Poisson-Lie T-plurality of three-dimensional conformally invariant sigma models II: Nondiagonal metrics and dilaton puzzle

We look for 3-dimensional Poisson-Lie dualizable sigma models that satisfy the vanishing beta-function equations with constant dilaton field. Using the Poisson-Lie T-plurality we then construct 3-dimensional sigma models that correspond to various decompositions of Drinfeld double. Models with nontrivial dilaton field may appear. It turns out that for ``traceless'' dual algebras they satisfy the vanishing beta-function equations as well. In certain cases the dilaton cannot be defined in some of the dual models. We provide an explanation why this happens and give criteria predicting when it happens.Comment: 24 pages, the published version; changes compared to v1: typos corrected, conclusions extended, added reference

The Resolved Outer Population of NGC6822 with WFPC2

We present F336W (U), F439W (B), F555W (V), and F675W (R) Wide Field Planetary Camera 2 (WFPC2) photometry of two outer regions of the Local Group dwarf irregular galaxy NGC6822. The NE region is ~13 arcmin from the galaxy centre, while the W region lies 10 arcmin out, and within the wispy low surface brightness outer regions of the galaxy. The fields are not crowded and contain few NGC 6822 stars. We discuss errors and uncertainties and find that the W region contains a main sequence that extends to stars of about 2 solar masses, with an age of about 200 Myr. The NE region has no main sequence or stars younger than 1 Gyr, but does contain some luminous red stars that are not matched in the W field. These stars are not clumped in the field. The results suggest that the W region may be a trace of a tidal event that triggered the current star-formation in this isolated galaxy.Comment: 12 pages including 2 tables, plus 4 figures (#1 omitted) To appear in PAS

Hot and dense water in the inner 25 AU of SVS13-A

In the context of the ASAI (Astrochemical Surveys At IRAM) project, we carried out an unbiased spectral survey in the millimeter window towards the well known low-mass Class I source SVS13-A. The high sensitivity reached (3-12 mK) allowed us to detect at least 6 HDO broad (FWHM ~ 4-5 km/s) emission lines with upper level energies up to Eu = 837 K. A non-LTE LVG analysis implies the presence of very hot (150-260 K) and dense (> 3 10^7 cm-3) gas inside a small radius ($\sim$ 25 AU) around the star, supporting, for the first time, the occurrence of a hot corino around a Class I protostar. The temperature is higher than expected for water molecules are sublimated from the icy dust mantles (~ 100 K). Although we cannot exclude we are observig the effects of shocks and/or winds at such small scales, this could imply that the observed HDO emission is tracing the water abundance jump expected at temperatures ~ 220-250 K, when the activation barrier of the gas phase reactions leading to the formation of water can be overcome. We derive X(HDO) ~ 3 10-6, and a H2O deuteration > 1.5 10-2, suggesting that water deuteration does not decrease as the protostar evolves from the Class 0 to the Class I stage.Comment: MNRAS Letter

Simple model for quantum general relativity from loop quantum gravity

New progress in loop gravity has lead to a simple model of `general-covariant quantum field theory'. I sum up the definition of the model in self-contained form, in terms accessible to those outside the subfield. I emphasize its formulation as a generalized topological quantum field theory with an infinite number of degrees of freedom, and its relation to lattice theory. I list the indications supporting the conjecture that the model is related to general relativity and UV finite.Comment: 8 pages, 3 figure

New Ultraviolet Extinction Curves for Interstellar Dust in M31

New low-resolution UV spectra of a sample of reddened OB stars in M31 were obtained with HST/STIS to study the wavelength dependence of interstellar extinction and the nature of the underlying dust grain populations. Extinction curves were constructed for four reddened sightlines in M31 paired with closely matching stellar atmosphere models. The new curves have a much higher S/N than previous studies. Direct measurements of N(H I) were made using the Ly$\alpha$ absorption lines enabling gas-to-dust ratios to be calculated. The sightlines have a range in galactocentric distance of 5 to 14 kpc and represent dust from regions of different metallicities and gas-to-dust ratios. The metallicities sampled range from Solar to 1.5 Solar. The measured curves show similarity to those seen in the Milky Way and the Large Magellanic Cloud. The Maximum Entropy Method was used to investigate the dust composition and size distribution for the sightlines observed in this program finding that the extinction curves can be produced with the available carbon and silicon abundances if the metallicity is super-Solar.Comment: ApJ, in press, 9 pages, 5 figure

Asymptotics of LQG fusion coefficients

The fusion coefficients from SO(3) to SO(4) play a key role in the definition of spin foam models for the dynamics in Loop Quantum Gravity. In this paper we give a simple analytic formula of the EPRL fusion coefficients. We study the large spin asymptotics and show that they map SO(3) semiclassical intertwiners into $SU(2)_L\times SU(2)_R$ semiclassical intertwiners. This non-trivial property opens the possibility for an analysis of the semiclassical behavior of the model.Comment: 14 pages, minor change

The EPRL intertwiners and corrected partition function

Do the SU(2) intertwiners parametrize the space of the EPRL solutions to the simplicity constraint? What is a complete form of the partition function written in terms of this parametrization? We prove that the EPRL map is injective for n-valent vertex in case when it is a map from SO(3) into SO(3)xSO(3) representations. We find, however, that the EPRL map is not isometric. In the consequence, in order to be written in a SU(2) amplitude form, the formula for the partition function has to be rederived. We do it and obtain a new, complete formula for the partition function. The result goes beyond the SU(2) spin-foam models framework.Comment: RevTex4, 15 pages, 5 figures; theorem of injectivity of EPRL map correcte

Investigating Echo-State Networks Dynamics by Means of Recurrence Analysis

This is the author accepted manuscript. The final version is available from IEEE via the DOI in this record.In this paper, we elaborate over the well-known interpretability issue in echo-state networks (ESNs). The idea is to investigate the dynamics of reservoir neurons with time-series analysis techniques developed in complex systems research. Notably, we analyze time series of neuron activations with recurrence plots (RPs) and recurrence quantification analysis (RQA), which permit to visualize and characterize high-dimensional dynamical systems. We show that this approach is useful in a number of ways. First, the 2-D representation offered by RPs provides a visualization of the high-dimensional reservoir dynamics. Our results suggest that, if the network is stable, reservoir and input generate similar line patterns in the respective RPs. Conversely, as the ESN becomes unstable, the patterns in the RP of the reservoir change. As a second result, we show that an RQA measure, called Lmax, is highly correlated with the well-established maximal local Lyapunov exponent. This suggests that complexity measures based on RP diagonal lines distribution can quantify network stability. Finally, our analysis shows that all RQA measures fluctuate on the proximity of the so-called edge of stability, where an ESN typically achieves maximum computational capability. We leverage on this property to determine the edge of stability and show that our criterion is more accurate than two well-known counterparts, both based on the Jacobian matrix of the reservoir. Therefore, we claim that RPs and RQA-based analyses are valuable tools to design an ESN, given a specific problem

Organic molecules in the protoplanetary disk of DG Tau revealed by ALMA

Planets form in protoplanetary disks and inherit their chemical compositions. It is thus crucial to map the distribution and investigate the formation of simple organics, such as formaldehyde and methanol, in protoplanetary disks. We analyze ALMA observations of the nearby disk-jet system around the T Tauri star DG Tau in the o-H$_2$CO $3_{1,2}-2_{1,1}$ and CH$_3$OH $3_{-2,2}-4_{-1,4}$ E, $5_{0,5}-4_{0,4}$ A transitions at an unprecedented resolution of $\sim0.15"$, i.e., $\sim18$ au at a distance of 121 pc. The H$_2$CO emission originates from a rotating ring extending from $\sim40$ au with a peak at $\sim62$ au, i.e., at the edge of the 1.3mm dust continuum. CH$_3$OH emission is not detected down to an r.m.s. of 3 mJy/beam in the 0.162 km/s channel. Assuming an ortho-to-para ratio of 1.8-2.8 the ring- and disk-height-averaged H$_2$CO column density is $\sim0.3-4\times10^{14}$ cm$^{-2}$, while that of CH$_3$OH is $<0.04-0.7\times10^{14}$ cm$^{-2}$. In the inner $40$ au no o-H$_2$CO emission is detected with an upper limit on its beam-averaged column density of $\sim0.5-6\times10^{13}$ cm$^{-2}$. The H$_2$CO ring in the disk of DG Tau is located beyond the CO iceline (R$_{\rm CO}\sim30$ au). This suggests that the H$_2$CO abundance is enhanced in the outer disk due to formation on grain surfaces by the hydrogenation of CO ice. The emission peak at the edge of the mm dust continuum may be due to enhanced desorption of H$_2$CO in the gas phase caused by increased UV penetration and/or temperature inversion. The CH$_3$OH/H$_2$CO abundance ratio is $<1$, in agreement with disk chemistry models. The inner edge of the H$_2$CO ring coincides with the radius where the polarization of the dust continuum changes orientation, hinting at a tight link between the H$_2$CO chemistry and the dust properties in the outer disk and at the possible presence of substructures in the dust distribution.Comment: 8 pages, 6 figures, accepted for publication on A&A Letter

Focusing and imaging with increased numerical apertures through multimode fibers with micro-fabricated optics

The use of individual multimode optical fibers in endoscopy applications has the potential to provide highly miniaturized and noninvasive probes for microscopy and optical micromanipulation. A few different strategies have been proposed recently, but they all suffer from intrinsically low resolution related to the low numerical aperture of multimode fibers. Here, we show that two-photon polymerization allows for direct fabrication of micro-optics components on the fiber end, resulting in an increase of the numerical aperture to a value that is close to 1. Coupling light into the fiber through a spatial light modulator, we were able to optically scan a submicrometer spot (300 nm FWHM) over an extended region, facing the opposite fiber end. Fluorescence imaging with improved resolution is also demonstrated.Comment: 5 pages, 3 figure