Some estimates of Wang-Yau quasilocal energy

Given a spacelike 2-surface $\Sigma$ in a spacetime $N$ and a constant future timelike unit vector $T_0$ in $\R^{3,1}$, we derive upper and lower estimates of Wang-Yau quasilocal energy $E(\Sigma, X, T_0)$ for a given isometric embedding $X$ of $\Sigma$ into a flat 3-slice in $\R^{3,1}$. The quantity $E(\Sigma, X, T_0)$ itself depends on the choice of $X$, however the infimum of $E(\Sigma, X, T_0)$ over $T_0$ does not. In particular, when $\Sigma$ lies in a time symmetric 3-slice in $N$ and has nonnegative Brown-York quasilocal mass \mby(\Sigma), our estimates show that $\inf\limits_{T_0}E(\Sigma, X, T_0)$ equals \mby (\Sigma). We also study the spatial limit of $\inf\limits_{T_0}E(S_r,X_r,T_0)$, where $S_r$ is a large coordinate sphere in a fixed end of an asymptotically flat initial data set $(M, g, p)$ and $X_r$ is an isometric embeddings of $S_r$ into $\mathbb{R}^3 \subset \mathbb{R}^{3,1}$. We show that if $(M, g, p)$ has future timelike ADM energy-momentum, then $\lim\limits_{r\to\infty}\inf\limits_{T_0}E(S_r,X_r,T_0)$ equals the ADM mass of $(M, g, p)$.Comment: 17 page

Dominant Topologies in Euclidean Quantum Gravity

The dominant topologies in the Euclidean path integral for quantum gravity differ sharply according on the sign of the cosmological constant. For $\Lambda>0$, saddle points can occur only for topologies with vanishing first Betti number and finite fundamental group. For $\Lambda<0$, on the other hand, the path integral is dominated by topologies with extremely complicated fundamental groups; while the contribution of each individual manifold is strongly suppressed, the ``density of topologies'' grows fast enough to overwhelm this suppression. The value $\Lambda=0$ is thus a sort of boundary between phases in the sum over topologies. I discuss some implications for the cosmological constant problem and the Hartle-Hawking wave function.Comment: 14 pages, LaTeX. Minor additions (computability, relation to ``minimal volume'' in topology); error in eqn (3.5) corrected; references added. To appear in Class. Quant. Gra

A Novel Method of Characterizing Genetic Sequences: Genome Space with Biological Distance and Applications

Most existing methods for phylogenetic analysis involve developing an evolutionary model and then using some type of computational algorithm to perform multiple sequence alignment. There are two problems with this approach: (1) different evolutionary models can lead to different results, and (2) the computation time required for multiple alignments makes it impossible to analyse the phylogeny of a whole genome. This motivates us to create a new approach to characterize genetic sequences.To each DNA sequence, we associate a natural vector based on the distributions of nucleotides. This produces a one-to-one correspondence between the DNA sequence and its natural vector. We define the distance between two DNA sequences to be the distance between their associated natural vectors. This creates a genome space with a biological distance which makes global comparison of genomes with same topology possible. We use our proposed method to analyze the genomes of the new influenza A (H1N1) virus, human rhinoviruses (HRV) and mammalian mitochondrial. The result shows that a triple-reassortant swine virus circulating in North America and the Eurasian swine virus belong to the lineage of the influenza A (H1N1) virus. For the HRV and mammalian mitochondrial genomes, the results coincide with biologists' analyses.Our approach provides a powerful new tool for analyzing and annotating genomes and their phylogenetic relationships. Whole or partial genomes can be handled more easily and more quickly than using multiple alignment methods. Once a genome space has been constructed, it can be stored in a database. There is no need to reconstruct the genome space for subsequent applications, whereas in multiple alignment methods, realignment is needed to add new sequences. Furthermore, one can make a global comparison of all genomes simultaneously, which no other existing method can achieve

Holonomic functions of several complex variables and singularities of anisotropic Ising n-fold integrals

Lattice statistical mechanics, often provides a natural (holonomic) framework to perform singularity analysis with several complex variables that would, in a general mathematical framework, be too complex, or could not be defined. Considering several Picard-Fuchs systems of two-variables "above" Calabi-Yau ODEs, associated with double hypergeometric series, we show that holonomic functions are actually a good framework for actually finding the singular manifolds. We, then, analyse the singular algebraic varieties of the n-fold integrals $\chi^{(n)}$, corresponding to the decomposition of the magnetic susceptibility of the anisotropic square Ising model. We revisit a set of Nickelian singularities that turns out to be a two-parameter family of elliptic curves. We then find a first set of non-Nickelian singularities for $\chi^{(3)}$ and $\chi^{(4)}$, that also turns out to be rational or ellipic curves. We underline the fact that these singular curves depend on the anisotropy of the Ising model. We address, from a birational viewpoint, the emergence of families of elliptic curves, and of Calabi-Yau manifolds on such problems. We discuss the accumulation of these singular curves for the non-holonomic anisotropic full susceptibility.Comment: 36 page

Site-specific incorporation of phosphotyrosine using an expanded genetic code.

Access to phosphoproteins with stoichiometric and site-specific phosphorylation status is key to understanding the role of protein phosphorylation. Here we report an efficient method to generate pure, active phosphotyrosine-containing proteins by genetically encoding a stable phosphotyrosine analog that is convertible to native phosphotyrosine. We demonstrate its general compatibility with proteins of various sizes, phosphotyrosine sites and functions, and reveal a possible role of tyrosine phosphorylation in negative regulation of ubiquitination

Evaluation of the influence of kyphosis and scoliosis on intervertebral disc extrusion in French bulldogs

Although thoracic vertebral malformations with kyphosis and scoliosis are often considered incidental findings on diagnostic imaging studies of screw-tailed brachycephalic breeds, they have been suggested to interfere with spinal biomechanics and intervertebral disc degeneration. It is however unknown if an abnormal spinal curvature also predisposes dogs to develop clinically relevant intervertebral disc herniations. The aim of this study was to evaluate if the occurrence of thoracic vertebral malformations, kyphosis or scoliosis would be associated with a higher prevalence of cervical or thoracolumbar intervertebral disc extrusion in French bulldogs

Study of Vibrations in a Short-Span Bridge Under Resonance Conditions Considering Train-Track Interaction

[EN] Resonance is a phenomenon of utmost importance in railways engineering, leading to vast damages both in track and vehicles. A short-span bridge has been modeled by means of a finite elements method model, calibrated and validated with real data, to study resonance vibrations induced by the passage of trains. Furthermore, the influence of vehicle speed and track damping on the vibrations registered on the rail, the sleeper and the bridge has been assessed. Different track and vehicle pathologies have been proposed and their effect on the resonance of the bridge has been evaluated.Ribes-Llario, F.; Velarte-González, JL.; Pérez-Garnes, JL.; Real Herráiz, JI. (2016). Study of Vibrations in a Short-Span Bridge Under Resonance Conditions Considering Train-Track Interaction. Latin American Journal of Solids and Structures. 13(7):1236-1249. doi:10.1590/1679-78252773S12361249137Ahlström, J., & Karlsson, B. (1999). Microstructural evaluation and interpretation of the mechanically and thermally affected zone under railway wheel flats. Wear, 232(1), 1-14. doi:10.1016/s0043-1648(99)00166-0Bian, X., Chao, C., Jin, W., & Chen, Y. (2011). A 2.5D finite element approach for predicting ground vibrations generated by vertical track irregularities. Journal of Zhejiang University-SCIENCE A, 12(12), 885-894. doi:10.1631/jzus.a11gt012Grassie, S. L., & Kalousek, J. (1993). Rail Corrugation: Characteristics, Causes and Treatments. Proceedings of the Institution of Mechanical Engineers, Part F: Journal of Rail and Rapid Transit, 207(1), 57-68. doi:10.1243/pime_proc_1993_207_227_02Gupta, A., & Singh Ahuja, A. (2014). Dynamic Analysis of Railway Bridges under High Speed Trains. Universal Journal of Mechanical Engineering, 2(6), 199-204. doi:10.13189/ujme.2014.020604Ju, S. H., & Lin, H. T. (2003). Resonance characteristics of high-speed trains passing simply supported bridges. Journal of Sound and Vibration, 267(5), 1127-1141. doi:10.1016/s0022-460x(02)01463-3Kwark, J. W., Choi, E. S., Kim, Y. J., Kim, B. S., & Kim, S. I. (2004). Dynamic behavior of two-span continuous concrete bridges under moving high-speed train. Computers & Structures, 82(4-5), 463-474. doi:10.1016/s0045-7949(03)00054-3Lu, Y., Mao, L., & Woodward, P. (2012). Frequency characteristics of railway bridge response to moving trains with consideration of train mass. Engineering Structures, 42, 9-22. doi:10.1016/j.engstruct.2012.04.007Makino, T., Yamamoto, M., & Fujimura, T. (2002). Effect of material on spalling properties of railroad wheels. Wear, 253(1-2), 284-290. doi:10.1016/s0043-1648(02)00117-5Mao, L., & Lu, Y. (2013). Critical Speed and Resonance Criteria of Railway Bridge Response to Moving Trains. Journal of Bridge Engineering, 18(2), 131-141. doi:10.1061/(asce)be.1943-5592.0000336Museros, P., Romero, M. ., Poy, A., & Alarcón, E. (2002). Advances in the analysis of short span railway bridges for high-speed lines. Computers & Structures, 80(27-30), 2121-2132. doi:10.1016/s0045-7949(02)00261-4Pal, S., Valente, C., Daniel, W., & Farjoo, M. (2012). Metallurgical and physical understanding of rail squat initiation and propagation. Wear, 284-285, 30-42. doi:10.1016/j.wear.2012.02.013Sheng, X., Jones, C. J. C., & Thompson, D. J. (2004). A theoretical model for ground vibration from trains generated by vertical track irregularities. Journal of Sound and Vibration, 272(3-5), 937-965. doi:10.1016/s0022-460x(03)00782-xSimon, S., Saulot, A., Dayot, C., Quost, X., & Berthier, Y. (2013). Tribological characterization of rail squat defects. Wear, 297(1-2), 926-942. doi:10.1016/j.wear.2012.11.011Wang, Y., Wei, Q., Shi, J., & Long, X. (2010). Resonance characteristics of two-span continuous beam under moving high speed trains. Latin American Journal of Solids and Structures, 7(2), 185-199. doi:10.1590/s1679-78252010000200005Xia, H., Zhang, N., & Guo, W. W. (2006). Analysis of resonance mechanism and conditions of train–bridge system. Journal of Sound and Vibration, 297(3-5), 810-822. doi:10.1016/j.jsv.2006.04.022Yang, Y. B., & Lin, C. W. (2005). Vehicle–bridge interaction dynamics and potential applications. Journal of Sound and Vibration, 284(1-2), 205-226. doi:10.1016/j.jsv.2004.06.03

A Schwarz lemma for K\"ahler affine metrics and the canonical potential of a proper convex cone

This is an account of some aspects of the geometry of K\"ahler affine metrics based on considering them as smooth metric measure spaces and applying the comparison geometry of Bakry-Emery Ricci tensors. Such techniques yield a version for K\"ahler affine metrics of Yau's Schwarz lemma for volume forms. By a theorem of Cheng and Yau there is a canonical K\"ahler affine Einstein metric on a proper convex domain, and the Schwarz lemma gives a direct proof of its uniqueness up to homothety. The potential for this metric is a function canonically associated to the cone, characterized by the property that its level sets are hyperbolic affine spheres foliating the cone. It is shown that for an $n$-dimensional cone a rescaling of the canonical potential is an $n$-normal barrier function in the sense of interior point methods for conic programming. It is explained also how to construct from the canonical potential Monge-Amp\`ere metrics of both Riemannian and Lorentzian signatures, and a mean curvature zero conical Lagrangian submanifold of the flat para-K\"ahler space.Comment: Minor corrections. References adde

Measurement of χ c1 and χ c2 production with s√ = 7 TeV pp collisions at ATLAS

The prompt and non-prompt production cross-sections for the χ c1 and χ c2 charmonium states are measured in pp collisions at s√ = 7 TeV with the ATLAS detector at the LHC using 4.5 fb−1 of integrated luminosity. The χ c states are reconstructed through the radiative decay χ c → J/ψγ (with J/ψ → μ + μ −) where photons are reconstructed from γ → e + e − conversions. The production rate of the χ c2 state relative to the χ c1 state is measured for prompt and non-prompt χ c as a function of J/ψ transverse momentum. The prompt χ c cross-sections are combined with existing measurements of prompt J/ψ production to derive the fraction of prompt J/ψ produced in feed-down from χ c decays. The fractions of χ c1 and χ c2 produced in b-hadron decays are also measured