Mathematics Commons^™

Graph Structures In Bipolar Neutrosophic Environment, Florentin Smarandache, Muhammad Akram, Muzzamal Sitara

Branch Mathematics and Statistics Faculty and Staff Publications

A bipolar single-valued neutrosophic (BSVN) graph structure is a generalization of a bipolar fuzzy graph. In this research paper, we present certain concepts of BSVN graph structures. We describe some operations on BSVN graph structures and elaborate on these with examples. Moreover, we investigate some related properties of these operations.

Yang Mills Theories, Paul Bracken

School of Mathematical & Statistical Sciences Faculty Publications

Yang-Mills gauge theories have become an important way in which to describe matter at a fundamental level. This book explores some of the aspects of their structure, quantization applications and formalism in detail. The subject matter is approached from a number of different points of view. The path integral technique is used to study and quantize the theory. Some solvable low dimensional models are introduced as well.

Interproximal Distance Analysis Of Stereolithographic Casts Made By Cad-Cam Technology: An In Vitro Study, Melanie Hoffman, Seok-Hwan Cho, Naveen K. Bansal

Mathematics, Statistics and Computer Science Faculty Research and Publications

Statement of problem

The accuracy of interproximal distances of the definitive casts made by computer-aided design and computer-aided manufacturing (CAD-CAM) technology is not yet known.

Purpose

The purpose of this in vitro study was to compare the interproximal distances of stereolithographic casts made by CAD-CAM technology with those of stone casts made by the conventional method.

Material and methods

Dentoform teeth were prepared for a single ceramic crown on the maxillary left central incisor, a 3-unit fixed dental prosthesis (FDP) on the second premolar for a metal-ceramic crown, and a maxillary right first molar for a metal crown. Twenty digital …

On The Finite W-Algebra For The Lie Superalgebra Q(N) In The Non-Regular Case, Elena Poletaeva, Vera Serganova

School of Mathematical & Statistical Sciences Faculty Publications

In this paper, we study the finite W-algebra for the queer Lie superalgebra Q(N) associated with the non-regular even nilpotent coadjoint orbits in the case when N = nl, and the corresponding nilpotent element has Jordan blocks each of size l. We prove that this finite W-algebra is isomorphic to a quotient of the super-Yangian of Q(n).

Reinterpreting Tlön, Uqbar, Orbis Tertius: On The Antirealism Tendency In Modern Physics, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Borges has a rare ability to put wild ideas into detective stories with reporting style. At least that is the impression that we got on his short stories. In particular, one of his short story is worthnoting: Tlon, Uqbar, Orbis Tertius. The story told us about a mysterious country called Uqbar, in apparently an unofficial reprint of Encyclopedia Britannica. It also tells about Tlon, a mysterious planet, created purely by imaginative minds. While this story clearly criticizes Berkeley view and may be not related to our daily reality, a reinterpretation of this story leads us to a long standing discourse …

Multi-Type Branching Processes Modeling Of Nosocomial Epidemics, Zeinab Mohamed, Tamer Oraby

School of Mathematical & Statistical Sciences Faculty Publications

Nosocomial epidemics are infectious diseases which spread among different types of susceptible individuals in a health-care facility. To model this type of epidemics, we use a multi-type branching process with a multivariate negative binomial offspring distribution. In particular, we estimate the basic reproduction number R0 and study its relationship with the parameters of the offspring distribution. in case of a single-type epidemic, we investigate the effect of contact tracing on the estimates for R0.

Breaking Free Of The Cultural Biases That Surround Women (+ Math), Gerry Boyle

Colby Magazine

"I think what we have to do here is not only teach women to be strong in a place where they're a minority," she said, "but also teach the men how to be allies to women as they leave Colby and go into the workforce." - Kayla Freeman '19

Junction Trees Constructions In Bayesian Networks, Linda Smail

All Works

© Published under licence by IOP Publishing Ltd. Junction trees are used as graphical structures over which propagation will be carried out through a very important property called the ruining intersection property. This paper examines an alternative method for constructing junction trees that are essential for the efficient computations of probabilities in Bayesian networks. The new proposed method converts a sequence of subsets of a Bayesian network into a junction tree, in other words, into a set of cliques that has the running intersection property. The obtained set of cliques and separators coincide with the junction trees obtained by the …

Co2 Conversion Over Supported Coni Bimetallic And Conipd Trimetallic Catalyst Via Dry Reforming With Methane, Scott Bamonte

Discovery Day (formerly Post & Beyond)

Greenhouse gas emission is a problem for the earth, and is causing warming

of the climate, and acidification of the oceans. The primary objective of

this project is to develop novel cobalt based catalysts, to enhance catalytic

conversion of CO₂ by methane into, value added chemicals and fuels. The

heterogeneous Co-based bimetallic and tri metallic catalysts were synthesized

via a wet incipient impregnation method to uniformly coat the metal

salts to the pre-treated support (TiO₂, SiO₂, and La-ZrO₂). The catalyst was

dried in the oven at 80∞ C for two hours before subjected …

Signatures Of Somatic Inhibition And Dendritic Excitation In Auditory Brainstem Field Potentials, Joshua H. Goldwyn, M. Mclaughlin, E. Verschooten, P. X. Joris, J. Rinzel

Mathematics & Statistics Faculty Works

Extracellular voltage recordings (Vₑ; field potentials) provide an accessible view of in vivo neural activity, but proper interpretation of field potentials is a long-standing challenge. Computational modeling can aid in identifying neural generators of field potentials. In the auditory brainstem of cats, spatial patterns of sound-evoked Vₑ can resemble, strikingly, Vₑ generated by current dipoles. Previously, we developed a biophysically-based model of a binaural brainstem nucleus, the medial superior olive (MSO), that accounts qualitatively for observed dipole-like Vₑ patterns in sustained responses to monaural tones with frequencies >~1000 Hz (Goldwyn et al., 2014). We have observed, however, that Vₑ patterns …

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(Δ^m_n) 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(Δ^m_n). Furthermore, we determine the Euler characteristic of Ind(Δ^m_n) and prove that several homology groups of Ind(Δ^m_n) are non-zero.

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.

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 …

Presidential Job Approval Rating Analysis Through Social Media, Subramanian Venkataraman, Subramanian Venkataraman

Dissertations and Theses

The aim of this study is to identify patterns in President Trump’s approval in the

Twitter universe through Social Media and Sentiment Analysis, and compare

against scientific polling to get meaningful insights on the limitations of Social

Media Analytics. For the purposes for this exercise, results from scientific polling

will be considered the true measure of approval, and will be used as control. In

order to perform sentiment analysis, we have used supervisory learning using

Naive Bayes Classifier algorithm which produced 0.862667 accuracy levels.

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, 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, 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.

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.

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 …

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.