–Quillen theorem as a statement about genuine G–spectra and use it to give a new, categorical proof of the tom Dieck splitting theorem …
Mean Square Consistency On Numerical Solutions Of Stochastic Wave Equation With Cubic Nonlinearities On 2d Rectangles,
2017
Zayed University
Mean Square Consistency On Numerical Solutions Of Stochastic Wave Equation With Cubic Nonlinearities On 2d Rectangles, Haziem M. Hazaimeh
All Works
© The Authors, published by EDP Sciences, 2017. In this article we study the mean square consistency on numerical solutions of stochastic wave equations with cubic nonlinearities on two dimensional rectangles. In [8], we proved that the strong Fourier solution of these semi-linear wave equations exists and is unique on an appropriate Hilbert space. A linear-implicit Euler method is used to discretize the related Fourier coefficients. We prove that the linear-implicit Euler method applied to a solution of nonlinear stochastic wave equations in two dimensions is mean square consistency under the geometric condition.
Four Possible Ways To Model Rotating Universe,
2017
University of New Mexico
Four Possible Ways To Model Rotating Universe, Victor Christianto, Florentin Smarandache
Branch Mathematics and Statistics Faculty and Staff Publications
It is known that most existing cosmology models do not include rotation, with few exceptions such as rotating Bianchi and rotating Godel metrics. Therefore in this paper we aim to discuss four possible ways to model rotating universe, including Nurgaliev’s Ermakov-type equation. It is our hope that the new proposed method can be verified with observations, in order to open new possibilities of more realistic nonlinear cosmology models.
