Power law velocity fluctuations due to inelastic collisions in numerically simulated vibrated bed of powder}

Distribution functions of relative velocities among particles in a vibrated bed of powder are studied both numerically and theoretically. In the solid phase where granular particles remain near their local stable states, the probability distribution is Gaussian. On the other hand, in the fluidized phase, where the particles can exchange their positions, the distribution clearly deviates from Gaussian. This is interpreted with two analogies; aggregation processes and soft-to-hard turbulence transition in thermal convection. The non-Gaussian distribution is well-approximated by the t-distribution which is derived theoretically by considering the effect of clustering by inelastic collisions in the former analogy.Comment: 7 pages, using REVTEX (Figures are inculded in text body) %%%Replacement due to rivision (Europhys. Lett., in press)%%

Temporal patterns of gene expression via nonmetric multidimensional scaling analysis

Motivation: Microarray experiments result in large scale data sets that require extensive mining and refining to extract useful information. We have been developing an efficient novel algorithm for nonmetric multidimensional scaling (nMDS) analysis for very large data sets as a maximally unsupervised data mining device. We wish to demonstrate its usefulness in the context of bioinformatics. In our motivation is also an aim to demonstrate that intrinsically nonlinear methods are generally advantageous in data mining. Results: The Pearson correlation distance measure is used to indicate the dissimilarity of the gene activities in transcriptional response of cell cycle-synchronized human fibroblasts to serum [Iyer et al., Science vol. 283, p83 (1999)]. These dissimilarity data have been analyzed with our nMDS algorithm to produce an almost circular arrangement of the genes. The temporal expression patterns of the genes rotate along this circular arrangement. If an appropriate preparation procedure may be applied to the original data set, linear methods such as the principal component analysis (PCA) could achieve reasonable results, but without data preprocessing linear methods such as PCA cannot achieve a useful picture. Furthermore, even with an appropriate data preprocessing, the outcomes of linear procedures are not as clearcut as those by nMDS without preprocessing.Comment: 11 pages, 6 figures + online only 2 color figures, submitted to Bioinformatic