Lower Bounds for Electrical Reduction on Surfaces

We strengthen the connections between electrical transformations and homotopy from the planar setting - observed and studied since Steinitz - to arbitrary surfaces with punctures. As a result, we improve our earlier lower bound on the number of electrical transformations required to reduce an n-vertex graph on surface in the worst case [SOCG 2016] in two different directions. Our previous Omega(n^{3/2}) lower bound applies only to facial electrical transformations on plane graphs with no terminals. First we provide a stronger Omega(n^2) lower bound when the planar graph has two or more terminals, which follows from a quadratic lower bound on the number of homotopy moves in the annulus. Our second result extends our earlier Omega(n^{3/2}) lower bound to the wider class of planar electrical transformations, which preserve the planarity of the graph but may delete cycles that are not faces of the given embedding. This new lower bound follow from the observation that the defect of the medial graph of a planar graph is the same for all its planar embeddings

Minimal area of Finsler disks with minimizing geodesics

We show that the Holmes--Thompson area of every Finsler disk of radius $r$ whose interior geodesics are length-minimizing is at least $\frac{6}{\pi} r^2$. Furthermore, we construct examples showing that the inequality is sharp and observe that the equality case is attained by a non-rotationally symmetric metric. This contrasts with Berger's conjecture in the Riemannian case, which asserts that the round hemisphere is extremal. To prove our theorem we discretize the Finsler metric using random geodesics. As an auxiliary result, we show that the integral geometry formulas of Blaschke and Santal\'o hold on Finsler manifolds with almost no trapped geodesics

The Copernicus Marine Environment Monitoring Service Ocean State Report

The Copernicus Marine Environment Monitoring Service (CMEMS) Ocean State Report (OSR) provides an annual report of the state of the global ocean and European regional seas for policy and decision-makers with the additional aim of increasing general public awareness about the status of, and changes in, the marine environment. The CMEMS OSR draws on expert analysis and provides a 3-D view (through reanalysis systems), a view from above (through remote-sensing data) and a direct view of the interior (through in situ measurements) of the global ocean and the European regional seas. The report is based on the unique CMEMS monitoring capabilities of the blue (hydrography, currents), white (sea ice) and green (e.g. Chlorophyll) marine environment. This first issue of the CMEMS OSR provides guidance on Essential Variables, large-scale changes and specific events related to the physical ocean state over the period 1993–2015. Principal findings of this first CMEMS OSR show a significant increase in global and regional sea levels, thermosteric expansion, ocean heat content, sea surface temperature and Antarctic sea ice extent and conversely a decrease in Arctic sea ice extent during the 1993–2015 period. During the year 2015 exceptionally strong large-scale changes were monitored such as, for example, a strong El Niño Southern Oscillation, a high frequency of extreme storms and sea level events in specific regions in addition to areas of high sea level and harmful algae blooms. At the same time, some areas in the Arctic Ocean experienced exceptionally low sea ice extent and temperatures below average were observed in the North Atlantic Ocean

Copernicus Marine Service Ocean State Report

This is the final version. Available from Taylor & Francis via the DOI in this record

Copernicus Ocean State Report, issue 6

The 6th issue of the Copernicus OSR incorporates a large range of topics for the blue, white and green ocean for all European regional seas, and the global ocean over 1993–2020 with a special focus on 2020

Evaluation of operational ocean forecasting systems from the perspective of the users and the experts

The Intergovernmental Oceanographic Commission (IOC) has an Ocean Decade Implementation Plan (UNESCO-IOC, 2021) that states seven outcomes required for the ocean we want, with the fourth outcome being “A predicted ocean where society understands and can respond to changing ocean conditions.” To facilitate the achievement of this goal, the IOC has endorsed Mercator Ocean International to implement the Decade Collaborative Center (DCC) for OceanPrediction (https://www.mercator-ocean.eu/oceanprediction/, last access: 21 August 2023), which is a cross-cutting structure that will work to develop global-scale collaboration between Decade Actions related to ocean prediction

Intersection norms on surfaces and Birkhoff cross sections

Coauthor Marcos Cossarini has been added. He noted a gap in the previous proof of Thm B and proposed a shorter and correct proof. Several other minor changes.For every finite collection of curves on a surface, we define an associated (semi-)norm on the first homology group of the surface. The unit ball of the dual norm is the convex hull of its integer points. We give an interpretation of these points in terms of certain coorientations of the original collection of curves. Our main result is a classification statement: when the surface has constant curvature and the curves are geodesics, integer points in the interior of the dual unit ball classify isotopy classes of Birkhoff cross sections for the geodesic flow (on the unit tangent bundle to the surface) whose boundary is the symmetric lift of the collection of geodesics. Birkhoff cross sections in particular yield open-book decompositions of the unit tangent bundle

From observation to information and users: The Copernicus Marine Service Perspective

The Copernicus Marine Environment Monitoring Service (CMEMS) provides regular and systematic reference information on the physical and biogeochemical ocean and sea-ice state for the global ocean and the European regional seas. CMEMS serves a wide range of users (more than 15,000 users are now registered to the service) and applications. Observations are a fundamental pillar of the CMEMS value-added chain that goes from observation to information and users. Observations are used by CMEMS Thematic Assembly Centres (TACs) to derive high-level data products and by CMEMS Monitoring and Forecasting Centres (MFCs) to validate and constrain their global and regional ocean analysis and forecasting systems. This paper presents an overview of CMEMS, its evolution, and how the value of in situ and satellite observations is increased through the generation of high-level products ready to be used by downstream applications and services. The complementary nature of satellite and in situ observations is highlighted. Long-term perspectives for the development of CMEMS are described and implications for the evolution of the in situ and satellite observing systems are outlined. Results from Observing System Evaluations (OSEs) and Observing System Simulation Experiments (OSSEs) illustrate the high dependencies of CMEMS systems on observations. Finally future CMEMS requirements for both satellite and in situ observations are detailed. © 2019 Le Traon, Reppucci, Alvarez Fanjul, Aouf, Behrens, Belmonte, Bentamy, Bertino, Brando, Kreiner, Benkiran, Carval, Ciliberti, Claustre, Clementi, Coppini, Cossarini, De Alfonso Alonso-Muñoyerro, Delamarche, Dibarboure, Dinessen, Drevillon, Drillet, Faugere, Fernández, Fleming, Garcia-Hermosa, Sotillo, Garric, Gasparin, Giordan, Gehlen, Gregoire, Guinehut, Hamon, Harris, Hernandez, Hinkler, Hoyer, Karvonen, Kay, King, Lavergne, Lemieux-Dudon, Lima, Mao, Martin, Masina, Melet, Buongiorno Nardelli, Nolan, Pascual, Pistoia, Palazov, Piolle, Pujol, Pequignet, Peneva, Pérez Gómez, Petit de la Villeon, Pinardi, Pisano, Pouliquen, Reid, Remy, Santoleri, Siddorn, She, Staneva, Stoffelen, Tonani, Vandenbulcke, von Schuckmann, Volpe, Wettre and Zacharioudaki