Current Search: Mathematical optimization (x)
View All Items
- 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.
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 attractor-repeller 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 complex-valued 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 Lp-norm 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 complex-valued 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 Lp-norm 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 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.
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 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.
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 large-scale systems using perturbed frequency-domain 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 large-scale systems over a specified frequency range of operation is studied in this research and reported in this dissertation. Frequency-domain balanced structures with integration of singular perturbation are proposed for model reduction of large-scale continuous-time as well as discrete-time systems. This method is applied to both open-loop as well as closed-loop systems. It is shown that the response of reduced systems closely resemble that of full order systems within...
Show moreModel reduction of large-scale systems over a specified frequency range of operation is studied in this research and reported in this dissertation. Frequency-domain balanced structures with integration of singular perturbation are proposed for model reduction of large-scale continuous-time as well as discrete-time systems. This method is applied to both open-loop as well as closed-loop 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 large-scale, continuous and discrete-time 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 systems--Mathematical 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 zero-knowledge 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 zero-knowledge 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 zero-knowledge 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 systems--Security 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 non-existence of some combinatorial designs. We give the construction or proof of non-existence 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 non-separating 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 application-oriented 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 application-oriented 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 edge-graceful 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 super-edge-graceful 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
- Permutation-based 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 chunk-based 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 multiple-access (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 chunk-based resource allocation for OFDMA downlink, where data streams contain packets with diverse bit-errorrate (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 multiple-access (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 chunk-based resource allocation for OFDMA downlink, where data streams contain packets with diverse bit-errorrate (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 dual-based gradient iterations with fast convergence and low computational complexity per iteration. Relying on the stochastic optimization tools, we further develop a novel on-line 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 a-fair utility functions of average user rates, and show that such a utility maximization can nicely balance the trade-off 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
- Cross-Layer 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 cross-layer 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 cross-layer 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 systems--Design and construction, Evolutionary programming (Computer science), Mathematical optimization
- Format
- Document (PDF)
- Title
- Curve shortening in second-order lagrangian.
- Creator
- Adams, Ronald Edward, Kalies, William D., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
-
A second-order 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 lower-order derivatives play a key role in forcing certain types of dynamics. However, the application of...
Show moreA second-order 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 lower-order 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 second-order 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 non-uniform 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 non-uniform 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 non-uniform 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 non-uniform beam intensities. In inverse treatment planning, the treatment plan is achieved by using an optimization process. The optimized plan results to a high-quality 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
- Image-guided radiation therapy., Radiation--Dosage., Mathematical optimization., Evolutionary programming (Computer science), Medical physics., Medical radiology--Data processing.
- Format
- Document (PDF)