The Hurricane : March-Two Step

https://digitalcommons.library.umaine.edu/mmb-ps/2347/thumbnail.jp

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

Finding community structure in networks using the eigenvectors of matrices

We consider the problem of detecting communities or modules in networks, groups of vertices with a higher-than-average density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as "modularity" over possible divisions of a network. Here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix, which plays a role in community detection similar to that played by the graph Laplacian in graph partitioning calculations. This result leads us to a number of possible algorithms for detecting community structure, as well as several other results, including a spectral measure of bipartite structure in networks and a new centrality measure that identifies those vertices that occupy central positions within the communities to which they belong. The algorithms and measures proposed are illustrated with applications to a variety of real-world complex networks.Comment: 22 pages, 8 figures, minor corrections in this versio

Extremal Optimization for Graph Partitioning

Extremal optimization is a new general-purpose method for approximating solutions to hard optimization problems. We study the method in detail by way of the NP-hard graph partitioning problem. We discuss the scaling behavior of extremal optimization, focusing on the convergence of the average run as a function of runtime and system size. The method has a single free parameter, which we determine numerically and justify using a simple argument. Our numerical results demonstrate that on random graphs, extremal optimization maintains consistent accuracy for increasing system sizes, with an approximation error decreasing over runtime roughly as a power law t^(-0.4). On geometrically structured graphs, the scaling of results from the average run suggests that these are far from optimal, with large fluctuations between individual trials. But when only the best runs are considered, results consistent with theoretical arguments are recovered.Comment: 34 pages, RevTex4, 1 table and 20 ps-figures included, related papers available at http://www.physics.emory.edu/faculty/boettcher

Magnetic Setting and Transition-Region/Coronal Signatures of Sunspot Penumbral Jets

No abstract availabl

A Toy Model for Testing Finite Element Methods to Simulate Extreme-Mass-Ratio Binary Systems

Extreme mass ratio binary systems, binaries involving stellar mass objects orbiting massive black holes, are considered to be a primary source of gravitational radiation to be detected by the space-based interferometer LISA. The numerical modelling of these binary systems is extremely challenging because the scales involved expand over several orders of magnitude. One needs to handle large wavelength scales comparable to the size of the massive black hole and, at the same time, to resolve the scales in the vicinity of the small companion where radiation reaction effects play a crucial role. Adaptive finite element methods, in which quantitative control of errors is achieved automatically by finite element mesh adaptivity based on posteriori error estimation, are a natural choice that has great potential for achieving the high level of adaptivity required in these simulations. To demonstrate this, we present the results of simulations of a toy model, consisting of a point-like source orbiting a black hole under the action of a scalar gravitational field.Comment: 29 pages, 37 figures. RevTeX 4.0. Minor changes to match the published versio

Crustal structure of active deformation zones in Africa: Implications for global crustal processes

The Cenozoic East African rift (EAR), Cameroon Volcanic Line (CVL), and Atlas Mountains formed on the slow-moving African continent, which last experienced orogeny during the Pan-African. We synthesize primarily geophysical data to evaluate the role of magmatism in shaping Africa's crust. In young magmatic rift zones, melt and volatiles migrate from the asthenosphere to gas-rich magma reservoirs at the Moho, altering crustal composition and reducing strength. Within the southernmost Eastern rift, the crust comprises ~20% new magmatic material ponded in the lower crust sills, and intruded as sills and dikes at shallower depths. In the Main Ethiopian rift, intrusions comprise 30% of the crust below axial zones of dike-dominated extension. In the incipient rupture zones of the Afar rift, magma intrusions fed from crustal magma chambers beneath segment centers create new columns of mafic crust, as along slow-spreading ridges. Our comparisons suggest that transitional crust, including seaward-dipping sequences, is created as progressively smaller screens of continental crust are heated and weakened by magma intrusion into 15-20 km-thick crust. In the 30Ma-Recent CVL, which lacks a hotspot age-progression, extensional forces are small, inhibiting the creation and rise of magma into the crust. In the Atlas orogen, localized magmatism follows the strike of the Atlas Mountains from the Canary Islands hotspot towards the Alboran Sea. CVL and Atlas magmatism has had minimal impact on crustal structure. Our syntheses show that magma and volatiles are migrating from the asthenosphere through the plates, modifying rheology and contributing significantly to global carbon and water fluxes