<div><div>The blockchain offers a decentralized way to provide security guarantees for financial transactions. However, this ability comes with the cost of storing a large (distributed) blockchain state and introducing additional computation and communication overhead to all participants. All these drawbacks raise a challenging scalability problem, especially for resource-constrained blockchain clients. On the other hand, some scaling solutions typically require resource-constrained clients to rely on other nodes with higher computational and storage capabilities. However, such scaling solutions often expose the data of the clients to risks of compromise of the more powerful nodes they rely on (e.g., accidental, malicious through a break-in, insider misbehavior, or malware infestation). This potential for leakage raises a privacy concern for these constrained clients, in addition to other scaling-related concerns. This dissertation proposes several cryptographic constructions and system designs enabling resource-constrained devices to participate in the blockchain network securely and efficiently. </div><div><br></div><div>Our first proposal concerns the storage facet for which we propose two add-on privacy designs to address the scaling issue of storing a large blockchain state. </div><div>The first solution is an oblivious database framework, called T³, that allows resource-constrained clients to obliviously fetch blockchain data from potential malicious full clients. The second solution focuses on the problem of using and storing additional private-by-design blockchains (e.g., Monero or ZCash) to achieve privacy. We propose an add-on tumbler design, called AMR, that offers privacy directly to clients of non-private blockchains such as Ethereum without the cost of storing and using different blockchain states.</div><div><br></div><div>Our second proposal addresses the communication facet with focus on payment channels as a solution to address the communication overhead between the constrained clients and the blockchain network. A payment channel enables transactions between arbitrary pairs of constrained clients with a minimal communication overhead with the blockchain network. However, in popular blockchains like Ethereum and Bitcoin, the payment data of such channels are exposed to the public, which is undesirable for financial applications. Thus, to hide transaction data, one can use blockchains that are private by design like Monero. However, existing cryptographic primitives in Monero prevent the system from supporting any form of payment channels. Therefore, we present <i>Dual Linkable Spontaneous Anonymous Group Signature for Ad Hoc Groups (DLSAG),</i> a linkable ring signature scheme that enables, for the first time, off-chain scalability solutions in Monero. </div><div><br></div><div>To address the computation facet, we address the computation overhead of the gossip protocol used in all popular blockchain protocols. For this purpose, we propose a signature primitive called <i>Flexible Signature</i>. In a flexible signature scheme, the verification algorithm quantifies the validity of a signature based on the computational effort performed by the verifier. Thus, the resource-constrained devices can partially verify the signatures in the blockchain transactions before relaying transactions to other peers. This primitive allows the resource-constrained devices to prevent spam transactions from flooding the blockchain network with overhead that is consistent with their resource constraints. </div></div>

The first part of this dissertation investigates the possibility of an output cut by a firm as a result of an increase in demand in industries with constrained capacities. We are specially interested in the crude oil industry, although the paper has implications beyond that market. Two simple closely related models are developed. In both models a firm cuts the output at some point solely because of an increase in demand. We use this fact to explain the sharp decline of the crude oil prices in 1986. There are price and quantity hysteresis in the second model. The price hysteresis has two implications. First, the price path when the demand increases might be different from the price path when the demand decreases. This in turn implies that a temporary shock in the demand for (or supply of) crude oil can cause permanent changes in the price. We claim that the temporary changes in the supply of crude oil in 1973 resulted in the price hysteresis phenomenon described in the second model in such a way that it kept the prices high even after the return of the producers to the market. The second part investigates the relationship between the taste for public expenditure and the size and distribution of social groups in a society. Societies with ethnic heterogeneity spend less on redistribution and welfare programs and impose lower tax rates relative to homogeneous societies. We construct a theoretical model to explain these facts. There are two social groups in the model: a minority group and a majority group. When members of one group feel empathy for each other but not for members of the other group, then taxes, and redistribution depend upon the size and distribution of those groups. At first, the equilibrium tax rate and redistribution decrease as the size of the minority group increases from zero, then eventually, the relationship between them becomes positive. / Ph. D.

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Turbulent flows occur in various fields and are a central, yet an extremely complex, topic in fluid dynamics. Understanding the behaviour of fluids is vital for multiple research areas including, but not limited to: biological models, weather prediction, and engineering design models for automobiles and aircraft. In this thesis, we study a number of fundamental problems that arise in 2D turbulent flows, using the 2D Navier-Stokes system. Introducing optimization techniques for systems described by partial differential equations (PDE), we frame these problems such that they can be solved using computational methods. We utilize adjoint calculus to build the computational framework to be implemented in an iterative gradient flow procedure, using the "optimize-then-discretize" approach. Pseudospectral methods are employed for solving PDEs in a numerically efficient manner. The use of optimization methods together with computational mathematics in this work provides an illuminating perspective on fluid mechanics. We first apply these techniques to better understand enstrophy dissipation in 2D Navier-Stokes flows, in the limit of vanishing viscosity. By defining an optimization problem to determine optimal initial conditions, multiple branches of local maximizers were obtained each corresponding to a different mechanism producing maximum enstrophy dissipation. Viewing this quantity as a function of viscosity revealed quantitative agreement with an analytic bound, demonstrating the sharpness of this bound. We also introduce an extension of this problem, where enstrophy dissipation is maximized in the context of kinetic theory using the Boltzmann equation. Secondly, these PDE-constrained optimization techniques were used to probe the fundamental limitations on the performance of the Leith eddy-viscosity closure model for 2D Large-Eddy Simulations of the Navier-Stokes system. Obtained by solving an optimization problem with a non-standard structure, the results demonstrate the optimal eddy viscosities do not converge to a well-defined limit as regularization and discretization parameters are refined, hence the problem of determining an optimal eddy viscosity is ill-posed. Further extending the problem of finding optimal eddy-viscosity closures, we consider imposing an additional nonlinear constraint on the control variable in the problem, in the form of requiring the time-averaged enstrophy be preserved. To address this problem in a novel way, we employ adjoint calculus to characterize a subspace tangent to the constraint manifold, which allows one to approximately enforce the constraint. Not only do we demonstrate that this produces better results when compared to the case without constraints, but this also provides a flexible computational framework for approximate enforcement of general nonlinear constraints. Lastly in this thesis, we introduce an optimization problem to study the Kolmogorov-Richardson energy cascade, where a pathway towards solutions is outlined. / Thesis / Doctor of Philosophy (PhD)

The focus of Location-Aware Adaptive Vehicle Dynamics System (LAAVDS) research is to develop a system to avoid situations in which the vehicle exceeds its handling capabilities. The proposed method is predictive, estimating the ability of the vehicle to successfully navigate upcoming terrain, and it is assumed that the future vehicle states and local driving environment is known. An Intervention Strategy must be developed such that the vehicle is navigated successfully along a road via modest changes to the driver's commands and do so in a manner that is in harmony with the driver's intentions and not in a distracting or irritating manner. Clearly this research relies on the numerous new technologies being developed to capture and convey information about the local driving environment (e.g., bank angle, elevation changes, curvature, and friction coefficient) to the vehicle and driver. / Ph. D.

Frequency Hopping Spread Spectrum (FHSS) signaling is used across many devices operating in both regulated and unregulated bands. In either situation, if there is a malicious device operating within these bands, or more simply a user operating out of the required specifications, the identification this user important to insure communication link integrity and interference mitigation. The identification of a user involves the grouping of that users signal transmissions, and the separation of those transmission from transmissions of other users in a shared frequency band. Traditional signal separation methods often require difficult to obtain hardware fingerprinting characteristics or approximate geo-location estimates. This work will consider the characteristics of FHSS signals that can be extracted directly from signal detection. From estimates of these hopping characteristics, novel source separation with classic clustering algorithms can be performed. Background knowledge derived from the time domain representation of received waveforms can improve these clustering methods with the novel application of cannot-link pairwise constraints to signal separation. For equivalent clustering accuracy, constraint-based clustering tolerates higher parameter estimation error, caused by diminishing received signal-to-noise ratio (SNR), for example. Additionally, prior work does not fully cover the implications of detecting and estimating FHSS signals using image segmentation on a Time-Frequency (TF) waterfall. This work will compare several methods of FHSS signal detection, and discuss how each method may effect estimation accuracy and signal separation quality. The use of constraint-based clustering is shown to provide higher clustering accuracy, resulting in more reliable separation and identification of active users in comparison to traditional clustering methods. / Master of Science / The expansion of technology in areas such as smart homes and appliances, personal devices, smart vehicles, and many others, leads to more and more devices using common wireless communication techniques such as WiFi and Bluetooth. While the number of wirelessly connected users expands, the range of frequencies that support wireless communications does not. It is therefore essential that each of these devices unselfishly share the available wireless resources. If a device is using more resources than the required limits, or causing interference with other’s communications, this device will impact many others negatively and therefore preventative action must be taken to prevent further disruption in the wireless environment. Before action can be taken however, the device must first be identified in a mixture of other wireless activity. To identify a specific device, first, a wireless receiver must be in close enough proximity to detect the power that the malicious device is emitting through its wireless communication. This thesis provides a method that can be used to identify a problem user based only off of its wireless transmission behavior. The performance of this identification is shown with respect to the received signal power which represents the necessary range that a listening device must be to identify and separate a problem user from other cooperative users that are communicating wirelessly.

TRANSIMS (Transportation Analysis Simulation System) is part of a multi-track Travel Model Improvement Program sponsored by the U. S. Department of Transportation (DOT), and the Environmental Protection Agency (EPA). The main objective of this thesis is to enhance and implement a principal module in TRANSIMS, called the Route Planner Module. The purpose of the Route Planner Module is to find time-dependent label-constrained shortest paths for transportation activities performed by travelers in the system. There are several variations of shortest path problems and algorithms that vary by application, contexts, complexity, required data, and computer implementation techniques. In general, these variants require some combination of the following inputs: a network consisting of nodes and links, and a travel time function on each link, which could be a time-independent or a time-dependent function, where the time-dependent functions account for time-of-day delays resulting from actual travel conditions such as peak-hour congestion. The problem then seeks a shortest path between one or more origin-destination pairs. A new variant, introduced in the context of TRANSIMS and which is the focus of the present study, also specifies labels for each arc denoting particular modes of travel, along with strings of admissible labels that delineate the permissible travel mode sequences that could be adopted by the user in traveling from the origin to the destination of the trip. The technique adopted by TRANSIMS to identify a suitable travel route for any user is a variant of Dijkstra's procedure for finding shortest paths, which is suitably modified to accommodate time-dependent travel times and label sequence constraints. The underlying problem is referred to as a Time-Dependent Label-Constrained Shortest Path Problem. The main objective of this research is to improve upon this procedure and study its implementation in order to develop a more effective scheme for determining time-dependent label-constrained shortest paths as a practical routing tool in multimodal transportation networks. Specifically, we enhance the following features of this procedure: (a) We recommend a method to work implicitly with a certain composition graph G* that combines the transportation network with the admissible label-sequence graph. This graph G* captures all possible paths for a given single trip starting from the origin node and ending at the destination node, while conforming with the admissible mode string. (b) We use more modern partitioned shortest path algorithmic schemes to implement the time-dependent label-constrained procedure. (c) We introduce the notion of curtailing search based on various indicators of progress and projected travel times to complete the trip. Finally, computer programs in C++ are written to implement the proposed overall algorithm, and are applied to solve some real multimodal transportation network problems. The indicators used to evaluate the performance of the algorithm include (i) time taken for computation on the real network, (ii) quality of solution obtained, (iii) ease of implementation, and (iv) extensibility of the algorithm for solving other variants of the shortest path problem. The results exhibit that the proposed algorithm, even without the approximate curtailing of the search process, exhibits good performance in finding optimal routes for real multimodal transportation networks. Although the various heuristic curtailments result in only approximate solutions, typically, they run much faster than the exact algorithm for the intuitive reason that the shortest path tree developed grows more pointedly in the direction of the destination. Among the different strategies implemented, our results suggest that the scheme based on the geometric structure of the underlying network, using either a constant predictive term, or multiplying this term with a suitable exponential decay function, yields an attractive candidate for heuristically curtailing the search. / Master of Science