In the era of big data, it is essential to implement practical security and privacy measures to ensure the lawful use of data and provide users with trust and assurance. In the dissertation, I address this issue through several key steps. Firstly, I delve into the problem of conditional secret disclosure, representing it using graphs to determine the most efficient approach for storing and disclosing secrets. Secondly, I extend the conditional disclosure of secrets problem from a single secret to multiple secrets and from a bipartite graph to an arbitrary graph. Thirdly, I remove security constraints to observe how they affect the efficiency of storage and recovery. In our final paper, I explore the secure summation problem, aiming to determine the capacity of total noise. Throughout the dissertation, I leverage information-theoretic tools to address security and privacy concerns.

The goal of Low Impact Development (LID) is to mimic the pre-development hydrologic regime of a catchment through infiltration, filtration, storage, evaporation, and detention of post-development runoff using small-scale hydrologic controls close to the source. A LID facility located in Northern Virginia was examined for pollutant removal and hydrologic performance. The treatment train included four in-line grass swales followed by a bioretention cell with a gravel base. The facility retained 85% of the rainfall. Influent and effluent pollutant loads were calculated using three common substitution methods for datasets censored by values below the analytical detection limit. The Summation of Loads (SOL) method was used to facilitate understanding of how data censoring affected performance results when substitution methods were used. The SOL analysis showed positive removal performance for most nutrient species, sediment, oxygen demanding substances, selected trace metals and total petroleum hydrocarbons. Negative performance was observed for oxidized nitrogen, total dissolved solids and oil & grease. LID facility influent and effluent loads were also compared using the Effluent Probability Method (EPM). The EPM analysis showed statistically significant (p d 0.05) pollutant load removal performance over the entire range of sampled events for total suspended solids, total phosphorus, total nitrogen, total Kjeldahl nitrogen, ammonia nitrogen, chemical oxygen demand, copper, zinc and alkalinity. EPM analysis did not show significant removals of oxidized nitrogen, total dissolved solids, orthophosphate phosphorus and hardness. / Master of Science

Historically, the primary objective of traditional stormwater best management practices (BMPs) was to attenuate peak runoff discharges from urban areas. There has been growing demand to construct BMPs that improve stormwater runoff quality to reduce pollutant loading into downstream water bodies. A BMP located in Herndon, Virginia was retrofitted in 2009. Previously a dry detention pond, the new BMP design contains permanent wet pools as well as elements of Low Impact Development practices. A performance analysis was conducted on the retrofit to determine if the BMP was removing pollutants from stormwater runoff. Two mass-based methods were utilized for the performance analysis: the Summation of Loads Method and Effluent Probability Method. The Kaplan-Meier method and Robust Regression on ordered statistics (ROS) were used to make it possible to include censored datasets in the analysis. Analysis with the SOL method showed removal of suspended sediment, nitrogen, iron, and copper. Export of dissolved solids, phosphorus, organic carbon, and manganese was observed. The results of the Effluent Probability Method showed statistically significant reductions of sediment, iron, and copper across the entire range of monitored storm event sizes (p-value≤0.05). There was no statistical difference between the influent and effluent loads of nitrogen. Negative performance of dissolved solids, phosphorus, organic carbon, and manganese were observed for the entire range of monitored storm event sizes. The results of both methods indicated that the BMP retrofit is effectively removing sediment but failing to achieve significant nutrient reductions. This may be due to the creation of anoxic conditions from the oxygen demand of the micropool sediments and microbial degradation of vegetation within the BMP. Removal of the sediment bed and harvesting of the vegetation would likely improve the performance of the BMP. / Master of Science

In this paper we describe a parallel algorithm for calculating nonequispaced fast Fourier transforms on massively parallel distributed memory architectures. These algorithms are implemented in an open source software library called PNFFT. Furthermore, we derive a parallel fast algorithm for the computation of the Coulomb potentials and forces in a charged particle system, which is based on the parallel nonequispaced fast Fourier transform. To prove the high scalability of our algorithms we provide performance results on a BlueGene/P system using up to 65536 cores.

The computation of the Coulomb potentials and forces in charged particle systems under 3d-periodic boundary conditions is possible in an efficient way by utilizing the Ewald summation formulas and applying the fast Fourier transform (FFT). In this paper we consider the particle-particle NFFT (P2NFFT) approach, which is based on the fast Fourier transform for nonequispaced data (NFFT) and compare the error behaviors regarding different window functions, which are used in order to approximate the given continuous charge distribution by a mesh based charge density. While typically B-splines are applied in the scope of particle mesh methods, we consider for the first time also an approximation by Bessel functions. We show how the resulting root mean square errors in the forces can be predicted precisely and efficiently. The results show that if the parameters are tuned appropriately the Bessel window function can keep up with the B-spline window and is in many cases even the better choice with respect to computational costs.

<p>This thesis in analytic number theory consists of 3 parts and 13 individual papers.</p><p>In the first part we prove some results in Turán power sum theory. We solve a problem of Paul Erdös and disprove conjectures of Paul Turán and K. Ramachandra that would have implied important results on the Riemann zeta function.</p><p>In the second part we prove some new results on moments of the Hurwitz and Lerch zeta functions (generalized versions of the Riemann zeta function) on the critical line.</p><p>In the third and final part we consider the following question: What is the natural generalization of the classical Poisson summation formula from the Fourier analysis of the real line to the matrix group SL(2,R)? There are candidates in the literature such as the pre-trace formula and the Selberg trace formula.</p><p>We develop a new summation formula for sums over the matrix group SL(2,Z) which we propose as a candidate for the title "The Poisson summation formula for SL(2,Z)". The summation formula allows us to express a sum over SL(2,Z) of smooth functions f on SL(2,R) with compact support, in terms of spectral theory coming from the full modular group, such as Maass wave forms, holomorphic cusp forms and the Eisenstein series. In contrast, the pre-trace formula allows us to get such a result only if we assume that f is also SO(2) bi-invariant.</p><p>We indicate the summation formula's relationship with additive divisor problems and the fourth power moment of the Riemann zeta function as given by Motohashi. We prove some identities on Kloosterman sums, and generalize our main summation formula to a summation formula over integer matrices of fixed determinant D. We then deduce some consequences, such as the Kuznetsov summation formula, the Eichler-Selberg trace formula and the classical Selberg trace formula.</p>

The main aim of this thesis was to evaluate the performance of the contrast sensitivity clock (CSC), a new screening device for measuring contrast sensitivity (CS) and glare. This device allows CS without glare, with glare and disability glare scores to be recorded. After initial data collection the design of the CSC was slightly amended improving the performance of the device. The amended design of the CSC was shown to be a valid, discriminative and repeatable measure for purpose. The CSC is also a quick test to perform and is relatively cheap to produce. If all these factors are considered it shows potential to become the test of choice for the assessment of visual glare. A head-mounted display system was also evaluated in terms of the glare effects it may cause. The monocular display screen of the device significantly reduced the CS of the eye directly exposed but also had an effect on binocular performance, reducing amounts of binocular summation. Electronic devices, including head-mounted displays and satellite navigation systems can seriously affect CS at low luminance levels, similar to those found when driving at night.

Les systèmes électroniques bidimensionnels sont d'une grande actualité tout particulièrement depuis la découverte de la supraconductivité à haute température. Ici, on se restreint à l'étude d'un modèle de Hubbard étendu, à la limite d'un couplage faible. En général, le gaz électronique subit une instabilité supraconductrice même sans phonons. Cependant, dans le cas spécial d'une bande demi-remplie, la surface de Fermi est emboîtée et se trouve à une singularité de Van Hove. Cette situation conduit à une compétition entre six instabilités différentes. Outre la supraconductivité en onde $s$ et $d$, on trouve des ondes de densités de spin et de charge ainsi que deux phases qui sont caractérisées par des courants circulaires de charge et de spin respectivement. Le formalisme du groupe de renormalisation est présenté en reliant l'idée de la "< sommation parquet "> au concept plus moderne de l'action effective de Wilson. Comme résultat on obtient un diagramme de phases riche en fonction de l'interaction du modèle. Ce diagramme de phase est exact dans la limite d'une interaction infiniment faible, puisque dans ce cas les lignes de transitions sont fixées par des symétries du modèle. Les comportements à basse température de la susceptibilité de spin ainsi que de la compressibilité de charge complètent l'image physique de ces instabilités. Il s'avère que la surface de Fermi à une tendence générale de se déformer spontanément, mais l'emboîtement n'est pas détruit. En résumé, le modèle de Hubbard à couplage faible reproduit deux propriétés essentielles des cuprates: une phase antiferromagnetique à demi remplissage et la supraconductivité en onde $d$ dans le cas dopé. Mais elle n'éxplique pas les propriétés inhabituelles de l'état métallique dans le régime sous-dopé. Une extension systématique de l'approche perturbative pourrait aider à mieux comprendre ces propriétés, mais reste difficile puisque les techniques nécessaires ne sont pas encore complètement développées.

The perfectly matched layer (PML) is a novel technique to simulate the absorption of waves in unbounded domains. The underlying equations are often a system of second order hyperbolic partial differential equations. In the numerical treatment, second order systems are often rewritten and solved as first order systems. There are several benefits with solving the equations in second order formulation, though. However, while the theory and numerical methods for first order hyperbolic systems are well developed, numerical techniques to solve second order hyperbolic systems are less complete. We construct a strongly well-posed PML for second order systems in two space dimensions, focusing on the equations of linear elasto-dynamics. In the continuous setting, the stability of both first order and second order formulations are linearly equivalent. We have found that if the so-called geometric stability condition is violated, approximating the first order PML with standard central differences leads to a high frequency instability at most resolutions. In the second order setting growth occurs only if growing modes are well resolved. We determine the number of grid points that can be used in the PML to ensure a discretely stable PML, for several anisotropic elastic materials. We study the stability of the PML for problems where physical boundaries are important. First, we consider the PML in a waveguide governed by the scalar wave equation. To ensure the accuracy and the stability of the discrete PML, we derived a set of equivalent boundary conditions. Second, we consider the PML for second order symmetric hyperbolic systems on a half-plane. For a class of stable boundary conditions, we derive transformed boundary conditions and prove the stability of the corresponding half-plane problem. Third, we extend the stability analysis to rectangular elastic waveguides, and demonstrate the stability of the discrete PML. Building on high order summation-by-parts operators, we derive high order accurate and strictly stable finite difference approximations for second order time-dependent hyperbolic systems on bounded domains. Natural and mixed boundary conditions are imposed weakly using the simultaneous approximation term method. Dirichlet boundary conditions are imposed strongly by injection. By constructing continuous strict energy estimates and analogous discrete strict energy estimates, we prove strict stability.

This thesis in analytic number theory consists of 3 parts and 13 individual papers. In the first part we prove some results in Turán power sum theory. We solve a problem of Paul Erdös and disprove conjectures of Paul Turán and K. Ramachandra that would have implied important results on the Riemann zeta function. In the second part we prove some new results on moments of the Hurwitz and Lerch zeta functions (generalized versions of the Riemann zeta function) on the critical line. In the third and final part we consider the following question: What is the natural generalization of the classical Poisson summation formula from the Fourier analysis of the real line to the matrix group SL(2,R)? There are candidates in the literature such as the pre-trace formula and the Selberg trace formula. We develop a new summation formula for sums over the matrix group SL(2,Z) which we propose as a candidate for the title "The Poisson summation formula for SL(2,Z)". The summation formula allows us to express a sum over SL(2,Z) of smooth functions f on SL(2,R) with compact support, in terms of spectral theory coming from the full modular group, such as Maass wave forms, holomorphic cusp forms and the Eisenstein series. In contrast, the pre-trace formula allows us to get such a result only if we assume that f is also SO(2) bi-invariant. We indicate the summation formula's relationship with additive divisor problems and the fourth power moment of the Riemann zeta function as given by Motohashi. We prove some identities on Kloosterman sums, and generalize our main summation formula to a summation formula over integer matrices of fixed determinant D. We then deduce some consequences, such as the Kuznetsov summation formula, the Eichler-Selberg trace formula and the classical Selberg trace formula.