Compatible finite element methods for numerical weather prediction

This article takes the form of a tutorial on the use of a particular class of mixed finite element methods, which can be thought of as the finite element extension of the C-grid staggered finite difference method. The class is often referred to as compatible finite elements, mimetic finite elements, discrete differential forms or finite element exterior calculus. We provide an elementary introduction in the case of the one-dimensional wave equation, before summarising recent results in applications to the rotating shallow water equations on the sphere, before taking an outlook towards applications in three-dimensional compressible dynamical cores.Comment: To appear in ECMWF Seminar proceedings 201

Yields and Sward Characteristics of Timothy Cultivars under Grazing

Seven timothy (Phleum pratense L.) cultivars were evaluated over three pasture seasons under rotational grazing to 7 or 11 cm post-grazing heights and regrowth periods of four to seven weeks. There was a trend for the pasture type timothy cultivars to outyield Champ timothy (check). Dry matter yields were lower for the 7 cm than 11 cm post-grazing height. Although the overall cultivar x post-grazing height interaction was not significant (P \u3e 0.05), there was variability in grazing tolerance among timothy cultivars. Yield of Kahu was maintained and vegetative tiller density of Kahu increased over the experimental period under 7 cm grazing. Proportion of vegetative tillers among the cultivars ranged from 0.20 to 0.61 in the primary growth but this proportion increased to 0.95 in the fourth grazing

Height-related risk factors for prostate cancer

Previous studies have reported that adult height is positively associated with the risk of prostate cancer. The authors carried out a population-based case–control study involving 317 prostate cancer cases and 480 controls to further investigate the possibility that height is more strongly associated with advanced, compared with localized forms of this disease. Since the inherited endocrine factors, which in part determine height attained during the growing years, may influence the risk of familial prostate cancer later in life, the relationship with height was also investigated for familial versus sporadic prostate cancers. Adult height was not related to the risk of localized prostate cancer, but there was a moderate positive association between increasing height and the risk of advanced cancer (relative risk (RR) = 1.62; 95% confidence interval (CI) 0.97–2.73, upper versus lowest quartile, P -trend = 0.07). Height was more strongly associated with the risk of prostate cancer in men with a positive family history compared with those reporting a negative family history. The RR of advanced prostate cancer for men in the upper height quartile with a positive family history was 7.41 (95% CI 1.68–32.67, P -trend = 0.02) compared with a reference group comprised of men in the shortest height quartile with a negative family history. Serum insulin-like growth factor-1 levels did not correlate with height amongst men with familial or sporadic prostate cancers. These findings provide evidence for the existence of growth-related risk factors for prostate cancer, particularly for advanced and familial forms of this disease. The possible existence of inherited mechanisms affecting both somatic and tumour growth deserves further investigation. © 2000 Cancer Research Campaig

Iterated colorings of graphs

AbstractFor a graph property P, in particular maximal independence, minimal domination and maximal irredundance, we introduce iterated P-colorings of graphs. The six graph parameters arising from either maximizing or minimizing the number of colors used for each property, are related by an inequality chain, and in this paper we initiate the study of these parameters. We relate them to other well-studied parameters like chromatic number, give alternative characterizations, find graph classes where they differ by an arbitrary amount, investigate their monotonicity properties, and look at algorithmic issues

The Quantum Socket: Three-Dimensional Wiring for Extensible Quantum Computing

Quantum computing architectures are on the verge of scalability, a key requirement for the implementation of a universal quantum computer. The next stage in this quest is the realization of quantum error correction codes, which will mitigate the impact of faulty quantum information on a quantum computer. Architectures with ten or more quantum bits (qubits) have been realized using trapped ions and superconducting circuits. While these implementations are potentially scalable, true scalability will require systems engineering to combine quantum and classical hardware. One technology demanding imminent efforts is the realization of a suitable wiring method for the control and measurement of a large number of qubits. In this work, we introduce an interconnect solution for solid-state qubits: The quantum socket. The quantum socket fully exploits the third dimension to connect classical electronics to qubits with higher density and better performance than two-dimensional methods based on wire bonding. The quantum socket is based on spring-mounted micro wires the three-dimensional wires that push directly on a micro-fabricated chip, making electrical contact. A small wire cross section (~1 mmm), nearly non-magnetic components, and functionality at low temperatures make the quantum socket ideal to operate solid-state qubits. The wires have a coaxial geometry and operate over a frequency range from DC to 8 GHz, with a contact resistance of ~150 mohm, an impedance mismatch of ~10 ohm, and minimal crosstalk. As a proof of principle, we fabricated and used a quantum socket to measure superconducting resonators at a temperature of ~10 mK.Comment: Main: 31 pages, 19 figs., 8 tables, 8 apps.; suppl.: 4 pages, 5 figs. (HiRes figs. and movies on request). Submitte

CyberKnife(® )radiosurgery in the treatment of complex skull base tumors: analysis of treatment planning parameters

BACKGROUND: Tumors of the skull base pose unique challenges to radiosurgical treatment because of their irregular shapes, proximity to critical structures and variable tumor volumes. In this study, we investigate whether acceptable treatment plans with excellent conformity and homogeneity can be generated for complex skull base tumors using the Cyberknife(® )radiosurgical system. METHODS: At Georgetown University Hospital from March 2002 through May 2005, the CyberKnife(® )was used to treat 80 patients with 82 base of skull lesions. Tumors were classified as simple or complex based on their proximity to adjacent critical structures. All planning and treatments were performed by the same radiosurgery team with the goal of minimizing dosage to adjacent critical structures and maximizing target coverage. Treatments were fractionated to allow for safer delivery of radiation to both large tumors and tumors in close proximity to critical structures. RESULTS: The CyberKnife(® )treatment planning system was capable of generating highly conformal and homogeneous plans for complex skull base tumors. The treatment planning parameters did not significantly vary between spherical and non-spherical target volumes. The treatment parameters obtained from the plans of the complex base of skull group, including new conformity index, homogeneity index and percentage tumor coverage, were not significantly different from those of the simple group. CONCLUSION: Our data indicate that CyberKnife(® )treatment plans with excellent homogeneity, conformity and percent target coverage can be obtained for complex skull base tumors. Longer follow-up will be required to determine the safety and efficacy of fractionated treatment of these lesions with this radiosurgical system

Self-coalition graphs

A coalition in a graph $G = (V, E)$ consists of two disjoint sets $V_1$ and $V_2$ of vertices, such that neither $V_1$ nor $V_2$ is a dominating set, but the union $V_1 \cup V_2$ is a dominating set of $G$. A coalition partition in a graph $G$ of order $n = |V|$ is a vertex partition $\pi = \{V_1, V_2, \ldots, V_k\}$ such that every set $V_i$ either is a dominating set consisting of a single vertex of degree $n-1$, or is not a dominating set but forms a coalition with another set $V_j$ which is not a dominating set. Associated with every coalition partition $\pi$ of a graph $G$ is a graph called the coalition graph of $G$ with respect to $\pi$, denoted $CG(G,\pi)$, the vertices of which correspond one-to-one with the sets $V_1, V_2, \ldots, V_k$ of $\pi$ and two vertices are adjacent in $CG(G,\pi)$ if and only if their corresponding sets in $\pi$ form a coalition. The singleton partition $\pi_1$ of the vertex set of $G$ is a partition of order $|V|$, that is, each vertex of $G$ is in a singleton set of the partition. A graph $G$ is called a self-coalition graph if $G$ is isomorphic to its coalition graph $CG(G,\pi_1)$, where $\pi_1$ is the singleton partition of $G$. In this paper, we characterize self-coalition graphs