Approximate Two-Party Privacy-Preserving String Matching with Linear Complexity

Consider two parties who want to compare their strings, e.g., genomes, but do not want to reveal them to each other. We present a system for privacy-preserving matching of strings, which differs from existing systems by providing a deterministic approximation instead of an exact distance. It is efficient (linear complexity), non-interactive and does not involve a third party which makes it particularly suitable for cloud computing. We extend our protocol, such that it mitigates iterated differential attacks proposed by Goodrich. Further an implementation of the system is evaluated and compared against current privacy-preserving string matching algorithms.Comment: 6 pages, 4 figure

Rademacher-Carlitz Polynomials

We introduce and study the \emph{Rademacher-Carlitz polynomial} \RC(u, v, s, t, a, b) := \sum_{k = \lceil s \rceil}^{\lceil s \rceil + b - 1} u^{\fl{\frac{ka + t}{b}}} v^k where $a, b \in \Z_{>0}$, $s, t \in \R$, and $u$ and $v$ are variables. These polynomials generalize and unify various Dedekind-like sums and polynomials; most naturally, one may view \RC(u, v, s, t, a, b) as a polynomial analogue (in the sense of Carlitz) of the \emph{Dedekind-Rademacher sum} \r_t(a,b) := \sum_{k=0}^{b-1}\left(\left(\frac{ka+t}{b} \right)\right) \left(\left(\frac{k}{b} \right)\right), which appears in various number-theoretic, combinatorial, geometric, and computational contexts. Our results come in three flavors: we prove a reciprocity theorem for Rademacher-Carlitz polynomials, we show how they are the only nontrivial ingredients of integer-point transforms $$\sigma(x,y):=\sum_{(j,k) \in \mathcal{P}\cap \Z^2} x^j y^k$$ of any rational polyhedron $\mathcal{P}$, and we derive a novel reciprocity theorem for Dedekind-Rademacher sums, which follows naturally from our setup

A fully lagrangian approach for modeling abrasive wear

The decrease of efficiency of hydraulic machinery is a result of different mechanisms. The impairment of the performance, e.g. of a pump, caused by abrasive wear is thereby not negligible. Abrasive particles transported by the working fluid can lead to a mechanical damage of the surface of the hydraulic machinery components. In this work, a fully Lagrangian approach for modeling the process of abrasive wear is presented. The damage mechanism is a complex process that should be investigated during simulations with this approach. When analyzing abrasive wear of the components several facts have to be taken into account. For example, one important point that has to be taken into consideration is the shape of the abrasive particles, therefore a suitable model for the wear is applied. In contrast to classical computational fluid dynamic simulations, here the mesh-less Smoothed Particle Hydrodynamics method is used for the modeling of the fluid. The advantage in comparison to classical mesh-based methods, is the much easier description of the free surface of a fluid and the interface between the fluid and a solid body. The abrasive particles are modeled using the Discrete Element Method. For the modeling of the wear the erosion model of Finnie is applied. In this work the presented Lagrangian approach is used for the simulation of an impact of a free jet with loading and the analysis of the resulting wear. The boundary geometry is the bucket of a pelton turbine. First the theoretical background of this hybrid simulation approach is described and then the simulation results are discussed

Synthetic X-ray and radio maps for two different models of Stephan's Quintet

We present simulations of the compact galaxy group Stephan's Quintet (SQ) including magnetic fields, performed with the N-body/smoothed particle hydrodynamics (SPH) code \textsc{Gadget}. The simulations include radiative cooling, star formation and supernova feedback. Magnetohydrodynamics (MHD) is implemented using the standard smoothed particle magnetohydrodynamics (SPMHD) method. We adapt two different initial models for SQ based on Renaud et al. and Hwang et al., both including four galaxies (NGC 7319, NGC 7320c, NGC 7318a and NGC 7318b). Additionally, the galaxies are embedded in a magnetized, low density intergalactic medium (IGM). The ambient IGM has an initial magnetic field of $10^{-9}$ G and the four progenitor discs have initial magnetic fields of $10^{-9} - 10^{-7}$ G. We investigate the morphology, regions of star formation, temperature, X-ray emission, magnetic field structure and radio emission within the two different SQ models. In general, the enhancement and propagation of the studied gaseous properties (temperature, X-ray emission, magnetic field strength and synchrotron intensity) is more efficient for the SQ model based on Renaud et al., whose galaxies are more massive, whereas the less massive SQ model based on Hwang et al. shows generally similar effects but with smaller efficiency. We show that the large shock found in observations of SQ is most likely the result of a collision of the galaxy NGC 7318b with the IGM. This large group-wide shock is clearly visible in the X-ray emission and synchrotron intensity within the simulations of both SQ models. The order of magnitude of the observed synchrotron emission within the shock front is slightly better reproduced by the SQ model based on Renaud et al., whereas the distribution and structure of the synchrotron emission is better reproduced by the SQ model based on Hwang et al..Comment: 20 pages, 15 figures, accepted to MNRA

High-Order Numerical Integration on Domains Bounded by Intersecting Level Sets

We present a high-order method that provides numerical integration on volumes, surfaces, and lines defined implicitly by two smooth intersecting level sets. To approximate the integrals, the method maps quadrature rules defined on hypercubes to the curved domains of the integrals. This enables the numerical integration of a wide range of integrands since integration on hypercubes is a well known problem. The mappings are constructed by treating the isocontours of the level sets as graphs of height functions. Numerical experiments with smooth integrands indicate a high-order of convergence for transformed Gauss quadrature rules on domains defined by polynomial, rational, and trigonometric level sets. We show that the approach we have used can be combined readily with adaptive quadrature methods. Moreover, we apply the approach to numerically integrate on difficult geometries without requiring a low-order fallback method