Borcherds products and arithmetic intersection theory on Hilbert modular surfaces

We prove an arithmetic version of a theorem of Hirzebruch and Zagier saying that Hirzebruch-Zagier divisors on a Hilbert modular surface are the coefficients of an elliptic modular form of weight 2. Moreover, we determine the arithmetic selfintersection number of the line bundle of modular forms equipped with its Petersson metric on a regular model of a Hilbert modular surface, and we study Faltings heights of arithmetic Hirzebruch-Zagier divisors.

Galois representations, embedding problems and modular forms

To an odd irreducible 2-dimensional complex linear representation of the absolute Galois group of the field Q of rational numbers, a modular form of weight 1 is associated (modulo Artin's conjecture on the L-series of the representation in the icosahedral case). In addition, linear liftings of 2-dimensional projective Galois representations are related to solutions of certain Galois embedding problems. In this paper we present some recent results on the existence of liftings of projective representations and on the explicit resolution of embedding problems associated to orthogonal Galois representations, and explain how these results can be used to construct modular forms.

Chromosomal rearrangement and genetic structure in the shrews of the Sorex araneus group

ABSTRACT The role of chromosomal rearrangements in the speciation process is much debated and many theoretical models have been developed. The shrews of the Sorex araneus group offer extraordinary opportunities to study the relationship between chromosomal variation and speciation. Indeed, this group of morphologically very similar species received a great deal of attention due to its karyotypic variability, which is mainly attributed to Robertsonian fusions. To explore the impact of karyotypic changes on genetic differentiation, we first studied the relationship between genetic and karyotypic structure among Alpine species and among chromosome races of the S. araneus group using Bayesian admixture analyses. The results of these analyses confirmed the taxonomic status of the studied species even though introgression can still be detected between species. Moreover, the strong spatial sub-structure highlighted the role of historical factors (e.g. geographical isolation) on genetic structure. Next, we studied gene flow at the chromosome level to address the question of the impact of chromosomal rearrangements on genetic differentiation. We used flow sorted chromosomes from three different karyotypic taxa of the S. araneus group to map microsatellite markers at the chromosóme arm level. We have been able to map 24 markers and to show that the karyotypic organisation of these taxa is well conserved, which suggests that these markers can be used for further inter-taxa studies. A general prediction of chromosomal speciation models is that genetic differentiation between two taxa should be larger across rearranged chromosomes than across chromosomes common to both taxa. We combined two approaches using mapped microsatellites to test this prediction. First, we studied the genetic differentiation among five shrew taxa placed at different evolutionary levels (i.e. within and among species). In this large scale study, we detected an overall significant difference in genetic structure between rearranged vs. common chromosomes. Moreover, this effect varied among pairwise comparisons, which allowed us to differentiate the role of the karyotypic complexity of hybrids and of the evolutionary divergence between taxa. Secondly, we compared the levels of gene flow measured across common vs. rearranged chromosomes in two karyotypically different hybrid zones (strong vs. low complexity of hybrids), which show similar levels of genetic structure. We detected a significantly stronger genetic structure across rearranged chromosomes in the hybrid zone showing the highest level of hybrid complexity. The large variance observed among loci suggested that other factors, such as the position of markers within the chromosome, also certainly affects genetic structure. In conclusion, our results strongly support the role of chromosomal rearrangements in the reproductive barrier and suggest their importance in speciation process of the S. araneus group. RESUME Le rôle des réarrangements chromosomiques dans les processus de spéciation est fortement débattu et de nombreux modèles théoriques ont été développés sur le sujet. Les musaraignes du groupe Sorex araneus présentent de nombreuses opportunités pour étudier les relations entre les variations chromosomiques et la spéciation. En effet, ce groupe d'espèces morphologiquement très proches a attiré l'attention des chercheurs en raison de sa variabilité caryotypique principalement attribuée à des fusions Robertsoniennes. Pour explorer l'impact des changements caryotypiques sur la différenciation génétique, nous avons tout d'abord étudié les relations entre la structure génétique et caryotypique de races chromosomiques et d'espèces alpine du groupe S. araneus en utilisant des analyses Bayesiennes d' « admixture ». Les résultats de ces analyses ont confirmé le statut taxonomique des espèces étudiées bien que nous ayons détecté de l'introgression entre espèces. L'observation d'une sous structure spatiale relativement forte souligne l'importance des facteurs historiques (telle que l'isolation géographique) sur la structure génétique de ce groupe. Ensuite, nous avons étudié le flux de gène au niveau des chromosomes pour aborder de manière directe la question de l'impact des réarrangements chromosomiques sur la différenciation génétique. En conséquence, nous avons utilisé des tris de chromosomes de trois taxons du groupe S. araneus pour localiser des marqueurs microsatellites au niveau du bras chromosomique. Au cours de cette étude, nous avons pu localiser 24 marqueurs et montrer une forte conservation dans l'organisation du caryotype de ces taxa. Ce résultat suggère que leur utilisation est appropriée pour des études entre taxa. Une prédiction générale à tous les modèles de spéciation chromosomique correspond à la plus grande différenciation génétique des chromosomes réarrangés que des chromosomes communs. Nous avons combiné deux approches utilisant des microsatellites localisés au niveau du bras chromosomique pour tester cette prédiction. Premièrement, nous avons étudié la différenciation génétique entre cinq taxa du groupe S. araneus se trouvant à des niveaux évolutifs différents (i.e. à l'intérieur et entre espèce). Au cours de cette étude, nous avons détecté une différenciation globale significativement plus élevée sur les chromosomes réarrangés. Cet effet varie entre les comparaisons, ce qui nous a permis de souligner le rôle de la complexité caryotypique des hybrides et du niveau de divergence évolutive entre taxa. Deuxièmement, nous avons comparé le flux de gènes des chromosomes communs et réarrangés dans deux zones d'hybridation caryotypiquement différentes (forte vs. Faible complexité des hybrides) mais présentant un niveau de différenciation génétique similaire. Ceci nous a permis de détecter une structure génétique significativement plus élevée sur les chromosomes réarrangés au centre de la zone d'hybridation présentant la plus grande complexité caryotypic. La forte variance observée entre loci souligne en outre le fait que d'autres facteurs, tel que la position du marqueur sur le chromosome, affectent probablement aussi la structure génétique mesurée. En conclusion, nos résultats supportent fortement le rôle des réarrangements chromosomiques dans la barrière reproductive entre espèces ainsi que leur importance dans les processus de spéciation des musaraignes du groupe S. araneus.

Crystal structure of yeast peroxisomal multifunctional enzyme: structural basis for substrate specificity of (3R)-hydroxyacyl-CoA dehydrogenase units.

(3R)-hydroxyacyl-CoA dehydrogenase is part of multifunctional enzyme type 2 (MFE-2) of peroxisomal fatty acid beta-oxidation. The MFE-2 protein from yeasts contains in the same polypeptide chain two dehydrogenases (A and B), which possess difference in substrate specificity. The crystal structure of Candida tropicalis (3R)-hydroxyacyl-CoA dehydrogenase AB heterodimer, consisting of dehydrogenase A and B, determined at the resolution of 2.2A, shows overall similarity with the prototypic counterpart from rat, but also important differences that explain the substrate specificity differences observed. Docking studies suggest that dehydrogenase A binds the hydrophobic fatty acyl chain of a medium-chain-length ((3R)-OH-C10) substrate as bent into the binding pocket, whereas the short-chain substrates are dislocated by two mechanisms: (i) a short-chain-length 3-hydroxyacyl group ((3R)-OH-C4) does not reach the hydrophobic contacts needed for anchoring the substrate into the active site; and (ii) Leu44 in the loop above the NAD(+) cofactor attracts short-chain-length substrates away from the active site. Dehydrogenase B, which can use a (3R)-OH-C4 substrate, has a more shallow binding pocket and the substrate is correctly placed for catalysis. Based on the current structure, and together with the structure of the 2-enoyl-CoA hydratase 2 unit of yeast MFE-2 it becomes obvious that in yeast and mammalian MFE-2s, despite basically identical functional domains, the assembly of these domains into a mature, dimeric multifunctional enzyme is very different.

The effects of physiologically plausible connectivity structure on local and global dynamics in large scale brain models.

Functionally relevant large scale brain dynamics operates within the framework imposed by anatomical connectivity and time delays due to finite transmission speeds. To gain insight on the reliability and comparability of large scale brain network simulations, we investigate the effects of variations in the anatomical connectivity. Two different sets of detailed global connectivity structures are explored, the first extracted from the CoCoMac database and rescaled to the spatial extent of the human brain, the second derived from white-matter tractography applied to diffusion spectrum imaging (DSI) for a human subject. We use the combination of graph theoretical measures of the connection matrices and numerical simulations to explicate the importance of both connectivity strength and delays in shaping dynamic behaviour. Our results demonstrate that the brain dynamics derived from the CoCoMac database are more complex and biologically more realistic than the one based on the DSI database. We propose that the reason for this difference is the absence of directed weights in the DSI connectivity matrix.

Arithmetical problems in number fields, abelian varieties and modular forms

Number theory, a fascinating area in mathematics and one of the oldest, has experienced spectacular progress in recent years. The development of a deep theoretical background and the implementation of algorithms have led to new and interesting interrelations with mathematics in general which have paved the way for the emergence of major theorems in the area. This report summarizes the contribution to number theory made by the members of the Seminari de Teoria de Nombres (UB-UAB-UPC) in Barcelona. These results are presented in connection with the state of certain arithmetical problems, and so this monograph seeks to provide readers with a glimpse of some specific lines of current mathematical research.

Urocortins improve dystrophic skeletal muscle structure and function through both PKA- and Epac-dependent pathways.

In Duchenne muscular dystrophy, the absence of dystrophin causes progressive muscle wasting and premature death. Excessive calcium influx is thought to initiate the pathogenic cascade, resulting in muscle cell death. Urocortins (Ucns) have protected muscle in several experimental paradigms. Herein, we demonstrate that daily s.c. injections of either Ucn 1 or Ucn 2 to 3-week-old dystrophic mdx(5Cv) mice for 2 weeks increased skeletal muscle mass and normalized plasma creatine kinase activity. Histological examination showed that Ucns remarkably reduced necrosis in the diaphragm and slow- and fast-twitch muscles. Ucns improved muscle resistance to mechanical stress provoked by repetitive tetanizations. Ucn 2 treatment resulted in faster kinetics of contraction and relaxation and a rightward shift of the force-frequency curve, suggesting improved calcium homeostasis. Ucn 2 decreased calcium influx into freshly isolated dystrophic muscles. Pharmacological manipulation demonstrated that the mechanism involved the corticotropin-releasing factor type 2 receptor, cAMP elevation, and activation of both protein kinase A and the cAMP-binding protein Epac. Moreover, both STIM1, the calcium sensor that initiates the assembly of store-operated channels, and the calcium-independent phospholipase A(2) that activates these channels were reduced in dystrophic muscle by Ucn 2. Altogether, our results demonstrate the high potency of Ucns for improving dystrophic muscle structure and function, suggesting that these peptides may be considered for treatment of Duchenne muscular dystrophy.

A modular magnetic anastomotic device for minimally invasive digestive anastomosis: proof of concept and preliminary data in the pig model.

BACKGROUND: The aim of our study was to assess the feasibility of minimally invasive digestive anastomosis using a modular flexible magnetic anastomotic device made up of a set of two flexible chains of magnetic elements. The assembly possesses a non-deployed linear configuration which allows it to be introduced through a dedicated small-sized applicator into the bowel where it takes the deployed form. A centering suture allows the mating between the two parts to be controlled in order to include the viscerotomy between the two magnetic rings and the connected viscera. METHODS AND PROCEDURES: Eight pigs were involved in a 2-week survival experimental study. In five colorectal anastomoses, the proximal device was inserted by a percutaneous endoscopic technique, and the colon was divided below the magnet. The distal magnet was delivered transanally to connect with the proximal magnet. In three jejunojejunostomies, the first magnetic chain was injected in its linear configuration through a small enterotomy. Once delivered, the device self-assembled into a ring shape. A second magnet was injected more distally through the same port. The centering sutures were tied together extracorporeally and, using a knot pusher, magnets were connected. Ex vivo strain testing to determine the compression force delivered by the magnetic device, burst pressure of the anastomosis, and histology were performed. RESULTS: Mean operative time including endoscopy was 69.2 ± 21.9 min, and average time to full patency was 5 days for colorectal anastomosis. Operative times for jejunojejunostomies were 125, 80, and 35 min, respectively. The postoperative period was uneventful. Burst pressure of all anastomoses was ≥ 110 mmHg. Mean strain force to detach the devices was 6.1 ± 0.98 and 12.88 ± 1.34 N in colorectal and jejunojejunal connections, respectively. Pathology showed a mild-to-moderate inflammation score. CONCLUSIONS: The modular magnetic system showed enormous potential to create minimally invasive digestive anastomoses, and may represent an alternative to stapled anastomoses, being easy to deliver, effective, and low cost.

The mycorrhizal contribution to plant productivity, plant nutrition and soil structure in experimental grassland.

Previous studies have shown that arbuscular mycorrhizal fungi (AMF) can influence plant diversity and ecosystem productivity. However, little is known about the effects of AMF and different AMF taxa on other important community properties such as nutrient acquisition, plant survival and soil structure. We established experimental grassland microcosms and tested the impact of AMF and of different AMF taxa on a number of grassland characteristics. We also tested whether plant species benefited from the same or different AMF taxa in subsequent growing seasons. AMF enhanced phosphorus acquisition, soil aggregation and survival of several plant species, but AMF did not increase total plant productivity. Moreover, AMF increased nitrogen acquisition by some plant species, but AMF had no effect on total N uptake by the plant community. Plant growth responses to AMF were temporally variable and some plant species obtained the highest biomass with different AMF in different years. Hence the results indicate that it may be beneficial for a plant to be colonized by different AMF taxa in different seasons. This study shows that AMF play a key role in grassland by improving plant nutrition and soil structure, and by regulating the make-up of the plant community.

Towards a theory of the credit-risk balance sheet (II). The evolution of its structure

This article has an immediate predecessor, upon which it is based and with which readers must necessarily be familiar: Towards a Theory of the Credit-Risk Balance Sheet (Vallverdú, Somoza and Moya, 2006). The Balance Sheet is conceptualised on the basis of the duality of a credit-based transaction; it deals with its theoretical foundations, providing evidence of a causal credit-risk duality, that is, a true causal relationship; its characteristics, properties and its static and dynamic characteristics are analyzed. This article, which provides a logical continuation to the previous one, studies the evolution of the structure of the Credit-Risk Balance Sheet as a consequence of a business¿s dynamics in the credit area. Given the Credit-Risk Balance Sheet of a company at any given time, it attempts to estimate, by means of sequential analysis, its structural evolution, showing its usefulness in the management and control of credit and risk. To do this, it bases itself, with the necessary adaptations, on the by-now classic works of Palomba and Cutolo. The establishment of the corresponding transformation matrices allows one to move from an initial balance sheet structure to a final, future one, to understand its credit-risk situation trends, as well as to make possible its monitoring and control, basic elements in providing support for risk management.

Dynamic properties of human brain structure: learning-related changes in cortical areas and associated fiber connections.

Recent findings in neuroscience suggest that adult brain structure changes in response to environmental alterations and skill learning. Whereas much is known about structural changes after intensive practice for several months, little is known about the effects of single practice sessions on macroscopic brain structure and about progressive (dynamic) morphological alterations relative to improved task proficiency during learning for several weeks. Using T1-weighted and diffusion tensor imaging in humans, we demonstrate significant gray matter volume increases in frontal and parietal brain areas following only two sessions of practice in a complex whole-body balancing task. Gray matter volume increase in the prefrontal cortex correlated positively with subject's performance improvements during a 6 week learning period. Furthermore, we found that microstructural changes of fractional anisotropy in corresponding white matter regions followed the same temporal dynamic in relation to task performance. The results make clear how marginal alterations in our ever changing environment affect adult brain structure and elucidate the interrelated reorganization in cortical areas and associated fiber connections in correlation with improvements in task performance.