Mathematics Commons^™

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

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

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).

Biomarkers Of Cardiovascular Disease, Ying Huang, Kailash Gulshan, Truc Nguyen, Yuping Wu

Mathematics and Statistics Faculty Publications

No abstract provided.

Hybrid Extended Kalman Filtering And Noise Statistics Optimization For Produce Wash State Estimation, Vahid Azimi, Daniel Munther, Seyed Abolfazl Fakoorian, Thang Tien Nguyen, Daniel J. Simon

Mathematics and Statistics Faculty Publications

Food-borne diseases associated with fresh produce consistently cause serious public health issues. Although sanitization measures are utilized to enhance the safety of fresh produce, strategies that neglect the dynamic nature of commercial wash processes are limited, creating the potential for pathogen cross-contamination and major disease outbreaks. In light of this risk, there is an urgent need for new control approaches during produce washing to reduce the probability of outbreaks. As an important step in this direction, a hybrid extended Kalman filter (HEKF) and particle swarm optimization (PSO)-based noise statistics optimization are designed for a produce wash system. The HEKF uses …

Yang Mills Theories, Paul Bracken

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

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.

2017: Himcm International Mathematics Modeling Contest: Finalist Rating, Aryan Walia, Katie Lu, Mia Ye, Kevin Mikos

Distinguished Student Work

The integration of drones for light shows, alongside modes of delivery, have seen soaring popularity with modernity: both literally and physically. With the employment of drones in events like the Superbowl, and Intel light shows, drones’ uses have widespread implications that are quickly gaining momentum. In an order to implement these drones in light shows, adherence to regulations alongside quantifying and monitoring the path for a set number of drones is crucial.

For an outdoor aerial light show that will display a Ferris wheel, a dragon, and another unique image, various factors need to be taken into account including the …

2017: "Lighting Up The Night", Shyam Sai, Istvan Kovach, Abhay Gupta, James Wei

Distinguished Student Work

Drone technology is beginning to permeate many aspects of life in the modern world, and for good reason. Delivery drones can efficiently deliver packages better than any existing methods. Medical drones can reach emergency patients faster than any ambulance. Security drones can surveil areas more quickly and more thoroughly than a team of human guards. The advent of commercial and industrial uses for drones, however, begets the vital question of how can drones be used outside the workplace. Intel's answer? Entertainment.

Thus, the Intel Shooting Star^TM drone was born, a quadcopter explicitly built for producing breathtaking aerial light shows …

2017: Himcm International Mathematics Modeling Contest: Meritorious Rating, Spoorthi Jakka, Claire Wang, Amy Wang, Claudia Zhu '18

Distinguished Student Work

Restatement of the Problem:

The integration of drones for light shows, alongside modes of delivery, have seen soaring popularity with modernity: both literally and physically. With the employment of drones in events like the Superbowl, and Intel light shows, drones’ uses have widespread implications that are quickly gaining momentum. In an order to implement these drones in light shows, adherence to regulations alongside quantifying and monitoring the path for a set number of drones is crucial.

For an outdoor aerial light show that will display a Ferris wheel, a dragon, and another unique image, various factors need to be taken …

2017: "The Wasatch Range Ski-Matic", Andy Liu, Bert Cao, Joshua Eberhardt, Allen Chen

Distinguished Student Work

Ski resorts are very popular among both avid skiers and families who are looking to have fun. In fact, winter resorts account for over 3 billion dollars in revenue, with an annual growth of 2.6% [IBI]. In addition to their use as recreational areas, ski resorts are also used for various winter competitions, most famously the Olympics. Our job was to design and create a suitable ski resort for both the Olympics and for recreational use in the Wasatch Peaks Range property. In addition, we were advised to create over 160km of trails and maintain a 20%- 40%-40% balance between …

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 and Statistical Sciences Faculty Publications and Presentations

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

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 …

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, 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.

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, 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.