On the preservation of combinatorial types for maps on trees

We study the preservation of the periodic orbits of an A-monotone tree map f:T→T in the class of all tree maps g:S→S having a cycle with the same pattern as A. We prove that there is a period-preserving injective map from the set of (almost all) periodic orbits of ƒ into the set of periodic orbits of each map in the class. Moreover, the relative positions of the corresponding orbits in the trees T and S (which need not be homeomorphic) are essentially preserved

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.

Linear and nonlinear terrain deformation maps from a reduced set of interferometric SAR images

In this paper, an advanced technique for the generation of deformation maps using synthetic aperture radar (SAR) data is presented. The algorithm estimates the linear and nonlinear components of the displacement, the error of the digital elevation model (DEM) used to cancel the topographic terms, and the atmospheric artifacts from a reduced set of low spatial resolution interferograms. The pixel candidates are selected from those presenting a good coherence level in the whole set of interferograms and the resulting nonuniform mesh tessellated with the Delauney triangulation to establish connections among them. The linear component of movement and DEM error are estimated adjusting a linear model to the data only on the connections. Later on, this information, once unwrapped to retrieve the absolute values, is used to calculate the nonlinear component of movement and atmospheric artifacts with alternate filtering techniques in both the temporal and spatial domains. The method presents high flexibility with respect to the required number of images and the baselines length. However, better results are obtained with large datasets of short baseline interferograms. The technique has been tested with European Remote Sensing SAR data from an area of Catalonia (Spain) and validated with on-field precise leveling measurements.

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.

Clustering of grape yield maps to delineate site-specific management zones

Zonal management in vineyards requires the prior delineation of stable yield zones within the parcel. Among the different methodologies used for zone delineation, cluster analysis of yield data from several years is one of the possibilities cited in scientific literature. However, there exist reasonable doubts concerning the cluster algorithm to be used and the number of zones that have to be delineated within a field. In this paper two different cluster algorithms have been compared (k-means and fuzzy c-means) using the grape yield data corresponding to three successive years (2002, 2003 and 2004), for a ‘Pinot Noir’ vineyard parcel. Final choice of the most recommendable algorithm has been linked to obtaining a stable pattern of spatial yield distribution and to allowing for the delineation of compact and average sized areas. The general recommendation is to use reclassified maps of two clusters or yield classes (low yield zone and high yield zone) and, consequently, the site-specific vineyard management should be based on the prior delineation of just two different zones or sub-parcels. The two tested algorithms are good options for this purpose. However, the fuzzy c-means algorithm allows for a better zoning of the parcel, forming more compact areas and with more equilibrated zonal differences over time.

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.

Geology of the Cerro-Quema Au-Cu deposit (Azuero Peninsula, Panama)

The Cerro Quema district, located on the Azuero Peninsula, Panama, is part of a large regional hydrothermal system controlled by regional faults striking broadly E-W, developed within the Río Quema Formation. This formation is composed of volcanic, sedimentary and volcano-sedimentary rocks indicating a submarine depositional environment, corresponding to the fore-arc basin of a Cretaceous-Paleogene volcanic arc. The structures observed in the area and their tectono-stratigraphic relationship with the surrounding formations suggest a compressive and/or transpressive tectonic regime, at least during Late Cretaceous-Oligocene times. The igneous rocks of the Río Quema Formation plot within the calc-alkaline field with trace and rare earth element (REE) patterns of volcanic arc affinity. This volcanic arc developed on the Caribbean large igneous province during subduction of the Farallon Plate. Mineralization consists of disseminations of pyrite and enargite as well as a stockwork of pyrite and barite with minor sphalerite, galena and chalcopyrite, hosted by a subaqueous dacitic lava dome of the Río Quema Formation. Gold is present as submicroscopic grains and associated with pyrite as invisible gold. A hydrothermal alteration pattern with a core of advanced argillic alteration (vuggy silica with alunite, dickite, pyrite and enargite) and an outer zone of argillic alteration (kaolinite, smectite and illite) has been observed. Supergene oxidation overprinted the hydrothermal alteration resulting in a thick cap of residual silica and iron oxides. The ore minerals, the alteration pattern and the tectono-volcanic environment of Cerro Quema are consistent with a high sulfidation epithermal system developed in the Azuero peninsula during pre-Oligocene times.

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.

Mesozoic geology of Cape Shirreff, Livingston Island, South Shetland Islands, Antarctica.

Al Cap de Shirr e ff (Fig. 1) hi aflora una successió volcànica de com a mínim 450 m de potència, constituïda principalment per laves i, en menor proporció, bretxes vulcanoclàstiques (Fig. 2). Les laves són basalts olivínics subalcalins i andesites basàltiques, que generalment tenen un aspecte massiu. Tot i això, la successió volcànica localment forma una alternança decimètrica de nivells durs i tous, amb potències va r i a bles i presència local de discordances angulars i onlaps, que reflecteixen geometries deposicionals complexes. A la zona nord del Cap de Shirr e ff hi ha aflorament de bretxes vulcanoclàstiques d"aspecte massiu, que localment tenen intercalacions de laves...

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.

Quaternary Glacial Geology of Alta Ribagorqa Basin (Central Southern Pyrenees)

This paper is an abstract of the doctoral thesis presented by the autor at the University of Barcelona on September 1983. It constitutes a regional study about the Quatemary Glacial Geology in the Ribagorca high valleys. It is the first work in relation to the geomorphology, sedimentology and stratigraphy of the glacial and related deposits in this zone of the Pyrenees. Several formations of quatemary deposits have been studied in detail (mainly in Llauset Valley and in Tall area); and the local quatemary stratigraphy is established and finally a correlation with some previously studied areas in the Pyrenees is attemped.

Engineering Geology for Society and Territory: volume 2: landslide processes

This book is one out of 8 IAEG XII Congress volumes, and deals with Landslide processes, including: field data and monitoring techniques, prediction and forecasting of landslide occurrence, regional landslide inventories and dating studies, modeling of slope instabilities and secondary hazards (e.g. impulse waves and landslide-induced tsunamis, landslide dam failures and breaching), hazard and risk assessment, earthquake and rainfall induced landslides, instabilities of volcanic edifices, remedial works and mitigation measures, development of innovative stabilization techniques and applicability to specific engineering geological conditions, use of geophysical techniques for landslide characterization and investigation of triggering mechanisms. Focuses is given to innovative techniques, well documented case studies in different environments, critical components of engineering geological and geotechnical investigations, hydrological and hydrogeological investigations, remote sensing and geophysical techniques, modeling of triggering, collapse, runout and landslide reactivation, geotechnical design and construction procedures in landslide zones, interaction of landslides with structures and infrastructures and possibility of domino effects. The Engineering Geology for Society and Territory volumes of the IAEG XII Congress held in Torino from September 15-19, 2014, analyze the dynamic role of engineering geology in our changing world and build on the four main themes of the congress: environment, processes, issues, and approaches.

Dynamics of integrable birational maps preserving genus 0 foliations

Pòster presentat al congrés NPDDS2014

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