Applied Mathematics Commons^™

Different Types Of Backward Bifurcations Due To Density-Dependent Treatments, Baojun Song, Wen Du, Jie Lou

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

A set of deterministic SIS models with density-dependent treatments are studied to understand the disease dynamics when different treatment strategies are applied. Qualitative analyses are carried out in terms of general treatment functions. It has become customary that a backward bifurcation leads to bistable dynamics. However, this study finds that finds that bistability may not be an option at all; the disease-free equilibrium could be globally stable when there is a backward bifurcation. Furthermore, when a backward bifurcation occurs, the fashion of bistability could be the coexistence of either dual stable equilibria or the disease-free equilibrium and a stable limit …

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 …

Mathematical Modelling And Control Of Echinococcus In Qinghai Province, China, Liumei Wu, Baojun Song, Wen Du, Jie Lou

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

In this paper, two mathematical models, the baseline model and the intervention model, are proposed to study the transmission dynamics of echinococcus. A global forward bifurcation completely characterizes the dynamical behavior of the baseline model. That is, when the basic reproductive number is less than one, the disease-free equilibrium is asymptotically globally stable; when the number is greater than one, the endemic equilibrium is asymptotically globally stable. For the intervention model, however, the basic reproduction number alone is not enough to describe the dynamics, particularly for the case where the basic reproductive number is less then one. The emergence of …

Some Minor-Closed Classes Of Signed Graphs, Dan Slilaty, Xiangqian Zhou

Mathematics and Statistics Faculty Publications

We define four minor-closed classes of signed graphs in terms of embeddability in the annulus, projective plane, torus, and Klein bottle. We give the full list of 20 excluded minors for the smallest class and make a conjecture about the largest class.

New Microarray Image Segmentation Using Segmentation Based Contours Method, Yuan Cheng

Doctoral Dissertations

The goal of the research developed in this dissertation is to develop a more accurate segmentation method for Affymetrix microarray images. The Affymetrix microarray biotechnologies have become increasingly important in the biomedical research field. Affymetrix microarray images are widely used in disease diagnostics and disease control. They are capable of monitoring the expression levels of thousands of genes simultaneously. Hence, scientists can get a deep understanding on genomic regulation, interaction and expression by using such tools.

We also introduce a novel Affymetrix microarray image simulation model and how the Affymetrix microarray image is simulated by using this model. This simulation …

Multiple Subject Barycentric Discriminant Analysis (Musubada): How To Assign Scans To Categories Without Using Spatial Normalization, Hervé Abdi, Lynne J. Williams, Andrew C. Connolly, M. Ida Gobbini

Dartmouth Scholarship

We present a new discriminant analysis (DA) method called Multiple Subject Barycentric Discriminant Analysis (MUSUBADA) suited for analyzing fMRI data because it handles datasets with multiple participants that each provides different number of variables (i.e., voxels) that are themselves grouped into regions of interest (ROIs). Like DA, MUSUBADA (1) assigns observations to predefined categories, (2) gives factorial maps displaying observations and categories, and (3) optimally assigns observations to categories. MUSUBADA handles cases with more variables than observations and can project portions of the data table (e.g., subtables, which can represent participants or ROIs) on the factorial maps. Therefore MUSUBADA can …

Analysing Domestic Electricity Smart Metering Data Using Self Organising Maps, Fintan Mcloughlin, Aidan Duffy, Michael Conlon

Conference Papers

This paper investigates a method of classifying domestic electricity load profiles through Self Organising Maps (SOMs). Approximately four thousand customers are divided into groups based on their electricity demand patterns. Dwelling and occupant characteristics are then investigated for each group. The results show that SOMs are an effective way of classifying customers into groups in terms of their electrical load profile and that certain dwelling and occupant characteristics are significant factors in determining which group they end up in.

Translation Representations And Scattering By Two Intervals, Palle Jorgensen, Steen Pedersen, Feng Tian

Mathematics and Statistics Faculty Publications

Studying unitary one-parameter groups in Hilbert space (U(t), H), we show that a model for obstacle scattering can be built, up to unitary equivalence, with the use of translation representations for L²-functions in the complement of two finite and disjoint intervals. The model encompasses a family of systems (U(t), H). For each, we obtain a detailed spectral representation, and we compute the scattering operator and scattering matrix. We illustrate our results in the Lax-Phillips model where (U(t), H) represents an acoustic wave equation …

Noise, Bifurcations, And Modeling Of Interacting Particle Systems, Luis Mier-Y-Teran-Romero, Eric Forgoston, Ira B. Schwartz

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

We consider the stochastic patterns of a system of communicating, or coupled, self-propelled particles in the presence of noise and communication time delay. For sufficiently large environmental noise, there exists a transition between a translating state and a rotating state with stationary center of mass. Time delayed communication creates a bifurcation pattern dependent on the coupling amplitude between particles. Using a mean field model in the large number limit, we show how the complete bifurcation unfolds in the presence of communication delay and coupling amplitude. Relative to the center of mass, the patterns can then be described as transitions between …

The Constructions Of Almost Binary Sequence Pairs And Binary Sequence Pairs With Three-Level Autocorrelation, Xiuping Peng, Chengqian Xu, Guang Li, Krishnasamy T. Arasu

Mathematics and Statistics Faculty Publications

In this letter, a new class of almost binary sequence pairs with a single zero element and three autocorrelation values is presented. The new almost binary sequence pairs are based on cyclic difference sets and difference set pairs. By applying the method to the binary sequence pairs, new binary sequence pairs with three-level autocorrelation are constructed. It is shown that new sequence pairs from our constructions are balanced or almost balanced and have optimal three-level autocorrelation when the characteristic sequences or sequence pairs of difference sets or difference set pairs are balanced or almost balanced and have optimal autocorrelations.

A Statistical Model For Long-Term Forecasting Of Strong Sand Dust Storms, Siqi Tan

UNLV Theses, Dissertations, Professional Papers, and Capstones

Dust elevated into the atmosphere by dust storms has numerous environmental consequences. These include contributing to climate change; modifying local weather conditions; producing chemical and biological changes in the oceans; and affecting soil formation, surface water, groundwater quality, crop growth, and survival (Goudie and Middleton, 1992). Societal impacts include disruptions to air, road and rail traffic; interruption of radio services; the myriad effects of static-electricity generation; property damage; and health effects on humans and animals (Warner, 2004).

In this thesis, we extend the idea of empirical recurrence rate (ERR), developed by Ho (2008), to model the temporal trend of the …

Multiple Solutions For An Elliptic Problem Related To Vortex Pairs, Yi Li, Shuangjie Peng

Mathematics and Statistics Faculty Publications

Let Ω be a bounded domain in RN (N⩾2), φ a harmonic function in Ω¯. In this paper we study the existence of solutions to the following problem arising in the study of vortex pairs(Pλ){−Δu=λ(u−φ)+p−1,x∈Ω,u=0,x∈∂Ω. The set Ωp={x∈Ω,u(x)>φ} is called “vortex core”. Existence of solutions whose “vortex core” consists of one component and asymptotic behavior of “vortex core” were studied by many authors for large λ recently. Under the condition that φ has k strictly local minimum points on the boundary ∂Ω, we obtain in this paper that for λ large enough, (Pλ) has a solution with “vortex core” …

Quantitative Interpretation Of A Genetic Model Of Carcinogenesis Using Computer Simulations, Donghai Dai, Brandon Beck, Xiaofang Wang, Cory Howk, Yi Li

Mathematics and Statistics Faculty Publications

The genetic model of tumorigenesis by Vogelstein et al. (V theory) and the molecular definition of cancer hallmarks by Hanahan and Weinberg (W theory) represent two of the most comprehensive and systemic understandings of cancer. Here, we develop a mathematical model that quantitatively interprets these seminal cancer theories, starting from a set of equations describing the short life cycle of an individual cell in uterine epithelium during tissue regeneration. The process of malignant transformation of an individual cell is followed and the tissue (or tumor) is described as a composite of individual cells in order to quantitatively account for intra-tumor …

Maximal Sensitive Dependence And The Optimal Path To Epidemic Extinction, Eric Forgoston, Simone Bianco, Leah B. Shaw, Ira B. Schwartz

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Extinction of an epidemic or a species is a rare event that occurs due to a large, rare stochastic fluctuation. Although the extinction process is dynamically unstable, it follows an optimal path that maximizes the probability of extinction. We show that the optimal path is also directly related to the finite-time Lyapunov exponents of the underlying dynamical system in that the optimal path displays maximum sensitivity to initial conditions. We consider several stochastic epidemic models, and examine the extinction process in a dynamical systems framework. Using the dynamics of the finite-time Lyapunov exponents as a constructive tool, we demonstrate that …

Projective-Planar Graphs With No K3,4-Minor, John Maharry, Dan Slilaty

Mathematics and Statistics Faculty Publications

An exact structure is described to classify the projective‐planar graphs that do not contain a K3, 4‐minor.

Epidemic Spread Of Influenza Viruses: The Impact Of Transient Populations On Disease Dynamics, Karen R. Ríos-Soto, Baojun Song, Carlos Castillo-Chavez

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

The recent H1N1 ("swine u") pandemic and recent H5N1 ("avian u") outbreaks have brought increased attention to the study of the role of animal populations as reservoirs for pathogens that could invade human populations. It is believed that pigs acquired u strains from birds and humans, acting as a mixing vessel in generating new influenza viruses. Assessing the role of animal reservoirs, particularly reservoirs involving highly mobile populations (like migratory birds), on disease dispersal and persistence is of interests to a wide range of researchers including public health experts and evolutionary biologists. This paper studies the interactions between transient and …

Studies In Sampling Techniques And Time Series Analysis, Florentin Smarandache, Rajesh Singh

Branch Mathematics and Statistics Faculty and Staff Publications

This book has been designed for students and researchers who are working in the field of time series analysis and estimation in finite population. There are papers by Rajesh Singh, Florentin Smarandache, Shweta Maurya, Ashish K. Singh, Manoj Kr. Chaudhary, V. K. Singh, Mukesh Kumar and Sachin Malik. First chapter deals with the problem of time series analysis and the rest of four chapters deal with the problems of estimation in finite population. The book is divided in five chapters as follows: Chapter 1. Water pollution is a major global problem. In this chapter, time series analysis is carried out …

The Positive Solutions Of The Matukuma Equation And The Problem Of Finite Radius And Finite Mass, Jurgen Batt, Yi Li

Mathematics and Statistics Faculty Publications

This work is an extensive study of the 3 different types of positive solutions of the Matukuma equation 1r2(r2ϕ′)′=−rλ−2(1+r2)λ/2ϕp,p>1,λ>0 : the E-solutions (regular at r = 0), the M-solutions (singular at r = 0) and the F-solutions (whose existence begins away from r = 0). An essential tool is a transformation of the equation into a 2-dimensional asymptotically autonomous system, whose limit sets (by a theorem of H. R. Thieme) are the limit sets of Emden–Fowler systems, and serve as a characterization of the different solutions. The emphasis lies on the study of the M …

The Generation Of Domestic Electricity Load Profiles Through Markov Chain Modelling, Aidan Duffy, Fintan Mcloughlin, Michael Conlon

Conference Papers

Micro-generation technologies such as photovoltaics and micro-wind power are becoming increasing popular among homeowners, mainly a result of policy support mechanisms helping to improve cost competiveness as compared to traditional fossil fuel generation. National government strategies to reduce electricity demand generated from fossil fuels and to meet European Union 20/20 targets is driving this change. However, the real performance of these technologies in a domestic setting is not often known as high time resolution models for domestic electricity load profiles are not readily available. As a result, projections in terms of reducing electricity demand and financial paybacks for these micro-generation …

On Construction Of The Smallest One-Sided Confidence Interval For The Difference Of Two Proportions, Weizhen Wang

Mathematics and Statistics Faculty Publications

For my class of one-sided 1 - α confidence intervals with a certain monotonicity ordering on the random confidence limit, the smallest interval, in the sense of the set inclusion for the difference of two proportions of two independent binomial random variables, is constructed based on a direct analysis of coverage probability function. A special ordering on the confidence limit is developed and the corresponding smallest confidence interval is derived. This interval is then applied to identify the minimum effective dose (MED) for binary data in dose-response studies, and a multiple test procedure that controls the familywise error rate at …

Software Internationalization: A Framework Validated Against Industry Requirements For Computer Science And Software Engineering Programs, John Huân Vũ

Master's Theses

View John Huân Vũ's thesis presentation at http://youtu.be/y3bzNmkTr-c.

In 2001, the ACM and IEEE Computing Curriculum stated that it was necessary to address "the need to develop implementation models that are international in scope and could be practiced in universities around the world." With increasing connectivity through the internet, the move towards a global economy and growing use of technology places software internationalization as a more important concern for developers. However, there has been a "clear shortage in terms of numbers of trained persons applying for entry-level positions" in this area. Eric Brechner, Director of Microsoft Development Training, suggested …

Integer Functions On The Cycle Space And Edges Of A Graph, Dan Slilaty

Mathematics and Statistics Faculty Publications

A directed graph has a natural Z-module homomorphism from the underlying graph’s cycle space to Z where the image of an oriented cycle is the number of forward edges minus the number of backward edges. Such a homomorphism preserves the parity of the length of a cycle and the image of a cycle is bounded by the length of that cycle. Pretzel and Youngs (SIAM J. Discrete Math. 3(4):544–553, 1990) showed that any Z-module homomorphism of a graph’s cycle space to Z that satisfies these two properties for all cycles must be such a map induced from an edge direction …

Traveling Wave Solutions For A Nonlocal Reaction-Diffusion Model Of Influenza A Drift, Joaquin Riviera, Yi Li

Mathematics and Statistics Faculty Publications

In this paper we discuss the existence of traveling wave solutions for a nonlocal reaction-diffusion model of Influenza A proposed in Lin et. al. (2003). The proof for the existence of the traveling wave takes advantage of the different time scales between the evolution of the disease and the progress of the disease in the population. Under this framework we are able to use the techniques from geometric singular perturbation theory to prove the existence of the traveling wave.

Random Walks With Elastic And Reflective Lower Boundaries, Lucas Clay Devore

Masters Theses & Specialist Projects

No abstract provided.

The Regular Excluded Minors For Signed-Graphic Matroids, Hongxun Qin, Dan Slilaty, Xiangqian Zhou

Mathematics and Statistics Faculty Publications

We show that the complete list of regular excluded minors for the class of signed-graphic matroids is M*(G₁),...,M*(G₂₉),R₁₅,R₁₆. Here G₁,...,G₂₉ are the vertically 2-connected excluded minors for the class of projective-planar graphs and R₁₅ and R₁₆ are two regular matroids that we will define in the article.

Pain As A Predictor Of Depression Treatment Outcomes In Women With Childhood Sexual Abuse, Ellen L. Poleshuck, Nancy L. Talbot, Haiyan Su, Xin Tu, Linda Chaudron, Stephanie Gamble, Donna E. Giles

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Objectives: Childhood sexual abuse (CSA) increases risk for both depression and pain in women. Pain is associated with worse depression treatment response. The contribution of pain to depression treatment outcomes in women with histories of CSA is unknown. This study examined whether clinically significant pain would be associated with worse depression and functioning outcomes among women with CSA histories treated with interpersonal psychotherapy. Method: Participants were 66 women with major depression and CSA who presented to a community mental health center. An interpersonal psychotherapy protocol planned for 14 weekly sessions followed by 2 biweekly sessions. Patients were classified as experiencing …

A Berry-Esseen Theorem For Sample Quantiles Under Weak Dependence, S. N. Lahiri, Shuxia Sun

Mathematics and Statistics Faculty Publications

This paper proves a Berry-Esseen theorem for sample quantiles of strongly-mixing random variables under a polynomial mixing rate. The rate of normal approximation is shown to be O(n^-1/2) as n -> infinity, where n denotes the sample size. This result is in sharp contrast to the case of the sample mean of strongly-mixing random variables where the rate O(n^-1/2) is not known even under an exponential strong mixing rate. The main result of the paper has applications in finance and econometrics as financial time series important data often are heavy-tailed and quantile …

A Direct Solution Of The Robin Inverse Problem, Weifu Fang, Suxing Zeng

Mathematics and Statistics Faculty Publications

We present a direct, linear boundary integral equation method for the inverse problem of recovering the Robin coefficient from a single partial boundary measurement of the solution to the Laplace equation.

A Note On The Positive Solutions Of An Inhomogeneous Elliptic Equation On Rn, Yinbin Deng, Yi Li, Fen Yang

Mathematics and Statistics Faculty Publications

This paper is contributed to the elliptic equation

(0.1) Δu+K(|x|)up+μf(|x|)=0,

where p>1, x∈Rn, n⩾3, and μ⩾0 is a constant. We study the structure of positive radial solutions of (0.1) and obtain the uniqueness of solution decaying faster than r−m at ∞ if μ is small enough under some assumptions on K and f, where m is the slow decay rate.

Periodic Traveling Waves In Sirs Endemic Models, Tong Li, Yi Li, Herbert W. Hethcote

Mathematics and Statistics Faculty Publications

Mathematical models are used to determine if infection wave fronts could occur by traveling geographically in a loop around a region or continent. These infection wave fronts arise by Hopf bifurcation for some spatial models for infectious disease transmission with distributed-contacts. Periodic traveling waves are shown to exist for the spatial analog of the SIRS endemic model, in which the temporary immunity is described by a delay, but they do not exist in a similar spatial SIRS endemic model without a delay. Specifically, we found that the ratio of the delay ω in the recovered class and the average infectious …