Resolvent Estimates in L^p for the Stokes Operator in Lipschitz Domains

We establish the $L^p$ resolvent estimates for the Stokes operator in Lipschitz domains in $R^d$, $d\ge 3$ for $|\frac{1}{p}-1/2|< \frac{1}{2d} +\epsilon$. The result, in particular, implies that the Stokes operator in a three-dimensional Lipschitz domain generates a bounded analytic semigroup in $L^p$ for (3/2)-\varep < p< 3+\epsilon. This gives an affirmative answer to a conjecture of M. Taylor.Comment: 28 page. Minor revision was made regarding the definition of the Stokes operator in Lipschitz domain

Some genus 3 curves with many points

Using an explicit family of plane quartic curves, we prove the existence of a genus 3 curve over any finite field of characteristic 3 whose number of rational points stays within a fixed distance from the Hasse-Weil-Serre upper bound. We also provide an intrinsic characterization of so-called Legendre elliptic curves

Computing Hilbert Class Polynomials

We present and analyze two algorithms for computing the Hilbert class polynomial $H_D$ . The first is a p-adic lifting algorithm for inert primes p in the order of discriminant D < 0. The second is an improved Chinese remainder algorithm which uses the class group action on CM-curves over finite fields. Our run time analysis gives tighter bounds for the complexity of all known algorithms for computing $H_D$, and we show that all methods have comparable run times

Equidistribution of Heegner Points and Ternary Quadratic Forms

We prove new equidistribution results for Galois orbits of Heegner points with respect to reduction maps at inert primes. The arguments are based on two different techniques: primitive representations of integers by quadratic forms and distribution relations for Heegner points. Our results generalize one of the equidistribution theorems established by Cornut and Vatsal in the sense that we allow both the fundamental discriminant and the conductor to grow. Moreover, for fixed fundamental discriminant and variable conductor, we deduce an effective surjectivity theorem for the reduction map from Heegner points to supersingular points at a fixed inert prime. Our results are applicable to the setting considered by Kolyvagin in the construction of the Heegner points Euler system

On multiplicities in length spectra of arithmetic hyperbolic three-orbifolds

Asymptotic laws for mean multiplicities of lengths of closed geodesics in arithmetic hyperbolic three-orbifolds are derived. The sharpest results are obtained for non-compact orbifolds associated with the Bianchi groups SL(2,o) and some congruence subgroups. Similar results hold for cocompact arithmetic quaternion groups, if a conjecture on the number of gaps in their length spectra is true. The results related to the groups above give asymptotic lower bounds for the mean multiplicities in length spectra of arbitrary arithmetic hyperbolic three-orbifolds. The investigation of these multiplicities is motivated by their sensitive effect on the eigenvalue spectrum of the Laplace-Beltrami operator on a hyperbolic orbifold, which may be interpreted as the Hamiltonian of a three-dimensional quantum system being strongly chaotic in the classical limit.Comment: 29 pages, uuencoded ps. Revised version, to appear in NONLINEARIT

What is the potential benefit of pre-hospital extracorporeal cardiopulmonary resuscitation for patients with an out-of-hospital cardiac arrest?:A predictive modelling study

AIM: In this predictive modelling study we aimed to investigate how many patients with an out-of-hospital cardiac arrest (OHCA) would benefit from pre-hospital as opposed to in-hospital initiation of extracorporeal cardiopulmonary resuscitation (ECPR).METHODS: A temporal spatial analysis of Utstein data was performed for all adult patients with a non-traumatic OHCA attended by three emergency medical services (EMS) covering the north of the Netherlands during a one-year period. Patients were considered potentially eligible for ECPR if they had a witnessed arrest with immediate bystander CPR, an initial shockable rhythm (or signs of life during resuscitation) and could be presented in an ECPR-centre within 45 minutes of the arrest. Endpoint of interest was defined as the hypothetical number of ECPR eligible patients after 10, 15 and 20 minutes of conventional CPR and upon (hypothetical) arrival in an ECPR-centre as a fraction of the total number of OHCA patients attended by EMS.RESULTS: During the study period 622 OHCA patients were attended, of which 200 (32%) met ECPR eligibility criteria upon EMS arrival. The optimal transition point between conventional CPR and ECPR was found to be after 15 minutes. Hypothetical intra-arrest transport of all patients in whom no return of spontaneous circulation (ROSC) was obtained after that point (n = 84) would have yielded 16/622 (2.5%) patients being potentially ECPR eligible upon hospital arrival (average low-flow time 52 minutes), whereas on-scene initiation of ECPR would have resulted in 84/622 (13.5%) potential candidates (average estimated low-flow time 24 minutes before cannulation).CONCLUSION: Even in healthcare systems with relatively short transport distances to hospital, consideration should be given to pre-hospital initiation of ECPR for OHCA as it shortens low-flow time and increases the number of potentially eligible patients.</p

Suppression of airway inflammation by Illicium verum and trans-anethole

_Background_ SH2 domain containing inositol-5-phosphatase (SHIP1) is an important modulator of innate and adaptive immunity. In mice, loss of SHIP1 provokes severe ileitis resembling Crohn's disease (CD), as a result of deregulated immune responses, altered cytokine production and intestinal fibrosis. Recently, SHIP1 activity was shown to be correlated to the presence of a CD-associated single nucleotide polymorphism in ATG16L1. Here, we studied SHIP1 activity and expression in an adult cohort of CD patients. _Methods_ SHIP1 activity, protein and mRNA expression in peripheral blood mononuclear cells from CD patients in clinical remission were determined by Malachite green assay, Western blotting an

A Novel Pzg-NURF Complex Regulates Notch Target Gene Activity

The Putzig (Pzg) protein is associated with the NURF nucleosome remodeling complex, thereby promoting Notch target gene expression. Our findings suggest a novel Pzg-NURF complex that is responsible for the epigenetic regulation of Notch target genes

The Nucleosome-Remodeling ATPase ISWI Is Regulated by Poly-ADP-Ribosylation

ATP-dependent nucleosome-remodeling enzymes and covalent modifiers of chromatin set the functional state of chromatin. However, how these enzymatic activities are coordinated in the nucleus is largely unknown. We found that the evolutionary conserved nucleosome-remodeling ATPase ISWI and the poly-ADP-ribose polymerase PARP genetically interact. We present evidence showing that ISWI is target of poly-ADP-ribosylation. Poly-ADP-ribosylation counteracts ISWI function in vitro and in vivo. Our work suggests that ISWI is a physiological target of PARP and that poly-ADP-ribosylation can be a new, important post-translational modification regulating the activity of ATP-dependent nucleosome remodelers

Stress-Induced PARP Activation Mediates Recruitment of Drosophila Mi-2 to Promote Heat Shock Gene Expression

Eukaryotic cells respond to genomic and environmental stresses, such as DNA damage and heat shock (HS), with the synthesis of poly-[ADP-ribose] (PAR) at specific chromatin regions, such as DNA breaks or HS genes, by PAR polymerases (PARP). Little is known about the role of this modification during cellular stress responses. We show here that the nucleosome remodeler dMi-2 is recruited to active HS genes in a PARP–dependent manner. dMi-2 binds PAR suggesting that this physical interaction is important for recruitment. Indeed, a dMi-2 mutant unable to bind PAR does not localise to active HS loci in vivo. We have identified several dMi-2 regions which bind PAR independently in vitro, including the chromodomains and regions near the N-terminus containing motifs rich in K and R residues. Moreover, upon HS gene activation, dMi-2 associates with nascent HS gene transcripts, and its catalytic activity is required for efficient transcription and co-transcriptional RNA processing. RNA and PAR compete for dMi-2 binding in vitro, suggesting a two step process for dMi-2 association with active HS genes: initial recruitment to the locus via PAR interaction, followed by binding to nascent RNA transcripts. We suggest that stress-induced chromatin PARylation serves to rapidly attract factors that are required for an efficient and timely transcriptional response