dataesr/scientific-paragraphs-categorization huggingface dataset:
, 2017; Schenkel and Hart, 2012; Murakami, 2014; Bell et al. , 2018). Only recently,  Zarzycki et al. (2021)  presented an evaluation of ERA5's TCs against other reanalyses. The study shows that ERA5 performs as well as reanalyses that include specific TC assimilation techniques such as JRA and NCEP, and that a significant improvement is brought about by the increase in resolution between ERA-Interim and ERA5. A comprehensive assessment of TCs in ERA5 will be presented in future work. The paper is organized as follows: after a description of the classification and datasets, we detail the algorithms of the four trackers as well as our track-matching method (Sect. 2). We then use the four trackers to track TCs in ERA5 and to match the detected tracks with IBTrACS tracks, and we present a detailed analysis of the population of missing and false alarm (FA) tracks so obtained (Sect.
3. 1). This knowledge is taken into account to develop two methods common to all trackers that aim to filter extra-tropical FAs from the results (Sect. 3. 2 and 3. 3). The filtered datasets are then used to analyze the sensitivity of traditional metrics to the choice of the trackers (Sect. 4). Finally, we gather the insight gained from this analysis to consider the complementarity of different trackers and provide some guidelines for applying TC trackers to model results (Sect. 5). The conclusion gives a summary of the trackers' common points and differences (Sect. 6).
Data and methods Our analysis combines resources available for both the database of observed TCs, namely IBTrACS  (Knapp et al. , 2010)  and the ERA5 reanalysis  (Hersbach et al. , 2020). Before describing these two datasets in detail, we first highlight our procedure to classify TCs according to their intensities. We next describe the specifics of the four trackers we compare in this paper, and explain our track-matching method.
IBTrACS The IBTrACS  (Knapp et al. , 2010)  version 4 is the most comprehensive database of observed TCs. We used the "since 1980" subset in the present paper  (Knapp et al. , 2018). It combines data provided by TC centers of WMO, namely the Regional Specialized Meteorological Centers (RSMCs) and Tropical Cyclone Warning Centers (TCWCs), as well as non-WMO centers, such as the China Meteorological Administration, the Hong Kong Observatory, and the Joint Typhoon Warning Center. Since IBTrACS sources are so diverse, the database is heterogeneous and requires careful treatment before one can safely use it. The steps we followed are summarized below and detailed in a workflow chart (Fig. B1 ). This study considers the cyclonic seasons from 1980 to 2019 in the Northern Hemisphere (NH, 40 seasons) and from 1981 to 2019 in the Southern Hemisphere (SH, 39 seasons).
We removed seasons after 2019 because they contain provisional tracks. We also filtered out all tracks labeled as "spur" since they correspond to "usually short-lived tracks associated with main track and often represent alternate positions at the beginning of a system [or] actual system interactions" 1. In the remaining tracks, we only kept 6-hourly time steps for consistency with ERA5. Winds and sea-level pressure (SLP) data were retrieved when available, prioritizing the WMO center responsible for the relevant region. Tracks lacking wind data (0. 5 % of all tracks) were dropped. Tracks lacking SLP data (7 % of TS intensity tracks) were kept but not be included in those parts of the analysis for which storm intensities are needed. Finally, we removed tracks that do not reach the TS stage (16 m s -1 ) and those that last less than 1 d.
TempestExtremes (see https://climate. ucdavis. edu/ tempestextremes. php, last access: 22 August 2022) has been developed by  Ullrich and Zarzycki (2017)  as a command-line software enabling a fast and versatile implementation of TC trackers. For the tracking of pointwise features, such as TCs, it provides two functions: (i) DetectNodes finds candidates "nodes" corresponding to local extrema of a given variable, and optionally satisfying a set of additional criteria (closedcontours, thresholds); and (ii) StitchNodes links candidates within a given distance of one another into a track. In this paper, we use TempestExtremes to implement two vastly different TC trackers, UZ and OWZ, respectively described by  Ullrich et al. (2021)  and  Tory et al. (2013c). We describe both algorithms below and provide the associated codes in Appendix C.
TRACK algorithm TRACK derives from an extra-tropical cyclone (ETC) tracking algorithm  (Hodges, 1994). It is versatile and has since been used to study many types of weather systems, including the detection and tracking of TCs  (Bengtsson et al. , 2007; Hodges et al. , 2017; Roberts et al. , 2020a). The rationale behind TRACK is different from the previously described trackers: because it aims to track all vorticity perturbations, it does not embed any warm-core criterion in its initial fundamental detection. The TC selection, including the warm core test, is only performed in the last step, independently of the tracking. In the present paper, we used the database of trajectories detected by TRACK in ERA5 that was recently published by  Roberts et al. (2020a)  without any modification. For completeness, we detail below the thresholds used in that case.
Tracks matching When using reanalysis products like ERA5, detected tracks can tentatively be associated with observed tracks  (Murakami, 2014; Hodges et al. , 2017; Ullrich et al. , 2021). We derived the following matching algorithm: consider the case of a given detected track D composed of n points (d 1 , d 2 ,. d n ) defined at times (t 1 , t 2 ,. , t n ). The observations O consist of a database of tracks and can be seen as a collection of points at given times. For each point After this matching is completed for all detected tracks, a final treatment is performed: if an observed track is paired with two or more detected tracks, these detected tracks are merged into a single track. Such cases arise when the detected track corresponds to different parts of the same observed tracks and occur when, for example, the TC temporarily weakened while going over an island before strengthening again.
These tracks correspond to TCs that reached their maximum intensities after a post-tropical transition. The lifetimes of hits (fourth row) also vary with trackers: UZ and the CNRM display the shortest tracks with a distribution that peaks between 5 and 10 d, followed by OWZ with storm durations peaking at 10 d, while TRACK tracks typically last for 15 d. We will revisit these properties in Sect. 4. 3. Missing tracks (green color in Fig. 1 ) correspond to TS or TCs that were observed and are reported in the IB-TS database but that a given tracker did not find in ERA5. They typically consist of weak (first row), tropical (second row), and short-lived (fourth row) perturbations for which the amplitude is probably not strong enough to exceed the detection thresholds for a long-enough time 2. This is why TRACK, with its relatively soft criteria, misses half as many tracks as the other trackers.
Results We now analyze the properties of the database of ERA5 tracks that we obtained after the post-treatment described above, focusing on the differences between trackers. We first revisit the detection skills of trackers (Sect. 4. 1). We then discuss the sensitivity of the metrics introduced by Zarzycki et al. (  2021 ) in Sect. 4. 2 and thereafter relate these sensitivities to the different tracks' duration as captured by the four trackers (Sect. 4. 3) and to the intensity distribution of the reanalyzed storms in ERA5 (Sect. 4. 4).
Even though there are arguments in the literature that dynamics-based trackers -e. g. , TRACK, OWZ -might be less dependent on resolution than physics-based methodologies  (Tory et al. , 2013a, b; Raavi and Walsh, 2020) , there is no quantitative assessment of this property. In general, we are lacking a quantification of the range of resolutions for which trackers are valid, with or without retuning. Finally, Table  4  provides practical considerations on the implementation of each tracker. The UZ tracker is implemented using the TempestExtremes command-line software, which is easily parallelizable using MPI, a fully open source. We also benchmarked UZ on 1-hourly data, proving that the computation time scales linearly with temporal resolution. The OWZ necessitates two steps: the first is the computation of the OWZ variable, which is done in Python, and the second is the tracking itself, done here with TempestExtremes (and therefore parallelized using MPI as well).
The code for OWZ is provided along with this paper. TRACK is run using shell scripts that read input from text files and run the FOR-TRAN code. Since it performs spectral filtering, it needs to be run globally, and because of the stitching step that is not independent, it is tricky to split it in the middle of a TC season. Therefore, the embarrassingly parallel potential is limited to parallelizing over the years. TRACK code is not open source but available upon request. The CNRM tracker is also implemented in FORTRAN, interfaced with shell scripts. It does not have any parallelization implemented so far, but it can be used embarrassingly parallel over space or time. In terms of computation time, if no parallelization is used, UZ, OWZ, and TRACK are roughly equivalent, while CNRM requires about twice as much time.
C2. 1 Original algorithm In  Bell et al. (2018) , the OWZ algorithm applied on ERA-Interim data is described as follows: 1. Each grid point at each time step is assessed based on the initial threshold values. The thresholds are provided in their Table  1. Tory et al. (2013b)  further specifies that "clumps in close proximity are reduced to one clump by discarding the weaker or smaller clumps", and that each clump must satisfy a set of clump conditions: "a minimum size limit, and a land-impact condition". The minimum size limit is two grid points and the radius to look for weaker or smaller clumps is 550 km. The land-impact condition tests whether the point is over the land or the ocean. In this paper, the latitude-dependent radius of step (4) "varies linearly from 600 to 400 km between 15 and 30 • latitude in both hemispheres, with constant values outside this latitude band", which does not correspond with the 350 km specified by  Bell et al.
C2. 3 Sensitivity analysis In the original algorithm, the thresholds must all be satisfied in the same grid point. However, it was used on ERA-Interim data interpolated onto a 1 • × 1 • grid, whereas ERA5 data present itself with 0. 25 • × 0. 25 • grid points. One can expect that this higher resolution might allow for the formation of an eye in the circulation, so that all the thresholds might be verified in the wall rather than in the center of the circulation. We test seven values for r threshold : 0 • (thresholds must be passed at the center), 0. 5, 1 •. The 350 km range in  Bell et al. (2018)  corresponds to 3 • , whereas the [400, 600 km] range in  Tory et al. (2013b) correspond to [3. 5, 5. 5  • ]. In UZ, the range is set to 8 •. We test r range values between 3 and 8 •. To assess the sensitivity of the detection to these thresholds, we compute the number of tracks detected.
Figure12. Venn diagrams representing common tracks between each algorithm and IB-TS. The figures in the circles are the annual frequency of each group. Venn diagrams are used to show logical relations between sets. Each set of tracks is represented by a circle, whose area is proportional to the size of the set -i. e. the number of tracks. The different circles superpose on an area proportional to the number of tracks that each ensemble have in common. We used the matplotlib-venn package in Python, available on PyPI (https://pypi. org/project/matplotlib-venn/, last access: 22 August 2022) to draw the Venn diagrams.
Acknowledgements. The research is supported by public funding to the  CEA  and  CNRM. Stella Bourdin  and  Sébastien Fromang  were also financially supported by the  EUR IPSL-Climate Graduate School  through the  ICOCYCLONES  project. The authors are grateful to  Kevin Hodges  for providing the TRACK dataset, for insightful scholar discussion and literature provision and for his review of an earlier version of this manuscript. The authors thank  Paul Ullrich  and  Colin Zarzycki  for their help regarding  TempestExtremes. Stella Bourdin  thanks colleagues at the LSCE for helpful discussion and feedback, and especially  Robin Noyelle  for the idea of using the Hart phase space. The authors appreciated the constructive and insightful comments from  Malcolm Roberts  and one anonymous reviewer, which helped improve the present manuscript.
Code and data availability. ERA5 data are available on the Copernicus Climate Change Service Climate Data Store (CDS, https://cds. climate. copernicus. eu/cdsapp#!/ dataset/reanalysis-era5-pressure-levels, last access: 22 August 2022). The IBTrACS database is provided by NOAA at https://www. ncdc. noaa. gov/ibtracs/ (last access: 22 August 2022). All the scripts used to produce the present paper's results are available at https://doi. org/10. 5281/zenodo. 6424432 (Bourdin,  2022a). These include the code to run the UZ and OWZ trackers and the original TRACK and CNRM databases, the code for the post-treatment and the tracks matching Python scripts for the whole analysis, the code to reproduce the figures, and finally, a copy of v. 0. 5 of the dynamicoPy package used in the Python scripts (https://doi.
A similar setting is used hereafter to compare the prediction performance of five prediction scores within L: the OLS, Naive, Ridge, PLS prediction scores and the proposed adaptive regression method. Additionally, two alternative methods are introduced in the comparative study: scout(1,1), with 1 -penalized estimation of both the partial correlation matrix and the regression coefficients, as in  Witten and Tibshirani (2009)  for the same simulation setting, and Principal Component Regression (PCR), identified in Section 3 of the main document as being out of L. When needed, hyperparameters (Ridge, PLS, PCR, Scout and proposed method) are optimized using a 10-fold cross validation procedure. The PLS and PCR methods are implemented using the R package pls  (Mevik et al. , 2020) , the Ridge method using the R package glmnet  (Friedman et al.
, 2010)  and the Scout method using the R package scout  (Witten and Tibshirani, 2015). The proposed Adaptive method is implemented using the R package AdaptiveRegression, available at https://github. com/fhebert. All simulated datasets have n = 20 observations on p = 19 normally distributed explanatory variables with mean 0 and standard deviations 1. The first 10 variables have correlation 0. 9 with each other (in  Witten and Tibshirani (2009)  this equicorrelation parameter is 0. 5); the rest are uncorrelated. The response variable Y is generated under the model Y = Xβ + ε, where: • β j = j for j ≤ 10 and β j = 0 for j > 10 (scenario 1 as in  Witten and Tibshirani (2009) ), • β j = 0 for j ≤ 10 and β j = p -j for j > 10 (scenario 2), and where ε ∼ N (0; 25). In addition, β is multiplied by a constant so that the asymptotic squared correlation between the response and the prediction score is 0.
8 (arbitrarily chosen). For each simulation scenario, 1,000 training datasets are randomly generated. For each training dataset, a test dataset with 1,000 individuals is generated following the same   1  reproduces the mean squared correlations between the response observed on the test dataset and the seven prediction scores. In the first scenario, the seven prediction methods can be grouped as follows, regarding their prediction performance: a first group composed of Naive, Adaptive and Scout showing the best prediction performance (0. 76 ≤ R 2 ≤ 0. 79), Ridge (with R 2 = 0. 73), a group composed of PCR and PLS showing markedly lower prediction performance (0. 66 ≤ R 2 ≤ 0. 68) and OLS being clearly outperformed. In the second scenario, the composition of the groups of methods regarding their prediction performance is changed: a group composed of Ridge, Scout and Adaptive showing the best prediction performance (0.
52 ≤ R 2 ≤ 0. 55) and a group composed of OLS, Naive, PLS and PCR with poor prediction performance (0. 21 ≤ R 2 ≤ 0. 28). This simple example, with a limited simulation setup, demonstrates that, with the same dependence across explanatory variables, some prediction methods can show very different prediction performance, here Naive, PLS, PCR, depending on the pattern of association with the response variable. Others, including Adaptive and Scout remain among the best methods in the two scenarios. The simulation study above is completed in Section 5 of the main document by more intensive simulations and a comparison using two public datasets. 3 Data-driven simulation study in Section 5. 1 Detailed results of the data-driven simulation study introduced in Section 5. 1 of the main paper are given below.
, 20, i = j, Σ 2 ij = 0. 9 and for all i = 1,. , 20, Σ 2 ii = 1. Then, Σ x = Σ 1 ⊗ Σ 2. • Scenario 6: n = 25, p = 400 (n/p = 0. 06) • For j = 1,. , 75, β j = 1 (sparsity rate: 0. 81) • Let B stand for the p × 5 matrix whose nonzero coefficients are as follows: for i = 1,. , 150, B i1 = 1, for i = 51,. , 200, B i2 = -1, for i = 101,. , 250, B i3 = 2, for i = 151,. , 300, B i4 = -2, for i = 301,. , 400, B i5 = 3. Σ x is obtained by scaling rows and columns of 0. 1I p + BB , so that the diagonal entries of Σ x are all equal to one. Furthermore, all vectors of regression coefficients are scaled so that the ratio β Σ x β/σ 2 y between the variance of E(Y | X) and the variance of Y is 0. 8. Figures 1 to 6 display for each scenario an image plot of Σ x and a plot of β. For each scenario, a large dataset of 100,000 profiles of explanatory variables and corresponding response variable are generated.
Training datasets are obtained by randomly choosing n profiles within this population and for each training dataset, a test dataset is obtained by randomly choosing 10,000 profiles in the rest of the population. Table  6  gives the average MSEP of all methods over 1,000 simulations. Similarly as in the data-driven simulation study reported in Section 5. 1 of the main paper, the proposed adaptive prediction method shows either the best prediction performance     over the nine methods or is close to the best performance, depending on the simulation scenario. In scenario 1, with a very sparse vector of regression coefficients and two large independent blocks of equicorrelated explanatory variables, the adaptive regression method and the naive prediction score outperform all the other methods.
The CRF quantifies the ability to transport oxygen from atmosphere to the mitochondria, and is thus closely related to athletes' performances, but is also a strong predictor of cardiovascular disease and all-cause mortality in the general population  [21]. The possibility to use the HRV decay constant to estimate the CRF using only cardiac data stemming from portable heart rate measurement devices, such as Holters or chest heart rate monitors, would be a major benefit. Indeed, CRF is usually measured either directly by the measured peak oxygen consumption, or derived from the maximum work rate achieved during a test, both methods requiring an important material setup. Estimating the CRF from cardiac measurements acquired during variable effort would extend the estimation of CRF to easier to implement effort test, such as the 6 min walk test, and to field measurements.
Participants The database used in this work  [26]  consists of records of a cycling graded effort test (GET) (Cf. the section below for details) performed by 18 young athletes (10 males and 8 females; 15. 2 [14. 0, 16. 8] year-old, 174. 0 cm [165. 0, 182. 0] height and 62. 9 kg [54. 3, 76. 5] weight, see Table  1 ) of the Regional Physical and Sports Education Centre (CREPS) of French West Indies (Guadeloupe, France), belonging to a national division of fencing (n = 10), or a regional division of sprint kayak (n = 6) and triathlon (n = 2). All athletes completed a medical screening questionnaire, and a written informed consent from the participants and the legal guardians was obtained prior to the study. The study was approved by the CREPS Committee of Guadeloupe (Ministry of Youth and Sports), the ethics committee of the University of French West Indies and performed according to the Declaration of Helsinki.
Statistical analysis All signal processing and statistical analysis have been performed with the R 4. 1 open source software  [31]. The comparison between regression models is based on Akaike information criterion (AIC) and Bayesian Information criterion (BIC)  [32] , which are two estimator of the prediction error used to compare regression models. The calculation of the correlations between the estimated HRV decay coefficients and the CRF indices has been performed using Pearson linear correlation coefficients r  [33]. The regression of the three models proposed in equation is operationalized with a nonlinear least square regression using the packages nls. The ggplot2 was used for graphical representation  [34]  and data. table for data manipulation. All code used to perform the analysis and generate the tables and figures can be found at the following Gitlab repository: https://gitlab.
Comparison of models In this first part we want to determine which representation of the evolution of SDRR along exercise corresponds best to an exponential decay. The ensemble of the SDRR values along the GET of all 18 participants are represented in Fig  3   [12] , the values of HRV at high work rate do not align with the rest of them in a linear-log scale. Furthermore, the HRV calculated before and after the effort have a wide variety of values for the same null power. Finally, when represented as a function of %VO 2 max, although SDRR values plotted in linear-log scale display a clear linear trend during exercise, they do not align with the values calculated before and after effort (Fig 3C  model 3 ). When performing the least square nonlinear regressions of these three models on the entire dataset (the estimated model is plotted as a solid red line in Fig  3 ), the model 1 in Eq 2 describing SDRR as an exponential decay of the mean HR has a significantly lower AIC and BIC than the two others (see Table  2 ).
, θ 6 , is then fitted to the entry values of Γ for (x, y) ∈ G, by solving the least squares problem min θ∈R 6 ∑ (n,m)∈G [ p θ (n, m) -γ(n, m)] 2 , ( 11 ) where G is the grid defined in  (6). The first counterexample with synthetic images has been chosen for its simplicity so 140 that it can be easily reproduced. The Matlab code for generating the presented result is 141 available for download  [16]. To show the robustness of this counterexample, the Matlab 142 code can be optionally run with some random noises added to the generated synthetic 143 images, though the result presented below is noise-free. Counterexamples based on true 144 images (as presented in Examples 2 and 3) are also included in  [16]. 145 Consider two binary images of 18 × 18 pixels as shown in Figure  3 , with the template 146 (ROI) chosen as the red square window of 8 × 8 pixels in each image.
164 For the chosen template illustrated by the red windows in Figure  5 , the fitted 165 quadratic surface is shown in Figure  6. The surface exhibiting a saddle point has no 166 maximum. This result can be reproduced with the Matlab code downloadable from  [16]. example. The details of this result are available from  [16]. 173 The examples presented in this section confirm that, in some rare situations, the   As a subpixel refinement, the maximum of the fitted surface should satisfy |x * | < 1 and |y * | < 1, which is not the case in this example. See  [16]  for the details of this example. After the answer to the first question raised at the end of Section 2, the following 178 sections will then answer the other two remaining questions. 179.