Bottom of spectra and amenability of coverings

For a Riemannian covering $\pi\colon M_1\to M_0$, the bottoms of the spectra of $M_0$ and $M_1$ coincide if the covering is amenable. The converse implication does not always hold. Assuming completeness and a lower bound on the Ricci curvature, we obtain a converse under a natural condition on the spectrum of $M_0$

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

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

Enhanced Coupling of Light into a Turbid Medium through Microscopic Interface Engineering

There are many optical detection and sensing methods used today that provide powerful ways to diagnose, characterize, and study materials. For example, the measurement of spontaneous Raman scattering allows for remote detection and identification of chemicals. Many other optical techniques provide unique solutions to learn about biological, chemical, and even structural systems. However, when these systems exist in a highly scattering or turbid medium, the optical scattering effects reduce the effectiveness of these methods. In this article, we demonstrate a method to engineer the geometry of the optical interface of a turbid medium, thereby drastically enhancing the coupling efficiency of light into the material. This enhanced optical coupling means that light incident on the material will penetrate deeper into (and through) the medium. It also means that light thus injected into the material will have an enhanced interaction time with particles contained within the material. These results show that, by using the multiple scattering of light in a turbid medium, enhanced light-matter interaction can be achieved; this has a direct impact on spectroscopic methods such as Raman scattering and fluorescence detection in highly scattering regimes. Furthermore, the enhanced penetration depth achieved by this method will directly impact optical techniques that have previously been limited by the inability to deposit sufficient amounts of optical energy below or through highly scattering layers

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

Enhanced Optical Coupling and Raman Scattering via Microscopic Interface Engineering

Spontaneous Raman scattering is an extremely powerful tool for the remote detection and identification of various chemical materials. However, when those materials are contained within strongly scattering or turbid media, as is the case in many biological and security related systems, the sensitivity and range of Raman signal generation and detection is severely limited. Here, we demonstrate that through microscopic engineering of the optical interface, the optical coupling of light into a turbid material can be substantially enhanced. This improved coupling facilitates the enhancement of the Raman scattering signal generated by molecules within the medium. In particular, we detect at least two-orders of magnitude more spontaneous Raman scattering from a sample when the pump laser light is focused into a microscopic hole in the surface of the sample. Because this approach enhances both the interaction time and interaction region of the laser light within the material, its use will greatly improve the range and sensitivity of many spectroscopic techniques, including Raman scattering and fluorescence emission detection, inside highly scattering environments

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

Human AdV-20-42-42, a promising novel adenoviral vector for gene therapy and vaccine product development

Preexisting immune responses toward adenoviral vectors limit the use of a vector based on particular serotypes and its clinical applicability for gene therapy and/or vaccination. Therefore, there is a significant interest in vectorizing novel adenoviral types that have low seroprevalence in the human population. Here, we describe the discovery and vectorization of a chimeric human adenovirus, which we call HAdV-20-42-42. Full-genome sequencing revealed that this virus is closely related to human serotype 42, except for the penton base, which is derived from serotype 20. The HAdV-20-42-42 vector could be propagated stably to high titers on existing E1-complementing packaging cell lines. Receptor-binding studies revealed that the vector utilized both CAR and CD46 as receptors for cell entry. Furthermore, the HAdV-20-42-42 vector was potent in transducing human and murine cardiovascular cells and tissues, irrespective of the presence of blood coagulation factor X. In vivo characterizations demonstrate that when delivered intravenously (i.v.) in mice, HAdV-20-42-42 mainly targeted the lungs, liver, and spleen and triggered robust inflammatory immune responses. Finally, we demonstrate that potent T-cell responses against vector-delivered antigens could be induced upon intramuscular vaccination in mice. In summary, from the data obtained we conclude that HAdV-20-42-42 provides a valuable addition to the portfolio of adenoviral vectors available to develop efficacious products in the fields of gene therapy and vaccination