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 Title
 MAC LAYER AND ROUTING PROTOCOLS FOR WIRELESS AD HOC NETWORKS WITH ASYMMETRIC LINKS AND PERFORMANCE EVALUATION STUDIES.
 Creator

Wang, Guoqiang, Marinescu, Dan, University of Central Florida
 Abstract / Description

In a heterogeneous mobile ad hoc network (MANET), assorted devices with different computation and communication capabilities coexist. In this thesis, we consider the case when the nodes of a MANET have various degrees of mobility and range, and the communication links are asymmetric. Many routing protocols for ad hoc networks routinely assume that all communication links are symmetric, if node A can hear node B and node B can also hear node A. Most current MAC layer protocols are unable to...
Show moreIn a heterogeneous mobile ad hoc network (MANET), assorted devices with different computation and communication capabilities coexist. In this thesis, we consider the case when the nodes of a MANET have various degrees of mobility and range, and the communication links are asymmetric. Many routing protocols for ad hoc networks routinely assume that all communication links are symmetric, if node A can hear node B and node B can also hear node A. Most current MAC layer protocols are unable to exploit the asymmetric links present in a network, thus leading to an inefficient overall bandwidth utilization, or, in the worst case, to lack of connectivity. To exploit the asymmetric links, the protocols must deal with the asymmetry of the path from a source node to a destination node which affects either the delivery of the original packets, or the paths taken by acknowledgments, or both. Furthermore, the problem of hidden nodes requires a more careful analysis in the case of asymmetric links. MAC layer and routing protocols for ad hoc networks with asymmetric links require a rigorous performance analysis. Analytical models are usually unable to provide even approximate solutions to questions such as endtoend delay, packet loss ratio, throughput, etc. Traditional simulation techniques for largescale wireless networks require vast amounts of storage and computing cycles rarely available on single computing systems. In our search for an effective solution to study the performance of wireless networks we investigate the timeparallel simulation. Timeparallel simulation has received significant attention in the past. The advantages, as well as, the theoretical and practical limitations of timeparallel simulation have been extensively researched for many applications when the complexity of the models involved severely limits the applicability of analytical studies and is unfeasible with traditional simulation techniques. Our goal is to study the behavior of large systems consisting of possibly thousands of nodes over extended periods of time and obtain results efficiently, and timeparallel simulation enables us to achieve this objective. We conclude that MAC layer and routing protocols capable of using asymmetric links are more complex than traditional ones, but can improve the connectivity, and provide better performance. We are confident that approximate results for various performance metrics of wireless networks obtained using timeparallel simulation are sufficiently accurate and able to provide the necessary insight into the inner workings of the protocols.
Show less  Date Issued
 2007
 Identifier
 CFE0001736, ucf:47302
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0001736
 Title
 STUDIES OF A QUANTUM SCHEDULING ALGORITHM AND ON QUANTUM ERROR CORRECTION.
 Creator

Lu, Feng, Marinescu, Dan, University of Central Florida
 Abstract / Description

Quantum computation has been a rich field of study for decades because it promises possible spectacular advances, some of which may run counter to our classically rooted intuitions. At the same time, quantum computation is still in its infancy in both theoretical and practical areas. Efficient quantum algorithms are very limited in number and scope; no real breakthrough has yet been achieved in physical implementations. Grover's search algorithm can be applied to a wide range of problems;...
Show moreQuantum computation has been a rich field of study for decades because it promises possible spectacular advances, some of which may run counter to our classically rooted intuitions. At the same time, quantum computation is still in its infancy in both theoretical and practical areas. Efficient quantum algorithms are very limited in number and scope; no real breakthrough has yet been achieved in physical implementations. Grover's search algorithm can be applied to a wide range of problems; even problems not generally regarded as searching problems can be reformulated to take advantage of quantum parallelism and entanglement leading to algorithms which show a square root speedup over their classical counterparts. This dissertation discusses a systematic way to formulate such problems and gives as an example a quantum scheduling algorithm for an RC_max problem. This thesis shows that quantum solution to such problems is not only feasible but in some cases advantageous. The complexity of the error correction circuitry forces us to design quantum error correction codes capable of correcting only a single error per error correction cycle. Yet, timecorrelated errors are common for physical implementations of quantum systems; an error corrected during a certain cycle may reoccur in a later cycle due to physical processes specific to each physical implementation of the qubits. This dissertation discusses quantum error correction for a restricted class of timecorrelated errors in a spinboson model. The algorithm proposed allows the correction of two errors per error correction cycle, provided that one of them is timecorrelated. The algorithm can be applied to any stabilizer code, perfect or nonperfect, and simplified the circuit complexity significantly comparing to the classic quantum error correction codes.
Show less  Date Issued
 2007
 Identifier
 CFE0001873, ucf:47391
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0001873
 Title
 PLANNING AND SCHEDULING FOR LARGESCALEDISTRIBUTED SYSTEMS.
 Creator

Yu, Han, Marinescu, Dan, University of Central Florida
 Abstract / Description

Many applications require computing resources well beyond those available on any single system. Simulations of atomic and subatomic systems with application to material science, computations related to study of natural sciences, and computeraided design are examples of applications that can benefit from the resourcerich environment provided by a large collection of autonomous systems interconnected by highspeed networks. To transform such a collection of systems into a user's virtual...
Show moreMany applications require computing resources well beyond those available on any single system. Simulations of atomic and subatomic systems with application to material science, computations related to study of natural sciences, and computeraided design are examples of applications that can benefit from the resourcerich environment provided by a large collection of autonomous systems interconnected by highspeed networks. To transform such a collection of systems into a user's virtual machine, we have to develop new algorithms for coordination, planning, scheduling, resource discovery, and other functions that can be automated. Then we can develop societal services based upon these algorithms, which hide the complexity of the computing system for users. In this dissertation, we address the problem of planning and scheduling for largescale distributed systems. We discuss a model of the system, analyze the need for planning, scheduling, and plan switching to cope with a dynamically changing environment, present algorithms for the three functions, report the simulation results to study the performance of the algorithms, and introduce an architecture for an intelligent largescale distributed system.
Show less  Date Issued
 2005
 Identifier
 CFE0000781, ucf:46595
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0000781
 Title
 CONTRIBUTIONS TO AUTOMATIC PARTICLE IDENTIFICATION IN ELECTRON MICROGRAPHS: ALGORITHMS, IMPLEMENTATION, AND APPLICATIONS.
 Creator

Singh, Vivek, Marinescu, Dan, University of Central Florida
 Abstract / Description

Three dimensional reconstruction of large macromolecules like viruses at resolutions below 8 \AA~  10 \AA~ requires a large set of projection images and the particle identification step becomes a bottleneck. Several automatic and semiautomatic particle detection algorithms have been developed along the years. We present a general technique designed to automatically identify the projection images of particles. The method utilizes Markov random field modelling of the projected images and...
Show moreThree dimensional reconstruction of large macromolecules like viruses at resolutions below 8 \AA~  10 \AA~ requires a large set of projection images and the particle identification step becomes a bottleneck. Several automatic and semiautomatic particle detection algorithms have been developed along the years. We present a general technique designed to automatically identify the projection images of particles. The method utilizes Markov random field modelling of the projected images and involves a preprocessing of electron micrographs followed by image segmentation and post processing for boxing of the particle projections. Due to the typically extensive computational requirements for extracting hundreds of thousands of particle projections, parallel processing becomes essential. We present parallel algorithms and load balancing schemes for our algorithms. The lack of a standard benchmark for relative performance analysis of particle identification algorithms has prompted us to develop a benchmark suite. Further, we present a collection of metrics for the relative performance analysis of particle identification algorithms on the micrograph images in the suite, and discuss the design of the benchmark suite.
Show less  Date Issued
 2005
 Identifier
 CFE0000705, ucf:46610
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0000705
 Title
 COORDINATION, MATCHMAKING, AND RESOURCE ALLOCATION FOR LARGESCALE DISTRIBUTED SYSTEMS.
 Creator

Bai, Xin, Marinescu, Dan, University of Central Florida
 Abstract / Description

While existing grid environments cater to specific needs of a particular user community, we need to go beyond them and consider generalpurpose largescale distributed systems consisting of large collections of heterogeneous computers and communication systems shared by a large user population with very diverse requirements. Coordination, matchmaking, and resource allocation are among the essential functions of largescale distributed systems. Although deterministic approaches for...
Show moreWhile existing grid environments cater to specific needs of a particular user community, we need to go beyond them and consider generalpurpose largescale distributed systems consisting of large collections of heterogeneous computers and communication systems shared by a large user population with very diverse requirements. Coordination, matchmaking, and resource allocation are among the essential functions of largescale distributed systems. Although deterministic approaches for coordination, matchmaking, and resource allocation have been well studied, they are not suitable for largescale distributed systems due to the largescale, the autonomy, and the dynamics of the systems. We have to seek for nondeterministic solutions for largescale distributed systems. In this dissertation we describe our work on a coordination service, a matchmaking service, and a macroeconomic resource allocation model for largescale distributed systems. The coordination service coordinates the execution of complex tasks in a dynamic environment, the matchmaking service supports finding the appropriate resources for users, and the macroeconomic resource allocation model allows a broker to mediate resource providers who want to maximize their revenues and resource consumers who want to get the best resources at the lowest possible price, with some global objectives, e.g., to maximize the resource utilization of the system.
Show less  Date Issued
 2006
 Identifier
 CFE0001172, ucf:46845
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0001172
 Title
 SCHEDULING AND RESOURCE MANAGEMENT FOR COMPLEX SYSTEMS: FROM LARGESCALE DISTRIBUTED SYSTEMS TO VERY LARGE SENSOR NETWORKS.
 Creator

Yu, Chen, Marinescu, Dan, University of Central Florida
 Abstract / Description

In this dissertation, we focus on multiple levels of optimized resource management techniques. We first consider a classic resource management problem, namely the scheduling of dataintensive applications. We define the Divisible Load Scheduling (DLS) problem, outline the system model based on the assumption that data staging and all communication with the sites can be done in parallel, and introduce a set of optimal divisible load scheduling algorithms and the related faulttolerant...
Show moreIn this dissertation, we focus on multiple levels of optimized resource management techniques. We first consider a classic resource management problem, namely the scheduling of dataintensive applications. We define the Divisible Load Scheduling (DLS) problem, outline the system model based on the assumption that data staging and all communication with the sites can be done in parallel, and introduce a set of optimal divisible load scheduling algorithms and the related faulttolerant coordination algorithm. The DLS algorithms introduced in this dissertation exploit parallel communication, consider realistic scenarios regarding the time when heterogeneous computing systems are available, and generate optimal schedules. Performance studies show that these algorithms perform better than divisible load scheduling algorithms based upon sequential communication. We have developed a selforganization model for resource management in distributed systems consisting of a very large number of sites with excess computing capacity. This selforganization model is inspired by biological metaphors and uses the concept of varying energy levels to express activity and goal satisfaction. The model is applied to Pleiades, a serviceoriented architecture based on resource virtualization. The selforganization model for complex computing and communication systems is applied to Very Large Sensor Networks (VLSNs). An algorithm for selforganization of anonymous sensor nodes called SFSN (Scalefree Sensor Networks) and an algorithm utilizing the Smallworlds principle called SWAS (Smallworlds of Anonymous Sensors) are introduced. The SFSN algorithm is designed for VLSNs consisting of a fairly large number of inexpensive sensors with limited resources. An important feature of the algorithm is the ability to interconnect sensors without an identity, or physical address used by traditional communication and coordination protocols. During the selforganization phase, the collisionfree communication channels allowing a sensor to synchronously forward information to the members of its proximity set are established and the communication pattern is followed during the activity phases. Simulation study shows that the SFSN ensures the scalability, limits the amount of communication and the complexity of coordination. The SWAS algorithm is further improved from SFSN by applying the Smallworlds principle. It is unique in its ability to create a sensor network with a topology approximating smallworld networks. Rather than creating shortcuts between pairs of diametrically positioned nodes in a logical ring, we end up with something resembling a doublestranded DNA. By exploiting Smallworlds principle we combine two desirable features of networks, namely high clustering and small path length.
Show less  Date Issued
 2009
 Identifier
 CFE0002907, ucf:48004
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0002907
 Title
 VIRTUALIZATION AND SELFORGANIZATION FOR UTILITY COMPUTING.
 Creator

Saleh, Mehdi, Marinescu, Dan, University of Central Florida
 Abstract / Description

We present an alternative paradigm for utility computing when the delivery of service is subject to binding contracts; the solution we propose is based on resource virtualization and a selfmanagement scheme. A virtual cloud aggregates set virtual machines to work in concert for the tasks specified by the service agreement. A first step for the establishment of a virtual cloud is to create a scalefree overlay network through a biased random walk; scalefree networks enjoy a set of remarkable...
Show moreWe present an alternative paradigm for utility computing when the delivery of service is subject to binding contracts; the solution we propose is based on resource virtualization and a selfmanagement scheme. A virtual cloud aggregates set virtual machines to work in concert for the tasks specified by the service agreement. A first step for the establishment of a virtual cloud is to create a scalefree overlay network through a biased random walk; scalefree networks enjoy a set of remarkable properties such as: robustness against random failures, favorable scaling, and resilience to congestion, small diameter, and average path length. Constrains such as limits on the cost of per unit of service, total cost, or the requirement to use only "green" computing cycles are then considered when a node of this overlay network decides whether to join the virtual cloud or not. A VIRTUAL CLOUD consists of a subset of the nodes assigned to the tasks specified by a Service Level Agreement, SLA, as well as a virtual interconnection network, or overlay network, for the virtual cloud. SLAs could serve as a congestion control mechanism for an organization providing utility computing; this mechanism allows the system to reject new contracts when there is the danger of overloading the system and failing to fulfill existing contractual obligations. The objective of this thesis is to show that biased random walks in power law networks are capable of responding to dynamic changes of the workload in utility computing.
Show less  Date Issued
 2011
 Identifier
 CFE0003725, ucf:48768
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0003725
 Title
 Resource Management in Largescale Systems.
 Creator

Paya, Ashkan, Marinescu, Dan, Wocjan, Pawel, Bassiouni, Mostafa, Mucciolo, Eduardo, University of Central Florida
 Abstract / Description

The focus of this thesis is resource management in largescale systems. Our primary concerns are energy management and practical principles for selforganization and selfmanagement. The main contributions of our work are:1. Models. We proposed several models for different aspects of resource management, e.g., energyaware load balancing and application scaling for the cloud ecosystem, hierarchical architecture model for selforganizing and selfmanageable systems and a new cloud delivery...
Show moreThe focus of this thesis is resource management in largescale systems. Our primary concerns are energy management and practical principles for selforganization and selfmanagement. The main contributions of our work are:1. Models. We proposed several models for different aspects of resource management, e.g., energyaware load balancing and application scaling for the cloud ecosystem, hierarchical architecture model for selforganizing and selfmanageable systems and a new cloud delivery model based on auctiondriven selforganization approach.2. Algorithms. We also proposed several different algorithms for the models described above. Algorithms such as coalition formation, combinatorial auctions and clustering algorithm for scalefree organizations of scalefree networks.3. Evaluation. Eventually we conducted different evaluations for the proposed models and algorithms in order to verify them. All the simulations reported in this thesis had been carried out on different instances and services of Amazon Web Services (AWS).All of these modules will be discussed in detail in the following chapters respectively.
Show less  Date Issued
 2015
 Identifier
 CFE0005862, ucf:50913
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0005862
 Title
 On the security of NoSQL cloud database services.
 Creator

Ahmadian, Mohammad, Marinescu, Dan, Wocjan, Pawel, Heinrich, Mark, Brennan, Joseph, University of Central Florida
 Abstract / Description

Processing a vast volume of data generated by web, mobile and Internetenabled devices, necessitates a scalable and flexible data management system. DatabaseasaService (DBaaS) is a new cloud computing paradigm, promising a costeffective and scalable, fullymanaged database functionality meeting the requirements of online data processing. Although DBaaS offers many benefits it also introduces new threats and vulnerabilities. While many traditional data processing threats remain, DBaaS...
Show moreProcessing a vast volume of data generated by web, mobile and Internetenabled devices, necessitates a scalable and flexible data management system. DatabaseasaService (DBaaS) is a new cloud computing paradigm, promising a costeffective and scalable, fullymanaged database functionality meeting the requirements of online data processing. Although DBaaS offers many benefits it also introduces new threats and vulnerabilities. While many traditional data processing threats remain, DBaaS introduces new challenges such as confidentiality violation and information leakage in the presence of privileged malicious insiders and adds new dimension to the data security. We address the problem of building a secure DBaaS for a public cloud infrastructure where, the Cloud Service Provider (CSP) is not completely trusted by the data owner. We present a high level description of several architectures combining modern cryptographic primitives for achieving this goal. A novel searchable security scheme is proposed to leverage secure query processing in presence of a malicious cloud insider without disclosing sensitive information. A holistic database security scheme comprised of data confidentiality and information leakage prevention is proposed in this dissertation. The main contributions of our work are:(i) A searchable security scheme for nonrelational databases of the cloud DBaaS; (ii) Leakage minimization in the untrusted cloud.The analysis of experiments that employ a set of established cryptographic techniques to protect databases and minimize information leakage, proves that the performance of the proposed solution is bounded by communication cost rather than by the cryptographic computational effort.
Show less  Date Issued
 2017
 Identifier
 CFE0006848, ucf:51777
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0006848
 Title
 Mathematical Foundations of Adaptive Quantum Processing.
 Creator

Bonior, Daniel, Mucciolo, Eduardo, Martin, Keye, Argenti, Luca, Shivamoggi, Bhimsen, Marinescu, Dan, University of Central Florida
 Abstract / Description

Quantum information has the potential to revolutionize the way we store, process, transfer and acquire information [1,14,15,21,37]. In particular, quantum information offers exciting new approaches to secure communication, computation and sensing. However, in order to realize such technologies, we must first understand the effect that environmental noise has on a quantum system. This dissertation builds upon recent studies that have explored the underlying structure of quantum information and...
Show moreQuantum information has the potential to revolutionize the way we store, process, transfer and acquire information [1,14,15,21,37]. In particular, quantum information offers exciting new approaches to secure communication, computation and sensing. However, in order to realize such technologies, we must first understand the effect that environmental noise has on a quantum system. This dissertation builds upon recent studies that have explored the underlying structure of quantum information and the effects of qubit channels in quantum communication protocols.This work is divided into five main chapters, with Chapter 1 being a brief introduction to quantum information. We then begin Chapter 2 by defining the error function for our qubit communication protocols. From there we explore the properties of our error functions and the topological space that they form. In Chapter 3 we consider the newly patented process Adaptive Quantum Information Processing, patent number US9838141 B2; originally outlined by Martin in [23]. We restate the adaptive scheme and exemplify its application through the Prepare and Send Protocol and Quantum Key Distribution. Applying our results from Chapter 2, we obtain an expression for the adaptability of unital channels in these two protocols and classify the channels that admit the most improvement. We dedicate Chapter 4 to the derivation of gravitational noise, and show that in certain circumstances gravity results in a channel that can be maximally improved in Adaptive QKD [3,14,16]. Lastly, we study the set of error functions through the lens of domain theory. Domain theory is a subset of mathematics that was developed in order to rigorously formalize computations. The first four chapters are all consequences of past discoveries in the mathematical structure of quantum channels. In Chapter 5 we characterize the set of error functions through domain theory, extending the mathematical foundations of quantum information. [12,18,20, 22, 23,25].
Show less  Date Issued
 2018
 Identifier
 CFE0007313, ucf:52124
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0007313
 Title
 The Power of Quantum Walk: Insights, Implementation, and Applications.
 Creator

Chiang, ChenFu, Wocjan, Pawel, Marinescu, Dan, Dechev, Damian, Mucciolo, Eduardo, University of Central Florida
 Abstract / Description

In this thesis, I investigate quantum walks in quantum computing from threeaspects: the insights, the implementation, and the applications. Quantum walks are the quantum analogue of classical random walks. For the insights of quantum walks, I list and explain the required components for quantizing a classical random walk into a quantum walk. The components are, for instance, Markov chains, quantum phase estimation, and quantum spectrum theorem. I then demonstrate how the product of two...
Show moreIn this thesis, I investigate quantum walks in quantum computing from threeaspects: the insights, the implementation, and the applications. Quantum walks are the quantum analogue of classical random walks. For the insights of quantum walks, I list and explain the required components for quantizing a classical random walk into a quantum walk. The components are, for instance, Markov chains, quantum phase estimation, and quantum spectrum theorem. I then demonstrate how the product of two reflections in the walk operator provides a quadratic speedup, in comparison to the classical counterpart. For the implementation of quantum walks, I show the construction of an efficient circuit for realizing one single step of the quantum walk operator. Furthermore, I devise a more succinct circuit to approximately implement quantum phase estimation with constant precision controlled phase shift operators. From an implementation perspective, efficient circuits are always desirable because the realization of a phase shift operator with high precision would be a costly task and a critical obstacle. For the applications of quantum walks, I apply the quantum walk technique along with other fundamental quantum techniques, such as phase estimation, to solve the partition function problem. However, there might be some scenario in which the speedup of spectral gap is insignificant. In a situation like that that,I provide an amplitude amplificationbased approach to prepare the thermal Gibbs state. Such an approach is useful when the spectral gap is extremely small. Finally, I further investigate and explore the effect of noise (perturbation)on the performance of quantum walks.
Show less  Date Issued
 2011
 Identifier
 CFE0004094, ucf:49148
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0004094
 Title
 Quantum Algorithms for: Quantum Phase Estimation, Approximation of the Tutte Polynomial and Blackbox Structures.
 Creator

Ahmadi Abhari, Seyed Hamed, Brennan, Joseph, Mucciolo, Eduardo, Li, Xin, Marinescu, Dan, University of Central Florida
 Abstract / Description

In this dissertation, we investigate three different problems in the field of Quantum computation. First, we discuss the quantum complexity of evaluating the Tutte polynomial of a planar graph. Furthermore, we devise a new quantum algorithm for approximating the phase of a unitary matrix. Finally, we provide quantum tools that can be utilized to extract the structure of blackbox modules and algebras. While quantum phase estimation (QPE) is at the core of many quantum algorithms known to date...
Show moreIn this dissertation, we investigate three different problems in the field of Quantum computation. First, we discuss the quantum complexity of evaluating the Tutte polynomial of a planar graph. Furthermore, we devise a new quantum algorithm for approximating the phase of a unitary matrix. Finally, we provide quantum tools that can be utilized to extract the structure of blackbox modules and algebras. While quantum phase estimation (QPE) is at the core of many quantum algorithms known to date, its physical implementation (algorithms based on quantum Fourier transform (QFT)) is highly constrained by the requirement of highprecision controlled phase shift operators, which remain difficult to realize. In the second part of this dissertation, we introduce an alternative approach to approximately implement QPE with arbitrary constantprecision controlled phase shift operators.The new quantum algorithm bridges the gap between QPE algorithms based on QFT and Kitaev's original approach. For approximating the eigenphase precise to the nth bit, Kitaev's original approach does not require any controlled phase shift operator. In contrast, QPE algorithms based on QFT or approximate QFT require controlled phase shift operators with precision of at least Pi/2n. The new approach fills the gap and requires only arbitrary constantprecision controlled phase shift operators. From a physical implementation viewpoint, the new algorithm outperforms Kitaev's approach.The other problem we investigate relates to approximating the Tutte polynomial. We show that the problem of approximately evaluating the Tutte polynomial of triangular graphs at the points (q,1/q) of the Tutte plane is BQPcomplete for (most) roots of unity q. We also consider circular graphs and show that the problem of approximately evaluating the Tutte polynomial of these graphs at a point is DQC1complete and at some points is in BQP.To show that these problems can be solved by a quantum computer, we rely on the relation of the Tutte polynomial of a planar G graph with the Jones and HOMFLY polynomial of the alternating link D(G) given by the medial graph of G. In the case of our graphs the corresponding links are equal to the plat and trace closures of braids. It is known how to evaluate the Jones and HOMFLY polynomial for closures of braids.To establish the hardness results, we use the property that the images of the generators of the braid group under the irreducible JonesWenzl representations of the Hecke algebra have finite order. We show that for each braid we can efficiently construct a braid such that the evaluation of the Jones and HOMFLY polynomials of their closures at a fixed root of unity leads to the same value and that the closures of the resulting braid are alternating links.The final part of the dissertation focuses on finding the structure of a blackbox module or algebra. Suppose we are given blackbox access to a finite module M or algebra over a finite ring R and a list of generators for M and R. We show how to find a linear basis and structure constants for M in quantum poly (logM) time. This generalizes a recent quantum algorithm of Arvind et al. which finds a basis representation for rings. We then show that our algorithm is a useful primitive allowing quantum computer to determine the structure of a finite associative algebra as a direct sum of simple algebras. Moreover, it solves a wide variety of problems regarding finite modules and rings. Although our quantum algorithm is based on Abelian Fourier transforms, it solves problems regarding the multiplicative structure of modules and algebras, which need not be commutative. Examples include finding the intersection and quotient of two modules, finding the additive and multiplicative identities in a module, computing the order of an module, solving linear equations over modules, deciding whether an ideal is maximal, finding annihilators, and testing the injectivity and surjectivity of ring homomorphisms. These problems appear to be exponentially hard classically.
Show less  Date Issued
 2012
 Identifier
 CFE0004239, ucf:49526
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0004239
 Title
 Variance in FadeTime of a GammaGamma Distributed Irradiance Signal.
 Creator

Leclerc, Troy, Phillips, Ronald, Weeks, Arthur, Richardson, Martin, Marinescu, Dan, Andrews, Larry, University of Central Florida
 Abstract / Description

Freespace optical communications are predominantly hindered by optical turbulence, an effect caused by temperature and pressure variations within the atmosphere. The result is an optical wave interfering with itself due to multipath propagation via tiny refractiveindex fluctuations across the wavefront. Optical communication systems are affected when the channel conditions induce fading in the irradiance signal that is received at the detector. The nature of optical interference imparted...
Show moreFreespace optical communications are predominantly hindered by optical turbulence, an effect caused by temperature and pressure variations within the atmosphere. The result is an optical wave interfering with itself due to multipath propagation via tiny refractiveindex fluctuations across the wavefront. Optical communication systems are affected when the channel conditions induce fading in the irradiance signal that is received at the detector. The nature of optical interference imparted by the atmosphere is a random process and therefore the received irradiance signal is often characterized by an appropriate probability density function (PDF). Data collected during past freespace optical experiments in the atmosphere support the gammagamma distribution as a practical PDF model for received irradiance fluctuations, although the irradiance fluctuations do occasionally tend towards a lognormal distribution.Utilization of the gammagamma irradiance PDF allows for calculation of statistical moments of the irradiance threshold levelcrossing distribution. Presented analysis focuses on the results of the gammagamma irradiance PDF. Previously, expressions were developed for the expected number of gammagamma distributed irradiance threshold levelcrossings. Expressions for the mean square number of gammagamma distributed irradiance threshold levelcrossings are derived and presented. The derived expressions lead to the mean and variance of signal fade time. Outcomes of the derived expressions are presented in relation to freespace optical communication system performance.Comparisons are made between the theoretical analysis and experimental data taken at the Innovative Science and Technology Facility (ISTEF) located at the Kennedy Space Center in Cape Canaveral, Florida. The strength of the atmospheric turbulence is often characterized by three measurable parameters: the refractive index structure constant Cn2, the inner scale l0, and the outer scale L0. The optical path (L~1km) was instrumented such that direct comparisons could be drawn between the measured atmospheric turbulence parameters and the parameters of the gammagamma irradiance model. Variance of fade time data were found to agree well for smaller apertures where effects of aperture averaging are not present and in cases where scintillation is weak to moderate. It is suggested that a more appropriate PDF, with a heavier focus on aperture averaging, may be applied in future studies of these fade statistics.
Show less  Date Issued
 2012
 Identifier
 CFE0004397, ucf:53153
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0004397
 Title
 Extensions of Sspaces.
 Creator

Losert, Bernd, Richardson, Gary, Mikusinski, Piotr, Dutkay, Dorin, Brennan, Joseph, Marinescu, Dan, University of Central Florida
 Abstract / Description

Given a convergence space X, a continuous action of a convergence semigroup S on X and a compactification Y of X, under what conditions on X and the action on X is it possible to extend the action to a continuous action on Y. Similarly, given a Cauchy space X, a Cauchy continuous action of a Cauchy semigroup S on X and a completion Y of X, under what conditions on X and the action on X is it possible to extend the action to a Cauchy continuous action on Y. We answer the first question for...
Show moreGiven a convergence space X, a continuous action of a convergence semigroup S on X and a compactification Y of X, under what conditions on X and the action on X is it possible to extend the action to a continuous action on Y. Similarly, given a Cauchy space X, a Cauchy continuous action of a Cauchy semigroup S on X and a completion Y of X, under what conditions on X and the action on X is it possible to extend the action to a Cauchy continuous action on Y. We answer the first question for some particular compactifications like the onepoint compactification and the star compactification as well as for the class of regular compactifications. We answer the second question for the class of regular strict completions. Using these results, we give sufficient conditions under which the pseudoquotient of a compactification/completion of a space is the compactification/completion of the pseudoquotient of the given space.
Show less  Date Issued
 2013
 Identifier
 CFE0004881, ucf:49661
 Format
 Document (PDF)
 PURL
 http://purl.flvc.org/ucf/fd/CFE0004881