Smooth 2D Coordinate Systems on Discrete Surfaces

International audienceWe introduce a new method to compute conformal param- eterizations using a recent definition of discrete conformity, and estab- lish a discrete version of the Riemann mapping theorem. Our algorithm can parameterize triangular, quadrangular and digital meshes. It can be adapted to preserve metric properties. To demonstrate the efficiency of our method, many examples are shown in the experiment section

The geometry of a vorticity model equation

We provide rigorous evidence of the fact that the modified Constantin-Lax-Majda equation modeling vortex and quasi-geostrophic dynamics describes the geodesic flow on the subgroup of orientation-preserving diffeomorphisms fixing one point, with respect to right-invariant metric induced by the homogeneous Sobolev norm $H^{1/2}$ and show the local existence of the geodesics in the extended group of diffeomorphisms of Sobolev class $H^{k}$ with $k\ge 2$.Comment: 24 page

Statins but Not Aspirin Reduce Thrombotic Risk Assessed by Thrombin Generation in Diabetic Patients without Cardiovascular Events: The RATIONAL Trial

The systematic use of aspirin and statins in patients with diabetes and no previous cardiovascular events is controversial. We sought to assess the effects of aspirin and statins on the thrombotic risk assessed by thrombin generation (TG) among patients with type II diabetes mellitus and no previous cardiovascular events.Prospective, randomized, open, blinded to events evaluation, controlled, 2×2 factorial clinical trial including 30 patients randomly allocated to aspirin 100 mg/d, atorvastatin 40 mg/d, both or none. Outcome measurements included changes in TG levels after treatment (8 to 10 weeks), assessed by a calibrated automated thrombogram. At baseline all groups had similar clinical and biochemical profiles, including TG levels. There was no interaction between aspirin and atorvastatin. Atorvastatin significantly reduced TG measured as peak TG with saline (85.09±55.34 nmol vs 153.26±75.55 nmol for atorvastatin and control groups, respectively; p = 0.018). On the other hand, aspirin had no effect on TG (121.51±81.83 nmol vs 116.85±67.66 nmol, for aspirin and control groups, respectively; p = 0.716). The effects of treatments on measurements of TG using other agonists were consistent.While waiting for data from ongoing large clinical randomized trials to definitively outline the role of aspirin in primary prevention, our study shows that among diabetic patients without previous vascular events, statins but not aspirin reduce thrombotic risk assessed by TG.ClinicalTrials.gov NCT00793754

The Astrocyte-Targeted Therapy by Bushi for the Neuropathic Pain in Mice

BACKGROUND: There is accumulating evidence that the activation of spinal glial cells, especially microglia, is a key event in the pathogenesis of neuropathic pain. However, the inhibition of microglial activation is often ineffective, especially for long-lasting persistent neuropathic pain. So far, neuropathic pain remains largely intractable and a new therapeutic strategy for the pain is still required. METHODS/PRINCIPAL FINDINGS: Using Seltzer model mice, we investigated the temporal aspect of two types of neuropathic pain behaviors, i.e., thermal hyperalgesia and mechanical allodynia, as well as that of morphological changes in spinal microglia and astrocytes by immunohistochemical studies. Firstly, we analyzed the pattern of progression in the pain behaviors, and found that the pain consisted of an "early induction phase" and subsequent "late maintenance phase". We next analyzed the temporal changes in spinal glial cells, and found that the induction and the maintenance phase of pain were associated with the activation of microglia and astrocytes, respectively. When Bushi, a Japanese herbal medicine often used for several types of persistent pain, was administered chronically, it inhibited the maintenance phase of pain without affecting the induction phase, which was in accordance with the inhibition of astrocytic activation in the spinal cord. These analgesic effects and the inhibition of astrocytic activation by Bushi were mimicked by the intrathecal injection of fluorocitrate, an inhibitor of astrocytic activation. Finally, we tested the direct effect of Bushi on astrocytic activation, and found that Bushi suppressed the IL-1β- or IL-18-evoked ERK1/2-phosphorylation in cultured astrocytes but not the ATP-evoked p38- and ERK1/2-phosphorylation in microglia in vitro. CONCLUSIONS: Our results indicated that the activation of spinal astrocytes was responsible for the late maintenance phase of neuropathic pain in the Seltzer model mice and, therefore, the inhibition of astrocytic activation by Bushi could be a useful therapeutic strategy for treating neuropathic pain

Preclinical lead optimization of a 1,2,4-triazole based tankyrase inhibitor

Tankyrases 1 and 2 are central biotargets in the WNT/β-catenin signaling and Hippo signaling pathways. We have previously developed tankyrase inhibitors bearing a 1,2,4-triazole moiety and binding predominantly to the adenosine binding site of the tankyrase catalytic domain. Here we describe a systematic structure-guided lead optimization approach of these tankyrase inhibitors. The central 1,2,4-triazole template and trans-cyclobutyl linker of the lead compound 1 were left unchanged, while side-group East, West, and South moieties were altered by introducing different building blocks defined as point mutations. The systematic study provided a novel series of compounds reaching picomolar IC(50) inhibition in WNT/β-catenin signaling cellular reporter assay. The novel optimized lead 13 resolves previous atropisomerism, solubility, and Caco-2 efflux liabilities. 13 shows a favorable ADME profile, including improved Caco-2 permeability and oral bioavailability in mice, and exhibits antiproliferative efficacy in the colon cancer cell line COLO 320DM in vitro