On the low detection efficiency of disk water megamasers in Seyfert 2 AGN

Disk megamasers are a unique tool to study active galactic nuclei (AGN) sub-pc environment, and precisely measure some of their fundamental parameters. While the majority of disk megamasers are hosted in heavily obscured (i.e., Seyfert 2, Sy2) AGN, the converse is not true, and disk megamasers are very rarely found even in obscured AGN. The very low detection rate of such systems in Sy2 AGN could be due to the geometry of the maser beaming, which requires a strict edge-on condition. We explore some other fundamental factors which could play a role in a volume-limited survey of disk megamasers in Sy2 galaxies, most importantly the radio luminosity.Comment: 2 pages, 2 figures. To appear in the Proceedings IAU Symposium No. 336, 2017 "Astrophysical Masers: Unlocking the Mysteries of the Universe

Nash estimates and upper bounds for non-homogeneous Kolmogorov equations

We prove a Gaussian upper bound for the fundamental solutions of a class of ultra-parabolic equations in divergence form. The bound is independent on the smoothness of the coefficients and generalizes some classical results by Nash, Aronson and Davies. The class considered has relevant applications in the theory of stochastic processes, in physics and in mathematical finance.Comment: 21 page

Towards a Maude tool for model checking temporal graph properties

We present our prototypical tool for the verification of graph transformation systems. The major novelty of our tool is that it provides a model checker for temporal graph properties based on counterpart semantics for quantified m-calculi. Our tool can be considered as an instantiation of our approach to counterpart semantics which allows for a neat handling of creation, deletion and merging in systems with dynamic structure. Our implementation is based on the object-based machinery of Maude, which provides the basics to deal with attributed graphs. Graph transformation systems are specified with term rewrite rules. The model checker evaluates logical formulae of second-order modal m-calculus in the automatically generated CounterpartModel (a sort of unfolded graph transition system) of the graph transformation system under study. The result of evaluating a formula is a set of assignments for each state, associating node variables to actual nodes

Fluid-fluid demixing curves for colloid-polymer mixtures in a random colloidal matrix

We study fluid-fluid phase separation in a colloid-polymer mixture adsorbed in a colloidal porous matrix close to the \theta -point. For this purpose we consider the Asakura-Oosawa model in the presence of a quenched matrix of colloidal hard spheres. We study the dependence of the demixing curve on the parameters that characterize the quenched matrix, fixing the polymer-to-colloid size ratio to 0.8. We find that, to a large extent, demixing curves depend only on a single parameter f, which represents the volume fraction which is unavailable to the colloids. We perform Monte Carlo simulations for volume fractions f equal to 40% and 70%, finding that the binodal curves in the polymer and colloid packing-fraction plane have a small dependence on disorder. The critical point instead changes significantly: for instance, the colloid packing fraction at criticality increases with increasing f. Finally, we observe for some values of the parameters capillary condensation of the colloids: a bulk colloid-poor phase is in chemical equilibrium with a colloid-rich phase in the matrix.Comment: 26 pages, 8 figures. In publication in Molecular Physics, special volume dedicated to Luciano Reatto for his 70th birthda

Framed sheaves on projective space and Quot schemes

We prove that, given integers $m\geq 3$, $r\geq 1$ and $n\geq 0$, the moduli space of torsion free sheaves on $\mathbb P^m$ with Chern character $(r,0,\ldots,0,-n)$ that are trivial along a hyperplane $D \subset \mathbb P^m$ is isomorphic to the Quot scheme $\mathrm{Quot}_{\mathbb A^m}(\mathscr O^{\oplus r},n)$ of $0$-dimensional length $n$ quotients of the free sheaf $\mathscr O^{\oplus r}$ on $\mathbb A^m$.Comment: Minor improvement

How log-normal is your country? An analysis of the statistical distribution of the exported volumes of products

We have considered the statistical distributions of the volumes of the different products exported by 148 countries. We have found that the form of these distributions is not unique but heavily depends on the level of development of the nation, as expressed by macroeconomic indicators like GDP, GDP per capita, total export and a recently introduced measure for countries' economic complexity called fitness. We have identified three major classes: a) an incomplete log-normal shape, truncated on the left side, for the less developed countries, b) a complete log-normal, with a wider range of volumes, for nations characterized by intermediate economy, and c) a strongly asymmetric shape for countries with a high degree of development. The ranking curves of the exported volumes from each country seldom cross each other, showing a clear hierarchy of export volumes. Finally, the log-normality hypothesis has been checked for the distributions of all the 148 countries through different tests, Kolmogorov-Smirnov and Cramer-Von Mises, confirming that it cannot be rejected only for the countries of intermediate economy.Comment: 10 pages, 5 figures, submitted to IWcee15 conferenc