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Title: Application of stochastical mixture theory in the design of electromagnetic composite materials.
Creator: Katragadda, Subramaniam., Florida Atlantic University, Neelakanta, Perambur S., College of Engineering and Computer Science, Department of Computer and Electrical Engineering and Computer Science
Abstract/Description: This Thesis is concerned with the application of stochastical mixture considerations in the analytical modeling of certain classes of electromagnetic composites. It refers to the elucidation of the electromagnetic properties of such composite materials when used in engineering applications. The analytical studies refer to the extension of the existing stochastical mixture permittivity formulations to characterize magnetic mixture materials as well as chiralic mixture media. In both cases the...
Show moreThis Thesis is concerned with the application of stochastical mixture considerations in the analytical modeling of certain classes of electromagnetic composites. It refers to the elucidation of the electromagnetic properties of such composite materials when used in engineering applications. The analytical studies refer to the extension of the existing stochastical mixture permittivity formulations to characterize magnetic mixture materials as well as chiralic mixture media. In both cases the mixture medium is presumed to consist of a host (receptacle) and dispersed particulates (inclusions). The effects of particulate shape in both chiralic and achiralic systems are also considered. Further, the concept of particulate polarization in deciding the permittivity and/or permeability characteristics of orderly-textured mixture media is addressed so as to determine the electromagnetic properties of such orderly-textured media. Application potentials of the present studies in the design of electromagnetic composites are indicated and the scope for the future research is portrayed.
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Date Issued: 1992
PURL: http://purl.flvc.org/fcla/dt/14807
Subject Headings: Composite materials, Stochastic processes
Format: Document (PDF)

Title: Nonlinear stochastic systems.
Creator: Cai, Guo-Qiang, Florida Atlantic University, Lin, Y. K., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
Abstract/Description: This thesis is concerned with nonlinear dynamical systems subject to random or combined random and deterministic excitations. To this end, a systematic procedure is first developed to obtain the exact stationary probability density for the response of a nonlinear system under both additive and multiplicative excitations of Gaussian white noises. This procedure is applicable to a class of systems called the class of generalized stationary potential. The basic idea is to separate the...
Show moreThis thesis is concerned with nonlinear dynamical systems subject to random or combined random and deterministic excitations. To this end, a systematic procedure is first developed to obtain the exact stationary probability density for the response of a nonlinear system under both additive and multiplicative excitations of Gaussian white noises. This procedure is applicable to a class of systems called the class of generalized stationary potential. The basic idea is to separate the circulatory probability flow from the noncirculatory flow, thus obtaining two sets of equations for the probability potential. It is shown that previously published exact solutions are special cases of this class. For those nonlinear systems not belonging to the class of generalized stationary potential, an approximate solution technique is developed on the basis of weighted residuals. The original system is replaced by the closest system belonging to the class of generalized stationary potential, in the sense that the statistically weighted residuals are zero for some suitably selected weighting functions. The consistency of the approximation technique is proved in terms of certain statistical moments. The above exact and approximate solution techniques are extended to two types of nonlinear systems: one subjected to non-Gaussian impulsive noise excitations and another subjected to combined harmonic and broad-band random excitations. Approximation procedures are devised to obtain stationary probabilistic solutions for these two types of problems. Monte Carlo simulations are performed to substantiate the accuracy of the approximate solution procedures.
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Date Issued: 1992
PURL: http://purl.flvc.org/fcla/dt/12293
Subject Headings: Nonlinear theories, Stochastic systems, Stochastic processes
Format: Document (PDF)

Title: Stochastic earthquake ground motion modeling.
Creator: Zhang, Ruichong., Florida Atlantic University, Lin, Y. K., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
Abstract/Description: A model for earthquake ground motion is developed in this dissertation using principles of geophysics and stochastics. The earth is idealized as being composed of horizontally stratified layers, with uniform physical properties for each layer. The seismic source is assumed to be the result of shear dislocation propagating on a fault line, which is further discretized into a series of point sources at equal intervals. The fundamental problem of the ground motion in a layered medium due to a...
Show moreA model for earthquake ground motion is developed in this dissertation using principles of geophysics and stochastics. The earth is idealized as being composed of horizontally stratified layers, with uniform physical properties for each layer. The seismic source is assumed to be the result of shear dislocation propagating on a fault line, which is further discretized into a series of point sources at equal intervals. The fundamental problem of the ground motion in a layered medium due to a point source at a given source location is first considered. The governing equations of three-dimensional wave motion in a uniform layer are presented and solved in both Cartesian and cylindrical coordinates. Wave propagation in a multi-layered medium is then analyzed in detail, in which the wave scattering matrices are introduced so that stability and accuracy in numerical calculation can be guaranteed. A detailed review of the mechanism of seismic point source is also provided. Based on the fundamental solution for a point source, an earthquake model is constructed by superposing the solutions associated with a series of point sources along a line which are activated sequentially at random times. Statistical characteristics of earthquake ground motion is then obtained by applying a generalized version of the random-pulse-train theory and its evolutionary spectral representation. Finally the effects of uneven interface on the earthquake ground motion is also analyzed using a first-order perturbation approach.
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Date Issued: 1992
PURL: http://purl.flvc.org/fcla/dt/12290
Subject Headings: Earth movements, Earthquakes, Stochastic processes
Format: Document (PDF)

Title: Alopex for handwritten digit recognition: Algorithmic verifications.
Creator: Martin, Gregory A., Florida Atlantic University, Shankar, Ravi, College of Engineering and Computer Science, Department of Computer and Electrical Engineering and Computer Science
Abstract/Description: Alopex is a biologically influenced computation paradigm that uses a stochastic procedure to find the global optimum of linear and nonlinear functions. It maps to a hierarchical SIMD (Single-Instruction-Multiple-Data) architecture with simple neuronal processing elements (PE's), therefore the large amount of interconnects in other types of neural networks are not required and more efficient utilization of chip level and board level "real estate" is realized. In this study, verifications were...
Show moreAlopex is a biologically influenced computation paradigm that uses a stochastic procedure to find the global optimum of linear and nonlinear functions. It maps to a hierarchical SIMD (Single-Instruction-Multiple-Data) architecture with simple neuronal processing elements (PE's), therefore the large amount of interconnects in other types of neural networks are not required and more efficient utilization of chip level and board level "real estate" is realized. In this study, verifications were performed on the use of a simplified Alopex algorithm in handwritten digit recognition with the intent that the verified algorithm be digitally implementable. The inputs to the simulated Alopex hardware are a set of 32 features extracted from the input characters. Although the goal of verifying the algorithm was not achieved, a firm direction for future studies has been established and a flexible software model for these future studies is available.
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Date Issued: 1992
PURL: http://purl.flvc.org/fcla/dt/14842
Subject Headings: Algorithms--Data processing, Stochastic processes
Format: Document (PDF)

Title: STABILITY ANALYSIS AND PARAMETER ESTIMATION OF A STOCHASTIC LOGISTIC GROWTH MODEL WITH MULTIPLICATIVE α-STABLE LÉVY NOISE.
Creator: Bhusal, Bikram, Long, Hongwei, Florida Atlantic University, Department of Mathematical Sciences, Charles E. Schmidt College of Science
Abstract/Description: Since the population growth systems may suffer impulsive environmental disturbances such as earthquakes, epidemics, tsunamis, hurricanes, and so on, stochastic differential equations(SDEs) that are driven not only by Brownian motion but also by α-stable Lévy noises are more appropriate to model such statistical behavior of non-Gaussian processes with heavy-tailed distribution, having infinite variance and in some cases infinite first moment. In this dissertation, we study stochastic processes...
Show moreSince the population growth systems may suffer impulsive environmental disturbances such as earthquakes, epidemics, tsunamis, hurricanes, and so on, stochastic differential equations(SDEs) that are driven not only by Brownian motion but also by α-stable Lévy noises are more appropriate to model such statistical behavior of non-Gaussian processes with heavy-tailed distribution, having infinite variance and in some cases infinite first moment. In this dissertation, we study stochastic processes defined as solutions to stochastic logistic differential equations driven by multiplicative α-stable Lévy noise. We mainly focus on one-dimensional stochastic logistic jump-diffusion processes driven by Brownian motion and α-stable Lévy motion. First, we present the stability analysis of the solution of a stochastic logistic growth model with multiplicative α-stable Lévy. We establish the existence of a unique global positive solution of this model under certain conditions. Then, we find the sufficient conditions for the almost sure exponential stability of the trivial solution of the model. Next, we provide parameter estimation for the proposed model. In parameter estimation, we use statistical methods to get an optimal and applicable estimator. We also investigate the consistency and asymptotics of the proposed estimator. We assess the validity of the estimators with a simulation study.
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Date Issued: 2022
PURL: http://purl.flvc.org/fau/fd/FA00014043
Subject Headings: Parameter estimation, Stochastic processes, Lévy processes
Format: Document (PDF)

Title: Characterizing the Geometry of a Random Point Cloud.
Creator: Tyree, Zachariah, Lundberg, Erik, Long, Hongwei, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: This thesis is composed of three main parts. Each chapter is concerned with characterizing some properties of a random ensemble or stochastic process. The properties of interest and the methods for investigating them di er between chapters. We begin by establishing some asymptotic results regarding zeros of random harmonic mappings, a topic of much interest to mathematicians and astrophysicists alike. We introduce a new model of harmonic polynomials based on the so-called "Weyl ensemble" of...
Show moreThis thesis is composed of three main parts. Each chapter is concerned with characterizing some properties of a random ensemble or stochastic process. The properties of interest and the methods for investigating them di er between chapters. We begin by establishing some asymptotic results regarding zeros of random harmonic mappings, a topic of much interest to mathematicians and astrophysicists alike. We introduce a new model of harmonic polynomials based on the so-called "Weyl ensemble" of random analytic polynomials. Building on the work of Li and Wei [28] we obtain precise asymptotics for the average number of zeros of this model. The primary tools used in this section are the famous Kac-Rice formula as well as classical methods in the asymptotic analysis of integrals such as the Laplace method. Continuing, we characterize several topological properties of this model of harmonic polynomials. In chapter 3 we obtain experimental results concerning the number of connected components of the orientation-reversing region as well as the geometry of the distribution of zeros. The tools used in this section are primarily Monte Carlo estimation and topological data analysis (persistent homology). Simulations in this section are performed within MATLAB with the help of a computational homology software known as Perseus. While the results in this chapter are empirical rather than formal proofs, they lead to several enticing conjectures and open problems. Finally, in chapter 4 we address an industry problem in applied mathematics and machine learning. The analysis in this chapter implements similar techniques to those used in chapter 3. We analyze data obtained by observing CAN tra c. CAN (or Control Area Network) is a network for allowing micro-controllers inside of vehicles to communicate with each other. We propose and demonstrate the e ectiveness of an algorithm for detecting malicious tra c using an approach that discovers and exploits the natural geometry of the CAN surface and its relationship to random walk Markov chains.
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Date Issued: 2018
PURL: http://purl.flvc.org/fau/fd/FA00013118
Subject Headings: Stochastic processes, Harmonic functions, Random point cloud
Format: Document (PDF)

Title: Multiple-period supply chain contract modeling with dynamic stochastic and price-elastic demand.
Creator: Gu, Qian-nong., Florida Atlantic University, Han, Chingping (Jim), College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
Abstract/Description: In this study we developed a supply chain contract model for multiple scheduling period with dynamic demand patterns of stochastic nature, and with elastic price structures. The model presented here combined and enhanced several supply chain contract models developed previously. It is unique in that it considered multiple periods, dynamic, stochastic and price-elastic demand patterns, and flexible order quantities. Using a linear demand price-elastic relation and normal distribution pattern,...
Show moreIn this study we developed a supply chain contract model for multiple scheduling period with dynamic demand patterns of stochastic nature, and with elastic price structures. The model presented here combined and enhanced several supply chain contract models developed previously. It is unique in that it considered multiple periods, dynamic, stochastic and price-elastic demand patterns, and flexible order quantities. Using a linear demand price-elastic relation and normal distribution pattern, optimal solutions for minimum cost, maximum profit, price structure, and order policies for the entire supply chain were derived. Sensitivity analyses performed in this study gave a better understanding of relative importance of various system variables.
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Date Issued: 2001
PURL: http://purl.flvc.org/fcla/dt/11964
Subject Headings: Stochastic processes, Elasticity (Economics), Business logistics
Format: Document (PDF)

Title: Numerical path integration of stochastic systems.
Creator: Yu, Jinshou., Florida Atlantic University, Lin, Y. K., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
Abstract/Description: The present dissertation is focused on the numerical method of path integration for stochastic systems. The existing procedures of numerical path integration are re-examined. A comparison study is made of the results obtained using various interpolation schemes. The amounts of computation time and relative accuracies of the existing procedures are tested with different mesh sizes and different time step sizes. A new numerical procedure based on Gauss-Legendre integration formula is proposed,...
Show moreThe present dissertation is focused on the numerical method of path integration for stochastic systems. The existing procedures of numerical path integration are re-examined. A comparison study is made of the results obtained using various interpolation schemes. The amounts of computation time and relative accuracies of the existing procedures are tested with different mesh sizes and different time step sizes. A new numerical procedure based on Gauss-Legendre integration formula is proposed, which requires no explicit numerical interpolation. The probability evolution is represented in terms of the transition probabilities among Gauss points in various sub-intervals. Each transition probability is assumed to be Gaussian, and it can be obtained from the moment equations. Gaussian closure is used to truncate the moment equations in the case of a nonlinear system. The computation parameters of the new procedure, such as size of time-step and number of sub-intervals, can be determined in a systematic manner. The approximate Gaussianity of the transition probability obtained from the moment equations is first tested by comparing it with the simulation results, from which a proper time-step size is selected. The standard deviation of the transition probability in each direction of the state space can then be obtained from the moment equations, and is used to determine the size of the sub-intervals in that direction. The new numerical path integration procedure is applied to several one-dimensional and two-dimensional stochastic systems, for which the responses are homogeneous Markov processes. It is shown that the new procedure is not only accurate and efficient, but also numerically stable and highly adaptable. The new procedure is also applied to a nonlinear stochastic system subjected to both sinusoidal and random excitations. The system response in this case is a non-homogeneous Markov process. The algorithm is adapted for this case, so that re-computation of the transition probability density at every time step can be avoided.
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Date Issued: 1997
PURL: http://purl.flvc.org/fcla/dt/12506
Subject Headings: Stochastic systems, Numerical integration, Markov processes
Format: Document (PDF)

Title: The microprocessor design team assignment problem with a new multistage stochastic/Brownian motion model.
Creator: O'Grady, Thomas James., Florida Atlantic University, Han, Chingping (Jim), College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
Abstract/Description: The Microprocessor Design Team Assignment Problem models the microprocessor design efforts of Intel Corporation over a 29-year period from 1972 until 2001. The basic model is a Erlang queuing system based probability model of the individual programming-design team daily operations. After extensive research the Erlang Loss/Delay Blocked Multiserver Model is utilized throughout the dissertation The Erlang loss-delay model takes into account the Key Man Constraint for team leaders and...
Show moreThe Microprocessor Design Team Assignment Problem models the microprocessor design efforts of Intel Corporation over a 29-year period from 1972 until 2001. The basic model is a Erlang queuing system based probability model of the individual programming-design team daily operations. After extensive research the Erlang Loss/Delay Blocked Multiserver Model is utilized throughout the dissertation The Erlang loss-delay model takes into account the Key Man Constraint for team leaders and programming team personnel. The Microprocessor Design Team Assignment Problem Case Study and massive research effort, into Intel Corporations design efforts, is complicated by modeling a major programming-design team operation without any current data or assistance from Intel Corporation. However much of the lack of assistance and data was obtained by utilizing a critical managerial design team decomposition which answered most major questions about Intels lack of adequate personnel and overutilization of team leaders and asst. team leaders throughout the 48 months of most major design projects. The study-dissertation concludes that Intels and Hewlett Packards current positions in the computer industry are relatively secure because of extremely high entry level costs exceeding $850,000,000.00 million dollars. Many individual issues about programming-design team operations are analyzed in a great amount of detail. This is the first time that much of this design-programming team material and information is being made public for future research and continuing improvement upon large scale project managerial methods and techniques. The basic design-programming team effort is also modeled with Erlang probability models and stochastic Riccati differential equations. This modeling effort is discussed in great detail in chapter 5 and Appendix Alpha. It is believed that this fundamental research leads the way for more advanced efforts in manufacturing systems and possibly mechatronics for further models utilizing strong Markov properties. This research effort substantially advances the basic research and knowledge of Partially Observable Markov Decision Processes and Strong Brownian Motion with the basic unit being strong Markov properties.
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Date Issued: 2001
PURL: http://purl.flvc.org/fcla/dt/11962
Subject Headings: Brownian motion processes, Stochastic analysis, Microprocessors
Format: Document (PDF)

Title: THE CHANGE POINT PROBLEM FOR TWO CLASSES OF STOCHASTIC PROCESSES.
Creator: Ball, Cory, Long, Hongwei, Florida Atlantic University, Department of Mathematical Sciences, Charles E. Schmidt College of Science
Abstract/Description: The change point problem is a problem where a process changes regimes because a parameter changes at a point in time called the change point. The objective of this problem is to estimate the change point and each of the parameters of the stochastic process. In this thesis, we examine the change point problem for two classes of stochastic processes. First, we consider the volatility change point problem for stochastic diffusion processes driven by Brownian motions. Then, we consider the drift...
Show moreThe change point problem is a problem where a process changes regimes because a parameter changes at a point in time called the change point. The objective of this problem is to estimate the change point and each of the parameters of the stochastic process. In this thesis, we examine the change point problem for two classes of stochastic processes. First, we consider the volatility change point problem for stochastic diffusion processes driven by Brownian motions. Then, we consider the drift change point problem for Ornstein-Uhlenbeck processes driven by _-stable Levy motions. In each problem, we establish the consistency of the estimators, determine asymptotic behavior for the changing parameters, and finally, we perform simulation studies to computationally assess the convergence of parameters.
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Date Issued: 2020
PURL: http://purl.flvc.org/fau/fd/FA00013462
Subject Headings: Stochastic processes, Change-point problems, Brownian motion processes, Ornstein-Uhlenbeck process, Computer simulation
Format: Document (PDF)

$The topology of archaeological site distributions: the lacunarity and fractality of prehistoric oaxacan settlements$

Title: The topology of archaeological site distributions: the lacunarity and fractality of prehistoric oaxacan settlements.
Creator: Flanagan, Kelin, Brown, Clifford T., Florida Atlantic University, Dorothy F. Schmidt College of Arts and Letters, Department of Anthropology
Abstract/Description: Survey is time-consuming and expensive. Therefore, it needs to be both effective and efficient. Some archaeologists have argued that current survey techniques are not effective (Shott 1985, 1989), but most archaeologists continue to employ these methods and therefore must believe they are effective. If our survey techniques are effective, why do simulations suggest otherwise? If they are ineffective, can we improve them? The answers to these practical questions depend on the topological...
Show moreSurvey is time-consuming and expensive. Therefore, it needs to be both effective and efficient. Some archaeologists have argued that current survey techniques are not effective (Shott 1985, 1989), but most archaeologists continue to employ these methods and therefore must believe they are effective. If our survey techniques are effective, why do simulations suggest otherwise? If they are ineffective, can we improve them? The answers to these practical questions depend on the topological characteristics of archaeological site distributions. In this study I analyze archaeological site distributions in the Valley of Oaxaca, Mexico, using lacunarity and fractal dimension. Fractal dimension is a parameter of fractal patterns, which are complex, space-filling designs exhibiting self-similarity and power-law scaling. Lacunarity is a statistical measure that describes the texture of a spatial dispersion. It is useful in understanding how archaeological tests should be spaced during surveys. Between these two measures, I accurately describe the regional topology and suggest new considerations for archaeological survey design.
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Date Issued: 2014
PURL: http://purl.flvc.org/fau/fd/FA00004109, http://purl.flvc.org/fau/fd/FA00004109
Subject Headings: Excavations (Archaeology) -- Methodology, Fractals, Social sciences -- Mathematical models, Stochastic processes
Format: Document (PDF)

Title: PARAMETER ESTIMATION FOR GEOMETRIC L EVY PROCESSES WITH STOCHASTIC VOLATILITY.
Creator: Chhetri, Sher B., Long, Hongwei, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: In finance, various stochastic models have been used to describe the price movements of financial instruments. After Merton's [38] seminal work, several jump diffusion models for option pricing and risk management have been proposed. In this dissertation, we add alpha-stable Levy motion to the process related to dynamics of log-returns in the Black-Scholes model where the volatility is assumed to be constant. We use the sample characteristic function approach in order to study parameter...
Show moreIn finance, various stochastic models have been used to describe the price movements of financial instruments. After Merton's [38] seminal work, several jump diffusion models for option pricing and risk management have been proposed. In this dissertation, we add alpha-stable Levy motion to the process related to dynamics of log-returns in the Black-Scholes model where the volatility is assumed to be constant. We use the sample characteristic function approach in order to study parameter estimation for discretely observed stochastic differential equations driven by Levy noises. We also discuss the consistency and asymptotic properties of the proposed estimators. Simulation results of the model are also presented to show the validity of the estimators. We then propose a new model where the volatility is not a constant. We consider generalized alpha-stable geometric Levy processes where the stochastic volatility follows the Cox-Ingersoll-Ross (CIR) model in Cox et al. [9]. A number of methods have been proposed for estimating parameters for stable laws. However, a complication arises in estimation of the parameters in our model because of the presence of the unobservable stochastic volatility. To combat this complication we use the sample characteristic function method proposed by Press [48] and the conditional least squares method as mentioned in Overbeck and Ryden [47] to estimate all the parameters. We then discuss the consistency and asymptotic properties of the proposed estimators and establish a Central Limit Theorem. We perform simulations to assess the validity of the estimators. We also present several tables to show the comparison of estimators using different choices of arguments ui's. We conclude that all the estimators converge as expected regardless of the choice of ui's.
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Date Issued: 2019
PURL: http://purl.flvc.org/fau/fd/FA00013294
Subject Headings: Stochastic models, Lévy processes, Parameter estimation, Finance, Simulations
Format: Document (PDF)

Title: Finite element methods for stochastic structures and conditional simulation.
Creator: Ren, Yongjian., Florida Atlantic University, Elishakoff, Isaac, College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
Abstract/Description: This dissertation deals with the non-perturbative finite element methods for stochastic structures and conditional simulation techniques for random fields. Three different non-perturbative finite element schemes have been proposed to compute the first and second moments of displacement responses of stochastic structures. These three methods are based, respectively, on (i) the exact inverse of the global stiffness matrix for simple stochastic structures; (ii) the variational principles for...
Show moreThis dissertation deals with the non-perturbative finite element methods for stochastic structures and conditional simulation techniques for random fields. Three different non-perturbative finite element schemes have been proposed to compute the first and second moments of displacement responses of stochastic structures. These three methods are based, respectively, on (i) the exact inverse of the global stiffness matrix for simple stochastic structures; (ii) the variational principles for statically-determinate beams; and (iii)Â the element-level flexibility for general stochastic statically indeterminate structures. The non-perturbative finite element method for stochastic structures possesses several advantages over the conventional perturbation-based finite element method for stochastic structures, including (i) applicability to large values of the coefficient of variation of random parameters; (ii) convergence to exact solutions when the finite element mesh is refined; (iii) requirement of less statistical information than that demanded by the high-order perturbation methods. Conditional simulation of random fields has been an extremely important research field in most recent years due to its application in urban earthquake monitoring systems. This study generalizes the available simulation technique for one-variate Gaussian random fields, conditioned by realizations of the fields, to multi-variate vector random field, conditioned by the realizations of the fields themselves as well as the realizations of the fields derivatives. Furthermore, a conditional simulation for non-Gaussian random fields is also proposed in this study by combining the unconditional simulation technique of non-Gaussian fields and the conditional simulation technique of Gaussian fields. Finally, the dissertation incorporates the simulation technique of random field into the non-perturbation finite element method for stochastic structures, to handle the cases where only one-dimensional probability density function and the correlation function of the random parameters are available, the demanded two-dimensional probability density function is unavailable. Simulation technique is applied to generate the samples of random fields which are used to estimate the correlation between flexibilities over elements. The estimated correlation of flexibility is then used in finite element analysis for stochastic structures. For each proposed approach, numerous examples and numerical results have been implemented.
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Date Issued: 1998
PURL: http://purl.flvc.org/fcla/dt/12580
Subject Headings: Finite element method, Stochastic processes, Random fields--Mathematical models
Format: Document (PDF)

Title: Stochastical aspects of neuronal activity, neural networks, and communication.
Creator: De Groff, Dolores F., Florida Atlantic University, Neelakanta, Perambur S., College of Engineering and Computer Science, Department of Computer and Electrical Engineering and Computer Science
Abstract/Description: By revisiting the popular framework of depicting neuronal (collective) activities as analogous to Ising's spin-glass theory of interacting magnetic spins, the contradictions that coexist with such an analogy are extracted and discussed. To alleviate such contradictions, an alternative strategy of equating the neuronal interactions to the partially anisotropic nematic phase of disorder pertaining to liquid crystals is proposed. Hence, the extent of anisotropy in the neuronal system, quantified...
Show moreBy revisiting the popular framework of depicting neuronal (collective) activities as analogous to Ising's spin-glass theory of interacting magnetic spins, the contradictions that coexist with such an analogy are extracted and discussed. To alleviate such contradictions, an alternative strategy of equating the neuronal interactions to the partially anisotropic nematic phase of disorder pertaining to liquid crystals is proposed. Hence, the extent of anisotropy in the neuronal system, quantified in terms of an order-function, is specified to elucidate the nonlinear squashing action of the input-output relations in a neuronal cell. The relevant approach thereof, is based on Langevin's theory considerations as applied to dipole molecules. Further, in view of the stochastical properties due to the inherent disorder associated with the neuronal assembly, the progression of state-transitions across the interconnected cells is modeled as a momentum flow relevant to particle dynamics. Hence, corresponding wave mechanics attributions of such a collective movement of state-transition activity are described in terms of a probabilistic wave function. Lastly, the stochastical aspects of noise-perturbed neuronal dynamics are studied via Fokker-Planck equation representing the Langevin-type relaxational (nonlinear) process associated with the neuronal states. On each of these topics portraying the stochastical characteristics of the neuronal assembly and its activities, newer and/or more exploratory inferences are made, logical conclusions are enumerated and relevant discussions are presented along with the scope for future research to be pursued.
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Date Issued: 1993
PURL: http://purl.flvc.org/fcla/dt/12326
Subject Headings: Neurons--Mathematical models, Stochastic processes, Neural networks (Computer science)
Format: Document (PDF)

Title: Simulation study on option pricing under jump diffusion models.
Creator: Rodrigues, Justin, Long, Hongwei, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: The main objective of this thesis is to simulate, evaluate and discuss several methods for pricing European-style options. The Black-Scholes model has long been considered the standard method for pricing options. One of the downfalls of the Black-Scholes model is that it is strictly continuous and does not incorporate discrete jumps. This thesis will consider two alternate Levy models that include discretized jumps; The Merton Jump Diffusion and Kou's Double Exponential Jump Diffusion. We...
Show moreThe main objective of this thesis is to simulate, evaluate and discuss several methods for pricing European-style options. The Black-Scholes model has long been considered the standard method for pricing options. One of the downfalls of the Black-Scholes model is that it is strictly continuous and does not incorporate discrete jumps. This thesis will consider two alternate Levy models that include discretized jumps; The Merton Jump Diffusion and Kou's Double Exponential Jump Diffusion. We will use each of the three models to price real world stock data through software simulations and explore the results.Keywords: Levy Processes, Brownian motion, Option pricing, Simulation, Black-Scholes, Merton Jump Diffusion, Kou, Kou's Double Exponential Jump Diffusion.
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Date Issued: 2013
PURL: http://purl.flvc.org/fau/fd/FA0004051
Subject Headings: Finance -- Mathematical models, Levy processes, Prices -- Econometric models, Statistical physics, Stochastic processes, Valuation -- Econometric models
Format: Document (PDF)

Title: Design and analysis of an ocean current turbine performance assessment system.
Creator: Young, Matthew T., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
Abstract/Description: This thesis proposes a sensor approach for quantifying the hydrodynamic performance of Ocean Current Turbines (OCT), and investigates the influence of sensor-specific noise and sampling rates on calculated turbine performance. Numerical models of the selected sensors are developed, and then utilized to add stochastic measurement error to numerically-generated, non-stochastic OCT data. Numerically-generated current velocity and turbine performance measurements are used to quantify the relative...
Show moreThis thesis proposes a sensor approach for quantifying the hydrodynamic performance of Ocean Current Turbines (OCT), and investigates the influence of sensor-specific noise and sampling rates on calculated turbine performance. Numerical models of the selected sensors are developed, and then utilized to add stochastic measurement error to numerically-generated, non-stochastic OCT data. Numerically-generated current velocity and turbine performance measurements are used to quantify the relative influence of sensor-specific error and sampling limitations on sensor measurements and calculated OCT performance results. The study shows that the addition of sensor error alters the variance and mean of OCT performance metric data by roughly 7.1% and 0.24%, respectively, for four evaluated operating conditions. It is shown that sensor error results in a mean, maximum and minimum performance metric to Signal to Noise Ration (SNR) of 48.6% and 6.2%, respectively.
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Date Issued: 2012
PURL: http://purl.flvc.org/FAU/3359164
Subject Headings: Marine turbines, Mathematical models, Fluid dynamics, Structural dynamics, Stochastic processes, Rotors, Design and construction, Testing
Format: Document (PDF)

Title: Geoacoustic inversion of subbottom channels using mulitple frequency input parameters.
Creator: Weeks, Rebecca., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
Abstract/Description: This thesis investigates inversion techniques used to determine the geoacoustic properties of a shallow-water waveguide. The data used were obtained in the Shallow Water '06 Modal Mapping Experiment in which four buoys drifted over a system of subbottom channels. The method used was perturbative inversion using modal eigenvalues as input parameters, which were found using an autoregressive spectral estimator. This work investigates the differences between a "channel" region and a "no channel"...
Show moreThis thesis investigates inversion techniques used to determine the geoacoustic properties of a shallow-water waveguide. The data used were obtained in the Shallow Water '06 Modal Mapping Experiment in which four buoys drifted over a system of subbottom channels. The method used was perturbative inversion using modal eigenvalues as input parameters, which were found using an autoregressive spectral estimator. This work investigates the differences between a "channel" region and a "no channel" region based on an inferred stratigraphic model. Inversions were performed on data from a single buoy both at individual frequencies and multiple frequencies simultaneously. Since the use of multiple frequencies and a certain set of constraints proved to be an effective method of inversion, the method was applied to data from the other three buoys as well. It is shown that the "channel" and "no channel" regions have significantly different sound speed profiles.
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Date Issued: 2010
PURL: http://purl.flvc.org/FAU/1930486
Subject Headings: Oceanographic buoys, Stochastic processes, Acoustic surface waves, Underwater acoustics, Wave equation, Numerical solutions
Format: Document (PDF)

Title: Vibration analysis for ocean turbine reliability models.
Creator: Wald, Randall David., College of Engineering and Computer Science, Department of Computer and Electrical Engineering and Computer Science
Abstract/Description: Submerged turbines which harvest energy from ocean currents are an important potential energy resource, but their harsh and remote environment demands an automated system for machine condition monitoring and prognostic health monitoring (MCM/PHM). For building MCM/PHM models, vibration sensor data is among the most useful (because it can show abnormal behavior which has yet to cause damage) and the most challenging (because due to its waveform nature, frequency bands must be extracted from...
Show moreSubmerged turbines which harvest energy from ocean currents are an important potential energy resource, but their harsh and remote environment demands an automated system for machine condition monitoring and prognostic health monitoring (MCM/PHM). For building MCM/PHM models, vibration sensor data is among the most useful (because it can show abnormal behavior which has yet to cause damage) and the most challenging (because due to its waveform nature, frequency bands must be extracted from the signal). To perform the necessary analysis of the vibration signals, which may arrive rapidly in the form of data streams, we develop three new wavelet-based transforms (the Streaming Wavelet Transform, Short-Time Wavelet Packet Decomposition, and Streaming Wavelet Packet Decomposition) and propose modifications to the existing Short-TIme Wavelet Transform. ... The proposed algorithms also create and select frequency-band features which focus on the areas of the signal most important to MCM/PHM, producing only the information necessary for building models (or removing all unnecessary information) so models can run on less powerful hardware. Finally, we demonstrate models which can work in multiple environmental conditions. ... Our results show that many of the transforms give similar results in terms of performance, but their different properties as to time complexity, ability to operate in a fully streaming fashion, and number of generated features may make some more appropriate than others in particular applications, such as when streaming data or hardware limitations are extremely important (e.g., ocean turbine MCM/PHM).
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Date Issued: 2012
PURL: http://purl.flvc.org/FAU/3359158
Subject Headings: Marine turbines, Mathematical models, Fluid dynamics, Structural dynamics, Vibration, Measurement, Stochastic processes
Format: Document (PDF)

Title: A novel optimization algorithm and other techniques in medicinal chemistry.
Creator: Santos, Radleigh G., Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: In this dissertation we will present a stochastic optimization algorithm and use it and other mathematical techniques to tackle problems arising in medicinal chemistry. In Chapter 1, we present some background about stochastic optimization and the Accelerated Random Search (ARS) algorithm. We then present a novel improvement of the ARS algorithm, DIrected Accelerated Random Search (DARS), motivated by some theoretical results, and demonstrate through numerical results that it improves upon...
Show moreIn this dissertation we will present a stochastic optimization algorithm and use it and other mathematical techniques to tackle problems arising in medicinal chemistry. In Chapter 1, we present some background about stochastic optimization and the Accelerated Random Search (ARS) algorithm. We then present a novel improvement of the ARS algorithm, DIrected Accelerated Random Search (DARS), motivated by some theoretical results, and demonstrate through numerical results that it improves upon ARS. In Chapter 2, we use DARS and other methods to address issues arising from the use of mixture-based combinatorial libraries in drug discovery. In particular, we look at models associated with the biological activity of these mixtures and use them to answer questions about sensitivity and robustness, and also present a novel method for determining the integrity of the synthesis. Finally, in Chapter 3 we present an in-depth analysis of some statistical and mathematical techniques in combinatorial chemistry, including a novel probabilistic approach to using structural similarity to predict the activity landscape.
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Date Issued: 2012
PURL: http://purl.flvc.org/FAU/3352830
Subject Headings: Drugs, Design, Mathematical models, Combinatorial optimization, Combinatorial chemistry, Genetic algorithms, Mathematical optimization, Stochastic processes
Format: Document (PDF)

Title: Modal analysis of plates with uncertain properties: Theory and applications.
Creator: Wu, Jingshu., Florida Atlantic University, Stevens, Karl K., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
Abstract/Description: This dissertation is concerned with modal analysis of plates with properties which vary over the structures. The uncertain geometric and material parameters are treated as random fields which are discretized over individual regions by using a local averaging technique. These discretized properties are then combined with a random perturbation procedure based upon traditional finite element methods. The result is a stochastic finite element method (SFEM) program for modal analysis of plates....
Show moreThis dissertation is concerned with modal analysis of plates with properties which vary over the structures. The uncertain geometric and material parameters are treated as random fields which are discretized over individual regions by using a local averaging technique. These discretized properties are then combined with a random perturbation procedure based upon traditional finite element methods. The result is a stochastic finite element method (SFEM) program for modal analysis of plates. This SFEM method is applied to two problems areas. The first application is to provide a new approach for modal analysis of printed circuit boards wherein the circuit board is modeled as an elastic plate with random spatial variation of its properties. The SFEM program is used to predict the effect of this variation on the natural frequencies and mode shapes of the board. Predicted results are compared with those obtained from modal testing of a circuit board. It is shown that variations between the measured and predicted modal parameters can be accounted for by small random variations in the board properties. This approach offers a simple, realistic, and cost-effective way for prediction of board modal properties. The second application is on vibration control of plates by application of surface viscoelastic damping treatments. Existing works generally treat the geometric and material properties of the damping layer as deterministic parameters, although uncertainties in the values of these parameters are commonplace. No work has been done regarding surface damping treatments with uncertain properties. In this thesis, the modal properties of plates with random spatial variation of the damping layer properties are investigated. The effects of this variation on the system natural frequencies, modal loss factors, and mode shapes are calculated by the SFEM program developed. Results are presented for a cantilever aluminum plate with complete PVC surface damping treatment with uncertain properties. In the SFEM modeling of both PC boards and plates with surface damping treatments, the effects on the system eigenvalues/eigenvectors of the correlation distance of the random property field, the correlation constant between the random fluctuations, and the magnitude of the random property variations, are investigated.
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Date Issued: 1993
PURL: http://purl.flvc.org/fcla/dt/12335
Subject Headings: Modal analysis, Stochastic processes, Finite element method, Plates (Engineering)--Testing
Format: Document (PDF)

Stochastic processes (21)	+ -
Mathematical models (5)	+ -
Brownian motion processes (2)	+ -
Code division multiple access (2)	+ -
Computer network protocols (2)	+ -

Finite element method (2)	+ -
Fluid dynamics (2)	+ -
Lévy processes (2)	+ -
Marine turbines (2)	+ -
Parameter estimation (2)	+ -
Stochastic systems (2)	+ -
Structural dynamics (2)	+ -
Wireless communication systems (2)	+ -
Acoustic surface waves (1)	+ -
Algorithms--Data processing (1)	+ -
Animal populations -- Estimates (1)	+ -
Bottlenose dolphin -- Florida -- Indian River Lagoon -- Geographical distribution (1)	+ -
Business cycles (1)	+ -
Business logistics (1)	+ -
Change-point problems (1)	+ -
Combinatorial chemistry (1)	+ -
Combinatorial optimization (1)	+ -
Composite materials (1)	+ -
Composite materials--Electric properties (1)	+ -
Composite materials--Magnetic properties (1)	+ -
Computer simulation (1)	+ -
Consumption (Economics) (1)	+ -
Data processing (1)	+ -
Design (1)	+ -
Design and construction (1)	+ -

Florida Atlantic University (18)	+ -
College of Engineering and Computer Science (16)	+ -
Department of Ocean and Mechanical Engineering (9)	+ -
Charles E. Schmidt College of Science (8)	+ -
Department of Computer and Electrical Engineering and Computer Science (7)	+ -

Department of Mathematical Sciences (6)	+ -
Long, Hongwei (5)	+ -
Lin, Y. K. (3)	+ -
Neelakanta, Perambur S. (3)	+ -
Han, Chingping (Jim) (2)	+ -
Wang, Di (2)	+ -
Ball, Cory (1)	+ -
Bhusal, Bikram (1)	+ -
Brown, Clifford T. (1)	+ -
Cai, Guo-Qiang (1)	+ -
Chhetri, Sher B. (1)	+ -
De Groff, Dolores F. (1)	+ -
Department of Anthropology (1)	+ -
Department of Biological Sciences (1)	+ -
Department of Physics (1)	+ -
Dorothy F. Schmidt College of Arts and Letters (1)	+ -
Elishakoff, Isaac (1)	+ -
Flanagan, Kelin (1)	+ -
Gu, Qian-nong. (1)	+ -
Katragadda, Subramaniam. (1)	+ -
Lundberg, Erik (1)	+ -
Martin, Gregory A. (1)	+ -
Morgera, Salvatore D. (1)	+ -
Noonburg, Erik G. (1)	+ -
O'Grady, Thomas James. (1)	+ -

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