Applied Mathematics Commons^™

Modeling Public Opinion, Arden Baxter

Honors Program Theses

The population dynamics of public opinion have many similarities to those of epidemics. For example, models of epidemics and public opinion share characteristics like contact rates, incubation times, and recruitment rates. Generally, epidemic dynamics have been presented through epidemiological models. In this paper we adapt an epidemiological model to demonstrate the population dynamics of public opinion given two opposing viewpoints. We find equilibrium solutions for various cases of the system and examine the local stability. Overall, our system provides sociological insight on the spread and transition of a public opinion.

Computing Eigenmodes Of Elliptic Operators On Manifolds Using Radial Basis Functions, Vladimir Delengov

CGU Theses & Dissertations

In this work, a numerical approach based on meshless methods is proposed to obtain eigenmodes of Laplace-Beltrami operator on manifolds, and its performance is compared against existing alternative methods. Radial Basis Function (RBF)-based methods allow one to obtain interpolation and differentiation matrices easily by using scattered data points. We derive expressions for such matrices for the Laplace-Beltrami operator via so-called Reilly’s formulas and use them to solve the respective eigenvalue problem. Numerical studies of proposed methods are performed in order to demonstrate convergence on simple examples of one-dimensional curves and two-dimensional surfaces.

Switching Mechanism In The B-1revtilted Phase Of Bent-Core Liquid Crystals, Carlos J. García-Cervera, Tiziana Giorgi, Sookyung Joo, Xin Yang Lu

Mathematics & Statistics Faculty Publications

The B_1RevTilted is a uniformly smectic tilted columnar phase in which the macroscopic polarization can be reorientated via electric field. To study the effects on the reorientation mechanism of the various physical parameters, we analyze a local, and a non-local Landau-de Gennes-type energy functional. For the case of large columnar samples, we show that both energies give the same qualitative behavior, with a relevant role played by the terms that describe the interaction between polarization and nematic directors. We also obtain existence of the L²-gradient flow in metric spaces for the full local energy.

Sdes, Jumps And Estimates, Jose L. Menaldi

Mathematics Faculty Research Publications

Long Title: Stochastic Ordinary Differential Equations with Jumps: Theory and Estimates. Chapters: Stochastic Integrals - Initial Approach to SDEs - Estimates of SDEs - Other Formulations of SDEs - SDEs with Reflection - PDE Connections.

The Study Of Non-Newtonian Nanofluid With Hall And Ion Slip Effects On Peristaltically Induced Motion In A Non-Uniform Channel, Sara I. Abdelsalam, M. M. Bhatti

Basic Science Engineering

In this study, we considered the unsteady peristaltic motion of a non-Newtonian nanofluid under the influence of a magnetic field and Hall currents. The simultaneous effects of ion slip and chemical reaction were also taken into consideration. The flow problem was suggested on the basis of the continuity, thermal energy, linear momentum, and nanoparticle concentration, which were further reduced with the help of Ohm's law. Mathematical modelling was executed using the lubrication approach. The resulting highly nonlinear partial differential equations were solved semi-analytically using the homotopy perturbation technique. The impacts of all the pertinent parameters were investigated mathematically and graphically. …

Switching Diffusion Systems With Past-Dependent Switching Having A Countable State Space, Hai Dang Nguyen

Wayne State University Dissertations

Emerging and existing applications in wireless communications, queueing networks, biological models, financial engineering, and social networks demand the

mathematical modeling and analysis of hybrid models in which continuous dynamics and discrete events coexist.

Assuming that the systems are in continuous times,

stemming from stochastic-differential-equation-based models and random discrete events,

switching diffusions come into being. In such systems, continuous states and discrete events

(discrete states)

coexist and interact.

A switching diffusion is a two-component process $(X(t),\alpha(t))$, a continuous component and a discrete component taking values in a discrete set (a set consisting of isolated points).

When the discrete component takes a …

A Two-Dimensional Finite Element Model Of The Grain Boundary Based On Thermo-Mechanical Strain Gradient Plasticity, Yooseob Song, George Z. Voyiadjis

Civil Engineering Faculty Publications

In this work, a two-dimensional finite element model for the grain boundary flow rule is developed based on the thermo-mechanical gradient-enhanced plasticity theory. The proposed model is temperature-dependent. A special attention is given to physical and micromechanical nature of dislocation interactions in combination with thermal activation on stored and dissipated energy. Thermodynamic conjugate microforces are decomposed into energetic and dissipative components. Correspondingly, two different grain boundary material length scales are present in the proposed model. Finally, numerical examples are solved in order to explore characteristics of the proposed grain boundary flow rule.

Monotonicity Of Set-Valued Mappings And Full Stability Of General Parametrical Variational Systems, Dat Pham

Wayne State University Dissertations

The dissertation introduces and studies the notions of Lipschitzian and Holderian full stability of solutions to three-parametric variational systems described in the generalized equation formalism involving nonsmooth base mappings and partial subgradients of prox-regular functions acting in Hilbert spaces. Employing advanced tools and techniques of second-order variational analysis allows us to establish complete characterizations of, as well as directly variable sufficient conditions for, such full stability properties under mild assumptions. Furthermore, we derive exact formulas and effective quantitative estimates for the corresponding moduli.

Iterative Matrix Factorization Method For Social Media Data Location Prediction, Natchanon Suaysom

HMC Senior Theses

Since some of the location of where the users posted their tweets collected by social media company have varied accuracy, and some are missing. We want to use those tweets with highest accuracy to help fill in the data of those tweets with incomplete information. To test our algorithm, we used the sets of social media data from a city, we separated them into training sets, where we know all the information, and the testing sets, where we intentionally pretend to not know the location. One prediction method that was used in (Dukler, Han and Wang, 2016) requires appending one-hot …

Borrowing Capacity, Financial Instability, And Contagion: Case Study Of The U.S. Subprime Mortgage Crisis, Youngna Choi

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

We use the case of the 2007 United States subprime mortgage crisis to investigate the impact of borrowing capacity limitations on financial instability and contagion. We divide an economy into agents that interact via flow of funds and express the financial instability level of each agent as a function of time derivatives of its wealth, cash inflows, and borrowing capacity. We show that among these factors, the borrowing capacity, which is determined by other economic constraints, has the largest impact on financial instability. It is suggested that borrowing capacity limitations could even cause contagion through feedback loop formed by flow …

Investigation Of Volatile Organic Compounds (Vocs) Detected At Vapor Intrusion Sites, Mohammadyousef Roghani

Theses and Dissertations--Civil Engineering

This dissertation investigates unexplained vapor intrusion field data sets that have been observed at hazardous waste sites, including: 1) non-linear soil gas concentration trends between the VOC source (i.e. contaminated groundwater plume) and the ground surface; and, 2) alternative pathways that serve as entry points for vapors to infiltrate into buildings and serve to increase VOC exposure risks as compared to the classic vapor intrusion model, which primarily considered foundation cracks as the route for vapor entry. The overall hypothesis of this research is that theoretical knowledge of fate and transport processes can be systematically applied to vapor intrusion field …

Climate Modeling, Outgoing Longwave Radiation, And Tropical Cyclone Forecasting, Thomas Rechtman

Honors Undergraduate Theses

Climate modeling and tropical cyclone forecasting are two significant is- sues that are continuously being improved upon for more accurate weather forecasting and preparedness. In this thesis, we have studied three climate models and formulated a new model with a view to determine the outgoing longwave radiation (OLR) budget at the top of the atmosphere (TOA) as ob- served by the National Oceanic and Atmospheric Administration’s (NOAA) satellite based Advanced Very High Resolution Radiometer (AVHRR). In 2006, Karnauskas proposed the African meridional OLR as an Atlantic hur- ricane predictor, the relation was further proven in 2016 by Karnauskas and Li …

Mathematical Models Of Mosquito Populations, Hanna Reed

Honors Undergraduate Theses

The intent of this thesis is to develop ordinary differential equation models to better understand the mosquito population. We first develop a framework model, where we determine the condition under which a natural mosquito population can persist in the environment. Wolbachia is a bacterium which limits the replication of viruses inside the mosquito which it infects. As a result, infecting a mosquito population with Wolbachia can decrease the transmission of viral mosquito-borne diseases, such as dengue. We develop another ODE model to investigate the invasion of Wolbachia in a mosquito population. In a biologically feasible situation, we determine three coexisting …

Computational Methods In Civil Engineering, Nir Krakauer

Open Educational Resources

No abstract provided.

Material Thermal Property Estimation Of Fibrous Insulation: Heat Transfer Modeling And The Continuous Genetic Algorithm, Elora Frye

Theses and Dissertations

Material thermal properties are highly sought after to better understand the performance of a material under particular conditions. As new materials are created, their physical properties will determine their performance for various applications. These properties have been estimated using many techniques including experimental testing, numerical modeling, and a combination of both. Existing methods can be time consuming, thus, a time-efficient and precise method to estimate these thermal properties was desired. A one-dimensional finite difference numerical model was developed to replicate the heat transfer through an experimental apparatus. A combination of this numerical model and the Continuous Genetic Algorithm optimization technique …

Direct Immunoassays And Their Performance: Theoretical Modelling Of The Effects Of Antibody Orientation And Associated Kinetics, Dana Mackey, Eilis Kelly, Robert Nooney, Richard O'Kennedy

Articles

The orientation and activity of antibodies immobilized on solid surfaces are of direct relevance to many immunosensing applications. We therefore investigate a mathematical model which estimates the fraction of antibodies which are available for reaction in a randomly adsorbed sample. Numerical simulations are presented which highlight the separate effects of antibody orientation, accessibility and loss of binding ability on the amount of captured antigen. The assay response can then be expressed as a function of total antibody density and used for optimizing the surface coverage strategy under various conditions.

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 …

Decoding Book Barcode Images, Yizhou Tao

CMC Senior Theses

This thesis investigated a method of barcode reconstruction to address the recovery of a blurred and convoluted one-dimensional barcode. There are a lot of types of barcodes used today, such as Code 39, Code 93, Code 128, etc. Our algorithm applies to the universal barcode, EAN 13. We extend the methodologies proposed by Iwen et al. (2013) in the journal article "A Symbol-Based Algorithm for Decoding barcodes." The algorithm proposed in the paper requires a signal measured by a laser scanner as an input. The observed signal is modeled as a true signal corrupted by a Gaussian convolution, additional noises, …

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 …