Karl Entacher

Bad subsequences of well-known linear congruential pseudorandom number generators

We present a spectral test analysis of full-period subsequences with small step sizes generated by well-known linear congruential pseudorandom number generators. Subsequences may occur in certain simulation problems or as a method to get parallel streams of pseudorandom numbers. Applying the spectral test, it is possible to find bad subsequences with small step sizes for almost all linear pseudorandom number generators currently in use.

Quasi-Monte Carlo methods for numerical integration of multivariate Haar series II

The present paper contains a comparison of different classes of multivariate Haar series that have been studied with respect to numerical integration, new properties ofEsα-classes and numerical results.

Linear Congruential Generators for Parallel Monte Carlo: the Leap-Frog Case

In this paper we consider parallel streams of pseudorandom numbers (PRNs) which are obtained by splitting linear congruential generators (LCGs) using the leap-frog technique. We employ the spectral test to compute an a priori figure of merit which rates the amount of correlation that is present in such sequences for given step size and dimension. It is shown that for some widely used LCGs there exist practically relevant splitting parameters such that the according parallel streams have poor quality. As can be seen from a sample Monte Carlo integration study, these theoretical findings have high practical importance.

Linear and inversive pseudorandom numbers for parallel and distributed simulation

We discuss the use and possible abuse of linear and inversive pseudorandom numbers (PRNs) in parallel and distributed environments. After an investigation of properties of PRNs which determine how these may be applied in such environments, we introduce a software package which provides a unified and easy to use approach to the generating and handling of parallel streams of such PRNs. Experimental results are conducted which describe the features of the software package and compare the performance of two selected types of pseudorandom number generators.

Parallel streams of linear random numbers in the spectral test

This paper reports analyses of subsequences of linear congruential pseudorandom numbers by means of the spectral test. Such subsequences occur in particular simulation setups or as methods to obtain parallel streams of pseudorandom numbers for parallel and distributed simulation. Especially in the latter case, two kinds of substreams are of special interest: lagged random numbers with step sizes k, and consecutive streams of random numbers of length l. We show how to analyze correlations within and between lagged subsequences with arbitrary step sizes k. Analyzing consecutive streams with the spectral test is related to the well-known long-range correlation analysis of linear congruential generators. Whereas the latter was carried out to show correlations between pairs of processors only, the spectral test provides a convenient method to study correlations between larger numbers of parallel streams as well.

Towards an Automated Generation of Tree Ring Profiles from CT-Images

In this paper we present an efficient algorithm for the fully automatic creation of tree ring profiles from CT-images that show the cross-section of a piece of wood. This kind of pattern is needed in wood technology for annual ring feature detection in general and in the field of dendrochronology which concerns itself with the dating of past events through the study of tree ring growth.

Parallel Random Number Generation: Long-Range Correlations Among Multiple Processors

We use an empirical study based on simple Monte Carlo integrations to exhibit the well known long-range correlations between linear congruential random numbers. In contrast to former studies, our long-range correlation test is carried out to assess more than only two parallel streams. In addition we perform our test also with explicit inversive generators which from the theoretical point of view have to be stable against long-range correlations.

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.

Multi-patient finite element simulation of keeled versus pegged glenoid implant designs in shoulder arthroplasty

This study investigates the mechanical behaviour of keeled and pegged implant designs used in shoulder arthroplasty for the first time using multiple 3D models. Thus, this study should provide valuable insights into the preferable use of either of these two controversial implant designs. Three-dimensional models of a scapula were derived from the CT scans of five patients, and an inter-patient-specific finite element analysis with special attention to bone density and boundary conditions was carried out. A distinct decrease in the investigated parameters was evident with the pegged implant in all of the patients, specifically for the implant and the bone cement. The relevance of the stress reduction within the bone is minor, whereas the reduction in the stress of the bone cement contributes to an increase in the bone cement survival. The particular construction of the pegged implant provides better stability and therefore supports bone ingrowth. The large variations between the patients show the necessity of patient-specific simulations and the use of multiple models to derive valuable results. In the conducted inter-patient-specific FEA, the pegged glenoid implants were found to exhibit superior behaviour compared with keeled implants. The results confirm the general clinical findings and demonstrate the FEA as a valuable tool in prosthetic and orthopaedic problems.

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.