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 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 mixturebased 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 indepth analysis of some statistical and mathematical techniques in combinatorial chemistry, including a novel probabilistic approach to using structural similarity to predict the activity landscape.
Show less  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
 Computing Global Decompositions of Dynamical Systems.
 Creator
 Ban, Hyunju, Kalies, William D., Florida Atlantic University
 Abstract/Description

In this dissertation we present a computational approach to Conley's Decomposition Theorem, which gives a global decomposition of dynamical systems, and introduce an explicit numerical algorithm with computational complexity bounds for computing global dynamical structures of a continous map including attractorrepeller pairs and Conley's Lyapunov function. The approach is based on finite spatial discretizations and combinatorial multivalued maps. The method is successful in exhibiting...
Show moreIn this dissertation we present a computational approach to Conley's Decomposition Theorem, which gives a global decomposition of dynamical systems, and introduce an explicit numerical algorithm with computational complexity bounds for computing global dynamical structures of a continous map including attractorrepeller pairs and Conley's Lyapunov function. The approach is based on finite spatial discretizations and combinatorial multivalued maps. The method is successful in exhibiting approximations of attractorrepeller pairs, invariant sets, and Conley's Lyapunov function. We used the C++ language to code the algorithm.
Show less  Date Issued
 2006
 PURL
 http://purl.flvc.org/fau/fd/FA00000848
 Subject Headings
 Lyapunov functions, Control theory, Mathematical optimization, Differentiable dynamical systems
 Format
 Document (PDF)
 Title
 General monotonicity, interpolation of operators, and applications.
 Creator
 Grigoriev, Stepan M., Sagher, Yoram, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

Assume that {φn} is an orthonormal uniformly bounded (ONB) sequence of complexvalued functions de ned on a measure space (Ω,Σ,µ), and f ∈ L1(Ω,Σ,µ). Let be the Fourier coefficients of f with respect to {φn} . R.E.A.C. Paley proved a theorem connecting the Lpnorm of f with a related norm of the sequence {cn}. Hardy and Littlewood subsequently proved that Paley’s result is best possible within its context. Their results were generalized by Dikarev, Macaev, Askey, Wainger, Sagher, and later by...
Show moreAssume that {φn} is an orthonormal uniformly bounded (ONB) sequence of complexvalued functions de ned on a measure space (Ω,Σ,µ), and f ∈ L1(Ω,Σ,µ). Let be the Fourier coefficients of f with respect to {φn} . R.E.A.C. Paley proved a theorem connecting the Lpnorm of f with a related norm of the sequence {cn}. Hardy and Littlewood subsequently proved that Paley’s result is best possible within its context. Their results were generalized by Dikarev, Macaev, Askey, Wainger, Sagher, and later by Tikhonov, Li yand, Booton and others.The present work continues the generalization of these results.
Show less  Date Issued
 2014
 PURL
 http://purl.flvc.org/fau/fd/FA00004290, http://purl.flvc.org/fau/fd/FA00004290
 Subject Headings
 Combinatorial optimization, Differential dynamical systems, Functions of complex variables, Inequalities (Mathematics), Nonsmooth optimization
 Format
 Document (PDF)
 Title
 Stability analysis for nonlinear systems with timedelays.
 Creator
 Tiwari, Shanaz, Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

In this work, we investigate inputtostate stability (ISS) and other related stability properties for control systems with timedelays. 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 delayfree systems in the context of ISS instead of carrying...
Show moreIn this work, we investigate inputtostate stability (ISS) and other related stability properties for control systems with timedelays. 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 delayfree 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 inputtoinput stability properties based on the Razumikhin approach. We then turn our attention to largescale interconnected systems. It has been well recognized that the smallgain theory is a powerful tool for stability analysis of interconnected systems. Using the Razumikhin approach, we develop smallgain theorems for interconnected systems consisting of two or more subs ystems with timedelays 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 timevarying systems with delays in the framework of ISS., In particular, we consider LyapunovRazumikhin functions whose decay rates are affected by timevarying functions that can be zero or even negative on some sets of nonzero 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 smallgain theorems to the timevarying case by treating the timevarying system as an auxiliary timeinvariant system.
Show less  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
 Revisiting the methodology and application of ValueatRisk.
 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 ValueatRisk (VaR) : Historical simulation, the Variancecovariance method and Monte Carlo simulations. Historical simulation is the most common nonparametric method. The Variancecovariance and Monte Carlo simulations are widely used parametric methods. This thesis defines the three aforementioned VaR methodologies, and uses each to calculate 1day VaR for a hypothetical...
Show moreThe main objective of this thesis is to simulate, evaluate and discuss three standard methodologies of calculating ValueatRisk (VaR) : Historical simulation, the Variancecovariance method and Monte Carlo simulations. Historical simulation is the most common nonparametric method. The Variancecovariance and Monte Carlo simulations are widely used parametric methods. This thesis defines the three aforementioned VaR methodologies, and uses each to calculate 1day VaR for a hypothetical portfolio through MATLAB simulations. The evaluation of the results shows that historical simulation yields the most reliable 1day VaR for the hypothetical portfolio under extreme market conditions. Finally, this paper concludes with a suggestion for further studies : a heavytail distribution should be used in order to imporve the accuracy of the results for the two parametric methods used in this study.
Show less  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
 Model reduction of largescale systems using perturbed frequencydomain balanced structure.
 Creator
 Zadegan, Abbas Hassan., Florida Atlantic University, Zilouchian, Ali, College of Engineering and Computer Science, Department of Computer and Electrical Engineering and Computer Science
 Abstract/Description

Model reduction of largescale systems over a specified frequency range of operation is studied in this research and reported in this dissertation. Frequencydomain balanced structures with integration of singular perturbation are proposed for model reduction of largescale continuoustime as well as discretetime systems. This method is applied to both openloop as well as closedloop systems. It is shown that the response of reduced systems closely resemble that of full order systems within...
Show moreModel reduction of largescale systems over a specified frequency range of operation is studied in this research and reported in this dissertation. Frequencydomain balanced structures with integration of singular perturbation are proposed for model reduction of largescale continuoustime as well as discretetime systems. This method is applied to both openloop as well as closedloop systems. It is shown that the response of reduced systems closely resemble that of full order systems within a specified frequency range of operation. Simulation experiments for the model reduction of several largescale, continuous and discretetime systems demonstrate the superiority of the proposed technique over the previously available methods.
Show less  Date Issued
 2004
 PURL
 http://purl.flvc.org/fcla/dt/12114
 Subject Headings
 System analysis, Large scale systemsMathematical models, System design, Control theory, 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.
Show less  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
 Efficient implementation of zeroknowledge based identification protocols.
 Creator
 Barella, Michelle Elizabeth., Florida Atlantic University, Mullin, Ronald C.
 Abstract/Description

A zero knowledge identification protocol is an interactive proof system that allows a person to prove that he knows a secret key associated with his identity without revealing the secret key. This type of protocol is the topic of a fairy tale, by Gustavus Simmons called the King's Dilemma, about a king and the problem he has with thieves impersonating his tax collectors. It describes a zeroknowledge identification protocol that will rid the king of his problem. I present this system, the...
Show moreA zero knowledge identification protocol is an interactive proof system that allows a person to prove that he knows a secret key associated with his identity without revealing the secret key. This type of protocol is the topic of a fairy tale, by Gustavus Simmons called the King's Dilemma, about a king and the problem he has with thieves impersonating his tax collectors. It describes a zeroknowledge identification protocol that will rid the king of his problem. I present this system, the motivation for this thesis, and the transformations from this protocol, that uses lead weights and containers, to protocols that use mathematical elements. The security of these protocols is determined by the complexity of the underlying mathematical problem, such as the knapsack and discrete logarithm problem, and three properties: completeness, soundness, and zero knowledge.
Show less  Date Issued
 2004
 PURL
 http://purl.flvc.org/fcla/dt/13181
 Subject Headings
 Cryptography, Telecommunication systemsSecurity measures, Knapsack problem (Mathematics), Mathematical optimization, Finite fields (Algebra), Data encryption (Computer science)
 Format
 Document (PDF)
 Title
 Construction of combinatorial designs with prescribed automorphism groups.
 Creator
 Kolotoglu, Emre., Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

In this dissertation, we study some open problems concerning the existence or nonexistence of some combinatorial designs. We give the construction or proof of nonexistence of some Steiner systems, large sets of designs, and graph designs, with prescribed automorphism groups.
 Date Issued
 2013
 PURL
 http://purl.flvc.org/fcla/dt/3360795
 Subject Headings
 Combinatorial designs and configurations, Finite geometries, Curves, Algebraic, Automorphisms, Mathematical optimization, Steiner systems
 Format
 Document (PDF)
 Title
 Graph labeling and nonseparating trees.
 Creator
 Gottipati, Chenchu B., Locke, Stephen C., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

This dissertation studies two independent problems, one is about graph labeling and the other problem is related to connectivity condition in a simple graph. Graph labeling is a rapidly developing area of research in graph theory, having connections with a variety of applicationoriented areas such as VLSI optimization, data structures and data representation. Furthermore, the connectivity conditions in a simple graphs may help us to study the new aspects of ad hoc networks, social networks...
Show moreThis dissertation studies two independent problems, one is about graph labeling and the other problem is related to connectivity condition in a simple graph. Graph labeling is a rapidly developing area of research in graph theory, having connections with a variety of applicationoriented areas such as VLSI optimization, data structures and data representation. Furthermore, the connectivity conditions in a simple graphs may help us to study the new aspects of ad hoc networks, social networks and web graphs. In chapter 2, we study path systems, reduced path systems and how to construct a super edgegraceful tree with any number of edges using path systems. First, we give an algorithm to reduce a labeled path system to a smaller labeled path system of a different type. First, we investigate the cases (m, k) = (3; 5) and (m, k) = (4; 7), where m is the number of paths and 2k is the length of each path, and then we give a generalization for any k, m = 3 and m = 4. We also describe a procedure to construct a superedgegraceful tree with any number of edges.
Show less  Date Issued
 2014
 PURL
 http://purl.flvc.org/fau/fd/FA00004289, http://purl.flvc.org/fau/fd/FA00004289
 Subject Headings
 Computational complexity, Computer graphics, Graph theory, Integrated circuits  Very large scale integration, Mathematical optimization
 Format
 Document (PDF)
 Title
 Permutationbased data compression.
 Creator
 Mihnea, Amalya, Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

The use of permutations in data compression is an aspect that is worthy of further exploration. The work that has been done in video compression based on permutations was primarily oriented towards lossless algorithms. The study of previous algorithms has led to a new algorithm that could be either lossless or lossy, for which the amount of compression and the quality of the output can be controlled. The lossless version of our algorithm performs close to lossy versions of H.264 and it...
Show moreThe use of permutations in data compression is an aspect that is worthy of further exploration. The work that has been done in video compression based on permutations was primarily oriented towards lossless algorithms. The study of previous algorithms has led to a new algorithm that could be either lossless or lossy, for which the amount of compression and the quality of the output can be controlled. The lossless version of our algorithm performs close to lossy versions of H.264 and it improves on them for the majority of the videos that we analyzed. Our algorithm could be used in situations where there is a need for lossless compression and the video sequences are part of a single scene, e.g., medical videos, where loss of information could be risky or expensive. Some results on permutations, which may be of independent interest, arose in developing this algorithm. We report on these as well.
Show less  Date Issued
 2011
 PURL
 http://purl.flvc.org/FAU/3333054
 Subject Headings
 Data compression (Telecommunication), Combinatorics, Network architecture and design, Computer network architectures, Mathematical optimization
 Format
 Document (PDF)
 Title
 Optimal chunkbased resource allocation for OFDMA systems with multiple BER requirements.
 Creator
 He, Tianzhou, Wang, Xin, Florida Atlantic University, College of Engineering and Computer Science, Department of Computer and Electrical Engineering and Computer Science
 Abstract/Description

In wireless orthogonal frequency division multipleaccess (OFDMA) standards, subcarriers are grouped into chunks and a chunk of subcarriers is made as the minimum allocation unit for subcarrier allocation. We investigate the chunkbased resource allocation for OFDMA downlink, where data streams contain packets with diverse biterrorrate (BER) requirements. Supposing that adaptive transmissions are based on a number of discrete modulation and coding modes, we derive the optimal resource...
Show moreIn wireless orthogonal frequency division multipleaccess (OFDMA) standards, subcarriers are grouped into chunks and a chunk of subcarriers is made as the minimum allocation unit for subcarrier allocation. We investigate the chunkbased resource allocation for OFDMA downlink, where data streams contain packets with diverse biterrorrate (BER) requirements. Supposing that adaptive transmissions are based on a number of discrete modulation and coding modes, we derive the optimal resource allocation scheme that maximizes the weighted sum of average user rates under the multiple BER and total power constraints. With proper formulation, the relevant optimization problem is cast as an integer linear program (ILP). We can rigorously prove that the zero duality gap holds for the formulated ILP and its dual problem. Furthermore, it is shown that the optimal strategy for this problem can be obtained through Lagrange dualbased gradient iterations with fast convergence and low computational complexity per iteration. Relying on the stochastic optimization tools, we further develop a novel online algorithm capable of dynamically learning the underlying channel distribution and asymptotically approaching the optimal strategy without knowledge of intended wireless channels a priori. In addition, we extend the proposed approach to maximizing the afair utility functions of average user rates, and show that such a utility maximization can nicely balance the tradeoff between the total throughput and fairness among users.
Show less  Date Issued
 2014
 PURL
 http://purl.flvc.org/fau/fd/FA00004291, http://purl.flvc.org/fau/fd/FA00004291
 Subject Headings
 Adaptive signal processing, Mathematical optimization, Orthogonal frequency division multiplexing, Wireless communication systems
 Format
 Document (PDF)
 Title
 CrossLayer Network Design using Controllers.
 Creator
 Slavik, Michael J., Mahgoub, Imad, Florida Atlantic University, College of Engineering and Computer Science, Department of Computer and Electrical Engineering and Computer Science
 Abstract/Description

A crosslayer design architecture featuring a new network stack component called a controller is presented. The controller takes system status information from the protocol components and uses it to tune the behavior of the network stack to a given performance objective. A controller design strategy using a machine learning algorithm and a simulator is proposed, implemented, and tested. Results show the architecture and design strategy are capable of producing a network stack that outperforms...
Show moreA crosslayer design architecture featuring a new network stack component called a controller is presented. The controller takes system status information from the protocol components and uses it to tune the behavior of the network stack to a given performance objective. A controller design strategy using a machine learning algorithm and a simulator is proposed, implemented, and tested. Results show the architecture and design strategy are capable of producing a network stack that outperforms the existing protocol stack for arbitrary performance objectives. The techniques presented give network designers the flexibility to easily tune the performance of their networks to suit their application. This cognitive networking architecture has great potential for high performance in future wireless networks.
Show less  Date Issued
 2007
 PURL
 http://purl.flvc.org/fau/fd/FA00012555
 Subject Headings
 Computer architecture, Wireless communication systemsDesign and construction, Evolutionary programming (Computer science), Mathematical optimization
 Format
 Document (PDF)
 Title
 Curve shortening in secondorder lagrangian.
 Creator
 Adams, Ronald Edward, Kalies, William D., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
 Abstract/Description

A secondorder Lagrangian system is a generalization of a classical mechanical system for which the Lagrangian action depends on the second derivative of the state variable. Recent work has shown that the dynamics of such systems c:an be substantially richer than for classical Lagrangian systems. In particular, topological properties of the planar curves obtained by projection onto the lowerorder derivatives play a key role in forcing certain types of dynamics. However, the application of...
Show moreA secondorder Lagrangian system is a generalization of a classical mechanical system for which the Lagrangian action depends on the second derivative of the state variable. Recent work has shown that the dynamics of such systems c:an be substantially richer than for classical Lagrangian systems. In particular, topological properties of the planar curves obtained by projection onto the lowerorder derivatives play a key role in forcing certain types of dynamics. However, the application of these techniques requires an analytic restriction on the Lagrangian that it satisfy a twist property. In this dissertation we approach this problem from the point of view of curve shortening in an effort to remove the twist condition. In classical curve shortening a family of curves evolves with a velocity which is normal to the curve and proportional to its curvature. The evolution of curves with decreasing action is more general, and in the first part of this dissertation we develop some results for curve shortening flows which shorten lengths with respect to a Finsler metric rather than a Riemannian metric. The second part of this dissertation focuses on analytic methods to accommodate the fact that the Finsler metric for secondorder Lagrangian system has singularities. We prove the existence of simple periodic solutions for a general class of systems without requiring the twist condition. Further; our results provide a frame work in which to try to further extend the topological forcing theorems to systems without the twist condition.
Show less  Date Issued
 2014
 PURL
 http://purl.flvc.org/fau/fd/FA00004175, http://purl.flvc.org/fau/fd/FA00004175
 Subject Headings
 Critical point theory (Mathematical analysis), Differentiable dynamical systems, Geometry,Differential, Lagrange equations, Lagrangian functions, Mathematical optimization, Surfaces of constant curvature
 Format
 Document (PDF)
 Title
 A Computational Study on Different Penalty Approaches for Constrained Optimization in Radiation Therapy Treatment Planning with a Simulated Annealing Algorithm.
 Creator
 Mohammadi Khoroushadi, Mohammad Sadegh, Kalantzis, Georgios, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Physics
 Abstract/Description

Intensity modulated radiation therapy (IMRT) is a cancer treatment method in which the intensities of the radiation beams are modulated; therefore these beams have nonuniform radiation intensities. The overall result is the delivery of the prescribed dose in the target volume. The dose distribution is conformal to the shape of the target and minimizes the dose to the nearby critical organs. An inverse planning algorithm is used to obtain those nonuniform beam intensities. In inverse...
Show moreIntensity modulated radiation therapy (IMRT) is a cancer treatment method in which the intensities of the radiation beams are modulated; therefore these beams have nonuniform radiation intensities. The overall result is the delivery of the prescribed dose in the target volume. The dose distribution is conformal to the shape of the target and minimizes the dose to the nearby critical organs. An inverse planning algorithm is used to obtain those nonuniform beam intensities. In inverse treatment planning, the treatment plan is achieved by using an optimization process. The optimized plan results to a highquality dose distribution in the planning target volume (PTV), which receives the prescribed dose while the dose that is received by the organs at risk (OARs) is reduced. Accordingly, an objective function has to be defined for the PTV, while some constraints have to be considered to handle the dose limitations for the OARs.
Show less  Date Issued
 2016
 PURL
 http://purl.flvc.org/fau/fd/FA00004765
 Subject Headings
 Imageguided radiation therapy., RadiationDosage., Mathematical optimization., Evolutionary programming (Computer science), Medical physics., Medical radiologyData processing.
 Format
 Document (PDF)