Onion Curve: A Space Filling Curve with Near-Optimal Clustering

Space filling curves (SFCs) are widely used in the design of indexes for spatial and temporal data. Clustering is a key metric for an SFC, that measures how well the curve preserves locality in moving from higher dimensions to a single dimension. We present the {\em onion curve}, an SFC whose clustering performance is provably close to optimal for the cube and near-cube shaped query sets, irrespective of the side length of the query. We show that in contrast, the clustering performance of the widely used Hilbert curve can be far from optimal, even for cube-shaped queries. Since the clustering performance of an SFC is critical to the efficiency of multi-dimensional indexes based on the SFC, the onion curve can deliver improved performance for data structures involving multi-dimensional data.Comment: The short version is published in ICDE 1

Computations of Multiphase Fluid Flows Using Marker-Based Adaptive, Multilevel Cartesian Grid Method

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76194/1/AIAA-2007-336-338.pd

Computation of Lebesgue’s Space-Filling Curve

The means of realizing or approximating the Lebesgue space-filling curve (SFC) with binary arithmetic on a uniformly spaced binary grid are not obvious, one problem being its formulation in terms of ternary representations; that impediment can be overcome via use of a binary-oriented Cantor set.  A second impediment, namely the Devil’s Staircase feature, also created by the role of the Cantor set, can be overcome via the definition of a “working inverse”, thereby providing means of achieving compatibility with such a grid. The results indicate an alternative way to proceed, in realizing an approximation to Lebesgue’s SFC, which circumvents any complication raised by Cantor sets and is compatible with binary and integer arithmetic. Well-known constructions such as the z-curve or Morton order, sometimes considered in association with Lebesgue’s SFC, are treated as irrelevant

Schnelle Löser für partielle Differentialgleichungen

The workshop Schnelle Löser für partielle Differentialgleichungen, organised by Randolph E. Bank (La Jolla), Wolfgang Hackbusch(Leipzig), Gabriel Wittum (Heidelberg) was held May 22nd - May 28th, 2005. This meeting was well attended by 47 participants with broad geographic representation from 9 countries and 3 continents. This workshop was a nice blend of researchers with various backgrounds

SFour: A Protocol for Cryptographically Secure Record Linkage at Scale

The prevalence of various (and increasingly large) datasets presents the challenging problem of discovering common entities dispersed across disparate datasets. Solutions to the private record linkage problem (PRL) aim to enable such explorations of datasets in a secure manner. A two-party PRL protocol allows two parties to determine for which entities they each possess a record (either an exact matching record or a fuzzy matching record) in their respective datasets — without revealing to one another information about any entities for which they do not both possess records. Although several solutions have been proposed to solve the PRL problem, no current solution offers a fully cryptographic security guarantee while maintaining both high accuracy of output and subquadratic runtime efficiency. To this end, we propose the first known efficient PRL protocol that runs in subquadratic time, provides high accuracy, and guarantees cryptographic security

Molecular Dynamics Simulation of Open Systems far from Equilibrium

Open systems have been the subject of interest in science for a long time because many complex molecular systems are open systems embedded in a large environment that serves as a reservoir of particles and energy. In order to test the methods' accuracy and applicability, simulations of open systems exposed to different non-equilibrium conditions are performed, and the results are compared to the results of full resolution simulations and the range of applicability of the method is investigated. Furthermore, a study on fluid flow through regular bead packings as a model of a porous medium was conducted to investigate the flow--pressure relation in these media and its dependence on geometry and porosity of the medium. These simulations are also done with AdResS for extension to open boundaries. The results presented in this thesis help to understand the capabilities of our simulation method to simulate open systems out of equilibrium. We found that by choosing proper boundary conditions and reservoir states, simulations of open systems embedded in large reservoirs of particles and energy can be done with low computational cost. The findings of this thesis pave the way for future research on applications in which a more realistic system is subjected to non-equilibrium conditions and flows of heat and mass