Physical Sciences and Mathematics Commons^™

A Functional Optimization Approach To Stochastic Process Sampling, Ryan Matthew Thurman

USF Tampa Graduate Theses and Dissertations

The goal of the current research project is the formulation of a method for the estimation and modeling of additive stochastic processes with both linear- and cycle-type trend components as well as a relatively robust noise component in the form of Levy processes. Most of the research in stochastic processes tends to focus on cases where the process is stationary, a condition that cannot be assumed for the model above due to the presence of the cyclical sub-component in the overall additive process. As such, we outline a number of relevant theoretical and applied topics, such as stochastic processes and …

Stability Analysis Of Delay-Driven Coupled Cantilevers Using The Lambert W-Function, Daniel Siebel-Cortopassi

USF Tampa Graduate Theses and Dissertations

A coupled delay-feedback system of two cantilevers can yield greater sensitivity than that of asingle cantilever system, with potential applications in atomic force microscopy. The Lambert W-function analysis concept for delay differential equations is used to more accurately model the behavior of specific configurations of these cantilever systems. We also use this analysis concept to find parameters which yield stability for greater parameter ranges, of the delay differential equations. The Q factor, or quality factor, is the ratio of energy stored in the system, to the energy lost per fixed oscillation/movement cycle. Having stability of the cantilevers corresponds to the …

Zeros Of Harmonic Polynomials And Related Applications, Azizah Alrajhi

USF Tampa Graduate Theses and Dissertations

In this thesis, we study topics related to harmonic functions, where we are interested in the maximum number of solutions of a harmonic polynomial equation and how it is related to gravitational lensing. In Chapter 2, we study the conditions that we should have on the real or complex coefficients of a polynomial p to get the maximum number of distinct solutions for the equation p(z) − z¯ 2 = 0, where deg p = 2. In Chapter 3, we discuss the lens equation when the lens is an ellipse, a limac¸on, or a Neumann Oval. Also, we give a …

Distributed Control Of Multiagent Systems Under Heterogeneity, Selahattin Burak Sarsilmaz

USF Tampa Graduate Theses and Dissertations

The overarching objective of this work is to propose solutions to quite a few distributed control problems arising from networks of heterogeneous agents or the heterogeneous nature of multiagent systems. Each problem with its solutions is concisely summarized below.

We consider the cooperative output regulation problem of heterogeneous linear multiagent systems over fixed directed communication graphs. The purpose of this problem is to design a distributed control law such that the overall closed-loop stability is ensured and the tracking error of each agent converges to zero asymptotically for a class of reference inputs and disturbances generated by a so-called exosystem. …

Field Quantization For Radiative Decay Of Plasmons In Finite And Infinite Geometries, Maryam Bagherian

USF Tampa Graduate Theses and Dissertations

We investigate field quantization in high-curvature geometries. The models and calculations can help with understanding the elastic and inelastic scattering of photons and electrons in nanostructures and probe-like metallic domains. The results find important applications in high-resolution photonic and electronic modalities of scanning probe microscopy, nano-optics, plasmonics, and quantum sensing.

Quasistatic formulation, leading to nonretarded quantities, is employed and justified on the basis of the nanoscale, here subwavelength, dimensions of the considered domains of interest.

Within the quasistatic framework, we represent the nanostructure material domains with frequency-dependent dielectric functions. Quantities associated with the normal modes of the electronic systems, the …

A Hybrid Dynamic Modeling Of Time-To-Event Processes And Applications, Emmanuel A. Appiah

USF Tampa Graduate Theses and Dissertations

In the survival and reliability data analysis, parametric and nonparametric methods are used to estimate the hazard/risk rate and survival functions. A parametric approach is based on the assumption that the underlying survival distribution belongs to some specific family of closed form distributions (normal, Weibull, exponential, etc.). On the other hand, a nonparametric approach is centered around the best-fitting member of a class of survival distribution functions. Moreover, the Kaplan-Meier and Nelson-Aalen type nonparametric approach do not assume either distribution class or closed-form distributions. Historically, well-known time-to-event processes are death of living specie in populations and failure of component in …

Structural Analysis Of Poloidal And Toroidal Plasmons And Fields Of Multilayer Nanorings, Kumar Vijay Garapati

USF Tampa Graduate Theses and Dissertations

Multilayered metallo-dielectric nanoparticles are increasingly considered in various applications to control the spatial and temporal behavior of electromagnetic fields. In particular, the surface mode excitation by photons or electrons in metal nanorings finds significant applications because of the implied field distribution and electromagnetic energy confinement. However, most solid nanorings that are multilayered and/or embedded in a medium have non-simply connected geometry resulting in surface modes which are not linearly independent. That is, unlike particle plasmon eigenmodes in other geometries, the amplitudes of the eigenmodes of tori exhibit a distinct forward and backward coupling. We investigate the surface modes of such …

Semantic Description Of Activities In Videos, Fillipe Dias Moreira De Souza

USF Tampa Graduate Theses and Dissertations

Description of human activities in videos results not only in detection of actions and objects but also in identification of their active semantic relationships in the scene. Towards this broader goal, we present a combinatorial approach that assumes availability of algorithms for detecting and labeling objects and actions, albeit with some errors. Given these uncertain labels and detected objects, we link them into interpretative structures using domain knowledge encoded with concepts of Grenander’s general pattern theory. Here a semantic video description is built using basic units, termed generators, that represent labels of objects or actions. These generators have multiple out-bonds, …

Dynamics Of Multicultural Social Networks, Kristina B. Hilton

USF Tampa Graduate Theses and Dissertations

Historically human endeavors around the globe are in search of bilateral relationships. Knowledge and commerce has played a very significant role in increasing the ability for humans to connect for the betterment of the human species. As the means of communication improve, mutual benefits to the community as a whole also increase. Moreover, the benefits are filtered down to members of the overall community. Recent advancement in electronic communication technologies and in knowledge, in particular, physical, chemical, engineering and medical sciences and philosophies, have facilitated nearly instantaneous multi-cultural interactions. Local problems and solutions have become global. This has generated a …

Global Attractors And Random Attractors Of Reaction-Diffusion Systems, Junyi Tu

USF Tampa Graduate Theses and Dissertations

The dissertation studies about the existence of three different types of attractors of three multi-component reaction-diffusion systems. These reaction-diffusion systems play important role in both chemical kinetics and biological pattern formation in the fast-growing area of mathematical biology.

In Chapter 2, we prove the existence of a global attractor and an exponential attractor for the solution semiflow of a reaction-diffusion system called Boissonade equations in the L² phase space. We show that the global attractor is an (H, E) global attractor with the L^∞ and H² regularity and that the Hausdorff dimension and the …

Statistical Analysis And Modeling Health Data: A Longitudinal Study, Bhikhari Prasad Tharu

USF Tampa Graduate Theses and Dissertations

Lung cancer has been considered one of the leading causes of deaths while cancer re- mains the second most common cause of deaths in the USA. Understanding the behavior of a disease over time could yield important information to make decisions about the disease. Statistical models could provide crucial clues and help to make a decision about the dis- ease, budget allocation, evaluation, and implement prevention. Longitudinal trend analysis of the diseases helps to understand long term effects and nature. Cholesterol level is one of the most contributing risk factors for Coronary Heart Disease. Studying cholesterol statistically helps to know …

Active Tile Self-Assembly And Simulations Of Computational Systems, Daria Karpenko

USF Tampa Graduate Theses and Dissertations

Algorithmic self-assembly has been an active area of research at the intersection of computer science, chemistry, and mathematics for almost two decades now, motivated by the natural self-assembly mechanism found in DNA and driven by the desire for precise control of nanoscale material manufacture and for the development of nanocomputing and nanorobotics. At the theoretical core of this research is the Abstract Tile Assembly Model (aTAM), the original abstract model of DNA tile self-assembly. Recent advancements in DNA nanotechnology have been made in developing strand displacement mechanisms that could allow DNA tiles to modify themselves during the assembly process by …

Dynamic Processes In Network Goods: Modeling, Analysis And Applications, Arnut Paothong

USF Tampa Graduate Theses and Dissertations

The network externality function plays a very important role in the study of economic network industries. Moreover, the consumer group dynamic interactions coupled with network externality concept is going to play a dominant role in the network goods in the 21st century. The existing literature is stemmed on a choice of externality function with certain quantitative properties. The utility function coupled with the network externality function is used to investigate static properties of rational equilibrium. The aim of this work is to systematically initiate a development of quantitative effects of the concept of network externality and its influence on the …

Nonlinear Techniques For Stochastic Systems Of Differential Equations, Tadesse G. Zerihun

USF Tampa Graduate Theses and Dissertations

Two of the most well-known nonlinear methods for investigating nonlinear dynamic processes in sciences and engineering are nonlinear variation of constants parameters and comparison method. Knowing the existence of solution process, these methods provide a very powerful tools for investigating variety of problems, for example, qualitative and quantitative properties of solutions, finding error estimates between solution processes of stochastic system and the corresponding nominal system, and inputs for the designing engineering and industrial problems. The aim of this work is to systematically develop mathematical tools to undertake the mathematical frame-work to investigate a complex nonlinear nonstationary stochastic systems of differential …

Stochastic Modeling Of Network-Centric Epidemiological Processes, Divine Wanduku

USF Tampa Graduate Theses and Dissertations

The technological changes and educational expansion have created the heterogeneity in the human species. Clearly, this heterogeneity generates a structure in the population

dynamics, namely: citizen, permanent resident, visitor, and etc. Furthermore, as the heterogeneity in the population increases, the human mobility between meta-populations patches

also increases. Depending on spatial scales, a meta-population patch can be decomposed into sub-patches, for examples: homes, neighborhoods, towns, etc. The dynamics of human

mobility in a heterogeneous and scaled structured population is still its infancy level. We develop and investigate (1) an algorithmic two scale human mobility dynamic model for a meta-population. Moreover,the two …