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Data Node Encrypted File System
(2013)We propose the Data Node Encrypted File System (DNEFS), which uses on-the-fly encryption and decryption of file system data nodes to eciently and securely delete data on flash memory systems. DNEFS is a generic modication of existing flashfile systems or controllers that enables secure data deletion while preserving the underlying systems' desirable properties: application-independence,finegrained data access, wear-levelling, and efficiency. ...Report -
User-Level Secure Deletion on Log-structured File Systems
(2013)We address the problem of secure data deletion on logstructured file systems. We focus on the YAFFS file system, used on Android smartphones, and on the flash translation layer (FTL), used in SD cards and USB memory sticks. We show that neither of these systems provide temporal data deletion guarantees and that deleted data remains indefinitely on these systems if the storage medium is not used after the data is marked for deletion. ...Report -
Quasi-Monte Carlo finite element methods for elliptic PDEs with log-normal random coefficient
(2013)SAM Research ReportIn this paper we analyze the numerical approximation of diffusion problems over polyhedral domains in $R^d$ (d=1,2,3), with diffusion coefficient a(x,ω) given as a lognormal random field, i.e., a(x,ω)=exp(Z(x,ω)) where x is the spatial variable and Z(x,⋅) is a Gaussian random field. The analysis presents particular challenges since the corresponding bilinear form is not uniformly bounded away from 0 or ∞ over all possible realizations of ...Report -
A Note on Sparse, Adaptive Smolyak Quadratures for Bayesian Inverse Problems
(2013)SAM Research ReportWe present a novel, deterministic approach to inverse problems for identification of parameters in differential equations from noisy measurements. Based on the parametric deterministic formulation of Bayesian inverse problems with unknown input parameter from infinite dimensional, separable Banach spaces, we develop a practical computational algorithm for the efficient approximation of the infinite-dimensional integrals with respect to ...Report -
Isotropic Gaussian random fields on the sphere: regularity, fast simulation, and stochastic partial differential equations
(2013)SAM Research ReportIsotropic Gaussian random fields on the sphere are characterized by Karhunen-Loève expansions with respect to the spherical harmonic functions and the angular power spectrum. The smoothness of the covariance is connected to the decay of the angular power spectrum and the relation to sample Hölder continuity and sample differentiability of the random fields is discussed. Rates of convergence of their finitely truncated Karhunen-Loève ...Report -
Sparsity in Bayesian Inversion of Parametric Operator Equations
(2013)SAM Research ReportWe establish posterior sparsity in Bayesian inversion for systems with distributed parameter uncertainty subject to noisy data. We generalize the particular case of scalar diffusion problems with random coefficients in [29] to broad classes of operator equations. For countably parametric, deterministic representations of uncertainty in the forward problem which belongs to a certain sparsity class, we quantify analytic regularity of the ...Report -
Multilevel Monte Carlo for random degenerate scalar convection diffusion equation
(2013)SAM Research ReportThis paper proposes a Finite Difference Multilevel Monte Carlo algorithm for degenerate parabolic convection diffusion equations where the convective and diffusive fluxes are allowed to be random. We establish a notion of stochastic entropy solutions to these. Our chief goal is to efficiently compute approximations to statistical moments of these stochastic entropy solutions. To this end we design a multilevel Monte Carlo method based on ...Report -
Tensor approximation of stationary distributions of chemical reaction networks
(2013)SAM Research ReportWe prove that the stationary distribution of a system of reacting species with a weakly- reversible reaction network of zero deficiency in the sense of Feinberg admits tensor- structured approximation of complexity which scales linearly with respect to the number of species and logarithmically in the maximum copy numbers as well as in the desired accuracy. Our results cover the classical mass-action and also Michaelis-Menten kinetics which ...Report -
Multi-Level Monte-Carlo Finite Element Methods for stochastic elliptic variational inequalities
(2013)SAM Research ReportMulti-Level Monte-Carlo Finite Element (MLMC--FE) methods for the solution of stochastic elliptic variational inequalities are introduced, analyzed, and numerically investigated. Under suitable assumptions on the random diffusion coefficient, the random forcing function, and the deterministic obstacle, we prove existence and uniqueness of solutions of ``mean-square'' and ``pathwise'' formulations. Suitable regularity results for deterministic, ...Report