Numerical analysis of an inverse problem for the eikonal equation

We are concerned with the inverse problem for an eikonal equation of determining the speed function using observations of the arrival time on a fixed surface. This is formulated as an optimisation problem for a quadratic functional with the state equation being the eikonal equation coupled to the so-called Soner boundary condition. The state equation is discretised by a suitable finite difference scheme for which we obtain existence, uniqueness and an error bound. We set up an approximate optimisation problem and show that a subsequence of the discrete mimina converges to a solution of the continuous optimisation problem as the mesh size goes to zero. The derivative of the discrete functional is calculated with the help of an adjoint equation which can be solved efficiently by using fast marching techniques. Finally we describe some numerical results

An overview of the GEEP Workshop

This paper reviews the main highlights of the GEEP Workshop, both its successes and failures, draws conclusions from these and from lessons learnt in convening and participating in the workshop, and suggests a way forward for research and application of biological effects techniques. We point to the importance of maintaining close links between the research effort and the evaluation of procedures that emerge, in the context of a wide spectrum of climatic and environmental regimes. The utility of measures of biological responses to pollution will depend on the extent to which a suite of such measurements can be put together so as to link In a cause/effect manner the results of chemical analyses and responses at the biochemical, cellular physiological, population and community levels Some hopeful trends and some basic difficulties are indicated. We suggest that further practical workshops on the same model as the GEEP Workshop, but held in different climatic regions and with different faunas, will play an essential part in furthering the development of techniques for measuring the biological effects of pollutants

Proposed approaches for indicator integration. EcApRHA Deliverable WP 4.1

Executive SummaryThe Marine Strategy Framework Directive (MSFD) aims to achieve Good Environmental Status (GES) withinEuropean Commission waters through an ecosystem‐based approach. The MSFD requires Member Statessharing a marine region or sub‐region to cooperate to ensure that the Directive’s objectives are achievedWorking towards an ecosystem perspective: Proposals for the integration of pelagic, benthic and food web indicatorsand to coordinate their actions through Regional Seas Conventions e.g. the OSPAR Commission for theNorth‐East Atlantic. As part of the ‘applying an Ecosystem Approach to (sub) Regional Habitat Assessments’(EcApRHA) project, integration of indicators under Descriptor 1 (biodiversity), 4 (food webs) and 6 (seafloorintegrity), relating to pelagic and benthic habitats and food webs have been forwarded to work towards anecosystem’s approach in assessing habitats regionally. The content of this report covers differentapproaches developed to integrate indicators forwarded within the project.Five methods are described, four of which were developed to integrate indicators developed under theEcApRHA project. The fifth, OSPAR’s cumulative effect approach has also been summarised as an additionalapproach to integrate indicators. For each method, management implications; the advantages anddisadvantages in relation to being able to work toward assessment of GES; and the confidence in theassessments, are highlighted. The time it would take for the approach to become fully operational, itsfeasibility and costs are also discussed.From the five methods described, three main approaches are discussed:I. A quantitative method to draw links between indicators to assess pressures that have effectson the different aspects of the marine ecosystem (Chapters 3‐4).II. Use of the Nested Environmental status Assessment Tool (NEAT) to integrate differentindicators to provide an overall assessment (Chapters 5 and 6).III. Use of an industry led risk assessment tool (Bow‐Ties) to assess cumulative effects (Chapter 7).The integration approaches outlined within this document demonstrate the developments made within theEcApRHA project to ensure the various indicators under the different descriptors are not only operational,but also integrated in a way which permits a more holistic assessment of the marine environment. Usingsuch a two‐tiered approach of individual indicator and integrated analysis, will enable an understanding ofwhy certain aspects of the marine environment may not be in good condition, and thereby recommendspecific management measures to ameliorate them. Although the approaches forwarded have been initiallytrialled in the North‐East Atlantic, they are able to be applied to other MSFD Regional seas areas. Eachmethod addresses different levels of integration (indicator, habitat or ecosystem) and requires furtherdevelopment and testing. They should be thus considered as complementary and gaps should beprogressed in parallel to ensure coherent progress towards an overall ecosystem approach. In addition,with some further comparative testing between the different methods outlined within this document,options to continue forwarding integrated assessment of OSPAR indicators could be proposed. Themethods outlined within this document are a first step in applying an ecosystem’s approach to assessingthe state of our seas

Hamilton–Jacobi–Bellman Equations

International audienceIn this chapter we present recent developments in the theory of Hamilton–Jacobi–Bellman (HJB) equations as well as applications. The intention of this chapter is to exhibit novel methods and techniques introduced few years ago in order to solve long-standing questions in nonlinear optimal control theory of Ordinary Differential Equations (ODEs)

Sensitivity of the Cherenkov Telescope Array for probing cosmology and fundamental physics with gamma-ray propagation

The Cherenkov Telescope Array (CTA), the new-generation ground-based observatory for γ astronomy, provides unique capabilities to address significant open questions in astrophysics, cosmology, and fundamental physics. We study some of the salient areas of γ cosmology that can be explored as part of the Key Science Projects of CTA, through simulated observations of active galactic nuclei (AGN) and of their relativistic jets. Observations of AGN with CTA will enable a measurement of γ absorption on the extragalactic background light with a statistical uncertainty below 15% up to a redshift z=2 and to constrain or detect γ halos up to intergalactic-magnetic-field strengths of at least 0.3 pG . Extragalactic observations with CTA also show promising potential to probe physics beyond the Standard Model. The best limits on Lorentz invariance violation from γ astronomy will be improved by a factor of at least two to three. CTA will also probe the parameter space in which axion-like particles could constitute a significant fraction, if not all, of dark matter. We conclude on the synergies between CTA and other upcoming facilities that will foster the growth of γ cosmology