dataesr/scientific-paragraphs-categorization huggingface dataset:
oup. com/cardiovascres/advance-article/doi/10. 1093/cvr/cvab370/6499268 by  Leiden University / LUMC  user on 18 January  2022 CVR-2021-0198 28  by the  Netherlands CardioVascular Research Initiative CVON  ( CVON2014 RECONNECT  and  CVON2016 ARENA-PRIME ); The work of TE was supported by the  European Research Council (ERC-AG IndivuHeart) , the  Deutsche Forschungsgemeinschaft  ( DFG Es 88/12-1 ), the  European Union Horizon 2020  (REANIMA and TRAINHEART), the  German Ministry of Education and Research (BMBF)  and the  Centre for Cardiovascular Research (DZHK) ; LF was supported by  European Union Horizon 2020  (grant agreement No  633196  [CATCH ME] and 965286 [MAESTRIA];  British Heart Foundation  ( FS/13/43/30324 ;  PG/17/30/32961 ;  PG/20/22/35093 ;  AA/18/2/34218 );  DFG FA413. The  Institute of Cardiovascular Sciences, University of Birmingham  is a recipient of a  BHF Accelerator Award  ( AA/18/2/34218 ); PF was supported by the  National Research, Development and Innovation Office of Hungary  ( Research Excellence Program -TKP; National Heart Program   NVKP 16-1-2016-0017 ); by the  Higher Education Institutional Excellence Program of the Ministry of Human Capacities in Hungary , within the framework of the  Therapeutic Development thematic program  of the  Semmelweis University ; and by the  European Union Horizon 2020  (COVIRNA, CRYTAL); HG is supported by  PAC  " NETDIAMOND "  POCI-01-0145-FEDER-016385 ;  HealthyAging2020 CENTRO-01-0145-FEDER-000012-N2323 ;  POCI-01-0145-FEDER-007440 ,  CENTRO-01-0145-FEDER-032179 ,  CENTRO-01-0145-FEDER-032414 ,  POCI-01-0145-FEDER-022122 ,  UID/NEU/04539/2019 ,  UIDB/04539/2020  and  UIDP/04539/2020 ; CGT was supported by the  Austrian Science Fund  ( P 32821 ); SH acknowledges the  European Union Commission 's  Seventh Framework programme  under grant agreement  N° 305507  ( HOMAGE0 , IMI2-CARDIATEAM (N° 821508 ) and support from the  Netherlands Cardiovascular Research Initiative , an initiative with support of the  Dutch Heart Foundation ,  CVON2016-Early HFPEF, 2015-10 ,  CVON She-PREDICTS , grant  2017-21 , CVON Arena-PRIME, 2017-18, CVON  Double Dosis , and support of  FWO   G091018N  and  FWO G0B5930N ; AGH acknowledges support from the  INSIST  project (www.
insist-h2020. eu) and the  CompBioMed2  project (https://www. compbiomed. eu) that both received funding from the  European Union 's  Horizon 2020 research and innovation programme  under respectively grant agreement No  777072  and No 823712; DH was supported by the  Deutsche Forschungsgemeinschaft (DFG ,  Hi 842/4-3; 842/10-2 ; ) and the  Leducq Foundation  (transatlantic network of excellence:  Targeted Approaches for Prevention and Treatment of Anthracycline-Induced Cardiotoxicity ) and Volkswagenstiftung (A128871); AH was/is supported by the  Deutsche Forschungsgemeinschaft (DFG)  via the Cluster of Excellence " From regenerative biology  to reconstructive therapy" (REBIRTH), via the project  C7  of  TRR127  (Biology of xeno-geneic cell and organ transplantation-from bench to bedside), and via the Project  HA 13 06/9-1 , the  BMBF Project  " AUREKA ", the project  B4  of  R2N  by the  Federal State of Lower Saxony, the Fördergemeinschaft "Deutsche Kinderherzzentren e.
V. "  and the "Cortiss" foundation; JSH is supported by  AP-HP, INSERM , the  French National Research Agency  (NADHeart  ANR-17-CE17-0015-02 ,  PACIFIC ANR-18-CE14-0032-01 ,  CORRECT_LMNA ANR-19-CE17-0013-02 ), the  ERA-Net-CVD  ( ANR-16-ECVD-0011-03 ,  Clarify  project),  Fédération Française de Cardiologie , the  Fondation pour la Recherche Médicale  ( EQU201903007852 ), and by a grant from the  Leducq Foundation  ( 18CVD05 ), and is coordinating a  French PIA Project  ( 2018-PSPC-07 , PACIFIC-preserved, BPIFrance) and a University Research Federation against heart failure ( FHU2019 ,  PREVENT Heart Failure ); DK acknowledges the PPP Allowance made available by Health_Holland,  Top Sector Life Sciences & Health , to stimulate publicprivate partnerships; LVL is supported by the  Netherlands Heart Foundation  ( Dekker Senior Clinical Scientist  ( 2019T056 ),  Health Holland TKI-LSH  ( LSHM19035 ) and  TUe/UMCU/UU Alliance Fund ; SL is supported by grants from the  south African National Foundation , the  Cancer Association of South Africa and Winetech ; TL is supported by the  Netherlands Heart Foundation/Applied & Engineering Sciences  grant number  14741  and Institutional research grant by  Dutch Technology Foundation  ( P15-26 ) with participation of  Pie Medical Imaging and Philips Healthcare ;  Institutional research  grant by  Dutch Technology Foundation  ( 12726 ) with participation of Pie Medical Imaging; Institutional research grant by The  Netherlands Organisation for Health Research and Development with participation of Pie Medical Imaging ;  Industrial research grant by Pie Medical Imaging ; JL was supported by the  Netherlands Organisation for Scientific Research (NWO-ZonMw , grant  016.
003. 001 );CP was supported by  Ministero dell'Istruzione, Università e Ricerca Scientifica  grant ( 2015583WMX ) and Programma STAR grant by  Federico II University and Compagnia di San Paolo ; MP is supported by grants of the  Italian Ministry of Health  ( Ricerca Corrente , 5 per 1000) and from  Regione Lombardia ; CAR is supported by the  Netherlands CardioVascular Research Initiative CVON  ( CVON2018-30  and  CVON2015-12 ) and the  Netherlands Organisation for Health Research and Development  ( ZonMw 91714371 ); US is supported by grants of the  Netherlands Heart Foundation  ( CVON2014-09 ,  RACE V Reappraisal of Atrial Fibrillation: Interaction between hyperCoagulability , Electrical remodeling, and  Vascular Destabilisation in the Progression of AF)  and the  European Union  ( ITN Network Personalize AF: Personalized Therapies for Atrial Fibrillation: a translational network , grant number  860974 ;  MAESTRIA: Machine Learning Artificial Intelligence Early Detection Stroke Atrial Fibrillation , grant number  965286 ; REPAIR: Restoring cardiac mechanical function by polymeric artificial muscular tissue, grant number  952166 ); RS was supported by  Deutsche Forschungsgemeinschaft (DFG, German Research Foundation ) [Project number  268555672 -SFB 1213 , Project  B05 ]; JS was supported by  European Union   H2020 program  to the project  TECHNOBEAT  (grant number  66724 ),  EVICARE  (grant number  725229 ) and  BRAV3  (grant number  874827 ), and  ZonMw program  No.
We present a topological analysis of the temperature fluctuation maps from the Planck 2020 Data Release 4 (DR4) NPIPE dataset and the Planck 2018 Data Release 3 (DR3) FFP10 dataset. We performed a multiscale analysis in terms of the homology characteristics of the maps, invoking relative homology to account for the analysis in the presence of masks. We performed our analysis for a range of smoothing scales spanning sub-and super-horizon scales corresponding to a full width at half maximum (FWHM) of 5 , 10 , 20 , 40 , 80 , 160 , 320 , and 640 , and employed simulations based on the standard model for comparison, which assumes the initial fluctuation field to be an isotropic and homogeneous Gaussian random field. Examining the behavior of topological components, represented by the 0D homology group, we find the observations to be approximately 2σ or less deviant from the simulations for all resolutions and scales for the NPIPE dataset.
For the FFP10 dataset, we detect a 2. 96σ deviation between the observations and simulations at N = 128, FWHM = 80. For the topological loops, represented by the first homology group, the simulations and observations are consistent within 2σ for most resolutions and scales for both the datasets. However, for the NPIPE dataset, we observe a high deviation between the observation and simulations in the number of loops at FWHM = 320 , but at a low dimensionless threshold ν = -2. 5. Under a Gaussian assumption, this would amount to a deviation of ∼ 4σ. However, the distribution in this bin is manifestly non-Gaussian and does not obey Poisson statistics either. In the absence of a true theoretical understanding, we simply note that the significance is higher than what may be resolved by 600 simulations, yielding an empirical p-value of at most 0.
0016. Specifically in this case, our tests indicate that the numbers arise from a statistically stable regime, despite being based on small numbers. For the FFP10 dataset, the differences are not as strong as for the NPIPE dataset, indicating a 2. 77σ deviation at this resolution and threshold. The Euler characteristic, which is the alternating sum of the ranks of relative homology groups, reflects the deviations in the components and loops. To assess the significance of combined levels for a given scale, we employed the empirical and theoretical versions of the χ 2 test as well as the nonparametric Tukey depth test. Although all statistics exhibit a stable distribution, we favor the empirical version of the χ 2 test in the final interpretation, as it indicates the most conservative differences.
For the NPIPE dataset, we find that the components and loops differ at more than 95%, but agree within the 99% confidence level with respect to the base model at N = 32, FWHM = 320. The Euler characteristic at this resolution displays a per mil deviation. In contrast, the FFP10 dataset shows that the observations are consistent with the base model within the 95% confidence level, at this and smaller scales. This is consistent with the observations of the Planck analysis pipeline via Minkowski functionals. For the largest smoothing scale, N = 16, FWHM = 640 , both datasets exhibit an anomalous behavior of the loops, where FFP10 data exhibit a deviation that is larger by an order of magnitude than that of the NPIPE dataset. In contrast, the values for the topological components and the Euler characteristic agree between observations and model to within a confidence level of 99%.
However, for the largest scales, the statistics are based on low numbers and may have to be regarded with caution. Even though both datasets exhibit mild to significant discrepancies, they also exhibit contrasting behaviors at various instances. Therefore, we do not find it feasible to convincingly accept or reject the null hypothesis. Disregarding the large-scale anomalies that persist at similar scales in WMAP and Planck, observations of the cosmic microwave background are largely consistent with the standard cosmological model within 2σ.
, D, and ω j is the volume of the j-dimensional unit ball. There are d such quantifiers for a Ddimensional set, where d = 0,. , D. All but one are purely geometrical quantities that are related to the d-dimensional volume of the manifold. The exception is the 0-th Lifshitz-Killing curvature, or equivalently, the D-th Minkowski functional, which is related to a purely topological quantity, the Euler characteristic  (Euler 1758; Adler 1981; Pranav et al. 2019b; Telschow et al. 2019) , via Gauss's Theorema Egrerium  (Gauss 1900; Adler 1981; Pranav et al. 2019b). The Minkowski functional computations of the CMB have consistently shown the observations to be congruent with the standard model  (Planck Collaboration et al. 2016a). More recently, developments in computational topology have paved the way for extracting topological information from datasets at the level of homology  (Munkres 1984; Edelsbrunner & Harer 2010; van de Weygaert et al.
2020a ). We perform our experiments on the fourth and final data release, Planck 2020 Data Release 4 (DR4), which is based on the NPIPE dataprocessing pipeline  (Planck Collaboration et al. 2020b ). The NPIPE dataset represents a natural evolution of the Planck dataprocessing pipeline, integrating the best practices from the LFI and HFI pipelines separately. The result is an overall amplification of signal and reduction in the associated systematic, noise, and residuals at almost all angular scales  (Planck Collaboration et al. 2020b). For comparison, we also present results for the Planck 2018 Data Release 3 (DR3)  (Planck Collaboration et al. 2020a) , which is based on the Full Focal Plane (FFP) data processing pipeline  (Planck Collaboration et al. 2016c) , resulting in the FFP10 simulations  (Planck Collaboration et al.
2020d ). The paper follows the spirit of  Pranav et al. (2019a)  in methods and analysis, where we present results for the intermediate Planck 2015 Data Release 2 (DR2)  (Planck Collaboration et al. 2016a ); also see  Adler et al. (2017). The novel aspect of the methods presented here and in  Pranav et al. (2019a)  is an analysis pipeline that takes regions with unreliable data on S 2 into account. In the case of CMB, this is reflected in the obfuscation effects of the measurements that are due to foreground objects such as our own galaxy, as well as other extra-and intragalactic foreground sources. We masked these regions and computed the homology of the excursion sets relative to the mask. We present a brief description of the topological background in Section 2, followed by the results in Section 3.
Results In this section, we present our results in terms of the ranks of homology groups, b p , p = 0, 1, as well as the Euler characteristic, EC rel , relative to the mask. Section 3. 1 presents results from the DR4 NPIPE dataset based on 600 simulations, obtained using the SEVEM component separation pipeline. Similar results for the DR3 FFP10 dataset based on 300 simulations, obtained using the SMICA component separation pipeline, are presented in Section 3. 2 2. The latter dataset facilitates a direct comparison with the topo-geometrical studies of the CMB performed by the Planck team in Planck  Collaboration et al. (2020c). For both datasets, we begin by examining the graphs of b 0 , b 1 , and of the (relative) Euler characteristic, EC rel. This is followed by statistical tests that estimate the significance of results, taking into account all of the levels together for a given resolution and scale.
Planck 2020 Data Release 4: NPIPE dataset In this section, we analyze the graphs of the topological descriptors for the NPIPE dataset. Treating the topological descriptors as discrete random variables, we compute the mean, µ sim , and the standard deviation, σ sim , from the simulations in the usual sense for each of the levels. We use them to assess the modelindependent significance of the difference between the simulations and observations. Concentrating on the top left panel of Figure  6 , at a Gaussian smoothing scale of FWHM = 320 , approximately 5 degrees, and at a moderately low dimensionless density threshold ν = -2. 5, we find a 3. 91σ deviation between the simulations and the observation. We examine the behavior of b 1 at this level further in Figure  7 , where we present the histogram of the distribution of b 1 from the simulations in gray boxes.
Graph of b 1 Figure  10  presents the graphs for the topological loops. The deviations between the observations and simulations are within ap-proximately 2σ for most of the smoothing scales and thresholds. However, for the dimensionless threshold, ν = -2. 5, we note a more than 2σ deviation for N = 64, FWHM = 160 onward toward higher smoothing scales. For N = 32, FWHM = 320 , the deviation is 2. 77σ, and similar for N = 16, FWHM = 640. These deviations, while not as significant as exhibited in the NPIPE dataset, occur at similar scales and thresholds. In addition, we also note a more than 4σ deviation for N = 16, FWHM = 640 at ν = -3. However, we reject this as a possible statistical fluke because of the extremely low numbers involved, which are about 5 or fewer. commensurate deviations with respect to b 0 (b 1 ) because of their contributions in the alternating sum.
NPIPE dataset All entries before the last in Table  1 , panel (a), present p-values for the variables, computed from maps degraded at specific resolutions, with additional Gaussian smoothing applied. The χ 2 results are presented for the theoretical and empirical distributions in the left and middle blocks, respectively. The results for the Tukey depth are presented in the rightmost block. When we consider all the three tests, the p-values computed from the empirical distribution using the χ 2 statistic yield the most conser-vative estimate of the significance, and we favor it in order to be conservative in our interpretation. b 1 shows a significant difference between the observational maps and the simulations for N = 32 and N = 16. Additionally, b 0 also shows a significant difference at N = 32.
FFP10 dataset Results for the FFP10 dataset are presented in panel (b) of Table 1. We concentrate our analysis on the middle block, which presents the p-values from the χ 2 statistic using the empirical distribution. For N = 32, FWHM = 320 , we note that all the topological descriptors show a nonsignificant deviation between the simulations and the observation, which is in contrast with the behavior at the same resolution in the NPIPE dataset, where the values are an order of magnitude lower. For the next larger scale of probing, N = 16, FWHM = 640 , we note a per mil significance of the difference between simulations and observations for the number of loops, which is an order of magnitude smaller than in the NPIPE dataset. Additionally, we also note the low p-value for b 0 at N = 128, FWHM = 80 , which is the scale at which an approximately 3σ deviation occurs for the number of components between the simulations and the observation.
When examining the Euler characteristic at this scale, we note that the values are mildly significant, in contrast with the NPIPE dataset, which exhibits nonsignificant behavior. The Tukey depth test shows the observations to be true outliers in instances at different resolutions for all the three variables, yielding p-values of 0. 0. As in the case with the NPIPE dataset, these instances occur when the χ 2 test also exhibits small p-values.
Eriksen et al. (2004b)  reported that the Euler characteristic at negative density thresholds is anomalous with the base model simulations at more than 3σ for the northern hemisphere at smoothing scales of FWHM = 3. 40 •. The corresponding χ 2 value reported for this scale is at the 95% confidence level, which translates into a p-value of 0. 05. Park (2004)  reported an anomalous genus at more than 2. 5σ. The anomalous behavior of genus or the Euler characteristic, specifically at negative levels, is linked to and generated by the anomalous behavior of the first homology group, represented by topological loops, and establishes a connection between our results and previous results, showing a consistency across datasets. than the Planck results. In this context, it is important to note that in the Planck analysis pipeline, it has been the practice to combine all the Minkowski functionals to perform the statistical tests and subsequently present the combined p-values.
Discussions and conclusion We presented a topological analysis of the temperature fluctuations in the CMB in terms of homology. To account for re-gions with unreliable data, we computed the homology of the excursion sets relative to the mask covering these areas. We performed a multiscale analysis by degrading and smoothing the maps for a range of pixel resolutions, and a subsequent convolution with a Gaussian filter for a range of scales. We performed our analysis on the fourth and final NPIPE data release from the Planck team. The pipeline represents a natural evolution of the data-processing pipeline, commensurate with better understanding of systematics, residuals, and noise over a period of time in successive data releases. It incorporates the best strategies from the LFI and HFI processing pipeline, so that the level of noise and residuals at all scales is reduced (Planck  Collaboration et al.
2020b ). We also investigated the Planck 2018 Data release 3 (DR3), accompanied by the FFP10 simulations (Planck  Examining the behavior of topological components or isolated objects represented by the 0D homology group, we find that the observations deviate by approximately 2σ or less from the simulations for the NPIPE dataset. For the FFP10 dataset, b 0 exhibits a deviation of 2. 96σ at N = 128, FWHM = 80. The 1D homology group, representing and quantifying the topological loops, is also consistent with the base model at 2σ for most of the resolutions and scales. However, for FWHM = 320 and at moderately low negative thresholds, we record a high deviation between the simulations and observations for the NPIPE dataset. In a Gaussian setting, this would amount to an approximately 4σ significance.
However, the distribution characteristics at this threshold are manifestly non-Gaussian, rendering the usual σ significance nonviable. The distribution characteristics do not obey the Poisson statistics either. In view of this, and because we lack a true theoretical understanding of the distribution characteristics, we simply note that the significance is larger than what may be resolved by 600 simulations, yielding an empirical p-value of at most 0. 0016. The FFP10 dataset exhibits a deviant behavior at ∼ 2. 8σ at the same threshold and resolu-tion for the loops. Although the deviation occurs in a regime in which the low threshold and large smoothing scale may indicate statistics with low numbers, we find the statistics to be well behaved and stable. The high significance value, combined with the fact that the deviation is at a scale at which anomalies have been reported in several methods and datasets  (Eriksen et al.
2004b; Park 2004; Schwarz et al. 2016) , the case merits consideration. However, in this context, we also note that the statistical analysis is based on merely 600 and 300 simulations for the NPIPE and FFP10 datasets, respectively. For the Euler characteristic, the NPIPE dataset exhibits a high significance due to the high significance exhibited by the loops. However, for the FFP10 data set, the Euler characteristic is within approximately the 2. 5σ band computed from simulations, which is largely consistent with the observations in Planck  Collaboration et al. (2020c). However, we note that our results generally exhibit stronger differences than the Planck analysis pipeline. While ascertaining the source of this discrepancy is beyond the scope of this paper, a plausible source of the difference may be the different methods adopted in estimating the Euler characteristic and Minkowski functionals in general in Planck  Collaboration et al.
(2020c) , which are based on theoretical equations for boundary-less manifolds. At the next higher smoothing scale, N = 16, FWHM = 640 , both datasets exhibit a significantly anomalous behavior with respect to the number of loops, but not the number of components. However, we disregard this resolution because of the low numbers involved in computing the statistics, owing to the large smoothing scale and low thresholds. Fig. 12 : Visualization of the loops surrounding the low-density regions at a moderately negative threshold. The gaps in the manifold correspond to the mask that has been removed. We clearly note the equatorial belt corresponding to our galaxy, and more patches in the visible cap. Some loops live fully in the excursion region that is not influenced by the mask. We show them in red.
We also depict some representative relative loops whose end points are masked. We draw closed loops for this category as well and show the portions in which they overlap the masked regions in white. The visualization is based on the observed CMB map from the NPIPE data set smoothed at 5 degrees. In order to test for nonrandom discrepancies, we computed the p-values using the theoretical model-dependent χ 2 test, as well as its nonparametric version computed from empirical distributions, by combining all relevant thresholds at a given resolution. We also presented the nonparametric and modelindependent Tukey depth test, which indicated that the observations are true outliers with respect to the simulations in numerous instances. However, in the final interpretation, we focused on the most conservative p-values, estimated using the χ 2 test from the empirical distributions.