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In modern data analysis, privacy is a critical concern when dealing with user-related databases. Ensuring user anonymity while extracting meaningful correlations from the data poses a significant challenge, especially when side information can potentially enable de-anonymization. This dissertation explores the standard information-theoretic problems in the correlated databases model. We define a "database" as a simple probabilistic model that contains a random feature vector for each user, with user labels shuffled to ensure anonymity. We first investigate correlation detection between two databases, formulating it as a composite binary hypothesis testing problem. Under the alternate hypothesis, there exists an unknown permutation that aligns users in the first database with those in the second, thereby matching correlated entries. The null hypothesis assumes that the databases are independent, with no such alignment. For the special case of Gaussian feature vectors, we derive both upper and lower bounds on the correlation required to achieve or fail to achieve this statistical problem. Our results are tight up to a constant factor when the feature length exceeds the number of users. Regarding our achievability boundary, we draw connections to the user labeling recovery problem, highlighting significant parallels and insights. Additionally, for the two databases model, we initially examine the potential gaps in the statistical analysis conducted thus far for the large number of users regime by drawing parallels with similar problems in the literature. Motivated by these comparisons, we propose a novel approach to address the detection problem, focusing on the hidden permutation structure and intricate dependencies characterizing these relationships. Building on our research, we present a comprehensive model for handling multiple correlated databases. In this multiple-databases setting, we address another fundamental information-theoretic problem: user label recovery. We evaluate the performance of the typicality matching estimator in relation to the asymptotic behavior of feature length, demonstrating an impossibility result that holds up to a multiplicative constant factor. This exploration into multiple databases not only broadens the scope of our study but also underscores the complexity and richness of correlation detection in a more generalized framework. In conclusion, we summarize the statistical gaps identified in our findings, exploring their possible origins. We also discuss the limitations of our simple probabilistic model and propose strategies to address them. Finally, we outline potential future research directions, including the information-theoretic problem of change detection, which remains an open area of significant interest.

Evaluated were correlated responses to 54-generations of divergent selection for 8-week body weight (BW) and of BW at other ages and reproductive traits. Evaluated first was the influence of scaling on phenotypic responses to selection, phenotypic correlations of means and standard deviations, and unadjusted vs. standardized responses. Measured was BW at 4 (BW4), 8 (BW8), 24 (BW24), and 38 (BW38) weeks of age. Correlations between means and standard deviations were positive and greater in the LWS than HWS. Scaling masked the degree more than the pattern of response and was line specific with the magnitude of response greater in the LWS than HWS. While BW ratios across ages were not influenced by scaling in LWS, they were evident in HWS. Also measured were correlated responses of reproductive traits in selected and relaxed lines. Traits were age at first egg (AFE), body weight at first egg (WFE), their ratio (WAFE), and hen-day normal egg production (HDP). Although sexual maturity was delayed, the effect was more pronounced in the low than high weight lines. Selection for low BW decreased WFE, WAFE and HDP. Selection for high BW resulted in lower HDP, while WFE and WAFE were generally higher. Minimum AFE, WFE and WAFE in relation to sexual maturity were line specific. Opposition between relaxed and artificial selection resulted in a higher reproductive performance and fitness with relaxed than artificial selection. Overall, results demonstrate that correlated responses to long-term divergent selection were masked by scaling and negative correlated reproductive responses. / Master of Science

The stochastic dynamics of an array of closely spaced micron scale cantilevers in a viscous fluid is considered. The stochastic cantilever dynamics are due to the constant buffeting of fluid particles by Brownian motion and the dynamics of adjacent cantilevers are correlated due to long range effects of fluid dynamics. The measurement sensitivity of an experimental setup is limited by the magnitude of inherent stochastic motion. However, the magnitude of this noise can be decreased using correlated measurements allowing for improved force resolution. A correlated scheme is proposed using two atomic force microscope cantilevers for the purpose of analyzing the dynamics of single molecules in real time, a regime that is difficult to observe using current technologies. Using a recently proposed thermodynamic approach the hydrodynamic coupling of an array of cantilevers is quantified for precise experimental conditions through deterministic numerical simulations. Results are presented for an array of two readily available micron-scale cantilevers yielding the possible force sensitivity and time resolution of correlated measurements. This measurement scheme is capable of achieving a force resolution that is more than three fold more sensitive than that of a single cantilever when the two cantilevers are separated by 200 nm, with a time scale on the order of tens of microseconds. / Master of Science

Master of Science / Department of Statistics / Paul I. Nelson / The standard Chi-square test for the equality of proportions of positive responses to c specified binary questions is valid when the observed responses arise from independent random samples of units. When the responses to all c questions are recorded on the same unit, a situation called correlated proportions, the assumptions under which this test is derived are no longer valid. Under the additional assumption of compound symmetry, the Cochran-Q test is a valid test for the equality of proportions of positive responses. The purpose of this report is to use simulation to examine and compare the performance of the Cochran-Q test and the standard Chisquare test when testing for the equality of correlated proportions. It is found that the Cochran-Q test is superior to the Chi-square test in terms of size and power, especially when the common correlation among the binary responses is large.

Strong effective photon-photon interactions mediated by atom-photon couplings have been routinely achievable in QED setups for some time now. Recently, there have been several proposals to push the physics of interacting photons into many- body distributed architectures. The essential idea is to coherently couple together arrays of QED resonators, such that photons can hop between resonators while interacting with each other inside each resonator. These proposed structures have attracted intense theoretical attention while simultaneously inspiring experimental efforts to realise this novel regime of strongly-correlated many-body states of light. A central challenge of both theoretical and practical importance is to understand the physics of such coupled resonator arrays (CRAs) beyond equilibrium, when unavoidable (or sometimes even desired) photon loss processes are accounted for. This thesis presents several studies whose purpose can roughly be divided in two aims. The first part studies just what constitutes a valid physical and computational representation of non-equilibrium driven-dissipative CRAs. Addressing these ques- tions constitutes essential groundwork for further investigations of CRA phenomena, as numerical experiments are likely to guide and interpret near-future experimen- tal array observations. The relatively small body of existing work on CRAs out of equilibrium has often truncated their full, rich physics. It is important to establish the effects and validity of these approximations. To this end we introduce powerful numerical algorithms capable of efficiently simulating the full dynamics of CRAs, and use them to characterise the non-equilibrium steady states of arrays reached under the combined influence of dissipation and pumping. Having established the rigour necessary to realistically describe CRAs, we exam- ine two novel phenomena observable in near-future small arrays. Firstly we relate a counter-intuitive ‘super bunching’ in the statistics of photons emitted from arrays engineered to demonstrate strong effective photon-photon repulsion at the single and two-photon level, to an interplay between the underlying eigen-structure and details of the non-equilibrium operation. Secondly we characterise a dynamical phenomenon in which domains of ‘frozen’ photons remain trapped in sufficiently nonlinear arrays. Finally we present a preliminary characterisation of a previously unexplored phase diagram of arrays under coherent two-photon pumping. Com- petition between the coherence injected by the pumping, photon interactions and delocalisation processes lead to interesting new physical signatures.

ITC/USA 2015 Conference Proceedings / The Fifty-First Annual International Telemetering Conference and Technical Exhibition / October 26-29, 2015 / Bally's Hotel & Convention Center, Las Vegas, NV / Spatial modulation (SM) reduces transceiver complexity and inter-channel interference over traditional multiple input multiple output (MIMO) systems. It has been shown recently in the literature that the use of a precoder in an SM or a generalized spatial modulation (GSM) system can significantly improve error performance. This paper investigates two issues related to precoders: 1) the use of a precoder in Alamouti-GSM systems, and 2) the effects of power constraints on the precoder design. The results in this paper show that Alamouti-GSM can improve system performance by several dB. On power constraint issues, the paper shows that there is a trade-off between limiting antenna power fluctuations and the potential gain due to precoders.

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Hedging a contingent claim with an asset which is not perfectly correlated with the underlying asset results in an imperfect hedge. The residual risk from hedging with a correlated asset is priced using an actuarial standard deviation principle in infinitesmal time, which gives rise to a nonlinear partial differential equation (PDE). A fully implicit, monotone discretization method is developed for solving the pricing PDE. This method is shown to converge to the viscosity solution. Certain grid conditions are required to guarantee monotonicity. An algorithm is derived which, given an initial grid, inserts a finite number of nodes in the grid to ensure that the monotonicity condition is satisfied. At each timestep, the nonlinear discretized algebraic equations are solved using an iterative algorithm, which is shown to be globally convergent. Monte Carlo hedging examples are given, which show the standard deviation of the profit and loss at the expiry of the option.