Coherent states on Hilbert modules

We generalize the concept of coherent states, traditionally defined as special families of vectors on Hilbert spaces, to Hilbert modules. We show that Hilbert modules over C*-algebras are the natural settings for a generalization of coherent states defined on Hilbert spaces. We consider those Hilbert C*-modules which have a natural left action from another C*-algebra, say A. The coherent states are well defined in this case and they behave well with respect to the left action by A. Certain classical objects like the Cuntz algebra are related to specific examples of coherent states. Finally we show that coherent states on modules give rise to a completely positive definite kernel between two C*-algebras, in complete analogy to the Hilbert space situation. Related to this, there is a dilation result for positive operator-valued measures, in the sense of Naimark. A number of examples are worked out to illustrate the theory. Some possible physical applications are also mentioned.

Hilbert W*-modules and coherent states

Hilbert C*-module valued coherent states was introduced earlier by Ali, Bhattacharyya and Shyam Roy. We consider the case when the underlying C*-algebra is a W*-algebra. The construction is similar with a substantial gain. The associated reproducing kernel is now algebra valued, rather than taking values in the space of bounded linear operators between two C*-algebras.

Multidimensional operator multipliers

We introduce multidimensional Schur multipliers and characterise them, generalising well-known results by Grothendieck and Peller. We define a multidimensional version of the two-dimensional operator multipliers studied recently by Kissin and Shulman. The multidimensional operator multipliers are defined as elements of the minimal tensor product of several C *-algebras satisfying certain boundedness conditions. In the case of commutative C*-algebras, the multidimensional operator multipliersreduce to continuousmul-tidimensional Schur multipliers. We show that the multiplierswith respect to some given representations of the corresponding C*-algebrasdo not change if the representations are replaced by approximately equivalent ones. We establish a non-commutative and multidimensional version of the characterisations by Grothendieck and Peller which shows that universal operator multipliers can be obtained ascertain weak limits of elements of the algebraic tensor product of the corresponding C *-algebras.

Compactness properties of operator multipliers

We continue the study of multidimensional operator multipliers initiated in~cite{jtt}. We introduce the notion of the symbol of an operator multiplier. We characterise completely compact operator multipliers in terms of their symbol as well as in terms of approximation by finite rank multipliers. We give sufficient conditions for the sets of compact and completely compact multipliers to coincide and characterise the cases where an operator multiplier in the minimal tensor product of two C*-algebras is automatically compact. We give a description of multilinear modular completely compact completely bounded maps defined on the direct product of finitely many copies of the C*-algebra of compact operators in terms of tensor products, generalising results of Saar

Tensor products of operator systems

The purpose of the present paper is to lay the foundations for a systematic study of tensor products of operator systems. After giving an axiomatic definition of tensor products in this category, we examine in detail several particular examples of tensor products, including a minimal, maximal, maximal commuting, maximal injective and some asymmetric tensor products. We characterize these tensor products in terms of their universal properties and give descriptions of their positive cones. We also characterize the corresponding tensor products of operator spaces induced by a certain canonical inclusion of an operator space into an operator system. We examine notions of nuclearity for our tensor products which, on the category of C*-algebras, reduce to the classical notion. We exhibit an operator system S which is not completely order isomorphic to a C*-algebra yet has the property that for every C*-algebra A, the minimal and maximal tensor product of S and A are equal.

Characterisations of the weak expectation property

We use representations of operator systems as quotients to deduce various characterisations of the weak expectation property (WEP) for C∗ -algebras. By Kirchberg’s work on WEP, these results give new formulations of Connes’ embedding problem.

Caractérisation de la migration du virus Herpès simplex de type 1 (HSV-1) par protéomique

Le virus Herpès simplex de type 1 (HSV-1), agent étiologique des feux sauvages, possède une structure multicouche comprenant une capside icosaédrale qui protège le génome viral d’ADN, une couche protéique très structurée appelée tégument et une enveloppe lipidique dérivant de la cellule hôte et parsemée de glycoprotéines virales. Tous ces constituants sont acquis séquentiellement à partir du noyau, du cytoplasme et du réseau trans-golgien. Cette structure multicouche confère à HSV-1 un potentiel considérable pour incorporer des protéines virales et cellulaires. Toutefois, l’ensemble des protéines qui composent ce virus n’a pas encore été élucidé. De plus, malgré son rôle critique à différentes étapes de l’infection, le tégument demeure encore mal défini et ce, tant dans sa composition que dans la séquence d’addition des protéines qui le composent. Toutes ces incertitudes quant aux mécanismes impliqués dans la morphogenèse du virus nous amènent à l’objectif de ce projet, soit la caractérisation du processus de maturation d’HSV-1. Le premier article présenté dans cette thèse et publié dans Journal of Virology s’attarde à la caractérisation protéique des virus extracellulaires matures. Grâce à l’élaboration d’un protocole d’isolation et de purification de ces virions, une étude protéomique a pu être effectuée. Celle-ci nous a permis de réaliser une cartographie de la composition globale en protéines virales des virus matures (8 protéines de la capside, 23 protéines du tégument et 13 glycoprotéines) qui a fait la page couverture de Journal of Virology. De plus, l’incorporation potentielle de 49 protéines cellulaires différentes a été révélée. Lors de cette étude protéomique, nous avons aussi relevé la présence de nouveaux composants du virion dont UL7, UL23, ICP0 et ICP4. Le deuxième article publié dans Journal of General Virology focalise sur ces protéines via une analyse biochimique afin de mieux comprendre les interactions et la dynamique du tégument. Ces résultats nous révèlent que, contrairement aux protéines ICP0 et ICP4, UL7 et UL23 peuvent être relâchées de la capside en présence de sels et que les cystéines libres jouent un rôle dans cette relâche. De plus, cet article met en évidence la présence d’ICP0 et d’ICP4 sur les capsides nucléaires suggérant une acquisition possible du tégument au noyau. La complexité du processus de morphogenèse du virus ainsi que la mise en évidence d’acquisition de protéines du tégument au noyau nous ont incités à poursuivre nos recherches sur la composition du virus à un stade précoce de son cycle viral. Les capsides C matures, prémisses des virus extracellulaires, ont donc été isolées et purifiées grâce à un protocole innovateur basé sur le tri par cytométrie en flux. L’analyse préliminaire de ces capsides par protéomique a permis d’identifier 28 protéines virales et 39 protéines cellulaires. Les données recueilles, comparées à celles obtenues avec les virus extracellulaires, suggèrent clairement un processus séquentiel d’acquisition des protéines du tégument débutant dans le noyau, site d’assemblage des capsides. Finalement, tous ces résultats contribuent à une meilleure compréhension du processus complexe de maturation d’HSV-1 via l’utilisation de techniques variées et innovatrices, telles que la protéomique et la cytométrie en flux, pouvant être appliquées à d’autres virus mais aussi permettre le développement de meilleurs traitements pour vaincre l’HSV-1.

On the universal TRO of a JC*-triple, ideals and tensor products

In a development from material introduced in recent work, we discuss the interconnections between ternary rings of operators (TROs) and right C*-algebras generated by JC*-triples, deducing that every JC*-triple possesses a largest universally reversible ideal, that the universal TRO commutes with appropriate tensor products and establishing a reversibility criterion for type I JW*-triples.

Filogeografia e sistemática molecular de répteis de alguns arquipélagos africanos do Atlântico oriental

Os répteis, nomeadamente os lagartos, lagartixas e osgas, constituem um dos grupos de vertebrados com maior sucesso de colonização das ilhas oceânicas. Juntamente com as aves, devem constituir o grupo que naturalmente melhor se disseminou pelas ilhas oceânicas. Os mamíferos e anfíbios que aí possam existir são na sua maioria de introdução antropogénica. Como são bons colonizadores constituem bons modelos para o estudo de fenómenos e padrões de colonização das ilhas sobretudo tendo em conta que possuem ainda baixa dispersão dentro de cada ilha. Neste trabalho utilizamos marcadores do DNA mitocondrial (12S rRNA, 16S rRNA, citocromo b), marcadores do DNA nuclear (c-mos e enolase) assim como marcadores enzimáticos, para estudar os padrões de colonização, as relações entre espécies, a detecção de espécies introduzidas, a importância dos dados moleculares em relação a outro tipo de dados, nos répteis terrestres dos Arquipélagos da Madeira, Selvagens e Cabo Verde, e ilhas do Golfo da Guiné (São Tomé, Príncipe e Annobon). As sequências de DNA quer mitocondrial quer nuclear permitiram revelar a existência de uma estrutura geográfica em Mabuya spp. de São Tomé (de natureza intraespecífica) e de Cabo Verde (interespecífica) bem como em Lacerta dugesii (intraespecífica) do Arquipélago da Madeira. Esta estrutura é mais evidente em Lacerta dugesii, que apresenta haplótipos típicos e exclusivos de cada um dos quatro grupos principais de ilhas (Madeira, Porto Santo, Desertas e Selvagens), sem que se tivessem observado haplótipos comuns a mais do que um grupo de ilhas. Os dados moleculares obtidos permitem ainda inferir os casos de expansões demográficas recentes como no caso das populações de Lacerta dugesii da Madeira e Porto Santo ou pelo contrário indicativas de subdivisão geográfica da população como no Arquipélago das Selvagens. Nesta espécie apenas terá ocorrido um evento de colonização, e os nossos dados não corroboram a possibilidade de introdução nas Ilhas Selvagens mediada pelo homem. Mabuya spp. de Cabo Verde também forma um grupo monofilético, subentendendo a exemplo de L.dugesii um evento de colonização mas bem mais antigo, dando origem a eventos de radiação evolutiva, tendo-se formado novas espécies que por sua vez terão sido actores na colonização entre ilhas. Usando como modelo os Arquipélagos das Canárias e Cabo Verde, o número de eventos de colonização é menor nos escincídeos do que nos geconídeos. As ilhas do Golfo da Guiné parecem introduzir uma excepção à regra. Assim Mabuya spp. do Golfo da Guiné (São Tomé, Príncipe e Annobon) serão resultantes de 4 eventos de colonização, sendo dois responsáveis pelo aparecimento de M. maculilabris (uma forma no Príncipe e outra em São Tomé), M. ozorii (Annobon) e M. affinis (Príncipe). A exemplo de Lacerta dugesii, Mabuya maculilabris apresenta uma forte estruturação geográfica. Fazendo recurso a sequências já publicadas no GenBank, podemos propor um novo arranjo taxonómico no género Mabuya, não se devendo considerar quatro grupos (sensu Mausfeld), mas sim cinco, em que se adiciona um novo grupo que contempla as espécies do Norte de África e Turquia. As osgas em Cabo Verde, a exemplo das Canárias, apresentam grande variabilidade e terão sido resultado de maior número de eventos de colonização do que os Escincídeos. A nossa análise revela que existem em Cabo Verde maior número de grupos geneticamente distintos do género Tarentola, do que havia sido registado anteriormente. Os Hemidactylus também devem ter sido resultantes de mais do que um evento de colonização: um para Hemidactylus bouvieri e um para Hemidactylus brooki da Ilha do Sal. Hemidactylus brooki existente nas restantes ilhas bem como Hemidactylus mabouia são muito provavelmente de introdução antropogénica. No Golfo da Guiné o número de eventos de colonização não é maior nas osgas do que nos Escincídeos, constituindo assim uma excepção à regra, sendo os Hemidactylus resultantes de pelo menos dois eventos de colonização (quatro em Mabuya). Utilizando Lacerta dugesii como modelo, não encontramos qualquer congruência entre dados enzimáticos, morfológicos e moleculares. Com a aplicação de técnicas moleculares foi possível identificar espécies introduzidas como Hemidactylus mabouia na Madeira, Cabo Verde, São Tomé e Príncipe e Annobon bem como Ramphotyphlops braminus em Annobon. Estas espécies caracterizam-se por serem geneticamente homogéneas. Foi ainda possível verificar o estatuto taxonómico das várias espécies. Em Lacerta dugesii as três subespécies não deverão ser omitidas. Em Mabuya de Cabo Verde dever-se–ão manter as espécies consideradas e as relações estabelecidas. Em Tarentola spp. uma nova subespécie de Tarentola gigas deverá ser considerada e alvo de novas investigações. Os restantes grupos obtidos, geneticamente distintos, são em maior número do que havia sido registado, e deverão ser alvo dum estudo exaustivo.Confirmou-se a presença duma Mabuya em Annobon, muito provavelmente Mabuya ozorii, espécie esquecida ou omitida em muitas listas de espécies como na “EMBL Reptile database”. Duas formas de M. maculilabris em São Tomé e Príncipe, deixam transparecer a possibilidade da existência dum complexo de espécies. A análise de dados moleculares permitiu também referir que M. maculilabris não parece ter sido introduzida pelo homem nestas ilhas. Do ponto de vista conservacionista é fundamental monitorizar as espécies introduzidas pois podem levar à extinção de espécies indígenas, e monitorizar a manutenção dos vários grupos geneticamente distintos encontrados, muitos deles com distribuições restritas. Por fim, ao testar o c-mos na filogenia de Lacerta dugesii, podemos dizer que este gene nuclear pode também ser utilizado sob determinadas condições, ao nível intraespecífico. A região controle do DNA mitocondrial revelou-se também adequada na estimativa das relações filogenéticas. Verificou-se que esta estrutura é em Lacerta dugesii, bem menos variável que o gene do citocromo b (também mitocondrial). Mostra ainda uma variação entre populações e apresenta aspectos curiosos relacionados com a sua estrutura no contexto do que é conhecido actualmente dentro dos vertebrados.

Análises Estruturais e atividades biológicas de exopolissacarídeo extraído do fungo comestível pleurotus Sajor-Caju e de seu derivado sulfatado quimicamente.

The exopolysaccharides are extracellular compounds produced by some species of fungi and bacteria. It is suggested that these molecules, even when in the form of complex polysaccharide-peptide, are the main bioactive molecules of many fungus. Some of the biological activities displayed by these compounds can be accentuated and others may arise when you add chemically polar or nonpolar groups to polysaccharides. The fruiting body of Pleurotus sajor-caju produces a heteropolysaccharide with antineoplastic and antimicrobial activity, but other biological activities of this polymer have not been evaluated. In this work the exopolysaccharide of Pleurotus sajor-caju was sulfated chemically and structurally characterized. We also evaluated the antiproliferative, antioxidant and anticoagulant activities from native exopolysaccharide (PN) and its sulfated derivated (PS). Polyacrylamide gel electrophoresis, infrared spectroscopy and nuclear magnetic resonance (¹³C) proved successful in sulfation of PN to obtain PS. Analysis by gas chromatography-mass spectroscopy showed that PN and PS are composed of mannose, galactose, 3-O-methyl-galactose and glucose in proportion percentage of 44,9:16,3:19,8:19 and 49, 7:14,4:17,7:18,2, respectively. The percentage of sulfate found in PS was 22.5%. Antioxidants assays revealed that the sulfation procedure affects differently the activities of exopolysaccharides, while the total antioxidant capacity, the scavenging activity of superoxide radical and ferric chelating were not affected by sulfation, on the other hand the chemical modification of PN enhanced the scavenging activity of hydroxyl radical and reducing power. PS also showed anticoagulant activity in a dose-dependent manner and clotting time was 3.0 times higher than the baseline value in APTT at 2 mg/mL. The exopolysaccharide not presented antiproliferative activity against HeLa tumor cells, but PS affects the cellular proliferation in a time-dependent manner. After 72 h, the inhibition rate of PS (2.0 mg/mL) on HeLa cells was about 60%. The results showed that PN sulfation increase some of their activities.

Molecular phylogeny of advanced snakes (Serpentes, Caenophidia) with an emphasis on South American xenodontines: A revised classification and descriptions of new taxa

We present a molecular phylogenetic analysis of caenophidian (advanced) snakes using sequences from two mitochondrial genes (12S and 16S rRNA) and one nuclear (c-mos) gene (1681 total base pairs), and with 131 terminal taxa sampled from throughout all major caenophidian lineages but focussing on Neotropical xenodontines. Direct optimization parsimony analysis resulted in a well-resolved phylogenetic tree, which corroborates some clades identified in previous analyses and suggests new hypotheses for the composition and relationships of others. The major salient points of our analysis are: (1) placement of Acrochordus, Xenodermatids, and Pareatids as successive outgroups to all remaining caenophidians (including viperids, elapids, atractaspidids, and all other colubrid groups); (2) within the latter group, viperids and homalopsids are sucessive sister clades to all remaining snakes; (3) the following monophyletic clades within crown group caenophidians: Afro-Asian psammophiids (including Mimophis from Madagascar), Elapidae (including hydrophiines but excluding Homoroselaps), Pseudoxyrhophiinae, Colubrinae, Natricinae, Dipsadinae, and Xenodontinae. Homoroselaps is associated with atractaspidids. Our analysis suggests some taxonomic changes within xenodontines, including new taxonomy for Alsophis elegans, Liophis amarali, and further taxonomic changes within Xenodontini and the West Indian radiation of xenodontines. Based on our molecular analysis, we present a revised classification for caenophidians and provide morphological diagnoses for many of the included clades; we also highlight groups where much more work is needed. We name as new two higher taxonomic clades within Caenophidia, one new subfamily within Dipsadidae, and, within Xenodontinae five new tribes, six new genera and two resurrected genera. We synonymize Xenoxybelis and Pseudablabes with Philodryas; Erythrolamprus with Liophis; and Lystrophis and Waglerophis with Xenodon.

Cryptic species in Iphisa elegans Gray, 1851 (Squamata: Gymnophthalmidae) revealed by hemipenial morphology and molecular data

Iphisa elegans Gray, 1851 is a ground-dwelling lizard widespread over Amazonia that displays a broadly conserved external morphology over its range. This wide geographical distribution and conservation of body form contrasts with the expected poor dispersal ability of the species, the tumultuous past of Amazonia, and the previously documented prevalence of cryptic species in widespread terrestrial organisms in this region. Here we investigate this homogeneity by examining hemipenial morphology and conducting phylogenetic analyses of mitochondrial (CYTB) and nuclear (C-MOS) DNA sequence data from 49 individuals sampled across Amazonia. We detected remarkable variation in hemipenial morphology within this species, with multiple cases of sympatric occurrence of distinct hemipenial morphotypes. Phylogenetic analyses revealed highly divergent lineages corroborating the patterns suggested by the hemipenial morphotypes, including co-occurrence of different lineages. The degrees of genetic and morphological distinctness, as well as instances of sympatry among mtDNA lineages/morphotypes without nuDNA allele sharing, suggest that I. elegans is a complex of cryptic species. An extensive and integrative taxonomic revision of the I. elegans complex throughout its wide geographical range is needed. (c) 2012 The Linnean Society of London, Zoological Journal of the Linnean Society, 2012, 166, 361376.

Thermal relaxation for particle systems in interaction with several bosonic heat reservoirs

The present thesis is concerned with the study of a quantum physical system composed of a small particle system (such as a spin chain) and several quantized massless boson fields (as photon gasses or phonon fields) at positive temperature. The setup serves as a simplified model for matter in interaction with thermal "radiation" from different sources. Hereby, questions concerning the dynamical and thermodynamic properties of particle-boson configurations far from thermal equilibrium are in the center of interest. We study a specific situation where the particle system is brought in contact with the boson systems (occasionally referred to as heat reservoirs) where the reservoirs are prepared close to thermal equilibrium states, each at a different temperature. We analyze the interacting time evolution of such an initial configuration and we show thermal relaxation of the system into a stationary state, i.e., we prove the existence of a time invariant state which is the unique limit state of the considered initial configurations evolving in time. As long as the reservoirs have been prepared at different temperatures, this stationary state features thermodynamic characteristics as stationary energy fluxes and a positive entropy production rate which distinguishes it from being a thermal equilibrium at any temperature. Therefore, we refer to it as non-equilibrium stationary state or simply NESS. The physical setup is phrased mathematically in the language of C*-algebras. The thesis gives an extended review of the application of operator algebraic theories to quantum statistical mechanics and introduces in detail the mathematical objects to describe matter in interaction with radiation. The C*-theory is adapted to the concrete setup. The algebraic description of the system is lifted into a Hilbert space framework. The appropriate Hilbert space representation is given by a bosonic Fock space over a suitable L2-space. The first part of the present work is concluded by the derivation of a spectral theory which connects the dynamical and thermodynamic features with spectral properties of a suitable generator, say K, of the time evolution in this Hilbert space setting. That way, the question about thermal relaxation becomes a spectral problem. The operator K is of Pauli-Fierz type. The spectral analysis of the generator K follows. This task is the core part of the work and it employs various kinds of functional analytic techniques. The operator K results from a perturbation of an operator L0 which describes the non-interacting particle-boson system. All spectral considerations are done in a perturbative regime, i.e., we assume that the strength of the coupling is sufficiently small. The extraction of dynamical features of the system from properties of K requires, in particular, the knowledge about the spectrum of K in the nearest vicinity of eigenvalues of the unperturbed operator L0. Since convergent Neumann series expansions only qualify to study the perturbed spectrum in the neighborhood of the unperturbed one on a scale of order of the coupling strength we need to apply a more refined tool, the Feshbach map. This technique allows the analysis of the spectrum on a smaller scale by transferring the analysis to a spectral subspace. The need of spectral information on arbitrary scales requires an iteration of the Feshbach map. This procedure leads to an operator-theoretic renormalization group. The reader is introduced to the Feshbach technique and the renormalization procedure based on it is discussed in full detail. Further, it is explained how the spectral information is extracted from the renormalization group flow. The present dissertation is an extension of two kinds of a recent research contribution by Jakšić and Pillet to a similar physical setup. Firstly, we consider the more delicate situation of bosonic heat reservoirs instead of fermionic ones, and secondly, the system can be studied uniformly for small reservoir temperatures. The adaption of the Feshbach map-based renormalization procedure by Bach, Chen, Fröhlich, and Sigal to concrete spectral problems in quantum statistical mechanics is a further novelty of this work.

Random lattice models

This thesis deals with three different physical models, where each model involves a random component which is linked to a cubic lattice. First, a model is studied, which is used in numerical calculations of Quantum Chromodynamics.In these calculations random gauge-fields are distributed on the bonds of the lattice. The formulation of the model is fitted into the mathematical framework of ergodic operator families. We prove, that for small coupling constants, the ergodicity of the underlying probability measure is indeed ensured and that the integrated density of states of the Wilson-Dirac operator exists. The physical situations treated in the next two chapters are more similar to one another. In both cases the principle idea is to study a fermion system in a cubic crystal with impurities, that are modeled by a random potential located at the lattice sites. In the second model we apply the Hartree-Fock approximation to such a system. For the case of reduced Hartree-Fock theory at positive temperatures and a fixed chemical potential we consider the limit of an infinite system. In that case we show the existence and uniqueness of minimizers of the Hartree-Fock functional. In the third model we formulate the fermion system algebraically via C*-algebras. The question imposed here is to calculate the heat production of the system under the influence of an outer electromagnetic field. We show that the heat production corresponds exactly to what is empirically predicted by Joule's law in the regime of linear response.

Plakoglobin-dependent disruption of the desmosomal plaque in pemphigus vulgaris

We recently reported that the pathogenesis of pemphigus vulgaris (PV), an autoimmune blistering skin disorder, is driven by the accumulation of c-Myc secondary to abrogation of plakoglobin (PG)-mediated transcriptional c-Myc suppression. PG knock-out mouse keratinocytes express high levels of c-Myc and resemble PVIgG-treated wild-type keratinocytes in most respects. However, they fail to accumulate nuclear c-Myc and loose intercellular adhesion in response to PVIgG-treatment like wild-type keratinocytes. This suggested that PG is also required for propagation of the PVIgG-induced events between augmented c-Myc expression and acantholysis. Here, we addressed this possibility by comparing PVIgG-induced changes in the desmosomal organization between wild-type and PG knock-out keratinocytes. We found that either bivalent PVIgG or monovalent PV-Fab (known to trigger blister formation in vivo) disrupt the linear organization of all major desmosomal components along cell borders in wild-type keratinocytes, simultaneously with a reduction in intercellular adhesive strength. In contrast, PV-Fab failed to affect PG knock-out keratinocytes while PVIgG cross-linked their desmosomal cadherins without significantly affecting desmoplakin. These results identify PG as a principle effector of the PVIgG-induced signals downstream of c-Myc that disrupt the desmosomal plaque at the plasma membrane.