dataesr/scientific-paragraphs-categorization huggingface dataset:
Indeed, the principle of no free lunch in machine learning tells that no model can guarantee convergence on its final sample performance. Therefore when a finite amount of sample is available, the practitioner should evaluate several model and stick to a heuristic, as the one we suggest, in order to select the best model. In order to strengthen this point and also address the comment on the use of different architecture and their impact on the estimation, we produce yet another experimental result. Inspired by  [34] , we consider the problem of estimating the Bayes error rate (BER, aka Bayes risk or Bayes leakage) using the MNIST dataset (a benchmark dataset for ML classification problems). In  [34] , the authors use an empirical method to estimate bounds for the BER and, in order to do so, they need to perform dimensionality reduction (they try both principal component analysis, or PCA, and auto-encoding via an auto-encoder neural network).
Indeed MNIST, being a 28px ˆ28px images dataset, contains high dimensionality samples and all the three applied methods (bounds estimation, k-NN and random forest) benefit from dimensionality reduction. Given that the samples distribution for MNIST is unknown, in  [34]  the authors aim at checking whether the three estimations confirm each other. And indeed they do. However, it is well known that in many image classification tasks, the state-of-the-art is represented by deep learning and, for instance convolutional neural nets. While in  [34]  the authors study how the addition of new layers to the model affects the bound estimation, we focus on the comparison between two network models, a dense and a convolutional one. In particular, the dense network model we consider has one hidden layer with 128 hidden units and ReLu activation function.
As we can see in fig. 15 , the box-plot corresponding to the estimation not based on the majority vote is the same already reported (cfr. section 5. 4). Compared to it, the one based on majority vote shows a higher (and therefore more precise) average estimation and a lower dispersion. However, it is important to notice that, when in this case we consider a majority vote ensemble, since we are exploiting the "expertise" of many models trained on i. i. d. training samples of size 10K, we are actually exploiting the knowledge coming from 50K samples. We therefore analyze the case in which, according to what has already been done in section 5. 4, the same 50K samples, obtained by merging the 5 datasets with 10K samples each, are used to train a single model. The results are showed in fig. 16.
ACKNOWLEDGMENTS This research was supported by  DATAIA  " Programme d'Investissement d'Avenir"  ( ANR-17-CONV-0003 ). It was also supported by the  ANR  project  REPAS , and by the  Inria/DRI  project  LOGIS. The work of  Catuscia Palamidessi  was supported by the project  HYPA-TIA , funded by the  European Research Council (ERC)  under the European Union's  Horizon 2020 research and innovation program , grant agreement n. 835294. This project has received funding from the  European Union 's  Horizon 2020 research and innovation programme  under the  Marie Skłodowska-Curie  grant agreement No  792464.
We present a database and velocity catalogue towards the region of the Shapley Supercluster based on 18,146 measured velocities for 10,719 galaxies in the approximately 300 square degree area between 12h43m00s < R. A. < 14h17m00s and -23 • 30 00 > Dec > -38 • 30 00. The data catalogue contains velocities from the literature found until 2015. It also includes 5,084 velocities, corresponding to 4,617 galaxies, observed by us at Las Campanas and CTIO observatories and not reported individually until now. Of these, 2,585 correspond to galaxies with no other previously published velocity measurement before 2015. Every galaxy in the velocity database has been identified with a galaxy extracted from the SuperCOSMOS photometric catalogues. We also provide a combined average velocity catalogue for all 10,719 galaxies with measured velocities, adopting the SuperCOSMOS positions as a homogeneous base.
In this paper, we present a compilation of velocities in a wide area (20 • × 15 • ), including our previously unreported data. The latter were obtained mainly from a survey carried out over several years with the fiber and multislit spectrographs at the 100" du Pont telescope at Las Campanas Observatory (LCO), as well as the Hydra spectrograph at the Blanco 4. 0 m telescope at Cerro-Tololo Interamerican Observatory (CTIO). Here, we present all the data resulting from these observations, which represent a set of 5,084 new velocities among which 2,585 are newly observed galaxies. Combined with already published redshift sets from several surveys and papers, compiled until 2015, we built up the most extensive velocity database for the SSC area, containing 18,146 velocity measurements for 10,719 galaxies.
The observing runs and instrumentation used in the spectroscopic observations are described in Sect. 2. In Sect. 3 we present the extraction and build-up of a photometric galaxy catalogue from the SuperCOSMOS Sky Surveys (hereafter SSS) 1 for the approximately 300 square degree area of the sky. The extended velocity database is described in Sect. 4, while Sect. 5 describes the average velocity and photometry catalogue, obtained from cross-combining the velocities from the database and the photometry and astrometry from the galaxy catalogue derived from the SSS. This section includes comparisons between the galaxy velocities in common among different data sets, as well as the velocity zero-point shifts required to equalize the combined average catalogue. In Sect. 6, we discuss the completeness of this average velocity catalogue and analyze the galaxy number density over the whole and the intercluster survey regions.
The KPGL2 grating resolution was 0. 7Å/pix with a spectral range 3600-7400Å/mm and tilt 5. 74 •. We made 3 exposures of 480s, 720s, or 1200s depending on the average brightness of the galaxies in the field. Table  1  gives a schedule of the observing sessions and a code for the corresponding observation sets used in the following Database. In Fig. 1  we plot the fields covered by the spectroscopic observations, as explained in its caption. From the above observing runs, we obtained a set of 5,084 new velocities for 4,617 galaxies (some of them were observed two or more times) in the general direction of the SSC.
The object catalogues produce positions, proper motions (disregarded), magnitudes in all four bands, image ellipticity fits, position angle, ellipse area, image quality, and class. The ESO SkyCat software package (http://www. eso. org/sci/observing/tools/skycat. html) permits to display the survey images overlapped by the object catalogues, each object represented by an ellipse with its center coordinates, area, ellipticity, and position angle parameters. Different colors or symbols also allow simultaneous overlays of several catalogues. Due to the not uncommon presence of blended galaxy images in clusters, we kept both the parent object defined by the common low isophotal contour and the daughter objects, represented by ellipses around the individual galaxies, at higher isophote contours.
These were fairly bright E0 ellipticals, with clear diffuse edges. We transferred these entries to the galaxy catalogue but kept their CLASS 2 for easy later reference. As a further step in the verification of the galaxy identifications we simultaneously plotted the NED database 4  with different symbols over the survey images. This was of particular help near the cut-off photometric limit R2=18. 0 mag. In total, we extracted more than 1,184,000 objects of all classes. The number of CLASS 2 (star) entries was roughly one million. The number of original CLASS 1 (galaxy) objects was close to 173,000. All of them were checked individually by eye, as a majority were false or problem classifications (as a result of using the quality image parameter 4096, as discussed). The number of galaxy objects kept was slightly more than 60,400.
Velocity database By combining our new velocity measurements with existing ones from the literature, we produced a large velocity database containing 19,708 velocity measurements corresponding to 11,910 galaxies, over an area slighly bigger than the one finally chosen as defined earlier, and covering most of the SSC. When limited to the 300 square degrees, we obtained the quoted 18,146 velocities and 10,719 galaxies finally retained in the database. Our search of the literature is not intended to be complete, particularly for velocities < 6,000 km s -1. We added source references as we found them for one or another reason. We realize that several literature papers include previous data along with their own measurements, and thus the same velocity data point could inadvertently be considered several times, coming from different sources.
A difficulty comes from the fact that in the literature the individual source of a velocity measurement is not always given. When the duplication is clear (because it coincides with an older value already included in the database), we eliminated the entry, keeping the original measurement. A comment was added in these entries. Besides, there are references to databases dynamically varying in time, such as ZCAT (https://heasarc. gsfc. nasa. gov/W3Browse/all/ zcat. html) or NED. The FLASH survey uses these references as only source or to average values with their own measurements (http://ned. ipac. caltech. edu/). If there has been an update of the those databases, the old values source may be lost or are hard to find. Moreover, When an author quotes a velocity value which is an average of his measurement and an older NED and/or ZCAT value, it is hard to know which both those velocities were (unless NED or ZCAT has kept the old value).
More complex is the case when the NED or ZCAT later updates their values exactly to the average given by the same reference. Here we give individual velocity values with references for each of them, trying, as far as possible, to quote the original measurement only. However, when a literature average is given, we listed it as well, since it can contain new partial information from velocities unavailable today, for the reasons just given (and we warn about this in the comments). Generally we have also tried to give in the database the original numbers for the several parameters of the literature entry, as far as given by the authors. We used the reported coordinates of each velocity measurement to compare with the SASSSG catalogue, grouping together multiple measurements of the same object, while identifying its visual counterpart.
This was an iterative process done by finding the closest SASSSG galaxy counterpart to each entry in our preliminary database, up to a maximum allowable distance of 20", and comparing cross-match velocities for consistency. The SSS images where used for visual inspection in case of conflicts encountered by our automatic analysis software. After a first matching run, we identified all the SASSSG objects that were assigned to more than a single counterpart in the velocity catalog, producing a list of duplicate matches. To resolve these cases, we began by accepting the closest match within each set to be correct, and then asked whether the other velocity measurements corresponded or not to that same SASSSG counterpart. If no other SASSSG object was found within 20" of the other velocity measurement, and if the velocities lied within 500 km s -1 , then we merged the two velocity measurements as different measurements of the same object.
If otherwise there was another SASSSG candidate closer than 20", or if velocities differed by more than 500 km s -1 , then we marked those for visual inspection. This was done overlapping survey images and positions on the screen, both from the SASSSG and velocity object positions. When two or more velocity positions fell close to a visual galaxy, with greatly discordant velocities, we took several steps. First, we did a search of the original ref-erences, to discard typos, precession errors or relevant updates, and obvious identification errors. Some were resolved at this level. Then, we evaluated the given redshifts against the apparent galaxy image brightness, compactness and morphological details, to try to discard the less sensible velocity. Simultaneously, we considered the quoted velocity errors or spectra quality factors (if given) and similar discordant problems in the same reference, to try to decide which velocity to keep for the database.
In nearly all cases, we could allocate a preferred velocity. For completeness of the raw data, velocities not considered for further calculation were kept in the velocity database, but flagged accordingly. In a few rare cases, a velocity position fell midway between two galaxy images with similar magnitude and morphology. Similar steps were followed, looking in the references and finding charts or descriptions. In most cases the problem was solved. Only in two or three cases, the uncertainty remained and these data were deleted from the database. One persistent problem was posed by contact and/or close double galaxies. First, the COSMOS software rarely produced two separate catalogued objects when the distance between centers was less than around 10"-20". As described earlier, we introduced a second image, adjusting the centers and ellipticities correspondingly.
Moreover, the velocity data from different authors usually listed a velocity for one component only, with position errors of the same magnitude as the distance between centers. If the velocities of the components were not very different, it was difficult to allocate the correct identification. We did our best using all the information available (if at least one author gave the two velocities, or we tried to choose the brightest as the observed one, or trust the accuracy of the relative positions of one author, etc. ). For some of these cases, we had to manually force the identifications in the automatic identification procedure. No more than two or three cases of allocation remain uncertain. Unidentified velocities were mostly associated to blank spots in the SSS images, due to position errors (as was the case with some IRAS objects  (Allen et al.
1991, or HIPASS galaxies)  or misprints in the galaxy positions in the published velocity tables that made them fall on blank sky or near a star. In most of the latter cases, we could find the real target galaxy and corrected the misprint. Manually resolved conflicts were incorporated into the database manually in the next matching run. Most often, we moved the velocity entry with good positional consistency to the first line of the group of velocities corresponding to one galaxy, which was used for the positional correlation. The reduced database contained a grand total of 18,146 velocities corresponding to 10,719 galaxies. Our velocity database groups different measurements for each galaxy, cross-identified as described above. For traceability, we kept the original position entries (unless a misprint was detected or we were forced to use NED positions for identification purposes), followed by all the velocity parameters as published in the corresponding reference or in our own work.
Each entry line gives an individual velocity measurement, including a reference code to identify the reference source and a FLAG (1 or 0) to indicate if the velocity should be used, or not, to compute the average velocity of the object. Different galaxies are separated by a line containing only an index number. A sample of these data appears in Table  4 , where we also give the list of all velocity references. The comments column contains further information regarding the references, problems with the identification and/or indicate the criteria used or choices made. Discrepant velocity values were also noted. In Appendix I we discuss some individual galaxies that have wrong or complex optical identifications.
Combined velocity-photometry catalogue The large velocity database permits the extraction of a velocity catalogue, with one average velocity for each galaxy observed in the region. We obtained this in two steps: 1) try to correct for the small, in principle systematic, differences in the literature, produced by different instrumentation or measurement procedures. 2) Do a weighted average of the available velocities for each object. The result is a velocity catalogue based on the database. From the database, each future worker can calculate its own corrections for a velocity catalogue. It is debatable whether the best catalogue should be built taking the best velocity measurement for each galaxy (as the NED or ZCAT were built), or whether a weighted mean is more suitable, as this value would be influenced by poor data, even if properly weighted down.
2000)  that there were no systematic velocity differences between observations carried out with the fiber spectrograph and the earlier Reticon spectrograph (both built by S. Shectman, Shectman 1989 ), mounted at the du Pont Telescope, as both used the same Carnegie Image Tube as final detector, used for the much earlier observations with the same telescope reported in  (Quintana et al. 1995). In most sessions we also carried out repeated observations of some galaxies (as listed in the database), to check that we had a consistent velocity system and to reduce statistical errors. For each of the other surveys (both our own with the WFCCD and Hydra, and all those from the literature), we identified the galaxies in common with the reference set. Starting by the survey with the largest number of velocities in common with the reference set, N com , we used the average of the velocity differences between the survey and the reference set, ∆v, as our zero-point correction.
After correcting the survey by its zeropoint, we included it in our reference set, increasing the number of measurements available for comparison with the remaining surveys, and continued the process with the next one with largest N com. Assuming Gaussian measurement errors, the significance of the zero-point correction can be quantified by computing the standard deviation of the velocity differences, σ ∆v , such that the error on the mean becomes σ ∆v = σ ∆v / √ N com. The significance can then be written as S/N ≡ |∆v|/σ ∆v. Table  3  summarizes these results, where N re f is the number of galaxies of the corresponding reference given in column 2. Table  2. Shapley Supercluster velocity Database. A running number separates different galaxies, with one or more velocity entries from indicated reference.
Reported velocity calculation The combined velocity catalogue presents one entry per galaxy. The heliocentric velocity assigned to each galaxy is the average of all available values, v i , weighted by their respective errors as reported in the database, ∆v i. It is given by v = i v i ∆v -2 i i ∆v -2 i. (1) The error in the combined velocities incorporates both direct measurement errors reported in the original catalogues and the deviation of the individual measurements from the mean, being given by ∆v = i (v i -v) 2 + ∆v 2 i ∆v -4 i i ∆v -2 i. ( 2 ) Galaxy entries are identified by their SASSSG positions, following the previously discussed cross-identifications. These identification codes are consistent with the ones provided in the velocity database, in which each independent velocity measurement is identified using a letter (e.
All these data products are now available for the scientific community in digital format, and can be accessed here: http://www. astro. puc. cl/Shapley-catalogs. By adding velocity measurements covering areas between known clusters, we improved our understanding of filaments connecting the central clusters, revealing a complicated structure of gravitationally interacting elements. These elements are yet to be proven gravitationally bound, an analysis that we are leaving for a future publication. The extended catalog also reveals the possible existence of several new groups and poor cluster can- didates, also allowing to test the reality of some proposed structures, which will also be explored in a future study. Appendix A: HI velocity measurements and possible wrong or confused identifications.
ESO 381-020, a low-surface-brightness (disaggregated) Irr galaxy. Data is #22 in Database (and comments). NED and other catalogues give a low z derived from HI velocities. Problem: Dr91 gives 3,399 km s -1 , while Ka03 (source ZCAT from HI data) and Ko04 (HIPPASS) give 585 km s -1 , discrepant velocities from Dr91. All 3 have positions consistent with ESO381-020. The velocity quoted by Ka03 may not be an independent measurement. The Cosmos galaxy image has morphology consistent with v ≈600 km s -1. Its large angular extension means the 3 positions are spread over the central very irregular area. There are no other nearby Sp or Irr galaxies within 15'. Either the Dr91 measurement is faulty, or the Dr91 velocity corresponds to a background galaxy, hard to distinguish among irregularities of the main lsb Irr galaxy image.
ESO 507-036, an Sp galaxy. Data is #8463 in Database (and comments). The 6dFGS survey gives a velocity of 13,803 km s -1 and a well centered position on the Sp nucleus. Huchtmeier et al. (2005, Hu05)  gives an HI value of 3,364 km s -1 with a position within the optical edge-on Sp image. Another 6dFGS Sp at 13,551 km s -1 is located ≈5. 5'to the north. Both publications give the coordinates of the ESO galaxy, with highly discrepant velocities, but 6dFGS is an exact direct coordinate measurement. The Cosmos optical image of the edge-on spiral suggests a warp of the main disk with a hotspot, or maybe it is a possible background, also edge-on, spiral aligned with the main disk. However, the most likely option is that the Hu05 value is a velocity of a different Sp, as there are several smaller spirals within 5', and there is another edge-on Sp with 3,000 km s -1 at ≈20' to the SE.
ESO 443-059, a bright spiral. Data is #1472 in Database (and comments). Three optical velocities (6dFGS, Dr91, Da87) and one HI  (Maia et al. (1996, Ma96 in NED)  are consistent at ≈3,400 km s -1 and consistent with the ESO443-059 position. Problem: the FLASH survey Ka03 quotes a NED HI source that gives 2,293 km s -1. The discrepant FLASH velocity indicates a wrong id for the HI source. Most likely the source could be identified with Database #1492 Sp at ≈3' to the NE, which has 3 velocity measurements around 2,310 km s -1. Alternatively, but less likely, the Ka03 velocity could be identified with #1507 with v= 2266 (velocity from Ba97) located ≈9' away to the NE. Both are likely members of a group around nearby NGC 4965 at ≈2,300 km s -1. ESO 443-061, a spiral. Data is #1504 in Database (and comments).
There are two independent and consistent optical velocities (6dFGS and LC97) at ≈9,500 km s -1. The Ko04 HIPASS brightest-1000 survey measures a velocity of 2,282 km s -1 from a position 5'15" away from this galaxy. NED and others assign this Ko04 HI velocity to ESO 443-061, which is a wrong optical identification. The HIPASS velocity is consistent with some NGC 4965 group members. Alternatively, it could be a rare HI cloud, or another galaxy. In fact, the most likely identification for this HIPASS source is with #1507 from our Database. At 2'10" this is closer to the HIPASS position than to ESO 443-061. IC 4254 a bright peculiar galaxy. Data is #3681 in Database (and comments). Two optical, independent and consistent velocities (Dr88, St96) give ≈15,350 km s -1 and a make it a likely member of the A1736 cluster (old velocity NED value used by Ka03).