Characterization of non-degenerate plane curve singularities

We characterize plane curve germes non-degenerate in Kouchnirenko's sense in terms of characteristics and intersection multiplicities of branches.Comment: LaTeX2e, 10 page

Ultrametric spaces of branches on arborescent singularities

Let $S$ be a normal complex analytic surface singularity. We say that $S$ is arborescent if the dual graph of any resolution of it is a tree. Whenever $A,B$ are distinct branches on $S$, we denote by $A \cdot B$ their intersection number in the sense of Mumford. If $L$ is a fixed branch, we define $U_L(A,B)= (L \cdot A)(L \cdot B)(A \cdot B)^{-1}$ when $A \neq B$ and $U_L(A,A) =0$ otherwise. We generalize a theorem of P{\l}oski concerning smooth germs of surfaces, by proving that whenever $S$ is arborescent, then $U_L$ is an ultrametric on the set of branches of $S$ different from $L$. We compute the maximum of $U_L$, which gives an analog of a theorem of Teissier. We show that $U_L$ encodes topological information about the structure of the embedded resolutions of any finite set of branches. This generalizes a theorem of Favre and Jonsson concerning the case when both $S$ and $L$ are smooth. We generalize also from smooth germs to arbitrary arborescent ones their valuative interpretation of the dual trees of the resolutions of $S$. Our proofs are based in an essential way on a determinantal identity of Eisenbud and Neumann.Comment: 37 pages, 16 figures. Compared to the first version on Arxiv, il has a new section 4.3, accompanied by 2 new figures. Several passages were clarified and the typos discovered in the meantime were correcte

Self-Association of an Activating Natural Killer Cell Receptor, KIR2DS1

As a major component of the innate immune system, natural killer cells are responsible for activating the cytolytic killing of certain pathogen-infected or tumor cells. The self-recognition of natural killer cells is achieved in part by the killer cell immunoglobulin-like receptors (KIRs) protein family. In the current study, using a suite of biophysical methods, we investigate the self-association of an activating KIR, KIR2DS1. This KIR is of particular interest because when in the presence of the HLA-Cw6 protein, KIR2DS1 becomes a major risk factor for psoriasis, an autoimmune chronic skin disease. Using circular dichroism spectroscopy, dynamic light scattering, and atomic force microscopy, we reveal that KIR2DS1 self-associates in a well-defined fashion. Our novel results on an activating KIR allow us to suggest a working model for the KIR2DS1- HLA class I molecular mechanism

Population Carrier Rates of Pathogenic ARSA Gene Mutations: Is Metachromatic Leukodystrophy Underdiagnosed?

BACKGROUND: Metachromatic leukodystrophy (MLD) is a severe neurometabolic disease caused mainly by deficiency of arylsulfatase A encoded by the ARSA gene. Based on epidemiological surveys the incidence of MLD per 100,000 live births varied from 0.6 to 2.5. Our purpose was to estimate the birth prevalence of MLD in Poland by determining population frequency of the common pathogenic ARSA gene mutations and to compare this estimate with epidemiological data. METHODOLOGY: We studied two independently ascertained cohorts from the Polish background population (N∼3000 each) and determined carrier rates of common ARSA gene mutations: c.459+1G>A, p.P426L, p.I179S (cohort 1) and c.459+1G>A, p.I179S (cohort 2). PRINCIPAL FINDINGS: Taking into account ARSA gene mutation distribution among 60 Polish patients, the expected MLD birth prevalence in the general population (assuming no selection against homozygous fetuses) was estimated as 4.0/100,000 and 4.1/100,000, respectively for the 1(st) and the 2(nd) cohort with a pooled estimate of 4.1/100,000 (CI: 1.8-9.4) which was higher than the estimate of 0.38 per 100,000 live births based on diagnosed cases. The p.I179S mutation was relatively more prevalent among controls than patients (OR = 3.6, P = 0.0082, for a comparison of p.I179S frequency relative to c.459+1G>A between controls vs. patients). CONCLUSIONS/SIGNIFICANCE: The observed discrepancy between the measured incidence of metachromatic leukodystrophy and the predicted carriage rates suggests that MLD is substantially underdiagnosed in the Polish population. The underdiagnosis rate may be particularly high among patients with p.I179S mutation whose disease is characterized mainly by psychotic symptoms