Facets and Levels of Mathematical Abstraction

International audienceMathematical abstraction is the process of considering and manipulating operations, rules, methods and concepts divested from their reference to real world phenomena and circumstances, and also deprived from the content connected to particular applications. There is no one single way of performing mathematical abstraction. The term "abstraction" does not name a unique procedure but a general process, which goes many ways that are mostly simultaneous and intertwined ; in particular, the process does not amount only to logical subsumption. I will consider comparatively how philosophers consider abstraction and how mathematicians perform it, with the aim to bring to light the fundamental thinking processes at play, and to illustrate by significant examples how much intricate and multi-leveled may be the combination of typical mathematical techniques which include axiomatic method, invarianceprinciples, equivalence relations and functional correspondences.L'abstraction mathématique consiste en la considération et la manipulation d'opérations, règles et concepts indépendamment du contenu dont les nantissent des applications particulières et du rapport qu'ils peuvent avoir avec les phénomènes et les circonstances du monde réel. L'abstraction mathématique emprunte diverses voies. Le terme " abstraction " ne désigne pasune procédure unique, mais un processus général où s'entrecroisent divers procédés employés successivement ou simultanément. En particulier, l'abstraction mathématique ne se réduit pas à la subsomption logique. Je vais étudier comparativement en quels termes les philosophes expliquent l'abstraction et par quels moyens les mathématiciens la mettent en oeuvre. Je voudrais parlà mettre en lumière les principaux processus de pensée en jeu et illustrer par des exemples divers niveaux d'intrication de techniques mathématiques récurrentes, qui incluent notamment la méthode axiomatique, les principes d'invariance, les relations d'équivalence et les correspondances fonctionnelles

Tarski’s Practice and Philosophy: Between Formalism and Pragmatism: What has Become of Them?

Collection : Synthese Library, n°341International audienceConsidering works by Tarski, the author claims that Tarski’s fundamental aim was to establish formal semantics as a new branch of mathematics

Indicators for mapping ecosystem services: a review

Ecosystem services are the benefits that humans derive from ecosystems, such as food provisioning, water regulating and provisioning, soil productivity, and use of natural areas for recreation. The current challenge is to mainstream ecosystem services into policies and practices in order to ensure the continuous provision of these benefits to humans. The European Union has adopted an EU Biodiversity Strategy for 2020 in which the target of safeguarding ecosystem services is explicitly included. One crucial step to account for ecosystem services is the spatial quantification of the service supply. To this end, the development of robust indicators is needed. In this report we give an overview of spatial information used for mapping and modelling ecosystem services according to the scientific literature and evaluate the potential contribution of the JRC in supporting such initiatives at global, continental, and national level. We found a large diversity of indicators used for mapping different ecosystem services. The most common indicators are based on data related to land use/cover, soils, vegetation, and nutrients. Most of these data are available in and outside the JRC to a large extent and at low resolution. The JRC holds 82% of the data types used to map ecosystem services and could support the Member States and other initiatives involved by directly providing spatial information.JRC.H.1 - Water Resource

Carbon K-shell Photo Ionization of CO: Molecular frame angular Distributions of normal and conjugate shakeup Satellites

We have measured the molecular frame angular distributions of photoelectrons emitted from the Carbon K shell of fixed-in-space CO molecules for the case of simultaneous excitation of the remaining molecular ion. Normal and conjugate shake up states are observed. Photo electrons belonging to normal \Sigma -satellite lines show an angular distribution resembling that observed for the main photoline at the same electron energy. Surprisingly a similar shape is found for conjugate shake up states with \Pi -symmetry. In our data we identify shake rather than electron scattering (PEVE) as the mechanism producing the conjugate lines. The angular distributions clearly show the presence of a \Sigma -shape resonance for all of the satellite lines.Comment: 8 pages, 2 figure

Current Status and Future Prospects for the Assessment of Marine and Coastal Ecosystem Services: A Systematic Review

Background: Research on ecosystem services has grown exponentially during the last decade. Most of the studies have focused on assessing and mapping terrestrial ecosystem services highlighting a knowledge gap on marine and coastal ecosystem services (MCES) and an urgent need to assess them. Methodology/Principal Findings: We reviewed and summarized existing scientific literature related to MCES with the aim of extracting and classifying indicators used to assess and map them. We found 145 papers that specifically assessed marine and coastal ecosystem services from which we extracted 476 indicators. Food provision, in particular fisheries, was the most extensively analyzed MCES while water purification and coastal protection were the most frequently studied regulating and maintenance services. Also recreation and tourism under the cultural services was relatively well assessed. We highlight knowledge gaps regarding the availability of indicators that measure the capacity, flow or benefit derived from each ecosystem service. The majority of the case studies was found in mangroves and coastal wetlands and was mainly concentrated in Europe and North America. Our systematic review highlighted the need of an improved ecosystem service classification for marine and coastal systems, which is herein proposed with definitions and links to previous classifications. Conclusions/Significance: This review summarizes the state of available information related to ecosystem services associated with marine and coastal ecosystems. The cataloging of MCES indicators and the integrated classification of MCES provided in this paper establish a background that can facilitate the planning and integration of future assessments. The final goal is to establish a consistent structure and populate it with information able to support the implementation of biodiversity conservation policies.JRC.H.1-Water Resource