On two-dimensional surface attractors and repellers on 3-manifolds

We show that if $f: M^3\to M^3$ is an $A$-diffeomorphism with a surface two-dimensional attractor or repeller $\mathcal B$ and $M^2_ \mathcal B$ is a supporting surface for $\mathcal B$, then $\mathcal B = M^2_{\mathcal B}$ and there is $k\geq 1$ such that: 1) $M^2_{\mathcal B}$ is a union $M^2_1\cup...\cup M^2_k$ of disjoint tame surfaces such that every $M^2_i$ is homeomorphic to the 2-torus $T^2$. 2) the restriction of $f^k$ to $M^2_i$ $(i\in\{1,...,k\})$ is conjugate to Anosov automorphism of $T^2$

Effects of the high-density lipoprotein mimetic agent CER-001 on coronary atherosclerosis in patients with acute coronary syndromes: a randomized trial†

Aim High-density lipoproteins (HDLs) have several potentially protective vascular effects. Most clinical studies of therapies targeting HDL have failed to show benefits vs. placebo. Objective: To investigate the effects of an HDL-mimetic agent on atherosclerosis by intravascular ultrasonography (IVUS) and quantitative coronary angiography (QCA). Design and setting A prospective, double-blinded, randomized trial was conducted at 51 centres in the USA, the Netherlands, Canada, and France. Intravascular ultrasonography and QCA were performed to assess coronary atherosclerosis at baseline and 3 (2–5) weeks after the last study infusion. Patients Five hundred and seven patients were randomized; 417 and 461 had paired IVUS and QCA measurements, respectively. Intervention Patients were randomized to receive 6 weekly infusions of placebo, 3 mg/kg, 6 mg/kg, or 12 mg/kg CER-001. Main outcome measures The primary efficacy parameter was the nominal change in the total atheroma volume. Nominal changes in per cent atheroma volume on IVUS and coronary scores on QCA were also pre-specified endpoints. Results: The nominal change in the total atheroma volume (adjusted means) was −2.71, −3.13, −1.50, and −3.05 mm3 with placebo, CER-001 3 mg/kg, 6 mg/kg, and 12 mg/kg, respectively (primary analysis of 12 mg/kg vs. placebo: P = 0.81). There was also no difference among groups for the nominal change in per cent atheroma volume (0.02, −0.02, 0.01, and 0.19%; nominal P = 0.53 for 12 mg/kg vs. placebo). Change in the coronary artery score was −0.022, −0.036, −0.022, and −0.015 mm (nominal P = 0.25, 0.99, 0.55), and change in the cumulative coronary stenosis score was −0.51, 2.65, 0.71, and −0.77% (compared with placebo, nominal P = 0.85 for 12 mg/kg and nominal P = 0.01 for 3 mg/kg). The number of patients with major cardiovascular events was 10 (8.3%), 16 (13.3%), 17 (13.7%), and 12 (9.8%) in the four groups. Conclusion: CER-001 infusions did not reduce coronary atherosclerosis on IVUS and QCA when compared with placebo. Whether CER-001 administered in other regimens or to other populations could favourably affect atherosclerosis must await further study. Name of the trial registry: Clinicaltrials.gov; Registry's URL: http://clinicaltrials.gov/ct2/show/NCT01201837?term=cer-001&rank=2; Trial registration number: NCT01201837

Classification Of Supertransitive 2-Webs On Surfaces

We obtain a complete classi cation of supertransitive 2-webs on a closed oriented surface of genus p 1 in terms of asymptotic directions of leaves on the universal covering surface and represent all topological classes of 2-webs by means of compatible pairs of transversal perfect geodesic laminations