Riemann solvers and undercompressive shocks of convex FPU chains

We consider FPU-type atomic chains with general convex potentials. The naive continuum limit in the hyperbolic space-time scaling is the p-system of mass and momentum conservation. We systematically compare Riemann solutions to the p-system with numerical solutions to discrete Riemann problems in FPU chains, and argue that the latter can be described by modified p-system Riemann solvers. We allow the flux to have a turning point, and observe a third type of elementary wave (conservative shocks) in the atomistic simulations. These waves are heteroclinic travelling waves and correspond to non-classical, undercompressive shocks of the p-system. We analyse such shocks for fluxes with one or more turning points. Depending on the convexity properties of the flux we propose FPU-Riemann solvers. Our numerical simulations confirm that Lax-shocks are replaced by so called dispersive shocks. For convex-concave flux we provide numerical evidence that convex FPU chains follow the p-system in generating conservative shocks that are supersonic. For concave-convex flux, however, the conservative shocks of the p-system are subsonic and do not appear in FPU-Riemann solutions

On the Quantum Invariant for the Brieskorn Homology Spheres

We study an exact asymptotic behavior of the Witten-Reshetikhin-Turaev invariant for the Brieskorn homology spheres $\Sigma(p_1,p_2,p_3)$ by use of properties of the modular form following a method proposed by Lawrence and Zagier. Key observation is that the invariant coincides with a limiting value of the Eichler integral of the modular form with weight 3/2. We show that the Casson invariant is related to the number of the Eichler integrals which do not vanish in a limit $\tau\to N \in \mathbb{Z}$. Correspondingly there is a one-to-one correspondence between the non-vanishing Eichler integrals and the irreducible representation of the fundamental group, and the Chern-Simons invariant is given from the Eichler integral in this limit. It is also shown that the Ohtsuki invariant follows from a nearly modular property of the Eichler integral, and we give an explicit form in terms of the L-function.Comment: 26 pages, 2 figure

An Exact Black Hole Entropy Bound

We show that a Rademacher expansion can be used to establish an exact bound for the entropy of black holes within a conformal field theory framework. This convergent expansion includes all subleading corrections to the Bekenstein-Hawking term.Comment: 6 pages, Latex, v2 minor re-wording, additional reference, to appear in Phyical Review D (title changed in journal

Spherical Casimir energies and Dedekind sums

Casimir energies on space-times having general lens spaces as their spatial sections are shown to be given in terms of generalised Dedekind sums related to Zagier's. These are evaluated explicitly in certain cases as functions of the order of the lens space. An easily implemented recursion approach is used.Comment: 18 pages, 2 figures, v2:typos corrected, inessential equation in Discussion altered. v3:typos corrected, 1 reference and comments added. v4:typos corrected. Ancillary results added in an appendi

Identification of the Allosteric Binding Site for Thiazolopyrimidine on the C-Type Lectin Langerin

Langerin is a mammalian C-type lectin expressed on Langerhans cells in the skin. As an innate immune cell receptor, Langerin is involved in coordinating innate and adaptive immune responses against various incoming threats. We have previously reported a series of thiazolopyrimidines as murine Langerin ligands. Prompted by the observation that its human homologue exhibits different binding specificities for these small molecules, we report here our investigations to define their exact binding site. By using structural comparison and molecular dynamics simulations, we showed that the nonconserved short loops have a high degree of conformational flexibility between the human and murine homologues. Sequence analysis and mutational studies indicated that a pair of residues are essential for the recognition of the thiazolopyrimidines. Taking solvent paramagnetic relaxation enhancement NMR studies together with a series of peptides occupying the same site, we could define the cleft between the short and long loops as the allosteric binding site for these aromatic heterocycles

Identification of the allosteric binding site for thiazolopyrimidine on the C-type lectin langerin

Langerin is a mammalian C-type lectin expressed on Langerhans cells in the skin. As an innate immune cell receptor, Langerin is involved in coordinating innate and adaptive immune responses against various incoming threats. We have previously reported a series of thiazolopyrimidines as murine Langerin ligands. Prompted by the observation that its human homologue exhibits different binding specificities for these small molecules, we report here our investigations to define their exact binding site. By using structural comparison and molecular dynamics simulations, we showed that the nonconserved short loops have a high degree of conformational flexibility between the human and murine homologues. Sequence analysis and mutational studies indicated that a pair of residues are essential for the recognition of the thiazolopyrimidines. Taking solvent paramagnetic relaxation enhancement NMR studies together with a series of peptides occupying the same site, we could define the cleft between the short and long loops as the allosteric binding site for these aromatic heterocycles

Older-Patient-Specific Cancer Trials: A Pooled Analysis of 2,277 Patients (A151715).

BACKGROUND: Less than 3% of older patients with cancer are enrolled in clinical trials. To reverse this underrepresentation, we compared older patients enrolled with older-patient-specific trials, defined as those designed for older patients with cancer, with those enrolled in age-unspecified trials. MATERIALS AND METHODS: We focused on individual patient data from those ≥65 years (younger patients excluded) and included all Alliance phase III adjuvant breast cancer trials from 1985-2012. RESULTS: Among 2,277 patients, 1,014 had been enrolled to older-patient-specific and 1,263 to age-unspecified trials. The median age (range) in the older-patient-specific trials was 72 (65-89) years compared with 68 (65-84) years in the cohort of older patients in age-unspecified trials; CONCLUSION: Older-patient-specific trials appear to address this underrepresentation of older patients with ostensibly comparable outcomes

A natural Finsler--Laplace operator

We give a new definition of a Laplace operator for Finsler metric as an average with regard to an angle measure of the second directional derivatives. This definition uses a dynamical approach due to Foulon that does not require the use of connections nor local coordinates. We show using 1-parameter families of Katok--Ziller metrics that this Finsler--Laplace operator admits explicit representations and computations of spectral data.Comment: 25 pages, v2: minor modifications, changed the introductio