Applied Mathematics Commons^™

Predicting Successful Long-Term Weight Loss From Short-Term Weight-Loss Outcomes: New Insights From A Dynamic Energy Balance Model (The Pounds Lost Study), Diana Thomas, W Andrada Ivanescu, Corby K. Martin, Steven B. Heymsfield, Kaitlyn Marshall, Victoria E. Bodrato, Donald Williamson, Stephen Anton, Frank M. Sacks, Donna Ryan, George A. Bray

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Background: Currently, early weight-loss predictions of long-term weight-loss success rely on fixed percent-weight-loss thresholds.

Objective: The objective was to develop thresholds during the first 3 mo of intervention that include the influence of age, sex, baseline weight, percent weight loss, and deviations from expected weight to predict whether a participant is likely to lose 5% or more body weight by year 1.

Design: Data consisting of month 1, 2, 3, and 12 treatment weights were obtained from the 2-y Preventing Obesity Using Novel Dietary Strategies (POUNDS Lost) intervention. Logistic regression models that included covariates of age, height, sex, baseline weight, …

Generalized Least-Squares Regressions V: Multiple Variables, Nataniel Greene

Publications and Research

The multivariate theory of generalized least-squares is formulated here using the notion of generalized means. The multivariate generalized least-squares problem seeks an m dimensional hyperplane which minimizes the average generalized mean of the square deviations between the data and the hyperplane in m + 1 variables. The numerical examples presented suggest that a multivariate generalized least-squares method can be preferable to ordinary least-squares especially in situations where the data are ill- conditioned.

Modeling Neurovascular Coupling From Clustered Parameter Sets For Multimodal Eeg-Nirs, M. Tanveer Talukdar, H. Robert Frost, Solomon G. G. Diamond

Dartmouth Scholarship

Despite significant improvements in neuroimaging technologies and analysis methods, the fundamental relationship between local changes in cerebral hemodynamics and the underlying neural activity remains largely unknown. In this study, a data driven approach is proposed for modeling this neurovascular coupling relationship from simultaneously acquired electroencephalographic (EEG) and near-infrared spectroscopic (NIRS) data. The approach uses gamma transfer functions to map EEG spectral envelopes that reflect time-varying power variations in neural rhythms to hemodynamics measured with NIRS during median nerve stimulation. The approach is evaluated first with simulated EEG-NIRS data and then by applying the method to experimental EEG-NIRS data measured from …

Best Practice Recommendations For Data Screening, Justin A. Desimone, Peter D. Harms, Alice J. Desimone

Department of Management: Faculty Publications

Survey respondents differ in their levels of attention and effort when responding to items. There are a number of methods researchers may use to identify respondents who fail to exert sufficient effort in order to increase the rigor of analysis and enhance the trustworthiness of study results. Screening techniques are organized into three general categories, which differ in impact on survey design and potential respondent awareness. Assumptions and considerations regarding appropriate use of screening techniques are discussed along with descriptions of each technique. The utility of each screening technique is a function of survey design and administration. Each technique has …

Qualitative Theory Of Functional Differential And Integral Equations, Muhammad Islam, Cemil Tunc, Mouffak Benchohra, Bingwen Lui, Samir H. Saker

Mathematics Faculty Publications

Functional differential equations arise in many areas of science and technology: whenever a deterministic relationship involving some varying quantities and their rates of change in space and/or time (expressed as derivatives or differences) is known or postulated. This is illustrated in classical mechanics, where the motion of a body is described by its position and velocity as the time varies. In some cases, this differential equation (called an equation of motion) may be solved explicitly. In fact, differential equations play an important role in modelling virtually every physical, technical, biological, ecological, and epidemiological process, from celestial motion, to bridge design, …

Spin Glass Reflection Of The Decoding Transition For Quantum Error Correcting Codes, Alexey Kovalev, Leonid P. Pryadko

Department of Physics and Astronomy: Faculty Publications

We study the decoding transition for quantum error correcting codes with the help of a mapping to random-bond Wegner spin models. Families of quantum low density parity-check (LDPC) codes with a finite decoding threshold lead to both known models (e.g., random bond Ising and random plaquette Z₂ gauge models) as well as unexplored earlier generally non-local disordered spin models with non-trivial phase diagrams. The decoding transition corresponds to a transition from the ordered phase by proliferation of "post-topological" extended defects which generalize the notion of domain walls to non-local spin models. In recently discovered quantum LDPC code families with …

Bounded, Asymptotically Stable, And L^1 Solutions Of Caputo Fractional Differential Equations, Muhammad Islam

Mathematics Faculty Publications

The existence of bounded solutions, asymptotically stable solutions, and L¹ solutions of a Caputo fractional differential equation has been studied in this paper. The results are obtained from an equivalent Volterra integral equation which is derived by inverting the fractional differential equation. The kernel function of this integral equation is weakly singular and hence the standard techniques that are normally applied on Volterra integral equations do not apply here. This hurdle is overcomed using a resolvent equation and then applying some known properties of the resolvent. In the analysis Schauder's fixed point theorem and Liapunov's method have been employed. …

Firing Rate Dynamics In Recurrent Spiking Neural Networks With Intrinsic And Network Heterogeneity, Cheng Ly

Statistical Sciences and Operations Research Publications

Heterogeneity of neural attributes has recently gained a lot of attention and is increasing recognized as a crucial feature in neural processing. Despite its importance, this physiological feature has traditionally been neglected in theoretical studies of cortical neural networks. Thus, there is still a lot unknown about the consequences of cellular and circuit heterogeneity in spiking neural networks. In particular, combining network or synaptic heterogeneity and intrinsic heterogeneity has yet to be considered systematically despite the fact that both are known to exist and likely have significant roles in neural network dynamics. In a canonical recurrent spiking neural network model, …

Modeling Contagion In The Eurozone Crisis Via Dynamical Systems, Giuseppe Castellacci, Youngna Choi

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

We recently (Castellacci and Choi, 2013) formulated a theoretical framework for the modeling of financial instability contagion using the theories of dynamical systems. Here, our main goal is to model the Eurozone financial crisis within that framework. The underlying system comprises many economic agents that belong to several subsystems. In each instantiation of this framework, the hierarchy and nesting of the subsystems is dictated by the nature of the problem at hand. We describe in great detail how a suitable model can be set up for the Eurozone crisis. The dynamical system is defined by the evolution of the wealths …

The Coupled Within- And Between-Host Dynamics In The Evolution Of Hiv/Aids In China, Jie Lou, Hongna Zhou, Dong Liang, Zhen Jin, Baojun Song

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

In this work, we develop and analyze mathematical models for the coupled within-host and between-host dynamics caricaturing the evolution of HIV/AIDS. The host population is divided into susceptible, the infected without receiving treatment and the infected receiving ART treatment in accordance with China’s Four-Free-One-Care Policy. The within-host model is a typical ODE model adopted from literatures. The between-host model incorporates age-since-infection described by a system of integrodifferential equations. The two models are coupled via the viral load and number of CD4+ T cells of within the hosts. For the between-host model with an arbitrarily selected HIV infected individual, we focus …

Sobriety In Delta Not Sober, Joe Mashburn

Mathematics Faculty Publications

We will show that the space delta not sober defined by Coecke and Martin is sober in the Scott topology, but not in the weakly way below topology.

Unavoidable Minors Of Large 4-Connected Bicircular Matroids, Deborah Chun, Tyler Moss, Dan Slilaty, Xiangqian Zhou

Mathematics and Statistics Faculty Publications

It is known that any 3-connected matroid that is large enough is certain to contain a minor of a given size belonging to one of a few special classes of matroids. This paper proves a similar unavoidable minor result for large 4-connected bicircular matroids. The main result follows from establishing the list of unavoidable minors of large 4-biconnected graphs, which are the graphs representing the 4-connected bicircular matroids. This paper also gives similar results for internally 4-connected and vertically 4-connected bicircular matroids.

Application Of Loglinear Models To Claims Triangle Runoff Data, Netanya Lee Martin

Masters Theses

"In this thesis, we presented in detail different aspects of Verrall's chain ladder method and their advantages and disadvantages. Insurance companies must ensure there are enough reserves to cover future claims. To that end, it is useful to estimate mean expected losses. The chain ladder technique under a general linear model is the most widely used method for such estimation in property and casualty insurance. Verrall's chain ladder technique develops estimators for loss development ratios, mean expected ultimate claims, Bayesian premiums, and Bühlmann credibility premiums. The chain ladder technique can be used to estimate loss development in cases where data …

Evaluating The Long-Term Effects Of Logging Residue Removals In Great Lakes Aspen Forests, Michael I. Premer

Dissertations, Master's Theses and Master's Reports

Commercial aspen (Populus spp.) forests of the Great Lakes region are primarily managed for timber products such as pulp fiber and panel board, but logging residues (topwood and non-merchantable bolewood) are potentially important for utilization in the bioenergy market. In some regions, pulp and paper mills already utilize residues as fuel in combustion for heat and electricity, and progressive energy policies will likely cause an increase in biomass feedstock demand. The effects of removing residues, which have a comparatively high concentration of macronutrients, is poorly understood when evaluating long-term site productivity, future timber yields, plant diversity, stand dynamics, and …

The Simulation & Evaluation Of Surge Hazard Using A Response Surface Method In The New York Bight, Michael H. Bredesen

UNF Graduate Theses and Dissertations

Atmospheric features, such as tropical cyclones, act as a driving mechanism for many of the major hazards affecting coastal areas around the world. Accurate and efficient quantification of tropical cyclone surge hazard is essential to the development of resilient coastal communities, particularly given continued sea level trend concerns. Recent major tropical cyclones that have impacted the northeastern portion of the United States have resulted in devastating flooding in New York City, the most densely populated city in the US. As a part of national effort to re-evaluate coastal inundation hazards, the Federal Emergency Management Agency used the Joint Probability Method …

A Semiparametric Estimation For Regression Functions In The Partially Linear Autoregressive Time Series Model, R. Farnoosh, M. Hajebi, S. J. Mortazavi

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a semiparametric method is proposed for estimating regression function in the partially linear autoregressive time series model . Here, we consider a combination of parametric forms and nonlinear functions, in which the errors are independent. Semiparametric and nonparametric curve estimation provides a useful tool for exploring and understanding the structure of a nonlinear time series data set to make for a more efficient study in the partially linear autoregressive model. The unknown parameters are estimated using the conditional nonlinear least squares method, and the nonparametric adjustment is also estimated by defining and minimizing the local L2 -fitting …

Generalized Least-Squares Regressions Iv: Theory And Classification Using Generalized Means, Nataniel Greene

Publications and Research

The theory of generalized least-squares is reformulated here using the notion of generalized means. The generalized least-squares problem seeks a line which minimizes the average generalized mean of the square deviations in x and y. The notion of a generalized mean is equivalent to the generating function concept of the previous papers but allows for a more robust understanding and has an already existing literature. Generalized means are applied to the task of constructing more examples, simplifying the theory, and further classifying generalized least-squares regressions.

Light Pollution Research Through Citizen Science, John Kanemoto

STAR Program Research Presentations

Light pollution (LP) can disrupt and/or degrade the health of all living things, as well as, their environments. The goal of my research at the NOAO was to check the accuracy of the citizen science LP reporting systems entitled: Globe at Night (GaN), Dark Sky Meter (DSM), and Loss of the Night (LoN). On the GaN webpage, the darkness of the night sky (DotNS) is reported by selecting a magnitude chart. Each magnitude chart has a different density/number of stars around a specific constellation. The greater number of stars implies a darker night sky. Within the DSM iPhone application, a …

Convergence Of A Reinforcement Learning Algorithm In Continuous Domains, Stephen Carden

All Dissertations

In the field of Reinforcement Learning, Markov Decision Processes with a finite number of states and actions have been well studied, and there exist algorithms capable of producing a sequence of policies which converge to an optimal policy with probability one. Convergence guarantees for problems with continuous states also exist. Until recently, no online algorithm for continuous states and continuous actions has been proven to produce optimal policies. This Dissertation contains the results of research into reinforcement learning algorithms for problems in which both the state and action spaces are continuous. The problems to be solved are introduced formally as …

What Is Higher Mathematics? Why Is It So Hard To Interpret? What Can Be Done?, John Tabak

Journal of Interpretation

Courses and seminars in higher mathematics are some of the most challenging assignments faced by academic interpreters. Difficulties interpreting higher mathematics can adversely impact the academic and professional aspirations of deaf mathematics students and professionals. This paper discusses the nature of higher mathematics with the goal of identifying what distinguishes higher mathematics from other subjects; it then reviews the history of attempts to sign/interpret higher mathematics with particular attention to current challenges associated with expressing higher mathematics in sign. The final part of the paper discusses strategies for more effectively expressing higher mathematics in American Sign Language.

A New Adjustment Of Laplace Transform For Fractional Bloch Equation In Nmr Flow, Sunil Kumar, Devendra Kumar, U. S. Mahabaleshwar

Applications and Applied Mathematics: An International Journal (AAM)

This work purpose suggest a new analytical technique called the fractional homotopy analysis transform method (FHATM) for solving time fractional Bloch NMR (nuclear magnetic resonance) flow equations, which are a set of macroscopic equations that are used for modeling nuclear magnetization as a function of time. The true beauty of this article is the coupling of the homotopy analysis method and the Laplace transform method for systems of fractional differential equations. The solutions obtained by the proposed method indicate that the approach is easy to implement and computationally very attractive.

Stochastic Modeling Of A Concrete Mixture Plant With Preventive Maintenance, Ashish Kumar, Monika Saini, S. C. Malik

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a stochastic model for concrete mixture plant with Preventive Maintenance (PM) is analyzed in detail by using a supplementary variable technique. In a concrete mixture plant eight subsystems are arranged in a series. The system goes under PM after a maximum operation time and work as new after PM. The time to failure of each subsystem follows a negative exponential distribution while PM and repair time distributions are taken as arbitrary. A sufficient repair facility is provided to the system for conducting PM and repair of the system. Repair, maintenance and switch devices are perfect. All random …

A Ranking Method Based On Common Weights And Benchmark Point, Ali Payan, Abbas A. Noora, Farhad H. Lotfi

Applications and Applied Mathematics: An International Journal (AAM)

The highest efficiency score 1 (100% efficiency) is regarded as a common benchmark for Decision Making Units (DMUs). This brings about the existence of more than one DMU with the highest score. Such a case normally occurs in all Data Envelopment Analysis (DEA) models and also in all the Common Set of Weights (CSWs) methods and it may lead to the lack of thorough ranking of DMUs. And ideal DMU based on its specific structure is a unit that no unit would do better than. Therefore, it can be utilized as a benchmark for other units. We are going to …

High Frequency Data: Modeling Durations Via The Acd And Log Acd Models, Lilian Cheung

Honors Scholar Theses

This thesis proposes a method of finding initial parameter estimates in the Log ACD₁ model for use in recursive estimation. The recursive estimating equations method is applied to the Log ACD₁ model to find recursive estimates for the unknown parameters in the model. A literature review is provided on the ACD and Log ACD models, and on the theory of estimating equations. Monte Carlo simulations indicate that the proposed method of finding initial parameter estimates is viable. The parameter estimation process is demonstrated by fitting an ACD model and a Log ACD model to a set of IBM …

Are Highly Dispersed Variables More Extreme? The Case Of Distributions With Compact Support, Benedict E. Adjogah

Electronic Theses and Dissertations

We consider discrete and continuous symmetric random variables X taking values in [0; 1], and thus having expected value 1/2. The main thrust of this investigation is to study the correlation between the variance, Var(X) of X and the value of the expected maximum E(Mn) = E(X1,...,Xn) of n independent and identically distributed random variables X1,X2,...,Xn, each distributed as X. Many special cases are studied, some leading to very interesting alternating sums, and some progress is made towards a general theory.

Experimental Validation Of Robotic Manifold Tracking In Gyre-Like Flows, Matthew Michini, M. Ani Hsieh, Eric Forgoston, Ira B. Schwartz

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

In this paper, we present a first attempt toward experimental validation of a multi-robot strategy for tracking manifolds and Lagrangian coherent structures (LCS) in flows. LCS exist in natural fluid flows at various scales, and they are time-varying extensions of stable and unstable manifolds of time invariant dynamical systems. In this work, we present the first steps toward experimentally validating our previously proposed real-time manifold and LCS tracking strategy that relies solely on local measurements. Although we have validated the strategy in simulations using analytical flow models, experimental flow data, and actual ocean data, the strategy has never been implemented …

Transportation Of Perishable And Refrigerated Foods In Mylar Foil Bags And Insulated Containers: A Time-Temperature Study, Yanyan Li, John P. Schrade, Haiyan Su, John Specchio

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Data are lacking on the temperature changes of food during transport without the use of refrigerated trucks. The purpose of this study was to evaluate the ability of several insulated and noninsulated containers with or without frozen gel packs to keep perishable and refrigerated foods within the temperature safe zone in relationship to duration of transport. The study was designed to duplicate the practices exhibited by customers purchasing perishable food products from a cash-and-carry business. Approximately 40 perishable food items were evaluated. Four types of containers were tested: a mylar foil bag, a commercial insulated bag, a generic insulated bag, …

Generalized Least-Squares Regressions Iii: Further Theory And Classification, Nataniel Greene

Publications and Research

This paper continues the work of this series with two results. The first is an exponential equivalence theorem which states that every generalized least-squares regression line can be generated by an equivalent exponential regression. It follows that every generalized least-squares line has an effective normalized exponential parameter between 0 and 1 which classifies the line on the spectrum between ordinary least-squares and the extremal line for a given set of data. The second result is the presentation of fundamental formulas for the generalized least-squares slope and y-intercept.

A Generalization Of Poincaré-Cartan Integral Invariants Of A Nonlinear Nonholonomic Dynamical System, Muhammad Usman, M. Imran

Mathematics Faculty Publications

Based on the d'Alembert-Lagrange-Poincar\'{e} variational principle, we formulate general equations of motion for mechanical systems subject to nonlinear nonholonomic constraints, that do not involve Lagrangian undetermined multipliers. We write these equations in a canonical form called the Poincar\'{e}-Hamilton equations, and study a version of corresponding Poincar\'{e}-Cartan integral invariant which are derived by means of a type of asynchronous variation of the Poincar\'{e} variables of the problem that involve the variation of the time. As a consequence, it is shown that the invariance of a certain line integral under the motion of a mechanical system of the type considered characterizes the …

Lyapunov Functionals That Lead To Exponential Stability And Instability In Finite Delay Volterra Difference Equations, Catherine Kublik, Youssef Raffoul

Mathematics Faculty Publications

We use Lyapunov functionals to obtain sufficient conditions that guarantee exponential stability of the zero solution of the finite delay Volterra difference equation.

Also, by displaying a slightly different Lyapunov functional, we obtain conditions that guarantee the instability of the zero solution. The highlight of the paper is the relaxing of the condition |a(t)| < 1. Moreover, we provide examples in which we show that our theorems provide an improvement of some recent results.