Ricci-flat graphs with girth at least five

A graph is called Ricci-flat if its Ricci-curvatures vanish on all edges. Here we use the definition of Ricci-cruvature on graphs given in [Lin-Lu-Yau, Tohoku Math., 2011], which is a variation of [Ollivier, J. Funct. Math., 2009]. In this paper, we classified all Ricci-flat connected graphs with girth at least five: they are the infinite path, cycle $C_n$ ($n\geq 6$), the dodecahedral graph, the Petersen graph, and the half-dodecahedral graph. We also construct many Ricci-flat graphs with girth 3 or 4 by using the root systems of simple Lie algebras.Comment: 14 pages, 15 figure

Unprecedented spin localisation in a metal-metal bonded dirhenium complex

he molecular and electronic structure of edge-sharing bioctahedral [N(n-Bu)4]3[Re2(mnt)5] is reported here. Despite the short intermetal bond length of 2.6654(2) Å with computed bond order of 1.2, the unpaired electron is localised by the asymmetric ligand distribution, as demonstrated by its remarkable EPR spectrum

Performance Analysis of a Novel GPU Computation-to-core Mapping Scheme for Robust Facet Image Modeling

Though the GPGPU concept is well-known in image processing, much more work remains to be done to fully exploit GPUs as an alternative computation engine. This paper investigates the computation-to-core mapping strategies to probe the efficiency and scalability of the robust facet image modeling algorithm on GPUs. Our fine-grained computation-to-core mapping scheme shows a significant performance gain over the standard pixel-wise mapping scheme. With in-depth performance comparisons across the two different mapping schemes, we analyze the impact of the level of parallelism on the GPU computation and suggest two principles for optimizing future image processing applications on the GPU platform

M\"{o}bius deconvolution on the hyperbolic plane with application to impedance density estimation

In this paper we consider a novel statistical inverse problem on the Poincar\'{e}, or Lobachevsky, upper (complex) half plane. Here the Riemannian structure is hyperbolic and a transitive group action comes from the space of $2\times2$ real matrices of determinant one via M\"{o}bius transformations. Our approach is based on a deconvolution technique which relies on the Helgason--Fourier calculus adapted to this hyperbolic space. This gives a minimax nonparametric density estimator of a hyperbolic density that is corrupted by a random M\"{o}bius transform. A motivation for this work comes from the reconstruction of impedances of capacitors where the above scenario on the Poincar\'{e} plane exactly describes the physical system that is of statistical interest.Comment: Published in at http://dx.doi.org/10.1214/09-AOS783 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Monoclinic and Correlated Metal Phase in VO_2 as Evidence of the Mott Transition: Coherent Phonon Analysis

In femtosecond pump-probe measurements, the appearance of coherent phonon oscillations at 4.5 THz and 6.0 THz indicating the rutile metal phase of VO_2 does not occur simultaneously with the first-order metal-insulator transition (MIT) near 68^oC. The monoclinic and correlated metal(MCM) phase between the MIT and the structural phase transition (SPT) is generated by a photo-assisted hole excitation which is evidence of the Mott transition. The SPT between the MCM phase and the rutile metal phase occurs due to subsequent Joule heating. The MCM phase can be regarded as an intermediate non-equilibrium state.Comment: 4 pages, 2 figure