Semidiscretization and long-time asymptotics of nonlinear diffusion equations

We review several results concerning the long time asymptotics of nonlinear diffusion models based on entropy and mass transport methods. Semidiscretization of these nonlinear diffusion models are proposed and their numerical properties analysed. We demonstrate the long time asymptotic results by numerical simulation and we discuss several open problems based on these numerical results. We show that for general nonlinear diffusion equations the long-time asymptotics can be characterized in terms of fixed points of certain maps which are contractions for the euclidean Wasserstein distance. In fact, we propose a new scaling for which we can prove that this family of fixed points converges to the Barenblatt solution for perturbations of homogeneous nonlinearities for values close to zero.

Cat(0) and Cat (-1) dimensions of torsion free

We show that a particular free-by-cyclic group has CAT(0) dimension equal to 2, but CAT(-1) dimension equal to 3. We also classify the minimal proper 2-dimensional CAT(0) actions of this group; they correspond, up to scaling, to a 1-parameter family of locally CAT(0) piecewise Euclidean metrics on a fixed presentation complex for the group. This information is used to produce an infinite family of 2-dimensional hyperbolic groups, which do not act properly by isometries on any proper CAT(0) metric space of dimension 2. This family includes a free-by-cyclic group with free kernel of rank 6.

Note on homology of expanding foliations

This note contains some remarks about the homologies that can be associated to a foliation which is invariant and uniformly expanded by a diffeomorphism. We construct a family of 'dynamical' closed currents supported on the foliation which help us relate the geometric volume growth of the leaves under the diffeomorphism with the map induced on homology in the case when these currents have nonzero homology.

Synthesis of medium-chain-length polyhydroxyalkanoates in arabidopsis thaliana using intermediates of peroxisomal fatty acid beta-oxidation.

Polyhydroxyalkanoate (PHA) is a family of polymers composed primarily of R-3-hydroxyalkanoic acids. These polymers have properties of biodegradable thermoplastics and elastomers. Medium-chain-length PHAs (MCL-PHAs) are synthesized in bacteria by using intermediates of the beta-oxidation of alkanoic acids. To assess the feasibility of producing MCL-PHAs in plants, Arabidopsis thaliana was transformed with the PhaC1 synthase from Pseudomonas aeruginosa modified for peroxisome targeting by addition of the carboxyl 34 amino acids from the Brassica napus isocitrate lyase. Immunocytochemistry demonstrated that the modified PHA synthase was appropriately targeted to leaf-type peroxisomes in light-grown plants and glyoxysomes in dark-grown plants. Plants expressing the PHA synthase accumulated electron-lucent inclusions in the glyoxysomes and leaf-type peroxisomes, as well as in the vacuole. These inclusions were similar to bacterial PHA inclusions. Analysis of plant extracts by GC and mass spectrometry demonstrated the presence of MCL-PHA in transgenic plants to approximately 4 mg per g of dry weight. The plant PHA contained saturated and unsaturated 3-hydroxyalkanoic acids ranging from six to 16 carbons with 41% of the monomers being 3-hydroxyoctanoic acid and 3-hydroxyoctenoic acid. These results indicate that the beta-oxidation of plant fatty acids can generate a broad range of R-3-hydroxyacyl-CoA intermediates that can be used to synthesize MCL-PHAs.

Functional differentiation of tbf1 orthologues in fission and budding yeasts.

In Saccharomyces cerevisiae, TBF1, an essential gene, influences telomere function but also has other roles in the global regulation of transcription. We have identified a new member of the tbf1 gene family in the mammalian pathogen Pneumocystis carinii. We demonstrate by transspecies complementation that its ectopic expression can provide the essential functions of Schizosaccharomyces pombe tbf1 but that there is no rescue between fission and budding yeast orthologues. Our findings indicate that an essential function of this family of proteins has diverged in the budding and fission yeasts and suggest that effects on telomere length or structure are not the primary cause of inviability in S. pombe tbf1 null strains.

Formal deformations of Poisson structures in low dimensions

In this paper, we study formal deformations of Poisson structures, especially for three families of Poisson varieties in dimensions two and three. For these families of Poisson structures, using an explicit basis of the second Poisson cohomology space, we solve the deformation equations at each step and obtain a large family of formal deformations for each Poisson structure which we consider. With the help of an explicit formula, we show that this family contains, modulo equivalence, all possible formal eformations. We show moreover that, when the Poisson structure is generic, all members of the family are non-equivalent.

The spatial inequality of wage income in Barcelona Metropolitan Area

ABSTRACT The measure and estimation of income levels in Barcelona Metropolitan Area (BMA) goes back a long way. Using different approaches and focusing on different municipalities, there is a lot of work in the field. The majority of the literature has focused on the estimation of income levels using variables related to consumption. The empirical evidence on wage differentials has shown an important growth during 80’s and 90’s especially in United Kingdom and USA. Less is known on spatial distribution of inequality. This paper presents a new data set for analyzing spatial distribution of wage income. This data is obtained by matching Wage Structure Survey (WSS) with data from Census disaggregated by census tracts. In this way we have a unique data set with wage incomes for every census track for 36 municipalities belonging to BMA. We develop a descriptive analysis of spatial distribution, testing for spatial autocorrelation and use the family of Generalised Entropy Indices to measure inequality. Properties of the index allow us to decompose inequality into inter and intra-municipality measures. Since we have two cross-sectional data for WSS (1995-2002) we can also analyze the evolution of the inequality in this period of economic growth. Key words: spatial distribution of wages, spatial autocorrelation, inequality indices.

Lock-in, path dependence, and the Internationalization of QWERTY

This paper looks at the emergence of what is described here as the QWERTY family of standards (QWERTY and its international adaptations QZERTY, AZERTY, and QWERTZ). QWERTY has been described as an inferior solution and an accident of history. However, the analysis here finds that each member of the family represented highly efficient adaptations to specific user needs and technical challenges encountered in their own environments. These findings may be seen to have wider implications given QWERTY’s role as paradigm case in the literature on increasing returns and path dependence, and these are pursued in the paper

An axiomatization of difference-form contest success functions

This paper presents an axiomatic characterization of difference-form group contests, that is, contests fought among groups and where their probability of victory depends on the difference of their effective efforts. This axiomatization rests on the property of Equalizing Consistency, stating that the difference between winning probabilities in the grand contest and in the smaller contest should be identical across all participants in the smaller contest. This property overcomes some of the drawbacks of the widely-used ratio-form contest success functions. Our characterization shows that the criticisms commonly-held against difference-form contests success functions, such as lack of scale invariance and zero elasticity of augmentation, are unfounded.By clarifying the properties of this family of contest success functions, this axiomatization can help researchers to find the functional form better suited to their application of interest.

Identification and characterization of novel molecular mechanisms involved in initiation and progression of myelination

Schwann cells synthesize a large amount of membrane that form a specialized structure called myelin that surrounds axons and facilitate the transmission of electrical signal along neurons in peripheral nervous system (PNS). Previous studies demonstrated that both Schwann cell differentiation and de-differentiation (in the situation of a nerve injury or demyelinating disease) are regulated by cell-intrinsic regulators including several transcription factors. In particular, the de-differentiation of mature Schwann cells is driven by the activation of multiple negative regulators of myelination including Sox2, c-Jun, Notch and Pax3, all usually expressed in immature Schwann cells and suppressed at the onset of myelination. In order to identify new regulators of myelination involved in the development of the PNS, we analyzed the gene-expression profiling data from developing PNS and from three models of demyelinating neuropathies. This analysis led to the identification of Sox4, a member of the Sox family of transcription factors, as a potential candidate. To characterize the molecular function of Sox4 in PNS, we generated two transgenic lines of mice, which overexpress Sox4 specifically in Schwann cells. Detailed analysis of these mice showed that the overexpression of Sox4 in Schwann cells causes a delay in progression of myelination between post-natal day 2 (P2) and P5. Our in vitro analysis suggested that Sox4 cDNA can be overexpressed while the protein translation is tightly regulated. Interestingly, we observed that Sox4 protein is stabilized in nerves of the CMT4C mouse, a model of the human neuropathy. We therefore crossed Sox4 transgenic mice with CMT4C mice and we observed that Sox4 overexpression exacerbated the neuropathy phenotype in these mice. While recognized as being crucial for the normal function of both neurons and myelinating glial cells, the processes that regulate the beginning of myelination and the nature of the neuro-glial cross-talk remains mostly unknown. In order to gain insight into the molecular pathways involved in the interactions between neurons and associated glial cells, we developed a neuron-glia co-culture system based on microfluidic chambers and successfully induced myelination in this system by ascorbic acid. Importantly, we observed that in addition to acting on Schwann cells, ascorbic acid also modulate neuronal/axonal NRG1/ErbB2-B3 signalling. The experimental setting used in our study thus allowed us to discover a novel phenomena of propagation for myelination in vitro. The further characterization of this event brought us to identify other compounds able to induce myelination: ADAMs secretases inhibitor GM6001 and cyclic-AMP. The results generated during my thesis project are therefore not only important for the advancement of our understanding of how the PNS works, but may also potentially help to develop new therapies aiming at improvement of PNS myelination under disease conditions. - Les cellules de Schwann synthétisent une grande quantité de membrane formant une structure spécialisée appelée myéline qui entoure les axones et facilite la transmission du signal électrique le long des neurones du système nerveux périphérique (SNP). Des études antérieures ont démontré que la différenciation et la dédifférenciation des cellules de Schwann (dans la situation d'une lésion nerveuse ou d'une maladie démyélinisante) sont régulées par des régulateurs cellulaires intrinsèques, incluant plusieurs facteurs de transcription. En particulier, la dédifférenciation des cellules de Schwann matures est contrôlée par l'activation de plusieurs régulateurs négatifs de la myélinisation dont Sox2, c-Jun, Notch et Pax3, tous habituellement exprimés dans des cellules de Schwann immatures et supprimés au début de la myélinisation. Afin d'identifier de nouveaux régulateurs de myélinisation impliqués dans le développement du SNP, nous avons analysé le profil d'expression génique durant le développement du SNP ainsi que dans trois modèles de neuropathies démyélinisantes. Cette analyse a mené à l'identification de Sox4, un membre de la famille des facteurs de transcription Sox, comme étant un candidat potentiel. Dans le but de caractériser la fonction moléculaire de Sox4 dans le SNP, nous avons généré deux lignées transgéniques de souris qui surexpriment Sox4 spécifiquement dans les cellules de Schwann. L'analyse détaillée de ces souris a montré que la surexpression de Sox4 dans les cellules de Schwann provoque un retard dans la progression de la myélinisation entre le jour postnatal 2 (P2) et P5. Notre analyse in vitro a suggéré que l'ADNc de Sox4 peut être surexprimé alors que la traduction des protéines est quand à elle étroitement régulée. De façon intéressante, nous avons observé que la protéine Sox4 est stabilisée dans les nerfs des souris CMT4C, un modèle de neuropathie humaine. Nous avons donc croisé les souris transgéniques Sox4 avec des souris CMT4C et avons observé que la surexpression de Sox4 exacerbe le phénotype de neuropathie chez ces souris. Bien que reconnus comme étant cruciaux pour le fonctionnement normal des neurones et des cellules gliales myélinisantes, les processus qui régulent le début de la myélinisation ainsi que la nature des interactions neurone-glie restent largement méconnus. Afin de mieux comprendre les mécanismes moléculaires impliqués dans les interactions entre les neurones et les cellules gliales leur étant associés, nous avons développé un système de co-culture neurone-glie basé sur des chambres microfluidiques et y avons induit avec succès la myélinisation avec de l'acide ascorbique. Étonnamment, nous avons remarqué que, en plus d'agir sur les cellules de Schwann, l'acide ascorbique module également la voie de signalisation neuronale/axonale NRG1/ErbB2-B3. Le protocole expérimental utilisé dans notre étude a ainsi permis de découvrir un nouveau phénomène de propagation de la myélinisation in vitro. La caractérisation plus poussée de ce phénomène nous a menés à identifier d'autres composés capables d'induire la myélinisation: L'inhibiteur de sécrétases ADAMs GM6001 et l'AMP cyclique. Les résultats obtenus au cours de mon projet de thèse ne sont donc pas seulement importants pour l'avancement de notre compréhension sur la façon dont le SNP fonctionne, mais peuvent aussi potentiellement aider à développer de nouvelles thérapies visant à l'amélioration de la myélinisation du SNP dans des conditions pathologiques.

Characterisation of microbial communities colonising the hyphal surfaces of arbuscular mycorrhizal fungi.

Arbuscular mycorrhizal fungi (AMF) are symbiotic soil fungi that are intimately associated with the roots of the majority of land plants. They colonise the interior of the roots and the hyphae extend into the soil. It is well known that bacterial colonisation of the rhizosphere can be crucial for many pathogenic as well as symbiotic plant-microbe interactions. However, although bacteria colonising the extraradical AMF hyphae (the hyphosphere) might be equally important for AMF symbiosis, little is known regarding which bacterial species would colonise AMF hyphae. In this study, we investigated which bacterial communities might be associated with AMF hyphae. As bacterial-hyphal attachment is extremely difficult to study in situ, we designed a system to grow AMF hyphae of Glomus intraradices and Glomus proliferum and studied which bacteria separated from an agricultural soil specifically attach to the hyphae. Characterisation of attached and non-attached bacterial communities was performed using terminal restriction fragment length polymorphism and clone library sequencing of 16S ribosomal RNA (rRNA) gene fragments. For all experiments, the composition of hyphal attached bacterial communities was different from the non-attached communities, and was also different from bacterial communities that had attached to glass wool (a non-living substratum). Analysis of amplified 16S rRNA genes indicated that in particular bacteria from the family of Oxalobacteraceae were highly abundant on AMF hyphae, suggesting that they may have developed specific interactions with the fungi.

On the existence of hysteresis in the Kuramoto model with bimodal frequency distributions

We investigate the transition to synchronization in the Kuramoto model with bimodal distributions of the natural frequencies. Previous studies have concluded that the model exhibits a hysteretic phase transition if the bimodal distribution is close to a unimodal one, due to the shallowness the central dip. Here we show that proximity to the unimodal-bimodal border does not necessarily imply hysteresis when the width, but not the depth, of the central dip tends to zero. We draw this conclusion from a detailed study of the Kuramoto model with a suitable family of bimodal distributions.

Normal hemopoiesis and lymphopoiesis in the combined absence of numb and numblike.

The mammalian ortholog of the conserved Drosophila adaptor protein Numb (Nb) and its homolog Numblike (Nbl) modulate neuronal cell fate determination at least in part by antagonizing Notch signaling. Because the Notch pathway has been implicated in regulating hemopoietic stem cell self-renewal and T cell fate specification in mammals, we investigated the role of Nb and Nbl in hemopoiesis using conditional gene targeting. Surprisingly simultaneous deletion of both Nb and Nbl in murine bone marrow precursors did not affect the ability of stem cells to self-renew or to give rise to differentiated myeloid or lymphoid progeny, even under competitive conditions in mixed chimeras. Furthermore, T cell fate specification and intrathymic T cell development were unaffected in the combined absence of Nb and Nbl. Collectively our data indicate that the Nb family of adaptor proteins is dispensable for hemopoiesis and lymphopoiesis in mice, despite their proposed role in neuronal stem cell development.

A numerical algorithm for finding solutions of a generalized Nash equilibrium problem

A family of nonempty closed convex sets is built by using the data of the Generalized Nash equilibrium problem (GNEP). The sets are selected iteratively such that the intersection of the selected sets contains solutions of the GNEP. The algorithm introduced by Iusem-Sosa (2003) is adapted to obtain solutions of the GNEP. Finally some numerical experiments are given to illustrate the numerical behavior of the algorithm.

Exponentially small splitting of separatrices in the perturbed McMillan map

The McMillan map is a one-parameter family of integrable symplectic maps of the plane, for which the origin is a hyperbolic fixed point with a homoclinic loop, with small Lyapunov exponent when the parameter is small. We consider a perturbation of the McMillan map for which we show that the loop breaks in two invariant curves which are exponentially close one to the other and which intersect transversely along two primary homoclinic orbits. We compute the asymptotic expansion of several quantities related to the splitting, namely the Lazutkin invariant and the area of the lobe between two consecutive primary homoclinic points. Complex matching techniques are in the core of this work. The coefficients involved in the expansion have a resurgent origin, as shown in [MSS08].