Analytic curves in algebraic varieties over number fields

We establish algebraicity criteria for formal germs of curves in algebraic varieties over number fields and apply them to derive a rationality criterion for formal germs of functions, which extends the classical rationality theorems of Borel-Dwork and P\'olya-Bertrandias valid over the projective line to arbitrary algebraic curves over a number field. The formulation and the proof of these criteria involve some basic notions in Arakelov geometry, combined with complex and rigid analytic geometry (notably, potential theory over complex and $p$-adic curves). We also discuss geometric analogues, pertaining to the algebraic geometry of projective surfaces, of these arithmetic criteria.Comment: 55 pages. To appear in "Algebra, Arithmetic, and Geometry: In Honor of Y.i. Manin", Y. Tschinkel & Yu. Manin editors, Birkh\"auser, 200

Affine modifications and affine hypersurfaces with a very transitive automorphism group

We study a kind of modification of an affine domain which produces another affine domain. First appeared in passing in the basic paper of O. Zariski (1942), it was further considered by E.D. Davis (1967). The first named author applied its geometric counterpart to construct contractible smooth affine varieties non-isomorphic to Euclidean spaces. Here we provide certain conditions which guarantee preservation of the topology under a modification. As an application, we show that the group of biregular automorphisms of the affine hypersurface $X \subset C^{k+2}$ given by the equation $uv=p(x_1,...,x_k)$ where $p \in C[x_1,...,x_k],$ acts $m-$transitively on the smooth part reg$X$ of $X$ for any $m \in N.$ We present examples of such hypersurfaces diffeomorphic to Euclidean spaces.Comment: 39 Pages, LaTeX; a revised version with minor changes and correction

Propositional Dynamic Logic for Message-Passing Systems

We examine a bidirectional propositional dynamic logic (PDL) for finite and infinite message sequence charts (MSCs) extending LTL and TLC-. By this kind of multi-modal logic we can express properties both in the entire future and in the past of an event. Path expressions strengthen the classical until operator of temporal logic. For every formula defining an MSC language, we construct a communicating finite-state machine (CFM) accepting the same language. The CFM obtained has size exponential in the size of the formula. This synthesis problem is solved in full generality, i.e., also for MSCs with unbounded channels. The model checking problem for CFMs and HMSCs turns out to be in PSPACE for existentially bounded MSCs. Finally, we show that, for PDL with intersection, the semantics of a formula cannot be captured by a CFM anymore

Lack of association of the CIITA -168A→G promoter SNP with myasthenia gravis and its role in autoimmunity

<p>Abstract</p> <p>Background</p> <p>The major histocompatibility complex class II transactivator (CIITA) regulates MHC class II gene expression. A promoter SNP -168A→G (rs3087456) has previously been shown to be associated with susceptibility to several immune mediated disorders, including rheumatoid arthritis (RA), multiple sclerosis (MS) and myocardial infarction (MI). Myasthenia gravis (MG) is an autoimmune disorder which has previously been shown to be associated with polymorphisms of several autoimmune predisposing genes, including <it>IL-1</it>, <it>PTPN22</it>, <it>TNF-α </it>and the <it>MHC</it>. In order to determine if allelic variants of rs3087456 increase predisposition to MG, we analyzed this SNP in our Swedish cohort of 446 MG patients and 1866 controls.</p> <p>Results</p> <p>No significant association of the SNP with MG was detected, neither in the patient group as a whole, nor in any clinical subgroup. The vast majority of previous replication studies have also not found an association of the SNP with autoimmune disorders.</p> <p>Conclusions</p> <p>We thus conclude that previous findings with regard to the role of the <it>CIITA </it>-168A→G SNP in autoimmunity may have to be reconsidered.</p

Decreased Prevalence of Lymphatic Filariasis among Diabetic Subjects Associated with a Diminished Pro-Inflammatory Cytokine Response (CURES 83)

Epidemiological studies have shown an inverse correlation between the incidence of lymphatic filariasis (LF) and the incidence of allergies and autoimmunity. However, the interrelationship between LF and type-2 diabetes is not known and hence, a cross sectional study to assess the baseline prevalence and the correlates of sero-positivity of LF among diabetic subjects was carried out (n = 1416) as part of the CURES study. There was a significant decrease in the prevalence of LF among diabetic subjects (both newly diagnosed [5.7%] and those under treatment [4.3%]) compared to pre-diabetic subjects [9.1%] (p = 0.0095) and non-diabetic subjects [10.4%] (p = 0.0463). A significant decrease in filarial antigen load (p = 0.04) was also seen among diabetic subjects. Serum cytokine levels of the pro-inflammatory cytokines—IL-6 and GM-CSF—were significantly lower in diabetic subjects who were LF positive, compared to those who were LF negative. There were, however, no significant differences in the levels of anti-inflammatory cytokines—IL-10, IL-13 and TGF-β—between the two groups. Although a direct causal link has yet to be shown, there appears to be a striking inverse relationship between the prevalence of LF and diabetes, which is reflected by a diminished pro-inflammatory cytokine response in Asian Indians with diabetes and concomitant LF

BAFF Promotes Th17 Cells and Aggravates Experimental Autoimmune Encephalomyelitis

BAFF, in addition to promoting B cell survival and differentiation, may affect T cells. The objective of this study was to determine the effect of BAFF on Th17 cell generation and its ramifications for the Th17 cell-driven disease, EAE.Th17 cells were increased in BAFF-Tg B6 (B6.BTg) mice and decreased in B6.Baff(-/-) mice. Th17 cells in B6.Baff(-/-) mice bearing a BAFF Tg (B6.Baff(-/-).BTg mice) were identical to those in B6.BTg mice, indicating that membrane BAFF is dispensable for Th17 cell generation as long as soluble BAFF is plentiful. In T + non-T cell criss-cross co-cultures, Th17 cell generation was greatest in cultures containing B6.BTg T cells and lowest in cultures containing B6.Baff(-/-) T cells, regardless of the source of non-T cells. In cultures containing only T cells, Th17 cell generation followed an identical pattern. CD4(+) cell expression of CD126 (IL-6R α chain) was increased in B6.BTg mice and decreased in B6.Baff(-/-) mice, and activation of STAT3 following stimulation with IL-6 + TGF-β was also greatest in B6.BTg cells and lowest in B6.Baff(-/-) cells. EAE was clinically and pathologically most severe in B6.BTg mice and least severe in B6.Baff(-/-) mice and correlated with MOG(35-55) peptide-induced Th17 cell responses.Collectively, these findings document a contribution of BAFF to pathogenic Th17 cell responses and suggest that BAFF antagonism may be efficacious in Th17 cell-driven diseases

Diabetic foot infections: a team-oriented review of medical and surgical management

As the domestic and international incidence of diabetes and metabolic syndrome continues to rise, health care providers need to continue improving management of the long-term complications of the disease. Emergency department visits and hospital admissions for diabetic foot infections are increasingly commonplace, and a like-minded multidisciplinary team approach is needed to optimize patient care. Early recognition of severe infections, medical stabilization, appropriate antibiotic selection, early surgical intervention, and strategic plans for delayed reconstruction are crucial components of managing diabetic foot infections. The authors review initial medical and surgical management and staged surgical reconstruction of diabetic foot infections in the inpatient setting