Matching Items (35)

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Relativistic quantum tunneling of a Dirac fermion in nonhyperbolic chaotic systems

Description

Nonhyperbolicity, as characterized by the coexistence of Kolmogorov-Arnold-Moser (KAM) tori and chaos in the phase space, is generic in classical Hamiltonian systems. An open but fundamental question in physics concerns

Nonhyperbolicity, as characterized by the coexistence of Kolmogorov-Arnold-Moser (KAM) tori and chaos in the phase space, is generic in classical Hamiltonian systems. An open but fundamental question in physics concerns the relativistic quantum manifestations of nonhyperbolic dynamics. We choose the mushroom billiard that has been mathematically proven to be nonhyperbolic, and study the resonant tunneling dynamics of a massless Dirac fermion. We find that the tunneling rate as a function of the energy exhibits a striking "clustering" phenomenon, where the majority of the values of the rate concentrate on a narrow region, as a result of the chaos component in the classical phase space. Relatively few values of the tunneling rate, however, spread outside the clustering region due to the integrable component. Resonant tunneling of electrons in nonhyperbolic chaotic graphene systems exhibits a similar behavior. To understand these numerical results, we develop a theoretical framework by combining analytic solutions of the Dirac equation in certain integrable domains and physical intuitions gained from current understanding of the quantum manifestations of chaos. In particular, we employ a theoretical formalism based on the concept of self-energies to calculate the tunneling rate and analytically solve the Dirac equation in one dimension as well as in two dimensions for a circular-ring-type of tunneling systems exhibiting integrable dynamics in the classical limit. Because relatively few and distinct classical periodic orbits are present in the integrable component, the corresponding relativistic quantum states can have drastically different behaviors, leading to a wide spread in the values of the tunneling rate in the energy-rate plane. In contrast, the chaotic component has embedded within itself an infinite number of unstable periodic orbits, which provide far more quantum states for tunneling. Due to the nature of chaos, these states are characteristically similar, leading to clustering of the values of the tunneling rate in a narrow band. The appealing characteristic of our work is a demonstration and physical understanding of the "mixed" role played by chaos and regular dynamics in shaping relativistic quantum tunneling dynamics.

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  • 2013-09-18

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Quantum chaotic tunneling in graphene systems with electron-electron interactions

Description

An outstanding and fundamental problem in contemporary physics is to include and probe the many-body effect in the study of relativistic quantum manifestations of classical chaos. We address this problem

An outstanding and fundamental problem in contemporary physics is to include and probe the many-body effect in the study of relativistic quantum manifestations of classical chaos. We address this problem using graphene systems described by the Hubbard Hamiltonian in the setting of resonant tunneling. Such a system consists of two symmetric potential wells separated by a potential barrier, and the geometric shape of the whole domain can be chosen to generate integrable or chaotic dynamics in the classical limit. Employing a standard mean-field approach to calculating a large number of eigenenergies and eigenstates, we uncover a class of localized states with near-zero tunneling in the integrable systems. These states are not the edge states typically seen in graphene systems, and as such they are the consequence of many-body interactions. The physical origin of the non-edge-state type of localized states can be understood by the one-dimensional relativistic quantum tunneling dynamics through the solutions of the Dirac equation with appropriate boundary conditions. We demonstrate that, when the geometry of the system is modified to one with chaos, the localized states are effectively removed, implying that in realistic situations where many-body interactions are present, classical chaos is capable of facilitating greatly quantum tunneling. This result, besides its fundamental importance, can be useful for the development of nanoscale devices such as graphene-based resonant-tunneling diodes.

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  • 2014-12-16

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Fundamental limits in data privacy: from privacy measures to economic foundations

Description

Data privacy is emerging as one of the most serious concerns of big data analytics, particularly with the growing use of personal data and the ever-improving capability of data analysis.

Data privacy is emerging as one of the most serious concerns of big data analytics, particularly with the growing use of personal data and the ever-improving capability of data analysis. This dissertation first investigates the relation between different privacy notions, and then puts the main focus on developing economic foundations for a market model of trading private data.

The first part characterizes differential privacy, identifiability and mutual-information privacy by their privacy--distortion functions, which is the optimal achievable privacy level as a function of the maximum allowable distortion. The results show that these notions are fundamentally related and exhibit certain consistency: (1) The gap between the privacy--distortion functions of identifiability and differential privacy is upper bounded by a constant determined by the prior. (2) Identifiability and mutual-information privacy share the same optimal mechanism. (3) The mutual-information optimal mechanism satisfies differential privacy with a level at most a constant away from the optimal level.

The second part studies a market model of trading private data, where a data collector purchases private data from strategic data subjects (individuals) through an incentive mechanism. The value of epsilon units of privacy is measured by the minimum payment such that an individual's equilibrium strategy is to report data in an epsilon-differentially private manner. For the setting with binary private data that represents individuals' knowledge about a common underlying state, asymptotically tight lower and upper bounds on the value of privacy are established as the number of individuals becomes large, and the payment--accuracy tradeoff for learning the state is obtained. The lower bound assures the impossibility of using lower payment to buy epsilon units of privacy, and the upper bound is given by a designed reward mechanism. When the individuals' valuations of privacy are unknown to the data collector, mechanisms with possible negative payments (aiming to penalize individuals with "unacceptably" high privacy valuations) are designed to fulfill the accuracy goal and drive the total payment to zero. For the setting with binary private data following a general joint probability distribution with some symmetry, asymptotically optimal mechanisms are designed in the high data quality regime.

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  • 2016

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Optimal power allocation and scheduling of real-time data for cognitive radios

Description

In this dissertation, I propose potential techniques to improve the quality-of-service (QoS) of real-time applications in cognitive radio (CR) systems. Unlike best-effort applications, real-time applications, such as audio and video,

In this dissertation, I propose potential techniques to improve the quality-of-service (QoS) of real-time applications in cognitive radio (CR) systems. Unlike best-effort applications, real-time applications, such as audio and video, have a QoS that need to be met. There are two different frameworks that are used to study the QoS in the literature, namely, the average-delay and the hard-deadline frameworks. In the former, the scheduling algorithm has to guarantee that the packet's average delay is below a prespecified threshold while the latter imposes a hard deadline on each packet in the system. In this dissertation, I present joint power allocation and scheduling algorithms for each framework and show their applications in CR systems which are known to have strict power limitations so as to protect the licensed users from interference.

A common aspect of the two frameworks is the packet service time. Thus, the effect of multiple channels on the service time is studied first. The problem is formulated as an optimal stopping rule problem where it is required to decide at which channel the SU should stop sensing and begin transmission. I provide a closed-form expression for this optimal stopping rule and the optimal transmission power of secondary user (SU).

The average-delay framework is then presented in a single CR channel system with a base station (BS) that schedules the SUs to minimize the average delay while protecting the primary users (PUs) from harmful interference. One of the contributions of the proposed algorithm is its suitability for heterogeneous-channels systems where users with statistically low channel quality suffer worse delay performances. The proposed algorithm guarantees the prespecified delay performance to each SU without violating the PU's interference constraint.

Finally, in the hard-deadline framework, I propose three algorithms that maximize the system's throughput while guaranteeing the required percentage of packets to be transmitted by their deadlines. The proposed algorithms work in heterogeneous systems where the BS is serving different types of users having real-time (RT) data and non-real-time (NRT) data. I show that two of the proposed algorithms have the low complexity where the power policies of both the RT and NRT users are in closed-form expressions and a low-complexity scheduler.

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  • 2016

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Security and privacy in mobile computing: challenges and solutions

Description

Mobile devices are penetrating everyday life. According to a recent Cisco report [10], the number of mobile connected devices such as smartphones, tablets, laptops, eReaders, and Machine-to-Machine (M2M) modules will

Mobile devices are penetrating everyday life. According to a recent Cisco report [10], the number of mobile connected devices such as smartphones, tablets, laptops, eReaders, and Machine-to-Machine (M2M) modules will hit 11.6 billion by 2021, exceeding the world's projected population at that time (7.8 billion). The rapid development of mobile devices has brought a number of emerging security and privacy issues in mobile computing. This dissertation aims to address a number of challenging security and privacy issues in mobile computing.

This dissertation makes fivefold contributions. The first and second parts study the security and privacy issues in Device-to-Device communications. Specifically, the first part develops a novel scheme to enable a new way of trust relationship called spatiotemporal matching in a privacy-preserving and efficient fashion. To enhance the secure communication among mobile users, the second part proposes a game-theoretical framework to stimulate the cooperative shared secret key generation among mobile users. The third and fourth parts investigate the security and privacy issues in mobile crowdsourcing. In particular, the third part presents a secure and privacy-preserving mobile crowdsourcing system which strikes a good balance among object security, user privacy, and system efficiency. The fourth part demonstrates a differentially private distributed stream monitoring system via mobile crowdsourcing. Finally, the fifth part proposes VISIBLE, a novel video-assisted keystroke inference framework that allows an attacker to infer a tablet user's typed inputs on the touchscreen by recording and analyzing the video of the tablet backside during the user's input process. Besides, some potential countermeasures to this attack are also discussed. This dissertation sheds the light on the state-of-the-art security and privacy issues in mobile computing.

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Date Created
  • 2017

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Steady State Analysis of Load Balancing Algorithms in the Heavy Traffic Regime

Description

This dissertation studies load balancing algorithms for many-server systems (with N servers) and focuses on the steady-state performance of load balancing algorithms in the heavy traffic regime. The framework of

This dissertation studies load balancing algorithms for many-server systems (with N servers) and focuses on the steady-state performance of load balancing algorithms in the heavy traffic regime. The framework of Stein’s method and (iterative) state-space collapse (SSC) are used to analyze three load balancing systems: 1) load balancing in the Sub-Halfin-Whitt regime with exponential service time; 2) load balancing in the Beyond-Halfin-Whitt regime with exponential service time; 3) load balancing in the Sub-Halfin-Whitt regime with Coxian-2 service time.

When in the Sub-Halfin-Whitt regime, the sufficient conditions are established such that any load balancing algorithm that satisfies the conditions have both asymptotic zero waiting time and zero waiting probability. Furthermore, the number of servers with more than one jobs is o(1), in other words, the system collapses to a one-dimensional space. The result is proven using Stein’s method and state space collapse (SSC), which are powerful mathematical tools for steady-state analysis of load balancing algorithms. The second system is in even “heavier” traffic regime, and an iterative refined procedure is proposed to obtain the steady-state metrics. Again, asymptotic zero delay and waiting are established for a set of load balancing algorithms. Different from the first system, the system collapses to a two-dimensional state-space instead of one-dimensional state-space. The third system is more challenging because of “non-monotonicity” with Coxian-2 service time, and an iterative state space collapse is proposed to tackle the “non-monotonicity” challenge. For these three systems, a set of load balancing algorithms is established, respectively, under which the probability that an incoming job is routed to an idle server is one asymptotically at steady-state. The set of load balancing algorithms includes join-the-shortest-queue (JSQ), idle-one-first(I1F), join-the-idle-queue (JIQ), and power-of-d-choices (Pod) with a carefully-chosen d.

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Date Created
  • 2019

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Connectivity in Complex Networks: Measures, Inference and Optimization

Description

Networks naturally appear in many high-impact applications. The simplest model of networks is single-layered networks, where the nodes are from the same domain and the links are of the

Networks naturally appear in many high-impact applications. The simplest model of networks is single-layered networks, where the nodes are from the same domain and the links are of the same type. However, as the world is highly coupled, nodes from different application domains tend to be interdependent on each other, forming a more complex network model called multi-layered networks.

Among the various aspects of network studies, network connectivity plays an important role in a myriad of applications. The diversified application areas have spurred numerous connectivity measures, each designed for some specific tasks. Although effective in their own fields, none of the connectivity measures is generally applicable to all the tasks. Moreover, existing connectivity measures are predominantly based on single-layered networks, with few attempts made on multi-layered networks.

Most connectivity analyzing methods assume that the input network is static and accurate, which is not realistic in many applications. As real-world networks are evolving, their connectivity scores would vary by time as well, making it imperative to keep track of those changing parameters in a timely manner. Furthermore, as the observed links in the input network may be inaccurate due to noise and incomplete data sources, it is crucial to infer a more accurate network structure to better approximate its connectivity scores.

The ultimate goal of connectivity studies is to optimize the connectivity scores via manipulating the network structures. For most complex measures, the hardness of the optimization problem still remains unknown. Meanwhile, current optimization methods are mainly ad-hoc solutions for specific types of connectivity measures on single-layered networks. No optimization framework has ever been proposed to tackle a wider range of connectivity measures on complex networks.

In this thesis, an in-depth study of connectivity measures, inference, and optimization problems will be proposed. Specifically, a unified connectivity measure model will be introduced to unveil the commonality among existing connectivity measures. For the connectivity inference aspect, an effective network inference method and connectivity tracking framework will be described. Last, a generalized optimization framework will be built to address the connectivity minimization/maximization problems on both single-layered and multi-layered networks.

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Date Created
  • 2019

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FPGA-based implementation of QR decomposition

Description

This thesis report aims at introducing the background of QR decomposition and its application. QR decomposition using Givens rotations is a efficient method to prevent directly matrix inverse in solving

This thesis report aims at introducing the background of QR decomposition and its application. QR decomposition using Givens rotations is a efficient method to prevent directly matrix inverse in solving least square minimization problem, which is a typical approach for weight calculation in adaptive beamforming. Furthermore, this thesis introduces Givens rotations algorithm and two general VLSI (very large scale integrated circuit) architectures namely triangular systolic array and linear systolic array for numerically QR decomposition. To fulfill the goal, a 4 input channels triangular systolic array with 16 bits fixed-point format and a 5 input channels linear systolic array are implemented on FPGA (Field programmable gate array). The final result shows that the estimated clock frequencies of 65 MHz and 135 MHz on post-place and route static timing report could be achieved using Xilinx Virtex 6 xc6vlx240t chip. Meanwhile, this report proposes a new method to test the dynamic range of QR-D. The dynamic range of the both architectures can be achieved around 110dB.

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Date Created
  • 2014

New multi-nodal wireless communication system method

Description

The purpose of this paper is to introduce a new method of dividing wireless communication (such as the 802.11a/b/g
and cellular UMTS MAC protocols) across multiple unreliable communication links

The purpose of this paper is to introduce a new method of dividing wireless communication (such as the 802.11a/b/g
and cellular UMTS MAC protocols) across multiple unreliable communication links (such as Ethernet). The purpose is to introduce the appropriate hardware, software, and system architecture required to provide the basis for a wireless system (using a 802.11a/b/g
and cellular protocols as a model) that can scale to support thousands of users simultaneously (say in a large office building, super chain store, etc.) or in a small, but very dense communication RF region. Elements of communication between a base station and a Mobile Station will be analyzed statistically to demonstrate higher throughput, fewer collisions and lower bit error rates (BER) with the given bandwidth defined by the 802.11n wireless specification (use of MIMO channels will be evaluated). A new network nodal paradigm will be presented. Alternative link layer communication techniques will be recommended and analyzed for the affect on mobile devices. The analysis will describe how the algorithms used by state machines implemented on Mobile Stations and Wi-Fi client devices will be influenced by new base station transmission behavior. New hardware design techniques that can be used to optimize this architecture as well as hardware design principles in regard to the minimal hardware functional blocks required to support such a system design will be described. Hardware design and verification simulation techniques to prove the hardware design will accommodate an acceptable level of performance to meet the strict timing as it relates to this new system architecture.

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Date Created
  • 2014

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System identification using discontinuous data sets and PID loop-shaping control of a vertical take-off and landing drone

Description

Vertical taking off and landing (VTOL) drones started to emerge at the beginning of this century, and finds applications in the vast areas of mapping, rescuing, logistics, etc. Usually a

Vertical taking off and landing (VTOL) drones started to emerge at the beginning of this century, and finds applications in the vast areas of mapping, rescuing, logistics, etc. Usually a VTOL drone control system design starts from a first principles model. Most of the VTOL drones are in the shape of a quad-rotor which is convenient for dynamic analysis.

In this project, a VTOL drone with shape similar to a Convair XFY-1 is studied and the primary focus is developing and examining an alternative method to identify a system model from the input and output data, with which it is possible to estimate system parameters and compute model uncertainties on discontinuous data sets. We verify the models by designing controllers that stabilize the yaw, pitch, and roll angles for the VTOL drone in the hovering state.

This project comprises of three stages: an open-loop identification to identify the yaw and pitch dynamics, an intermediate closed-loop identification to identify the roll action dynamic and a closed-loop identification to refine the identification of yaw and pitch action. In open and closed loop identifications, the reference signals sent to the servos were recorded as inputs to the system and the angles and angular velocities in yaw and pitch directions read by inertial measurement unit were recorded as outputs of the system. In the intermediate closed loop identification, the difference between the reference signals sent to the motors on the contra-rotators was recorded as input and the roll angular velocity is recorded as output. Next, regressors were formed by using a coprime factor structure and then parameters of the system were estimated using the least square method. Multiplicative and divisive uncertainties were calculated from the data set and were used to guide PID loop-shaping controller design.

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Date Created
  • 2015