dataesr/scientific-paragraphs-categorization huggingface dataset:
, 2008). Utilizing multimodal Utterance Representation Markup Language, gesture expressions inside the Articulated Communicator Engine (ACE) framework may be defined in two distinct ways  (Salem et al. , 2012). A gesture's exterior representation, such as the posture of the gesture stroke, can be clearly articulated in verbal words and co-verbal gestures, which are classified as feature-based explanations  (Gozzi et al. , 2022). By correlating temporal markers, gesture association to certain language pieces is discovered. Secondly, gestures may be defined as keyframe animation, where each keyframe defines a "key posture, " a component of the general gesture motion that describes the condition of each joint at that particular moment. Assigned time IDs are used to gather speed data for the interpolation between every two key postures and the related association to portions of speech.
Chae et al. (2022)  developed a methodology that enables robots to generate co-speech gestures automatically, based on a morphemic analysis of the sentence of utterance. After determining the expression unit and the corresponding gesture type, a database of motion primitives is used to retrieve an appropriate gesture that conveys the robot's thoughts and feelings. The method showed promising results, with 83% accuracy in determining expression units and gesture types, and positive feedback from a user study with a humanoid robot.
Unlike traditional, single-viewpoint methods, the SDM solves the ambiguity based on observations only, without any assumption about the magnetic field. Paper I also used numerically simulated vector magnetograms to show that the SDM can remove the ambiguity with great accuracy over a large range of stereoscopic angles. In this article we present the very first application of the SDM to real observations. We use co-temporal observations from the SO/PHI High Resolution Telescope (SO/PHI-HRT;  Gandorfer et al. 2018 ) and from the Helioseismic and Magnetic Imager (HMI;  Scherrer et al. 2012; Schou et al. 2012 ) on board the Solar Dynamics Observatory (SDO;  Pesnell et al. 2012). The SDM and its application are described in Sect. 2. In Sect. 3  we provide details of the data sets used in the presented tests, both from SO/PHI-HRT and from two distinct SDO/HMIdata product series.
SDM: Application to observations Equations (  5 ) and (  6 ) can be applied in several ways to data from SO/PHI-HRT and SDO/HMI. First, one can disambiguate A magnetograms using information from B (the "direct" case of Sect 3. 3. 1 in Paper I), or vice versa (the "reverse" case). Second, the sign ζ of the transverse component can be determined by either Eq. (  5 ) or Eq. (  6 ), or a combination of the two (see Sect. 3. 3. 2 in Paper I in particular). Finally, different SDO/HMI data series can be used as input for the SDM. In this paper we consider the disambiguation of the SO/PHI-HRT data set using two different SDO/HMI series (Sect. 3. 2). In the terminology of Paper I, this case corresponds to the reverse application of the SDM with the associations A = SO/PHI-HRT and B = SDO/HMI. In this first application we do not consider disambiguation of SDO/HMI using SO/PHI-HRT because of the unfavorable position of the target active region (AR) on the solar disk (see Sect.
SDM: Numerical implementation In order to use Eqs. (  5 ) and (  6 ) in real applications, the observed vector magnetic field from each telescope must be first transformed from the image plane to the corresponding SDM reference system. In this section we provide an example of the SDM workflow for the reverse applications presented in the following sections. The SDM software is developed using the Solar-Soft suite of programs  (Freeland & Handy 2012). The following steps are performed to apply the SDM to a given SO/PHI-HRT data set: SDO/HMI data selection  (1). The SDO/HMI magnetogram should be chosen as the one closest in time to the considered SO/PHI-HRT observation. However, due to the generally smaller distance of Solar Orbiter from the Sun, the difference in light travel-time between Solar Orbiter and SDO must be considered.
Hence, the selected SDO/HMI data set is chosen as the closest in time (as specified by the T_OBS FITS keyword; see  Couvidat et al. 2016)  to the time at which the light measured by SO/PHI-HRT would have reached Earth. The latter is readily provided by the FITS keyword DATE_EAR in the FITS header of the SO/PHI-HRT data set. No further time adjustments is considered at this stage. Image co-registration (2). This step is crucial for the application of the SDM, which intrinsically requires the alignment between images to have subpixel accuracy. Currently, the World Coordinate System (WCS;  Thompson 2006 ) keywords in SO/PHI-HRT do not match the SDO/HMI ones to such a degree of accuracy; therefore, a co-registration step is unavoidable. The co-registration is performed using the field strength as comparison when possible, which is ideally independent of the viewing angle, unless only B los is available (as in Sect.
5). The SDO/HMI image is first remapped onto the SO/PHI-HRT detector frame, then a sub-domain of co-registration is chosen. The remapping includes the (bi-linear) interpolation of the SDO/HMI image onto the SO/PHI-HRT uniform grid. The coregistration technique is a simple but fast and accurate Fourier matching technique that provides the co-registration shifts to apply to the SO/PHI-HRT reference pixel identified by the WCS keywords CRPIX1 and CRPIX2. The remapping/co-registration steps are repeated, each time using the newly updated SO/PHI-HRT WCS keywords, until convergence is reached to the desired precision (to better than 1/100th of a pixel, in the application here). We verified that, for the SO/PHI-HRT data set considered here, the correction to the WCS keyword CROTA, representing the rotation angle of the detector with respect to solar north, is negligible.
The co-registration procedure is in principle independent of the sub-domain where the SDM is applied, although here we use the same field of view (FoV) for both. Remapping of the SDO/HMI Cartesian magnetic field components on the SO/PHI-HRT detector frame (3). This step uses the co-registered SO/PHI-HRT WCS information as updated in step 2. The remapping entails a (bi-linear) interpolation of the SDO/HMI magnetogram (upscaling SDO/HMI to the SO/PHI-HRT resolution in the cases presented here). Computation of the separation angle, γ, and the SDM rotation angles θ A and θ B (4). These angles are directly computed from the observer Carrington coordinates as included in the FITS headers of the considered SO/PHI-HRT and SDO/HMI data set. Re-projection of the SO/PHI-HRT and SDO/HMI vector magnetic fields on the SDM reference systems, S A and S B respectively (5).
(2022). The above constitutes the currently standard version of the SO/PHI-HRT pipeline, and no additional processing was applied to the data. In particular, the employed data have not been reconstructed and aberration-corrected, as described by  Kahil et al. (2023;  see our Sect. 6. 1 for further details). In addition to the disambiguation using the SDM, we also performed a disambiguation of the same data set using a classical method that, unlike the SDM, only uses data from a single telescope. The disambiguation that we applied, hereafter ME0, is an adaptation of the disambiguation code in the SDO/HMI pipeline  (Hoeksema et al. 2014) , which, in turn, implements the "minimal energy method"  (Metcalf 1994; Metcalf et al. 2006 ). The parameters used for the ME0 disambiguation are similar to those used in the HMI pipeline, and no particular attempt was made to optimize them.
Acknowledgements. We wish to thank the referee for their competent and constructive comments that helped us improve the article. The authors thank  Marco Stangalini  for providing the co-registration routine,  Bill Thompson  for the development of the WCS routines that are part of the SolarSoft analysis package, and  Pradeep Chitta  for his insightful comments. E. P. acknowledges financial support from the  French national space agency (CNES)  through the  APR program. E. P. was also supported by the  French Programme National PNST of CNRS/INSU  co-funded by  CNES  and  CEA. Solar Orbiter is a space mission of international collaboration between  ESA  and  NASA , operated by  ESA. We are grateful to the  ESA SOC  and MOC teams for their support. The German contribution to SO/PHI is funded by the  BMWi  through DLR and by  MPG  central funds.
The Spanish contribution is funded by  AEI/MCIN/10. 13039/501100011033/  and  European Union  " NextGenerationEU/PRTR " ( RTI2018-096886-C5 ,  PID2021-125325OB-C5 ,  PCI2022-135009-2 , PCI2022-135029-2 ) and  ERDF "A way of making Europe "; " Center of Excellence Severo Ochoa " awards to  IAA-CSIC  ( SEV-2017-0709 ,  CEX2021-001131-S ); and a  Ramón y Cajal fellowship  awarded to DOS. The French contribution is funded by  CNES. The HMI data are courtesy of  NASA/SDO  and the  HMI science  team.
Therefore, a simulation of the fast transients in the system can be very useful to understand the consequences of such phenomena. In this context, this document aims to propose a model of high voltage capacitive graded oil impregnated paper (OIP) bushing based on a distributed electrical circuit. The equivalent circuit is constructed based on the geometric design and electrical properties of the materials. The model was developed and implemented using Matlab/Simulink® software, and was validated with experimental measurements based on impedance sweep frequency analysis. The modeling results are in a good agreement with the experimental ones.
B. MEASUREMENT PROTOCOL For accurate measurements, an experimental protocol of several steps was followed: 1) Adjustment and configuration of the impedance analyzer by choosing the number of data to be collected (in our case, the choice was made on 801 points. ), initial and final frequency of the Sweep as well as the logarithmic display scale. 2) A calibration process is carried out (open circuit, short circuit, and load) for each measurement configuration due to the length of the wires which changes for each test. 3) Verification of the calibration quality with the minimum loss resistor of 25 Ω. 4) Make the connection on the bushing and start the measurement of the impedance spectrum and save the data. 6) Repeat the same steps for each measurement configuration shown in Figure  1. It should be noted that the maximum studied frequency is 20 MHz.
III. BUSHING MODELING In this work, a distributed electric circuit method is used because of its simplicity, and its proved applicability for modeling several electrical systems such as power transformers  [24] , transmission lines  [30] , etc. In this section, the analytical equations allowing the calculation of R, L and C elements of the equivalent circuit will be presented and validated by finite element simulation on COMSOL Multiphysics®. The simulation aims to identify in which frequency range the analytical equations are valid. The equivalent circuit is implemented on Matlab/Simulink® and will be subjected to impedance analysis tests to extract its signature, which will be compared with the results of the experimental study.
V. CONCLUSION The aim of this work is to develop a model of high voltage bushings capable to simulate the bushing behavior till 20 MHz. This model will make it possible to study the behavior of bushings under fast and very fast transient overvoltages. To model such a system, the equivalent electrical circuit approach has been adopted. This approach of modeling has the advantage of reduced computing time and it provides access to the electrical quantities in each part of the bushing. To determine each element of the equivalent circuit, analytical formulas have been used. A numerical simulation by COMSOL Multiphysics® has been also carried out in this work in order to check the validity of these equations over the studied frequency range. The calculation of the model parameters as well as the modeling itself have been executed on Matlab/Simulink®.
SimGrid  [8]  is a framework that allows the development of simulators to be used for prototyping, evaluating, and comparing system designs, platform configurations, and algorithmic approaches. On top of this framework, Batsim  [29]  was developed as a resource and job management system (RJMS) simulator. Scheduling algorithms are used for several reasons, such as to minimize function response time, to save costs, and to reduce data movements or energy consumption. Shmoys and Tardos developed a dual-approximation algorithm  [30]  to assign independent tasks to unrelated machines and bound their approximation to, at most, the cost and twice the makespan of the optimal solution. It uses a linear program to get an assignment of tasks to machines, but its solutions are not necessarily integral, and hence an integral matching is required.
The properties and existence of such a matching are detailed in depth by Plummer and Lovász  [31]. Inspired by the dual-approximation algorithm of Schmoys and Tardos, we propose our scheduling policy, called FOA, to assign independent serverless functions to heterogeneous serverless platforms at the edge-cloud continuum. Rausch et al. propose a container scheduling system called Skippy that enables serverless frameworks to support edge functions  [4]. They exploit Kubernetes standard scheduler to attach and tune weights to priority mechanisms that may lead to low function execution time, efficient resource usage, and reduced network traffic and costs. In addition, they leverage the container layer sharing mechanism by estimating a sharing percentage among their Python functions on their workload and using it during the scheduling phase.
Instead of creating containers with the basis that can be used by different functions that may arrive on the platform, our algorithm decides where to deploy a function knowing in advance which container is already available on the nodes. Aumala et al. proposed a scheduling policy based on the packages needed to execute a function  [33]. The packageaware scheduling proposed, PASch, considers the package affinity during scheduling. They map two affinity workers that cache the largest package required by the functions and choose the least loaded one. Similarly, we are concerned about function requirements locality. However, we deal with them at the container. We prioritize the machines with the required container available. Suresh and Gandhi used OpenWhisk to implement a scheduling policy, named FnSched, which focused on costs (resources) reduction  [34].
E. A Simulated Environment As illustrated in Figure  3 , Batsim receives as input a workload, a platform description, and connects to scheduling policy. During the simulation, the scheduling policy allocates each function from the workload to the machines described in the platform. When a function allocation decision is taken, Batsim communicates it to Simgrid, which will perform the actual simulation. Finally, to build the evaluated scheduling policies, we used a Python API layer on top of Batsim called PyBatsim.
For the experimental campaign, we adapt serverless functions from the FunctionBench benchmark. We deploy the OpenWhisk serverless platform on the academic cluster GRID5000 and then execute the adapted functions there. With that, we model our workloads, which are used in a simulated environment on top of the Batsim/SimGrid simulators. To study the impacts of the heterogeneity of the platforms, we model slight levels of heterogeneity on top of our serverless platform. Our experimental results show that standard cloud greedy algorithms, such as our baseline, may not profit from the best efficiency of heterogeneous serverless platforms at the edge. FOA, on the contrary, optimizes the placement of functions by its multi-objective policy. It outperforms our baseline for both data transfers and makespan criteria, in addition to the system utilization by up to two orders of magnitudes.
We remark that FOA is robust regarding the heterogeneity, and it is not affected by the different levels of heterogeneity studied, producing results with the same quality for all of them. However, FOA is very time-consuming. It is based on a linear program with several constraints, which is costly in terms of processing time. Our results showed a processing time in orders of minutes for FOA, while K8S ImageLocality performed in order of a second. We conclude that even with light levels of heterogeneity, the gains of FOA are important in serverless computing at the edge-cloud continuum, and we believe that with a more accurate model of heterogeneity, these gains may increase. By reducing the amount of data transferred to download containers, we minimize cold start delays through faster container deployments.
AUTHORS  CONTRIBUTION Modeling of serverless edge cloud platforms: DA SILVA ,  GEORGIOU , and MERCIER; Problem modeling: All authors; Design and implementation of algorithms (FOA): DA SILVA, ANGELELLI, MOUNI É, and TRYSTRAM; Design and implementation of algorithms (K8S ImageLocality): DA SILVA, MERCIER, and GEORGIOU; Design and execution of experiments: DA SILVA; Analysis and investigation: DA SILVA, MOUNI É, and TRYSTRAM; Writing: DA SILVA, MOUNI É, TRYSTRAM,  GEORGIOU , and MERCIER; Reproducible artifact: DA SILVA. All authors have read and agreed to the published version of the manuscript. ACKNOWLEDGMENTS This work was supported by the research program on Edge Intelligence of the  Multi-disciplinary Institute on Artificial Intelligence MIAI at Grenoble Alpes  ( ANR-19-P3IA-0003 ), and by the  European Union 's Project  H2020   PHYSICS  ( GA 101017047 ).
We illustrate FLOP capabilities on diverse datasets comprising samples from end-stage heart failure patients and cancer cell lines in both basal and drug-perturbed states. We found that the correlation between gene set enrichment analysis results can vary significantly for alternative pipelines. Additionally, we observed that not filtering the data had the highest impact on the correlation between pipelines in the gene set space, especially in settings with limited statistical power. Overall, our results underscore the impact of carefully evaluating the consequences of the choice of preprocessing methods on downstream enrichment analyses. We envision FLOP as a valuable tool to measure the robustness of functional analyses, ultimately leading to more reliable and conclusive biological findings.
The goal of DE analysis is to compare the normalised expression measurements between samples. Also in this step, there are multiple available methods, and three of them are commonly included in most pipelines: Limma  [16] , edgeR  [17]  and DESeq2  [18]. Limma requires a previous normalisation step and models gene expression as a linear function of variables that encode the experimental design. edgeR and DESeq2 directly model count-level data using parametric models that assume an underlying negative binomial distribution of the data. Such models are then used to perform the comparison between samples  [9, 19]. DE analyses output results for thousands of genes, making direct biological interpretation challenging. [20]. To reduce dimensionality and enhance interpretability of DE results, genes are usually grouped into functional categories.
We grouped the methods into three processing modules: (I) filtering, (II) normalisation and DE, and (III) functional analysis. We also created two evaluation modules (Figure  1 ). In the first module, the count matrix is either le intact or filtered using edgeR's function filterByExpr with user defined parameters. The second module takes the filtered or non-filtered count matrix as input and applies multiple combinations of normalisation and differential expression (DE) methods. We coupled TMM, vsn, log quantile normalisation and voom normalisation with limma, in addition to edgeR and DESeq2, which employ raw counts as input. This results in a total of 6 combinations of normalisation and differential expression analysis tools that coupled to the filtering module creates 12 alternative pipelines.
We unify the output of each individual pipeline in a single table, which contains at least an effect size estimate (e. g. log fold change), a statistical estimate (e. g. t-values) and a significance estimate (e. g. adjusted p-value) of gene expression changes. As recommended by Zyla et al. [36] , we use the statistical estimate as input for the functional analysis module. In the third module, we use the univariate linear model (ulm) method from the decoupleR package  [25] , along with three prior-knowledge sources storing different collections of gene sets: signalling pathway footprints (PROGENy,  [37] ), transcription factor targets (DoRothEA,  [38] ) and transcriptional hallmarks (MSigDB hallmarks,  [39] ). We chose the ulm method because it indicates at the same time the direction of the enrichment, positive or negative, and its significance in a single score, and also was observed to be stable and to outperform other methods in a previous benchmark  [25].
The number of features to compare is a user-defined parameter. To showcase the capabilities of FLOP, we applied it to datasets studying different biological contexts and with varying sample sizes. In the first case, we utilised datasets used for a recent meta-analysis, which focused on studying the transcriptomic profiles of patients with end-stage heart failure  [40]. We then applied FLOP to analyse a large transcriptomic dataset that evaluated the basal transcriptomic profiles of various types of cancer cell lines  [41]. Finally, we employed FLOP to analyse the recently published PANACEA DREAM challenge data, which explored the transcriptional response of 11 cell lines to 32 kinase inhibitors  [42].
Application of FLOP to end-stage heart failure transcriptomic studies We first applied FLOP to five transcriptomics datasets collected from the ReHeaT resource  [43] [44] [45] [46] [47] , a compendium of case-control bulk transcriptomics datasets of human heart failure profiling the le -ventricle of patients with dilated or ischemic cardiomyopathy and control myocardium from healthy donors. To exemplify the different data modalities generated and compared during FLOP execution, we focused on a single study (Spurrel et al. [44] ), a single contrast (heart failure versus control samples), and on the comparison of two specific pipelines: filtered counts analysed with DESEq2 versus unfiltered counts analysed with edgeR. As expected, the total number of genes and differentially expressed genes is higher in the pipeline on which the count matrix was not filtered.
Specifically, these low-expressed genes show a significant decrease in the t-value in the HALLMARK_IL6_JAK_STAT3_SIGNALING pathway (Supplementary Figure  1B ). This leads to a lower score for this pathway for the unfiltered+edger pipeline. We observed similar results when we evaluated different pipelines in the same dataset (Supplementary Figure  2 ) and when we employed a different dataset (Supplementary Figure  3 ). The aforementioned example describes one dataset, two pipelines, and one gene set collection. When we applied FLOP to the studies from the ReHeaT resource, we evaluated 5 different datasets, 12 alternative pipelines and 3 different gene set collections. This resulted in a total of 234 pipeline comparisons, each of them evaluated with the module 4 (Spearman correlation) and module 5 (top/bottom features overlap).