dataesr/scientific-paragraphs-categorization huggingface dataset:
Compliance in wearing the device Among the 91 healthy controls who wore the wearable device for one month, 90% recorded more than 50 h, and 77% recorded more than 180 h at baseline. During the second period, 86% recorded more than 50 h, and 73% recorded more than 180 h. The main reason reported by subjects who recorded less than 50 h was 'technical issues'. There was no age or gender effect evident on the recording duration (data not shown).
Correlations between timed tests, stride parameters and walking activity Table  2  presents correlation coefficients between stride parameters obtained using the wearable device and clinical measures at baseline in both subgroups. We also present data from the 82 subjects who achieved more than 50 h of recording at baseline. 6MWD was significantly correlated with SV50C, SV95C, and SL95C in the younger group. In the adult group, 6MWD was only correlated with 'maximum performance' measures SV95C and SL95C. In the younger population, the impact of age and height was more obvious than in the adult population (Table  2 ). Among the group aged 5 to 17 years, height was highly correlated with age, 6MWD, 10MW, SV50C, SL50C, and weakly correlated with SV95C and SL95C. In adults, height was only correlated with stride length measures SL50C and SL95C.
Longitudinal data Changes after 12 months are presented in Table  3  and evolution of the measures obtained with the magnetoinertial device in children are displayed in Fig. 2. We present data on the 73 subjects who achieved more than 50 h of recording both at baseline and on follow-up visits. Given the effects of growth, we investigated two subgroups separately. In the younger group, we observed a significant increase in functional measures (6MWD, 4SC, 10MW) after one year. Of the measures obtained with the magneto-inertial device, only SL50C increased after one year. We did not observe a significant change after a year in adults in stride length, stride velocity, distance walked, 6MWD, or RFF with the exception of a slight improvement in the 10MW performance.
Discussion As a result of this study, we provide normative data for spontaneous stride velocity, stride length and walking distance per hour obtained passively with a wearable device during a one-month recording period in a noncontrolled setting and the one-year evolution thereafter. Most previous studies using wearable devices provide us with quantitative parameters  [24]. Qualitative gait analysis as stride length and velocity were mostly obtained based on evaluations inside clinical facilities  [25, 26]. Recently, several efforts were made to collect, in a homebased setting, qualitative data from subjects with various diseases and control populations  [18, 19, 22, 27]. However, to the best of our knowledge, we found no other published data regarding normative longitudinal evaluations of spontaneous stride velocity, stride length, and walking activity in an everyday setting.
As suggested in previous findings  [28] , acquiring normative data was feasible. The overall compliance with device use was good. More than 90% of subjects wore the device more than the minimum requirement of 50 h, which indicates that wearing devices at the ankle and at the wrist for one month was acceptable for most participants. The main reason given for data collection below the 50-h threshold was 'technical issues' , and compliance was not influenced by gender or age. In addition, the recording duration did not influence the variables that were studied. As expected, results of timed tests were growth dependent  [22]. We also observed the influence of height (in adults) and height and growth (in children) on stride length. These results support previous findings  [29, 30]. Height did not influence SV95C, for which only a very weak inverse correlation was found with height in the adult subgroup only.
Acknowledgements We would like to thank all of the participants, including parents and guardians, for the time they have provided to this study. We would also like to thank the team at the  Citadelle Regional Hospital Centre in Liège , as well as Sysnav in Vernon. We are extremely grateful to the  Foundation for Action Duchenne  for financial support. The authors are thankful to Dominic Tromans for English correction Academic authors declare no competing interests. Melanie Annoussamy  and  Damien Eggenspieler  are employed by  Synsav , the medium-sized enterprise responsible for ActiMyo ® development. David Vissière is the CEO, founder and main shareholder of Sysnav.
* This work was partly supported by the  University of Rome Tor Vergata  (Consolidate the Foundations 2015) and by the  Istituto Nazionale di Alta Matematica "F. Severi " (GNAMPA 2016 Research Projects). The authors acknowledge the  MIUR Excellence Department Project  awarded to the  Department of Mathematics, University of Rome Tor Vergata ,  CUP E83C18000100006. The second author is grateful to the  Università Italo Francese  ( Vinci  Project  2015 ). The work was also partly supported by the  ANR (Agence Nationale de la Recherche)  project  ANR-16-CE40-0015-01.
For clarity of these points, we applied a histogramequalization process, which is one of the well-known methods for enhancing the contrast of digital images  [40] , to the terahertz image of Figure  4c. Figure  4d  shows the histogramequalized terahertz transmission image reproduced by commercial software (Origin Pro 2021). Compared with the original image of Figure  4c , we are able to more effectively visualize the distinction between the IDC region and the DCIS region as well as the inhomogeneities of the terahertz amplitude distribution in each region. In the DCIS compartment, terahertz amplitudes are locally high in the area designated by the white dashed box in Figure  4d. This may be affected by an abnormal paraffin state, probably arising from some paraffin removal in the region during the sample fabrication.
For clarity of these points, we applied a histogram-equalization process, which is one of the well-known methods for enhancing the contrast of digital images  [40] , to the terahertz image of Figure  4c. Figure  4d  shows the histogram-equalized terahertz transmission image reproduced by commercial software (Origin Pro 2021). Compared with the original image of Figure  4c , we are able to more effectively visualize the distinction between the IDC region and the DCIS region as well as the inhomogeneities of the terahertz amplitude distribution in each region. In the DCIS compartment, terahertz amplitudes are locally high in the area designated by the white dashed box in Figure  4d. This may be affected by an abnormal paraffin state, probably arising from some paraffin removal in the region during the sample fabrication.
Grid load is measured at the medium-voltage/low-voltage (MV/LV) transformer level of the residential neighbourhood. Data are provided by CAHORS group, which is involved in the Smart Occitania project, and ENEDIS. Because grid load data show that the portion of reactive power remains under 5% of the apparent power, both the inductive and capacitive aspects of the power grid components are neglected. Solar PV power generation is inferred from global horizontal irradiance (GHI) measurements taken by a pyranometer installed at PROMES-CNRS, located just a few kilometres from the residential neighbourhood. Grid load and solar PV power generation data used in the case study are presented in Figure  1. Both the biogas plant and the water tower used herein match the characteristics of two real installations located in the Occitania region.
Results and Analysis In this section, a performance analysis of the switch control strategy (see Section 3. 2) is carried out. These performances are compared to those of the weekly planning strategy and the MPC scheme based on the relaxed optimisation problem, both explained in Section 3. 3. First, the results yielded by the weekly planning using all four datasets are presented. Then, a sensitivity analysis is conducted in order to assess the impact of the MPC's sliding window length on its performance. Lastly, a sliding window is chosen based on the aforementioned sensitivity analysis and a detailed examination of its results is done. All results presented in this paper were obtained using MATLAB 2018a (MathWorks, Natick, MA, USA).
To do so, an examination of the evolution of the computational cost required by the optimisation algorithm is carried out with respect to the length of the sliding window of the MPC-based strategy. Figure  7  shows the computational cost of the implementation of an iteration of the MPC scheme with varying lengths of the sliding window in order to assess the computational burden for the relaxed problem and the switch control. Herein, as opposed to simply registering the time consumed by the MPC scheme's implementation, the computational complexity is quantified by the overall number of objective function evaluations per window. This metric is provided as an output argument of the optimisation function fmincon of MATLAB, which has been selected because it provided the best compromise between quality of results, computational cost, and simplicity of implementation.
Acknowledgments: The authors would like to thank the French agency for ecological transition for its financial support. We also thank all the academic and industrial entities involved in the Smart Occitania project for their contribution to this work and the Universidad de O'Higgins for its financial support during the stay of Nouha Dkhili in Chile. Powered@NLHPC: This research was partially supported by the supercomputing infrastructure of the NLHPC (ECM-02).
Functional data can be found in a wide variety of contexts, among which we can mention: environmental sciences  (Besse et al. , 2005; Febrero-Bande et al. , 2008) , medical sciences  (Juang et al. , 2017) , economy  (Sen and Klüppelberg, 2019)  and others. In the context of this paper, our work is motivated by the use of expensive simulation codes  (Santner et al. , 2003; Roustant et al. , 2010)  that are commonly used in the nuclear industry in order to complement the nuclear safety assessment reports  (IAEA, 2003) , and which require specific statistical tools. These thermal-hydraulic simulators, such as the system code CATHARE2  (Geffraye et al. , 2011) , are capable of simulating the evolution of the essential physical parameters during a nuclear transient, and they are expensive to evaluate (several hours per run) and analyze due to the complexity of the simulated phenomena (highly non linear interactions between its parameters).
This quantity can differ by several orders of magnitude in the case of numerical simulators depending on the restrictions imposed to time steps in order to guarantee the convergence, as well as the presence or not of random noise etc. For a more profound analysis on the importance of these subjects the reader can refer to  James et al. (2000). In this paper we focus on a functional outlier detection technique, showing its sensitivity to both magnitude and shape outliers, and its ranking capabilities. The importance of this work is closely related to the data quality domain, since the presence of anomalous behaviors that might have been originated by measurement errors, non-convergence of algorithms or the existence of non-physical values of numerical simulators may produce spurious results when treating a dataset.
Functional data representation and modeling As mentioned in the introduction, functional data are elements of a functional space, typically functions defined on a continuous interval of R. Measuring, storing and analyzing these data is however realized by using numerical devices and computers, and hence impose a digital representation of data. For this reason, the value of functions is available only on a finitedimensional sub-domain of their theoretical definition domain, that is in a discretized version. When dealing with time dependent physical quantities, this discretization basically consists in a projection on a time grid which can be regular or not. To achieve an efficient detection of outlying functions, a transformation of the dataset is required, which brings out the features of the data that discriminate outlying ones from the rest of the set.
As an example, a set of measurements could have a small amount of incorrect data points (measurement errors) that may not be obvious at first (these data are not generated the same way as the others). This can also happen in the simulation domain. Simply changing the compilers, computers or the version of simulation codes can significantly change the outcome of any physical simulation. Finding these abnormalities is fundamental in order to ensure the quality of any dataset. Let us suppose that a certain number of features are available to describe our functional data and are able to capture the specific characteristics of both central and abnormal observations. If U = {u 1 ,. , u r ,. , u R } represents this set of features, with no imposed a priori restrictions on its size, such that ∀u r ∈ U, u r : F → R, then it would be possible to quantify the anomalous behavior according to each measure through the extreme-value analysis theory.
The generalization of this theory is based on the use of probabilistic models that can be adjusted to the data. Generally, these models are generative, i. e. , they are based on the estimation of the probability of occurrence of a data point (multivariate features in our case) accordingly with an assumed underlying model. Once a parametric family has been chosen for the generative model, its values must be estimated through an optimization algorithm. The use of joint multivariate probabilistic models also has the advantage of providing a tool able of taking into account the interaction between the different features used to evaluate the dataset, in addition to providing a score of outlyingness related to a probability of occurrence. When the underlying process that generates the data is unknown, the use of Gaussian Mixture Models (GMM)  (Reynolds, 2009)  is practical due to the vast existent knowledge of these models.
( 15 ) This integral must be solved by numerical methods. For R = 1, 2, there exists efficient software able to solve it, whereas several algorithms based on the Cholesky decomposition have been developed for the higher-dimensional cases  (Genz, 2000). In the applications presented here we will limit ourselves to two components, orienting each one of them to magnitude or shape outlier detection. The above presented level set notion gives an unambiguous way of defining to what extend an observation is unlikely to be observed when assuming it was generated in accordance to the same probability law as the rest of the dataset. The GMM provides in turn the required underlying probabilistic model allowing this definition. With the resulting outlyingness scores θ i , we have now available a properly constructed quantification tool for the degree of outlyingness of an observation.
Proposed detection algorithm The practical implementation of the detection algorithm is presented below, and several clarifications will be made. Firstly, the approach does not include a projection of the considered functional data onto a functional expansion in order to homogenize the dataset. This preliminary step may be important in applications with heterogeneous time grids, if the data are observed with noise etc. Here, it will be supposed that the domain of the data is already uniform. Furthermore, this kind of projections are not necessary most times when estimating non-parametric features, such as L 2 norms. Secondly, it is important to note that, in the ideal case, the estimation of the GMM should be made on the basis of a non-contaminated dataset, i. e. , without outliers. These existent outliers should be separated before the estimation if the objective is to model the joint distribution of the desired features in order to avoid the introduction of a non-controlled bias.
However, this knowledge is not available a priori, which justifies the trimming procedure of Algorithm 1. It is worth mentioning the iterative step. Even though it is not explicitly noted, the K components that are retained depend on the chosen sample for each bootstrap group. The task of reestimating the parameters for each GMM in order to optimize the number of components is not computationally expensive for small values of K, which is appropriate for datasets that do not present a high degree of multimodality and to avoid overfitting the data. In our simulations, K max = 10. Another important remark on the algorithm is the extraction step, where the most outlying functions on the set according to the θi are separated from the original dataset, and the procedure is re-applied to the remaining functions until a desired homogeneity level is reached.
Separating (trimming) all of these data may introduce a bias in the estimation of the successive GMM. This is a known problem in the outlier detection domain. An example for the functional data case can be found in  Febrero-Bande et al. (2008). Such simulations make it possible to check whether a method succeeds in recognizing different kinds of outliers, when these are purposefully inserted in the dataset. Thus, inserted outliers are constructed so as to mimic typical outlying data engineers engineers are facing in their daily practice. Some common notations for the analytical models are summarized in Table  1.
Presentation In this section the outlier detection methodology is applied to a real industrial dataset of time-dependent numerical simulations. We consider a Intermediate Break Loss of Coolant Accident (commonly called IBLOCA or simply LOCA) in a nuclear power plant, simulated with the CATHARE2 code. CATHARE2 is a best estimate computer code capable of recreating the main physical phenomena that may occur in the different systems involved in nuclear reactors, in particular in the 900 MW French Pressurized Water Reactors (PWR). It embeds two-phase modeling to calculate the thermal-hydraulic behavior of the coolant fluid in the reactor. A LOCA accident is originated by a breach in the primary circuit, which is designed to evacuate the heat generated by the nuclear core. The sudden loss of large quantities of coolant implies a fast increase of the water temperature nearby the nuclear fuel rods, due to the residual power generated by the core during the accidental transient.
The study of two-dimensional scatter plots between these input parameters and the outlying score θ could already prove to be useful in order to visualize how the inputs affect the outlying This paper has dealt with a fundamental branch of functional data analysis: the outlier detection problem. The main aspects to take into account when dealing with functional data or high-dimensional objects in general have also been developed, exposing its main challenges and advantages. A new time-dependent outlier detection methodology based on the use of non-parametric features has been proposed, assessed with synthetic data, and illustrated on thermal-hydraulic simulations, aiming at capturing the outlyingness of the elements of any considered functional dataset both in the magnitude and the shape senses.
The most encountered aspects consist of minimizing: the support volume or area, the build time, the build height, the material consumption, the projected area and the distortions. Today more and more commercial software are used to compute these criteria on parts as indicated in Table  1. These tools are globally using physical parameters of diferent scales (e. g. support volume, part height, etc. ) that cannot be compared to each other. Most of them propose optimum solutions computed by assigning weights to the aforementioned dimensional physical parameters. These weights remain the only values on which the operator can intervene, as the algorithms used by the commercial tools are black boxes. Beyond the criteria computation, some of the tools allow the deinition of surface category (3DXpert, Netfabb and Magics).
The surfaces with potential support diicult to remove are computed by a dedicated algorithm, since their manual selection would be diicult to achieve. The evaluation of the ARs on the geometry is made using a C ++ program based on Opencascade libraries (for geometry processing). This tool makes it possible to easily add Attributes to the shape entities. The rotations around X-axis (Rx) range from 0° to 180° and those around Y-axis (Ry) range from 0° to 360°. The results displayed in the form of response surfaces.
In this paper, we take an empirical approach to test this assumption by analyzing the characteristics of ads deemed political by ordinary people, the characteristics of ads that lead to disagreement, and whether there are differences between what advertisers consider political and what ordinary people consider political. Our analysis is based on a dataset from ProPublica that contains 55k Facebook ads received by U. S. residents, labeled by at least one volunteer as political, and that received three or more votes (Section 2). The dataset was collected by a browser extension that collects the ads users see when they browse their Facebook timeline and allows users to label whether the ads they see are political. First, we investigate whether ad platforms, volunteers, and advertisers agree on which ads should be considered political (Section 3).
All ad platforms agree that ads from or about political actors and ads about elections and voting should be considered political. However, only Facebook and TikTok consider ads about social issues (such as climate change or immigration) as political. Our results show that volunteers disagree on whether an ad is political for more than 50% of the ads in the dataset, and only 83% of the ads labeled as political by advertisers are also labeled as political by a majority of volunteers. Hence, the fundamental assumption that we can clearly distinguish political from non-political ads does not hold, since there is no consensus even on what constitutes a political ad, and volunteers and advertisers label different sets of ads as political. Next, we analyze the characteristics of ads that are labeled as political by volunteers and advertisers in the ProPublica dataset, which can be useful to inform the debate on definitions of political ads (Section 4).
To that end, we gathered data about the advertisers sending political ads and the content of their ads. We hired Prolific users to annotate 2300 ads with the political or social issues the ad is referring to. Our analysis shows that a wide range of advertisers (from political actors to NGOs and businesses) are posting political ads on Facebook and that ads about social issues account for a large fraction of the ads labeled as political; hence emphasizing the importance of including such ads in political ads definitions. Our analysis also shows that the ads labeled as political by volunteers and advertisers are very diverse. We see ads with a clear political message from advocacy groups (e. g. , ads addressing abortion issues in the U. S. ); but also ads from NGOs that address humanitarian issues and do not seem to directly or indirectly impact U.
While all classifiers achieve high accuracy in detecting ads everyone agrees are political; their accuracy drops on ads that only a few find political. Another important question is whether (and to which extent) models trained with labels from advertisers would declare as political the same ads as models trained with labels from volunteers (i. e. , reliable detection of political ads). Theoretically, if ads labeled as political by advertisers and volunteers are representative of political ads in general, the resulting models should declare the same ads as political. Our results show that the overlap between different models is relatively high (ranging from 82% to 97%), but that discrepancies in the input data transfer to discrepancies in the output data. This suggests that existing labeled datasets are not providing a representative set of political ads needed to build reliable detection schemes.