Modularity and community detection in bipartite networks

The modularity of a network quantifies the extent, relative to a null model network, to which vertices cluster into community groups. We define a null model appropriate for bipartite networks, and use it to define a bipartite modularity. The bipartite modularity is presented in terms of a modularity matrix B; some key properties of the eigenspectrum of B are identified and used to describe an algorithm for identifying modules in bipartite networks. The algorithm is based on the idea that the modules in the two parts of the network are dependent, with each part mutually being used to induce the vertices for the other part into the modules. We apply the algorithm to real-world network data, showing that the algorithm successfully identifies the modular structure of bipartite networks.Comment: RevTex 4, 11 pages, 3 figures, 1 table; modest extensions to conten

Universality in solar flare and earthquake occurrence

Earthquakes and solar flares are phenomena involving huge and rapid releases of energy characterized by complex temporal occurrence. By analysing available experimental catalogs, we show that the stochastic processes underlying these apparently different phenomena have universal properties. Namely both problems exhibit the same distributions of sizes, inter-occurrence times and the same temporal clustering: we find afterflare sequences with power law temporal correlations as the Omori law for seismic sequences. The observed universality suggests a common approach to the interpretation of both phenomena in terms of the same driving physical mechanism

Continuum-plasma solution surrounding nonemitting spherical bodies

The classical problem of the interaction of a nonemitting spherical body with a zero mean-free-path continuum plasma is solved numerically in the full range of physically allowed free parameters (electron Debye length to body radius ratio, ion to electron temperature ratio, and body bias), and analytically in rigorously defined asymptotic regimes (weak and strong bias, weak and strong shielding, thin and thick sheath). Results include current-voltage characteristics as well as floating potential and capacitance, for both continuum and collisionless electrons. Our numerical computations show that for most combinations of physical parameters, there exists a closest asymptotic regime whose analytic solutions are accurate to 15% or better

Transition-Region/Coronal Signatures of Penumbral Microjets: Hi-C, SDO/AIA and Hinode (SOT/FG) Observations

Penumbral microjets are bright, transient features seen in the chromosphere of sunspot penumbrae. Katsuaka et al. (2007) noted their ubiquity and characterized them using the Ca II H-line filter on Hinode's Solar Optical Telescope (SOT). The jets are 1000{4000 km in length, 300{400 km in width, and last less than one minute. It was proposed that these penumbral microjets could contribute to the transition-region and coronal heating above sunspots. We examine whether these microjets appear in the transition-region (TR) and/or corona or are related{ temporally and spatially{ to similar brightenings in the TR and/or corona. First, we identify penumbral microjets with the SOT's Ca II H-line filter. The chosen sunspot is observed on July 11, 2012 from 18:50:00 UT to 20:00:00 UT at approx. 14 inches, -30 inches. We then examine the sunspot in the same field of view and at the same time in other wavelengths. We use the High Resolution Coronal Imager Telescope (Hi-C) at 193A and the 1600A, 304A, 171A, 193A, and 94A passbands of the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamic Observatory. We include examples of these jets and where they should appear in the other passbands, but find no signifcant association, except for a few jets with longer lifetimes and bigger sizes seen at locations in the penumbra with repeated stronger brightenings. We conclude that the normal microjets are not heated to transition-region/coronal temperatures, but the larger jets are

On the Maximum Crossing Number

Research about crossings is typically about minimization. In this paper, we consider \emph{maximizing} the number of crossings over all possible ways to draw a given graph in the plane. Alpert et al. [Electron. J. Combin., 2009] conjectured that any graph has a \emph{convex} straight-line drawing, e.g., a drawing with vertices in convex position, that maximizes the number of edge crossings. We disprove this conjecture by constructing a planar graph on twelve vertices that allows a non-convex drawing with more crossings than any convex one. Bald et al. [Proc. COCOON, 2016] showed that it is NP-hard to compute the maximum number of crossings of a geometric graph and that the weighted geometric case is NP-hard to approximate. We strengthen these results by showing hardness of approximation even for the unweighted geometric case and prove that the unweighted topological case is NP-hard.Comment: 16 pages, 5 figure

Near-infrared thermal emissivity from ground based atmospheric dust measurements at ORM

We present an analysis of the atmospheric content of aerosols measured at Observatorio del Roque de los Muchachos (ORM; Canary Islands). Using a laser diode particle counter located at the Telescopio Nazionale Galileo (TNG) we have detected particles of 0.3, 0.5, 1.0, 3.0, 5.0 and 10.0 um size. The seasonal behavior of the dust content in the atmosphere is calculated. The Spring has been found to be dustier than the Summer, but dusty conditions may also occur in Winter. A method to estimate the contribution of the aerosols emissivity to the sky brightness in the near-infrared (NIR) is presented. The contribution of dust emission to the sky background in the NIR has been found to be negligible comparable to the airglow, with a maximum contribution of about 8-10% in the Ks band in the dusty days.Comment: 6 pages, 3 figures, 6 tables, accepted for publication in MNRA