dataesr/scientific-paragraphs-categorization huggingface dataset:
Significant differences are visible between the two resulting hybrid products. Patterns visible in the probability map (Figure  4 ) are sometimes apparent in Hybrid Map 1 (Figure  5 ). An example of this is Australia where barren areas appear in stark contrast to herbaceous areas. Hybrid Map 2, with its focus on areas of complete disagreement among the input datasets, produces a map which differs less from the original input datasets (Figure  6 ). A quantitative validation of the hybrid products was performed using cross-tabulation. Results are presented here from sample matrices for Hybrid Map 1 and Hybrid Map 2 (Tables  3  and 4 ). Note that because of edge effects, the different resolutions of the input maps, and the methodologies used to produce Hybrid Maps 1 and 2, around 200 validation samples fell outside of a land boundary and were therefore not used in the final validation.
Although the GLC2000 is for the year 2000, the majority of spatial disagreements between the products are not about land cover change but about incorrect classifications. Thus the merging of the products is really about trying to find the best land cover representation more generally for that time period. The two hybrid products were compared with the individual global land cover products using performance metrics suggested by  Pontius and Millones (2011)  as well as overall accuracy as an additional relative measure. The first hybrid map outperformed the individual land cover maps based on the validation data set used while the second hybrid map was not as good as the individual MODIS land cover product on three out of four performance measures. We offered potential explanations for this including the use of the GLC2000 in the development of GlobCover and the continued improvement of MODIS over time.
Other variations that might be tried are to: take the land cover at a given point only when MODIS agrees with one of the other land cover products (or all three agree); and use the two crowdsourced training datasets and GWR at all locations to create a single hybrid product. The use of crowdsourced data for both calibration and validation of the hybrid products as well as for the development of future land cover products represents an area of great potential. Although quality is clearly a very important issue, some initial research in this area has shown that the data are of sufficient quality for use in further scientific research or that methods can be put in place to correct for errors and biases automatically  (Foody et al. , 2013; See et al. , 2013). There is much to be learned from ongoing quality control measures implemented in ecological citizen science projects that are using the data for rigorous scientific research as well as from businesses who need to control for quality (Delaney et al.
The aim of this paper is to describe a Matlab toolbox, called µ-diff, for modeling and numerically solving two-dimensional complex multiple scattering by a large collection of circular cylinders. The approximation methods in µ-diff are based on the Fourier series expansions of the four basic integral operators arising in scattering theory. Based on these expressions, an efficient spectrally accurate finite-dimensional solution of multiple scattering problems can be simply obtained for complex media even when many scatterers are considered as well as large frequencies. The solution of the global linear system to solve can use either direct solvers or preconditioned iterative Krylov subspace solvers for block Toeplitz matrices. Based on this approach, this paper explains how the code is built and organized.
Introduction Let us consider M regular, bounded and disjoint scatterers Ω - p , p = 1,. , M , distributed in R 2 , with boundary Γ p := Ω - p. The scatterer Ω -is defined as the collection of the M separate obstacles, i. e. Ω -= ∪ M p=1 Ω - p , with boundary Γ = ∪ M p=1 Γ p. The homogeneous and isotropic exterior domain of propagation is Ω + = R 2 \ Ω -. For the sake of conciseness in the presentation, we first assume that the scatterers are sound-soft (Dirichlet boundary condition), but other situations can be handled by the µ-diff (multiple-diff raction) Matlab toolbox (e. g. sound-hard scatterers, impedance boundary conditions, penetrable scatterers) as it will be shown during the numerical examples (see  section 7). We now consider a time-harmonic incident acoustic plane wave u inc (x) = e ikβ•x (with x = (x 1 , x 2 ) ∈ R 2 ) illuminating Ω -, with an incidence direction β = (cos(β), sin(β)) and a time dependence e -iωt , where ω is the wave pulsation and k is the wavenumber.
Indeed, for example, analytical expressions of the integral operators can be obtained, and spectrally accurate and fast solutions can be derived. This is the case when considering a disk  [7, 37]. The Matlab toolbox µ-diff considers the case of a collection of M homogeneous circular cylinders where Fourier basis expansions can be used (see section 4). Even if disks can be considered as simple geometries, a reliable and highly accurate solution is required for wave propagation problems (acoustics, electromagnetics, optics, nanophotonics, elasticity) that involve many circular scatterers, modeling structured or disordered media, most particularly when k and M are large (see e. g. [9, 15, 19, 20, 21, 22, 24, 33, 34, 35, 36, 39, 40, 42, 45, 49, 50, 52] ). Let us note that all the developments in this paper directly apply to 2D TM/TE electromagnetic scattering waves  [37]  even if our presentation is more related to acoustics.
Furthermore, since multiple scattering is a highly complex problem with unusual properties, it is desirable to have a simple modeling tool that helps to understand the physics properties of such structures. Finally, having a reference solution method for multiple scattering leads to the possibility of evaluating the accuracy and performance of other more general numerical methods like finite element or general integral equation solvers. The goal of the µ-diff Matlab toolbox is to contribute to these different questions. The structure of the paper is the following. In section 3, we describe the basics of integral operators that are used in µ-diff and review the most standard integral equation formulations when one wants to solve the sound-soft scattering problem. In Section 4, we explain the approximation method that is used in µ-diff to solve the integral equation problems through Fourier series expansions and how to formulate post-processing data (near-and far-fields for example).
In section 5, we describe the finite-dimensional approximation leading to concrete linear systems. Some numerical aspects of the resolution methods are also discussed. Section 6 details the structure of the µ-diff code and the main functions that are included. To illustrate the use of µ-diff, we provide in sections 7. 1 and 7. 2 some numerical examples for direct multiple scattering problems (sound-soft, soundhard, penetrable scatterers). In addition, we consider in section 7. 3 a more advanced example related to the DORT method (Time Reversal method) in the presence of homogeneous penetrable circular scatterers. All the related files are available in the µ-diff package when downloaded and the simulations can be reproduced. Finally, we conclude in section 8. 3 Basic theory behind µ-diff: integral equations and formulations for 2D scattering problems.
As a consequence, for a given integral equation, the resulting matrix is of size N tot × N tot and has the same block structure as e. g. L (see equation (  10 )). The finite-dimensional linear system (9) (or (  11 )) is accurately solved in µ-diff by using the Matlab direct solver or a preconditioned Krylov subspace linear solver that uses fast matrix-vector products based on Fast Fourier Transforms (FFTs), the choice of the linear algebra strategy (direct vs. iterative) depending on the configuration with respect to ka p and M. The preconditioner included in µ-diff is based on the diagonal of the integral operator matrix representation which is solved and corresponding to single scattering. The use of FFTs is made possible since the off-diagonal blocks of the integral operators can be written as the products of diagonal and Toeplitz matrices  [3, 8]  (see e.
g. the matrices S p,q m,n in section 4. 2). In addition, low memory is only necessary when ka p is large enough since the storage of the Toeplitz matrices can be optimized. This resulting storage technique is called sparse representation in µ-diff, in contrast with the dense (full) storage of the complex-valued matrices. Let us assume that a p ≈ a, for 1 p M. In terms of storage, the dense version of a matrix requires to store about 4M 2 [ka] 2 coefficients (assuming that N p are fixed by formula  (8) , and [r] denotes the integer part of a real number r) while the sparse storage needs about 4M 2 [ka] complex-valued coefficients. In terms of computational time for solving the linear system, the direct (multithreaded) gaussian solver included in Matlab leads to a cost that scales with O(M 3 (ka) 3 ).
Structure of the µ-diff Matlab toolbox Because µ-diff includes all the integral operators that are needed in scattering (traces and normal derivative traces of the single-and double-layer potentials), a large class of scattering problems can be solved. Concerning the geometrical configurations, any deterministic or random distribution of disks is possible. Finally, µ-diff includes post-processing facilities like e. g. : surface and far-fields computations, total and scattered exterior (near-field) visualization. We now introduce the µ-diff Matlab toolbox by explaining the main predefined functions and their relations with the previous mathematical derivations. Section 6. 1 shows how to define the scattering configuration (geometry and physical parameters). Section 6. 2 presents the way the integral equations must be defined and solved.
Without entering too much into details, each block of the final global matrix can be specified thanks to this numbering (instead of a vector, a 2D-or a 3D-array is then considered as argument). For the sparse version, the operators are stored using the Matlab cell structure. Building a linear combination of the different integral operators is then slightly different: each operator is assembled separately and all the integral operators are next combined during the sparse matrix-vector product as shown below. Once the dense or sparse integral operator has been defined and the right-hand side has been computed, then the integral equation can be solved. For the dense representation of the integral operator, it is possible to use a direct Gauss solver (based on the backslash \ Matlab operator) or any iterative Krylov subspace solver available in Matlab (GMRES, BiCGStab,.
In addition, far-fields can be obtained by applying the FarField function. For the Radar Cross Section, the µ-diff function is called RCS. Each of these functions needs the integral representation of the scattered field. To help the user, each function has an interface function for the single-and the double-layer potential only (e. g. ExternalSingleLayerPotential, FarFieldSingleLayer,. ). Even if the far-field is efficiently computed, the user should be aware that the computation of the volume potentials on a huge discrete grid can need more time than assembling and solving the linear system. The reader can find in the example subdirectory mudiff/Examples/Benchmark many examples of manipulation of the code in the files BenchmarkDirichlet (sound-soft scattering) and BenchmarkNeumann (sound-hard scattering).
An effort has been made to show all the possible combinations of operators available in µ-diff, trying to use the main functions. The user can clearly play with the parameters sets, the only limit being given by the memory of the computer used. The notation concerning the integral equations are related to the present paper (EFIE, MFIE, CFIE, BWIE). 7 Numerical examples with µ-diff 7. 1 Example I: scattering by randomly distributed sound-soft or sound-hard circular cylinders To show an example of problem solved by µ-diff, we consider that we use the EFIE to solve the scattering problem by a collection of sound-soft or sound-hard randomly distributed scatterers. The corresponding script (BenchmarkDN) for simulating the results of this section is available in the examples directory. We consider a plane wave (for a wavenumber k = 6π and an incidence angle β = π (rad.
Example II: multiple scattering by a cluster of homogeneous penetrable obstacles Extending the previous example, the script BenchmarkPenetrable solves the transmission problem with penetrable obstacles. The wavenumber k is now piecewise constant with value k + outside the obstacles and k -inside. The scattered field u + and the transmitted wavefield u -are then the solution to the following transmission boundary-value problem                ∆u -+ (k -) 2 u -= 0, in Ω -, ∆u + + (k + ) 2 u + = 0, in Ω + , u + -u -= -u inc , on Γ, ∂ n u + -∂ n u -= -∂ n u inc , on Γ, lim ||x||→+∞ ||x|| 1/2 ∇u + • x ||x|| -iku = 0. ( 13 ) The total (physical) field u tot is given by u tot = u + + u inc outside and by u tot = u -inside the obstacles. To solve this problem through an integral equation, we consider a single-layer representation of the wavefields u + and u - u + = L + ρ + and u -= L -ρ -, (14) where L + (resp.
Once F has been computed, the matrix T is obtained by the relation: T = F T F. All the elementary operations described above can be easily coded by using µ-diff and the Matlab function eigen which provides the eigenvalues and eigenvectors of T. The Herglotz waves are computed thanks to the function HerglotzWave available in the µ-diff directory related to the examples. Finally, running the script DORT Impenetrable. m generates a DORT experiment. An example is given on figures 4(a)-4(d). We consider a medium with three penetrable circular scatterers, with centers [0, 20],  [10, -10] , [-10, -20] and respective radius 0. 02, 0. 01, 0. 005. The wavenumber is equal to k = 2π. As shown on figure 4(a), the time reversal matrix T has three significant eigenvalues. We report on figures 4(b)-4(d) the amplitude of the Herglotz wavefunctions associated with the three largest eigenvalues.
Conclusion This paper presented a new flexible, efficient and robust Matlab toolbox called µ-diff 2. This open source code is based on the theory of integral representations for solving two-dimensional multiple scattering problems by many circular cylinders. The spectral approximation method uses Fourier series expansion and efficient linear algebra algorithms in conjunction with optimized memory Eigenvalue label Amplitude of the eigenvalue (log scale)     storage techniques for solving the finite-dimensional approximate integral formulations. Pre-and post-processing facilities are included in µ-diff (near-and far-fields representations, surface fields). All the features are described with enough details so that the user can directly solve complex problems related to physics or engineering applications.
OpenMOLE is a scientific workflow engine with a strong emphasis on workload distribution. Workflows are designed using a high level Domain Specific Language (DSL) built on top of Scala. It exposes natural parallelism constructs to easily delegate the workload resulting from a workflow to a wide range of distributed computing environments. In this work, we briefly expose the strong assets of OpenMOLE and demonstrate its efficiency at exploring the parameter set of an agent simulation model. We perform a multi-objective optimisation on this model using computationally expensive Genetic Algorithms (GA). OpenMOLE hides the complexity of designing such an experiment thanks to its DSL, and transparently distributes the optimisation process. The example shows how an initialisation of the GA with a population of 200,000 individuals can be evaluated in one hour on the European Grid Infrastructure.
They are perfect candidates for distributed computing platforms. In an ideal world, the time required to process the whole DoE would be almost equivalent to the execution time of a single experiment. However the methodological and technical costs of using distributed execution environments imply that most parameter space explorations are achieved either on a single desktop computer and occasionally on a multi-core server with shared memory. Larger scale platforms are rarely used, although clusters or worldwide computing infrastructures like EGI (European Grid Initiative) are well suited for this kind of applications. Compared to other workflow processing engines, OpenMOLE promotes a zero-deployment approach by accessing the computing environments from bare metal, and copies on-the-fly any software component required for a reliable remote execution.
OpenMOLE also encourages the use of software components developed in heterogeneous programming languages and enables users to easily replace the elements involved in the workflow. Workflows can be designed using either a Graphical User Interface (GUI), or a Domain Specific Language (DSL) which exposes advanced workflow design constructs. Apart from these core elements of the platform, OpenMOLE ships with its own software ecosystem. It contains among others GridScale a , a library to access a wide range of computing environment, and Yapa b , a packaging tool ensuring the successful re-execution of applications across heterogeneous platforms. For more details regarding the core implementation and features of OpenMOLE, interested readers can refer to  [Reuillon et al. , 2010 , Reuillon et al.
, 2013]  and the OpenMOLE website  [Reuillon et al. , 2015]. OpenMOLE focuses on making distributed computing available in the most straightforward way to the scientific community. Depending on the applications, several problems might arise when attempting to distribute the execution. Software tools can help scientists overcome these barriers. This paper describes the input of OpenMOLE and its software ecosystem to the distribution of complex scientific applications to remote execution environments. We first detail the problems faced by the scientific community to effectively distribute an application. Then, we present how the tools from the OpenMOLE ecosystem can answer these problems. The last section presents a test case showing how an actual simulation application was successfully distributed using OpenMOLE.
What is OpenMOLE? OpenMOLE is a scientific workflow engine with facilities to delegate its workload to a wide range of distributed computing environments. It shows several main advantages with respect to the other workflow management tools available. First, OpenMOLE distinguishes as a tool that does not target a specific scientific community, but offers generic tools to explore large parameter sets. Second, OpenMOLE features a Domain Specific Language (DSL) to describe the workflows. According to  [Barker and Van Hemert, 2008] , workflow platforms should not introduce new languages but rely on established ones. OpenMOLE s DSL is based on the high level Scala programming language  [Odersky et al. , 2004]. In addition to the DSL, a web interface is currently under development, and will permit expressing workflows graphically.
Finally, OpenMOLE features a great range of platforms to distribute the execution of workflows, thanks to the underlying GridScale library c. GridScale is part of the OpenMOLE ecosystem and acts as one of its foundation layers. It is responsible for accessing the different execution environments. The last release of OpenMOLE can target SSH servers, multiple cluster managers and computing grids ruled by the gLite/EMI middleware. In this section, we describe two main components of the OpenMOLE platform: the Domain Specific Language and the distributed environments. They contribute to make the exploration of a parameter set simple to distribute.
A DSL to describe workflows Scientific experiments are characterised by their ability to be reproduced. This implies capturing all the processing stages leading to the result. Many execution platforms introduce the notion of workflow to do so  [Barker and Van Hemert, 2008, Mikut et al. , 2013]. Likewise, OpenMOLE manipulates workflows and distribute their execution across various computing environments. A workflow is a set of tasks linked with each other through transitions. From a high level point of view, tasks comprise inputs, outputs and optional default values. Tasks describe what OpenMOLE should execute and delegate to remote environments. They embed the actual applications to study. Depending on the kind of program (binary executable, Java. ) to embed in OpenMOLE, the user chooses the corresponding task.
Tasks execution depends on inputs variables, which are provided by the dataflow. Each task produces outputs returned to the dataflow and transmitted to the input of consecutive tasks. OpenMOLE c https://github. com/openmole/gridscale exposes several facilities to inject data in the dataflow (sources) and extract useful results at the end of the experiment (hooks). Two choices are available when it comes to describe a workflow in Open-MOLE: the Graphical User Interface (GUI) and the Domain Specific Language (DSL). Both strategies result in identical workflows. They can be shared by users as a way to reproduce their execution. OpenMOLE s DSL is based upon the Scala programming language, and embeds new operators to manage the construction and execution of the workflow. The advantage of this approach lies in the fact that workflows can exist even outside the OpenMOLE environment.
As a high-level language, the DSL can be assimilated to an algorithm described in pseudocode, understandable by most scientists. Moreover, it denotes all the types and data used within the workflow, as well as their origin. This reinforces the capacity to reproduce workflow execution both within the OpenMOLE platform or using another tool. The philosophy of OpenMOLE is test small (on your computer) and scale for free (on remote distributed computing environments). The DSL supports all the Scala constructs and provides additional operators and classes especially designed to compose workflows. OpenMOLE workflows expose explicit parallel aspects of the workload that can be delegated to distributed computing environments in a transparent manner. The next sections introduces the available computing environments.
This is the approach championed by tools like CDE  [Guo, 2012]  or CARE  [Janin et al. , 2014]. Considering all these aspects, the OpenMOLE platform has for long chosen to couple with tools providing standalone packages. While CDE was the initial choice, recent requirements in the OpenMOLE user community have led the development team to switch to the more flexible CARE. The next section will detail how OpenMOLE relies on CARE to package applications.
Combining OpenMOLE with CARE The first step towards spreading the workload across heterogeneous computing elements is to make the studied application executable on the greatest number of environments. We have seen previously that this could be difficult with the entanglement of complex software environments available nowadays. For instance, a Python script will run only in a particular version of the interpreter and may also make use of binary dependencies. The best solution to make sure the execution will run as seamlessly on a remote host as it does on the desktop machine of the scientist is to track all the dependencies of the application and ship them with it on the execution site. OpenMOLE used to provide this feature through a third-party tool called CDE (Code, Data, and Environment packaging)  [Guo, 2012].