Approximation of Hölder continuous homeomorphisms by piecewise affine homeomorphisms

This paper is concerned with the problem of approximating a homeomorphism by piecewise affine homeomorphisms. The main result is as follows: every homeomorphism from a planar domain with a polygonal boundary to ℝ2 that is globally Hölder continuous of exponent α ∈ (0, 1], and whose inverse is also globally Hölder continuous of exponent α can be approximated in the Hölder norm of exponent β by piecewise affine homeomorphisms, for some β ∈ (0,α) that only depends on α. The proof is constructive. We adapt the proof of simplicial approximation in the supremum norm, and measure the side lengths and angles of the triangulation over which the approximating homeomorphism is piecewise affine. The approximation in the supremum norm, and a control on the minimum angle and on the ratio between the maximum and minimum side lengths of the triangulation suffice to obtain approximation in the Hölder norm

DIFFERENTIAL TEMPORAL AND SPATIAL DISTRIBUTION OF ADULT LOGGERHEAD SEA TURTLES FROM GULF OF CÁDIZ TO WESTERN MEDITERRANEAN SEA

The aim of this paper was to search for and model spatial and seasonal trends in occurrences (stranding or by-catches) of adult loggerhead turtles in the western Mediterranean area and Gulf of Cádiz (Atlantic) independently of their origin. Adult turtles were only bycaught on longlines from May to August. Adults were stranded in the eastern and western areas of the Strait of Gibraltar threshold throughout the year. In the Gulf of Cádiz (Atlantic), strandings were significantly concentrated in May and June, whereas in the Alboran Sea (Mediterranean), strandings mainly occurred in June and July. The probability of catching a mature loggerhead increases during June and July south of the Balearic Islands. The results suggest that adult loggerhead turtles move (migrate) from the Atlantic area (Gulf of Cádiz) to the Mediterranean (Alboran Sea) from May to June, and subsequently move to the Balearic Sea from June to July. These results are in line with those obtained by previous studies.Postprin

Integrating local environmental data and information from non-driven citizen science to estimate jellyfish abundance in Costa del Sol (southern Spain)

Tourism, fishing and aquaculture are key economic sectors of Costa del Sol (southern Iberian Peninsula). The management of these activities is sometimes disturbed by the onshore arrival and stranding of jellyfish swarms. In the absence data on the occurrence of these organisms, it may be interesting to explore data from non-driven systems, such as social networks. The present study show how data in text format from a mobile app called Infomedusa can be processed and used to model the relationship between estimated abundance of jellyfish on the beaches and local environmental conditions. The data retrieved from this app using artificial intelligence procedures (transition network or TN algorithm), were used as input for GAM models to estimate the abundance of jellyfish based on wind speed and direction. The analysis of data provided by Infomedusa indicated that only 30.39% of messages provided by the users had information about absence/presence of jellyfishes in the beaches. On the other hand, the TN processing capacity showed an accuracy level to discriminate messages with information on absence/presence of jellyfish slightly higher than 80%. GAM models considering the wind direction and speed of previous day explained between 37% and 77% of the variance of jellyfish abundance estimate from Infomedusa data. In conclusion, this approach may contribute to the development of a system for predicting the onshore arrival of jellyfish in the Costa del Sol.Versión del edito

An Observational Test of Two-field Inflation

We study adiabatic and isocurvature perturbation spectra produced by a period of cosmological inflation driven by two scalar fields. We show that there exists a model-independent consistency condition for all two-field models of slow-roll inflation, despite allowing for model-dependent linear processing of curvature and isocurvature perturbations during and after inflation on super-horizon scales. The scale-dependence of all spectra are determined solely in terms of slow-roll parameters during inflation and the dimensionless cross-correlation between curvature and isocurvature perturbations. We present additional model-dependent consistency relations that may be derived in specific two-field models, such as the curvaton scenario.Comment: 6 pages, latex with revtex, no figures; v2, minor changes, to appear in Physical Review

WMAP constraints on scalar-tensor cosmology and the variation of the gravitational constant

We present observational constraints on a scalar-tensor gravity theory by $\chi^2$ test for CMB anisotropy spectrum. We compare the WMAP temperature power spectrum with the harmonic attractor model, in which the scalar field has its harmonic effective potential with curvature $\beta$ in the Einstein conformal frame and the theory relaxes toward Einstein gravity with time. We found that the present value of the scalar coupling, i.e. the present level of deviation from Einstein gravity $(\alpha_0^2)$, is bounded to be smaller than $5\times 10^{-4-7\beta}$ ($2\sigma$), and $10^{-2-7\beta}$ ($4\sigma$) for $0< \beta<0.45$. This constraint is much stronger than the bound from the solar system experiments for large $\beta$ models, i.e., $\beta> 0.2$ and 0.3 in $2\sigma$ and $4\sigma$ limits, respectively. Furthermore, within the framework of this model, the variation of the gravitational constant at the recombination epoch is constrained as $|G(z=z_{rec})-G_0|/G_0 < 0.05(2\sigma)$, and $0.23(4\sigma)$.Comment: 7 page