Coordinate Singularities in Harmonically-sliced Cosmologies

Harmonic slicing has in recent years become a standard way of prescribing the lapse function in numerical simulations of general relativity. However, as was first noticed by Alcubierre (1997), numerical solutions generated using this slicing condition can show pathological behaviour. In this paper, analytic and numerical methods are used to examine harmonic slicings of Kasner and Gowdy cosmological spacetimes. It is shown that in general the slicings are prevented from covering the whole of the spacetimes by the appearance of coordinate singularities. As well as limiting the maximum running times of numerical simulations, the coordinate singularities can lead to features being produced in numerically evolved solutions which must be distinguished from genuine physical effects.Comment: 21 pages, REVTeX, 5 figure

Extremal Graph Theory for Metric Dimension and Diameter

A set of vertices $S$ \emph{resolves} a connected graph $G$ if every vertex is uniquely determined by its vector of distances to the vertices in $S$. The \emph{metric dimension} of $G$ is the minimum cardinality of a resolving set of $G$. Let $\mathcal{G}_{\beta,D}$ be the set of graphs with metric dimension $\beta$ and diameter $D$. It is well-known that the minimum order of a graph in $\mathcal{G}_{\beta,D}$ is exactly $\beta+D$. The first contribution of this paper is to characterise the graphs in $\mathcal{G}_{\beta,D}$ with order $\beta+D$ for all values of $\beta$ and $D$. Such a characterisation was previously only known for $D\leq2$ or $\beta\leq1$. The second contribution is to determine the maximum order of a graph in $\mathcal{G}_{\beta,D}$ for all values of $D$ and $\beta$. Only a weak upper bound was previously known

Fluctuations of wave functions about their classical average

Quantum-classical correspondence for the average shape of eigenfunctions and the local spectral density of states are well-known facts. In this paper, the fluctuations that quantum mechanical wave functions present around the classical value are discussed. A simple random matrix model leads to a Gaussian distribution of the amplitudes. We compare this prediction with numerical calculations in chaotic models of coupled quartic oscillators. The expectation is broadly confirmed, but deviations due to scars are observed.Comment: 9 pages, 6 figures. Sent to J. Phys.

Femtochemistry of mass-selected negative-ion clusters of dioxygen: Charge-transfer and solvation dynamics

Femtosecond, time-resolved photoelectron spectroscopy is used to investigate the dissociation dynamics of mass-selected anionic molecular-oxygen clusters. The observed transient photoelectron signal for the clusters (O_2)^−_n  (n = 3–5) shows the O^−_2 production; for n = 1 and 2, we observe no time-dependence at this wavelength of 800 nm. The observed transients are bi-exponential in form with two distinct time constants, but with clear trends, for all investigated cluster sizes. These striking observations describe the reaction pathways of the solvated core and we elucidate two primary processes: Charge transfer with concomitant nuclear motion, and direct dissociation of the O^−_4 core-ion via electron recombination; the former takes 700–2700 fs, while the latter is on a shorter time scale, 110–420 fs. Both rates decrease differently upon increasing cluster size, indicating the critical role of step-wise solvation

New explicit spike solution -- non-local component of the generalized Mixmaster attractor

By applying a standard solution-generating transformation to an arbitrary vacuum Bianchi type II solution, one generates a new solution with spikes commonly observed in numerical simulations. It is conjectured that the spike solution is part of the generalized Mixmaster attractor.Comment: Significantly revised. Colour figures simplified to accommodate non-colour printin

A randomised trial evaluating Bevacizumab as adjuvant therapy following resection of AJCC stage IIB, IIC and III cutaneous melanoma : an update

At present, there are no standard therapies for the adjuvant treatment of malignant melanoma. Patients with primary tumours with a high-Breslow thickness (stages IIB and IIC) or with resected loco-regional nodal disease (stage III) are at high risk of developing metastasis and subsequent disease-related death. Given this, it is important that novel therapies are investigated in the adjuvant melanoma setting. Since angiogenesis is essential for primary tumour growth and the development of metastasis, anti-angiogenic agents are attractive potential therapeutic candidates for clinical trials in the adjuvant setting. Therefore, we initiated a phase II trial in resected high-risk cutaneous melanoma, assessing the efficacy of bevacizumab versus observation. In the interim safety data analysis, we demonstrate that bevacizumab is a safe therapy in the adjuvant melanoma setting with no apparent increase in the surgical complication rate after either primary tumour resection and/or loco-regional lymphadenectomy

Manufacture of Gowdy spacetimes with spikes

In numerical studies of Gowdy spacetimes evidence has been found for the development of localized features (spikes) involving large gradients near the singularity. The rigorous mathematical results available up to now did not cover this kind of situation. In this work we show the existence of large classes of Gowdy spacetimes exhibiting features of the kind discovered numerically. These spacetimes are constructed by applying certain transformations to previously known spacetimes without spikes. It is possible to control the behaviour of the Kretschmann scalar near the singularity in detail. This curvature invariant is found to blow up in a way which is non-uniform near the spike in some cases. When this happens it demonstrates that the spike is a geometrically invariant feature and not an artefact of the choice of variables used to parametrize the metric. We also identify another class of spikes which are artefacts. The spikes produced by our method are compared with the results of numerical and heuristic analyses of the same situation.Comment: 25 page

Locally U(1)*U(1) Symmetric Cosmological Models: Topology and Dynamics

We show examples which reveal influences of spatial topologies to dynamics, using a class of spatially {\it closed} inhomogeneous cosmological models. The models, called the {\it locally U(1)$\times$U(1) symmetric models} (or the {\it generalized Gowdy models}), are characterized by the existence of two commuting spatial {\it local} Killing vectors. For systematic investigations we first present a classification of possible spatial topologies in this class. We stress the significance of the locally homogeneous limits (i.e., the Bianchi types or the `geometric structures') of the models. In particular, we show a method of reduction to the natural reduced manifold, and analyze the equivalences at the reduced level of the models as dynamical models. Based on these fundamentals, we examine the influence of spatial topologies on dynamics by obtaining translation and reflection operators which commute with the dynamical flow in the phase space.Comment: 32 pages, 1 figure, LaTeX2e, revised Introduction slightly. To appear in CQ

Data Fusion of Left Ventricle Electro-Anatomic Mapping and Multislice Computerized Tomography for Cardiac Resynchronisation Therapy Optimization

Cardiac Resynchronization Therapy is a treatment for bi-ventricular asynchronism. It can be optimized by the identification of the most effective pacing sites. The aim of this study is to provide a helpful tool to perform this identification by the fusion of electrical and anatomical information resulting from Electro-Anatomic Mapping (EAM) data and Multislice Computerized Tomography (MSCT) imaging. EAM data provide an approximation of the left ventricle (LV) 3D-surface (SEAM). Left cardiac chambers are segmented from MSCT imaging and surfaces are reconstructed (SCT). In order to represent this information in a unified framework, a three steps method is proposed: (1) the LV is separated from the left auricle on SCT providing S ′ CT; (2) a semi-automatic rigid registration method; (3) activation time delays is applied to SEAM and S ′ CT are estimated on S ′ CT from the EAM data. This method results in a graphical interface offering to clinicians means to identify abnormal electrical activity sites