Bounded derived categories of very simple manifolds

An unrepresentable cohomological functor of finite type of the bounded derived category of coherent sheaves of a compact complex manifold of dimension greater than one with no proper closed subvariety is given explicitly in categorical terms. This is a partial generalization of an impressive result due to Bondal and Van den Bergh.Comment: 11 pages one important references is added, proof of lemma 2.1 (2) and many typos are correcte

Highest weight categories arising from Khovanov's diagram algebra II: Koszulity

This is the second of a series of four articles studying various generalisations of Khovanov's diagram algebra. In this article we develop the general theory of Khovanov's diagrammatically defined "projective functors" in our setting. As an application, we give a direct proof of the fact that the quasi-hereditary covers of generalised Khovanov algebras are Koszul.Comment: Minor changes, extra sections on Kostant modules and rigidity of cell modules adde

Descent of Equivalences and Character Bijections

Categorical equivalences between block algebras of finite groups—such as Morita and derived equivalences—are well known to induce character bijections which commute with the Galois groups of field extensions. This is the motivation for attempting to realise known Morita and derived equivalences over non-splitting fields. This article presents various results on the theme of descent to appropriate subfields and subrings. We start with the observation that perfect isometries induced by a virtual Morita equivalence induce isomorphisms of centres in non-split situations and explain connections with Navarro’s generalisation of the Alperin–McKay conjecture. We show that Rouquier’s splendid Rickard complex for blocks with cyclic defect groups descends to the non-split case. We also prove a descent theorem for Morita equivalences with endopermutation source

Exploring the functional role of the CHRM2 gene in human cognition: results from a dense genotyping and brain expression study

<p>Abstract</p> <p>Background</p> <p>The <it>CHRM2 </it>gene, located on the long arm of chromosome 7 (7q31-35), is involved in neuronal excitability, synaptic plasticity and feedback regulation of acetylcholine release, and has been implicated in higher cognitive processing. The aim of this study is the identification of functional (non)coding variants underlying cognitive phenotypic variation.</p> <p>Methods</p> <p>We previously reported an association between polymorphisms in the 5'UTR regions of the <it>CHRM2 </it>gene and intelligence.. However, no functional variants within this area have currently been identified. In order to identify the relevant functional variant(s), we conducted a denser coverage of SNPs, using two independent Dutch cohorts, consisting of a children's sample (N = 371 ss; mean age 12.4) and an adult sample (N= 391 ss; mean age 37.6). For all individuals standardized intelligence measures were available. Subsequently, we investigated genotype-dependent <it>CHRM2 </it>gene expression levels in the brain, to explore putative enhancer/inhibition activity exerted by variants within the muscarinic acetylcholinergic receptor.</p> <p>Results</p> <p>Using a test of within-family association two of the previously reported variants – rs2061174, and rs324650 – were again strongly associated with intelligence (<it>P </it>< 0.01). A new SNP (rs2350780) showed a trend towards significance. SNP rs324650, is located within a short interspersed repeat (SINE). Although the function of short interspersed repeats remains contentious, recent research revealed potential functionality of SINE repeats in a gene-regulatory context. Gene-expression levels in post-mortem brain material, however were not dependent on rs324650 genotype.</p> <p>Conclusion</p> <p>Using a denser coverage of SNPs in the <it>CHRM2 </it>gene, we confirmed the 5'UTR regions to be most interesting in the context of intelligence, and ruled out other regions of this gene. Although no correlation between genomic variants and gene expression was found, it would be interesting to examine allele-specific effects on CHRM2 transcripts expression in much more detail, for example in relation to transcripts specific halve-life and their relation to LTP and memory.</p

Expression of Odorant Receptor Family, Type 2 OR in the Aquatic Olfactory Cavity of Amphibian Frog Xenopus tropicalis

Recent genome wide in silico analyses discovered a new family (type 2 or family H) of odorant receptors (ORs) in teleost fish and frogs. However, since there is no evidence of the expression of these novel OR genes in olfactory sensory neurons (OSN), it remains unknown if type 2 ORs (OR2) function as odorant receptors. In this study, we examined expression of OR2 genes in the frog Xenopus tropicalis. The overall gene expression pattern is highly complex and differs depending on the gene and developmental stage. RT-PCR analysis in larvae showed that all of the OR2η genes we identified were expressed in the peripheral olfactory system and some were detected in the brain and skin. Whole mount in situ hybridization of the larval olfactory cavity confirmed that at least two OR2η genes so far tested are expressed in the OSN. Because tadpoles are aquatic animals, OR2η genes are probably involved in aquatic olfaction. In adults, OR2η genes are expressed in the nose, brain, and testes to different degrees depending on the genes. OR2η expression in the olfactory system is restricted to the medium cavity, which participates in the detection of water-soluble odorants, suggesting that OR2ηs function as receptors for water-soluble odorants. Moreover, the fact that several OR2ηs are significantly expressed in non-olfactory organs suggests unknown roles in a range of biological processes other than putative odorant receptor functions

Co-regulation of a large and rapidly evolving repertoire of odorant receptor genes

The olfactory system meets niche- and species-specific demands by an accelerated evolution of its odorant receptor repertoires. In this review, we describe evolutionary processes that have shaped olfactory and vomeronasal receptor gene families in vertebrate genomes. We emphasize three important periods in the evolution of the olfactory system evident by comparative genomics: the adaptation to land in amphibian ancestors, the decline of olfaction in primates, and the delineation of putative pheromone receptors concurrent with rodent speciation. The rapid evolution of odorant receptor genes, the sheer size of the repertoire, as well as their wide distribution in the genome, presents a developmental challenge: how are these ever-changing odorant receptor repertoires coordinated within the olfactory system? A central organizing principle in olfaction is the specialization of sensory neurons resulting from each sensory neuron expressing only ~one odorant receptor allele. In this review, we also discuss this mutually exclusive expression of odorant receptor genes. We have considered several models to account for co-regulation of odorant receptor repertoires, as well as discussed a new hypothesis that invokes important epigenetic properties of the system

An analogue of row removal for diagrammatic cherednik algebras

We prove an analogue of James–Donkin row removal theorems for diagrammatic Cherednik algebras. This is one of the first results concerning the (graded) decomposition numbers of these algebras over fields of arbitrary characteristic. As a special case, our results yield a new reduction theorem for graded decomposition numbers and extension groups for cyclotomic q-Schur algebras

Actes des rencontres lyonnaises des jeunes chercheurs en linguistique historique

International audienceActes des Rencontres lyonnaises des jeunes chercheurs en linguistique historique qui se sont tenues à Lyon le 6 juin 2019, organisées par l'association de jeunes chercheurs Diachronies Contemporaines