On Hyperbolic once-punctured-torus bundles II. Fractal tessellations of the plane

We describe fractal tessellations of the complex plane that arise naturally from Cannon-Thurston maps associated to complete, hyperbolic, once-punctured-torus bundles. We determine the symmetry groups of these tessellations.

Mixing invariants of hyperbolic 3-manifolds

Let M be a compact hyperbolic 3-manifold with incompressible boundary. Consider a complete hyperbolic metric on int(M). To each geometrically finite end of int(M) are traditionnaly associated 3 different invariants : the hyperbolic metric associated to the conformal structure at infinity, the hyperbolic metric on the boundary of the convex core and the bending measured lamination of the convex core. In this note we show how invariants of different types can be realised in the different ends.

Non-hyperbolic boundary equilibrium bifurcations in planar Filippov systems: a case study approach

Boundary equilibrium bifurcations in piecewise smooth discontinuous systems are characterized by the collision of an equilibrium point with the discontinuity surface. Generically, these bifurcations are of codimension one, but there are scenarios where the phenomenon can be of higher codimension. Here, the possible collision of a non-hyperbolic equilibrium with the boundary in a two-parameter framework and the nonlinear phenomena associated with such collision are considered. By dealing with planar discontinuous (Filippov) systems, some of such phenomena are pointed out through specific representative cases. A methodology for obtaining the corresponding bi-parametric bifurcation sets is developed.

Horospheres in hyperbolic geometry

In this paper we investigate the role of horospheres in Integral Geometry and Differential Geometry. In particular we study envelopes of families of horocycles by means of “support maps”. We define invariant “linear combinations” of support maps or curves. Finally we obtain Gauss-Bonnet type formulas and Chern-Lashof type inequalities.

The entropy conjecture for partially hyperbolic diffeomorphisms with 1-D center

We prove that if f is a partially hyperbolic diffeomorphism on the compact manifold M with one dimensional center bundle, then the logarithm of the spectral radius of the map induced by f on the real homology groups of M is smaller or equal to the topological entropy of f. This is a particular case of the Shub's entropy conjecture, which claims that the same conclusion should be true for any C1 map on any compact manifold.

On hyperbolic once-punctured-torus bundles IV: automata for lightning curves

"Vegeu el resum a l'inici del document del fitxer adjunt."

On uniform conjugators in torsion-free hyperbolic groups

"Vegeu el resum a l'inici del document del fitxer adjunt."

Moduli of flat conformal structures of hyperbolic type

"Vegeu el resum a l'inici del document del fitxer adjunt."

Hyperbolic reaction-diffusion equations for a forest fire model

Forest fire models have been widely studied from the context of self-organized criticality and from the ecological properties of the forest and combustion. On the other hand, reaction-diffusion equations have interesting applications in biology and physics. We propose here a model for fire propagation in a forest by using hyperbolic reaction-diffusion equations. The dynamical and thermodynamical aspects of the model are analyzed in detail

Speed of wave-front solutions to hyperbolic reaction-diffusion equations

The asymptotic speed problem of front solutions to hyperbolic reaction-diffusion (HRD) equations is studied in detail. We perform linear and variational analyses to obtain bounds for the speed. In contrast to what has been done in previous work, here we derive upper bounds in addition to lower ones in such a way that we can obtain improved bounds. For some functions it is possible to determine the speed without any uncertainty. This is also achieved for some systems of HRD (i.e., time-delayed Lotka-Volterra) equations that take into account the interaction among different species. An analytical analysis is performed for several systems of biological interest, and we find good agreement with the results of numerical simulations as well as with available observations for a system discussed recently

Globally aligned photomosaic of the Lucky Strike hydrothermal vent field (Mid-Atlantic Ridge, 37°18.5’N): Release of georeferenced data, mosaic construction, and viewing software

We present a georeferenced photomosaic of the Lucky Strike hydrothermal vent field (Mid-Atlantic Ridge, 37°18’N). The photomosaic was generated from digital photographs acquired using the ARGO II seafloor imaging system during the 1996 LUSTRE cruise, which surveyed a ~1 km2 zone and provided a coverage of ~20% of the seafloor. The photomosaic has a pixel resolution of 15 mm and encloses the areas with known active hydrothermal venting. The final mosaic is generated after an optimization that includes the automatic detection of the same benthic features across different images (feature-matching), followed by a global alignment of images based on the vehicle navigation. We also provide software to construct mosaics from large sets of images for which georeferencing information exists (location, attitude, and altitude per image), to visualize them, and to extract data. Georeferencing information can be provided by the raw navigation data (collected during the survey) or result from the optimization obtained from imatge matching. Mosaics based solely on navigation can be readily generated by any user but the optimization and global alignment of the mosaic requires a case-by-case approach for which no universally software is available. The Lucky Strike photomosaics (optimized and navigated-only) are publicly available through the Marine Geoscience Data System (MGDS, http://www.marine-geo.org). The mosaic-generating and viewing software is available through the Computer Vision and Robotics Group Web page at the University of Girona (http://eia.udg.es/_rafa/mosaicviewer.html)

Average performance analysis of circular and hyperbolic geolocation

A comparative performance analysis of four geolocation methods in terms of their theoretical root mean square positioning errors is provided. Comparison is established in two different ways: strict and average. In the strict type, methods are examined for a particular geometric configuration of base stations(BSs) with respect to mobile position, which determines a givennoise profile affecting the respective time-of-arrival (TOA) or timedifference-of-arrival (TDOA) estimates. In the average type, methodsare evaluated in terms of the expected covariance matrix ofthe position error over an ensemble of random geometries, so thatcomparison is geometry independent. Exact semianalytical equationsand associated lower bounds (depending solely on the noiseprofile) are obtained for the average covariance matrix of the positionerror in terms of the so-called information matrix specific toeach geolocation method. Statistical channel models inferred fromfield trials are used to define realistic prior probabilities for therandom geometries. A final evaluation provides extensive resultsrelating the expected position error to channel model parametersand the number of base stations.

Stable isotopes unveil habitat partitioning among the marine mammals off NW Africa and reveal unique trophic niches for two globally threatened species.

Stable isotope abundances of carbon (δ13C) and nitrogen (δ15N) in the bone of 13 species of marine mammals from the northwest coast of Africa were investigated to assess their positions in the local trophic web and their preferred habitats. Also, samples of primary producers and potential prey species from the study area were collected to characterise the local isotopic landscape. This characterisation indicated that δ13C values increased from offshore to nearshore and that δ15N was a good proxy for trophic level. Therefore, the most coastal species were Monachus monachus and Sousa teuszii, whereas the most pelagic were Physeter macrocephalus and Balaenoptera acutorostrata. δ15N values indicated that marine mammals located at the lowest trophic level were B. acutorostrata, Stenella coeruleoalba and Delphinus sp., and those occupying the highest trophic level were M. monachus and P. macrocephalus. The trophic level of Orcinus orca was similar to that of M. monachus, suggesting that O. orca preys on fish. Conservation of coastal and threatened species (M. monachus and S. teuszii) off NW Africa should be a priority because these species, as the main apex predators, cannot be replaced by other marine mammals.

A systematic review of Twitter’s hashtags in public health: an example of a globally adopted standard

The objective is to find evidence and make recommendations on the use of Twitter in public health,particularly through the study of hashtags(#). This systematic review shows the use of Twitter in different areas of public health: epidemiological surveillance, health promotion, health protection and disease prevention. Articles on this subject published in indexed journals with impact factor show the importance of conversations to engage the attention of Twitter users by using citations (@ user) and retweets(RT); however, not much importance seems to be given to the use of hashtags(#), which are often assimilated to the concept of keywords. Although tracking recurring hashtagsshould be less expensive than computing Twitter content, the potential of hashtaggeddata has not been properly exploited or recognized over the past years, probably due to the lack of efficient tools.