Thomas Schell

Defects in parallel Monte Carlo and quasi-Monte Carlo integration using the leap-frog technique

Currently, the most efficient numerical techniques for evaluating high-dimensional integrals are based on Monte Carlo and quasi-Monte Carlo techniques. These tasks require a significant amount of computation and are therefore often executed on parallel computer systems. In order to keep the communication amount within a parallel system to a minimum, each processing element (PE) requires its own source of integration nodes. Therefore, techniques for using separately initialized and disjoint portions of a given point set on a single PE are classically employed. Using the so-called substreams may lead to dramatic errors in the results under certain circumstances. In this work, we compare the possible defects employing leaped quasi-Monte Carlo and Monte Carlo substreams. Apart from comparing the magnitude of the observed integration errors we give an overview under which circumstances (i.e. parallel programming models) such errors can occur.

Efficient lattice assessment for LCG and GLP parameter searches

In the present paper we show how to speed up lattice parameter searches for Monte Carlo and quasi-Monte Carlo node sets. The classical measure for such parameter searches is the spectral test which is based on a calculation of the shortest nonzero vector in a lattice. Instead of the shortest vector we apply an approximation given by the LLL algorithm for lattice basis reduction. We empirically demonstrate the speed-up and the quality loss obtained by the LLL reduction, and we present important applications for parameter selections.

Optimization and assessment of wavelet packet decompositions with evolutionary computation

In image compression, the wavelet transformation is a state-of-the-art component. Recently, wavelet packet decomposition has received quite an interest. A popular approach for wavelet packet decomposition is the near-best-basis algorithm using nonadditive cost functions. In contrast to additive cost functions, the wavelet packet decomposition of the near-best-basis algorithm is only suboptimal. We apply methods from the field of evolutionary computation (EC) to test the quality of the near-best-basis results. We observe a phenomenon: the results of the near-best-basis algorithm are inferior in terms of cost-function optimization but are superior in terms of rate/distortion performance compared to EC methods.

Mixed size tournament selection

Abstract In genetic algorithms, tournament schemes are often applied as selection operators. The advantage is simplicity and efficiency. On the other hand, major deficiencies related to tournament selection are the coarse scaling of the selection pressure and the poor sampling accuracy. We introduce a new variant of tournament selection which provides an adjustable probability distribution, a fine-tuning facility for the selection pressure and an improved sampling accuracy at the cost of a minimal increase of the complexity and with almost no loss of efficiency.

Optimization of random number generators: efficient search for high-quality LCGs

In this work we will discuss how to optimize multipliers for prime-modulus linear congruential pseudo-random number generators with respect to the spectral test. The optimization efficiency has shown itself to be strongly dependent on the encoding strategy for the multipliers within the random search process. The optimal encoding technique will be demonstrated to be a representation in terms of powers of a primitive root. A sample distributed large-scale parameter search for subsequence stable LCGs will be conducted using the developed concepts.

Bad Lattice Points

We introduce and discuss the term “bad lattice points” which can be seen as a counterpart to the method of good lattice points for Monte Carlo and quasi-Monte Carlo integration. We show several examples of the occurrence of bad lattice points in the latter fields and perform a computer search for such point sets.

Measures of Uniform Distribution in Wavelet Based Image Compression

In still image compression, the wavelet transformation is a state-of-the-art tool. Recently, wavelet packet decomposition has received quite an interest. One popular approach for wavelet packet decomposition is the near best basis algorithm of Taswell. We extend his set of non-additive cost-functions by measures of uniform distribution, i.e. discrepancy and probability distribution distance. In contrast to usual application of the latter measures, we are interested in point-sets which are maximally not uniformly distributed to enhance entropy-encoding.

Application of a Genetic Algorithm to the refinement of complex Mössbauer spectra

The present contribution includes the results of the application of a program consisting of a genetic algorithm routine and a conventional refinement part (“hybrid method’) for the evaluation of Mossbauer spectra published elsewhere. The saving of total evaluation time compared with conventional refinement routines is very high due to the rapid finding of adequate starting parameters. Contrary to previous work on a similar topic our algorithm provides solutions of the combined interaction Hamiltonian with a minimum of conventional input data. The reader is referred to a web-address where he may test the routine on his own.