Counting Carambolas

We give upper and lower bounds on the maximum and minimum number of geometric configurations of various kinds present (as subgraphs) in a triangulation of $n$ points in the plane. Configurations of interest include \emph{convex polygons}, \emph{star-shaped polygons} and \emph{monotone paths}. We also consider related problems for \emph{directed} planar straight-line graphs.Comment: update reflects journal version, to appear in Graphs and Combinatorics; 18 pages, 13 figure

Lattice extraction of K→ππ K \to \pi \pi amplitudes to NLO in partially quenched and in full chiral perturbation theory

We show that it is possible to construct $\epsilon^\prime/\epsilon$ to NLO using partially quenched chiral perturbation theory (PQChPT) from amplitudes that are computable on the lattice. We demonstrate that none of the needed amplitudes require three-momentum on the lattice for either the full theory or the partially quenched theory; non-degenerate quark masses suffice. Furthermore, we find that the electro-weak penguin ($\Delta I=3/2$ and 1/2) contributions to $\epsilon^\prime/\epsilon$ in PQChPT can be determined to NLO using only degenerate ($m_K=m_\pi$) $K\to\pi$ computations without momentum insertion. Issues pertaining to power divergent contributions, originating from mixing with lower dimensional operators, are addressed. Direct calculations of $K\to\pi\pi$ at unphysical kinematics are plagued with enhanced finite volume effects in the (partially) quenched theory, but in simulations when the sea quark mass is equal to the up and down quark mass the enhanced finite volume effects vanish to NLO in PQChPT. In embedding the QCD penguin left-right operator onto PQChPT an ambiguity arises, as first emphasized by Golterman and Pallante. With one version (the "PQS") of the QCD penguin, the inputs needed from the lattice for constructing $K\to\pi\pi$ at NLO in PQChPT coincide with those needed for the full theory. Explicit expressions for the finite logarithms emerging from our NLO analysis to the above amplitudes are also given.Comment: 54 pages, 3 figures; Important revisions: Corrections to formulas for K->pi pi with degenerate quark masses have been mad

Improving the worthiness of the Elder problem as a benchmark for buoyancy driven convection models

An important trapping mechanism associated with the geosequestration of CO~2~ is that of dissolution into the formation water. Although supercritical CO~2~ is significantly less dense than water, experimental data reported in the literature show that the density of an aqueous solution of CO~2~ could be slightly greater. Under normal situations, the transfer of gas to solution is largely controlled by the relatively slow process of molecular diffusion. However, the presence of variable densities can trigger off gravity instabilities leading to much larger-scale convection processes. Such processes can potentially enhance rates of dissolution by an order of magnitude. Consequently there is a need for future performance assessment models to incorporate buoyancy driven convection (BDC). A major issue associated with BDC models is that of grid convergence when benchmarking to the Elder problem. The Elder problem originates from a heat convection experiment whereby a rectangular Hele-Shaw cell was heated over the central half of its base. A quarter of the way through the experiment, Elder (1967) observed six plumes, with four narrow plumes in the center and two larger plumes at the edges. As the experiment progressed, only four plumes remained. The issue is that depending on the grid resolution used when seeking to model this problem, modelers have found that different schemes yield steady states with either one, two or three plumes. The aim of this paper is to clarify and circumvent the issue of multiple steady state solutions in the Elder problem using a pseudospectral method

A new view on the ISM of galaxies: far-infrared and submillimetre spectroscopy with Herschel

The FIR/submm window is amongst the least explored spectral regions of the electromagnetic spectrum. It is, however, a key to study the general properties of the interstellar medium of galaxies, as it contains important spectral line diagnostics from the neutral, ionized and molecular ISM. The Herschel Space Observatory, successfully launched on 14 May 2009, is the first observatory to cover the entire FIR/submm range between 57 and 672 mum. We discuss the main results from the ISO era on FIR spectroscopy of galaxies and the enormous science potential of the Herschel mission through a presentation of its spectroscopic extragalactic key programs.Comment: 10 pages, 4 figures, accepted for publication in New Astronomy Review

Can a One-Item Mood Scale Do the Trick? Predicting Relapse over 5.5-Years in Recurrent Depression

To examine whether a simple Visual Analogue Mood Scale (VAMS) is able to predict time to relapse over 5.5-years.187 remitted recurrently depressed out-patients were interviewed using the Structured Clinical Interview for DSM-IV Axis I Disorders (SCID-I) and the 17-item Hamilton Depression rating scale (HAM-D) to verify remission status (HAM-D <10). All patients rated their current mood with the help of a Visual Analogue Mood Scale (VAMS) at baseline and at a follow-up assessment three months later. Relapse over 5.5-years was assessed by the SCID-I. Cox regression revealed that both the VAMS at baseline and three months later significantly predicted time to relapse over 5.5-years. Baseline VAMS even predicted time to relapse when the number of previous depressive episodes and HAM-D scores were controlled for. The baseline VAMS explained 6.3% of variance in time to relapse, comparable to the HAM-D interview.Sad mood after remission appears to play a pivotal role in the course of depression. Since a simple VAMS predicted time to relapse, the VAMS might be an easy and time-effective way to monitor mood and risk of early relapse, and offers possibilities for daily monitoring using e-mail and SMS.International Standard Randomized Controlled Trial Register Identifier: ISRCTN68246470

Managing interactions between household food security and preschooler health:

Food security does not assure good nutrition. The nutritional status of an individual is influenced not only by food but also by nonfood factors, such as clean water, sanitation, and health care. The effect of all of these factors must be considered in efforts to rid the world of malnutrition. Food security will result in good nutrition only if nonfood factors are effectively dealt with. In this paper, Lawrence Haddad, Saroj Bhattarai, Maarten Immink, and Shubh Kumar show how malnutrition among preschool children is determined by a complex interaction of illness and lack of food. The authors look at three countries —Ethiopia, Pakistan, and the Philippines — to study how food availability and diarrhea interact and what this interaction means for preschooler malnutrition. Their results show that the links between food consumption, diarrhea, and malnutrition are stronger than most economic studies have assumed. When diarrhea is prevalent, the effects of food shortages on child malnutrition are worse, and when food is scarce, the effects of diarrhea on child malnutrition are worse.Food security Ethiopia., Malnutrition in children Ethiopia., Food security Pakistan., Malnutrition in children Pakistan., Food security Philippines., Malnutrition in children Philippines.,

Composite biasing in Monte Carlo radiative transfer

Biasing or importance sampling is a powerful technique in Monte Carlo radiative transfer, and can be applied in different forms to increase the accuracy and efficiency of simulations. One of the drawbacks of the use of biasing is the potential introduction of large weight factors. We discuss a general strategy, composite biasing, to suppress the appearance of large weight factors. We use this composite biasing approach for two different problems faced by current state-of-the-art Monte Carlo radiative transfer codes: the generation of photon packages from multiple components, and the penetration of radiation through high optical depth barriers. In both cases, the implementation of the relevant algorithms is trivial and does not interfere with any other optimisation techniques. Through simple test models, we demonstrate the general applicability, accuracy and efficiency of the composite biasing approach. In particular, for the penetration of high optical depths, the gain in efficiency is spectacular for the specific problems that we consider: in simulations with composite path length stretching, high accuracy results are obtained even for simulations with modest numbers of photon packages, while simulations without biasing cannot reach convergence, even with a huge number of photon packages.Comment: 12 pages, accepted for publication in A&