Applied Mathematics Commons^™

Non-Stationary Counts With Mixture Distributions, Ziqiang Lin

Legacy Theses & Dissertations (2009 - 2024)

We study a new non--stationary mixture Pengram and thinning model for time series of counts that include the effect of covariate variables on the outcome variable. Properties of the model and performance are discussed. It has a simpler likelihood function than the non--stationary INAR(1) model and therefore MLE estimators for the model's parameters are easier to find. Therefore the model offers an alternative to non--stationary INAR(1).

Diagnostic Effects Of An Early Mastery Activity In College Algebra And Precalculus, Nathan Wakefield, Joe Champion, Jessalyn Bolkema, Douglas Dailey

Department of Mathematics: Faculty Publications

The purpose of this study was to investigate implementation of an early intervention mastery activity during the first two weeks of college algebra and precalculus courses at a large U.S. public university. Statistical modeling of (N = 935) students’ performance in the courses, including a logistic regression model of pass/fail course achievement with students’ high school rank, ACT Mathematics scores, and performance on the intervention as explanatory variables, suggested significant independent differences in course performance across performance levels on the early mastery activity. An evaluation of diagnostic validity for the model yielded a 19% false negative rate (predicted to …

Improving Time-Of-Flight And Other Depth Images: Super-Resolution And Denoising Using Variational Methods, Salvador Canales Andrade

Open Access Theses & Dissertations

Depth information is a new important source of perception for machines, which allow them to have a better representation of the surroundings. The depth information provides a more precise map of the location of every object and surfaces in a space of interest in comparison with conventional cameras. Time of flight (ToF) cameras provide one of the techniques to acquire depth maps, however they produce low spatial resolution and noisy maps. This research proposes a framework to enhance and up-scale depth maps by using two different regularization terms: Total Generalized Variation (TGV) and Total Generalized Variation with a Structure Tensor …

Strong Stability Of A Class Of Difference Equations Of Continuous Time And Structured Singular Value Problem, Qian Ma, Keqin Gu, Narges Choubedar

SIUE Faculty Research, Scholarship, and Creative Activity

This article studies the strong stability of scalar difference equations of continuous time in which the delays are sums of a number of independent parameters tau_i, i = 1, 2, . . . ,K. The characteristic quasipolynomial of such an equation is a multilinear function of exp(-tau_i s). It is known that the characteristic quasipolynomial of any difference equation set in the form of one-delayper- scalar-channel (ODPSC) model is also in such a multilinear form. However, it is shown in this article that some multilinear forms of quasipolynomials are not characteristic quasipolynomials of any ODPSC difference equation set. The equivalence …

Strong Stability Of A Class Of Difference Equations Of Continuous Time And Structured Singular Value Problem, Qian Ma, Keqin Gu, Narges Choubedar

SIUE Faculty Research, Scholarship, and Creative Activity

This article studies the strong stability of scalar difference equations of continuous time in which the delays are sums of a number of independent parameters τi, i = 1, 2, . . . , K. The characteristic quasipolynomial of such an equation is a multilinear function of e−τis. It is known that the characteristic quasipolynomial of any difference equation set in the form of one-delay-per-scalar-channel (ODPSC) model is also in such a multilinear form. However, it is shown in this article that some multilinear forms of quasipolynomials are not characteristic quasipolynomials of any ODPSC difference equation set. The equivalence between …

Numerical Simulation For A Rising Bubble Interacting With A Solid Wall: Impact, Bounce, And Thin Film Dynamics, Changjuan Zhang, Jie Li, Li-Shi Luo, Tiezheng Qian

Mathematics & Statistics Faculty Publications

Using an arbitrary Lagrangian-Eulerian method on an adaptive moving unstructured mesh, we carry out numerical simulations for a rising bubble interacting with a solid wall. Driven by the buoyancy force, the axisymmetric bubble rises in a viscous liquid toward a horizontal wall, with impact on and possible bounce from the wall. First, our simulation is quantitatively validated through a detailed comparison between numerical results and experimental data. We then investigate the bubble dynamics which exhibits four different behaviors depending on the competition among the inertial, viscous, gravitational, and capillary forces. A phase diagram for bubble dynamics has been produced using …

Hopf Bifurcation Analysis Of Chaotic Chemical Reactor Model, Daniel Mandragona

Honors Undergraduate Theses

Bifurcations in Huang's chaotic chemical reactor system leading from simple dynamics into chaotic regimes are considered. Following the linear stability analysis, the periodic orbit resulting from a Hopf bifurcation of any of the six fixed points is constructed analytically by the method of multiple scales across successively slower time scales, and its stability is then determined by the resulting final secularity condition. Furthermore, we run numerical simulations of our chemical reactor at a particular fixed point of interest, alongside a set of parameter values that forces our system to undergo Hopf bifurcation. These numerical simulations then verify our analysis of …

Homogenization In Perforated Domains And With Soft Inclusions, Brandon C. Russell

Theses and Dissertations--Mathematics

In this dissertation, we first provide a short introduction to qualitative homogenization of elliptic equations and systems. We collect relevant and known results regarding elliptic equations and systems with rapidly oscillating, periodic coefficients, which is the classical setting in homogenization of elliptic equations and systems. We extend several classical results to the so called case of perforated domains and consider materials reinforced with soft inclusions. We establish quantitative H¹-convergence rates in both settings, and as a result deduce large-scale Lipschitz estimates and Liouville-type estimates for solutions to elliptic systems with rapidly oscillating periodic bounded and measurable coefficients. Finally, …

Spherulitic Growth And Thermodynamic Equilibrium In Multicomponent Elastic Films Under Solvent-Vapor Annealing, Ding Zhao

Theses and Dissertations--Mathematics

In this dissertation, we will study solvent-vapor induced spherulitic growth in multicomponent thin films modeled as prestressed elastic solids. The interface between the crystalline phase and the amorphous phase will be treated as an evolving thermodynamic system and no diffusion of any component will be considered.

The dissertation is divided into three parts. In Part I we will determine necessary conditions of thermodynamic equilibrium between the two solid phases, the inter- face, and the vapor. In Part II we will derive the thermodynamic driving force for spherulitic growth in multicomponent elastic thin films. In Part III we will investigate the …

A Representation Theorem For Material Tensors Of Textured Thin Sheets With Weak Planar Anisotropy, Yucong Sang

Theses and Dissertations--Mathematics

Herein we consider material tensors that pertain to thin sheets or thin films, which we model as two-dimensional objects. We assume that the thin sheet in question carries a crystallographic texture characterized by an orientation distribution function defined on the rotation group SO(3), which is almost transversely-isotropic about the sheet normal so that mechanical and physical properties of the thin sheet have weak planar-anisotropy. We present a procedure by which a special orthonormal basis can be determined in each tensor subspace invariant under the action of the orthogonal group O(2). We call members of such special bases irreducible basis tensors …

Concavity In Fractional Calculus, Paul W. Eloe, Jeffrey T. Neugebauer

Mathematics Faculty Publications

No abstract provided.

When Numerical Analysis Crosses Paths With Catalan And Generalized Motzkin Numbers, Paul W. Eloe, Catherine Kublik

Mathematics Faculty Publications

We study a linear doubly indexed sequence that contains the Catalan numbers and relates to a class of generalized Motzkin numbers. We obtain a closed form formula, a generating function and a nonlinear recursion relation for this sequence. We show that a finite difference scheme with compact stencil applied to a nonlinear differential operator acting on the Euclidean distance function is exact, and exploit this exactness to produce the nonlinear recursion relation. In particular, the nonlinear recurrence relation is obtained by using standard error analysis techniques from numerical analysis. This work shows a connection between numerical analysis and number theory, …

A Primer On Noise-Induced Transitions In Applied Dynamical Systems, Eric Forgoston, Richard O. Moore

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Noise plays a fundamental role in a wide variety of physical and biological dynamical systems. It can arise from an external forcing or due to random dynamics internal to the system. It is well established that even weak noise can result in large behavioral changes such as transitions between or escapes from quasi-stable states. These transitions can correspond to critical events such as failures or extinctions that make them essential phenomena to understand and quantify, despite the fact that their occurrence is rare. This article will provide an overview of the theory underlying the dynamics of rare events for stochastic …

Models For Decision-Making, Steven Cosares

Open Educational Resources

No abstract provided.

Generating Species Assemblages For Restoration And Experimentation: A New Method That Can Simultaneously Converge On Average Trait Values And Maximize Functional Diversity, David C. Laughlin, Loïc Chalmandrier, Chaitanya Joshi, Michael Renton, John M. Dwyer, Jennifer L. Funk

Biology, Chemistry, and Environmental Sciences Faculty Articles and Research

1.Restoring resilient ecosystems in an era of rapid environmental change requires a flexible framework for selecting assemblages of species based on functional traits. However, current trait‐based models have been limited to algorithms that select species assemblages that only converge on specified average trait values, and could not accommodate the common desire among restoration ecologists to generate functionally diverse assemblages.

2.We have solved this problem by applying a nonlinear optimization algorithm to solve for the species relative abundances that maximize Rao's quadratic entropy (Q) subject to other linear constraints. Rao's Q is a closed‐form algebraic expression of functional diversity …

Models For High Dimensional Spatially Correlated Risks And Application To Thunderstorm Loss Data In Texas, Tobias Merk

Masters Theses

"Insurance claims caused by natural disasters exhibit spatial dependence with the strength of dependence being based on factors such as physical distance and population density, to name a few. Accounting for spatial dependence is therefore of crucial importance when modeling these types of claims. In this work, we present an approach to assess spatially dependent insurance risks using a combination of linear regression and factor copula models. Specifically, in loss modeling, observed dependence patterns are highly nonlinear, thus copula-based models seem appropriate since they can handle both linear and nonlinear dependence. The factor copula approach for estimating the spatial dependence …

An Investigation Of The Influence Of The 2007-2009 Recession On The Day Of The Week Effect For The S&P 500 And Its Sectors, Marcel Alwin Trick

Masters Theses

"Several studies have shown that the mean returns and the volatility structure of stock markets change seasonally or by day of the week. For instance, some authors found out that Monday returns are lower compared to Friday returns or that volatility on Wednesdays are lower compared to the rest of the week. Other researchers showed that these effects have changed after certain periods of economic stress. This led to the question, whether the day of the week effects in returns and volatility are in the US stock market and if patterns have changed from pre-recession through the 2007-2009 recession into …

A Model To Predict Concentrations And Uncertainty For Mercury Species In Lakes, Ashley Hendricks

Dissertations, Master's Theses and Master's Reports

To increase understanding of mercury cycling, a seasonal mass balance model was developed to predict mercury concentrations in lakes and fish. Results indicate that seasonality in mercury cycling is significant and is important for a northern latitude lake. Models, when validated, have the potential to be used as an alternative to measurements; models are relatively inexpensive and are not as time intensive. Previously published mercury models have neglected to perform a thorough validation. Model validation allows for regulators to be able to make more informed, confident decisions when using models in water quality management. It is critical to quantify uncertainty; …

Evaporation Of A Sessile Droplet On A Slope, Mitch Timm

Dissertations, Master's Theses and Master's Reports

We theoretically examine the drying of a stationary liquid droplet on an inclined surface. Both analytical and numerical approaches are considered, while assuming that the evaporation results from a purely diffusive transport of the liquid vapor and that the contact line is a pinned circle. For the purposes of our analytical calculations, we suppose that the effect of gravity relative to the surface tension is weak, i.e. the Bond number (Bo) is small. Then, we express the shape of the drop and the vapor concentration field as perturbation expansions in terms of Bo. When the Bond number is zero, the …

Mental Models And Neutrosophic Cognitive Maps (Modelos Mentales Y Mapas Cognitivos Neutrosóficos), Maykel Leyva-Vazquez, Rebeca Escobar-Jara, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this work, elements related to mental models elicitation and analysis are addressed through causal models. Issues related to the need to include indeterminacy in causal relationships through neutrophic cognitive maps are discussed. A proposal for static analysis in neutrosophic cognitive maps is presented. The following activities are included in the proposal: Calculate, measures of centrality, Classify nodes, De-neutrosification, and Ranking nodes. As future works, the incorporation of new metrics of centrality in neutrosophic cognitive maps is proposed. The inclusion of scenario analysis to the proposal is another area of future work.