A hypercyclic finite rank perturbation of a unitary operator

A unitary operator $V$ and a rank $2$ operator $R$ acting on a Hilbert space \H are constructed such that $V+R$ is hypercyclic. This answers affirmatively a question of Salas whether a finite rank perturbation of a hyponormal operator can be supercyclic.Comment: published in Mathematische Annale

Telescopic actions

A group action H on X is called "telescopic" if for any finitely presented group G, there exists a subgroup H' in H such that G is isomorphic to the fundamental group of X/H'. We construct examples of telescopic actions on some CAT[-1] spaces, in particular on 3 and 4-dimensional hyperbolic spaces. As applications we give new proofs of the following statements: (1) Aitchison's theorem: Every finitely presented group G can appear as the fundamental group of M/J, where M is a compact 3-manifold and J is an involution which has only isolated fixed points; (2) Taubes' theorem: Every finitely presented group G can appear as the fundamental group of a compact complex 3-manifold.Comment: +higher dimension

Spherical structures on torus knots and links

The present paper considers two infinite families of cone-manifolds endowed with spherical metric. The singular strata is either the torus knot ${\rm t}(2n+1, 2)$ or the torus link ${\rm t}(2n, 2)$. Domains of existence for a spherical metric are found in terms of cone angles and volume formul{\ae} are presented.Comment: 17 pages, 5 figures; typo

Power quality monitoring data management and analysis for distribution networks

publishedVersionPeer reviewe

Genomic and exoproteomic diversity in plant biomass degradation approaches among Aspergilli

We classified the genes encoding carbohydrate-active enzymes (CAZymes) in 17 sequenced genomes representing 16 evolutionarily diverse Aspergillus species. We performed a phylogenetic analysis of the encoding enzymes, along with experimentally characterized CAZymes, to assign molecular function to the Aspergilli CAZyme families and subfamilies. Genome content analysis revealed that the numbers of CAZy genes per CAZy family related to plant biomass degradation follow closely the taxonomic distance between the species. On the other hand, growth analysis showed almost no correlation between the number of CAZyme genes and the efficiency in polysaccharide utilization. The exception is A. clavatus where a reduced number of pectinolytic enzymes can be correlated with poor growth on pectin. To gain detailed information on the enzymes used by Aspergilli to breakdown complex biomass, we conducted exoproteome analysis by mass spectrometry. These results showed that Aspergilli produce many different enzymes mixtures in the presence of sugar beet pulp and wheat bran. Despite the diverse enzyme mixtures produced, species of section Nigri, A. aculeatus, A. nidulans and A. terreus, produce mixtures of enzymes with activities that are capable of digesting all the major polysaccharides in the available substrates, suggesting that they are capable of degrading all the polysaccharides present simultaneously. For the other Aspergilli, typically the enzymes produced are targeted to a subset of polysaccharides present, suggesting that they can digest only a subset of polysaccharides at a given time.Peer reviewe

Genome sequence of the button mushroom Agaricus bisporus reveals mechanisms governing adaptation to a humic-rich ecological niche

Agaricus bisporus is the model fungus for the adaptation, persistence, and growth in the humic-rich leaf-litter environment. Aside from its ecological role, A. bisporus has been an important component of the human diet for over 200 y and worldwide cultivation of the "button mushroom" forms a multibillion dollar industry. We present two A. bisporus genomes, their gene repertoires and transcript profiles on compost andduringmushroomformation.The genomes encode a full repertoire of polysaccharide-degrading enzymes similar to that of wood-decayers. Comparative transcriptomics of mycelium grown on defined medium, casing-soil, and compost revealed genes encoding enzymes involved in xylan, cellulose, pectin, and protein degradation aremore highly expressed in compost. The striking expansion of heme-thiolate peroxidases and β-etherases is distinctive from Agaricomycotina wood-decayers and suggests a broad attack on decaying lignin and related metabolites found in humic acid-rich environment. Similarly, up-regulation of these genes together with a lignolytic manganese peroxidase, multiple copper radical oxidases, and cytochrome P450s is consistent with challenges posed by complex humic-rich substrates. The gene repertoire and expression of hydrolytic enzymes in A. bisporus is substantially different from the taxonomically related ectomycorrhizal symbiont Laccaria bicolor. A common promoter motif was also identified in genes very highly expressed in humic-rich substrates. These observations reveal genetic and enzymatic mechanisms governing adaptation to the humic-rich ecological niche formed during plant degradation, further defining the critical role such fungi contribute to soil structure and carbon sequestration in terrestrial ecosystems. Genome sequence will expedite mushroom breeding for improved agronomic characteristics

Finite covers of random 3-manifolds

A 3-manifold is Haken if it contains a topologically essential surface. The Virtual Haken Conjecture posits that every irreducible 3-manifold with infinite fundamental group has a finite cover which is Haken. In this paper, we study random 3-manifolds and their finite covers in an attempt to shed light on this difficult question. In particular, we consider random Heegaard splittings by gluing two handlebodies by the result of a random walk in the mapping class group of a surface. For this model of random 3-manifold, we are able to compute the probabilities that the resulting manifolds have finite covers of particular kinds. Our results contrast with the analogous probabilities for groups coming from random balanced presentations, giving quantitative theorems to the effect that 3-manifold groups have many more finite quotients than random groups. The next natural question is whether these covers have positive betti number. For abelian covers of a fixed type over 3-manifolds of Heegaard genus 2, we show that the probability of positive betti number is 0. In fact, many of these questions boil down to questions about the mapping class group. We are lead to consider the action of mapping class group of a surface S on the set of quotients pi_1(S) -> Q. If Q is a simple group, we show that if the genus of S is large, then this action is very mixing. In particular, the action factors through the alternating group of each orbit. This is analogous to Goldman's theorem that the action of the mapping class group on the SU(2) character variety is ergodic.Comment: 60 pages; v2: minor changes. v3: minor changes; final versio