Structural optimization by generalized, multilevel decomposition

The developments toward a general multilevel optimization capability and results for a three-level structural optimization are described. The method partitions a structure into a number of substructuring levels where each substructure corresponds to a subsystem in the general case of an engineering system. The method is illustrated by a portal framework that decomposes into individual beams. Each beam is a box that can be further decomposed into stiffened plates. Substructuring for this example spans three different levels: (1) the bottom level of finite elements representing the plates; (2) an intermediate level of beams treated as substructures; and (3) the top level for the assembled structure. The three-level case is now considered to be qualitatively complete

The strongest gravitational lenses: I. The statistical impact of cluster mergers

For more than a decade now, it has been controversial whether or not the high rate of giant gravitational arcs and the largest observed Einstein radii are consistent with the standard cosmological model. Recent studies indicate that mergers provide an efficient mechanism to substantially increase the strong-lensing efficiency of individual clusters. Based on purely semi-analytic methods, we investigated the statistical impact of cluster mergers on the distribution of the largest Einstein radii and the optical depth for giant gravitational arcs of selected cluster samples. Analysing representative all-sky realizations of clusters at redshifts z < 1 and assuming a constant source redshift of z_s = 2.0, we find that mergers increase the number of Einstein radii above 10 arcsec (20 arcsec) by ~ 35 % (~ 55 %). Exploiting the tight correlation between Einstein radii and lensing cross sections, we infer that the optical depth for giant gravitational arcs with a length-to-width ratio > 7.5 of those clusters with Einstein radii above 10 arcsec (20 arcsec) increases by ~ 45 % (85 %). Our findings suggest that cluster mergers significantly influence in particular the statistical lensing properties of the strongest gravitational lenses. We conclude that semi-analytic studies must inevitably take these events into account before questioning the standard cosmological model on the basis of the largest observed Einstein radii and the statistics of giant gravitational arcs.Comment: 23 pages, 18 figures; accepted for publication in Astronomy and Astrophysics; v2: minor corrections (added clarifying comments; added Fig. 19) to match the accepted versio

Domain discovery method for topological profile searches in protein structures

We describe a method for automated domain discovery for topological profile searches in protein structures. The method is used in a system TOPStructure for fast prediction of CATH classification for protein structures (given as PDB files). It is important for profile searches in multi-domain proteins, for which the profile method by itself tends to perform poorly. We also present an O(C(n)k +nk2) time algorithm for this problem, compared to the O(C(n)k +(nk)2) time used by a trivial algorithm (where n is the length of the structure, k is the number of profiles and C(n) is the time needed to check for a presence of a given motif in a structure of length n). This method has been developed and is currently used for TOPS representations of protein structures and prediction of CATH classification, but may be applied to other graph-based representations of protein or RNA structures and/or other prediction problems. A protein structure prediction system incorporating the domain discovery method is available at http://bioinf.mii.lu.lv/tops/