Intertwining operator for AG2AG_2 Calogero-Moser-Sutherland system

We consider generalised Calogero-Moser-Sutherland quantum Hamiltonian $H$ associated with a configuration of vectors $AG_2$ on the plane which is a union of $A_2$ and $G_2$ root systems. The Hamiltonian $H$ depends on one parameter. We find an intertwining operator between $H$ and the Calogero-Moser-Sutherland Hamiltonian for the root system $G_2$. This gives a quantum integral for $H$ of order 6 in an explicit form thus establishing integrability of $H$.Comment: 24 page

Accurate simulation estimates of phase behaviour in ternary mixtures with prescribed composition

This paper describes an isobaric semi-grand canonical ensemble Monte Carlo scheme for the accurate study of phase behaviour in ternary fluid mixtures under the experimentally relevant conditions of prescribed pressure, temperature and overall composition. It is shown how to tune the relative chemical potentials of the individual components to target some requisite overall composition and how, in regions of phase coexistence, to extract accurate estimates for the compositions and phase fractions of individual coexisting phases. The method is illustrated by tracking a path through the composition space of a model ternary Lennard-Jones mixture.Comment: 6 pages, 3 figure

The Cuntz-Toeplitz algebras have nuclear dimension one

We prove that unital extensions of Kirchberg algebras by separable stable AF algebras have nuclear dimension one. The title follows.Comment: Minor changes. Accepted Version. J. Funct. Anal., to appea

Quantification of Retrograde Axonal Transport in the Rat Optic Nerve by Fluorogold Spectrometry

PURPOSE: Disturbed axonal transport is an important pathogenic factor in many neurodegenerative diseases, such as glaucoma, an eye disease characterised by progressive atrophy of the optic nerve. Quantification of retrograde axonal transport in the optic nerve usually requires labour intensive histochemical techniques or expensive equipment for in vivo imaging. Here, we report on a robust alternative method using Fluorogold (FG) as tracer, which is spectrometrically quantified in retinal tissue lysate. METHODS: To determine parameters reflecting the relative FG content of a sample FG was dissolved in retinal lysates at different concentrations and spectra were obtained. For validation in vivo FG was injected uni- or bilaterally into the superior colliculus (SC) of Sprague Dawley rats. The retinal lysate was analysed after 3, 5 and 7 days to determine the time course of FG accumulation in the retina (n = 15). In subsequent experiments axona transport was impaired by optic nerve crush (n = 3), laser-induced ocular hypertension (n = 5) or colchicine treatment to the SC (n = 10). RESULTS: Spectrometry at 370 nm excitation revealed two emission peaks at 430 and 610 nm. We devised a formula to calculate the relative FG content (c(FG)), from the emission spectrum. c(FG) is proportional to the real FG concentration as it corrects for variations of retinal protein concentration in the lysate. After SC injection, c(FG) monotonously increases with time (p = 0.002). Optic nerve axonal damage caused a significant decrease of c(FG) (crush p = 0.029; hypertension p = 0.025; colchicine p = 0.006). Lysates are amenable to subsequent protein analysis. CONCLUSIONS: Spectrometrical FG detection in retinal lysates allows for quantitative assessment of retrograde axonal transport using standard laboratory equipment. It is faster than histochemical techniques and may also complement morphological in vivo analyses

Geokinematics of Central Europe: New insights from the CERGOP-2/Environment Project

The Central European Geodynamics Project CERGOP/2, funded by the European Union from 2003to 2006 under the 5th Framework Programme, benefited from repeated measurements of thecoordinates of epoch and permanent GPS stations of the Central European GPS Reference Network(CEGRN), starting in 1994. Here we report on the results of the systematic processing of availabledata up to 2005. The analysis has yielded velocities for some 60 sites, covering a variety of CentralEuropean tectonic provinces, from the Adria indenter to the Tauern window, the Dinarides, thePannonian Basin, the Vrancea seismic zone and the Carpathian Mountains. The estimated velocitiesdefine kinematical patterns which outline, with varying spatial resolution depending on the stationdensity and history, the present day surface kinematics in Central Europe. Horizontal velocities areanalyzed after removal from the ITRF2000 estimated velocities of a rigid rotation accounting forthe mean motion of Europe: a ~2.3 mm/yr north-south oriented convergence rate between Adria andthe Southern Alps that can be considered to be the present day velocity of the Adria indenterrelative to the European foreland. An eastward extrusion zone initiates at the Tauern Window. Thelateral eastward flow towards the Pannonian Basin exhibits a gentle gradient from 1-1.5 mm/yrimmediately east of the Tauern Window to zero in the Pannonian Basin. This kinematic continuityimplies that the Pannonian plate fragment recently suggested by seismic data does not require aspecific Eulerian pole. On the southeastern boundary of the Adria microplate, we report a velocitydrop from 4-4.5 mm/yr motion near Matera to ~1 mm/yr north of the Dinarides, in the southwesternpart of the Pannonian Basin. A positive velocity gradient as one moves south from West Ukraineacross Rumania and Bulgaria is estimated to be 2 mm/yr on a scale of 600-800 km, as if the crustwere dragged by the counterclockwise rotation along the North Anatolian Fault Zone. This regimeapparently does not interfere with the Vrancea seismic zone: earthquakes there are sufficiently deep(> 100 km) that the brittle deformation at depth can be considered as decoupled from the creep atthe surface. We conclude that models of the Quaternary tectonics of Central and Eastern Europeshould not neglect the long wavelength, nearly aseismic deformation affecting the upper crust in theRomanian and Bulgarian regions

A Novel High-Content Flow Cytometric Method for Assessing the Viability and Damage of Rat Retinal Ganglion Cells

PURPOSE: The aim of the study was to develop a high-content flow cytometric method for assessing the viability and damage of small, medium, and large retinal ganglion cells (RGCs) in N-methyl-D-aspartic acid (NMDA)-injury model. METHODS/RESULTS: Retinal toxicity was induced in rats by intravitreal injection of NMDA and RGCs were retrogradely labeled with Fluoro-Gold (FG). Seven days post-NMDA injection, flatmount and flow cytometric methods were used to evaluate RGCs. In addition, the RGC area diameter (D((a))) obtained from retinal flatmount imaging were plotted versus apparent volume diameter (D((v))) obtained from flow cytometry for the same cumulative cell number (sequentially from small to large RGCs) percentile (Q) to establish their relationship for accurately determining RGC sizes. Good correlation (r = 0.9718) was found between D((a)) and apparent D((v)). Both flatmount and flow cytometric analyses of RGCs showed that 40 mM NMDA significantly reduced the numbers of small and medium RGCs but not large RGCs. Additionally, flow cytometry showed that the geometric means of FG and thy-1 intensities in three types of RGCs decreased to 90.96±2.24% (P<0.05) and 91.78±1.89% (P>0.05) for small, 69.62±2.11% (P<0.01) and 69.07±2.98% (P<0.01) for medium, and 69.68±6.48% (P<0.05) and 69.91±6.23% (P<0.05) for large as compared with the normal RGCs. CONCLUSION: The established flow cytometric method provides high-content analysis for differential evaluation of RGC number and status and should be useful for the evaluation of various models of optic nerve injury and the effects of potential neuroprotective agents