Heterogeneous-k-core versus Bootstrap Percolation on Complex Networks

We introduce the heterogeneous-$k$-core, which generalizes the $k$-core, and contrast it with bootstrap percolation. Vertices have a threshold $k_i$ which may be different at each vertex. If a vertex has less than $k_i$ neighbors it is pruned from the network. The heterogeneous-$k$-core is the sub-graph remaining after no further vertices can be pruned. If the thresholds $k_i$ are $1$ with probability $f$ or $k \geq 3$ with probability $(1-f)$, the process forms one branch of an activation-pruning process which demonstrates hysteresis. The other branch is formed by ordinary bootstrap percolation. We show that there are two types of transitions in this heterogeneous-$k$-core process: the giant heterogeneous-$k$-core may appear with a continuous transition and there may be a second, discontinuous, hybrid transition. We compare critical phenomena, critical clusters and avalanches at the heterogeneous-$k$-core and bootstrap percolation transitions. We also show that network structure has a crucial effect on these processes, with the giant heterogeneous-$k$-core appearing immediately at a finite value for any $f > 0$ when the degree distribution tends to a power law $P(q) \sim q^{-\gamma}$ with $\gamma < 3$.Comment: 10 pages, 4 figure

Laue Lens Development for Hard X-rays (>60 keV)

Results of reflectivity measurements of mosaic crystal samples of Cu (111) are reported. These tests were performed in the context of a feasibility study of a hard X-ray focusing telescope for space astronomy with energy passband from 60 to 600 keV. The technique envisaged is that of using mosaic crystals in transmission configuration that diffract X-rays for Bragg diffraction (Laue lens). The Laue lens assumed has a spherical shape with focal length $f$. It is made of flat mosaic crystal tiles suitably positioned in the lens. The samples were grown and worked for this project at the Institute Laue-Langevin (ILL) in Grenoble (France), while the reflectivity tests were performed at the X-ray facility of the Physics Department of the University of Ferrara.Comment: 6 pages, 12 figures, accepted for publication in IEEE Transactions on Nuclear Scienc

STS-99 Shuttle Radar Topography Mission Stability and Control

The Shuttle Radar Topography Mission (SRTM) flew aboard Space Shuttle Endeavor February 2000 and used interferometry to map 80% of the Earth's landmass. SRTM employed a 200-foot deployable mast structure to extend a second antenna away from the main antenna located in the Shuttle payload bay. Mapping requirements demanded precision pointing and orbital trajectories from the Shuttle on-orbit Flight Control System (PCS). Mast structural dynamics interaction with the FCS impacted stability and performance of the autopilot for attitude maneuvers and pointing during mapping operations. A damper system added to ensure that mast tip motion remained with in the limits of the outboard antenna tracking system while mapping also helped to mitigate structural dynamic interaction with the FCS autopilot. Late changes made to the payload damper system, which actually failed on-orbit, required a redesign and verification of the FCS autopilot filtering schemes necessary to ensure rotational control stability. In-flight measurements using three sensors were used to validate models and gauge the accuracy and robustness of the pre-mission notch filter design

U-Pb zircon age of 548 Ma for the leptynites (high-grade felsic rocks) of the central part of the Maures Massif. Geodynamic significance of the so-called leptyno-amphibolitic complexes of the Variscan belt of western Europe

Le complexe leptyno-amphibolitique de la partie centrale du massif des Maures a fait l’objet d’une étude géochronologique U-Pb sur zircons et Rb-Sr, et isotopique Sm-Nd. La mise en place du protolithe des leptynites a été datée à 548 Ma, âge nettement plus ancien que ceux (Ordovicien inférieur) mesurés sur d’autres complexes leptyno-amphibolitiques. L’étude Rb-Sr sur roches totales et minéraux séparés a permis de dater l’amphibolitisation à 348 Ma. Les isotopes du Nd montrent que les amphibolites ont des signatures nettement mantelliques. Les trois faciès acides analysés portent une empreinte crustale relativement importante. L’un d’entre eux peut être interprêté comme un mélange simple entre deux sources, respectivement similaires à celle des amphibolites et à celle des deux autres leptynites. Ces dernières, quant à elles, témoignent d’un apport d’une autre source mantellique, distincte de celle des amphibolites, probablement du type basalte alcalin continental. Les résultats obtenus indiquent que les Maures centrales et le sud du Massif central faisaient peut-être partie de la même unité structurale pré-Varisque. L’absence d’indice de lien génétique clair entre les protolithes des deux termes du complexe leptyno-amphibolitique repose le problème de la signification géodynamique de ces formations

Exploring the Hard X-/soft gamma-ray Continuum Spectra with Laue Lenses

The history of X-ray astronomy has shown that any advancement in our knowledge of the X-ray sky is strictly related to an increase in instrument sensitivity. At energies above 60 keV, there are interesting prospects for greatly improving the limiting sensitivity of the current generation of direct viewing telescopes (with or without coded masks), offered by the use of Laue lenses. We will discuss below the development status of a Hard X-Ray focusing Telescope (HAXTEL) based on Laue lenses with a broad bandpass (from 60 to 600 keV) for the study of the X-ray continuum of celestial sources. We show two examplesof multi-lens configurations with expected sensitivity orders of magnitude better ($\sim 1 \times 10^{-8}$ photons cm$^{-2}$ s$^{-1}$ keV$^{-1}$ at 200 keV) than that achieved so far. With this unprecedented sensitivity, very exciting astrophysical prospects are opened.Comment: 4 pages, 10 figures, to be published in the Proc. of the 39th ESLAB Symosium, 19-21 April 200

Understanding edge-connectivity in the Internet through core-decomposition

Internet is a complex network composed by several networks: the Autonomous Systems, each one designed to transport information efficiently. Routing protocols aim to find paths between nodes whenever it is possible (i.e., the network is not partitioned), or to find paths verifying specific constraints (e.g., a certain QoS is required). As connectivity is a measure related to both of them (partitions and selected paths) this work provides a formal lower bound to it based on core-decomposition, under certain conditions, and low complexity algorithms to find it. We apply them to analyze maps obtained from the prominent Internet mapping projects, using the LaNet-vi open-source software for its visualization

Feasibility study of a Laue lens for hard X-rays for space astronomy

We report on the feasibility study of a Laue lens for hard X-rays (>60 keV)based on mosaic crystals, for astrophysical applications. In particular we discuss the scientific motivations, its functioning principle, the procedure followed to select the suitable crystal materials, the criteria adopted to establish crystal dimensions and their distribution on the lens in order to obtain the best lens focusing capabilities, and the criteria for optimizing the lens effective area in a given passband. We also discuss the effects of misalignments of the crystal tiles due to unavoidable mechanical errors in assembling the lens. A software was developed to face all these topics and to evaluate the expected lens performance.Comment: 10 pages, corrected Fig. 1b and Fig. 2, which are wrong in the published version, corrected typo

Organization of modular networks

We examine the global organization of heterogeneous equilibrium networks consisting of a number of well distinguished interconnected parts--``communities'' or modules. We develop an analytical approach allowing us to obtain the statistics of connected components and an intervertex distance distribution in these modular networks, and to describe their global organization and structure. In particular, we study the evolution of the intervertex distance distribution with an increasing number of interlinks connecting two infinitely large uncorrelated networks. We demonstrate that even a relatively small number of shortcuts unite the networks into one. In more precise terms, if the number of the interlinks is any finite fraction of the total number of connections, then the intervertex distance distribution approaches a delta-function peaked form, and so the network is united.Comment: 9 pages, 3 figure