Social distancing strategies against disease spreading

The recurrent infectious diseases and their increasing impact on the society has promoted the study of strategies to slow down the epidemic spreading. In this review we outline the applications of percolation theory to describe strategies against epidemic spreading on complex networks. We give a general outlook of the relation between link percolation and the susceptible-infected-recovered model, and introduce the node void percolation process to describe the dilution of the network composed by healthy individual, $i.e$, the network that sustain the functionality of a society. Then, we survey two strategies: the quenched disorder strategy where an heterogeneous distribution of contact intensities is induced in society, and the intermittent social distancing strategy where health individuals are persuaded to avoid contact with their neighbors for intermittent periods of time. Using percolation tools, we show that both strategies may halt the epidemic spreading. Finally, we discuss the role of the transmissibility, $i.e$, the effective probability to transmit a disease, on the performance of the strategies to slow down the epidemic spreading.Comment: to be published in "Perspectives and Challenges in Statistical Physics and Complex Systems for the Next Decade", Word Scientific Pres

Slow epidemic extinction in populations with heterogeneous infection rates

We explore how heterogeneity in the intensity of interactions between people affects epidemic spreading. For that, we study the susceptible-infected-susceptible model on a complex network, where a link connecting individuals $i$ and $j$ is endowed with an infection rate $\beta_{ij} = \lambda w_{ij}$ proportional to the intensity of their contact $w_{ij}$, with a distribution $P(w_{ij})$ taken from face-to-face experiments analyzed in Cattuto $et\;al.$ (PLoS ONE 5, e11596, 2010). We find an extremely slow decay of the fraction of infected individuals, for a wide range of the control parameter $\lambda$. Using a distribution of width $a$ we identify two large regions in the $a-\lambda$ space with anomalous behaviors, which are reminiscent of rare region effects (Griffiths phases) found in models with quenched disorder. We show that the slow approach to extinction is caused by isolated small groups of highly interacting individuals, which keep epidemic alive for very long times. A mean-field approximation and a percolation approach capture with very good accuracy the absorbing-active transition line for weak (small $a$) and strong (large $a$) disorder, respectively

Effect of degree correlations above the first shell on the percolation transition

The use of degree-degree correlations to model realistic networks which are characterized by their Pearson's coefficient, has become widespread. However the effect on how different correlation algorithms produce different results on processes on top of them, has not yet been discussed. In this letter, using different correlation algorithms to generate assortative networks, we show that for very assortative networks the behavior of the main observables in percolation processes depends on the algorithm used to build the network. The different alghoritms used here introduce different inner structures that are missed in Pearson's coefficient. We explain the different behaviors through a generalization of Pearson's coefficient that allows to study the correlations at chemical distances l from a root node. We apply our findings to real networks.Comment: In press EP

Evolution equation for a model of surface relaxation in complex networks

In this paper we derive analytically the evolution equation of the interface for a model of surface growth with relaxation to the minimum (SRM) in complex networks. We were inspired by the disagreement between the scaling results of the steady state of the fluctuations between the discrete SRM model and the Edward-Wilkinson process found in scale-free networks with degree distribution $P(k) \sim k^{-\lambda}$ for $\lambda <3$ [Pastore y Piontti {\it et al.}, Phys. Rev. E {\bf 76}, 046117 (2007)]. Even though for Euclidean lattices the evolution equation is linear, we find that in complex heterogeneous networks non-linear terms appear due to the heterogeneity and the lack of symmetry of the network; they produce a logarithmic divergency of the saturation roughness with the system size as found by Pastore y Piontti {\it et al.} for $\lambda <3$.Comment: 9 pages, 2 figure

Discrete surface growth process as a synchronization mechanism for scale free complex networks

We consider the discrete surface growth process with relaxation to the minimum [F. Family, J. Phys. A {\bf 19} L441, (1986).] as a possible synchronization mechanism on scale-free networks, characterized by a degree distribution $P(k) \sim k^{-\lambda}$, where $k$ is the degree of a node and $\lambda$ his broadness, and compare it with the usually applied Edward-Wilkinson process [S. F. Edwards and D. R. Wilkinson, Proc. R. Soc. London Ser. A {\bf 381},17 (1982) ]. In spite of both processes belong to the same universality class for Euclidean lattices, in this work we demonstrate that for scale-free networks with exponents $\lambda<3$ this is not true. Moreover, we show that for these ubiquitous cases the Edward-Wilkinson process enhances spontaneously the synchronization when the system size is increased, which is a non-physical result. Contrarily, the discrete surface growth process do not present this flaw and is applicable for every $\lambda$.Comment: 8 pages, 4 figure

Variability-selected quasars behind the Small Magellanic Cloud

We present followup spectroscopic observations of quasar candidates in the Small Magellanic Cloud selected by Eyer from the OGLE database. Of twelve observed objects identified as "QSO Candidate", five are confirmed quasars, with the emission redshifts ranging from 0.28 to 2.16. Two of those quasars were also recently identified independently in the MACHO database by Geha et al. We discuss the prospects of using variability-based selection technique for quasar searches behind other dense stellar fields. An additional criterion utilizing the color-color diagram should reduce the number of stars in the candidate lists.Comment: Revised version, AASTeX, 11 pages, 3 EPS figures, one table, accepted 14 Nov 2002 for publication in the Astronomical Journal, March 2003 issu

Progress in the study of CdZnTe strip detectors

We report new performance measurements and computer simulations of a sub-millimeter pitch CdZnTe strip detector under study as a prototype imaging spectrometer for astronomical x-ray and gamma-ray observations. The prototype is 1.5 mm thick with 375 micron strip pitch in both the x and y dimensions. Previously reported work included demonstrations of half-pitch spatial resolution (approximately 190 microns) and good energy resolution and spectral uniformity. Strip detector efficiency measurements have also been presented. A model that includes the photon interaction, carrier transport and the electronics was developed that qualitatively reproduced the measurements. The new studies include measurements of the CdZnTe transport properties for this prototype in an effort to resolve quantitative discrepancies between the measurements and the simulations. Measurements of charge signals produced by laser pulses and (alpha) -rays are used to determine these transport properties. These are then used in the model to predict gamma-ray efficiencies that are compared with the data. The imaging performance of the detector is studied by scanned laser and gamma beam spot measurements. The results support the model\u27s prediction of nearly linear sharing of the charge for interactions occurring in the region between electrodes. The potential for strip detectors with spatial resolution much finer than the strip pitch is demonstrated. A new design scheme for strip detectors is shortly discussed

A variant of the Mukai pairing via deformation quantization

We give a new method to prove a formula computing a variant of Caldararu's Mukai pairing \cite{Cal1}. Our method is based on some important results in the area of deformation quantization. In particular, part of the work of Kashiwara and Schapira in \cite{KS} as well as an algebraic index theorem of Bressler, Nest and Tsygan in \cite{BNT},\cite{BNT1} and \cite{BNT2} are used. It is hoped that our method is useful for generalization to settings involving certain singular varieties.Comment: 8 pages. Comments and suggestions welcom