Geodesic excursions into cusps in finite-volume hyperbolic manifolds

18 pages, no figures.-- MSC1991 codes: Primary: 53C22; Secondary: 30F40, 58F17.MR#: MR1214056 (94d:53067)Zbl#: Zbl 0793.53052The main goal of the paper is to prove that, for a given non-compact hyperbolic $n$-manifold $M$ of finite volume, $p\in M$, and a number $\alpha$, $0\leq\alpha \leq 1$, the Hausdorff dimension of the set \{v\in T\sb p\sp 1(M): \lim\sb{t\to\infty} \sup (\text{dist} (\gamma\sb v(t),p)/t)\geq \alpha\} is equal to $n(1-\alpha)$, where \gamma\sb v(t) is the geodesic in $M$ emanating from $p$ in the direction of $v$. This generalize a result of [Acta Math. 149, 215-237 (1982)] that, for almost every direction $v$, such a limit is $1/n$, and it is one for just a countable set of directions $v$.\par However we remark that one has to restrict this claim to the class of hyperbolic manifolds with only Abelian parabolic cusps because the authors assume in fact such property for all considered manifolds $M$ [source: Zentralblatt MATH].Research supported by a grant from CICYT, Ministerio de Educación y Ciencia, Spain.Publicad

Quantitative mixing results and inner functions

19 pages, no figures.-- MSC2000 codes: 30D05, 30D50, 37A05, 37A25, 37F10, 28D05, 11K55.MR#: MR2262783 (2007j:37003)Zbl#: Zbl 1125.30019We study in this paper estimates on the size of the sets of points which are well approximated by orbits of other points under certain dynamical systems. We apply the results obtained to the particular case of the dynamical system generated by inner functions in the unit disk of the complex plane.D. Pestana was supported by Grants BFM2003-04780 and BFM-2003-06335-C03-02, Ministerio de Ciencia y Tecnología, Spain. J. L. Fernández and M. V. Melián were supported by Grant BFM2003-04780 from Ministerio de Ciencia y Tecnología, Spain.Publicad

Patterson measure and ubiquity

24 pages, no figures.-- MSC1991 codes: Primary 11K55; Secondary 11K60, 11F99.MR#: MR1304105 (95j:11074)Zbl#: Zbl 0816.11043Let $L$ be a closed subset of \bbfR\sp k, with Hausdorff dimension $\delta$, which supports a probability measure $m$ for which the $m$- measure of a ball of radius $r$ and centred at a point in $L$ is comparable to r\sp \delta. By extending the notion of ubiquity from $k$-dimensional Lebesgue measure to $m$, a natural lower bound for the Hausdorff dimension of a fairly general class of $\limsup$ subsets of $L$ is obtained. This is applied to Patterson measure supported on the limit set of a convex co-compact group to obtain the Hausdorff dimension of the set of 'well-approximable' points associated with the limit set of a convex co-compact group. The equivalent geometric result in terms of geodesic excursions on the quotient manifold is also obtained. These results are counterparts of the Jarník's theorem on simultaneous diophantine approximation.Research partially supported by the Royal Society European Programme.Publicad

Autoantibodies against type I IFNs in patients with life-threatening COVID-19

International audienceInterindividual clinical variability in the course of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection is vast. We report that at least 101 of 987 patients with life-threatening coronavirus disease 2019 (COVID-19) pneumonia had neutralizing immunoglobulin G (IgG) autoantibodies (auto-Abs) against interferon-ω (IFN-ω) (13 patients), against the 13 types of IFN-α (36), or against both (52) at the onset of critical disease; a few also had auto-Abs against the other three type I IFNs. The auto-Abs neutralize the ability of the corresponding type I IFNs to block SARS-CoV-2 infection in vitro. These auto-Abs were not found in 663 individuals with asymptomatic or mild SARS-CoV-2 infection and were present in only 4 of 1227 healthy individuals. Patients with auto-Abs were aged 25 to 87 years and 95 of the 101 were men. A B cell autoimmune phenocopy of inborn errors of type I IFN immunity accounts for life-threatening COVID-19 pneumonia in at least 2.6% of women and 12.5% of men

Rare predicted loss-of-function variants of type I IFN immunity genes are associated with life-threatening COVID-19

BackgroundWe previously reported that impaired type I IFN activity, due to inborn errors of TLR3- and TLR7-dependent type I interferon (IFN) immunity or to autoantibodies against type I IFN, account for 15-20% of cases of life-threatening COVID-19 in unvaccinated patients. Therefore, the determinants of life-threatening COVID-19 remain to be identified in similar to 80% of cases.MethodsWe report here a genome-wide rare variant burden association analysis in 3269 unvaccinated patients with life-threatening COVID-19, and 1373 unvaccinated SARS-CoV-2-infected individuals without pneumonia. Among the 928 patients tested for autoantibodies against type I IFN, a quarter (234) were positive and were excluded.ResultsNo gene reached genome-wide significance. Under a recessive model, the most significant gene with at-risk variants was TLR7, with an OR of 27.68 (95%CI 1.5-528.7, P=1.1x10(-4)) for biochemically loss-of-function (bLOF) variants. We replicated the enrichment in rare predicted LOF (pLOF) variants at 13 influenza susceptibility loci involved in TLR3-dependent type I IFN immunity (OR=3.70[95%CI 1.3-8.2], P=2.1x10(-4)). This enrichment was further strengthened by (1) adding the recently reported TYK2 and TLR7 COVID-19 loci, particularly under a recessive model (OR=19.65[95%CI 2.1-2635.4], P=3.4x10(-3)), and (2) considering as pLOF branchpoint variants with potentially strong impacts on splicing among the 15 loci (OR=4.40[9%CI 2.3-8.4], P=7.7x10(-8)). Finally, the patients with pLOF/bLOF variants at these 15 loci were significantly younger (mean age [SD]=43.3 [20.3] years) than the other patients (56.0 [17.3] years; P=1.68x10(-5)).ConclusionsRare variants of TLR3- and TLR7-dependent type I IFN immunity genes can underlie life-threatening COVID-19, particularly with recessive inheritance, in patients under 60 years old

The risk of COVID-19 death is much greater and age dependent with type I IFN autoantibodies

International audienceSignificance There is growing evidence that preexisting autoantibodies neutralizing type I interferons (IFNs) are strong determinants of life-threatening COVID-19 pneumonia. It is important to estimate their quantitative impact on COVID-19 mortality upon SARS-CoV-2 infection, by age and sex, as both the prevalence of these autoantibodies and the risk of COVID-19 death increase with age and are higher in men. Using an unvaccinated sample of 1,261 deceased patients and 34,159 individuals from the general population, we found that autoantibodies against type I IFNs strongly increased the SARS-CoV-2 infection fatality rate at all ages, in both men and women. Autoantibodies against type I IFNs are strong and common predictors of life-threatening COVID-19. Testing for these autoantibodies should be considered in the general population

The risk of COVID-19 death is much greater and age dependent with type I IFN autoantibodies

International audienceSignificance There is growing evidence that preexisting autoantibodies neutralizing type I interferons (IFNs) are strong determinants of life-threatening COVID-19 pneumonia. It is important to estimate their quantitative impact on COVID-19 mortality upon SARS-CoV-2 infection, by age and sex, as both the prevalence of these autoantibodies and the risk of COVID-19 death increase with age and are higher in men. Using an unvaccinated sample of 1,261 deceased patients and 34,159 individuals from the general population, we found that autoantibodies against type I IFNs strongly increased the SARS-CoV-2 infection fatality rate at all ages, in both men and women. Autoantibodies against type I IFNs are strong and common predictors of life-threatening COVID-19. Testing for these autoantibodies should be considered in the general population