dataesr/scientific-paragraphs-categorization huggingface dataset:
Conclusion Although the evidence presented here illustrates the accuracy of mortality indicators given by vital statistics data for rather advanced ages (until around the age of 108 and 103-104 for probabilities of death and life expectancy calculations, respectively), these data cannot be used to assess the shape of the age-trajectory of mortality at the highest ages because they include growing shares of false supercentenarians or even semi-supercentenarians with advancing age. As for "public" lists of individual supercentenarians, they are inappropriate too because in addition to possible exhaustiveness concerns, there is a risk of selection bias due to the fact that data collected using press reports, notably, tend to favor extreme ages. On the other hand, thanks to their high quality, RNIPP data offer much firmer grounds to derive the level and age pattern of mortality at very old ages.
The exhaustive validation of all deaths registered at the alleged ages of 110+ revealed that for cohorts born between 1883 and 1901 (all these cohorts are extinct today), errors are only few and easily explainable (either cases of disappearance when persons have gone missing or manual data entry errors), at least when dealing with individuals who were born and died in France. All corrections were effortless to make. Furthermore, for semisupercentenarians, individual age at death validation conducted on a very large sample showed that errors are extremely rare, indicating that RNIPP data can be used without any verification until at least age 108. However, a first analysis of these RNIPP data indicates that the number of "verified" supercentenarians from overseas French départements is dubious.
There is likely a long waiting time, however, for a conclusion about the shape of the mortality curve at very old age. Even the most accurate French data source today, namely the RNIPP, is not yet suitable to address this matter. But with the RNIPP, the ambition to reach a conclusion in a near future is not totally unrealistic, especially thanks to the rapidly-growing expected number of centenarians, semi-supercentenarians, and supercentenarians in coming decades. Furthermore, according to INSEE the RNIPP records are considered exhaustive only for cohorts born since 1890, meaning that the RNIPP covers all persons that died at age 110 since 2000 only, at age 111 since 2001 only, etc. Study of French supercentenarians has bright prospects in the next few years. The probabilities of death calculated using RNIPP data for female birth cohorts born between 1883 and 1901 in Metropolitan France appear to level-off at 0.
5 between ages 108 and 111, a finding in accordance with earlier studies  (Robine et al. 2005; Gampe 2010 ). After age 111, however, data becomes too scarce to assess the trend. Also, we obtain a quite low life expectancy value of 1. 2 years at age 108. A practical conclusion is thus to recognize the usefulness of pursuing the gathering and validation of data in the following two directions: below age 105 to improve the link between the RNIPP and vital statistics mortality data series, and above age 110 to increase as much as possible the number of observations at the most advanced ages.
Acknowledgements At the  University of Chicago , we thank  Klaus Nielsen  and  Jon Staley  for help with cryomilling,  Matthew Sullivan  and  Alex Ruthenburg  for help with FPLC,  Aarthi Kuppannan  for help with cell culture, and  Vytas Bindokas  for help at the  Integrated Light Microscopy Core Facility. We thank  Naomi Stover  ( Bradley University ) for gene annotation, and  Lev Tsypin  ( Caltech ) for stimulating and entertaining discussion. We thank the  FingerPrints Proteomic Facility at the University of Dundee  for excellent technical support. Work in APT's laboratory was supported by  NIH   GM105783  and in MCF's laboratory by  Wellcome Trust   Investigator Award   204697/Z/16/Z.
(2012)  is still worth working on, especially due to the fact that their LDA-based discrimination approach proved to be valuable (as shown in  Leroy et al. (2017) ). It can be further refined and confronted with other multivariate methods. Furthermore, such a refined method can be successfully applied for repeated analyses of datasets from earlier works, where only data on major oxides is available. The approach proposed in this paper consists in using as many as seven different classification techniques for the purpose of provenancing of analysed observations. These techniques are: Linear Discriminant Analysis (LDA), Supported Vector Machine (SVM), Random Forests (RF), Naïve Bayes (NB), K-Nearest Neighbours (KNN), Recursive Partitioning and Regression Trees (RPART) and Kernel Discriminant Analysis (KDA).
Data and research methods Data from three smelting experiments (marked in the paper as XP27, XP61, and XP90, or collectively XPA) conducted by Peter Crew and analysed by Thomas Birch  (Birch (2014) ) was used for the purpose of testing and presenting the proposed approach. This assemblage includes two groups: smelting slag (SLAG) and slag inclusions (SI) in the iron (see Electronic Supplements), which were analysed for their major element oxide and trace-element composition using a combination of SEM-EDS and LA-ICP-MS. The analytical methodology, accuracy and precision and a full dataset  (Birch (2014) ) are available online (Aberdeen University Library, https://digitool. abdn. ac. uk) or from the author. Major element oxides investigated were Non-Reduced Compounds. Concerning trace elements, strictly lithophile ones were selected.
A final selection of variables was made after a series of LDA-based experiments with major oxides alone, different combinations of trace elements and a "full set", containing both groups of data (see  Birch (2014) ). Concerning the smelting experiments themselves, although operating conditions were similar, there were some significant differences between the rich bog ores that were used. For XP27 ore from the River Perry in Shropshire was used (3% MnO, 3% P 2 O 5 ), XP61 was carried out with ore from Crawcwellt West (3% MnO, 0. 4% P 2 O 5 ), while for XP90 a manganese-rich bog ore blend from Crawcwellt South was used (11% MnO, 0. 1% P 2 O 5 ). The XP27 and XP90 blooms were processed to currency bars while the XP61 bloom remained unrefined (on the nature of these experiments see  Crew (2013)  and references therein).
Bearing in mind the fact that the ores that were used in XP27, XP61 and XP90 strongly differed from one another and thus they may not be perfectly suitable to fully demonstrate the classification ability of the proposed approach, it was decided to test the classifiers again using datasets from another three experiments (XP17, XP23 and XP26, called collectively XPB). These datasets have already been used for testing purposes in  Charlton et al. (2012)  and  Blakelock et al. (2009). For XP17, Blaenafon siderite ore (1. 0% MnO, 0. 4% P 2 O 5 ) was used, while XP23 and XP26 shared both design features as well as the ore (South African Sishen hematite, MnO below detection, 0. 1% P 2 O 5 ). For these experiments, however, only major oxide data was available. Therefore, the following oxides were taken into consideration for provenance identifications: MgO, Al 2 O 3 , SiO 2 , K 2 2O, CaO, TiO 2 , and MnO.
The first group of experimental data (XPA), which is used as training set in this paper, included 170 observations (XP27 -20; XP61 -70; XP90 -80). The other group (used as test set) encompasses slag inclusions in bars and billets. The total number of observations in this group before verification of smelting-related slag was 104 (XP27 -16; XP61 -44; XP90 -44). Concerning the other assemblage of experimental data (XPB), the relevant figures were the following: the training set -225 observations (XP17 -75; XP23 -45; XP26 -105); the test set before verification of smelting-related slag -153 observations (XP17 -64; XP23 -44; XP26 -45). In order to isolate smelting slag inclusions in both groups, the approach proposed by  Charlton et al. (2012)  was used. Oxide values below detection limits were replaced with minimum values recorded in a given regional assemblage for a given variable.
e. , proposed by  Charlton et al. (2012)  and  Disser et al. (2014) ) were compared and they yielded similar results, see _ Zabi� nski et al. (  2018 ). After the verification, the total number of observations in the first group of the test data (XPA) was 97 (XP27 -15; XP61 -40; XP90 -42). In the next stage, positively verified smelting slag inclusions were analysed, taking the following variables into consideration: MgO, Al 2 O 3 , SiO 2 , K 2 O, CaO, TiO 2 , MnO, BaO (major elements), as well as V, Cr, Rb, Sr, Y, Zr, Nb, Ce, Nd, Sm, Eu, Tb, Tm, Yb, Hf, Ta, Th, and U (trace elements). Concerning the other group (XPB), the number of verified observations was 110 (XP17 -36; XP23 -32; XP26 -42). As for this group only data on major oxides was available, the following ones were included in further analyses: MgO, Al 2 O 3 , SiO 2 , K 2 O, CaO, TiO 2 , and MnO.
Datasets transformations In Electronic Supplements one can find a detailed specification of the datasets presented in Table  1. These four datasets are compositional data (or composition for short)  Aitchison (1986) ; van den Boogaart and Tolosana-Delgado (2013);  Pawlowsky-Glahn et al. (2015). There is no doubt that such data cannot be analysed directly. Two commonly used transformations are log-ratio transform (lr) and centred log-ratio transform (clr). These transformations are widely known, which is why we do not discuss them here in detail. Nevertheless, for the sake of completeness of the presentation, we provide relevant mathematical formulas in Electronic Supplements. There, we also make a brief comparison of the relevant transformations. In addition, we pay attention to a certain variant of transformations used in  Charlton et al.
Workflow for identifying SI provenance From Table  1  we can see that ten different datasets are used in this work. Below, we briefly discuss how these datasets are processed in computational experiments. In the first step, the M (major elements) and T (trace elements) datasets are combined into one set of M þ T components. In other words, we do not carry out separate experiments for the M and T sets. Before the M and T sets are combined into one result set they must be transformed accordingly. Since the M and T sets are in different units (in percent and ppm respectively), they must be reduced to one unit (percentages were selected as target). Finally, the clr transform is applied, as presented in Electronic Supplements. The entire procedure can be summarised in the following 3 steps: Step 1:T ppm →T % Step 2:T % þ M % →ðT þ MÞ % Step 3:ðT þ MÞ % →clrðT þ MÞ % We must also note that in case it is decided to use the lr transform, Step 2 should be followed by the z-score transformation (also known as z-values, normal scores, or standardized variables).
This transformation is done in order to avoid the situation where large values in the data will dominate over small ones. However, if the clr transform is applied, zscore is not strictly needed. Otherwise, an additional step would appear, i. e. Step 2a: ðT þ MÞ % →z scoreðT þ MÞ %. From now on, by using the XPA-SLAG, XPA-SI, XPB-SLAG, XPB-SI, AD-SLAG and AD-SI symbols, we mean data that underwent the transformations discussed above. If at any given time it does not matter whether we are dealing with SLAG or SI datasets (or both), we will simply use XPA, XPB, or AD abbreviations. Two types of numerical experiments were performed. In order to make our discussion more comprehensible, an illustrative workflow diagram was prepared, see Fig. 1. Individual nodes have been marked with capital letters and in the text we refer to these markings.
In Electronic Supplements, a script in the R language (workflow. R file) has been prepared, which complements the diagram and demonstrates how the actions presented on it can be performed in practice. In the first experiment, we take into account the XPA datasets. It is of importance that in both XPA-SLAG and XPA-SI datasets we have a reliable assignment to individual groups (i. e. , XP27, XP61, XP90). Therefore, we use XPA-SLAG assemblages as training dataset in order to present the methodology for creating classifiers, while XPA-SI assemblages are used as test dataset in order to demonstrate that the proposed approach is proper and works correctly. This experiment can be summarised as follows: 1. Both XPA-SLAG dataset and XPA-SI dataset were loaded (node A) and transformed, as it was shortly described in Electronic Supplements (see nodes B1 and B2).
2. Using the XPA-SLAG dataset a few classifiers were built (see nodes E and G). Six parametric (LDA, SVM, RF, NB, KNN, RPART) and one nonparametric (KDA) methods were used in this task (see nodes C1 and C2). The nonparametric method also requires dimensionality reduction. Some notes are given in Section 2. 4 (see nodes D1 and D2). 3. The quality of individual classifiers was determined using four techniques, that is: a) reclassification, b) holdout, c) k-fold cross validation and d) leave-one-out cross validation (see nodes E and G). In this way, it was checked whether individual methods allowed to build classifiers with sufficiently good properties. Details are given in Section 2. 5. 4. Finally, the XPA-SI dataset was classified (see nodes F and H) using the six aforementioned classifiers and the final result (that is, identification of SI provenance) was achieved using majority voting technique.
Details on this technique are given in Section 2. 6. As in this dataset we have a reliable assignment to individual groups, it has become possible to thoroughly check the practical usability of constructed classifiers (i. e. , building confusion matrices and calculating percentages of well-classified cases, see node J1). The results of the above steps are presented in Section 3. Then, the quality of the classifiers which are applied in this paper was tested again with the use of the XPB assemblage. The XPB dataset has the same structure as the XPA dataset. Therefore, its analysis is identical to that for the XPA set. Detailed results are included in Electronic Supplements. In the second experiment, we take into account the AD datasets. Note here that now only the SLAG dataset has a reliable assignment to seven individual regions (abbreviated as Baj, Bar, Bru, Fer, Min, SaH and SaM; see the caption of Table  1 ).
Classification methods The main purpose of this research is to classify the AD-SI observations to a correct class (region in this case). The classifier is built based on one dataset (the AD-SLAG dataset, called a training one) and then the classifier constructed in this way is used to classify a completely different dataset (the AD-SI dataset, called a test one). It is obvious that the test set is independent from the training dataset. The main problem associated with the classification technique is that the target vector (region in our case) in the test dataset is completely unknown. Consequently, one must trust that the created model (classifier) correctly classifies the test dataset. In practical terms, there are no reliable methods for assessing the correctness of this process. In order to improve the reliability of the final classification, it was decided to build several classifiers using different methods.
The obtained partial results were then averaged in an appropriate manner and the final classification of the test dataset is a resultant of the scores of individual classifiers. Six classical parametric classifiers and one nonparametric classifier were used. These are: These methods are widely known in the statistical world. On the other hand, we are fully aware that these may not necessarily be completely clear to every archaeologist. We do not discuss these methods in detail here, as all of them, are rather complex from a mathematical point of view. We realise that anyone who wishes to know them better will anyway need to make a thorough study of relevant literature. Anyway, it seems to us that a detailed theoretical knowledge of each of these methods is not necessary for using them effectively in practice.
The KDA classifier was used with two nD→2D dimensionality reduction methods, i. e. , LDA and PCA, see Section 2. 4 (note that the LDA abbreviation is used in two senses: a) as an independent classification method, b) as a method of dimensionality reduction). It must be noted that the QDA method (Quadratic Discriminat Analysis) was initially taken into account. However, due to the nature of our data (many variables and too few records; see Tables  1  and 2 ), it could not be applied. The QDA method requires that the number of records in each category cannot be less than the number of variables. For example, XP-SLAG dataset has as many as 26 variables and XP27 category has only 20 records. As 20 < 26, the QDA method cannot be used in this case.
Dimensionality reduction There are a couple of methods which can be used for dimensionality reduction. Many of them are mainly used as a convenient tool for representing (mainly as 2-dimensional plots) similarities and/or dissimilarites in data. In classification tasks the following two approaches are probably the most commonly used: � Multidimensional scaling based on Principal Components Analysis (PCA), � Multidimensional scaling based on Linear Discriminant Analysis (LDA). More general dimensionality reduction methods can be most broadly divided into Metrical Multidimensional Scaling (mMDS) and Nonmetrical Multidimensional Scaling (nMDS). The methods are based on calculating distances between individual samples using different distance measure methods. Different authors very often use here the default Euclidean measure, while we have also examined other available measures (for example, the distance function implemented in philentropy R package is able to compute 46 different distances/similarities measures).
Methods for assessing the quality of classifiers A natural step after building a classifier is to evaluate its performance. A large number of measures have been developed and, typically, the training dataset is used for this task. Four approaches are the most common: 1. Reclassification method. After building a classifier using the training dataset the same dataset is used for evaluating its performance. In a sense, these results can be considered less binding, because it can be considered as controversial to use exactly the same full training dataset both for building and assessment of the resulted classified. 2. Holdout method. This is the most typical type of validation, in which the training dataset is divided randomly into independent sets: the training and the test one. Typically, the test set is less than 1/3 of the training set.
Such procedure is carried out repeatedly hundreds of times and at the end the average rate of correct classifications is calculated. 3. K-fold cross validation method. The original dataset is randomly divided into K equal sized subsets. Out of these, a single subset is retained as the validation data for testing the model, and the remaining K 1 subsets are used as training data. The crossvalidation process is then repeated K times (the folds), with each of the K subsets being used exactly once as the validation data. The advantage of this method is that all observations are used for both training and validation, and each observation is used for validation exactly once. A 10-fold cross-validation is commonly used but in general K remains an unfixed parameter. 4. Leave-one-out cross validation method.
Classifier voting technique As it was stated in Section 2. 3 six different classifiers were used for the task of identifying the AD-SI provenance. Obviously, the returned six results are not identical. A natural approach here is to combine these results in order to obtain the final classification. It seems that this approach is the only one that can lead to an improvement of the final classification of the AD-SI dataset. We are dealing here with a kind of Ensemble Vote Classifier. This idea allows to immunise the result to various types of disorders, which is why it is a reliable solution when working with 'uncertain' data. In this case, the group G of N classifiers is a set which usually consists of less complicated base classifiers G ¼ fC 1 ; …; C k g; k ¼ 1…N based on which the final decision is taken.
Experiments with the XPA datasets (XP27, XP61, XP90) This section presents the classification results of the XPA datasets. In line with the workflow discussed in Section 2. 2, in the first step XPA-SLAG and XPA-SI datasets were transformed accordingly. The raw and transformed datasets are included as Electronic Supplements. They are the basis for all further calculations. The two XPA sets are used to present the methodology for creating and testing classifiers. The first task to be performed is to check the quality of constructed classifiers. This is based on the training dataset that was used to build them (see Section 3. 1). If the result of this test is satisfactory, one can proceed to the classification of the XPA-SI test dataset. This issue is described separately for the classical parametric classifiers (see Section 3.
Quality of the applied classifiers There is no question that it is indispensable to examine the quality of the constructed classifiers. Omitting this step may lead to a situation that we do not really know whether the classifiers have any practical value. Suggested methods for this task were briefly discussed in Section 2. 5. It is also worth remembering that the assessment of the classifier quality is made on the basis of the training dataset and not the test one. In consequence, we are not able to precisely determine how our classifier will work when we classify a completely different dataset than the one used to build the classifier. Nevertheless, the obtained results certainly tell us something about the quality of the classifiers we use. One has to be prepared for all kinds of surprises.
Results for parametric classifiers While interpreting results presented in Section 3. 1, one must remember that the assessment of the classifiers quality was made on the basis of the training dataset (i. e. , XPA-SLAG) and not the test one (i. e. , XPA-SI). Having built our classifiers, we can use them to properly classify the test data (i. e. , XPA-SI). One of the most natural ways to demonstrate the quality of the classifier is to show it in the form of a so-called confusion matrix. Each row of the matrix represents the instances in a predicted class while each column represents the instances in an actual class (or vice versa). Table  4  shows the results for classification of the XPA-SI dataset with the LDA, SVM, NB, RF, KNN and RPART parameric classification methods. The best result was obtained for the LDA method and the worst one for the SVM method.
Results for the KDA nonparametric classifier In order to choose the best method to reduce the dimensionality of the XPA-SLAG and the XPA-SI datasets we have made a simple experiment. The XPA-SLAG and the XPA-SI datasets were reduced to 2D by two methods mentioned above and the results were depicted in Fig. 2. One can easily see that for this particular data the LDA method (upper plots) gives evidently better results then the PCA method. Regarding the XPA-SLAG set, the results are quite similar. In both cases, data from individual classes are clearly separated. However, as for the XPA-SI set, it can be seen that for the LDA method the separation of XP61 and XP90 classes is clearly better comparing to the PCA method. There is still an overlapping zone between them in the upper right plot. In the lower left plot such a zone does not occur.