Projectively Solid Sets and an N-dimensional Piccard's Theorem

We discuss functions f : X × Y → Z such that sets of the form f (A × B) have non-empty interiors provided that A and B are non-empty sets of second category and have the Baire property.

Sheaves, local homeomorphisms and local sets as Hilbert locale modules

We give a thorough account of the various equivalent notions for \sheaf" on a locale, namely the separated and complete presheaves, the local home- omorphisms, and the local sets, and to provide a new approach based on quantale modules whereby we see that sheaves can be identi¯ed with certain Hilbert modules in the sense of Paseka. This formulation provides us with an interesting category that has immediate meaningful relations to those of sheaves, local homeomorphisms and local sets. The concept of B-set (local set over the locale B) present in [3] is seen as a simetric idempotent matrix with entries on B, and a map of B-sets as de¯ned in [8] is shown to be also a matrix satisfying some conditions. This gives us useful tools that permit the algebraic manipulation of B-sets. The main result is to show that the existing notions of \sheaf" on a locale B are also equivalent to a new concept what we call a Hilbert module with an Hilbert base. These modules are the projective modules since they are the image of a free module by a idempotent automorphism On the ¯rst chapter, we recall some well known results about partially ordered sets and lattices. On chapter two we introduce the category of Sup-lattices, and the cate- gory of locales, Loc. We describe the adjunction between this category and the category Top of topological spaces whose restriction to spacial locales give us a duality between this category and the category of sober spaces. We ¯nish this chapter with the de¯nitions of module over a quantale and Hilbert Module. Chapter three concerns with various equivalent notions namely: sheaves of sets, local homeomorphisms and local sets (projection matrices with entries on a locale). We ¯nish giving a direct algebraic proof that each local set is isomorphic to a complete local set, whose rows correspond to the singletons. On chapter four we de¯ne B-locale, study open maps and local homeo- morphims. The main new result is on the ¯fth chapter where we de¯ne the Hilbert modules and Hilbert modules with an Hilbert and show this latter concept is equivalent to the previous notions of sheaf over a locale.

Wetland maps including open water extent dynamics based on ENVISAT ASAR WS for Siberia, 2007 and 2008, links to GeoTIFFs

Wetlands store large amounts of carbon, and depending on their status and type, they release specific amounts of methane gas to the atmosphere. The connection between wetland type and methane emission has been investigated in various studies and utilized in climate change monitoring and modelling. For improved estimation of methane emissions, land surface models require information such as the wetland fraction and its dynamics over large areas. Existing datasets of wetland dynamics present the total amount of wetland (fraction) for each model grid cell, but do not discriminate the different wetland types like permanent lakes, periodically inundated areas or peatlands. Wetland types differently influence methane fluxes and thus their contribution to the total wetland fraction should be quantified. Especially wetlands of permafrost regions are expected to have a strong impact on future climate due to soil thawing. In this study ENIVSAT ASAR Wide Swath data was tested for operational monitoring of the distribution of areas with a long-term SW near 1 (hSW) in northern Russia (SW = degree of saturation with water, 1 = saturated), which is a specific characteristic of peatlands. For the whole northern Russia, areas with hSW were delineated and discriminated from dynamic and open water bodies for the years 2007 and 2008. The area identified with this method amounts to approximately 300,000 km**2 in northern Siberia in 2007. It overlaps with zones of high carbon storage. Comparison with a range of related datasets (static and dynamic) showed that hSW represents not only peatlands but also temporary wetlands associated with post-forest fire conditions in permafrost regions. Annual long-term monitoring of change in boreal and tundra environments is possible with the presented approach. Sentinel-1, the successor of ENVISAT ASAR, will provide data that may allow continuous monitoring of these wetland dynamics in the future complementing global observations of wetland fraction.

On the acquisition of high-resolution maps with open source software and commercials off-the-shelf quad-rotors

Mosaics are high-resolution images obtained aerially and employed in several scientific research areas, such for example, in the field of environmental monitoring and precision agriculture. Although many high resolution maps are obtained by commercial demand, they can also be acquired with commercial aerial vehicles which provide more experimental autonomy and availability. For what regard to mosaicing-based aerial mission planners, there are not so many - if any - free of charge software. Therefore, in this paper is presented a framework designed with open source tools and libraries as an alternative to commercial tools to carry out mosaicing tasks.

An algorithmic approach to estimating the minimal number of periodic points for smooth self-maps of simply-connected manifolds

For a given self-map f of M, a closed smooth connected and simply-connected manifold of dimension m ≥ 4, we provide an algorithm for estimating the values of the topological invariant Dm r [f], which equals the minimal number of r-periodic points in the smooth homotopy class of f. Our results are based on the combinatorial scheme for computing Dm r [f] introduced by G. Graff and J. Jezierski [J. Fixed Point Theory Appl. 13 (2013), 63–84]. An open-source implementation of the algorithm programmed in C++ is publicly available at http://www.pawelpilarczyk.com/combtop/.

Maps as risk mitigation tools. Adaptation of the Swiss hazard assessment and mapping methodology to a Moroccan site: Beni Mellal

Dans le contexte climatique actuel, les régions méditerranéennes connaissent une intensification des phénomènes hydrométéorologiques extrêmes. Au Maroc, le risque lié aux inondations est devenu problématique, les communautés étant vulnérables aux événements extrêmes. En effet, le développement économique et urbain rapide et mal maîtrisé augmente l'exposition aux phénomènes extrêmes. La Direction du Développement et de la Coopération suisse (DDC) s'implique activement dans la réduction des risques naturels au Maroc. La cartographie des dangers et son intégration dans l'aménagement du territoire représentent une méthode efficace afin de réduire la vulnérabilité spatiale. Ainsi, la DDC a mandaté ce projet d'adaptation de la méthode suisse de cartographie des dangers à un cas d'étude marocain (la ville de Beni Mellal, région de Tadla-Azilal, Maroc). La méthode suisse a été adaptée aux contraintes spécifiques du terrain (environnement semi-aride, morphologie de piémont) et au contexte de transfert de connaissances (caractéristiques socio-économiques et pratiques). Une carte des phénomènes d'inondations a été produite. Elle contient les témoins morphologiques et les éléments anthropiques pertinents pour le développement et l'aggravation des inondations. La modélisation de la relation pluie-débit pour des événements de référence, et le routage des hydrogrammes de crue ainsi obtenus ont permis d'estimer quantitativement l'aléa inondation. Des données obtenues sur le terrain (estimations de débit, extension de crues connues) ont permis de vérifier les résultats des modèles. Des cartes d'intensité et de probabilité ont été obtenues. Enfin, une carte indicative du danger d'inondation a été produite sur la base de la matrice suisse du danger qui croise l'intensité et la probabilité d'occurrence d'un événement pour obtenir des degrés de danger assignables au territoire étudié. En vue de l'implémentation des cartes de danger dans les documents de l'aménagement du territoire, nous nous intéressons au fonctionnement actuel de la gestion institutionnelle du risque à Beni Mellal, en étudiant le degré d'intégration de la gestion et la manière dont les connaissances sur les risques influencent le processus de gestion. L'analyse montre que la gestion est marquée par une logique de gestion hiérarchique et la priorité des mesures de protection par rapport aux mesures passives d'aménagement du territoire. Les connaissances sur le risque restent sectorielles, souvent déconnectées. L'innovation dans le domaine de la gestion du risque résulte de collaborations horizontales entre les acteurs ou avec des sources de connaissances externes (par exemple les universités). Des recommandations méthodologiques et institutionnelles issues de cette étude ont été adressées aux gestionnaires en vue de l'implémentation des cartes de danger. Plus que des outils de réduction du risque, les cartes de danger aident à transmettre des connaissances vers le public et contribuent ainsi à établir une culture du risque. - Severe rainfall events are thought to be occurring more frequently in semi-arid areas. In Morocco, flood hazard has become an important topic, notably as rapid economic development and high urbanization rates have increased the exposure of people and assets in hazard-prone areas. The Swiss Agency for Development and Cooperation (SADC) is active in natural hazard mitigation in Morocco. As hazard mapping for urban planning is thought to be a sound tool for vulnerability reduction, the SADC has financed a project aimed at adapting the Swiss approach for hazard assessment and mapping to the case of Morocco. In a knowledge transfer context, the Swiss method was adapted to the semi-arid environment, the specific piedmont morphology and to socio-economic constraints particular to the study site. Following the Swiss guidelines, a hydro-geomorphological map was established, containing all geomorphic elements related to known past floods. Next, rainfall / runoff modeling for reference events and hydraulic routing of the obtained hydrographs were carried out in order to assess hazard quantitatively. Field-collected discharge estimations and flood extent for known floods were used to verify the model results. Flood hazard intensity and probability maps were obtained. Finally, an indicative danger map as defined within the Swiss hazard assessment terminology was calculated using the Swiss hazard matrix that convolves flood intensity with its recurrence probability in order to assign flood danger degrees to the concerned territory. Danger maps become effective, as risk mitigation tools, when implemented in urban planning. We focus on how local authorities are involved in the risk management process and how knowledge about risk impacts the management. An institutional vulnerability "map" was established based on individual interviews held with the main institutional actors in flood management. Results show that flood hazard management is defined by uneven actions and relationships, it is based on top-down decision-making patterns, and focus is maintained on active mitigation measures. The institutional actors embody sectorial, often disconnected risk knowledge pools, whose relationships are dictated by the institutional hierarchy. Results show that innovation in the risk management process emerges when actors collaborate despite the established hierarchy or when they open to outer knowledge pools (e.g. the academia). Several methodological and institutional recommendations were addressed to risk management stakeholders in view of potential map implementation to planning. Hazard assessment and mapping is essential to an integrated risk management approach: more than a mitigation tool, danger maps represent tools that allow communicating on hazards and establishing a risk culture.

Gestión en el territorio de una empresa de seguridad mediante estándares GIS e integración de datos con Google Maps.

Estudi teòric sobre els Sistemes d'Informació Geogràfica (GIS) i sobre les especificacions que està publicant el Open Geospatial Consortium (OGC) com estàndards oberts que permetin les comunicacions entre distints GIS.

Gestión en el territorio de una empresa de seguridad mediante estándares SIG e integración de datos con GOOGLE MAPS

Amb l'evolució de les noves tecnologies, els Sistemes d'Informació Geogràfica (SIG) es basen cada vegada menys en plataformes propietàries (únicament a l'abast de grans companyies). L'objectiu que persegueix el Open Geospatial Consortium (OGC) és que tot el món pugui beneficiar-se de la informació geogràfica, fent que els serveis estiguin disponibles en qualsevol xarxa, aplicació o sistema.

Desenvolupament d'edició geogràfica segons l'estàndard WFS-T sobre l'API de Google Maps

El present treball tractarà d'aprofitar Google Maps i les eines lliures disponibles, per construir unes llibreries Javascript d'ús obert que permetin afegir serveis de persistència als serveis de cartografia ja disponibles.

Global periodicity conditions for maps and recurrences via Normal Forms

We face the problem of characterizing the periodic cases in parametric families of (real or complex) rational diffeomorphisms having a fixed point. Our approach relies on the Normal Form Theory, to obtain necessary conditions for the existence of a formal linearization of the map, and on the introduction of a suitable rational parametrization of the parameters of the family. Using these tools we can find a finite set of values p for which the map can be p-periodic, reducing the problem of finding the parameters for which the periodic cases appear to simple computations. We apply our results to several two and three dimensional classes of polynomial or rational maps. In particular we find the global periodic cases for several Lyness type recurrences

Periodic orbits of integrable birational maps on the plane: blending dynamics and algebraic geometry, the Lyness' case

Contingut del Pòster presentat al congrés New Trends in Dynamical Systems

Tarracomap: Development of an archaeological application on Google Maps navigation System

This paper describes the result of a research about diverse areas of the information technology world applied to cartography. Its final result is a complete and custom geographic information web system, designed and implemented to manage archaeological information of the city of Tarragona. The goal of the platform is to show on a web-focused application geographical and alphanumerical data and to provide concrete queries to explorate this. Various tools, between others, have been used: the PostgreSQL database management system in conjunction with its geographical extension PostGIS, the geographic server GeoServer, the GeoWebCache tile caching, the maps viewer and maps and satellite imagery from Google Maps, locations imagery from Google Street View, and other open source libraries. The technology has been chosen from an investigation of the requirements of the project, and has taken great part of its development. Except from the Google Maps tools which are not open source but are free, all design has been implemented with open source and free tools.

Dynamics of integrable birational maps preserving genus 0 foliations

Pòster presentat al congrés NPDDS2014

Wikiloc: software libre y APIs de Google Maps para visualizar y compartir rutas GPS

Wikiloc es un servicio web gratuito para visualizar y compartir rutas y puntos de interés GPS. Utilizando software libre y la API de Google Maps, Wikiloc hace la función de base de datos personal de localizaciones GPS. Desde cualquier acceso a Internet un usuario de GPS puede cargar sus datos GPS y al momento visualizar la ruta y waypoints con distinta cartografía de fondo, incluidos servidores de mapas externos WMS (Web Map Service) o descargarlo a Google Earth para ver en 3D. Paralelamente se muestra el perfil de altura, distancia, desniveles acumulados y las fotos o comentarios que el usuario quiera añadir

A numerical scheme for two-dimensional, open channel flows with non-rectangular geometries

An algorithm based on flux difference splitting is presented for the solution of two-dimensional, open channel flows. A transformation maps a non-rectangular, physical domain into a rectangular one. The governing equations are then the shallow water equations, including terms of slope and friction, in a generalized coordinate system. A regular mesh on a rectangular computational domain can then be employed. The resulting scheme has good jump capturing properties and the advantage of using boundary/body-fitted meshes. The scheme is applied to a problem of flow in a river whose geometry induces a region of supercritical flow.