Lojasiewicz exponent of families of ideals, Rees mixed multiplicities and Newton filtrations

We give an expression for the {\L}ojasiewicz exponent of a wide class of n-tuples of ideals $(I_1,..., I_n)$ in \O_n using the information given by a fixed Newton filtration. In order to obtain this expression we consider a reformulation of {\L}ojasiewicz exponents in terms of Rees mixed multiplicities. As a consequence, we obtain a wide class of semi-weighted homogeneous functions $(\mathbb{C}^n,0)\to (\mathbb{C},0)$ for which the {\L}ojasiewicz of its gradient map $\nabla f$ attains the maximum possible value.Comment: 25 pages. Updated with minor change

Thyroid Stimulating Hormone Receptor (TSHR) Intron 1 Variants Are Major Risk Factors for Graves' Disease in Three European Caucasian Cohorts

BACKGROUND: The thyroid stimulating hormone receptor (TSHR) gene is an established susceptibility locus for Graves' disease (GD), with recent studies refining association to two single nucleotide polymorphisms (SNPs), rs179247 and rs12101255, within TSHR intron 1. METHODOLOGY AND PRINCIPAL FINDINGS: We aimed to validate association of rs179247 and rs12101255 in Polish and UK Caucasian GD case-control subjects, determine the mode of inheritance and to see if association correlates with specific GD clinical manifestations. We investigated three case-control populations; 558 GD patients and 520 controls from Warsaw, Poland, 196 GD patients and 198 controls from Gliwice, Poland and 2504 GD patients from the UK National collection and 2784 controls from the 1958 British Birth cohort. Both rs179247 (P = 1.2×10(-2)-6.2×10(-15), OR = 1.38-1.45) and rs12101255 (P = 1.0×10(-4)-3.68×10(-21), OR = 1.47-1.87) exhibited strong association with GD in all three cohorts. Logistic regression suggested association of rs179247 is secondary to rs12101255 in all cohorts. Inheritance modeling suggested a co-dominant mode of inheritance in all cohorts. Genotype-phenotype correlations provided no clear evidence of association with any specific clinical characteristics. CONCLUSIONS: We have validated association of TSHR intron 1 SNPs with GD in three independent European cohorts and have demonstrated that the aetiological variant within the TSHR is likely to be in strong linkage disequilibrium with rs12101255. Fine mapping is now required to determine the exact location of the aetiological DNA variants within the TSHR

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

On the Milnor formula in arbitrary characteristic

The Milnor formula $\mu=2\delta-r+1$ relates the Milnor number $\mu$, the double point number $\delta$ and the number $r$ of branches of a plane curve singularity. It holds over the fields of characteristic zero. Melle and Wall based on a result by Deligne proved the inequality $\mu\geq 2\delta-r+1$ in arbitrary characteristic and showed that the equality $\mu=2\delta-r+1$ characterizes the singularities with no wild vanishing cycles. In this note we give an account of results on the Milnor formula in characteristic $p$. It holds if the plane singularity is Newton non-degenerate (Boubakri et al. Rev. Mat. Complut. (2010) 25) or if $p$ is greater than the intersection number of the singularity with its generic polar (Nguyen H.D., Annales de l'Institut Fourier, Tome 66 (5) (2016)). Then we improve our result on the Milnor number of irreducible singularities (Bull. London Math. Soc. 48 (2016)). Our considerations are based on the properties of polars of plane singularities in characteristic $p$.Comment: 18 page

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

A Machine-Learning-Based Approach to Prediction of Biogeographic Ancestry within Europe

Data obtained with the use of massive parallel sequencing (MPS) can be valuable in population genetics studies. In particular, such data harbor the potential for distinguishing samples from different populations, especially from those coming from adjacent populations of common origin. Machine learning (ML) techniques seem to be especially well suited for analyzing large datasets obtained using MPS. The Slavic populations constitute about a third of the population of Europe and inhabit a large area of the continent, while being relatively closely related in population genetics terms. In this proof-of-concept study, various ML techniques were used to classify DNA samples from Slavic and non-Slavic individuals. The primary objective of this study was to empirically evaluate the feasibility of discerning the genetic provenance of individuals of Slavic descent who exhibit genetic similarity, with the overarching goal of categorizing DNA specimens derived from diverse Slavic population representatives. Raw sequencing data were pre-processed, to obtain a 1200 character-long binary vector. A total of three classifiers were used—Random Forest, Support Vector Machine (SVM), and XGBoost. The most-promising results were obtained using SVM with a linear kernel, with 99.9% accuracy and F1-scores of 0.9846–1.000 for all classes

Clinical features, etiology, and survival in patients with restrictive cardiomyopathy: A single-center experience

Background: Numerous prognostic factors have been proposed for cardiac amyloidosis (CA). The knowledge about other subtypes of restrictive cardiomyopathy (RCM) is scant.Aims: This study aimed to elucidate the etiology and prognostic factors of RCM as well as assess cardiac biomarkers: high-sensitive troponin T (hs-TnT), growth differentiation factor-15 (GDF-15), N-terminal pro-B-type natriuretic peptide (NT-proBNP), and soluble suppression of tumorigenicity 2, as mortality predictors in RCM.Methods: We enrolled 36 RCM patients in our tertiary cardiac department. All patients were screened for CA. Genetic testing was performed in 17 patients without CA.Results: Pathogenic or likely pathogenic gene variants were found in 86% of patients, including 5 novel variants. Twenty patients died, and 4 had a heart transplantation during the study. Median overall survival was 29 months (8–55). The univariate Cox models analysis indicated that systolic and diastolic blood pressure, GDF-15, hs-TnT, NT-proBNP, left ventricular stroke volume, the ratio of the transmitral early peak velocity (E) estimated by pulsed wave Doppler over the early mitral annulus velocity (e’), tricuspid annulus plane systolic excursion, early tricuspid valve annular systolic velocity, the presence of pulmonary hypertension, and pericardial effusion influenced survival (P <0.05). A worse prognosis was observed in patients with GDF-15 >1316 pg/ml, hs-TnT >42 ng/l, NT-proBNP >3383 pg/ml, and pericardial effusion >3.5 mm (Kaplan-Meier analysis, log-rank test, P <0.001).Conclusions: Genetic testing should be considered in every RCM patient where light-chain amyloidosis has been excluded. Survival remains poor regardless of etiology. Increased concentrations of GDF-15, hs-TNT, NT-proBNP, and pericardial effusion are associated with worse prognosis. Further studies are warranted