The quantization of the symplectic groupoid of the standard Podles sphere

We give an explicit form of the symplectic groupoid that integrates the semiclassical standard Podles sphere. We show that Sheu's groupoid, whose convolution C*-algebra quantizes the sphere, appears as the groupoid of the Bohr-Sommerfeld leaves of a (singular) real polarization of the symplectic groupoid. By using a complex polarization we recover the convolution algebra on the space of polarized sections. We stress the role of the modular class in the definition of the scalar product in order to get the correct quantum space.Comment: 33 pages; minor correction

Guillain-Barré syndrome following the 2009 pandemic monovalent and seasonal trivalent influenza vaccination campaigns in Spain from 2009 to 2011: Outcomes from active surveillance by a neurologist network, and records from a country-wide hospital discharge database

Background: Studies have shown a slight excess risk in Guillain-Barré syndrome (GBS) incidence associated with A(H1N1)pdm09 vaccination campaign and seasonal trivalent influenza vaccine immunisations in 2009-2010. We aimed to assess the incidence of GBS as a potential adverse effect of A(H1N1)pdm09 vaccination. Methods: A neurologist-led network, active at the neurology departments of ten general hospitals serving an adult population of 4.68 million, conducted GBS surveillance in Spain in 2009-2011. The network, established in 1996, carried out a retrospective and a prospective study to estimate monthly alarm thresholds in GBS incidence and tested them in 1998-1999 in a pilot study. Such incidence thresholds additionally to observation of GBS cases with immunisation antecedent in the 42 days prior to clinical onset were taken as alarm signals for 2009-2011, since November 2009 onwards. For purpose of surveillance, in 2009 we updated both the available centres and the populations served by the network. We also did a retrospective countrywide review of hospital-discharged patients having ICD-9-CM code 357.0 (acute infective polyneuritis) as their principal diagnosis from January 2009 to December 2011. Results: Among 141 confirmed of 148 notified cases of GBS or Miller-Fisher syndrome, Brighton 1-2 criteria in 96 %, not a single patient was identified with clinical onset during the 42-day time interval following A(H1N1)pdm09 vaccination. In contrast, seven cases were seen during a similar period after seasonal campaigns. Monthly incidence figures did not, however, exceed the upper 95 % CI limit of expected incidence. A retrospective countrywide review of the registry of hospital-discharged patients having ICD-9-CM code 357.0 (acute infective polyneuritis) as their principal diagnosis did not suggest higher admission rates in critical months across the period December 2009-February 2010. Conclusions: Despite limited power and underlying reporting bias in 2010-2011, an increase in GBS incidence over background GBS, associated with A(H1N1)pdm09 monovalent or trivalent influenza immunisations, appears unlikely

C-reactive protein cut-off for early tocilizumab and dexamethasone prescription in hospitalized patients with COVID-19

Dexamethasone and tocilizumab have been associated with reduction in mortality, however, the beneficial effect is not for all patients and the impact on viral replication is not well defined. We hypostatized that C-reactive protein (CRP) could help in the identification of patients requiring anti-inflammatory therapy. Patients admitted for > 48 h in our hospital for a confirmed or suspected infection by SARS-CoV-2 from February 2020 to February 2021 were retrospectively evaluated. The primary outcome was mortality at 30 days. Demographics and the most relevant variables related with the outcome were included. CRP was stratified by percentiles. Univariate and multivariate analysis were performed. A total of 3218 patients were included with a median (IQR) age of 66 (74-78) years and 58.9% were males. The rate of intensive care unit admission was 24.4% and the 30-day mortality rate was 11.8%. Within the first 5 days from admission, 1018 (31.7%) patients received dexamethasone and 549 tocilizumab (17.1%). The crude analysis showed a mortality reduction in patients receiving dexamethasone when CRP was > 13.75 mg/dL and > 3.5 mg/dL for those receiving tocilizumab. Multivariate analysis identified the interaction of CRP > 13.75 mg/dL with dexamethasone (OR 0.57; CI 95% 0.37-0.89, P = 0014) and CRP > 3.5 mg/dL with tocilizumab (0.65; CI95%:0.44-0.95, P = 0.029) as independent predictors of mortality. Our results suggest that dexamethasone and tocilizumab are associated with a reduction in mortality when prescribed to patients with a certain inflammatory activity assessed by C-reactive protein

Data of "An accurate database of the fixation probabilities for all undirected graphs of order 10 or less"

The fixation probability is a fundamental concept in evolutionary dynamics, representing the probability that a gene spreads over a whole population. An interesting model to study both neutral drift and natural selection on homogeneous population was introduced by Moran in the '50, and later generalized to non uniform populations by Lieberman et al in 2005. Here we present an accurate database of the fixation probabilities for all undirected graphs with 10 or less vertices. Moreover, the database has been enriched with some graph invariants which have been related to the fixation probability. The fixation probabilities are computed with extreme accuracy with a relative error similar to the machine error. Using python and the h5py package it can be easily explored. The following lines describes how to read this data and plot a simple scatter of the probability of fixation at r=2 vs biconnectivity: import h5py as h5 import matplotlib.pyplot as plt infile = h5.File('fp_le10.hdf5', 'r') data = infile['FP'][:] infile.close() plt.plot( data['FP_2.0'], data['is_biconnected'], 'o' ) plt.show(

Unique ergodicity of the horocycle flow on Riemannnian foliations

International audienceA classic result due to Furstenberg is the strict ergodicity of the horocycle flow for a compact hyperbolic surface. Strict ergodicity is unique ergodicity with respect to a measure of full support, and therefore it implies minimality. The horocycle flow has been previously studied on minimal foliations by hyperbolic surfaces on closed manifolds, where it is known not to be minimal in general. In this paper, we prove that for the special case of Riemannian foliations, strict ergodicity of the horocycle flow still holds. This, in particular, proves that this flow is minimal, which establishes a conjecture proposed by Matsumoto. The main tool is a theorem due to Coudène, which he presented as an alternative proof for the surface case. It applies to two continuous flows defining a measure-preserving action of the affine group of the line on a compact metric space, precisely matching the foliated setting. In addition, we briefly discuss the application of Coudène’s theorem to other kinds of foliations