Reverse mathematics of matroids

Matroids generalize the familiar notion of linear dependence from linear algebra. Following a brief discussion of founding work in computability and matroids, we use the techniques of reverse mathematics to determine the logical strength of some basis theorems for matroids and enumerated matroids. Next, using Weihrauch reducibility, we relate the basis results to combinatorial choice principles and statements about vector spaces. Finally, we formalize some of the Weihrauch reductions to extract related reverse mathematics results. In particular, we show that the existence of bases for vector spaces of bounded dimension is equivalent to the induction scheme for \Sigma^0_2 formulas

Initial/boundary-value problems of tumor growth within a host tissue

This paper concerns multiphase models of tumor growth in interaction with a surrounding tissue, taking into account also the interplay with diffusible nutrients feeding the cells. Models specialize in nonlinear systems of possibly degenerate parabolic equations, which include phenomenological terms related to specific cell functions. The paper discusses general modeling guidelines for such terms, as well as for initial and boundary conditions, aiming at both biological consistency and mathematical robustness of the resulting problems. Particularly, it addresses some qualitative properties such as a priori nonnegativity, boundedness, and uniqueness of the solutions. Existence of the solutions is studied in the one-dimensional time-independent case.Comment: 30 pages, 5 figure

Congenital anterolateral tibial bowing and polydactyly: a case report

Congenital anterolateral bowing of the tibia is a rare deformity that may lead to pseudarthrosis and risk of fracture. This is commonly associated with neurofibromatosis type 1. In this report, we describe a 15-month old male with congenital anterolateral bowing of the right tibia and associated hallux duplication. This is a distinct entity with a generally favourable prognosis that should not be confused with other conditions such as neurofibromatosis type 1. Previously published cases are reviewed

A Storm in a Tea-Cup? 'Making a Difference' in Two Sure Start Children's Centres

Sure Start Children's Centres were central to the last UK Labour government in improving outcomes for children and families. Yet, participation by those who 'ought' to attend was and remains a focus of concern. Using the work of Foucault, this paper explores parental participation in two Centres to examine how 'government operates at a distance', through the everyday interactions of those who inhabit these spaces. In exploring micro-practices, the humble cup of tea can be seen, not only as a small act of caring but a site of power and struggle over what these spaces meant to parents and practitioners

Once more on the Witten index of 3d supersymmetric YM-CS theory

The problem of counting the vacuum states in the supersymmetric 3d Yang-Mills-Chern-Simons theory is reconsidered. We resolve the controversy between its original calculation by Witten at large volumes and the calculation based on the evaluation of the effective Lagrangian in the small volume limit. We show that the latter calculation suffers from uncertainties associated with the singularities in the moduli space of classical vacua where the Born-Oppenheimer approximation breaks down. We also show that these singularities can be accurately treated in the Hamiltonian Born-Oppenheimer method, where one has to match carefully the effective wave functions on the Abelian valley and the wave functions of reduced non-Abelian QM theory near the singularities. This gives the same result as original Witten's calculation.Comment: 27 page

Effect of maternal Schistosoma mansoni infection and praziquantel treatment during pregnancy on Schistosoma mansoni infection and immune responsiveness among offspring at age five years.

INTRODUCTION: Offspring of Schistosoma mansoni-infected women in schistosomiasis-endemic areas may be sensitised in-utero. This may influence their immune responsiveness to schistosome infection and schistosomiasis-associated morbidity. Effects of praziquantel treatment of S. mansoni during pregnancy on risk of S. mansoni infection among offspring, and on their immune responsiveness when they become exposed to S. mansoni, are unknown. Here we examined effects of praziquantel treatment of S. mansoni during pregnancy on prevalence of S. mansoni and immune responsiveness among offspring at age five years. METHODS: In a trial in Uganda (ISRCTN32849447, http://www.controlled-trials.com/ISRCTN32849447/elliott), offspring of women treated with praziquantel or placebo during pregnancy were examined for S. mansoni infection and for cytokine and antibody responses to SWA and SEA, as well as for T cell expression of FoxP3, at age five years. RESULTS: Of the 1343 children examined, 32 (2.4%) had S. mansoni infection at age five years based on a single stool sample. Infection prevalence did not differ between children of treated or untreated mothers. Cytokine (IFNγ, IL-5, IL-10 and IL-13) and antibody (IgG1, Ig4 and IgE) responses to SWA and SEA, and FoxP3 expression, were higher among infected than uninfected children. Praziquantel treatment of S. mansoni during pregnancy had no effect on immune responses, with the exception of IL-10 responses to SWA, which was higher in offspring of women that received praziquantel during pregnancy than those who did not. CONCLUSION: We found no evidence that maternal S. mansoni infection and its treatment during pregnancy influence prevalence and intensity of S. mansoni infection or effector immune response to S. mansoni infection among offspring at age five years, but the observed effects on IL-10 responses to SWA suggest that maternal S. mansoni and its treatment during pregnancy may affect immunoregulatory responsiveness in childhood schistosomiasis. This might have implications for pathogenesis of the disease

Follicular fluid levels of vascular endothelial growth factor and early corpus luteum function during assisted reproductive technology cycles

BACKGROUND: The relation between vascular endothelial growth factor (VEGF) and early luteal function has rarely been proven in humans. The purpose of this study was to define the relation between follicular fluid concentrations of VEGF (FF VEGF) and early luteal function at the preimplantation stage during assisted reproductive technology (ART) cycles. METHODS: 71 women were divided into two groups, based on reproductive outcome: women who became pregnant after embryo transfer (ET) (n = 18, Group A) and non-pregnant women (n = 53, Group B). Serum progesterone (Se P) and inhibin A on ET day, and FF VEGF levels were measured in all women. Data were expressed as mean ± standard deviation. Statistical analysis was performed using Excel Office 98 for Student's t-test, linear regression test and chi-square test. A p value of < 0.05 was considered statistically significant. RESULTS: The groups were comparable for age, ovarian reserve, number and quality of the oocytes retrieved and of the embryos obtained and transferred. FF VEGF levels were increased (4235 ± 1433 vs 3432 ± 1231 pg/ml), while Se P and inhibin A levels were significantly reduced (83.1 ± 34.1 vs 112.0 ± 58.8 ng/ml and 397.4 ± 223 vs 533.5 ± 283 pg/ml, respectively) in the non-pregnant group and were negatively correlated with FF VEGF (r = -0.482, p < 0.05; r = -0.468, p < 0.05) only in pregnant women. CONCLUSION: Much has to be learned about the regulation and role of VEGF during the early luteal phase. We advance the hypothesis that the existence of a negative correlation between FF VEGF/Se P and FF VEGF/inhibin A in pregnant women might indicate the existence of a normal VEGF-mediated paracrine response when Se P and inhibin A levels are decreased. Excess production of FF VEGF and the absence of a correlation between FF VEGF/Se P and FF VEGF/inhibin A in non-pregnant women may be a paracrine reaction to immature luteal vasculature, resulting in luteal dysfunction