Identifying short motifs by means of extreme value analysis

The problem of detecting a binding site -- a substring of DNA where transcription factors attach -- on a long DNA sequence requires the recognition of a small pattern in a large background. For short binding sites, the matching probability can display large fluctuations from one putative binding site to another. Here we use a self-consistent statistical procedure that accounts correctly for the large deviations of the matching probability to predict the location of short binding sites. We apply it in two distinct situations: (a) the detection of the binding sites for three specific transcription factors on a set of 134 estrogen-regulated genes; (b) the identification, in a set of 138 possible transcription factors, of the ones binding a specific set of nine genes. In both instances, experimental findings are reproduced (when available) and the number of false positives is significantly reduced with respect to the other methods commonly employed.Comment: 6 pages, 5 figure

Linear and nonlinear post-processing of numerically forecasted surface temperature

International audienceIn this paper we test different approaches to the statistical post-processing of gridded numerical surface air temperatures (provided by the European Centre for Medium-Range Weather Forecasts) onto the temperature measured at surface weather stations located in the Italian region of Puglia. We consider simple post-processing techniques, like correction for altitude, linear regression from different input parameters and Kalman filtering, as well as a neural network training procedure, stabilised (i.e. driven into the absolute minimum of the error function over the learning set) by means of a Simulated Annealing method. A comparative analysis of the results shows that the performance with neural networks is the best. It is encouraging for systematic use in meteorological forecast-analysis service operations

Autosomal-dominant myopia associated to a novel P4HA2 missense variant and defective collagen hydroxylation

We recently described a complex multisystem syndrome in which mild-moderate myopia segregated as an independent trait. A plethora of genes has been related to sporadic and familial myopia. More recently, in Chinese patients severe myopia (MYP25, OMIM:617238) has been linked to mutations in P4HA2 gene. Seven family members complaining of reduced distance vision especially at dusk underwent complete ophthalmological examination. Whole-exome sequencing was performed to identify the gene responsible for myopia in the pedigree. Moderate myopia was diagnosed in the family which was associated to the novel missense variant c.1147A > G p.(Lys383Glu) in the prolyl 4-hydroxylase,alpha-polypeptide 2 (P4HA2) gene, which catalyzes the formation of 4-hydroxyproline residues in the collagen strands. In vitro studies demonstrated P4HA2 mRNA and protein reduced expression level as well as decreased collagen hydroxylation and deposition in mutated fibroblast primary cultures compared to healthy cell lines. This study suggests that P4HA2 mutations may lead to myopic axial elongation of eyeball as a consequence of quantitative and structural alterations of collagen. This is the first confirmatory study which associates a novel dominant missense variant in P4HA2 with myopia in Caucasian patients. Further studies in larger cohorts are advisable to fully clarify genotype-phenotype correlations.We recently described a complex multisystem syndrome in which mild-moderate myopia segregated as an independent trait. A plethora of genes has been related to sporadic and familial myopia. More recently, in Chinese patients severe myopia (MYP25, OMIM:617238) has been linked to mutations in P4HA2 gene. Seven family members complaining of reduced distance vision especially at dusk underwent complete ophthalmological examination. Whole-exome sequencing was performed to identify the gene responsible for myopia in the pedigree. Moderate myopia was diagnosed in the family which was associated to the novel missense variant c.1147A > G p.(Lys383Glu) in the prolyl 4-hydroxylase,alpha-polypeptide 2 (P4HA2) gene, which catalyzes the formation of 4-hydroxyproline residues in the collagen strands. In vitro studies demonstrated P4HA2 mRNA and protein reduced expression level as well as decreased collagen hydroxylation and deposition in mutated fibroblast primary cultures compared to healthy cell lines. This study suggests that P4HA2 mutations may lead to myopic axial elongation of eyeball as a consequence of quantitative and structural alterations of collagen. This is the first confirmatory study which associates a novel dominant missense variant in P4HA2 with myopia in Caucasian patients. Further studies in larger cohorts are advisable to fully clarify genotype-phenotype correlations

Convergence Theorems for the Kohonen Feature Mapping Algorithms with VLRPs

Abstract--The convergence of the Kohonen feature mapping algorithm with vanishing learning rate parameters (VLRPs) is considered, which includes the simple competitive learning algorithm as a special case. A few examples show that the learning fails to converge to "global minima, " in general. Then, we present a novel approach which enables us to find out a new family of VLRPs such that the corresponding learning algorithm converges to the set of "global minima " with probability one. The new VLRPs is a generalization of the well-known rate parameters used in the simulated annealing. A numerical example is also included to confirm our theoretical approach. We believe that this discovery is of importance for a large class of learning algorithms in neural networks and statistics. Keywords--Kohonen feature mapping algorithm, Supermartingale, Global minima, Stochastic differential equation, Vanishing learning rate parameters (VLRPs)

THE SLLN FOR THE FREE-ENERGY OF A CLASS OF NEURAL NETWORKS

We first show the self-averaging property in the sense of almost sure convergence for the free energy of the spin glass model and of the Hopfield model with an infinite number of patterns. Then we prove the strong law of large number(SLLN) of the free energy in the Hopfield type model with finite number of patterns. Here the Hopfield type model implies that the interaction among neurons is higher order, the patterns embedded in the neural network are assumed to be independent random variables rather than only taking value +1 and -1 and i.i.d. The model with weighted patterns is certainly included in. The SLLN of the free energy in the Little model is proved. The convergence rate for above two cases is also estimated

Convergence theorems for a class of learning algorithms with VLRPs

We first consider the convergence of the simple competitive learning with vanishing learning rate parameters (VLRPs), Examples show that even in this setting the learning fails to converge in general, This brings us to consider the following problem, to find out a family of VLRPs such that an algorithm with the VLRPs reaches the global minima with probability one, Here, we present an approach different from stochastic approximation theory and determine a new family of VLRPs such that the corresponding learning algorithm gets out of the metastable states with probability one, In the literature it is generally believed that a family of reasonable VLRPs is of the order of 1/t(alpha) for 1/2 < alpha less than or equal to 1, where t is the time, However, we find that a family of VLRPs which makes the algorithm go to the global minima should be between 1/log t and 1/root log t