Topology and correlations in structured scale-free networks

We study a recently introduced class of scale-free networks showing a high clustering coefficient and non-trivial connectivity correlations. We find that the connectivity probability distribution strongly depends on the fine details of the model. We solve exactly the case of low average connectivity, providing also exact expressions for the clustering and degree correlation functions. The model also exhibits a lack of small world properties in the whole parameters range. We discuss the physical properties of these networks in the light of the present detailed analysis.Comment: 10 pages, 9 figure

Weblog patterns and human dynamics with decreasing interest

Weblog is the fourth way of network exchange after Email, BBS and MSN. Most bloggers begin to write blogs with great interest, and then their interests gradually achieve a balance with the passage of time. In order to describe the phenomenon that people's interest in something gradually decreases until it reaches a balance, we first propose the model that describes the attenuation of interest and reflects the fact that people's interest becomes more stable after a long time. We give a rigorous analysis on this model by non-homogeneous Poisson processes. Our analysis indicates that the interval distribution of arrival-time is a mixed distribution with exponential and power-law feature, that is, it is a power law with an exponential cutoff. Second, we collect blogs in ScienceNet.cn and carry on empirical studies on the interarrival time distribution. The empirical results agree well with the analytical result, obeying a special power law with the exponential cutoff, that is, a special kind of Gamma distribution. These empirical results verify the model, providing an evidence for a new class of phenomena in human dynamics. In human dynamics there are other distributions, besides power-law distributions. These findings demonstrate the variety of human behavior dynamics.Comment: 8 pages, 1 figure

Special fast diffusion with slow asymptotics. Entropy method and flow on a Riemannian manifold

We consider the asymptotic behaviour of positive solutions $u(t,x)$ of the fast diffusion equation $u_t=\Delta (u^{m}/m)={\rm div} (u^{m-1}\nabla u)$ posed for x\in\RR^d, $t>0$, with a precise value for the exponent $m=(d-4)/(d-2)$. The space dimension is $d\ge 3$ so that $m<1$, and even $m=-1$ for $d=3$. This case had been left open in the general study \cite{BBDGV} since it requires quite different functional analytic methods, due in particular to the absence of a spectral gap for the operator generating the linearized evolution. The linearization of this flow is interpreted here as the heat flow of the Laplace-Beltrami operator of a suitable Riemannian Manifold (\RR^d,{\bf g}), with a metric ${\bf g}$ which is conformal to the standard \RR^d metric. Studying the pointwise heat kernel behaviour allows to prove {suitable Gagliardo-Nirenberg} inequalities associated to the generator. Such inequalities in turn allow to study the nonlinear evolution as well, and to determine its asymptotics, which is identical to the one satisfied by the linearization. In terms of the rescaled representation, which is a nonlinear Fokker--Planck equation, the convergence rate turns out to be polynomial in time. This result is in contrast with the known exponential decay of such representation for all other values of $m$.Comment: 37 page

Steady-State Dynamics of the Forest Fire Model on Complex Networks

Many sociological networks, as well as biological and technological ones, can be represented in terms of complex networks with a heterogeneous connectivity pattern. Dynamical processes taking place on top of them can be very much influenced by this topological fact. In this paper we consider a paradigmatic model of non-equilibrium dynamics, namely the forest fire model, whose relevance lies in its capacity to represent several epidemic processes in a general parametrization. We study the behavior of this model in complex networks by developing the corresponding heterogeneous mean-field theory and solving it in its steady state. We provide exact and approximate expressions for homogeneous networks and several instances of heterogeneous networks. A comparison of our analytical results with extensive numerical simulations allows to draw the region of the parameter space in which heterogeneous mean-field theory provides an accurate description of the dynamics, and enlights the limits of validity of the mean-field theory in situations where dynamical correlations become important.Comment: 13 pages, 9 figure

Characterization of neutrino signals with radiopulses in dense media through the LPM effect

We discuss the possibilities of detecting radio pulses from high energy showers in ice, such as those produced by PeV and EeV neutrino interactions. It is shown that the rich radiation pattern structure in the 100 MHz to few GHz allows the separation of electromagnetic showers induced by photons or electrons above 100 PeV from those induced by hadrons. This opens up the possibility of measuring the energy fraction transmitted to the electron in a charged current electron neutrino interaction with adequate sampling of the angular distribution of the signal. The radio technique has the potential to complement conventional high energy neutrino detectors with flavor information.Comment: 5 pages, 4 ps figures. Submitted to Phys. Rev. Let

Measurement of the scintillation time spectra and pulse-shape discrimination of low-energy beta and nuclear recoils in liquid argon with DEAP-1

The DEAP-1 low-background liquid argon detector was used to measure scintillation pulse shapes of electron and nuclear recoil events and to demonstrate the feasibility of pulse-shape discrimination (PSD) down to an electron-equivalent energy of 20 keV. In the surface dataset using a triple-coincidence tag we found the fraction of beta events that are misidentified as nuclear recoils to be $<1.4\times 10^{-7}$ (90% C.L.) for energies between 43-86 keVee and for a nuclear recoil acceptance of at least 90%, with 4% systematic uncertainty on the absolute energy scale. The discrimination measurement on surface was limited by nuclear recoils induced by cosmic-ray generated neutrons. This was improved by moving the detector to the SNOLAB underground laboratory, where the reduced background rate allowed the same measurement with only a double-coincidence tag. The combined data set contains $1.23\times10^8$ events. One of those, in the underground data set, is in the nuclear-recoil region of interest. Taking into account the expected background of 0.48 events coming from random pileup, the resulting upper limit on the electronic recoil contamination is $<2.7\times10^{-8}$ (90% C.L.) between 44-89 keVee and for a nuclear recoil acceptance of at least 90%, with 6% systematic uncertainty on the absolute energy scale. We developed a general mathematical framework to describe PSD parameter distributions and used it to build an analytical model of the distributions observed in DEAP-1. Using this model, we project a misidentification fraction of approx. $10^{-10}$ for an electron-equivalent energy threshold of 15 keV for a detector with 8 PE/keVee light yield. This reduction enables a search for spin-independent scattering of WIMPs from 1000 kg of liquid argon with a WIMP-nucleon cross-section sensitivity of $10^{-46}$ cm$^2$, assuming negligible contribution from nuclear recoil backgrounds.Comment: Accepted for publication in Astroparticle Physic

Fitting the integrated Spectral Energy Distributions of Galaxies

Fitting the spectral energy distributions (SEDs) of galaxies is an almost universally used technique that has matured significantly in the last decade. Model predictions and fitting procedures have improved significantly over this time, attempting to keep up with the vastly increased volume and quality of available data. We review here the field of SED fitting, describing the modelling of ultraviolet to infrared galaxy SEDs, the creation of multiwavelength data sets, and the methods used to fit model SEDs to observed galaxy data sets. We touch upon the achievements and challenges in the major ingredients of SED fitting, with a special emphasis on describing the interplay between the quality of the available data, the quality of the available models, and the best fitting technique to use in order to obtain a realistic measurement as well as realistic uncertainties. We conclude that SED fitting can be used effectively to derive a range of physical properties of galaxies, such as redshift, stellar masses, star formation rates, dust masses, and metallicities, with care taken not to over-interpret the available data. Yet there still exist many issues such as estimating the age of the oldest stars in a galaxy, finer details ofdust properties and dust-star geometry, and the influences of poorly understood, luminous stellar types and phases. The challenge for the coming years will be to improve both the models and the observational data sets to resolve these uncertainties. The present review will be made available on an interactive, moderated web page (sedfitting.org), where the community can access and change the text. The intention is to expand the text and keep it up to date over the coming years.Comment: 54 pages, 26 figures, Accepted for publication in Astrophysics & Space Scienc

Understanding The Correlation Of Libs And Acoustic Measurements Of Rocks And Soils Found In The Traverse Of The Perseverance Rover Across The Jezero Crater, Mars

The SuperCam instrument of the NASA MARS 2020 Perseverance rover combines a suite of atomic and molecular spectroscopies intended for an extensive description of rocks, soils and minerals in the surroundings of the landing site of the mission – the Jezero crater. The microphone installed on the SuperCam instrument allows the acquisition of acoustic signals resulting from the expansion of laser-induced plasmas towards the atmosphere. Apart from being affected by the propagation characteristics of the Mars atmosphere, the acoustic signal has an additional component related to the properties of the target including surface morphology, hardness, deformation parameters, and elasticity, among others. This information is currently being investigated as a complementary resource for characterization of the ablated material and may well supplement the LIBS data gathered from coincident laser shots. This talk will present SuperCam acoustic data of rocks and minerals found in the traverse of the Perseverance rover and will discuss its correlation with LIBS spectra.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tec