All scale-free networks are sparse

We study the realizability of scale free-networks with a given degree sequence, showing that the fraction of realizable sequences undergoes two first-order transitions at the values 0 and 2 of the power-law exponent. We substantiate this finding by analytical reasoning and by a numerical method, proposed here, based on extreme value arguments, which can be applied to any given degree distribution. Our results reveal a fundamental reason why large scale-free networks without constraints on minimum and maximum degree must be sparse.Comment: 4 pages, 2 figure

Degree correlations in directed scale-free networks

Scale-free networks, in which the distribution of the degrees obeys a power-law, are ubiquitous in the study of complex systems. One basic network property that relates to the structure of the links found is the degree assortativity, which is a measure of the correlation between the degrees of the nodes at the end of the links. Degree correlations are known to affect both the structure of a network and the dynamics of the processes supported thereon, including the resilience to damage, the spread of information and epidemics, and the efficiency of defence mechanisms. Nonetheless, while many studies focus on undirected scale-free networks, the interactions in real-world systems often have a directionality. Here, we investigate the dependence of the degree correlations on the power-law exponents in directed scale-free networks. To perform our study, we consider the problem of building directed networks with a prescribed degree distribution, providing a method for proper generation of power-law-distributed directed degree sequences. Applying this new method, we perform extensive numerical simulations, generating ensembles of directed scale-free networks with exponents between~2 and~3, and measuring ensemble averages of the Pearson correlation coefficients. Our results show that scale-free networks are on average uncorrelated across directed links for three of the four possible degree-degree correlations, namely in-degree to in-degree, in-degree to out-degree, and out-degree to out-degree. However, they exhibit anticorrelation between the number of outgoing connections and the number of incoming ones. The findings are consistent with an entropic origin for the observed disassortativity in biological and technological networks.Comment: 10 pages, 5 figure

Depth-dependent ordering, two-length-scale phenomena and crossover behavior in a crystal featuring a skin-layer with defects

Structural defects in a crystal are responsible for the "two length-scale" behavior, in which a sharp central peak is superimposed over a broad peak in critical diffuse X-ray scattering. We have previously measured the scaling behavior of the central peak by scattering from a near-surface region of a V2H crystal, which has a first-order transition in the bulk. As the temperature is lowered toward the critical temperature, a crossover in critical behavior is seen, with the temperature range nearest to the critical point being characterized by mean field exponents. Near the transition, a small two-phase coexistence region is observed. The values of transition and crossover temperatures decay with depth. An explanation of these experimental results is here proposed by means of a theory in which edge dislocations in the near-surface region occur in walls oriented in the two directions normal to the surface. The strain caused by the dislocation lines causes the ordering in the crystal to occur as growth of roughly cylindrically shaped regions. After the regions have reached a certain size, the crossover in the critical behavior occurs, and mean field behavior prevails. At a still lower temperature, the rest of the material between the cylindrical regions orders via a weak first-order transition.Comment: 12 pages, 8 figure

Efficient and exact sampling of simple graphs with given arbitrary degree sequence

Uniform sampling from graphical realizations of a given degree sequence is a fundamental component in simulation-based measurements of network observables, with applications ranging from epidemics, through social networks to Internet modeling. Existing graph sampling methods are either link-swap based (Markov-Chain Monte Carlo algorithms) or stub-matching based (the Configuration Model). Both types are ill-controlled, with typically unknown mixing times for link-swap methods and uncontrolled rejections for the Configuration Model. Here we propose an efficient, polynomial time algorithm that generates statistically independent graph samples with a given, arbitrary, degree sequence. The algorithm provides a weight associated with each sample, allowing the observable to be measured either uniformly over the graph ensemble, or, alternatively, with a desired distribution. Unlike other algorithms, this method always produces a sample, without back-tracking or rejections. Using a central limit theorem-based reasoning, we argue, that for large N, and for degree sequences admitting many realizations, the sample weights are expected to have a lognormal distribution. As examples, we apply our algorithm to generate networks with degree sequences drawn from power-law distributions and from binomial distributions.Comment: 8 pages, 3 figure

Mapping structural diversity in networks sharing a given degree distribution and global clustering: Adaptive resolution grid search evolution with Diophantine equation-based mutations

Methods that generate networks sharing a given degree distribution and global clustering can induce changes in structural properties other than that controlled for. Diversity in structural properties, in turn, can affect the outcomes of dynamical processes operating on those networks. Since exhaustive sampling is not possible, we propose a novel evolutionary framework for mapping this structural diversity. The three main features of this framework are: (a) subgraph-based encoding of networks, (b) exact mutations based on solving systems of Diophantine equations, and (c) heuristic diversity-driven mechanism to drive resolution changes in the MapElite algorithm.We show that our framework can elicit networks with diversity in their higher-order structure and that this diversity affects the behaviour of the complex contagion model. Through a comparison with state of the art clustered network generation methods, we demonstrate that our approach can uncover a comparably diverse range of networks without needing computationally unfeasible mixing times. Further, we suggest that the subgraph-based encoding provides greater confidence in the diversity of higher-order network structure for low numbers of samples and is the basis for explaining our results with complex contagion model. We believe that this framework could be applied to other complex landscapes that cannot be practically mapped via exhaustive sampling

Impact of Space Weather on Climate and Habitability of Terrestrial Type Exoplanets

The current progress in the detection of terrestrial type exoplanets has opened a new avenue in the characterization of exoplanetary atmospheres and in the search for biosignatures of life with the upcoming ground-based and space missions. To specify the conditions favorable for the origin, development and sustainment of life as we know it in other worlds, we need to understand the nature of astrospheric, atmospheric and surface environments of exoplanets in habitable zones around G-K-M dwarfs including our young Sun. Global environment is formed by propagated disturbances from the planet-hosting stars in the form of stellar flares, coronal mass ejections, energetic particles, and winds collectively known as astrospheric space weather. Its characterization will help in understanding how an exoplanetary ecosystem interacts with its host star, as well as in the specification of the physical, chemical and biochemical conditions that can create favorable and/or detrimental conditions for planetary climate and habitability along with evolution of planetary internal dynamics over geological timescales. A key linkage of (astro) physical, chemical, and geological processes can only be understood in the framework of interdisciplinary studies with the incorporation of progress in heliophysics, astrophysics, planetary and Earth sciences. The assessment of the impacts of host stars on the climate and habitability of terrestrial (exo)planets will significantly expand the current definition of the habitable zone to the biogenic zone and provide new observational strategies for searching for signatures of life. The major goal of this paper is to describe and discuss the current status and recent progress in this interdisciplinary field and to provide a new roadmap for the future development of the emerging field of exoplanetary science and astrobiology.Comment: 206 pages, 24 figures, 1 table; Review paper. International Journal of Astrobiology (2019

Evaluating models' response of tropical low clouds to SST forcings using CALIPSO observations

Recent studies have shown that, in response to a surface warming, the marine tropical low-cloud cover (LCC) as observed by passive-sensor satellites substantially decreases, therefore generating a smaller negative value of the top-of-the-atmosphere (TOA) cloud radiative effect (CRE). Here we study the LCC and CRE interannual changes in response to sea surface temperature (SST) forcings in the GISS model E2 climate model, a developmental version of the GISS model E3 climate model, and in 12 other climate models, as a function of their ability to represent the vertical structure of the cloud response to SST change against 10 years of CALIPSO (Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations) observations. The more realistic models (those that satisfy the observational constraint) capture the observed interannual LCC change quite well (ΔLCC/ΔSST=-3.49±1.01&thinsp;%&thinsp;K−1 vs. ΔLCC/ΔSSTobs=-3.59±0.28&thinsp;%&thinsp;K−1) while the others largely underestimate it (ΔLCC/ΔSST=-1.32±1.28&thinsp;%&thinsp;K−1). Consequently, the more realistic models simulate more positive shortwave (SW) feedback (ΔCRE/ΔSST=2.60±1.13&thinsp;W&thinsp;m−2&thinsp;K−1) than the less realistic models (ΔCRE/ΔSST=0.87±2.63&thinsp;W&thinsp;m−2&thinsp;K−1), in better agreement with the observations (ΔCRE/ΔSSTobs=3±0.26&thinsp;W&thinsp;m−2&thinsp;K−1), although slightly underestimated. The ability of the models to represent moist processes within the planetary boundary layer (PBL) and produce persistent stratocumulus (Sc) decks appears crucial to replicating the observed relationship between clouds, radiation and surface temperature. This relationship is different depending on the type of low clouds in the observations. Over stratocumulus regions, cloud-top height increases slightly with SST, accompanied by a large decrease in cloud fraction, whereas over trade cumulus (Cu) regions, cloud fraction decreases everywhere, to a smaller extent.</p