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Giordano P.,University Svizzera Italiana
Russian Journal of Mathematical Physics

We introduce a ring of the so-called Fermat reals, which is an extension of the real field containing nilpotent infinitesimals. The construction is inspired by Smooth Infinitesimal Analysis (SIA) and provides a powerful theory of actual infinitesimals without any background in mathematical logic. In particular, in contrast to SIA, which admits models in intuitionistic logic only, the theory of Fermat reals is consistent with the classical logic. We face the problem of deciding whether or not a product of powers of nilpotent infinitesimals vanishes, study the identity principle for polynomials, and discuss the definition and properties of the total order relation. The construction is highly constructive, and every Fermat real admits a clear and order-preserving geometrical representation. Using nilpotent infinitesimals, every smooth function becomes a polynomial because the remainder in Taylor's formulas is now zero. Finally, we present several applications to informal classical calculations used in physics, and all these calculations now become rigorous, and at the same time, formally equal to the informal ones. In particular, an interesting rigorous deduction of the wave equation is given, which clarifies how to formalize the approximations tied with Hooke's law using the language of nilpotent infinitesimals. © 2010 Pleiades Publishing, Ltd. Source

Agency: Cordis | Branch: FP7 | Program: CP-CSA-Infra | Phase: INFRA-2012-1.1.2. | Award Amount: 7.12M | Year: 2014

The RISIS project aims at creating a distributed research infrastructure to support and advance science and innovation studies. This will give the field a strong scientific push forward, and at the same time, provide a radically improved evidence base for research and innovation policies, for research evaluation, and for the quality of policy relevant indicators. The field of science and innovation studies is interdisciplinary, and is related to political sciences, sociology, management and economics. It has a strong quantitative core - with specialties such as scientometrics, technometrics and more widely indicators design - but for many important questions data were lacking or small scale only. This has made the field too much dependent on a few pre-existing datasets. However, during the last decade important efforts have been undertaken to develop new datasets on burning issues such as industrial R&D globalisation, patenting activities of firms, university performance, Europeanisation through joint programming, or the dynamics of nano S&T. Another new characteristic of the field is the development together with computer scientists of software platforms for collecting, integrating and analysing ever more data. Data and platforms are currently owned and/or located at many different organizations, such as individual research groups, companies, and public organizations with very restricted access to others. Through deploying various networking and access strategies, and through joint research, RISIS will decisively open, harmonize, integrate, improve, and extend their availability, quality and use.

Agency: Cordis | Branch: H2020 | Program: CSA | Phase: ISSI-1-2014 | Award Amount: 3.57M | Year: 2015

SPARKS is an awareness-raising and engagement project to promote Responsible Research and Innovation (RRI) across 29 European countries (EU members plus Switzerland). It gathers 33 organisations as partners and linked Third Parties. SPARKS will organise an interactive touring exhibition and 232 innovative participatory activities on RRI (science cafs, pop-up Science Shops, incubation activities and scenario workshops) across Europe. The European dimension of the project is paired with a strong emphasis on local implementation through 29 experienced science communicators (one per country) that will adapt the exhibition and activities to their contexts and establish local multi-stakeholder collaborative partnerships. SPARKS will deploy complementary dissemination tools and actions to maximise its outreach and impact. It will collect and analyse important data on RRI throughout Europe and build on its learning to: - Further build the capacity of science actors and policy makers to promote RRI; - Better understand societys vision, interests and readiness concerning RRI in health; - Provide policy recommendations to feed R&I policies with societal inputs and facilitate RRI; - Develop the capacity of a group of European stakeholders to participate in RRI. SPARKS will use the appealing topic technology shifts in health and medicine to reach out to a wider public, make the RRI concept meaningful to it and establish a direct link with one of the priority societal challenges of Horizon 2020. Creative disruptions in the form of artistic inputs and questioning will help it to engage more stakeholders. SPARKS builds upon a number of relevant EU projects from RRI Tools to PERARES, from PLACES to VOICES or Twist and powerful European/ international networks the European Network of Science Centres and Museums (Ecsite), the international network of Science Shops (Living Knowledge) and the European Regions Research and Innovation Network (ERRIN).

Agency: Cordis | Branch: FP7 | Program: MC-IEF | Phase: FP7-PEOPLE-2011-IEF | Award Amount: 184.71K | Year: 2013

The scope of this project is to contribute to the development of conceptual foundations, engineering techniques, and computing infrastructure for the systematic development of dynamically adaptive software systems. Current Software Engineering aims at designing self-adaptive systems which are able to react and reconfigure themselves minimizing human intervention and ideally guaranteeing a lifelong requirement fulfillment. Current software engineering paradigms, systems do not anticipate events which may lead to failures, but only react accordingly to them. The RunMore project introduces the novel concept of Run-Time Model Projection for Failure Prediction. By this we mean the ability of a software system at run-time to automatically forecast potentially dangerous events by reasoning on models which represent the expected future behavior of the system (i.e., models projections) and thus work around predicted failures before their occurrence. This approach empowers self-adaptation capabilities of software systems obtaining an increased degree of dependability and availability. The project focuses on software self-adaptation in terms of performance and reliability and relies on statistical algorithms to predict the future behavior of the system and run-time model-checking to verify such behavior with respect to desired requirements.

Agency: Cordis | Branch: FP7 | Program: CP | Phase: ICT-2013.12.1 | Award Amount: 4.58M | Year: 2013

Numerical simulation is a crucial part of science and industry in Europe. The advancement of simulation as a discipline relies on increasingly compute intensive models that require more computational resources to run. This is the driver for the evolution to exascale. Due to limits in the increase in single processor performance, exascale machines will rely on massive parallelism on and off chip, with a complex hierarchy of resources. The large number of components and the machine complexity introduce severe problems for reliability and programmability. The former of these will require novel fault-aware algorithms and support software. In addition, the scale of the numerical models exacerbates the difficulties by making the use of more complex simulation algorithms necessary, for numerical stability reasons. A key example of this is increased reliance on solvers. Such solvers require global communication, which impacts scalability, and are often used with preconditioners, increasing complexity again. Unless there is a major rethink of the design of solver algorithms, their components and software structure, a large class of important numerical simulations will not scale beyond petascale. This in turn will hold back the development of European science and industry which will fail to reap the benefits from exascale.\nThe EXA2CT project brings together experts at the cutting edge of the development of solvers, related algorithmic techniques, and HPC software architects for programming models and communication. It will take a revolutionary approach to exascale solvers and programming models, rather than the incremental approach of other projects. We will produce modular open source proto-applications that demonstrate the algorithms and programming techniques developed in the project, to help boot-strap the creation of genuine exascale codes.

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