Efficient computation of the Weighted Clustering Coefficient

The clustering coefficient of an unweighted network has been extensively used to quantify how tightly connected is the neighbor around a node and it has been widely adopted for assessing the quality of nodes in a social network. The computation of the clustering coefficient is challenging since it requires to count the number of triangles in the graph. Several recent works proposed efficient sampling, streaming and MapReduce algorithms that allow to overcome this computational bottleneck. As a matter of fact, the intensity of the interaction between nodes, that is usually represented with weights on the edges of the graph, is also an important measure of the statistical cohesiveness of a network. Recently various notions of weighted clustering coefficient have been proposed but all those techniques are hard to implement on large-scale graphs. In this work we show how standard sampling techniques can be used to obtain efficient estimators for the most commonly used measures of weighted clustering coefficient. Furthermore we also propose a novel graph-theoretic notion of clustering coefficient in weighted networks. © 2016, Copyright © Taylor & Francis Group, LL

Constraints on secret neutrino interactions after Planck

(Abridged) Neutrino interactions beyond the standard model may affect the cosmological evolution and can be constrained through observations. We consider the possibility that neutrinos possess secret scalar or pseudoscalar interactions mediated by the Nambu-Goldstone boson of a still unknown spontaneously broken global $U(1)$ symmetry, as in, e.g. , Majoron models. In such scenarios, neutrinos still decouple at $T\simeq 1$ MeV, but become tightly coupled again ('recouple') at later stages of the cosmological evolution. We use available observations of CMB anisotropies, including Planck 2013 and the joint BICEP2/Planck 2015 data, to derive constraints on the quantity $\gamma_{\nu \nu}^4$, parameterizing the neutrino collision rate due to (pseudo)scalar interactions. We consider both a minimal extension of the standard $\Lambda$CDM model, and scenarios with extra relativistic species or non-vanishing tensors. We find a typical constraint $\gamma_{\nu \nu}^4 < 0.9\times 10^{-27}$ (95% C.L.), implying an upper limit on the redshift $z_{rec}$ of neutrino recoupling $< 8500$. In the framework of Majoron models, the upper limit on $\gamma_{\nu \nu}$ roughly translates on a constraint $g < 8.2\times 10^{-7}$ on the Majoron-neutrino coupling constant $g$. In general, the data show a weak ($\sim 1\sigma$) but intriguing preference for non-zero values of $\gamma_{\nu \nu}^4$, with best fits in the range $\gamma_{\nu \nu}^4 = (0.15 - 0.35)\times 10^{-27}$, depending on the particular dataset. This is more evident when either observations from ACT and SPT are included, or the possibility of non-vanishing tensor modes is considered. In particular, for the minimal model $\Lambda$CDM +$\gamma_{\nu \nu}$ and including the Planck 2013, ACT and SPT data, we report $\gamma_{\nu \nu}^4=( 0.45^{+0.15}_{-0.38} )\times10^{-27}$ ($200 < z_{rec} < 5700$) at 68% confidence level.Comment: 19 pages, 7 figures, 3 tables. Replaced to match version accepted for pubblication in JCA

The ν\nu generation: present and future constraints on neutrino masses from cosmology and laboratory experiments

We perform a joint analysis of current data from cosmology and laboratory experiments to constrain the neutrino mass parameters in the framework of bayesian statistics, also accounting for uncertainties in nuclear modeling, relevant for neutrinoless double $\beta$ decay ($0\nu2\beta$) searches. We find that a combination of current oscillation, cosmological and $0\nu2\beta$ data constrains $m_{\beta\beta}~<~0.045\,\mathrm{eV}$ ($0.014 \, \mathrm{eV} < m_{\beta\beta} < 0.066 \,\mathrm{eV}$) at 95\% C.L. for normal (inverted) hierarchy. This result is in practice dominated by the cosmological and oscillation data, so it is not affected by uncertainties related to the interpretation of $0\nu2\beta$ data, like nuclear modeling, or the exact particle physics mechanism underlying the process. We then perform forecasts for forthcoming and next-generation experiments, and find that in the case of normal hierarchy, given a total mass of $0.1\,$ eV, and assuming a factor-of-two uncertainty in the modeling of the relevant nuclear matrix elements, it will be possible to measure the total mass itself, the effective Majorana mass and the effective electron mass with an accuracy (at 95\% C.L.) of $0.05$, $0.015$, $0.02\,\mathrm{eV}$ respectively, as well as to be sensitive to one of the Majorana phases. This assumes that neutrinos are Majorana particles and that the mass mechanism gives the dominant contribution to $0\nu2\beta$ decay. We argue that more precise nuclear modeling will be crucial to improve these sensitivities.Comment: v2: 6 pages, 3 figures, 1 table; added definition of parameter minimal value from oscillation measurements; corrected confidence interval, that in v1 were reported at 90% C.L. and misidentified as 95% C.L.; accepted for publicatio

White Dwarf Planets from GAIA

We investigate the potential of high-precision astrometry with GAIA for detection of giant planetary companions to nearby white dwarfs. If one considers that, to date, no confirmed planets around single white dwarfs are known, the results from GAIA will be crucial to study the late-stage evolution of planetary systems and to verify the possibility that 2nd-generation planets are formed.Comment: Part of PlanetsbeyondMS/2010 proceedings http://arxiv.org/html/1011.6606v1, Proc. of the workshop on "Planetary Systems beyond the Main Sequence" (Bamberg, 11-14 August 2010), AIPC in press (eds. S. Schuh, H. Drechsel and U. Heber), 4 pages, 1 figur