Applied Mathematics Commons^™

Predicting Unobserved Exposures From Seasonal Epidemic Data, Eric Forgoston, Ira B. Schwartz

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

We consider a stochastic Susceptible-Exposed-Infected-Recovered (SEIR) epidemiological model with a contact rate that fluctuates seasonally. Through the use of a nonlinear, stochastic projection, we are able to analytically determine the lower dimensional manifold on which the deterministic and stochastic dynamics correctly interact. Our method produces a low dimensional stochastic model that captures the same timing of disease outbreak and the same amplitude and phase of recurrent behavior seen in the high dimensional model. Given seasonal epidemic data consisting of the number of infectious individuals, our method enables a data-based model prediction of the number of unobserved exposed individuals over very …

Peaklet Analysis: Software For Spectrum Analysis, Bruce Kessler

Mathematics Faculty Publications

This is the presentation I was invited to give at the Kentucky Innovation and Entrepreneurship Conference, regarding the software that I have developed and worked at commercializing with the help of Kentucky Science and Technology Corporation.

On The Performance Of A Hybrid Genetic Algorithm In Dynamic Environments, Quan Yuan, Zhixin Yang

Mathematics Faculty Research Publications

The ability to track the optimum of dynamic environments is important in many practical applications. In this paper, the capability of a hybrid genetic algorithm (HGA) to track the optimum in some dynamic environments is investigated for different functional dimensions, update frequencies, and displacement strengths in different types of dynamic environments. Experimental results are reported by using the HGA and some other existing evolutionary algorithms in the literature. The results show that the HGA has better capability to track the dynamic optimum than some other existing algorithms.

Long-Wave Model For Strongly Anisotropic Growth Of A Crystal Step, Mikhail Khenner

Mathematics Faculty Publications

A continuum model for the dynamics of a single step with the strongly anisotropic line energy is formulated and analyzed. The step grows by attachment of adatoms from the lower terrace, onto which atoms adsorb from a vapor phase or from a molecular beam, and the desorption is nonnegligible (the “one-sided” model). Via a multiscale expansion, we derived a long-wave, strongly nonlinear, and strongly anisotropic evolution PDE for the step profile. Written in terms of the step slope, the PDE can be represented in a form similar to a convective Cahn-Hilliard equation. We performed the linear stability analysis and computed …

Characterization Of The Drilling Via The Vibration Augmenter Of Rotary-Drills And Sound Signal Processing Of Impacted Pipe As A Potential Water Height Assessment Tool, Nicholas Morris

STAR Program Research Presentations

The focus of the internship has been on two topics: a) Characterize the drilling performance of a novel percussive augmenter – this drill was developed by the JPL’s Advanced Technologies Group and its performance was characterized; and b) Examine the feasibility of striking a pipe as a means of assessing the water height inside the pipe. The purpose of this investigation is to examine the possibility of using a simple method of applying impacts to a pipe wall and determining the water height from the sonic characteristic differences including damping, resonance frequencies, etc. Due to multiple variables that are relevant …

Every Scattered Space Is Subcompact, William Fleissner, Vladimir Tkachuk, Lynne Yengulalp

Mathematics Faculty Publications

We prove that every scattered space is hereditarily subcompact and any finite union of subcompact spaces is subcompact. It is a long-standing open problem whether every Čech-complete space is subcompact. Moreover, it is not even known whether the complement of every countable subset of a compact space is subcompact. We prove that this is the case for linearly ordered compact spaces as well as for ω -monolithic compact spaces. We also establish a general result for Tychonoff products of discrete spaces which implies that dense G_δ-subsets of Cantor cubes are subcompact.

Investigating Graph Clustering For The Power Grid, Gabriela Radu, Emilie Hogan

STAR Program Research Presentations

Given time series data from multiple power generators containing measurements of phase angle taken at many points in time. The goal is to cluster together generators which have similar phase angle behavior.

In order to achieve this goal, Fast Fourier Transforms and Euclidean distances were used to quantify similarities between generators. A graph was created in which two generators were connected if they were sufficiently similar (known as a nearest neighbor graph). Using different nearest neighbor values, matrices were generated based on similarities between generators. Specific time intervals were taken from the large data set to assess the time dependency …

Brief Report: Parental Child-Directed Speech As A Predictor Of Receptive Language In Children With Autism Symptomatology, Twyla Y. Perryman, Alice S. Carter, Daniel S. Messinger, Wendy L. Stone, Andrada Ivanescu, Paul J. Yoder

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Facilitative linguistic input directly connected to children's interest and focus of attention has become a recommended component of interventions for young children with autism spectrum disorder (ASD). This longitudinal correlational study used two assessment time points and examined the association between parental undemanding topic-continuing talk related to the child's attentional focus (i.e.; follow-in comments) and later receptive language for 37 parent-child dyads with their young (mean = 21 months, range 15-24 months) children with autism symptomology. The frequency of parental follow-in comments positively predicted later receptive language after considering children's joint attention skills and previous receptive language abilities.

Juxtaposing Nasa’S Aeronet Aod With Carb Pm Data Over The San Joaquin Valley To Facilitate Multi-Angle Imaging Spectroradiometer (Misr) Pm Pollution Research, John Kanemoto

STAR Program Research Presentations

Airborne particulate matter (PM) has been shown to increase the risk for asthma, chronic bronchitis, cardiopulmonary complications, and respiratory cell membrane damage/infection/leakage. PM levels are currently analyzed from two perspectives: stationary land-based monitoring (LBM) sites and total Aerosol Optical Depth (AOD) atmospheric column measurements. Both perspectives often leave miles of space between measuring locations and will have a continually increasing cost from introducing/maintaining sites. The Multi-angle Imaging SpectroRadiometer (MISR) satellite team hopes to begin investigating/archiving PM levels comprehensively via inputting MISR AOD measurements into a function/model which predicts the amount of ground level PM.

In the future, multivariable spatial correlations …

Field Control Of The Surface Electroclinic Effect In Liquid Crystal Displays, Dana Hipolite

Physics

Liquid crystals (LCs) are a fascinating class of materials exhibiting a range of phases intermediate between liquid and crystalline. Smectic LCs consist of elongated molecules arranged in a periodic stack (along z) of liquid like layers. In the smectic-A (Sm-A) phase, the average molecular long axis (director) points along z. In the smectic-C (Sm-C) phase, it is tilted relative to z, thus picking out a special direction within the layers. Typically, the Sm-A* to Sm- C* transition will occur as temperature is decreased. In chiral smectics (Sm-*A or Sm-C*) it is possible to induce director titling (i.e. the Sm-C* phase) …

On Fuzzy Soft Matrix Based On Reference Function, Florentin Smarandache, Said Broumi, Mamoni Dhar

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we study fuzzy soft matrix based on reference function. Firstly, we define some new operations such as fuzzy soft complement matrix and trace of fuzzy soft matrix based on reference function. Then, we introduced some related properties, and some examples are given. Lastly, we define a new fuzzy soft matrix decision method based on reference function.

Accuracy Analysis Of Parallel Method Based On Non-Overlapping Domain Decomposition Method, Moonho Tak, Yooseob Song, Hye-Kwan Jeon, Taehyo Park

Civil Engineering Faculty Publications

In this paper, an accuracy analysis of parallel method based on non-overlapping domain decomposition method is carried out. In this approach, proposed by Tak et al.(2013), the decomposed subdomains do not overlap each other and the connection between adjacent subdomains is determined via simple connective finite element named interfacial element. This approach has two main advantages. The first is that a direct method such as gauss elimination is available even in a singular problem because the singular stiffness matrix from floating domain can be converted to invertible matrix by assembling the interfacial element. The second is that computational time and …

On The Cuspidality Of Maass-Gritsenko And Mixed Level Lifts, Dania Zantout

All Dissertations

your words

Advancements In Finite Element Methods For Newtonian And Non-Newtonian Flows, Keith Galvin

All Dissertations

This dissertation studies two important problems in the mathematics of computational fluid dynamics. The first problem concerns the accurate and efficient simulation of incompressible, viscous Newtonian flows, described by the Navier-Stokes equations. A direct numerical simulation of these types of flows is, in most cases, not computationally feasible. Hence, the first half of this work studies two separate types of models designed to more accurately and efficient simulate these flows. The second half focuses on the defective boundary problem for non-Newtonian flows. Non-Newtonian flows are generally governed by more complex modeling equations, and the lack of standard Dirichlet or Neumann …

Mathematical Optimization For Engineering Design Problems, Brian Dandurand

All Dissertations

Applications in engineering design and the material sciences motivate the development of optimization theory in a manner that additionally draws from other branches of mathematics including the functional, complex, and numerical analyses.
The first contribution, motivated by an automotive design application, extends multiobjective optimization theory under the assumption that the problem information is not available in its entirety to a single decision maker as traditionally assumed in the multiobjective optimization literature. Rather, the problem information and the design control are distributed among different decision makers. This requirement appears in the design of an automotive system whose subsystem components themselves correspond …

Packings And Coverings Of Complete Graphs With A Hole With The 4-Cycle With A Pendant Edge, Yan Xia

Electronic Theses and Dissertations

In this thesis, we consider packings and coverings of various complete graphs with the 4-cycle with a pendant edge. We consider both restricted and unrestricted coverings. Necessary and sufficient conditions are given for such structures for (1) complete graphs K_v, (2) complete bipartite graphs K_m,n, and (3) complete graphs with a hole K(v,w).

Stability Aware Delaunay Refinement, Bishal Acharya

UNLV Theses, Dissertations, Professional Papers, and Capstones

Good quality meshes are extensively used for finding approximate solutions for partial differential equations for fluid flow in two dimensional surfaces. We present an overview of existing algorithms for refinement and generation of triangular meshes. We introduce the concept of node stability in the refinement of Delaunay triangulation. We present two algorithms for generating stable refinement of Delaunay triangulation. We also present an experimental investigation of a triangulation refinement algorithm based on the location of the center of gravity and the location of the center of circumcircle. The results show that the center of gravity based refinement is more effective …

Dynamical Behaviors Of Gonorrhea Strain Competition Model, Marisabel Rodriguez

Theses and Dissertations - UTB/UTPA

In the past decades, Gonorrhea, a sexually transmitted bacterial infection caused by Neisseria gonorrhoeae, has become resistant to a wider range of antibiotics. We apply a phenomenological model that takes into account essential ideas such as the effects of different treatment levels, the transformation and conjugation rates of bacteria, and the response of the immune system. Qualitative analysis provides a more integral view of how model parameters affect the emergence of within-host resistance.

The Word Problem For The Automorphism Groups Of Right-Angled Artin Groups Is In P, Carrie Anne Whittle

Graduate Theses and Dissertations

We provide an algorithm which takes any given automorphism f of any given right-angled Artin group G and determines whether or not f is the identity automorphism, thereby solving the word problem for the automorphism groups of right-angled Artin groups. We do this by solving the compressed word problem for right-angled Artin groups, a more general result. A key piece of this solution is the use of Plandowski's algorithm. We also demonstrate that our algorithm runs in polynomial time in the size of the given automorphism, written as a word in Laurence's generators of the automorphism group of the given …

Positive Equilibrium Solutions To General Population Model, Joon Hyuk Kang

Faculty Publications

In this paper, we investigate conditions for the existence of positive solution to the following general elliptic system with various growth conditions: {Δu + u(a + g(u, v)) = 0 Δv + v(d + h(u, v)) = 0 u|∂ω=v|∂ω=0 in ω. Our arguments mainly rely on super-sub solutions, maximum principles, spectrum estimates, and some detailed properties for the solution of logistic equations. © 2013 Academic Publications, Ltd.