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Yayın Mixture of Gaussian models and bayes error under differential privacy(2011) Xi, Bowei; Kantarcıoğlu, Murat; İnan, AliGaussian mixture models are an important tool in Bayesian decision theory. In this study, we focus on building such models over statistical database protected under differential privacy. Our approach involves querying necessary statistics from a database and building a Bayesian classifier over the noise added responses generated according to differential privacy. We formally analyze the sensitivity of our query set. Since there are multiple methods to query a statistic, either directly or indirectly, we analyze the sensitivities for different querying methods. Furthermore we establish theoretical bounds for the Bayes error for the univariate (one dimensional) case. We study the Bayes error for the multivariate (high dimensional) case in experiments with both simulated data and real life data. We discover that adding Laplace noise to a statistic under certain constraint is problematic. For example variance-covariance matrix is no longer positive definite after noise addition. We propose a heuristic method to fix the noise added variance-covariance matrix.Yayın Shocks in quasi-one-dimensional bubbly cavitating nozzle flows(Springer Berlin Heidelberg, 2013-01-01) Delale, Can Fuat; Schnerr, Giinter H.; Pasinlioǧlu, ŞenayStationary and propagating shock waves in bubbly cavitating flows through quasi-one-dimensional converging-diverging nozzles are considered by employing a homogeneous bubbly liquid flow model, where the nonlinear dynamics of cavitating bubbles is described by a modified Rayleigh-Plesset equation. The model equations are uncoupled by scale separation leading to two evolution equations, one for the flow speed and the other for the bubble radius. The initial/boundary value problem of the evolution equations is then formulated and a semi-analytical solution is constructed. The solution for the mixture pressure, the mixture density and the void fraction are then explicitly related to the solution of the evolution equations. The steady-state compressible limit of the solution with stationary shocks is obtained and the stability of such shocks are examined. Finally, results obtained using the semi-analytical constructed algorithm for propagating shock waves in bubbly cavitating flows through converging-diverging nozzles, which agree with those of previous numerical investigations, are presented.Yayın A quasi-one-dimensional bubbly cavitating flow model and comparison with experiments(European Turbomachinery Soc-Euroturbo, 2011) Delale, Can Fuat; Başkaya, Zafer; Pasinlioğlu, Şenay; Şen, Mete; Ayder, ErkanA bubbly cavitating flow model is constructed for unsteady quasi-one-dimensional and two-dimensional nozzle flows. In each case, the system of model equations is reduced to evolution equations for the flow velocity and bubble radius and the initial and boundary value problems of the evolution equations are formulated. The rest of the flow variables are then related to the solution of the evolution equations. Nozzle flow experiments are also carried out using water. The static wall pressures are measured at different locations of the nozzle and the partial cavitation cloud cycle is recorded using a high speed camera. Results of the numerical simulations obtained for quasi-one-dimensional nozzle flows, seem to capture the measured pressure losses due to cavitation, but they turn out to be insufficient in describing the two-dimensional cavitation cloud structures, suggesting the need for two-dimensional numerical solution of the model equations.
