2,027 research outputs found

    Grid-Obstacle Representations with Connections to Staircase Guarding

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    In this paper, we study grid-obstacle representations of graphs where we assign grid-points to vertices and define obstacles such that an edge exists if and only if an xyxy-monotone grid path connects the two endpoints without hitting an obstacle or another vertex. It was previously argued that all planar graphs have a grid-obstacle representation in 2D, and all graphs have a grid-obstacle representation in 3D. In this paper, we show that such constructions are possible with significantly smaller grid-size than previously achieved. Then we study the variant where vertices are not blocking, and show that then grid-obstacle representations exist for bipartite graphs. The latter has applications in so-called staircase guarding of orthogonal polygons; using our grid-obstacle representations, we show that staircase guarding is \textsc{NP}-hard in 2D.Comment: To appear in the proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

    Modularity and community detection in bipartite networks

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    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

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

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    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

    Universality in solar flare and earthquake occurrence

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    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

    On the Maximum Crossing Number

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    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

    Sequencing SARS-CoV-2 Genomes From Saliva

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    Genomic sequencing is crucial to understanding the epidemiology and evolution of Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). Often, genomic studies rely on remnant diagnostic material, typically nasopharyngeal (NP) swabs, as input into whole-genome SARS-CoV-2 next-generation sequencing pipelines. Saliva has proven to be a safe and stable specimen for the detection of SARS-CoV-2 RNA via traditional diagnostic assays; however, saliva is not commonly used for SARS-CoV-2 sequencing. Using the ARTIC Network amplicon-generation approach with sequencing on the Oxford Nanopore MinION, we demonstrate that sequencing SARS-CoV-2 from saliva produces genomes comparable to those from NP swabs, and that RNA extraction is necessary to generate complete genomes from saliva. In this study, we show that saliva is a useful specimen type for genomic studies of SARS-CoV-2
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