Antonio Díaz Ramos

A spectral sequence for fusion systems

We build a spectral sequence converging to the cohomology of a fusion system with a strongly closed subgroup. This spectral sequence is related to the Lyndon-Hochschild-Serre spectral sequence and coincides with it for the case of an extension of groups. Nevertheless, the new spectral sequence applies to more general situations like finite simple groups with a strongly closed subgroup and exotic fusion systems with a strongly closed subgroup. We prove an analogue of a result of Stallings in the context of fusion preserving homomorphisms and deduce Tates p-nilpotency criterion as a corollary.

How can functional annotations be derived from profiles of phenotypic annotations

BackgroundLoss-of-function phenotypes are widely used to infer gene function using the principle that similar phenotypes are indicative of similar functions. However, converting phenotypic to functional annotations requires careful interpretation of phenotypic descriptions and assessment of phenotypic similarity. Understanding how functions and phenotypes are linked will be crucial for the development of methods for the automatic conversion of gene loss-of-function phenotypes to gene functional annotations.ResultsWe explored the relation between cellular phenotypes from RNAi-based screens in human cells and gene annotations of cellular functions as provided by the Gene Ontology (GO). Comparing different similarity measures, we found that information content-based measures of phenotypic similarity were the best at capturing gene functional similarity. However, phenotypic similarities did not map to the Gene Ontology organization of gene function but to functions defined as groups of GO terms with shared gene annotations.ConclusionsOur observations have implications for the use and interpretation of phenotypic similarities as a proxy for gene functions both in RNAi screen data analysis and curation and in the prediction of disease genes.

Grid topologies for the self-organizing map

The original Self-Organizing Feature Map (SOFM) has been extended in many ways to suit different goals and application domains. However, the topologies of the map lattice that we can found in literature are nearly always square or, more rarely, hexagonal. In this paper we study alternative grid topologies, which are derived from the geometrical theory of tessellations. Experimental results are presented for unsupervised clustering, color image segmentation and classification tasks, which show that the differences among the topologies are statistically significant in most cases, and that the optimal topology depends on the problem at hand. A theoretical interpretation of these results is also developed.

Cohomology of p-groups of nilpotency class smaller than p

Abstract Let p be a prime number, let d be an integer and let G be a d-generated finite p-group of nilpotency class smaller than p. Then the number of possible isomorphism types for the mod p cohomology algebra H * ⁢ ( G ; 𝔽 p ) {H^{*}(G;{\mathbb{F}}_{p})} is bounded in terms of p and d.