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Title: Asymmetric information in fads models in Lâevy markets.
Creator: Buckley, Winston S., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: Fads models for stocks under asymmetric information in a purely continuous(GBM) market were first studied by P. Guasoni (2006), where optimal portfolios and maximum expected logarithmic utilities, including asymptotic utilities for the informed and uninformed investors, were presented. We generalized this theory to Lâevy markets, where stock prices and the process modeling the fads are allowed to include a jump component, in addition to the usual continuous component. We employ the methods of...
Show moreFads models for stocks under asymmetric information in a purely continuous(GBM) market were first studied by P. Guasoni (2006), where optimal portfolios and maximum expected logarithmic utilities, including asymptotic utilities for the informed and uninformed investors, were presented. We generalized this theory to Lâevy markets, where stock prices and the process modeling the fads are allowed to include a jump component, in addition to the usual continuous component. We employ the methods of stochastic calculus and optimization to obtain analogous results to those obtained in the purely continuous market. We approximate optimal portfolios and utilities using the instantaneous centralized and quasi-centralized moments of the stocks percentage returns. We also link the random portfolios of the investors, under asymmetric information to the purely deterministic optimal portfolio, under symmetric information.
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Date Issued: 2009
PURL: http://purl.flvc.org/FAU/3337187
Subject Headings: Investments, Mathematical models, Capital market, Mathematical models, Finance, Mathematical models, Information theory in economics, Capital asset pricing model, Lâevy processes
Format: Document (PDF)

Title: A comparison of pixel based and object based vegetation community classification in the Arthur R. Marshall Loxahatchee National Wildlife Refuge.
Creator: Barone, Dorianne M., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Geosciences
Abstract/Description: Pixel based and object based vegetation community classification methods were performed using 30 meter spatial resolution Landsat satellite imagery of the Arthur R. Marshall Loxahatchee National Wildlife Refuge (Refuge), a remnant of the northern Everglades. Supervised classification procedures using maximum likelihood and parallelepiped algorithms were used to produce thematic maps with the following vegetation communities : wet prairie, sawgrass, cattail, tree island, brush, aquatic/open...
Show morePixel based and object based vegetation community classification methods were performed using 30 meter spatial resolution Landsat satellite imagery of the Arthur R. Marshall Loxahatchee National Wildlife Refuge (Refuge), a remnant of the northern Everglades. Supervised classification procedures using maximum likelihood and parallelepiped algorithms were used to produce thematic maps with the following vegetation communities : wet prairie, sawgrass, cattail, tree island, brush, aquatic/open water. Spectral data, as well as NDVI, texture and principal component data were used to produce vegetation community classification maps. The accuracy levels of the thematic maps produced were calculated and compared to one another. The pixel based approach using the parallelepiped classification algorithm on the spectral and NDVI dataset had the highest accuracy level. A generalized form of this classification using only three vegetation communities (all wet prairie, tree island/brush and aquatic/open water) was compared to a previously published classification which used 1987 SPOT imagery in order to extract information on possible vegetation community transitions that are occurring within the Refuge. Results of the study indicate that 30 meter spatial resolution may be useful for understanding broad vegetation community trends but not species level trends. Pixel based procedures provide a more accurate classification than object based procedures for this landscape when using 30 meter imagery. Lastly, since 1987 there may be a trend of tree island/brush communities replacing wet prairie communities in the northern part of the Refuge and a transition to wet prairie communities in place of tree island/brush communities in the southern portion of the Refuge.
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Date Issued: 2008
PURL: http://purl.flvc.org/FAU/58002
Subject Headings: Ecosystem management, Vegetation dynamics, Vegetation classification, Spatial ecology, Mathematical models
Format: Document (PDF)

Title: Differentiating decomposition rates within the ridge-slough microtopography of the central Florida Everglades.
Creator: Van der Heiden, Sheryl R., Charles E. Schmidt College of Science, Department of Biological Sciences
Abstract/Description: The relative rates of detrital decomposition in four vegetation communities within the Everglades' ridge-slough microtopography were evaluated during two trials. Litterbags with community-specific detritus in proportion to each community's composition were put into the four communities; namely, submerged marsh, emergent marsh, short Cladium ridge, and tall Cladium ridge. These litterbags were paired with litterbags containing control leaf litter from Chrysobalanus icaco and Salix caroliniana...
Show moreThe relative rates of detrital decomposition in four vegetation communities within the Everglades' ridge-slough microtopography were evaluated during two trials. Litterbags with community-specific detritus in proportion to each community's composition were put into the four communities; namely, submerged marsh, emergent marsh, short Cladium ridge, and tall Cladium ridge. These litterbags were paired with litterbags containing control leaf litter from Chrysobalanus icaco and Salix caroliniana during the wet and dry season trials, respectively. No regional differences in decomposition were shown, but there were significant differences across communities, attributed to the initial C:N ratio of the detritus, with the fastest decomposition occurring in the deepest submerged marsh followed by emergent marsh, and the shallower ridge communities had equally slower decomposition. Additionally, both controls followed the same pattern. Thus, decomposition contributes to an active self-maintenance mechanism within the vegetation communities which ultimately helps to conserve the ridges and sloughs.
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Date Issued: 2008
PURL: http://purl.flvc.org/FAU/166456
Subject Headings: Biogeochemistry, Surfaces (Technology), Measurement, Vegatation dynamics, Mathematical models, Wetland ecology
Format: Document (PDF)

Title: Gravitational signature of core-collapse supernova results of CHIMERA simulations.
Creator: Yakunin, Konstantin., Charles E. Schmidt College of Science, Department of Physics
Abstract/Description: Core-collapse supernovae (CCSN) are among the most energetic explosions in the universe, liberating ~1053 erg of gravitational binding energy of the stellar core. Most of this energy ( ~99%) is emitted in neutrinos and only 1% is released as electromagnetic radiation in the visible spectrum. Energy radiated in the form of gravitational waves (GWs) is about five orders smaller. Nevertheless, this energy corresponds to a very strong GW signal and, because of this CCSN are considered as one of...
Show moreCore-collapse supernovae (CCSN) are among the most energetic explosions in the universe, liberating ~1053 erg of gravitational binding energy of the stellar core. Most of this energy ( ~99%) is emitted in neutrinos and only 1% is released as electromagnetic radiation in the visible spectrum. Energy radiated in the form of gravitational waves (GWs) is about five orders smaller. Nevertheless, this energy corresponds to a very strong GW signal and, because of this CCSN are considered as one of the prime sources of gravitational waves for interferometric detectors. Gravitational waves can give us access to the electromagnetically hidden compact inner core of supernovae. They will provide valuable information about the angular momentum distribution and the baryonic equation of state, both of which are uncertain. Furthermore, they might even help to constrain theoretically predicted SN mechanisms. Detection of GW signals and analysis of the observations will require realistic signal predi ctions from the non-parameterized relativistic numerical simulations of CCSN. This dissertation presents the gravitational wave signature of core-collapse v supernovae. Previous studies have considered either parametric models or nonexploding models of CCSN. This work presents complete waveforms, through the explosion phase, based on first-principles models for the first time. We performed 2D simulations of CCSN using the CHIMERA code for 12, 15, and 25M non-rotating progenitors. CHIMERA incorporates most of the criteria for realistic core-collapse modeling, such as multi-frequency neutrino transport coupled with relativistic hydrodynamics, eective GR potential, nuclear reaction network, and an industry-standard equation of state., Based on the results of our simulations, I produced the most realistic gravitational waveforms including all postbounce phases of core-collapse supernovae: the prompt convection, the stationary accretion shock instability, and the corresponding explosion. Additionally, the tracer particles applied in the analysis of the GW signal reveal the origin of low-frequency component in the prompt part of gravitational waveform. Analysis of detectability of the GW signature from a Galactic event shows that the signal is within the band-pass of current and future GW observatories such as AdvLIGO, advanced Virgo, and LCGT.
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Date Issued: 2011
PURL: http://purl.flvc.org/FAU/3322512
Subject Headings: Mathematical physics, Continuum mechanics, Supernovae, Mathematical models
Format: Document (PDF)

Title: INFECTION AGE STRUCTURED VECTOR BORNE DISEASE MODEL WITH DIRECT TRANSMISSION.
Creator: Giri, Sunil, Tuncer, Necibe, Florida Atlantic University, Department of Mathematical Sciences, Charles E. Schmidt College of Science
Abstract/Description: Mathematical modeling is a powerful tool to study and analyze the disease dynamics prevalent in the community. This thesis studies the dynamics of two time since infection structured vector borne models with direct transmission. We have included disease induced death rate in the first model to form the second model. The aim of this thesis is to analyze whether these two models have same or different disease dynamics. An explicit expression for the reproduction number denoted by R0 is derived....
Show moreMathematical modeling is a powerful tool to study and analyze the disease dynamics prevalent in the community. This thesis studies the dynamics of two time since infection structured vector borne models with direct transmission. We have included disease induced death rate in the first model to form the second model. The aim of this thesis is to analyze whether these two models have same or different disease dynamics. An explicit expression for the reproduction number denoted by R0 is derived. Dynamical analysis reveals the forward bifurcation in the first model. That is when the threshold value R0 < 1, disease free-equilibrium is stable locally implying that if there is small perturbation of the system, then after some time, the system will return to the disease free equilibrium. When R0 > 1 the unique endemic equilibrium is locally asymptotically stable. For the second model, analysis of the existence and stability of equilibria reveals the existence of backward bifurcation i.e. where the disease free equilibrium coexists with the endemic equilibrium when the reproduction number R02 is less than unity. This aspect shows that in order to control vector borne disease, it is not sufficient to have reproduction number less than unity although necessary. Thus, the infection can persist in the population even if the reproduction number is less than unity. Numerical simulation is presented to see the bifurcation behaviour in the model. By taking the reproduction number as the bifurcation parameter, we find the system undergoes backward bifurcation at R02 = 1. Thus, the model has backward bifurcation and have two positive endemic equilibrium when R02 < 1 and unique positive endemic equilibrium whenever R02 > 1. Stability analysis shows that disease free equilibrium is locally asymptotically stable when R02 < 1 and unstable when R02 > 1. When R02 < 1, lower endemic equilibrium in backward bifurcation is locally unstable.
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Date Issued: 2020
PURL: http://purl.flvc.org/fau/fd/FA00013552
Subject Headings: Vector Borne Diseases, Mathematical models, Simulations, Dynamics--Mathematical models
Format: Document (PDF)

Title: Mathematical model of the dynamics of psychotherapy.
Creator: Norman, Michael D., Charles E. Schmidt College of Science, Center for Complex Systems and Brain Sciences
Abstract/Description: This is a novel attempt to produce a rigorous mathematical model of a complex system. The complex system under study is the relationship between therapists and their clients. The success of psychotherapy depends on the nature of the relationship between a therapist and a client. We use dynamical systems theory to model the dynamics of the emotional interaction between a therapist and client. We determine how the therapeutic endpoint and the dynamics of getting there depend on the parameters...
Show moreThis is a novel attempt to produce a rigorous mathematical model of a complex system. The complex system under study is the relationship between therapists and their clients. The success of psychotherapy depends on the nature of the relationship between a therapist and a client. We use dynamical systems theory to model the dynamics of the emotional interaction between a therapist and client. We determine how the therapeutic endpoint and the dynamics of getting there depend on the parameters of the model. ... We describe the emotional state of both the therapist and client with coupled, first order, nonlinear ordinary differential equations (ODE's). The rate of change of the emotional state of the therapist and client is proportional to their previous state, their uninfluenced state when alone, and an influence function which depends on the state of the other person. We formulated influence functions based on the research literature on psychotherapy and the therapeutic alliance. We then determined the critical points from the intersection of the nullclines and used a numerical ODE solver (Matlab ODE113) to compute the trajectories from different initial conditions. ... The results validate this prototypical approach to psychotherapy ; we have shown that human interaction (in the context of psychotherapy) can be quantified and modeled using differential equations.
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Date Issued: 2012
PURL: http://purl.flvc.org/FAU/3358758
Subject Headings: Psychotherapist and patient, Mathematical models, Counselor and client, Mathematical models, Therapeutic alliance, Mathematical models, Psychotherapy, Philosophy, Mathematical models, Evidence-based psychotherapy, Transference (Psychology), Countertransference (Psychology)
Format: Document (PDF)

Title: Mathematical modeling of plankton patchiness.
Creator: Ather, Simantha S., Charles E. Schmidt College of Science, Department of Biological Sciences
Abstract/Description: In natural systems, it has been observed that plankton exist in patches rather than in an even distribution across a body of water. However, the mechanisms behind this patchiness are not fully understood. Several previous modeling studies have examined the effects of abiotic and biotic factors on patch structure. Yet these models ignore a key point: zooplankton often undergo diel vertical migration. I have formulated a model that incorporates vertical movement into the Rosezweig-MacArthur (R...
Show moreIn natural systems, it has been observed that plankton exist in patches rather than in an even distribution across a body of water. However, the mechanisms behind this patchiness are not fully understood. Several previous modeling studies have examined the effects of abiotic and biotic factors on patch structure. Yet these models ignore a key point: zooplankton often undergo diel vertical migration. I have formulated a model that incorporates vertical movement into the Rosezweig-MacArthur (R-M) predator-prey model. The R-M model is stable only at a carrying capacity below a critical value. I found that adding vertical movement stabilizes the system even at a high carrying capacity. By analyzing temporal stability and spatial structure, my results show that vertical movement interacts with carrying capacity to determine patch structure.
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Date Issued: 2009
PURL: http://purl.flvc.org/FAU/368615
Subject Headings: Marine plankton, Vertical distribution, Marine ecology, Mathematical models, Macroecology, Mathematical models
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: Reduced representation of neural networks.
Creator: Stefanescu, Roxana A., Charles E. Schmidt College of Science, Department of Physics
Abstract/Description: Experimental and computational investigations addressing how various neural functions are achieved in the brain converged in recent years to a unified idea that the neural activity underlying most of the cognitive functions is distributed over large scale networks comprising various cortical and subcortical areas. Modeling approaches represent these areas and their connections using diverse models of neurocomputational units engaged in graph-like or neural field-like structures. Regardless of...
Show moreExperimental and computational investigations addressing how various neural functions are achieved in the brain converged in recent years to a unified idea that the neural activity underlying most of the cognitive functions is distributed over large scale networks comprising various cortical and subcortical areas. Modeling approaches represent these areas and their connections using diverse models of neurocomputational units engaged in graph-like or neural field-like structures. Regardless of the manner of network implementation, simulations of large scale networks have encountered significant difficulties mainly due to the time delay introduced by the long range connections. To decrease the computational effort, it is common to assume severe approximations to simplify the descriptions of the neural dynamics associated with the system's units. In this dissertation we propose an alternative framework allowing the prevention of such strong assumptions while efficiently representing th e dynamics of a complex neural network. First, we consider the dynamics of small scale networks of globally coupled non-identical excitatory and inhibitory neurons, which could realistically instantiate a neurocomputational unit. We identify the most significant dynamical features the neural population exhibits in different parametric configuration, including multi-cluster dynamics, multi-scale synchronization and oscillator death. Then, using mode decomposition techniques, we construct analytically low dimensional representations of the network dynamics and show that these reduced systems capture the dynamical features of the entire neural population. The cases of linear and synaptic coupling are discussed in detail. In chapter 5, we extend this approach for spatially extended neural networks., We consider the dynamical behavior of a neural field-like network, which incorporates many biologically realistic characteristics such as heterogeneous local and global connectivity as well as dispersion in the neural membrane excitability. We show that in this case as well, we can construct a reduced representation, which may capture well the dynamical features of the full system. The method outlined in this dissertation provides a consistent way to represent complex dynamical features of various neural networks in a computationally efficient manner.
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Date Issued: 2009
PURL: http://purl.flvc.org/FAU/369387
Subject Headings: Molecular neurobiology, Neural networks (Neurobiology), Brain, Mathematical models, Cognitive neuroscience, Recognition (Psychology)
Format: Document (PDF)

Title: Revisiting the methodology and application of Value-at-Risk.
Creator: Chung, Kyong., Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: The main objective of this thesis is to simulate, evaluate and discuss three standard methodologies of calculating Value-at-Risk (VaR) : Historical simulation, the Variance-covariance method and Monte Carlo simulations. Historical simulation is the most common nonparametric method. The Variance-covariance and Monte Carlo simulations are widely used parametric methods. This thesis defines the three aforementioned VaR methodologies, and uses each to calculate 1-day VaR for a hypothetical...
Show moreThe main objective of this thesis is to simulate, evaluate and discuss three standard methodologies of calculating Value-at-Risk (VaR) : Historical simulation, the Variance-covariance method and Monte Carlo simulations. Historical simulation is the most common nonparametric method. The Variance-covariance and Monte Carlo simulations are widely used parametric methods. This thesis defines the three aforementioned VaR methodologies, and uses each to calculate 1-day VaR for a hypothetical portfolio through MATLAB simulations. The evaluation of the results shows that historical simulation yields the most reliable 1-day VaR for the hypothetical portfolio under extreme market conditions. Finally, this paper concludes with a suggestion for further studies : a heavy-tail distribution should be used in order to imporve the accuracy of the results for the two parametric methods used in this study.
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Date Issued: 2012
PURL: http://purl.flvc.org/FAU/3358328
Subject Headings: Valuation, Econometric models, Prices, Econometric models, Financial risk management, Mathematical optimization, Finance, Mathematical models
Format: Document (PDF)

Title: Sparse Modeling Applied to Patient Identification for Safety in Medical Physics Applications.
Creator: Lewkowitz, Stephanie, Kalantzis, Georgios, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Physics
Abstract/Description: Every scheduled treatment at a radiation therapy clinic involves a series of safety protocol to ensure the utmost patient care. Despite safety protocol, on a rare occasion an entirely preventable medical event, an accident, may occur. Delivering a treatment plan to the wrong patient is preventable, yet still is a clinically documented error. This research describes a computational method to identify patients with a novel machine learning technique to combat misadministration.The patient...
Show moreEvery scheduled treatment at a radiation therapy clinic involves a series of safety protocol to ensure the utmost patient care. Despite safety protocol, on a rare occasion an entirely preventable medical event, an accident, may occur. Delivering a treatment plan to the wrong patient is preventable, yet still is a clinically documented error. This research describes a computational method to identify patients with a novel machine learning technique to combat misadministration.The patient identification program stores face and fingerprint data for each patient. New, unlabeled data from those patients are categorized according to the library. The categorization of data by this face-fingerprint detector is accomplished with new machine learning algorithms based on Sparse Modeling that have already begun transforming the foundation of Computer Vision. Previous patient recognition software required special subroutines for faces and di↵erent tailored subroutines for fingerprints. In this research, the same exact model is used for both fingerprints and faces, without any additional subroutines and even without adjusting the two hyperparameters. Sparse modeling is a powerful tool, already shown utility in the areas of super-resolution, denoising, inpainting, demosaicing, and sub-nyquist sampling, i.e. compressed sensing. Sparse Modeling is possible because natural images are inherrently sparse in some bases, due to their inherrant structure. This research chooses datasets of face and fingerprint images to test the patient identification model. The model stores the images of each dataset as a basis (library). One image at a time is removed from the library, and is classified by a sparse code in terms of the remaining library. The Locally Competetive Algorithm, a truly neural inspired Artificial Neural Network, solves the computationally difficult task of finding the sparse code for the test image. The components of the sparse representation vector are summed by `1 pooling, and correct patient identification is consistently achieved 100% over 1000 trials, when either the face data or fingerprint data are implemented as a classification basis. The algorithm gets 100% classification when faces and fingerprints are concatenated into multimodal datasets. This suggests that 100% patient identification will be achievable in the clinal setting.
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Date Issued: 2016
PURL: http://purl.flvc.org/fau/fd/FA00004721, http://purl.flvc.org/fau/fd/FA00004721
Subject Headings: Computer vision in medicine, Diagnostic imaging -- Data processing, Mathematical models, Medical errors -- Prevention, Medical physics, Sampling (Statistics)
Format: Document (PDF)

Title: Stability analysis for nonlinear systems with time-delays.
Creator: Tiwari, Shanaz, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: In this work, we investigate input-to-state stability (ISS) and other related stability properties for control systems with time-delays. To overcome the complexity caused by the presence of the delays, we adopt a Razumikhin approach. The underlying idea of this approach is to treat the delayed variables as system uncertainties. The advantage of this approach is that one works in the more familiar territory of stability analysis for delay-free systems in the context of ISS instead of carrying...
Show moreIn this work, we investigate input-to-state stability (ISS) and other related stability properties for control systems with time-delays. To overcome the complexity caused by the presence of the delays, we adopt a Razumikhin approach. The underlying idea of this approach is to treat the delayed variables as system uncertainties. The advantage of this approach is that one works in the more familiar territory of stability analysis for delay-free systems in the context of ISS instead of carrying out stability analysis on systems of functional differential equations. Our first step is to provide criteria on ISS and input-to-input stability properties based on the Razumikhin approach. We then turn our attention to large-scale interconnected systems. It has been well recognized that the small-gain theory is a powerful tool for stability analysis of interconnected systems. Using the Razumikhin approach, we develop small-gain theorems for interconnected systems consisting of two or more subs ystems with time-delays present either in the interconnection channels or within the subsystems themselves. As an interesting application, we apply our results to an existing model for hematopoesis, a blood cell production process,and improve the previous results derived by linear methods. Another important stability notion in the framework of ISS is the integral ISS (iISS) property. This is a weaker property than ISS, so it supplies to a larger class of systems. As in the case of ISS, we provide Razumikhin criteria on iISS for systems with delays. An example is presented to illustrate that though very useful in practice, the Razumikhin approach only provides sufficient conditions, not equivalent conditions. Finally, we address stability of time-varying systems with delays in the framework of ISS., In particular, we consider Lyapunov-Razumikhin functions whose decay rates are affected by time-varying functions that can be zero or even negative on some sets of non-zero measure. Our motivation is that it is often less demanding to find or construct such a Lyapunov function than one with a uniform decay rate. We also extend our small-gain theorems to the time-varying case by treating the time-varying system as an auxiliary time-invariant system.
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Date Issued: 2012
PURL: http://purl.flvc.org/FAU/3352880
Subject Headings: Nonlinear systems, Simulation methods, Control theory, Stability, Mathematical models, Mathematical optimization
Format: Document (PDF)

Title: Stochastic optimal impulse control of jump diffusions with application to exchange rate.
Creator: Perera, Sandun C., Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: We generalize the theory of stochastic impulse control of jump diffusions introduced by Oksendal and Sulem (2004) with milder assumptions. In particular, we assume that the original process is affected by the interventions. We also generalize the optimal central bank intervention problem including market reaction introduced by Moreno (2007), allowing the exchange rate dynamic to follow a jump diffusion process. We furthermore generalize the approximation theory of stochastic impulse control...
Show moreWe generalize the theory of stochastic impulse control of jump diffusions introduced by Oksendal and Sulem (2004) with milder assumptions. In particular, we assume that the original process is affected by the interventions. We also generalize the optimal central bank intervention problem including market reaction introduced by Moreno (2007), allowing the exchange rate dynamic to follow a jump diffusion process. We furthermore generalize the approximation theory of stochastic impulse control problems by a sequence of iterated optimal stopping problems which is also introduced in Oksendal and Sulem (2004). We develop new results which allow us to reduce a given impulse control problem to a sequence of iterated optimal stopping problems even though the original process is affected by interventions.
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Date Issued: 2009
PURL: http://purl.flvc.org/FAU/3174308
Subject Headings: Management, Mathematical models, Control theory, Stochastic differential equations, Distribution (Probability theory), Optimal stopping (Mathematical statistics), Economics, Mathematical
Format: Document (PDF)

Title: Stochastic processes in the social sciences: markets, prices and wealth distributions.
Creator: Romero, Natalia E., Charles E. Schmidt College of Science, Department of Physics
Abstract/Description: The present work uses statistical mechanics tools to investigate the dynamics of markets, prices, trades and wealth distribution. We studied the evolution of market dynamics in different stages of historical development by analyzing commodity prices from two distinct periods : ancient Babylon, and medieval and early modern England. We find that the first-digit distributrions of both Babylon and England commodity prices follow Benford's Law, indicating that the data represent empirical...
Show moreThe present work uses statistical mechanics tools to investigate the dynamics of markets, prices, trades and wealth distribution. We studied the evolution of market dynamics in different stages of historical development by analyzing commodity prices from two distinct periods : ancient Babylon, and medieval and early modern England. We find that the first-digit distributrions of both Babylon and England commodity prices follow Benford's Law, indicating that the data represent empirical observations typically arising from a free market. Further, we find that the normalized prices of both Babylon and England agricultural commodities are characterized by stretched exponential distributions, and exhibit persistent correlations of a power law type over long periods of up to several centuries, in contrast to contemporary markets. Our findings suggest that similar market interactions may underlie the dynamics of ancient agricultural commodity prices, and that these interactions may remain stable across centuries. To further investigate the dynamics of markets, we present the analogy between transfers of money between individuals and the transfer of energy through particle collisions by means of the kinetic theory of gases. We introduce a theoretical framework of how micro rules of trading lead to the emergence of income and wealth distribution. Particularly, we study the effects of different types of distribution of savings/investments among individuals in a society and different welfare/subsidies redistribution policies. Results show that while considering savings propensities, the models approach empirical distributions of wealth quite well. The effect of redistribution better captures specific features of the distributions which earlier models failed to do. Moreover, the models still preserve the exponential decay observed in empirical income distributions reported by tax data and surveys.
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Date Issued: 2012
PURL: http://purl.flvc.org/FAU/3352825
Subject Headings: Stochastic processes, Mathematical models, Consumption (Economics), Mathematical models, Business cycles, Mathematical models, Statics and dynamics (Social sciences), Mathematical models
Format: Document (PDF)

Title: Synchronization of coupled semiconductor lasers.
Creator: London, Michael S., Charles E. Schmidt College of Science, Department of Physics
Abstract/Description: The synchronization of coupled semiconductor lasers with delay is investigated by numerical simulations of the nonlinear dynamic models complemented by a stability analysis of the linearized system. The equations used in the dissertation are based on the well known "Lang-Kobayashi" model modified to include unidirectional and bidirectional coupling. Stability diagrams are calculated and supplemented by numerically integrated time series. Synchronization is determined and quantified by...
Show moreThe synchronization of coupled semiconductor lasers with delay is investigated by numerical simulations of the nonlinear dynamic models complemented by a stability analysis of the linearized system. The equations used in the dissertation are based on the well known "Lang-Kobayashi" model modified to include unidirectional and bidirectional coupling. Stability diagrams are calculated and supplemented by numerically integrated time series. Synchronization is determined and quantified by computing the cross-correlation function. It is found that synchronized states are achievable for a wide range of coupling constants and delay times. These findings have implications for experiment and technological applications, notably in cryptography.
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Date Issued: 2011
PURL: http://purl.flvc.org/FAU/3318673
Subject Headings: Semiconductor lasers, Optical bistability, Nonlinear theories, Diodes, Semiconductor, Mathematical models
Format: Document (PDF)

Title: Theoretical study of binary alloy thin film growth.
Creator: Bouwens, Mark R., Charles E. Schmidt College of Science, Department of Physics
Abstract/Description: Computer simulations of the growth of binary alloy thin films in two and three dimensions were performed using an extension of the Solid on Solid model. Snapshots for a range of interactions and diffusion rates are presented and critically compared to experiment. A wide variety of distinct phases is identified and their growth conditions analyzed. These findings are summarized in a phase diagram. In addition, a fractal analysis of the domains is performed. It is found that for negative...
Show moreComputer simulations of the growth of binary alloy thin films in two and three dimensions were performed using an extension of the Solid on Solid model. Snapshots for a range of interactions and diffusion rates are presented and critically compared to experiment. A wide variety of distinct phases is identified and their growth conditions analyzed. These findings are summarized in a phase diagram. In addition, a fractal analysis of the domains is performed. It is found that for negative interactions the islands are two-dimensional, while for positive interactions, regardless of diffusion rate, a fractal dimension of 1.78 is obtained.
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Date Issued: 2011
PURL: http://purl.flvc.org/FAU/3174504
Subject Headings: Binary systems (Metallurgy), Mathematical models, Thermal diffusivity, Phase diagrams, Phase transformations (Statistical physics)
Format: Document (PDF)

Mathematical optimization (3)	+ -
Control theory (2)	+ -
Finance (2)	+ -
Stochastic processes (2)	+ -
Binary systems (Metallurgy) (1)	+ -

Biogeochemistry (1)	+ -
Brain (1)	+ -
Business cycles (1)	+ -
Capital asset pricing model (1)	+ -
Capital market (1)	+ -
Cognitive neuroscience (1)	+ -
Combinatorial chemistry (1)	+ -
Combinatorial optimization (1)	+ -
Computer vision in medicine (1)	+ -
Consumption (Economics) (1)	+ -
Continuum mechanics (1)	+ -
Counselor and client (1)	+ -
Countertransference (Psychology) (1)	+ -
Design (1)	+ -
Diagnostic imaging -- Data processing (1)	+ -
Diodes, Semiconductor (1)	+ -
Distribution (Probability theory) (1)	+ -
Drugs (1)	+ -
Dynamics--Mathematical models (1)	+ -
Econometric models (1)	+ -
Economics, Mathematical (1)	+ -
Ecosystem management (1)	+ -
Evidence-based psychotherapy (1)	+ -
Financial risk management (1)	+ -

Florida (2)	+ -
Arthur R. Marshall Loxahatchee National Wildlife Refuge (Fla.) (1)	+ -
Everglades Region (1)	+ -

Department of Mathematical Sciences (6)	+ -
Department of Physics (6)	+ -
Florida Atlantic University (4)	+ -
Department of Biological Sciences (2)	+ -
Ather, Simantha S. (1)	+ -

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