The Brezis-Nirenberg type problem involving the square root of the Laplacian

We establish existence and non-existence results to the Brezis-Nirenberg type problem involving the square root of the Laplacian in a bounded domain with zero Dirichlet boundary condition.

Early antibiotic administration affects the gut barrier function and the immune response to oral antigen in suckling rats

Abstract: The increasingly high hygienic standards characterizing westernized societies correlate with an increasingly high prevalence of allergic disease. Initially based on these observations, the hygiene hypothesis postulates that reduced microbial stimulation during infancy impairs the immune system development and increases the risk of allergy. Moreover, there is increasing evidence that the crosstalk existing between the intestine and the resident microbiota is crucial for gut homeostasis. In particular, bacterial colonization of the gut affects the integrity of the gut barrier and stimulates the development of the gut associated immune tissue, both phenomena being essential for the immune system to mount a controlled response to food antigens. Therefore, alterations in the microbial colonization process, by compromising the barrier homeostasis, may increase the risk of food allergy. In this context, antibiotic treatment, frequently prescribed during infancy, affects gut colonization by bacteria. However, little is known about the impact of alterations in the colonization process on the maturation of the gut barrier and on the immunological response to oral antigens. The objective of this work was to determine the impact of a commercial antibiotic preparation employed in pediatric settings on the gut barrier status at the critical period of the suckling/weaning transition and to evaluate the physiological consequences of this treatment in terms of immune response to food antigens. We established an antibiotic-treated suckling rat model relevant to the pediatric population in terms of type, dose and route of administration of the antibiotic and of changes in the patterns of microbial colonization. Oral tolerance to a novel luminal antigen (ovalbumin) was impaired when the antigen was introduced during antibiotic treatment. These results paralleled to alterations in the intestinal permeability to macromolecules and reduced intestinal expression of genes coding for the major histocomptatibility complex II molecules, which suggest a reduced capacity of antigen handling and presentation in the intestine of the antibiotic-treated animals. In addition, low luminal IgA levels and reduced intestinal expression of genes coding for antimicrobial proteins suggest that protection against pathogens was reduced under antibiotic treatment. In conclusion, we observed in suckling rats that treatment with abroad-spectrum antibiotic commonly used in pediatric practices reduced the capacity of the immune system to develop tolerance. The impact of the antibiotic treatment on the immune response to the antigen-was likely mediated by the alterations of the gut microbiota, through impairment in the mechanisms of antigen handling and presentation. This work reinforces the body of data supporting a key role of the intestinal microbiota modulating the risk of allergy development and leads us to propose that the introduction of new food antigens should be avoided during antibiotic treatment in infants. Résumé: L'augmentation du niveau d'hygiène caractérisant les sociétés occidentales semble être fortement corrélée avec l'augmentation des cas d'allergie dans ces pays. De cette observation est née l'hypothèse qu'une diminution des stimuli microbiens pendant l'enfance modifie le développement du système immunitaire augmentant ainsi le risque d'allergie. En ce sens, un nombre croissant de données indiquent que les interactions existant entre l'intestin et les bactéries résidantes sont cruciales pour l'équilibre du système. En effet, la présence de bactéries dans l'intestin affecte l'intégrité de sa fonction de barrière et stimule le développement du système immunitaire intestinal. Ces deux paramètres étant essentiels à la mise en place d'une réponse contrôlée vis à vis d'un antigène reçu oralement, toute modification du processus naturel de colonisation compromettant l'équilibre intestinal pourrait augmenter le risque d'allergie. Les traitements aux antibiotiques, fréquemment prescrits en pédiatrie, modifient de façon conséquente le processus de colonisation bactérienne. Cependant peu de données existent concernant l'impact d'une altération du processus de colonisation sur la maturation de la barrière intestinale et de la réponse immunitaire dirigée contre un antigène. L'objectif de ce travail était de déterminer l'impact d'un antibiotique commercial et employé en pédiatrie sur l'état de la barrière intestinale au moment critique du sevrage et d'évaluer les conséquences physiologiques d'un tel traitement sur la réponse immune à un antigène alimentaire. Nous avons mis en place un modèle de rats allaités, traités à l'antibiotique, le plus proche possible des pratiques pédiatriques, en terme de nature, dose et voie d'administration de l'antibiotique. Nous avons constaté que l'établissement de la tolérance orale à un nouvel antigène (l'ovalbumine) est altéré quand celui-ci est donné pour la première fois au cours du traitement antibiotique. Ces résultats coïncident avec une diminution de la perméabilité intestinale aux macromolécules, ainsi qu'avec une diminution de l'expression des gènes codant pour les molécules du complexe majeur d'histocomptatibilité de classe II, suggérant une modification de l'apprêtement et de la présentation de l'antigène au niveau intestinal chez les rats traités à l'antibiotique. De plus, un faible taux d'IgA et une diminution de l'expression des gènes codant pour des protéines antimicrobiennes, observés après l'administration d'antibiotique, laissent à penser que la protection contre un pathogène est diminuée lors d'un traitement antibiotique. En conclusion, nous avons observé qu'un traitement antibiotique à large spectre d'activité, couramment utilisé en pédiatrie, réduit la capacité d'induction de la tolérance orale chez le rat allaité. L'impact du traitement antibiotique sur la réponse immune semble induite par l'altération de la flore intestinale via son effet sur les mécanismes d'apprêtement et de présentation de l'antigène. Ce travail renforce l'ensemble des données existantes qui accorde à la flore intestinale un rôle clef dans la modulation du risque de développement d'allergie et nous amène à recommander d'éviter l'introduction d'un nouvel aliment lorsqu'un enfant est traité aux antibiotiques.

Directional discrepancy in two dimensions

In the present paper, we study the geometric discrepancy with respect to families of rotated rectangles. The well-known extremal cases are the axis-parallel rectangles (logarithmic discrepancy) and rectangles rotated in all possible directions (polynomial discrepancy). We study several intermediate situations: lacunary sequences of directions, lacunary sets of finite order, and sets with small Minkowski dimension. In each of these cases, extensions of a lemma due to Davenport allow us to construct appropriate rotations of the integer lattice which yield small discrepancy.

Aspects of Iwasawa theory over function fields

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Ribet bimodules and the specialization of Heegner points

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Coefficients of Drinfeld modular forms and Hecke operators

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The complement inhibitor low molecular weight dextran sulfate prevents TLR4-induced phenotypic and functional maturation of human dendritic cells.

Low molecular weight dextran sulfate (DXS) has been reported to inhibit the classical, alternative pathway as well as the mannan-binding lectin pathway of the complement system. Furthermore, it acts as an endothelial cell protectant inhibiting complement-mediated endothelial cell damage. Endothelial cells are covered with a layer of heparan sulfate (HS), which is rapidly released under conditions of inflammation and tissue injury. Soluble HS induces maturation of dendritic cells (DC) via TLR4. In this study, we show the inhibitory effect of DXS on human DC maturation. DXS significantly prevents phenotypic maturation of monocyte-derived DC and peripheral myeloid DC by inhibiting the up-regulation of CD40, CD80, CD83, CD86, ICAM-1, and HLA-DR and down-regulates DC-SIGN in response to HS or exogenous TLR ligands. DXS also inhibits the functional maturation of DC as demonstrated by reduced T cell proliferation, and strongly impairs secretion of the proinflammatory mediators IL-1beta, IL-6, IL-12p70, and TNF-alpha. Exposure to DXS leads to a reduced production of the complement component C1q and a decreased phagocytic activity, whereas C3 secretion is increased. Moreover, DXS was found to inhibit phosphorylation of IkappaB-alpha and activation of NF-kappaB. These findings suggest that DXS prevents TLR-induced maturation of human DC and may therefore be a useful reagent to impede the link between innate and adaptive immunity.

On the zeroes of Goss polynomials

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Explicit methods for Hilbert modular forms

We exhibit algorithms to compute systems of Hecke eigenvalues for spaces of Hilbert modular forms over a totally real field. We provide many explicit examples as well as applications to modularity and Galois representations.

Eisenstein series for principal congruence subgroups of GL(2,Fq[T])

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An algorithm for semi-infinite polynomial optimization

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A survey on recent p-adic integration theories and arithmetic applications

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Sur les symboles modulaires de Manin-Teitelbaum pour Fq(T)

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EZH2 is essential for glioblastoma cancer stem cell maintenance.

Overexpression of the polycomb group protein enhancer of zeste homologue 2 (EZH2) occurs in diverse malignancies, including prostate cancer, breast cancer, and glioblastoma multiforme (GBM). Based on its ability to modulate transcription of key genes implicated in cell cycle control, DNA repair, and cell differentiation, EZH2 is believed to play a crucial role in tissue-specific stem cell maintenance and tumor development. Here, we show that targeted pharmacologic disruption of EZH2 by the S-adenosylhomocysteine hydrolase inhibitor 3-deazaneplanocin A (DZNep), or its specific downregulation by short hairpin RNA (shRNA), strongly impairs GBM cancer stem cell (CSC) self-renewal in vitro and tumor-initiating capacity in vivo. Using genome-wide expression analysis of DZNep-treated GBM CSCs, we found the expression of c-myc, recently reported to be essential for GBM CSCs, to be strongly repressed upon EZH2 depletion. Specific shRNA-mediated downregulation of EZH2 in combination with chromatin immunoprecipitation experiments revealed that c-myc is a direct target of EZH2 in GBM CSCs. Taken together, our observations provide evidence that direct transcriptional regulation of c-myc by EZH2 may constitute a novel mechanism underlying GBM CSC maintenance and suggest that EZH2 may be a valuable new therapeutic target for GBM management.