Rank rigidity for CAT(0) cube complexes

We prove that any group acting essentially without a fixed point at infinity on an irreducible finite-dimensional CAT(0) cube complex contains a rank one isometry. This implies that the Rank Rigidity Conjecture holds for CAT(0) cube complexes. We derive a number of other consequences for CAT(0) cube complexes, including a purely geometric proof of the Tits Alternative, an existence result for regular elements in (possibly non-uniform) lattices acting on cube complexes, and a characterization of products of trees in terms of bounded cohomology.Comment: 39 pages, 4 figures. Revised version according to referee repor

The type numbers of closed geodesics

A short survey on the type numbers of closed geodesics, on applications of the Morse theory to proving the existence of closed geodesics and on the recent progress in applying variational methods to the periodic problem for Finsler and magnetic geodesicsComment: 29 pages, an appendix to the Russian translation of "The calculus of variations in the large" by M. Mors

Dual-tip-enhanced ultrafast CARS nanoscopy

Coherent anti-Stokes Raman scattering (CARS) and, in particular, femtosecond adaptive spectroscopic techniques (FAST CARS) have been successfully used for molecular spectroscopy and microscopic imaging. Recent progress in ultrafast nanooptics provides flexibility in generation and control of optical near fields, and holds promise to extend CARS techniques to the nanoscale. In this theoretical study, we demonstrate ultrafast subwavelentgh control of coherent Raman spectra of molecules in the vicinity of a plasmonic nanostructure excited by ultrashort laser pulses. The simulated nanostructure design provides localized excitation sources for CARS by focusing incident laser pulses into subwavelength hot spots via two self-similar nanolens antennas connected by a waveguide. Hot-spot-selective dual-tip-enhanced CARS (2TECARS) nanospectra of DNA nucleobases are obtained by simulating optimized pump, Stokes and probe near fields using tips, laser polarization- and pulse-shaping. This technique may be used to explore ultrafast energy and electron transfer dynamics in real space with nanometre resolution and to develop novel approaches to DNA sequencing.Comment: 11 pages, 6 figure

A Multicenter Screening Study

Background In cystic fibrosis, highly variable glucose tolerance is suspected. However, no study provided within-patient coefficients of variation. The main objective of this short report was to evaluate within-patient variability of oral glucose tolerance. Methods In total, 4,643 standardized oral glucose tolerance tests of 1,128 cystic fibrosis patients (median age at first test: 15.5 [11.5; 21.5] years, 48.8% females) were studied. Patients included were clinically stable, non-pregnant, and had at least two oral glucose tolerance tests, with no prior lung transplantation or systemic steroid therapy. Transition frequency from any one test to the subsequent test was analyzed and within-patient coefficients of variation were calculated for fasting and two hour blood glucose values. All statistical analysis was implemented with SAS 9.4. Results A diabetic glucose tolerance was confirmed in 41.2% by the subsequent test. A regression to normal glucose tolerance at the subsequent test was observed in 21.7% and to impaired fasting glucose, impaired glucose tolerance or both in 15.2%, 12.0% or 9.9%. The average within-patient coefficient of variation for fasting blood glucose was 11.1% and for two hour blood glucose 25.3%. Conclusion In the cystic fibrosis patients studied, a highly variable glucose tolerance was observed. Compared to the general population, variability of two hour blood glucose was 1.5 to 1.8-fold higher

Vortices and Jacobian varieties

We investigate the geometry of the moduli space of N-vortices on line bundles over a closed Riemann surface of genus g > 1, in the little explored situation where 1 =< N < g. In the regime where the area of the surface is just large enough to accommodate N vortices (which we call the dissolving limit), we describe the relation between the geometry of the moduli space and the complex geometry of the Jacobian variety of the surface. For N = 1, we show that the metric on the moduli space converges to a natural Bergman metric on the Riemann surface. When N > 1, the vortex metric typically degenerates as the dissolving limit is approached, the degeneration occurring precisely on the critical locus of the Abel-Jacobi map at degree N. We describe consequences of this phenomenon from the point of view of multivortex dynamics.Comment: 36 pages, 2 figure

Entropy of semiclassical measures for nonpositively curved surfaces

We study the asymptotic properties of eigenfunctions of the Laplacian in the case of a compact Riemannian surface of nonpositive sectional curvature. We show that the Kolmogorov-Sinai entropy of a semiclassical measure for the geodesic flow is bounded from below by half of the Ruelle upper bound. We follow the same main strategy as in the Anosov case (arXiv:0809.0230). We focus on the main differences and refer the reader to (arXiv:0809.0230) for the details of analogous lemmas.Comment: 20 pages. This note provides a detailed proof of a result announced in appendix A of a previous work (arXiv:0809.0230, version 2

Manifolds with small Dirac eigenvalues are nilmanifolds

Consider the class of n-dimensional Riemannian spin manifolds with bounded sectional curvatures and diameter, and almost non-negative scalar curvature. Let r=1 if n=2,3 and r=2^{[n/2]-1}+1 if n\geq 4. We show that if the square of the Dirac operator on such a manifold has $r$ small eigenvalues, then the manifold is diffeomorphic to a nilmanifold and has trivial spin structure. Equivalently, if M is not a nilmanifold or if M is a nilmanifold with a non-trivial spin structure, then there exists a uniform lower bound on the r-th eigenvalue of the square of the Dirac operator. If a manifold with almost nonnegative scalar curvature has one small Dirac eigenvalue, and if the volume is not too small, then we show that the metric is close to a Ricci-flat metric on M with a parallel spinor. In dimension 4 this implies that M is either a torus or a K3-surface

Autophagy in the heart is enhanced and independent of disease progression in mus musculus dystrophinopathy models

Background: Duchenne muscular dystrophy is a muscle wasting disease caused by dystrophin gene mutations resulting in dysfunctional dystrophin protein. Autophagy, a proteolytic process, is impaired in dystrophic skeletal muscle though little is known about the effect of dystrophin deficiency on autophagy in cardiac muscle. We hypothesized that with disease progression autophagy would become increasingly dysfunctional based upon indirect autophagic markers. Methods: Markers of autophagy were measured by western blot in 7-week-old and 17-month-old control (C57) and dystrophic (mdx) hearts. Results: Counter to our hypothesis, markers of autophagy were similar between groups. Given these surprising results, two independent experiments were conducted using 14-month-old mdx mice or 10-month-old mdx/Utrn± mice, a more severe model of Duchenne muscular dystrophy. Data from these animals suggest increased autophagosome degradation. Conclusion: Together these data suggest that autophagy is not impaired in the dystrophic myocardium as it is in dystrophic skeletal muscle and that disease progression and related injury is independent of autophagic dysfunction

A National Plan for Assisting States, Federal Agencies, and Tribes in Managing White-Nose Syndrome in Bats

White-nose syndrome (WNS) is a disease responsible for unprecedented mortality in hibernating bats in the northeastern U.S. This previously unrecognized disease has spread very rapidly since its discovery in January 2007, and poses a considerable threat to hibernating bats throughout North America. As WNS spreads, the challenges for understanding and managing the disease continue to increase. Given the escalating complexity of these challenges, a highly coordinated effort is required for State, Federal, and Tribal wildlife agencies, and private partners to respond effectively to WNS and conserve species of bats. The plan proposed herein details the elements that are critical to the investigation and management of WNS, identifies key action items to address stated goals, and outlines the role(s) of agencies and entities involved in this continental effort