Note on homology of expanding foliations

This note contains some remarks about the homologies that can be associated to a foliation which is invariant and uniformly expanded by a diffeomorphism. We construct a family of 'dynamical' closed currents supported on the foliation which help us relate the geometric volume growth of the leaves under the diffeomorphism with the map induced on homology in the case when these currents have nonzero homology.

Sobolev mappings, degree, homotopy classes and rational homology spheres

"Vegeu el resum a l'inici del document del fitxer adjunt."

On homology searches by protein Blast and the characterization of the age of genes

Background: It has been shown in a variety of organisms, including mammals, that genes that appeared recently in evolution, for example orphan genes, evolve faster than older genes. Low functional constraints at the time of origin of novel genes may explain these results. However, this observation has been recently attributed to an artifact caused by the inability of Blast to detect the fastest genes in different eukaryotic genomes. Distinguishing between these two possible explanations would be of great importance for any studies dealing with the taxon distribution of proteins and the origin of novel genes. Results: Here we used simulations of protein sequences to examine the capacity of Blast to detect proteins of diverse evolutionary rates in the different species of an eukaryotic phylogenetic tree that included metazoans, fungi and plants. We simulated the evolution of protein genes with the same evolutionary rates than those observed in functional mammalian genes and with among-site rate heterogeneity. Under these conditions, we found that only a very small percentage of simulated ancestral eukaryotic proteins was affected by the Blast artifact. We show that the good detectability of Blast is due to the heterogeneity of protein evolutionary rates at different sites, since only a small conserved motif in a sequence suffices to detect its homologues. Our results indicate that Blast, at least when applied within eukaryotes, only misses homologues of extremely fast-evolving sequences, which are rare in the mammalian genome, as well as sequences evolving homogeneously or pseudogenes.Conclusion: Although great care should be exercised in the recognition of remote homologues, most functional mammalian genes can be detected in eukaryotic genomes by Blast. That is, the majority of functional mammalian genes are not as fast as for not being detected in other metazoans, fungi or plants, if they had been present in these organisms. Thus, the correlation previously found between age and rate seems not to be due to a pure Blast artifact, at least for mammals. This may have important implications to understand the mechanisms by which novel genes originate.

T-Coffee: a web server for the multiple sequence alignment of protein and RNA sequences using structural information and homology extension

This article introduces a new interface for T-Coffee, a consistency-based multiple sequence alignment program. This interface provides an easy and intuitive access to the most popular functionality of the package. These include the default T-Coffee mode for protein and nucleic acid sequences, the M-Coffee mode that allows combining the output of any other aligners, and template-based modes of T-Coffee that deliver high accuracy alignments while using structural or homology derived templates. These three available template modes are Expresso for the alignment of protein with a known 3D-Structure, R-Coffee to align RNA sequences with conserved secondary structures and PSI-Coffee to accurately align distantly related sequences using homology extension. The new server benefits from recent improvements of the T-Coffee algorithm and can align up to 150 sequences as long as 10 000 residues and is available from both http://www.tcoffee.org and its main mirror http://tcoffee.crg.cat.

Intersection Pairing and intersection motive of surfaces

We construct the Chow motive modelling intersection co-homology of a proper surface. We then study its functoriality properties. Using Murre's decompositions of the motive of a desingularization into KÄunneth components [Mr1], we show that such decompositions exist also for the intersection motive.

The entropy conjecture for partially hyperbolic diffeomorphisms with 1-D center

We prove that if f is a partially hyperbolic diffeomorphism on the compact manifold M with one dimensional center bundle, then the logarithm of the spectral radius of the map induced by f on the real homology groups of M is smaller or equal to the topological entropy of f. This is a particular case of the Shub's entropy conjecture, which claims that the same conclusion should be true for any C1 map on any compact manifold.

Homotopy Batalin-Vilkovisky algebras

This paper provides an explicit cofibrant resolution of the operad encoding Batalin-Vilkovisky algebras. Thus it defines the notion of homotopy Batalin-Vilkovisky algebras with the required homotopy properties. To define this resolution we extend the theory of Koszul duality to operads and properads that are defined by quadratic and linear relations. The operad encoding Batalin-Vilkovisky algebras is shown to be Koszul in this sense. This allows us to prove a Poincaré-Birkhoff-Witt Theorem for such an operad and to give an explicit small quasi-free resolution for it. This particular resolution enables us to describe the deformation theory and homotopy theory of BV-algebras and of homotopy BV-algebras. We show that any topological conformal field theory carries a homotopy BV-algebra structure which lifts the BV-algebra structure on homology. The same result is proved for the singular chain complex of the double loop space of a topological space endowed with an action of the circle. We also prove the cyclic Deligne conjecture with this cofibrant resolution of the operad BV. We develop the general obstruction theory for algebras over the Koszul resolution of a properad and apply it to extend a conjecture of Lian-Zuckerman, showing that certain vertex algebras have an explicit homotopy BV-algebra structure.

Selección de péptidos sintéticos del Virus de la Hepatitis G (GBV-C/HGV) inhibidores del Péptido de Fusión HIV-I

El GB virus C (GBV-C) o virus de l'hepatitis G (HGV) es un virus format per una única cadena de RNA que pertany a la familia Flaviviridae. En els últims anys, s'han publicat nombrosos treballs en els quals s'associa la coinfecció del GBV-C i del virus de la immunodeficiència humana (VIH) amb una menor progressió de l'esmentada malaltia així com amb una major supervivència dels pacients una vegada que la SIDA s'ha desenvolupat. El mecanisme pel qual el virus GBV-C/HGV exerceix un “efecte protector” en els pacients amb VIH encara no està descrit. L’estudi de la interacció entre els virus GBVC/HGV i VIH podria donar lloc al desenvolupament de nous agents terapèutics per al tractament de la SIDA.Treballs recents mostren com la capacitat inhibitòria del virus del GBV-C/HGV és deguda a la seva glicoproteina estructural E2. S’ha vist que aquesta proteina seria capaç d’inhibir la primera fase de replicació de VIH, així com la unió i la fusió amb les membranes cel•lulars. Sobre la base d’aquests estudis, l’objectiu d’aquest treball ha estat seleccionar inhibidors del pèptid de fusió del VIH utilitzant pèptids sintètics de la proteina E2 del GBV-C/HGV. El treball realitzat ha consistit en estudiar, utilitzant assajos biofísics de leakage i de lipid mixing, la capacitat dels pèptids de la proteina estructural del virus del GBV-C/HGV per inhibir la interacció i el procés de desestabilització de membranes induïdes pel pèptid de fusió de la glicoproteina de l’embolcall, GP41, del VIH. Aquests assajos, com es descriu en treballs anteriors, han resultat útils per a la selecció i la identificació de compostos amb activitat específica anti-GP41. Es pot afirmar que efectivament els pèptids seleccionats de la proteina E2 del virus del GBV-C/HGV inhibeixen l’activitat del pèptid de fusió del VIH probablement com a consequència d’un canvi conformacional en aquest darrer.

Homologia de Lawson i descens

La meva recerca en els tres anys de gaudiment de beca s'ha centrat en l'estudi de teories semitopològiques definides a través d'espais de cicles algebraics, introduïts per Friedlander i Lawson. Hem estudiat propietats de descens d'aquestes teories i hem construït una successió espectral que calcula explícitament la cohomologia mòrfica d'una varietat tòrica. D'altra banda, estem treballant en l'estudi de propietats d'invariància homotòpica per la cohomologia mòrfica, així com en l'estructura algebraica dels grups d'homologia de Lawson.

Human synthetic lethal inference as potential anti-cancer target gene detection

Background: Two genes are called synthetic lethal (SL) if mutation of either alone is not lethal, but mutation of both leads to death or a significant decrease in organism's fitness. The detection of SL gene pairs constitutes a promising alternative for anti-cancer therapy. As cancer cells exhibit a large number of mutations, the identification of these mutated genes' SL partners may provide specific anti-cancer drug candidates, with minor perturbations to the healthy cells. Since existent SL data is mainly restricted to yeast screenings, the road towards human SL candidates is limited to inference methods. Results: In the present work, we use phylogenetic analysis and database manipulation (BioGRID for interactions, Ensembl and NCBI for homology, Gene Ontology for GO attributes) in order to reconstruct the phylogenetically-inferred SL gene network for human. In addition, available data on cancer mutated genes (COSMIC and Cancer Gene Census databases) as well as on existent approved drugs (DrugBank database) supports our selection of cancer-therapy candidates.Conclusions: Our work provides a complementary alternative to the current methods for drug discovering and gene target identification in anti-cancer research. Novel SL screening analysis and the use of highly curated databases would contribute to improve the results of this methodology.

Gene finding in the chicken genome

Background: Despite the continuous production of genome sequence for a number of organisms,reliable, comprehensive, and cost effective gene prediction remains problematic. This is particularlytrue for genomes for which there is not a large collection of known gene sequences, such as therecently published chicken genome. We used the chicken sequence to test comparative andhomology-based gene-finding methods followed by experimental validation as an effective genomeannotation method.Results: We performed experimental evaluation by RT-PCR of three different computational genefinders, Ensembl, SGP2 and TWINSCAN, applied to the chicken genome. A Venn diagram wascomputed and each component of it was evaluated. The results showed that de novo comparativemethods can identify up to about 700 chicken genes with no previous evidence of expression, andcan correctly extend about 40% of homology-based predictions at the 5' end.Conclusions: De novo comparative gene prediction followed by experimental verification iseffective at enhancing the annotation of the newly sequenced genomes provided by standardhomology-based methods.

Homotopy Batalin-Vilkovisky algebras

This paper provides an explicit cofibrant resolution of the operad encoding Batalin-Vilkovisky algebras. Thus it defines the notion of homotopy Batalin-Vilkovisky algebras with the required homotopy properties. To define this resolution we extend the theory of Koszul duality to operads and properads that are defind by quadratic and linear relations. The operad encoding Batalin-Vilkovisky algebras is shown to be Koszul in this sense. This allows us to prove a Poincare-Birkhoff-Witt Theorem for such an operad and to give an explicit small quasi-free resolution for it. This particular resolution enables us to describe the deformation theory and homotopy theory of BV-algebras and of homotopy BV-algebras. We show that any topological conformal field theory carries a homotopy BV-algebra structure which lifts the BV-algebra structure on homology. The same result is proved for the singular chain complex of the double loop space of a topological space endowed with an action of the circle. We also prove the cyclic Deligne conjecture with this cofibrant resolution of the operad BV. We develop the general obstruction theory for algebras over the Koszul resolution of a properad and apply it to extend a conjecture of Lian-Zuckerman, showing that certain vertex algebras have an explicit homotopy BV-algebra structure.

André spectral sequences for Baues-Wirsching cohomology of categories

We construct spectral sequences in the framework of Baues-Wirsching cohomology and homology for functors between small categories and analyze particular cases including Grothendieck fibrations. We also give applications to more classical cohomology and homology theories including Hochschild-Mitchell cohomology and those studied before by Watts, Roos, Quillen and others