Airy functions over local fields

Airy integrals are very classical but in recent years they have been generalized to higher dimensions and these generalizations have proved to be very useful in studying the topology of the moduli spaces of curves. We study a natural generalization of these integrals when the ground field is a non-archimedean local field such as the field of p-adic numbers. We prove that the p-adic Airy integrals are locally constant functions of moderate growth and present evidence that the Airy integrals associated to compact p-adic Lie groups also have these properties.Comment: Minor change

Influence of caregiver network support and caregiver psychopathology on child mental health need and service use in the LONGSCAN study

Using structural equation modeling, this study examined the relationship of caregiver network support on caregiver and child mental health need, as well as child mental health service use among 1075 8-year-old children participating in the LONGSCAN study. The final model showed acceptable fit (χ2 = 301.476, df = 136, p<0.001; RMSEA = 0.052; CFI = 0.95). Caregiver and child mental health needs were positively related. As predicted, caregiver network support exerted a protective effect, with greater levels of caregiver network support predictive of lower caregiver and child need. Contrary to prediction, however, caregiver network support was not directly related to child service use. Higher child need was directly related to child service use, especially among children whose caregivers had mental health problems. The findings appear to indicate that lower levels of caregiver network support may exert its impact on child service use indirectly by increasing caregiver and child need, rather than by directly increasing the likelihood of receiving services, especially for African American children

Rheumatoid Arthritis is an Autoimmune Disease Triggered by Proteus Urinary Tract Infection

Rheumatoid arthritis (RA) is a chronic and disabling polyarthritic disease, which affects mainly women in middle and old age

The Tetraspanin Protein CD37 Regulates IgA Responses and Anti-Fungal Immunity

Immunoglobulin A (IgA) secretion by plasma cells in the immune system is critical for protecting the host from environmental and microbial infections. However, the molecular mechanisms underlying the generation of IgA+ plasma cells remain poorly understood. Here, we report that the B cell–expressed tetraspanin CD37 inhibits IgA immune responses in vivo. CD37-deficient (CD37−/−) mice exhibit a 15-fold increased level of IgA in serum and significantly elevated numbers of IgA+ plasma cells in spleen, mucosal-associated lymphoid tissue, as well as bone marrow. Analyses of bone marrow chimeric mice revealed that CD37–deficiency on B cells was directly responsible for the increased IgA production. We identified high local interleukin-6 (IL-6) production in germinal centers of CD37−/− mice after immunization. Notably, neutralizing IL-6 in vivo reversed the increased IgA response in CD37−/− mice. To demonstrate the importance of CD37—which can associate with the pattern-recognition receptor dectin-1—in immunity to infection, CD37−/− mice were exposed to Candida albicans. We report that CD37−/− mice are evidently better protected from infection than wild-type (WT) mice, which was accompanied by increased IL-6 levels and C. albicans–specific IgA antibodies. Importantly, adoptive transfer of CD37−/− serum mediated protection in WT mice and the underlying mechanism involved direct neutralization of fungal cells by IgA. Taken together, tetraspanin protein CD37 inhibits IgA responses and regulates the anti-fungal immune response

Reverse Effect of Mammalian Hypocalcemic Cortisol in Fish: Cortisol Stimulates Ca2+ Uptake via Glucocorticoid Receptor-Mediated Vitamin D3 Metabolism

Cortisol was reported to downregulate body-fluid Ca2+ levels in mammals but was proposed to show hypercalcemic effects in teleostean fish. Fish, unlike terrestrial vertebrates, obtain Ca2+ from the environment mainly via the gills and skin rather than by dietary means, and have to regulate the Ca2+ uptake functions to cope with fluctuating Ca2+ levels in aquatic environments. Cortisol was previously found to regulate Ca2+ uptake in fish; however, the molecular mechanism behind this is largely unclear. Zebrafish were used as a model to explore this issue. Acclimation to low-Ca2+ fresh water stimulated Ca2+ influx and expression of epithelial calcium channel (ecac), 11β-hydroxylase and the glucocorticoid receptor (gr). Exogenous cortisol increased Ca2+ influx and the expressions of ecac and hydroxysteroid 11-beta dehydrogenase 2 (hsd11b2), but downregulated 11β-hydroxylase and the gr with no effects on other Ca2+ transporters or the mineralocorticoid receptor (mr). Morpholino knockdown of the GR, but not the MR, was found to impair zebrafish Ca2+ uptake function by inhibiting the ecac expression. To further explore the regulatory mechanism of cortisol in Ca2+ uptake, the involvement of vitamin D3 was analyzed. Cortisol stimulated expressions of vitamin D-25hydroxylase (cyp27a1), cyp27a1 like (cyp27a1l), 1α-OHase (cyp27b1) at 3 dpf through GR, the first time to demonstrate the relationship between cortisol and vitamin D3 in fish. In conclusion, cortisol stimulates ecac expression to enhance Ca2+ uptake functions, and this control pathway is suggested to be mediated by the GR. Lastly, cortisol also could mediate vitamin D3 signaling to stimulate Ca2+ uptake in zebrafish

Open systems in classical mechanics

Generalized span categories provide a framework for formalizing mathematical models of open systems in classical mechanics. We introduce categories $\mathsf{LagSy}$ and $\mathsf{HamSy}$ that respectively provide a categorical framework for the Lagrangian and Hamiltonian descriptions of open classical mechanical systems. The morphisms of $\mathsf{LagSy}$ and $\mathsf{HamSy}$ correspond to such open systems, and composition of morphisms models the construction of systems from subsystems. The Legendre transformation gives rise to a functor from $\mathsf{LagSy}$ to $\mathsf{HamSy}$ that translates from the Lagrangian to the Hamiltonian perspective