The homotopy theory of dg-categories and derived Morita theory

The main purpose of this work is the study of the homotopy theory of dg-categories up to quasi-equivalences. Our main result provides a natural description of the mapping spaces between two dg-categories $C$ and $D$ in terms of the nerve of a certain category of $(C,D)$-bimodules. We also prove that the homotopy category $Ho(dg-Cat)$ is cartesian closed (i.e. possesses internal Hom's relative to the tensor product). We use these two results in order to prove a derived version of Morita theory, describing the morphisms between dg-categories of modules over two dg-categories $C$ and $D$ as the dg-category of $(C,D)$-bi-modules. Finally, we give three applications of our results. The first one expresses Hochschild cohomology as endomorphisms of the identity functor, as well as higher homotopy groups of the \emph{classifying space of dg-categories} (i.e. the nerve of the category of dg-categories and quasi-equivalences between them). The second application is the existence of a good theory of localization for dg-categories, defined in terms of a natural universal property. Our last application states that the dg-category of (continuous) morphisms between the dg-categories of quasi-coherent (resp. perfect) complexes on two schemes (resp. smooth and proper schemes) is quasi-equivalent to the dg-category of quasi-coherent complexes (resp. perfect) on their product.Comment: 50 pages. Few mistakes corrected, and some references added. Thm. 8.15 is new. Minor corrections. Final version, to appear in Inventione

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

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

A guided tour of asynchronous cellular automata

Research on asynchronous cellular automata has received a great amount of attention these last years and has turned to a thriving field. We survey the recent research that has been carried out on this topic and present a wide state of the art where computing and modelling issues are both represented.Comment: To appear in the Journal of Cellular Automat

Testing bibliometric indicators by their prediction of scientists promotions

We have developed a method to obtain robust quantitative bibliometric indicators for several thousand scientists. This allows us to study the dependence of bibliometric indicators (such as number of publications, number of citations, Hirsch index...) on the age, position, etc. of CNRS scientists. Our data suggests that the normalized h index (h divided by the career length) is not constant for scientists with the same productivity but differents ages. We also compare the predictions of several bibliometric indicators on the promotions of about 600 CNRS researchers. Contrary to previous publications, our study encompasses most disciplines, and shows that no single indicator is the best predictor for all disciplines. Overall, however, the Hirsch index h provides the least bad correlations, followed by the number of papers published. It is important to realize however that even h is able to recover only half of the actual promotions. The number of citations or the mean number of citations per paper are definitely not good predictors of promotion

Topological phase transition in a network model with preferential attachment and node removal

Preferential attachment is a popular model of growing networks. We consider a generalized model with random node removal, and a combination of preferential and random attachment. Using a high-degree expansion of the master equation, we identify a topological phase transition depending on the rate of node removal and the relative strength of preferential vs. random attachment, where the degree distribution goes from a power law to one with an exponential tail.Comment: The final publication is available at http://www.epj.or

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

INS-1 Cells Undergoing Caspase-Dependent Apoptosis Enhance the Regenerative Capacity of Neighboring Cells

Our results suggest that apoptosing INS-1 cells shed microparticles that may stimulate PSP/reg induction in neighboring cells, a mechanism that may facilitate the recovery of β-cell mass in HNF1A-MODY

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

The Evolution of Mammalian Gene Families

Gene families are groups of homologous genes that are likely to have highly similar functions. Differences in family size due to lineage-specific gene duplication and gene loss may provide clues to the evolutionary forces that have shaped mammalian genomes. Here we analyze the gene families contained within the whole genomes of human, chimpanzee, mouse, rat, and dog. In total we find that more than half of the 9,990 families present in the mammalian common ancestor have either expanded or contracted along at least one lineage. Additionally, we find that a large number of families are completely lost from one or more mammalian genomes, and a similar number of gene families have arisen subsequent to the mammalian common ancestor. Along the lineage leading to modern humans we infer the gain of 689 genes and the loss of 86 genes since the split from chimpanzees, including changes likely driven by adaptive natural selection. Our results imply that humans and chimpanzees differ by at least 6% (1,418 of 22,000 genes) in their complement of genes, which stands in stark contrast to the oft-cited 1.5% difference between orthologous nucleotide sequences. This genomic “revolving door” of gene gain and loss represents a large number of genetic differences separating humans from our closest relatives