Geometry and observables in (2+1)-gravity

We review the geometrical properties of vacuum spacetimes in (2+1)-gravity with vanishing cosmological constant. We explain how these spacetimes are characterised as quotients of their universal cover by holonomies. We explain how this description can be used to clarify the geometrical interpretation of the fundamental physical variables of the theory, holonomies and Wilson loops. In particular, we discuss the role of Wilson loop observables as the generators of the two fundamental transformations that change the geometry of (2+1)-spacetimes, grafting and earthquake. We explain how these variables can be determined from realistic measurements by an observer in the spacetime.Comment: Talk given at 2nd School and Workshop on Quantum Gravity and Quantum Geometry (Corfu, September 13-20 2009); 10 pages, 13 eps figure

Eukaryotic initiation factor-4E in superficial and muscle invasive bladder cancer and its correlation with vascular endothelial growth factor expression and tumour progression

Vascular endothelial growth factor (VEGF) is an important factor mediating tumour angiogenesis. VEGF mRNA is differentially expressed in bladder cancer with high expression in superficial tumours (stage pTaand pT1) contrasting with low expression in muscle invasive tumours (stage ≥ pT2). To investigate mechanisms regulating VEGF expression in bladder cancer, VEGF mRNA and protein were measured in normal bladder (n = 12) and primary bladder cancers (n = 57). VEGF protein levels correlated with mRNA expression in normal bladder (r = 0.68, P = 0.02) and bladder cancer (r = 0.46, P = 0.0007). Whilst VEGF mRNA expression was threefold higher in superficial compared to muscle invasive bladder cancers (P = 0.0001) there was no difference in VEGF protein (P = 0.81). Accordingly, the median protein:mRNA ratios increased more than 15-fold with increasing tumour stage (P< 0.0001) suggesting translational regulation. Expression of the eukaryotic initiation factor-4E (eIF-4E), a factor implicated in the translational regulation of VEGF, was greater in tumours than normal bladder (P< 0.0001) and correlated with VEGF protein:mRNA ratios (n = 43, r = 0.54, P = 0.0004) pointing to its role in the regulation of VEGF. In superficial tumours (n = 37) high expression of eIF-4E was associated with a poor prognosis and reduced stage progression-free survival (P = 0.04, Cox proportional hazards model). The study demonstrates that eIF-4E may be involved in translational regulation of VEGF in bladder cancer and might have a role as a prognostic factor in bladder cancer. © 2000 Cancer Research Campaig

Land cover classification using multi-temporal MERIS vegetation indices

The spectral, spatial, and temporal resolutions of Envisat's Medium Resolution Imaging Spectrometer (MERIS) data are attractive for regional- to global-scale land cover mapping. Moreover, two novel and operational vegetation indices derived from MERIS data have considerable potential as discriminating variables in land cover classification. Here, the potential of these two vegetation indices (the MERIS global vegetation index (MGVI), MERIS terrestrial chlorophyll index (MTCI)) was evaluated for mapping eleven broad land cover classes in Wisconsin. Data acquired in the high and low chlorophyll seasons were used to increase inter-class separability. The two vegetation indices provided a higher degree of inter-class separability than data acquired in many of the individual MERIS spectral wavebands. The most accurate landcover map (73.2%) was derived from a classification of vegetation index-derived data with a support vector machine (SVM), and was more accurate than the corresponding map derived from a classification using the data acquired in the original spectral wavebands

Laser beam coupling with capillary discharge plasma for laser wakefield acceleration applications

One of the most robust methods, demonstrated up to date, of accelerating electron beams by laser-plasma sources is the utilization of plasma channels generated by the capillary discharges. These channels, i.e., plasma columns with a minimum density along the laser pulse propagation axis, may optically guide short laser pulses, thereby increasing the acceleration length, leading to a more efficient electron acceleration. Although the spatial structure of the installation is simple in principle, there may be some important effects caused by the open ends of the capillary, by the supplying channels etc., which require a detailed 3D modeling of the processes taking place in order to get a detailed understanding and improve the operation. However, the discharge plasma, being one of the most crucial components of the laser-plasma accelerator, is not simulated with the accuracy and resolution required to advance this promising technology. In the present work, such simulations are performed using the code MARPLE. First, the process of the capillary filling with a cold hydrogen before the discharge is fired, through the side supply channels is simulated. The main goal of this simulation is to get a spatial distribution of the filling gas in the region near the open ends of the capillary. A realistic geometry is used for this and the next stage simulations, including the insulators, the supplying channels as well as the electrodes. Second, the simulation of the capillary discharge is performed with the goal to obtain a time-dependent spatial distribution of the electron density near the open ends of the capillary as well as inside the capillary. Finally, to evaluate effectiveness of the beam coupling with the channeling plasma wave guide and electron acceleration, modeling of laser-plasma interaction was performed with the code INF&RNOComment: 11 pages, 9 figure

Solvegeometry gravitational waves

In this paper we construct negatively curved Einstein spaces describing gravitational waves having a solvegeometry wave-front (i.e., the wave-fronts are solvable Lie groups equipped with a left-invariant metric). Using the Einstein solvmanifolds (i.e., solvable Lie groups considered as manifolds) constructed in a previous paper as a starting point, we show that there also exist solvegeometry gravitational waves. Some geometric aspects are discussed and examples of spacetimes having additional symmetries are given, for example, spacetimes generalising the Kaigorodov solution. The solvegeometry gravitational waves are also examples of spacetimes which are indistinguishable by considering the scalar curvature invariants alone.Comment: 10 pages; v2:more discussion and result

Fractal space-times under the microscope: A Renormalization Group view on Monte Carlo data

The emergence of fractal features in the microscopic structure of space-time is a common theme in many approaches to quantum gravity. In this work we carry out a detailed renormalization group study of the spectral dimension $d_s$ and walk dimension $d_w$ associated with the effective space-times of asymptotically safe Quantum Einstein Gravity (QEG). We discover three scaling regimes where these generalized dimensions are approximately constant for an extended range of length scales: a classical regime where $d_s = d, d_w = 2$, a semi-classical regime where $d_s = 2d/(2+d), d_w = 2+d$, and the UV-fixed point regime where $d_s = d/2, d_w = 4$. On the length scales covered by three-dimensional Monte Carlo simulations, the resulting spectral dimension is shown to be in very good agreement with the data. This comparison also provides a natural explanation for the apparent puzzle between the short distance behavior of the spectral dimension reported from Causal Dynamical Triangulations (CDT), Euclidean Dynamical Triangulations (EDT), and Asymptotic Safety.Comment: 26 pages, 6 figure

Attosecond electron spectroscopy using a novel interferometric pump-probe technique

We present an interferometric pump-probe technique for the characterization of attosecond electron wave packets (WPs) that uses a free WP as a reference to measure a bound WP. We demonstrate our method by exciting helium atoms using an attosecond pulse with a bandwidth centered near the ionization threshold, thus creating both a bound and a free WP simultaneously. After a variable delay, the bound WP is ionized by a few-cycle infrared laser precisely synchronized to the original attosecond pulse. By measuring the delay-dependent photoelectron spectrum we obtain an interferogram that contains both quantum beats as well as multi-path interference. Analysis of the interferogram allows us to determine the bound WP components with a spectral resolution much better than the inverse of the attosecond pulse duration.Comment: 5 pages, 4 figure

Exclusion processes with degenerate rates: convergence to equilibrium and tagged particle

Stochastic lattice gases with degenerate rates, namely conservative particle systems where the exchange rates vanish for some configurations, have been introduced as simplified models for glassy dynamics. We introduce two particular models and consider them in a finite volume of size $\ell$ in contact with particle reservoirs at the boundary. We prove that, as for non--degenerate rates, the inverse of the spectral gap and the logarithmic Sobolev constant grow as $\ell^2$. It is also shown how one can obtain, via a scaling limit from the logarithmic Sobolev inequality, the exponential decay of a macroscopic entropy associated to a degenerate parabolic differential equation (porous media equation). We analyze finally the tagged particle displacement for the stationary process in infinite volume. In dimension larger than two we prove that, in the diffusive scaling limit, it converges to a Brownian motion with non--degenerate diffusion coefficient.Comment: 25 pages, 3 figure

Results of two multi-chord stellar occultations by dwarf planet (1) Ceres

We report the results of two multi-chord stellar occultations by the dwarf planet (1) Ceres that were observed from Brazil on 2010 August 17, and from the USA on 2013 October 25. Four positive detections were obtained for the 2010 occultation, and nine for the 2013 occultation. Elliptical models were adjusted to the observed chords to obtain Ceres' size and shape. Two limb fitting solutions were studied for each event. The first one is a nominal solution with an indeterminate polar aspect angle. The second one was constrained by the pole coordinates as given by Drummond et al. Assuming a Maclaurin spheroid, we determine an equatorial diameter of 972 $\pm$ 6 km and an apparent oblateness of 0.08 $\pm$ 0.03 as our best solution. These results are compared to all available size and shape determinations for Ceres made so far, and shall be confirmed by the NASA's Dawn space mission.Comment: 9 pages, 6 figures. Accepted for publication in MNRA