Proximity Drawings of High-Degree Trees

A drawing of a given (abstract) tree that is a minimum spanning tree of the vertex set is considered aesthetically pleasing. However, such a drawing can only exist if the tree has maximum degree at most 6. What can be said for trees of higher degree? We approach this question by supposing that a partition or covering of the tree by subtrees of bounded degree is given. Then we show that if the partition or covering satisfies some natural properties, then there is a drawing of the entire tree such that each of the given subtrees is drawn as a minimum spanning tree of its vertex set

Reduction of the model noise in non-linear reconstruction via an efficient calculation of the incident field: application to a 434 MHz Scanner

Microwave tomography has been drastically boosted by the development of efficient reconstruction algorithms based on an iterative solution of the corresponding non-linear inverse problem. The accuracy of the electric field radiated by the antennas of a microwave scanner, inside the target area, has been shown to play a significant role on the overall image quality. Taking into account the antenna environment is of prime importance, especially when operating at low frequency. For instance, the wall of a 60 cm diameter whole-body microwave scanner cannot be neglected at 434 MHz, even when using the immersion technique consisting of putting the target in water. Indeed, at such a frequency, the attenuation introduced by water is not sufficient to avoid multiple reflections on the scanner boundary walls. Consequently, the method of calculating the incident field constitutes a key factor in iteratively solving non-linear inverse problems. The selected technique must accommodate high accuracy while maintaining acceptable calculation complexity. In this paper, three distinct techniques are analysed. They are based on the use of i) free-space and ii) non free-space Green's function, and iii) a FDTD approach. All these techniques have been firstly investigated for their 2D version, being used in 2D reconstruction algorithms. However, the scattered field data are collected in a 3D scanner. For assessing the validity of the previous 2D techniques, their results have been compared to both experimentally and 3D-FDTD results.Peer ReviewedPostprint (published version

Descripción geoquímica y geocronológica de secuencias volcánicas neógenas de Trasarco, en el extremo oriental de la Cadena Volcánica Transversal del Quevar (Noroeste de Argentina)

Se realizaron 34 nuevas dataciones K/Ar y 39 análisis geoquímicos de elementos mayoritarios, trazas y tierras raras, que implican nuevas aportaciones sobre las secuencias volcánicas neógenas de trasarco pertenecientes a la cadena volcánica transversal del Quevar. Esta cadena volcánica parte del arco volcánico actual con dirección W N W-ESE hasta las cercanías de la localidad de San Antonio de los Cobres. Se han reconocido y estudiado centros volcánicos ubicados en el extremo oriental de la misma. Los diferentes pulsos detectados en cada uno de estos centros (Aguas Calientes, Acay, El Morro-Orrganullo y Tocomar) son geoquímica y petrogr á ficamente homogéneos. Se interpreta que las cámaras magmáticas involucradas no han estado estratificadas composicionalmente ni han tenido sectores enriquecidos en cristales. Como excepción, el centro eruptivo Acay muestra un rango composicional desde términos andesíticos a riolíticos. En este caso, se interpreta un fraccionamiento de la cámara magmática en pulsos de edad similar. La composición isotópica del centro eruptivo Aguas Calientes indica una fuerte componente cortical en la formación de los magmas. Es posible explicar su origen a partir de fusión cortical. Las determinaciones geocronológicas realizadas muestran pulsos volcánicos a los 17-19 Ma, 13-12 Ma, 10 Ma, 7-6 Ma, 1-0.5 Ma en esta región de los Andes Centrales.New geochronological data (34) and 39 new geochemical analyses have been made in the Neogene backarc volcanic sequences in the “El Quevar Transversal Volcanic Chain” defined by Viramonte et al (1984a). This chain starts at the present N-S arc with WNW-ESE trend. New volcanic centres have been recognised and analysed at the eastern end of this chain. The different pulses from each volcanic centre (Aguas Calientes, Acay, El Morro - Organullo and Tocomar) are petrographically and geochemically homogeneous. This suggests that the magma chambers related in each volcano, were geochemically homogeneous and did not have crystal enriched sectors. The Acay eruptive centre is an exception of this assumption; a compositionally differentiated magmatic chamber could be inferred. The isotopic composition of the Aguas Calientes emission centre has a crust signature in its origin, related with melts generated by crustal fussion. The geochronological determinations show volcanic pulses at 17-19 Ma, 13-12 Ma, 10 Ma, 7-6 Ma, 1-0.5 Ma in this region of the Central Andes

Quadrature and polarization squeezing in a dispersive optical bistability model

We theoretically study quadrature and polarization squeezing in dispersive optical bistability through a vectorial Kerr cavity model describing a nonlinear cavity filled with an isotropic chi(3) medium in which self-phase and cross-phase modulation, as well as four--wave mixing, occur. We derive expressions for the quantum fluctuations of the output field quadratures as a function of which we express the spectrum of fluctuations of the output field Stokes parameters. We pay particular attention to study how the bifurcations affecting the non-null linearly polarized output mode squeezes the orthogonally polarized vacuum mode, and show how this produces polarization squeezing.Comment: 10 text pages + 12 figure

Planar magnetoinductive wave transducers : theory and applications

Transduction of magnetoinductive waves (MIWs) in planar technology is demonstrated. A transducer consisting of a one-dimensional periodic array of metallic split squared ring resonators (SSRR), placed between a pair of microstrip lines on a planar substrate has been fabricated and measured. The microstrip lines are inductively coupled to the SSRRs located at the ends of the periodic array and excite MIWs that propagate along the array. The theoretical model for the dispersion of MIWs is used to predict the dispersion relation and the delay time in the device. The delay time was measured and a good agreement was found with the theoretical predictions. The transmission coefficient of the device was also measured. The theoretical and experimental results suggest that the proposed configuration can find application in the design of delay lines and other microwave devices. In fact, the behavior of the proposed transducer is similar to that of the conventional ferritemagnetostatic-wavetransducer. However, ferrite devices are fragile, difficult to integrate, and require a heavy external magnet or electromagnet to magnetize the ferrite to saturation. Since all these drawbacks are not present in the proposed configuration, it may be a useful alternative to those devices for many practical applications

A polynomial bound for untangling geometric planar graphs

To untangle a geometric graph means to move some of the vertices so that the resulting geometric graph has no crossings. Pach and Tardos [Discrete Comput. Geom., 2002] asked if every n-vertex geometric planar graph can be untangled while keeping at least n^\epsilon vertices fixed. We answer this question in the affirmative with \epsilon=1/4. The previous best known bound was \Omega((\log n / \log\log n)^{1/2}). We also consider untangling geometric trees. It is known that every n-vertex geometric tree can be untangled while keeping at least (n/3)^{1/2} vertices fixed, while the best upper bound was O(n\log n)^{2/3}. We answer a question of Spillner and Wolff [arXiv:0709.0170 2007] by closing this gap for untangling trees. In particular, we show that for infinitely many values of n, there is an n-vertex geometric tree that cannot be untangled while keeping more than 3(n^{1/2}-1) vertices fixed. Moreover, we improve the lower bound to (n/2)^{1/2}.Comment: 14 pages, 7 figure

Risk-shifting Through Issuer Liability and Corporate Monitoring

This article explores how issuer liability re-allocates fraud risk and how risk allocation may reduce the incidence of fraud. In the US, the apparent absence of individual liability of officeholders and insufficient monitoring by insurers under-mine the potential deterrent effect of securities litigation. The underlying reasons why both mechanisms remain ineffective are collective action problems under the prevailing dispersed ownership structure, which eliminates the incentives to moni-tor set by issuer liability. This article suggests that issuer liability could potentially have a stronger deterrent effect when it shifts risk to individuals or entities holding a larger financial stake. Thus, it would enlist large shareholders in monitoring in much of Europe. The same risk-shifting effect also has implications for the debate about the relationship between securities litigation and creditor interests. Credi-tors’ claims should not be given precedence over claims of defrauded investors (e.g., because of the capital maintenance principle), since bearing some of the fraud risk will more strongly incentivise large creditors, such as banks, to monitor the firm in jurisdictions where corporate debt is relatively concentrated

The Zanclean megaflood of the Mediterranean – Searching for independent evidence

About six million years ago, the Mediterranean Sea underwent a period of isolation from the ocean and widespread salt deposition known as the Messinian Salinity Crisis (MSC), allegedly leading to a kilometer-scale level drawdown by evaporation. One of the competing scenarios proposed for the termination of this environmental crisis 5.3 million years ago consists of a megaflooding event refilling the Mediterranean Sea through the Strait of Gibraltar: the Zanclean flood. The main evidence supporting this hypothesis is a nearly 390 km long and several hundred meters deep erosion channel extending from the Gulf of Cádiz (Atlantic Ocean) to the Algerian Basin (Western Mediterranean), implying the excavation of ca. 1000 km3 of Miocene sediment and bedrock. Based on the understanding obtained from Pleistocene onshore megaflooding events and using ad-hoc hydrodynamic modeling, here we explore two predictions of the Zanclean outburst flood hypothesis: 1) The formation of similar erosion features at sills communicating sub-basins within the Mediterranean Sea, specifically at the Sicily Sill; and 2) the accumulation of the eroded materials as megaflood deposits in areas of low flow energy. Recent data show a 6-km-wide amphitheater-shaped canyon preserved at the Malta Escarpment that may represent the erosional expression of the Zanclean flood after filling the western Mediterranean and spilling into the Eastern Basin. Next to that canyon, a ~1600 km3 accumulation of chaotic, seismically transparent sediment has been found in the Ionian Sea, compatible in age and facies with megaflood deposits. Another candidate megaflood deposit has been identified in the Alborán Sea in the form of elongated sedimentary bodies that parallel the flooding channel and are seismically characterized by chaotic and discontinuous stratified reflections, that we interpret as equivalent to gravel and boulder megabars described in terrestrial megaflood settings. Numerical model predictions show that sand deposits found at the Miocene/Pliocene (M/P) boundary in ODP sites 974 and 975 (South Balearic and Tyrrhenian seas) are consistent with suspension transport from the Strait of Gibraltar during a flooding event at a peak water discharge of ~108 m3 s−1

The GOODSTEP project: General Object-Oriented Database for Software Engineering Processes

The goal of the GOODSTEP project is to enhance and improve the functionality of a fully object-oriented database management system to yield a platform suited for applications such as software development environments (SDEs). The baseline of the project is the O2 database management system (DBMS). The O2 DBMS already includes many of the features regulated by SDEs. The project has identified enhancements to O2 in order to make it a real software engineering DBMS. These enhancements are essentially upgrades of the existing O2 functionality, and hence require relatively easy extensions to the O2 system. They have been developed in the early stages of the project and are now exploited and validated by a number of software engineering tools built on top of the enhanced O2 DBMS. To ease tool construction, the GOODSTEP platform encompasses tool generation capabilities which allow for generation of integrated graphical and textual tools from high-level specifications. In addition, the GOODSTEP platform provides a software process toolset which enables modeling, analysis and enaction of software processes and is also built on top of the extended O2 database. The GOODSTEP platform is to be validated using two CASE studies carried out to develop an airline application and a business application