dataesr/scientific-paragraphs-categorization huggingface dataset:
How Does Latency Affect the Application Performance? First, we try to understand the impact of the data location on the application performance. While storage resources are co-located with Spark tasks under the data-centric paradigm (i. e. , when using Spark with HDFS), Spark tasks need to communicate with the parallel file system either to fetch the input data or to write the output data under the compute-centric paradigm (i. e. , when Spark is using PVFS as the storage space). This remote data access results in a higher latency compared to the data-centric paradigm which leverages data locality (i. e. , executing tasks on the machines where the input data resides). Figure  2  shows how latency can affect the application performance. Note that, intermediate data is stored locally on the aforementioned settings for Spark in order to focus on the latency resulting from reading the input data in map phase.
For the Sort workload, the amount of the output data is equal to the input data thus it suffers from a higher latency in the reduce phase as data is written to the parallel file system. As a result, having a higher latency on both input and output phases led to higher performance degradation for the compute-centric paradigm. Lastly, we ran the PageRank workload in both settings for Spark and Fig. 2(c ) shows the results. Here, performance degradation with the compute-centric paradigm is only 26%. The reason behind this is that I/O phases of the PageRank workload (i. e. , Stage 0 and Stage 5 (denoted as S0 and S5)) accounts for a small fraction of PageRank execution time and Spark computes the iterations (i. e. , Stage 1, 2, 3 and 4) locally. The Impact of the Input Data Sizes. We also investigated the impact of the input data size on the application performance.
4  and 5. Interestingly, Fig. 4 (a) shows that some map task durations are smaller for the compute-centric paradigm compared to the data-centric one. This is due to the fact that Spark employs delay scheduling  [35]  to increase the chances of a map task to be launched locally for the data-centric paradigm. This delay while launching the map tasks, which results in a performance degradation for the jobs with small input data sizes, is due to the default Spark configuration for the maximum waiting time (i. e. , 3 s) in scheduling the map tasks. This is only valid for the data-centric paradigm since there is no data locality objective when scheduling the tasks in the compute-centric paradigm where all the machines have an equivalent distance to the parallel file system. On the other hand, we observe an increase in the map task durations with larger input sizes for the compute-centric paradigm.
This results from the higher latency while fetching the input data from parallel file system with larger input sizes. Another interesting trend we observe is that the maximum map task duration also increases with the increasing data sizes, especially with 200 GB input data size in Fig. 4(c ). We believe that this behavior is due to the higher contention with the increased number of concurrent map tasks. It is important to note that there are 33, 594 and 800 concurrent map tasks with 2 GB, 20 GB and 200 GB input sizes. Moreover, we see that this increase is much higher with the compute-centric paradigm which can highlight the severity of the contention problem for this paradigm. We will further explain the impact of the contention on the application performance in Sect. 3. 2. In Fig. 5 , we observe a similar trend for the reduce task durations for the compute-centric paradigm.
With larger data sizes, we observe an increase in those durations too. This again stems from an increased amount of the remote data transfer while writing the reducer outputs to the parallel file system. Moreover, we discover that there is a high performance variability in the reduce phase and the maximum task duration is quite high even with 2 GB data size. This is due to the static Spark configuration which employs 800 reducers regardless of the input data size. These high number of reducers overload the parallel file system and results in this performance variability. Hence, we do not see the impact of latency in Fig. 3  for the reduce phase. However, when the output data size is large enough as shown for the Sort workload in the previous experiment (Fig. 2(b )), the impact of the I/O latency is quite clear as it results in a significant performance degradation.
Acknowledgment. This work is supported by the  ANR   KerStream  project ( ANR-16-CE25-0014-01 ). The experiments presented in this paper were carried out using the Grid' 5000/ALADDIN-G5K  experimental testbed, an initiative from the  French Ministry of Research  through the  ACI GRID incentive action ,  INRIA ,  CNRS  and  RENATER  and other contributing partners (see http://www. grid5000. fr/for details).
(2015) , and  Carrassi et al. (2017) , with however less emphasis than here on their performance as probabilistic estimators. A close comparison with these works would certainly be very instructive. If a code for variational assimilation is available, EnsVAR is very easy (if costly) to implement. It possesses the advantages and disadvantages of standard variational assimilation. The advantages are the easy propagation of information both forward and backward in time (smoothing) and easy introduction of observations of new types and of temporal correlations between data errors. What is usually considered to be a major disadvantage of variational assimilation is the need for developing and maintaining an adjoint code. Concerning that point, it must however be stressed that algorithms are being developed which might avoid the need for adjoints while keeping most of the advantages of variational assimilation.
Acknowledgements. This work has been supported by  Agence Nationale de la Recherche, France , through the  Prevassemble and Geo-Fluids projects , as well as by the programme Les enveloppes fluides et l'environnement of  Institut national des sciences de l'Univers, Centre national de la recherche scientifique, Paris. The authors acknowledge fruitful discussions with  Julien Brajard  and  Marc Bocquet. The latter also acted as a referee along with  Massimo Bonavita. Both  of them made further suggestions which significantly improved the paper. Edited by: Alberto Carrassi Reviewed by:  Marc Bocquet  and  Massimo Bonavita.
This contribution aims at providing a formal construct for the verification of refinement in time models, through the definition of an order between strict partial orders used to relate the different instants in asynchronous systems. This relation allows the designer at the concrete level to distinguish events that are coincident at the abstract level while preserving the properties assessed at the abstract level. This work has been conducted using the proof assistant Agda and is connected to a previous work on the asynchronous language CCSL, which has also been modelled using the same tool.
Horizontal separation is usually handled at design time through the expression of the various system parts in different Domain Specific Modelling Languages (DSML). Their execution, for validation and verification purposes, may rely on different Models of Computation (MOC). A sophisticated coordination of the various events occurring in the different parts is thus needed to observe the global behavior of the system. For CPS, the modeling of time in the various DSML and the coordination between the different time models is a major issue. This heterogenous modelling approach has been integrated in the Ptolemy toolset proposed by Lee et al. [11] , the ModHel'X toolset proposed by Boulanger et al. [20]  and the GEMOC studio proposed by Combemale et al. [12]. Our work targets a proof based formal modeling and verification framework to prove properties of languages and models in such toolsets.
Context Our work focuses on the modeling of time in GEMOC that mixes both horizontal and vertical separation of concerns. Indeed, GEMOC allows to define the DSML used to model the various parts in a CPS in each phase of their development. Thus, DSML are combined both in an horizontal and vertical manners. GEMOC relies on the UML MARTE CCSL (Clock Constraint Specific Language) to model both the MOC for the various DSML  [13, 15, 25]  and the coordination between DSML using the Behavioral Coordination Language (BECOOL)  [24]. Our work in GEMOC targeted an example of horizontal separation. This contribution targets the vertical separation. More precisely, we want to assess the relations between the various time concerns in the various models of the same system part in a vertical separation of concerns.
This relation can be integrated with any other concurrent languages. Formal mechanization of time models has already been done using other formal methods, for example  [19]  uses Higher Order Logic in Isabelle/HOL;  [17]  and  [34]  use the Calculus of Inductive Constructions in Coq, see  [8]. The use of Agda in this development is motivated by the expressiveness of the language and its underlying unification mechanism, which provides an efficient interactive proof experience that other tools might lack. More on Agda can be found in  [33] ,  [28]  and  [9]. Although Agda differs from Coq by several aspects, both of these tools rely on the same underlying intuitionist type theory, first described in  [30]  and clarified in  [31]. The paper version of CCSL denotational semantics, which is connected to this work, can be found in  [14].
Agda Agda is a dependently typed programming language developed by Ulf Norell at Chalmers University. As any other language, the types of which can depend on values, it is expressive enough to build mathematical theories, thanks to the Curry-Howard isomorphism, which ensures the correctness of any property whose equivalent type is inhabited. The core of the language is an intuitionist type theory, on which the well-known tool Coq is based as well. Although these two languages share the same heart, they are quite different when it comes to developing and proving properties. Coq uses named tactics, the action of which is hidden from the reader of the Coq file -as well as the underlying lambda-terms -while 1 http://montin. perso. enseeiht. fr Agda provides a framework to help the programmer write them by hand, thus making them visible in the Agda file.
This framework is what makes programming in Agda possible since typed lambda terms are arguably impossible to write without software assistance, assuming their type reaches a certain level of complexity. Agda also differs from Coq by its native unification mechanism, which is usually summarized by "Agda allows to pattern-match on equality proofs". Although unification can hardly be reduced to this simple sentence, Agda indeed allows to case-split on the equality proofs, thus unifying the operands of the equality. More generally, Agda is able to infer, by unification, the value of variables present in the context of a proof. Coq does not provide such a straight-forward mechanism and handles cases usually solved by unification in Agda with other ways that we find less convenient. The rest of this paper contains small pieces of Agda code, depicting either data structures, predicates or proofs established during our development.
Inspired by the specifications of a commercial Fresnel lens, simulations based on refractive surfaces generated by script are reported for the first time and preliminary comparisons between experimental and simulated irradiance spots are provided. Subsequently, a 3D analytic heat transfer model, based on the thermal quadrupole method, is introduced. A 2D time-resolved CPV temperature map can be computed from the combination of the absorbed flux map obtained from Tonatiuh and the thermal quadrupole model. In Section 3, simulation results are presented for a typical configuration of a CPV module, i. e. , a Fresnel lens to concentrate the solar radiation onto a CPV cell coupled to a passive heat sink. A parametric study is presented, revealing the best set of parameters for design optimization in order to keep operation temperatures within safe conditions.
On the other hand, Fresnel lens ray tracing implementation by means of the Tonatiuh open source software is reported for the first time. This is relevant as Fresnel lenses are extensively employed in CPV systems. A preliminary comparison between a real lens spot and the spot generated by script is discussed, indicating directions for more in-depth studies. However, this work's focus is on the thermal quadrupole model, its capabilities, and the advantages it brings in combination with the Tonatiuh open source ray tracing software.
Locations, Instruments, Software and Methodology Table  2  summarizes the resources employed for this work studies. The main purpose of this research is the development of analytic tools for CPV system thermal analysis resolved in space and time. The thermal model requires input stimuli, which is provided by a custom script representing Fresnel lens through Tonatiuh software, and delivering irradiance maps resolved in time and space; and inspired by real irradiance data and a real Fresnel lens. In order to accomplish the above-mentioned objectives, a methodology has been implemented: (1) First, a Fresnel Lens model has been implemented by script, based on the software Tonatiuh (Sections 2. 2 and 2. 2. 1). (2) Design parameters from a commercial lens (aperture, transmissivity and prism pitch) have been introduced to the Tonatiuh model.
2. 3). (7)  The irradiance data set is then introduced to the thermal quadrupole model described in Section 2. 3. Temperature maps for three solar cells with different sizes are computed and a parametric study is executed (Section 3. 2. 1), it allows scaling the concentration ratio and preserving the operation temperature within safe ranges. (8) Finally, the possibilities of this work approach concerning the assessment of thermal gradients induced by fast tracking point perturbations are discussed in Section 3. 2. 3. This work has been executed at two locations: CIO (Aguascalientes, Mexico) for the Fresnel Lens Experiments and CICY (Mérida, México) for the Tonatiuh implementation of a Fresnel lens and the thermal quadrupoles method. The following subsections describe thoroughly the methodology employed for this research.
Irradiance Map Definition Tonatiuh is an open-source ray tracing software based on Monte Carlo analysis with an extended library of geometrical surfaces  [30, 32, 33] , allowing custom modification of available topologies and script-based design of new ones. Tonatiuh delivers irradiance flux map simulations upon custom receiver surfaces for any hour, calendar day and worldwide location; providing valuable information for designing concentrated solar power (CSP) systems, including concentrator optical properties and solar tracking systems. Unfortunately, Tonatiuh does not provide any library nor support for refraction-based optical elements, like Fresnel lenses.
Nevertheless, as stated by Hornung and Nitz  [36] , diffraction losses are less than 1% for Fresnel lenses with pitches greater than 0. 3 mm; a condition which is often met for non-imaging Fresnel lenses designed for solar concentration. Accordingly, diffraction losses at simulation stage are negligible, so ignored in this work. The script model for the Fresnel lens has been inspired by commercial lens specifications. A summary of parameters of the real lens is shown in Table  3. Transmissivity, active area and pitch from the real lens were introduced into the Tonatiuh model. Then, the prism angles have been adjusted to deliver the same focal length as in manufacturer specifications, which is f = 22 cm. Next section describes the experimental design for the real lens irradiance maps measurements.
Accordingly, diffraction losses at simulation stage are negligible, so ignored in this work. The script model for the Fresnel lens has been inspired by commercial lens specifications. A summary of parameters of the real lens is shown in Table  3. Transmissivity, active area and pitch from the real lens were introduced into the Tonatiuh model. Then, the prism angles have been adjusted to deliver the same focal length as in manufacturer specifications, which is f = 22 cm. Next section describes the experimental design for the real lens irradiance maps measurements. An experimental design (shown in Figure  2 ) was conceived to compare the synthetic spot obtained with Tonatiuh, with the spot obtained by the commercial lens that inspired the script model. This design provides mechanical support for a rectangular Fresnel lenses and includes a manual solar tracking structure to ensure that the sun's rays strike perpendicular to the plane of the Fresnel lens.
In addition, an Allied Vision Technologies MAKO camera was positioned to image the receiver surface. An experimental design (shown in Figure  2 ) was conceived to compare the synthetic spot obtained with Tonatiuh, with the spot obtained by the commercial lens that inspired the script model. This design provides mechanical support for a rectangular Fresnel lenses and includes a manual solar tracking structure to ensure that the sun's rays strike perpendicular to the plane of the Fresnel lens. In addition, an Allied Vision Technologies MAKO camera was positioned to image the receiver surface. Local Direct Normal Irradiance (DNI) data was obtained from a scientific grade solarimetric station (Solys2 + SHP1 pyrheliometer, Kipp & Zonen, Delft, The Netherlands) located at the CIO Research Institute (Aguascalientes, México).
5 cm below the Fresnel lens focal plane, as previously mentioned (see Figure  2. Inset, bottom-right), at the center of the spot. The Gardon active area, a circle with a 1 cm diameter, generates a signal proportional to the integral of irradiance flux upon the active area. This mean flux measurement provides the calibration data for the spatially resolved flux acquired with the MAKO camera (Allied Vision, Exton, PA, USA). Indeed, the Gardon sensor delivers a signal proportional to the absorbed heat flux upon the sensor surface and measures the irradiant flux; thus obtaining the Fresnel lens optical concentration after radiation absorption, reflection and diffraction losses. The Gardon sensor was calibrated in accordance to the ISO 14934-3 Local Direct Normal Irradiance (DNI) data was obtained from a scientific grade solarimetric station (Solys2 + SHP1 pyrheliometer, Kipp & Zonen, Delft, The Netherlands) located at the CIO Research Institute (Aguascalientes, México).
5 cm below the Fresnel lens focal plane, as previously mentioned (see Figure  2. Inset, bottom-right), at the center of the spot. The Gardon active area, a circle with a 1 cm diameter, generates a signal proportional to the integral of irradiance flux upon the active area. This mean flux measurement provides the calibration data for the spatially resolved flux acquired with the MAKO camera (Allied Vision, Exton, PA, USA). Indeed, the Gardon sensor delivers a signal proportional to the absorbed heat flux upon the sensor surface and measures the irradiant flux; thus obtaining the Fresnel lens optical concentration after radiation absorption, reflection and diffraction losses. The Gardon sensor was calibrated in accordance to the ISO 14934-3 standard. Afterwards, the Gardon sensor was exchanged for a flat receiver covered in a Lambertian paint.
An image of the spot generated upon the Lambertian receiver surface was then acquired by means of the MAKO camera, to gather the spatial flux distribution with the CCD matrix. Indeed, as receiver surface, CCD pixel size and magnification, and Gardon sensor surface are all known, incident fluxes can be obtained. This procedure allowed the estimation of receiver surface incident flux with spatial resolution, providing an experimental flux map. A mean DNI experimental dataset was also introduced into the Tonatiuh Fresnel lens model in order to compare model results with measured fluxes acquired by the MAKO camera.
Combining Flux Maps Modeled through Tonatiuh with Synthetic Ambient Irradiance Series Tonatiuh can mimic direct solar irradiance evolution through daytime variation of zenith and azimuthal angles. Such a spatial distribution (Figure  3a ) depends on the Fresnel lens geometry, focal point, aperture and DNI incidence angle. However, Tonatiuh does not represent the unpredictable amplitude variation due to atmospheric absorption, refraction and cloud shading. To overcome this limitation, a synthetic, time-resolved DNI profile is generated by combining flux maps modeled through Tonatiuh, with a set of experimental irradiance data for the highest irradiance record available (Aguascalientes, Mexico, July 2015, Figure  3b ), throughout full daytime, with a sampling period of 60 s; in order to provide a synthetic flux dataset very close to real conditions.
Such a spatial distribution (Figure  3a ) depends on the Fresnel lens geometry, focal point, aperture and DNI incidence angle. However, Tonatiuh does not represent the unpredictable amplitude variation due to atmospheric absorption, refraction and cloud shading. To overcome this limitation, a synthetic, time-resolved DNI profile is generated by combining flux maps modeled through Tonatiuh, with a set of experimental irradiance data for the highest irradiance record available (Aguascalientes, Mexico, July 2015, Figure  3b ), throughout full daytime, with a sampling period of 60 s; in order to provide a synthetic flux dataset very close to real conditions. The irradiance time series of Figure  3b  appears clipped at 9:00 and 17:00 to simulate a hypothetical, angular dynamic range limitation of the tracking system.
Discussion Script-based Fresnel lenses simulations for concentration photovoltaics were proposed. They allow the use of Tonatiuh ray tracing open source software to represent refraction objects, and obtain synthetic receiver flux maps for any worldwide date, hour and latitude. Characteristics of a commercial Fresnel lens have been introduced to the Tonatiuh script, and experimental and simulated flux distributions were compared. It should be pinpointed that commercial lens is employed in order to inspire the script-based Fresnel lens model. For design purposes, the script-based lens was employed, as its design was inspired in the real lens, and it provides a synthetic irradiance spot similar to the real one. Additionally, it provided the maximum theoretical flux, and consequently, the highest foreseen operation temperatures.
Conclusions and Perspectives The thermal quadrupole model, in association with ray tracing analysis software Tonatiuh, applied to transient temperature maps, resolved in time and space was reported for the first time. Such an approach, by its analytic essence, is suitable for CPV engineering, including parametric studies, design optimization, and reliability studies. Additionally, the so-performed studies are executed in less computing time, as short as 9 s for a full month of simulated operation, with a generic laptop computer. Nowadays these tasks are accomplished with FEM tools, which are undeniably useful and mandatory when systems structures are geometrically complex and show non-linearities. Accordingly, the claim is not replacing FEM, but rather complement it, by providing them with narrowed ranges for design parameter optimization, when working with CPV designs whose complexity cannot be properly represented by thermal quadrupole models.