New Tetrahedral Global Minimum for the 98-atom Lennard-Jones Cluster

A new atomic cluster structure corresponding to the global minimum of the 98-atom Lennard-Jones cluster has been found using a variant of the basin-hopping global optimization algorithm. The new structure has an unusual tetrahedral symmetry with an energy of -543.665361, which is 0.022404 lower than the previous putative global minimum. The new LJ_98 structure is of particular interest because its tetrahedral symmetry establishes it as one of only three types of exceptions to the general pattern of icosahedral structural motifs for optimal LJ microclusters. Similar to the other exceptions the global minimum is difficult to find because it is at the bottom of a narrow funnel which only becomes thermodynamically most stable at low temperature.Comment: 3 pages, 2 figures, revte

Global Optimization by Basin-Hopping and the Lowest Energy Structures of Lennard-Jones Clusters Containing up to 110 Atoms

We describe a global optimization technique using `basin-hopping' in which the potential energy surface is transformed into a collection of interpenetrating staircases. This method has been designed to exploit the features which recent work suggests must be present in an energy landscape for efficient relaxation to the global minimum. The transformation associates any point in configuration space with the local minimum obtained by a geometry optimization started from that point, effectively removing transition state regions from the problem. However, unlike other methods based upon hypersurface deformation, this transformation does not change the global minimum. The lowest known structures are located for all Lennard-Jones clusters up to 110 atoms, including a number that have never been found before in unbiased searches.Comment: 8 pages, 3 figures, revte

GibbsST: a Gibbs sampling method for motif discovery with enhanced resistance to local optima

BACKGROUND: Computational discovery of transcription factor binding sites (TFBS) is a challenging but important problem of bioinformatics. In this study, improvement of a Gibbs sampling based technique for TFBS discovery is attempted through an approach that is widely known, but which has never been investigated before: reduction of the effect of local optima. RESULTS: To alleviate the vulnerability of Gibbs sampling to local optima trapping, we propose to combine a thermodynamic method, called simulated tempering, with Gibbs sampling. The resultant algorithm, GibbsST, is then validated using synthetic data and actual promoter sequences extracted from Saccharomyces cerevisiae. It is noteworthy that the marked improvement of the efficiency presented in this paper is attributable solely to the improvement of the search method. CONCLUSION: Simulated tempering is a powerful solution for local optima problems found in pattern discovery. Extended application of simulated tempering for various bioinformatic problems is promising as a robust solution against local optima problems