dataesr/scientific-paragraphs-categorization huggingface dataset:
25 dB (see Table  4 ). Complementary to these numerical results, Fig. 3  illustrates the visual differences resulting from various data fidelity terms in the case of image x 1. One can observe that a high number of low intensity components are lost when using a data fidelity term derived from Poisson statistics. Similarly, the shape of low intensity components is not well reconstructed when using a WL2 data fidelity term. Most artifacts are corrected when using the GAST data fidelity term while even better results are obtained with the Gaussian and SPoiss. Finally, one can hardly notice a visual difference between the EXP approximation and the exact data fidelity term. Finally, we indicate in the caption of Fig. 3  the computational time required to reach the algorithm convergence (typically, when the difference in norm between two consecutive iterates becomes small), when tests are performed on a quad-CPU, 32-core Intel Xeon L7555 1.
Our numerical examples have hence to be viewed as toy models which will enable us to be confident in the feasibility of our methods in more realistic 2D or 3D cases. As an application of the mixed formulation of quasi-reversibility for heat/wave equation with lateral Cauchy data we also consider the inverse obstacle problem: it consists in finding an unknown fixed Dirichlet obstacle from some lateral Cauchy data on a subpart of the boundary. In the one-dimensional case, the obstacle is a single point in some bounded interval. The method we use to solve such inverse obstacle problem, called the "exterior approach", is a coupling between the quasi-reversibility method and a level set method. In our one-dimensional context the level set method is very simple and inspired from the one introduced for the two-dimensional (but stationary) context in  [2]  and reused in  [5].
2. 2. The heat equation with lateral Cauchy data. Another classical ill-posed problem is the heat equation with lateral Cauchy data. To set the problem we need to correctly define the normal derivative of a solution to the heat equation on the subpart Γ 0 of the boundary. In the proof of lemma 2. 1 we have remarked that if u ∈ H 1 (Q) solves the heat equation ∂ t u -∂ 2 x u = 0 in Q, then u ∈ L 2 (0, T ; H 2 (0, 1)), hence ∂ x u| Γ0 ∈ L 2 (Γ 0 ). The heat equation with lateral Cauchy data consists, for (g 0 , g 1 ) ∈ H 1 2 (Γ 0 ) × L 2 (Γ 0 ), in finding u ∈ H 1 (Q) such that    ∂ t u -∂ 2 x u = 0 in Q u = g 0 on Γ 0 -∂ x u = g 1 on Γ 0. (11) It is well-known that the uniqueness property holds for that problem, that is (g 0 , g 1 ) = (0, 0) on Γ 0 implies that u = 0 in Q, due to Holmgren's theorem (see theorem  5.
3. 3 in [12] ). Let us now describe a slightly different problem with lateral Cauchy data and initial condition. To this aim, we now define H 1 2 S0 (Γ 0 ) as the subset of traces on Γ 0 of functions in H 1 (Q) that vanish on S 0. The problem is now the following: for (g 0 , g 1 ) ∈ H 1 2 S0 (Γ 0 ) × L 2 (Γ 0 ), find u ∈ H 1 (Q) such that        ∂ t u -∂ 2 x u = 0 in Q u = g 0 on Γ 0 -∂ x u = g 1 on Γ 0 u = 0 on S 0. (12) Both problems  (11)  and (  12 ) are ill-posed (see for example  [13] ). Several quasireversibility methods are proposed in  [1]  to regularize the problem  (11) , and a simplified one is proposed in  [14]. This last one consists in minimizing, for ε > 0 and appropriate data (g 0 , g 1 ), the cost function ||∂ t u -∂ 2 x u|| 2 L 2 (Q) + ε||u|| 2 H 2,1 (Q) among all functions u in H 2,1 (Q) which satisfy u(0, •) = g 0 and -∂ x u(0, •) = g 1 on Γ 0.
Here ν 2 denotes the outward unit normal to the 2-dimensional domain Q. As a result, the normal derivatives -∂ x u| Γ0 and -∂ t u| S0 are well defined in H -1 2 (Γ 0 ) and H -1 2 (S 0 ), which are respectively the restrictions to Γ 0 and S 0 of the distributions in H -1 2 (∂Q). We recall that H -1 2 (Γ 0 ) coincides with the dual space of H 1 2 00 (Γ 0 ), which denotes the subset of functions in H 1 2 (Γ 0 ) which once extended by 0 on the whole boundary ∂Q are still in H 1 2 (∂Q). The wave equation with lateral Cauchy data consists, for (g 0 , g 1 ) ∈ H 1 2 (Γ 0 ) × H -1 2 (Γ 0 ), in finding u ∈ H 1 (Q) such that    ∂ 2 t u -∂ 2 x u = 0 in Q u = g 0 on Γ 0 -∂ x u = g 1 on Γ 0. (19) Let us now introduce the wave equation with lateral Cauchy data and initial condition. We define H 1 2 Γ1,S T (Γ 0 ) as the set of traces on Γ 0 of functions in H 1 (Q) that vanish on Γ 1 and on S T , that is in other words the restrictions on Γ 0 of functions in Ṽ0.
1, 0. 6). The results are represented on figure  3  and has to be compared to those represented on figure  1. The quality of the results is approximately the same. 5. 2. The heat equation with lateral Cauchy data and inverse obstacle problem. We continue with some numerical experiments for the heat equation with lateral Cauchy data. First, we consider the solution u(x, t) = e -t cos(x) to  the heat equation, which enables us to obtain some lateral Cauchy data (g 0 , g 1 ) on Γ 0 , and then address problem  (11)  with such data. We impose a pointwise random noise to the Dirichlet data g 0 only (g 1 is noise free), the relative error in L 2 norm for such noisy data being again denoted by σ. The reason why we do not perturb the Neumann data g 1 is the following: in practice, the Neumann data is considered as the solicitation that we impose to the system while the Dirichlet data is considered as the measurement of the response of the system to such solicitation.
05 a wrong value of 0. 77 is obtained instead of 0. 8. Similarly, for σ = 0. 01, we observe that when the final time T increases from T = 0. 5 to T = 2, the exact value a is obtained with a higher speed of convergence. 5. 3. The wave equation with lateral Cauchy data and inverse obstacle problem. We complete this numerical section with some numerical experiments for the wave equation with lateral Cauchy data. First, we consider the solution u(x, t) = x 2 + t 2 to the wave equation for T = 3, which enables us to obtain some lateral Cauchy data (g 0 , g 1 ) on Γ 0 , and then to address problem  (19)  with such data. Like for the heat equation, we impose a pointwise random noise to the Dirichlet data g 0 only (g 1 is noise free), the relative error in L 2 norm for such noisy data being again denoted by σ.
Conclusion and perspectives. The numerical results that we have obtained in the one-dimensional case show the feasibility of our mixed formulations of quasireversibility to solve ill-posed problems for heat and wave equations, in particular the inverse obstacle problems from lateral Cauchy data on some subpart of the boundary. This is the reason why we intend to address the same kind of problems in the 2D case in a close future. The extension of our mixed formulation of quasireversibility to the 2D case is straightforward, and concerning the discretization with finite elements, it is again convenient to use a tensor product between some 2D Lagrange triangular finite elements for space variables and some 1D Lagrange finite elements for the time variable, which amounts to use some Lagrange prismatic finite elements in 3D.
Introduction. The method of quasi-reversibility has now a quite long history since the pioneering book of Lattès and Lions in 1967 [1]. The original idea of these authors was, starting from an ill-posed problem which satisfies the uniqueness property, to introduce a perturbation of such problem involving a small positive parameter ε. This perturbation has essentially two effects. Firstly the perturbation transforms the initial ill-posed problem into a well-posed one for any ε, secondly the solution to such problem converges to the solution (if it exists) to the initial illposed problem when ε tends to 0. Generally, the ill-posedness in the initial problem is due to unsuitable boundary conditions. As typical examples of linear ill-posed problems one may think of the backward heat equation, that is the initial condition is replaced by a final condition, or the heat or wave equations with lateral Cauchy data, that is the usual Dirichlet or Neumann boundary condition on the boundary of the domain is replaced by a pair of Dirichlet and Neumann boundary conditions on the same subpart of the boundary, no data being prescribed on the complementary part of the boundary.
Study site and equipment The study was conducted during the nesting season 2006 on Cayenne/Rémire-Montjoly beaches (4°53' N, 52°16' W, French Guiana, South America). Seven olive ridley turtles were equipped with Satellite-Relayed Data Loggers (SRDL 9000X; Sea Marine Research Unit, SMRU, St Andrews, UK, www. smru. st-and. ac. uk/, unit mass = 660 g) while nesting. SRDL units were glued on the highest scale of the carapace using 2-component fast set epoxy (Powerfast), with the antenna pointing perpendicular to the sea surface to improve communication with the satellites upon the turtle surfacing. Standard curved carapace length (SCCL) was measured with a flexible measuring tape (± 0. 5 cm) for all individuals prior to SRDL attachment. Individuals were weighed after SRDL attachment and once they had completed oviposition using a handmade harness and a handheld spring scale (± 0.
Horizontal movements At-sea movements were reconstructed using the Argos system (www. argos-system. org/). Location data were recovered from Collecte Localisation Satellites, CLS (www. cls. fr), and each track was processed following  Gaspar et al. (2006). Argos locations of any accuracy were used except those implying an apparent speed above 1. 5 m s -1 (i. e. 5 km h -1 ), as travel rates above this threshold are considered to be biologically unlikely  (Whiting et al. 2007 , Rees et al. 2012). The track was smoothed and re-sampled with a fixed sampling period of 3 h. It has been demonstrated that surface currents may contribute to sea turtles' offshore movements  (Gaspar et al. 2006 ), and such evidence has been considered in previous stud-ies (e. g. Fossette et al. 2010a ,b, Galli et al.
The straightness index is defined as the ratio of the straight line to the actual distance traveled by the animal (Batschelet 1981): S values vary from 0 to 1, with values near 0 indicating a sinuous path associated with foraging behavior, whereas values near 1 indicate a straight path associated with traveling behavior. Along each individual track, we calculated a daily straightness index with respect to the time-step of the dive data provided by SRDLs. Similarly to  Gaspar et al. (2006)  and  Fossette et al. (2010a) , visual examination of the frequency distribution of the straightness index values showed a bimodal distribution, with S = 0. 8 as the threshold value (see Fig. S1  in Supplement 1 at www. int-res. com/ articles/ suppl/ n026 p221_ supp/), suggesting that foraging and traveling could be identified for S < 0.
Water temperature The thermal habitat of migrating olive ridley turtles was assessed using sea surface temperatures (SSTs) provided by CLS for each Argos location and in situ temperature records provided by the SRDL units. SRDLs monitored the depth during the central phase of the 2 deepest dives in each 2 h period and collected temperature data (± 0. 1°C) every 4 s on the ascent. Data were then processed on board, and temperature-at-depth profiles (with 12 temperaturedepth pairs) were produced and relayed via the Argos system. These profiles allowed us to characterize the water column in terms of a thermal gradient and to calculate the mean water temperature experienced by the turtles throughout the water column.
Operational ocean forecast systems provide routine marine products to an ever-widening community of users and stakeholders. The majority of users need information about the quality and reliability of the products to exploit them fully. Hence, forecast centres have been developing improved methods for evaluating and communicating the quality of their products. Global Ocean Data Assimilation Experiment (GODAE) OceanView, along with the Copernicus European Marine Core Service and other national and international programmes, has facilitated the development of coordinated validation activities among these centres. New metrics, assessing a wider range of ocean parameters, have been defined and implemented in real-time. An overview of recent progress and emerging international standards is presented here.
2009 ). An overview of skill assessment using observations and other reference datasets representing this truth is given by  Stow et al. (2009). The calibration, validation, verification and quality control of OOFS products are core activities in ocean operational centres  (Lellouche et al. 2013; Oke et al. 2013; Blockley et al. 2014)   (OOCs). Usually calibration refers to a task in which model parameters are optimized. Here, the calibration phase refers to the last comprehensive scientific assessment of the new OOFS version before operation. The calibration phase is also often used to demonstrate that the new system performance is better than the existing system. Validation refers to the OOFS performance assessment while in operation. Verification is defined here as the quantification of OOFS skill based on independent data, i.
Experts in OOCs across the world who are assessing the skill of OOFSs face similar issues with the observational data sets available for validating their products. In general, in situ and satellite measurements are collected by dedicated data assembly centres (DACs) that pre-process the data and make it available for OOFSs. Hence, for similar components of operational systems, methods and tools for assessing the representation of ocean processes can be shared. Owing to the nature and quality of the observations, validation experts also face comparable issues, such as the validation of mesoscale chlorophyll or primary products using ocean colour satellite data, or the use of Lagrangian approaches and drifters to verify the realism of eddies in regional models for oil-spill forecast skill. As a result, there is a great potential for collaboration within the scientific community in this area.
Naturally, working groups were set up to tackle, as a community, these validation issues. This started earlier within the ocean observation community, which raised expert groups to develop guidelines and standards for providing state-of-theart ocean observation products. Some examples of these are the Ocean Surface Topography Science Team for sea surface height (SSH) and satellite altimetry (www. aviso. altimetry. fr), the Group for High Resolution Sea Surface Temperature (GHRSST) for sea surface temperature (SST) from various satellite and in situ sensors (www. ghrsst. org/), the Argo team for in situ vertical profiles of primarily temperature (T) and salinity (S) (www. argo. ucsd. edu), the Global Ocean Surface Underway Data group for sea surface salinity (SSS) (www. gosud. org) and the International Ocean Color Coordinating  Group (www.
s222 F. Hernandez et al. Rigorous skill assessment in the assimilation framework is a difficult task: most available observations are used to adjust models and reduce analysis errors. Thus, independent assessment is only possible by: (1) withholding part of the dataset for statistical quantification of errors (a trade-off between a sufficient population size to estimate a statistic while not significantly impacting the quality of the system performance being measured); or by (  2 ) using other sources of data that have not been assimilated  (Gregg et al. 2009 ). The latter is generally employed with data not available in near-real time, which is useful for reanalysis (or hindcast) evaluation, but not for operational routine verification.
A verification of SSH is performed in which forecasts are compared in real-time with along-track SSH data following the Class 4 metrics approach (i. e. in observation space; discussed below). Then, in model space, the ensemble is used to assess the probabilistic forecast skill. In Figure  2 , statistics of weekly comparisons against analyses for the period January-September 2013 show that forecasts remain skilful for approximately twice as long as persistence. The SSH anomaly variance agrees closely in the forecast and verifying analysis, but the ensemble standard deviation does not appear to predict the forecast error, suggesting that the ensemble spread does not fully capture the forecast error patterns. Adequately sampling the uncertainty in initial conditions, model physics and forcing is an important aspect of ocean ensemble prediction that requires further study.
Slope currents and water masses used for real-time applications are evaluated using all available data. A specific off-line verification is performed using independent surface drifters, moored data and SSH. Moreover, a dedicated multi-model realtime assessment has been performed, comparing estimates from ESPreSSO together with three other regional OOFS, and three global OOFS (including HYCOM-NCODA) in order to evaluate the OOFS' prediction skill for subtidal currents and shelf water mass changes. This assessment is comprehensively discussed in  Wilkin and Hunter (2013)  including a presentation of performance improvements through downscaling strategies. In their figures 4 and 5, improvements to Taylor and Target diagrams are proposed, to represent individual vs average performance, and seasonal model biases respectively.
Validation of sea-ice products Growing interest in polar regions has driven the need for improved sea-ice verification metrics to demonstrate the capacity and quality of sea-ice forecast skill to potential users. This effort has been hindered by the reliability and availability of observational datasets together with a lack of knowledge of how to adequately account for nonlinearities in the verification metrics. Contingency table-based metrics, introduced in the early twentieth century  (Pearson 1904) , have been re-popularized, as well as the root-mean-square distance of ice edge. However, these metrics may not be relevant for regional or processdependent verification. In particular, errors in ice edge location assessment are sensitive to the definition of 'ice edge', as multiple ice edges may be present and the total error will be sensitive to the length of the ice edge.
Hence, the metrics defined for the Arctic might not be suitable in the Baltic Sea, and definitions should consider subregional scaling (e. g. size of a gulf)  (Lagemaa 2013 ). However, even if the ice metric is not properly defined, it still gives valuable user information for the dense marine traffic regions like the Baltic Sea. An example of a contingency table-based metric from the Canadian Meteorological Centre Global Ice-Ocean Prediction Systems (GIOPSv1. 0) is shown in Figure  4. GIOPSv1. 0 uses a 3DVAR ice concentration analysis for correcting the Los Alamos sea-ice model by assimilating satellite data together with daily ice charts from the Canadian Ice Service. The reference dataset is given by the Interactive Multisensor Snow and Ice Mapping System (IMS) analyses from the National Oceanic and Atmospheric Administration (NOAA) National Ice Centre that provide binary fields of ice/open water on a 4 km grid.
Reliability assessment of input information Another recent aspect in OOFS validation strategy is the systematic feedback of errors and anomalies to providers of input data. For instance, validation of atmospheric forcing fields is now carried out for some wave-prediction systems  (Feng et al. 2006). Moreover, inputs of ocean assimilation systems, such as in situ data collected by TACs or DACs, can suffer in real-time from incomplete levels of quality control. While automatic procedures are applied for the rapid distribution of the observations in real-time, more detailed visual analysis is often left for delayed-time datasets. Other analyses usually depend on the level of expertise of the provider. In near-real time, s226 F. Hernandez et al. erroneous in situ profiles can drastically impact the quality of ocean analyses.
Development of integrated operational verification systems Several OOCs have recently taken steps to structure calibration, validation, and verification activities, in real-time or delayed mode, as an integrated component of the OOFSs. In the USA, the national backbone of real-time data, tidal predictions, data management and operational modelling supporting NOAA's missions (http:// tidesandcurrents. noaa. gov) under the National Operational Coastal Modeling Program now performs quality control and forecast skill verification in a centralized way for all OOFS through the Continuous Operational Real-Time Monitoring System. Similarly, the MyOcean IBI (Irish Biscay Iberian shelves) OOFS team (Puertos del Estado, Spain, and Mercator Océan, France) has developed a comprehensive tool called NARVAL (Numeric Assessment for Regional VALidation) to check its operational performance, in terms of consistency, accuracy and reliability.
Furthermore, a 'Delayed Mode Validation' provides an overall review of the IBI product quality over longer time periods (i. e. monthly, seasonal and annual). Real-time statistics are accumulated to provide a synthesis assessment over longer periods, while dedicated metrics using off-line datasets, can focus on particular ocean phenomena or parameters. Metrics are performed over the whole domain (26°N-56°N, 19°W-5°E), but also over specific sub-regions of interestboth for users and for verification teams, for example: Strait of Gibraltar, English Chanel, Western Mediterranean Sea, Gulf of Biscay, Western and Northern Iberian shelves, the Canary Islands area and the Irish Sea. Using NARVAL, the performance can be monitored for specific areas, dynamics and OOFS, as illustrated for SST using a Taylor diagram (Figure  7 ).
Reducing uncertainties by ensemble approach: ocean surface parameters multi-model estimation Major incidents, such as the AF447 Air France Rio-Paris airplane crash in June 2009, the DeepWater Horizon oil   (Masumoto et al. 2012; Kawamura et al. 2011). For all these events, national authorities have made requests to their respective OOCs in order to provide some assistance in near-real time or offline, to carry out dedicated studies to complement risk assessment. Ocean studies performed in support of the effort to find the Air France plane wreckage relied on several new aspects: (1) an international effort to collect forecasts from different OOCs and to provide different ocean datasets to assist rescue activities in real-time; (2) the use of multi-model datasets and ensemble approaches to reduce errors of ocean surface dynamics in hindcasts and forecasts, with the implementation of dedicated high resolution model simulations in the area, nested into global OOFSs; (3) a retrospective statistical analysis of the accuracy of ocean currents and, in particular, the reliability of mixing and transport properties; (4) the formation of an international task team, with contributions from many ocean experts from both the in situ and modelling communities  (Scott et al.
From these nowcasts/forecasts, a first multiple/ ensemble assessment has been made, focusing on SST, together with two observation-only datasets chosen as reference: the NCEP Real-Time Global (RTG)  (Thiébaux et al. 2003 ) and the GHRSST NAVO K10 level-4  (Martin et al. 2012)  dataset. Three ensemble computations are defined using daily OOFS outputs: (1) simple arithmetic mean average; (2) weighted average, based on root-meansquare (RMS) daily differences of each member with respect to the reference SST field; and (3) clustered average, based on a k-mean algorithm  (Hartigan & Wong 1979). A first hindcast comparison has now been performed for July 2013 compared with NCEP RTG (Figure  11 ). In this evaluation, Mercator_PSY3, FOAM and CFS perform better than the two other OOFSs. Note also that FOAM biases are slightly different using the NAVO K10 product (not shown).