Exact Recovery for a Family of Community-Detection Generative Models

Generative models for networks with communities have been studied extensively for being a fertile ground to establish information-theoretic and computational thresholds. In this paper we propose a new toy model for planted generative models called planted Random Energy Model (REM), inspired by Derrida's REM. For this model we provide the asymptotic behaviour of the probability of error for the maximum likelihood estimator and hence the exact recovery threshold. As an application, we further consider the 2 non-equally sized community Weighted Stochastic Block Model (2-WSBM) on $h$-uniform hypergraphs, that is equivalent to the P-REM on both sides of the spectrum, for high and low edge cardinality $h$. We provide upper and lower bounds for the exact recoverability for any $h$, mapping these problems to the aforementioned P-REM. To the best of our knowledge these are the first consistency results for the 2-WSBM on graphs and on hypergraphs with non-equally sized community

New VLT observations of the Fermi pulsar PSR J1048-5832

PSR J1048-5832 is a Vela-like (P=123.6 ms; tau~20.3 kyr) gamma-ray pulsar detected by Fermi, at a distance of ~2.7 kpc and with a rotational energy loss rate dot{E}_{SD} ~2 x 10^{36} erg/s. The PSR J1048-5832 field has been observed with the VLT in the V and R bands. We used these data to determine the colour of the object detected closest to the Chandra position (Star D) and confirm that it is not associated with the pulsar. For the estimated extinction along the line of sight, inferred from a re-analysis of the Chandra and XMM-Newton spectra, the fluxes of Star D (V~26.7; R~25.8) imply a -0.13 < (V-R)_0 < 0.6. This means that the PSR J1048-5832 spectrum would be unusually red compared to the Vela pulsar.Moreover, the ratio between the unabsorbed optical and X-ray flux of PSR J1048-5832 would be much higher than for other young pulsars. Thus, we conclude that Star D is not the PSR J1048-5832 counterpart. We compared the derived R and V-band upper limits (R>26.4; V>27.6) with the extrapolation of the X and gamma-ray spectra and constrained the pulsar spectrum at low-energies. In particular, the VLT upper limits suggest that the pulsar spectrum could be consistent with a single power-law, stretching from the gamma-rays to the optical.Comment: 5 pages, 2 figures, accepted for publication on Monthly Notices of the Royal Astronomical Society Main Journa

X-ray ionization of the intergalactic medium by quasars

We investigate the impact of quasars on the ionization of the surrounding intergalactic medium (IGM) with the radiative transfer code \texttt{CRASH4}, now accounting for X-rays and secondary electrons. After comparing with analytic solutions, we post-process a cosmic volume ($\approx 1.5\times 10^4$ Mpc$^3 h^{-3}$) containing a ULAS J1120+0641-like quasar (QSO) hosted by a $5 \times 10^{11} {\rm M}_\odot h^{-1}$ dark matter (DM) halo. We find that: (i) the average HII region ($R\sim3.2$~pMpc in a lifetime $t_f = 10^7$~yrs) is mainly set by UV flux, in agreement with semi-analytic scaling relations; (ii) a largely neutral ($x_{\textrm{HII}} < 0.001$), warm ($T\sim 10^3$~K) tail extends up to few Mpc beyond the ionization front, as a result of the X-ray flux; (iii) LyC-opaque inhomogeneities induce a line of sight (LOS) scatter in $R$ as high as few physical Mpc, consistent with the DLA scenario proposed to explain the anomalous size of the ULAS J1120+0641 ionized region. On the other hand, with an ionization rate $\dot{N}_{\gamma,0} \sim 10^{57}$~s$^{-1}$, the assumed DLA clustering and gas opacity, only one LOS shows an HII region compatible with the observed one. We deduce that either the ionization rate of the QSO is at least one order of magnitude lower or the ULAS J1120+0641 bright phase is shorter than $10^7$~yrs.Comment: Accepted for publication in MNRAS Main Journal, Accepted 2018 May 2

Strengthening gold-gold bonds by complexing gold clusters with noble gases

We report an unexpectedly strong and complex chemical bonding of rare-gas atoms to neutral gold clusters. The bonding features are consistently reproduced at different levels of approximation within density-functional theory and beyond: from GGA, through hybrid and double-hybrid functionals, up to renormalized second-order perturbation theory. The main finding is that the adsorption of Ar, Kr, and Xe reduces electron-electron repulsion within gold dimer, causing strengthening of the Au-Au bond. Differently from the dimer, the rare-gas adsorption effects on the gold trimer's geometry and vibrational frequencies are mainly due to electron occupation of the trimer's lowest unoccupied molecular orbital. For the trimer, the theoretical results are also consistent with far-infrared multiple photon dissociation experiments.Comment: To be published in Inorganic Chemistry Communication

On a problem of Pillai with k-generalized Fibonacci numbers and powers of 2

For an integer $k\geq 2$, let $\{F^{(k)}_{n} \}_{n\geq 0}$ be the $k$--generalized Fibonacci sequence which starts with $0, \ldots, 0, 1$ ($k$ terms) and each term afterwards is the sum of the $k$ preceding terms. In this paper, we find all integers $c$ having at least two presentations as a difference between a $k$--generalized Fibonacci number and a powers of 2 for any fixed $k \geqslant 4$. This paper extends previous work from [9] for the case $k=2$ and [6] for the case $k=3$

How do Banking Crises Impact on Income Inequality?

We show that banking crises have an important effect on income distribution: inequality increases before banking crisis episodes and sharply decline afterwards. We also find that,while a large government size does not per se seem to reduce inequality, a rise in financial depth (i.e. better access to credit provided by the banking sector) contributes to a more equal distribution of income.Inequality, banking crisis, financial depth, government size.

Target motion estimation via a multistatic FSR

The focus of this paper is on the estimation of the kinematic parameters of moving targets via a MIMO Forward Scatter Radar (FSR) system. A sub-optimum estimation technique is considered that exploits the information concerning the time instants at which the target crosses the individual baselines to retrieve the motion parameters. The accuracy of such technique is firstly investigated from a theoretical point of view and then the effectiveness of the proposed approach is demonstrated by applying it to live MIMO FSR data. Shown results prove the practical applicability of the proposed technique