Legendrian links, causality, and the Low conjecture

Let $(X^{m+1}, g)$ be a globally hyperbolic spacetime with Cauchy surface diffeomorphic to an open subset of $\mathbb R^m$. The Legendrian Low conjecture formulated by Nat\'ario and Tod says that two events x,y\in\ss are causally related if and only if the Legendrian link of spheres $\mathfrak S_x, \mathfrak S_y$ whose points are light geodesics passing through $x$ and $y$ is non-trivial in the contact manifold of all light geodesics in $X$. The Low conjecture says that for $m=2$ the events $x,y$ are causally related if and only if $\mathfrak S_x, \mathfrak S_y$ is non-trivial as a topological link. We prove the Low and the Legendrian Low conjectures. We also show that similar statements hold for any globally hyperbolic $(X^{m+1}, g)$ such that a cover of its Cauchy surface is diffeomorphic to an open domain in $\mathbb R^m.$Comment: Version 3 - minor improvements, references added 11 pages, 1 figur

Effect of multiple transverse modes in self-mixing sensors based on vertical-cavity surface-emitting lasers

We investigate the effect of coexisting transverse modes on the operation of self-mixing sensors based on vertical-cavity surface-emitting lasers (VCSELs). The effect of multiple transverse modes on the measurement of displacement and distance were examined by simulation and in laboratory experiment. The simulation model shows that the periodic change in the shape and magnitude of the self-mixing signal with modulation current can be properly explained by the different frequency-modulation coefficients of the respective transverse modes in VCSELs. The simulation results are in excellent agreement with measurements performed on single-mode and multimode VCSELs and on self-mixing sensors based on these VCSELs

Application of dispersion relations to low-energy meson-nucleon scattering

Relativistic dispersion relations are used to derive equations for low-energy S-, P-, and D-wave meson-nucleon scattering under the assumption that the (3,3) resonance dominates the dispersion integrals. The P-wave equations so obtained differ only slightly from those of the static fixed-source theory. The conclusions of the static theory are re-examined in the light of their new derivation

Multiple Reggeon Exchange from Summing QCD Feynman Diagrams

Multiple reggeon exchange supplies subleading logs that may be used to restore unitarity to the Low-Nussinov Pomeron, provided it can be proven that the sum of Feynman diagrams to all orders gives rise to such multiple regge exchanges. This question cannot be easily tackled in the usual way except for very low-order diagrams, on account of delicate cancellations present in the sum which necessitate individual Feynman diagrams to be computed to subleading orders. Moreover, it is not clear that sums of high-order Feynman diagrams with complicated criss-crossing of lines can lead to factorization implied by the multi-regge scenario. Both of these difficulties can be overcome by using the recently developed nonabelian cut diagrams. We are then able to show that the sum of $s$-channel-ladder diagrams to all orders does lead to such multiple reggeon exchanges.Comment: uu-encoded latex file with 11 postscript figures (20 pages

Simulating EGFR-ERK signaling control by scaffold proteins KSR and MP1 reveals differential Ligand-Sensitivity Co-Regulated by CBL-CIN85 and Endophilin

10.1371/journal.pone.0022933PLoS ONE68

Performance analysis of the Malaysian elite youth squash players

This study analysed the frequencies and court locations of squash strokes performed by elite Malaysian youth players before and during a national tournament. One hundred and seventy nine matches participated by six players (three men and three women) were analysed. Data collected via video recordings and coded post match using Studiocode® analysis software. The straight and cross court drives were the most frequent strokes used by both genders, with more on the backhand side. The drop shot and straight drives contributed to most winners for the men and women respectively. Most winners were produced by the players when they occupied the middle areas of the court. The areas that resulted most errors were the four corners of the court for the men whilst the women was on their backhand side areas. Objective feedback on the performance prior to a major competition provided some positive results.Keywords: performance analysis, squash, youth

Large-Scale Gravitational Instability and Star Formation in the Large Magellanic Cloud

Large-scale star formation in disk galaxies is hypothesized to be driven by global gravitational instability. The observed gas surface density is commonly used to compute the strength of gravitational instability, but according to this criterion star formation often appears to occur in gravitationally stable regions. One possible reason is that the stellar contribution to the instability has been neglected. We have examined the gravitational instability of the Large Magellanic Cloud (LMC) considering the gas alone, and considering the combination of collisional gas and collisionless stars. We compare the gravitationally unstable regions with the on-going star formation revealed by Spitzer observations of young stellar objects. Although only 62% of the massive young stellar object candidates are in regions where the gas alone is unstable, some 85% lie in regions unstable due to the combination of gas and stars. The combined stability analysis better describes where star formation occurs. In agreement with other observations and numerical models, a small fraction of the star formation occurs in regions with gravitational stability parameter Q > 1. We further measure the dependence of the star formation timescale on the strength of gravitational instability, and quantitatively compare it to the exponential dependence expected from numerical simulations.Comment: Accepted for publication in ApJ, 10 pages, 5 figure

Bound States and Threshold Resonances in Quantum Wires with Circular Bends

We study the solutions to the wave equation in a two-dimensional tube of unit width comprised of two straight regions connected by a region of constant curvature. We introduce a numerical method which permits high accuracy at high curvature. We determine the bound state energies as well as the transmission and reflection matrices, ${\cal T}$ and ${\cal R}$ and focus on the nature of the resonances which occur in the vicinity of channel thresholds. We explore the dependence of these solutions on the curvature of the tube and angle of the bend and discuss several limiting cases where our numerical results confirm analytic predictions.Comment: 24 pages, revtex file, one style file and 17 PostScript figures include

A New Hybrid Descent Method with Application to the Optimal Design of Finite Precision FIR Filters

In this paper, the problem of the optimal design of discrete coefficient FIR filters is considered. A novelhybrid descent method, consisting of a simulated annealing algorithm and a gradient-based method, isproposed. The simulated annealing algorithm operates on the space of orthogonal matrices and is used tolocate descent points for previously converged local minima. The gradient-based method is derived fromconverting the discrete problem to a continuous problem via the Stiefel manifold, where convergence canbe guaranteed. To demonstrate the effectiveness of the proposed hybrid descent method, several numericalexamples show that better discrete filter designs can be sought via this hybrid descent method

Structure, bonding and morphology of hydrothermally synthesised xonotlite

The authors have systematically investigated the role of synthesis conditions upon the structure and morphology of xonotlite. Starting with a mechanochemically prepared, semicrystalline phase with Ca/Si=1, the authors have prepared a series of xonotlite samples hydrothermally, at temperatures between 200 and 250 degrees C. Analysis in each case was by X-ray photoelectron spectroscopy, environmental scanning electron microscopy and X-ray diffraction. The authors’ use of a much lower water/solid ratio has indirectly confirmed the ‘through solution’ mechanism of xonotlite formation, where silicate dissolution is a key precursor of xonotlite formation. Concerning the role of temperature, too low a temperature (~200 degrees C) fails to yield xonotlite or leads to increased number of structural defects in the silicate chains of xonotlite and too high a temperature (>250 degrees C) leads to degradation of the xonotlite structure, through leaching of interchain calcium. Synthesis duration meanwhile leads to increased silicate polymerisation due to diminishing of the defects in the silicate chains and more perfect crystal morphologies