A note on the periodic orbits and topological entropy of graph maps

This paper deals with the relationship between the periodic orbits of continuous maps on graphs and the topological entropy of the map. We show that the topological entropy of a graph map can be approximated by the entropy of its periodic orbits.

A parameterization method for the computation of invariant tori and their whiskers in quasi-periodic maps: explorations and mechanisms for the breakdown of hyperbolicity

In two previous papers [J. Differential Equations, 228 (2006), pp. 530 579; Discrete Contin. Dyn. Syst. Ser. B, 6 (2006), pp. 1261 1300] we have developed fast algorithms for the computations of invariant tori in quasi‐periodic systems and developed theorems that assess their accuracy. In this paper, we study the results of implementing these algorithms and study their performance in actual implementations. More importantly, we note that, due to the speed of the algorithms and the theoretical developments about their reliability, we can compute with confidence invariant objects close to the breakdown of their hyperbolicity properties. This allows us to identify a mechanism of loss of hyperbolicity and measure some of its quantitative regularities. We find that some systems lose hyperbolicity because the stable and unstable bundles approach each other but the Lyapunov multipliers remain away from 1. We find empirically that, close to the breakdown, the distances between the invariant bundles and the Lyapunov multipliers which are natural measures of hyperbolicity depend on the parameters, with power laws with universal exponents. We also observe that, even if the rigorous justifications in [J. Differential Equations, 228 (2006), pp. 530-579] are developed only for hyperbolic tori, the algorithms work also for elliptic tori in Hamiltonian systems. We can continue these tori and also compute some bifurcations at resonance which may lead to the existence of hyperbolic tori with nonorientable bundles. We compute manifolds tangent to nonorientable bundles.

Self-Organising Maps and Correlation Analysis as a Tool to Explore Patterns in Excitation-Emission Matrix Data Sets and to Discriminate Dissolved Organic Matter Fluorescence Components

Dissolved organic matter (DOM) is a complex mixture of organic compounds, ubiquitous in marine and freshwater systems. Fluorescence spectroscopy, by means of Excitation-Emission Matrices (EEM), has become an indispensable tool to study DOM sources, transport and fate in aquatic ecosystems. However the statistical treatment of large and heterogeneous EEM data sets still represents an important challenge for biogeochemists. Recently, Self-Organising Maps (SOM) has been proposed as a tool to explore patterns in large EEM data sets. SOM is a pattern recognition method which clusterizes and reduces the dimensionality of input EEMs without relying on any assumption about the data structure. In this paper, we show how SOM, coupled with a correlation analysis of the component planes, can be used both to explore patterns among samples, as well as to identify individual fluorescence components. We analysed a large and heterogeneous EEM data set, including samples from a river catchment collected under a range of hydrological conditions, along a 60-km downstream gradient, and under the influence of different degrees of anthropogenic impact. According to our results, chemical industry effluents appeared to have unique and distinctive spectral characteristics. On the other hand, river samples collected under flash flood conditions showed homogeneous EEM shapes. The correlation analysis of the component planes suggested the presence of four fluorescence components, consistent with DOM components previously described in the literature. A remarkable strength of this methodology was that outlier samples appeared naturally integrated in the analysis. We conclude that SOM coupled with a correlation analysis procedure is a promising tool for studying large and heterogeneous EEM data sets.

Sierpinski curve Julia sets for quadratic rational maps

We investigate under which dynamical conditions the Julia set of a quadratic rational map is a Sierpiński curve.

Dynamics of integrable birational maps preserving genus 0 foliations

Pòster presentat al congrés NPDDS2014

High-density linkage maps fail to detect any genetic component to sex determination in a Rana temporaria family.

Sex chromosome differentiation in Rana temporaria varies strikingly among populations or families: whereas some males display well-differentiated Y haplotypes at microsatellite markers on linkage group 2 (LG2 ), others are genetically undistinguishable from females. We analysed with RADseq markers one family from a Swiss lowland population with no differentiated sex chromosomes, and where sibship analyses had failed to detect any association between the phenotypic sex of progeny and parental haplotypes. Offspring were reared in a common tank in outdoor conditions and sexed at the froglet stage. We could map a total of 2177 SNPs (1123 in the mother, 1054 in the father), recovering in both adults 13 linkage groups (= chromosome pairs) that were strongly syntenic to Xenopus tropicalis despite > 200 My divergence. Sexes differed strikingly in the localization of crossovers, which were uniformly distributed in the female but limited to chromosome ends in the male. None of the 2177 markers showed significant association with offspring sex. Considering the very high power of our analysis, we conclude that sex determination was not genetic in this family; which factors determined sex remain to be investigated.

High-density sex-specific linkage maps of a European tree frog (Hyla arborea) identify the sex chromosome without information on offspring sex.

Identifying homology between sex chromosomes of different species is essential to understanding the evolution of sex determination. Here, we show that the identity of a homomorphic sex chromosome pair can be established using a linkage map, without information on offspring sex. By comparing sex-specific maps of the European tree frog Hyla arborea, we find that the sex chromosome (linkage group 1) shows a threefold difference in marker number between the male and female maps. In contrast, the number of markers on each autosome is similar between the two maps. We also find strongly conserved synteny between H. arborea and Xenopus tropicalis across 200 million years of evolution, suggesting that the rate of chromosomal rearrangement in anurans is low. Finally, we show that recombination in males is greatly reduced at the centers of large chromosomes, consistent with previous cytogenetic findings. Our research shows the importance of high-density linkage maps for studies of recombination, chromosomal rearrangement and the genetic architecture of ecologically or economically important traits.

From Regional Landslide Detection to Site-Specific Slope Deformation Monitoring and Modelling Based on Active Remote Sensors

Landslide processes can have direct and indirect consequences affecting human lives and activities. In order to improve landslide risk management procedures, this PhD thesis aims to investigate capabilities of active LiDAR and RaDAR sensors for landslides detection and characterization at regional scales, spatial risk assessment over large areas and slope instabilities monitoring and modelling at site-specific scales. At regional scales, we first demonstrated recent boat-based mobile LiDAR capabilities to model topography of the Normand coastal cliffs. By comparing annual acquisitions, we validated as well our approach to detect surface changes and thus map rock collapses, landslides and toe erosions affecting the shoreline at a county scale. Then, we applied a spaceborne InSAR approach to detect large slope instabilities in Argentina. Based on both phase and amplitude RaDAR signals, we extracted decisive information to detect, characterize and monitor two unknown extremely slow landslides, and to quantify water level variations of an involved close dam reservoir. Finally, advanced investigations on fragmental rockfall risk assessment were conducted along roads of the Val de Bagnes, by improving approaches of the Slope Angle Distribution and the FlowR software. Therefore, both rock-mass-failure susceptibilities and relative frequencies of block propagations were assessed and rockfall hazard and risk maps could be established at the valley scale. At slope-specific scales, in the Swiss Alps, we first integrated ground-based InSAR and terrestrial LiDAR acquisitions to map, monitor and model the Perraire rock slope deformation. By interpreting both methods individually and originally integrated as well, we therefore delimited the rockslide borders, computed volumes and highlighted non-uniform translational displacements along a wedge failure surface. Finally, we studied specific requirements and practical issues experimented on early warning systems of some of the most studied landslides worldwide. As a result, we highlighted valuable key recommendations to design new reliable systems; in addition, we also underlined conceptual issues that must be solved to improve current procedures. To sum up, the diversity of experimented situations brought an extensive experience that revealed the potential and limitations of both methods and highlighted as well the necessity of their complementary and integrated uses.

Large slope deformations detection and monitoring along shores of the Potrerillos dam reservoir, Argentina, based on a small-baseline InSAR approach

The Argentina National Road 7 that crosses the Andes Cordillera within the Mendoza province to connect Santiago de Chile and Buenos Aires is particularly affected by natural hazards requiring risk management. Integrated in a research plan that intends to produce landslide susceptibility maps, we aimed in this study to detect large slope movements by applying a satellite radar interferometric analysis using Envisat data, acquired between 2005 and 2010. We were finally able to identify two large slope deformations in sandstone and clay deposits along gentle shores of the Potrerillos dam reservoir, with cumulated displacements higher than 25mm in 5years and towards the reservoir. There is also a body of evidences that these large slope deformations are actually influenced by the seasonal reservoir level variations. This study shows that very detailed information, such as surface displacements and above all water level variation, can be extracted from spaceborne remote sensing techniques; nevertheless, the limitations of InSAR for the present dataset are discussed here. Such analysis can then lead to further field investigations to understand more precisely the destabilising processes acting on these slope deformations.

The geologic and geomorphologic maps of Santa Coloma de Farners (Girona, Spain)

Notice about the geologic and geomorphologic maps of Santa Coloma de Farners, at scale 1:10,000 published by Unitat de Geologia of the Universitat de Girona

Geologic maps published by university de Girona's unity of geodynamics

In 1978 University de Girona's Unity of Geodynamics started publishing geological maps, in several themes and scales, of various areas of the Province of Girona (fig. 1). So far, up to 38 maps, gathered in several collections, have been published

A Note on the periodic orbits and topological entropy of graph maps

This paper deals with the relationship between the periodic orbits of continuous maps on graphs and the topological entropy of the map. We show that the topological entropy of a graph map can be approximated by the entropy of its periodic orbits

Chemotaxonomy of three genera of the annonaceae family using self-organizing maps and 13C NMR data of diterpenes

The Annonaceae family is distributed throughout Neotropical regions of the world. In Brazil, it covers nearly all natural formations particularly Annona, Xylopia and Polyalthia and is characterized chemically by the production of sources of terpenoids (mainly diterpenes), alkaloids, steroids, polyphenols and, flavonoids. Studies from 13C NMR data of diterpenes related with their botanical occurrence were used to generate self-organizing maps (SOM). Results corroborate those in the literature obtained from morphological and molecular data for three genera and the model can be used to project other diterpenes. Therefore, the model produced can predict which genera are likely to contain a compound.

Distortion properties of quasiconformal maps

In this Licentiate thesis we investigate the absolute ratio δ, j, ˜j and hyperbolic ρ metrics and their relations with each other. Various growth estimates are given for quasiconformal mpas both in plane and space. Some Hölder constants were refined with respect δ, j ˜j metrics. Some new results regarding the Hölder continuity of quasiconformal and quasiregular mapping of unit ball with respect to Euclidean and hyperbolic metrics are given, which were obtained by many authors in 1980’s. Applications are given to the study of metric space, quasiconformal and quasiregular maps in the plane and as well as in the space.