dataesr/scientific-paragraphs-categorization huggingface dataset:
Regarding the reading of different EEG formats, two modules are available in the current stage of the platform, namely GDF (". gdf") and Matlab (". mat"), and one is still in progress, i. e. , MNE (". fiff"). Future versions on BioPyC will offer more modules for reading data, starting with those for Python, i. e. , ". pkl" and ". dat". BioPyC currently offers tools for pre-processing the signals as well, all based on MNE  [15] : band-pass filtering and epoching. More pre-processing features are available in MNE, such as EOG-based artifacts removal. It would, therefore, be easy to add new modules for pre-processing data in the future versions of BioPyC. Indeed, EEG signals being noisy, artifact correction is an important part of the pre-processing step of the BCI process. This feature will, therefore, be the next future addition to BioPyC.
Materials and Methods Subjects. Sixteen healthy adults (age, 18-25 years of either sex), all with normal or corrected-to-normal vision and no reported history of neurologic or psychiatric disorders, were recruited from the University of Oxford. Subjects provided written consent before participating in the experiment and received £30 in compensation for their participation. Approximately £5 of bonuses could be additionally obtained depending on subjects' performance on the two-alternative forced-choice task. The study followed local ethics guidelines. The data from one participant was excluded because of eye artifacts. The investigation of subjects' decisions at the end of each sequence is reported in  Wyart et al. (2012). Procedure. The stimuli were displayed on a CRT monitor (1024 Â 768 pixels, refreshed at 60 Hz) placed ;80 cm away from subjects' eyes, and controlled with the MATLAB (MathWorks) Psychophysics Toolbox version 3  (Brainard, 1997; Pelli, 1997).
, blue: peak within analogous to the 5% percentile of the earliest responses across sources; red: peak beyond 95% percentile). D, Correlation coefficients between deltas and EEG amplitude. E, F, Analogous analyses tp B-C applied to the brain responses coding for the changes between successive stimuli (d ). G, Cross-validated encoding scores (Pearson's r) obtained with both angles (sin 1 cos) and deltas. Colors indicate EEG channels. The results can be visualized interactively at https://kingjr. github. io/chronicles/.
Research and  Innovation program  under the  Marie Sklodowska-Curie Grant  Agreement No. 660086  (J-R. K. ), the  Bettencourt-Schueller  and the Philippe Foundations (J-R. K. ), and the  Frontiers in Cognition Grant  to the  Département d'Études Cognitives at the École Normale Supérieure  ( ANR-17-EURE-0017 ). We thank  Gyorgy Buzsaki ,.
g. , blue: peak within analogous to the 5% percentile of the earliest responses across sources; red: peak beyond 95% percentile). D, Correlation coefficients between deltas and EEG amplitude. E, F, Analogous analyses tp B-C applied to the brain responses coding for the changes between successive stimuli (d ). G, Cross-validated encoding scores (Pearson's r) obtained with both angles (sin 1 cos) and deltas. Colors indicate EEG channels. The results can be visualized interactively at https://kingjr. github. io/chronicles/.
Introduction In sensory analysis, holistic techniques involving untrained subjects for product characterization are becoming increasingly popular due to their simplicity, speed, and cost effectiveness  (Delarue et al. , 2015; Varela & Ares, 2014). Moreover, the results obtained from these approaches have been shown to be largely similar to those obtained with a conventional profiling approach. Data collected from holistic techniques, such as free sorting or projective mapping, are usually recorded as a proximity matrix between the objects evaluated. Subsequently, a global representation is set up to highlight how the products are perceived by the subjects. Generally speaking, a set of objects can be visualized by means of either spatial or network representations on the basis of their proximity matrix.
To fill this gap, we propose a recursive strategy of tree rebuilding, which selects an edge to split at each step. The algorithm takes into account both the topology of the tree structure and the length of the edges between nodes. Once the partition of the objects is obtained, its stability can be evaluated using resampling techniques. In practice, a partition is assumed to be stable if small changes in the dataset do not have any significant effect on cluster membership. Among the various resampling techniques available, bootstrapping has been widely applied in sensory profiling to assess the stability of a configuration through the generation of confidence ellipses  (Blancher et al. , 2012; Cadoret & Husson, 2013; Courcoux et al. , 2012; Rossini et al. , 2012). In the present work, a bootstrapping procedure is applied to evaluate the quality of the partition obtained from an additive tree, through the use of cohesion and isolation indices  (Bel Mufti et al.
In our case study, a panel of 156 subjects performed a variation of a hierarchical sorting task that include 96 terms related to wine odors. The data collected from subjects were aggregated and represented as a dissimilarity matrix of 96 wine-odor terms. An additive tree representation was determined, which was subsequently partitioned into clusters of wine-odor terms. This study aims to present (a) an original method for the creation of a set of disjoint clusters from an additive tree representation, (b) a way to assess the stability of the clusters, by introducing criteria of cohesion and isolation computed with a bootstrapping strategy, and (c) guidelines for the construction of a wine-odor lexicon from a free sorting task. In the first section, the case study is introduced. Then, the methodology for the determination of a partition from an additive tree is detailed together with the stability of the partition thus obtained.
According to  Guénoche and Garetta (2002) , the homogeneity of a set of objects may be evaluated by its diameter, i. e. the maximum pairwise distance within the set. These authors also advocated the use of the diameter ratio as a useful measure of homogeneity. It corresponds to the diameter of any subset of objects divided by the diameter of the whole set of objects of the tree. The lower the diameter ratio, the more homogeneous the subset. This latter criterion is integrated in the algorithm as a stopping rule. More precisely, a threshold value equal to 80% has been set to decide if the subset under consideration should be split further or not. As in the case of the edge to be split criterion, such a threshold is an input parameter of the algorithm which can be adapted depending on the context under study or the dataset to be analyzed.
Conversely, the subset {Cherry, Strawberry, Rasberry} is further split into two groups: {Cherry} and {Strawberry, Raspberry}. Finally, a three clusters partition: {Apple, Pear}, {Cherry}, {Strawberry, Raspberry} is obtained from this toy example. The algorithm is written in R software 3. 4. 3 and the NJ algorithm is carried out using the nj function in the ape package  (Paradis & Schliep, 2019). The algorithm is available upon request to the corresponding author.
Cohesion and isolation of the clusters To evaluate the stability of a partition, it is necessary to measure the stability of its clusters. For this, several authors advocated the use of cohesion and isolation measures  (Bertrand & Bel Mufti, 2006; El Moubarki, 2009; Lenca et al. , 2008). A cluster is considered cohesive if the objects which belong to it, remain together after a perturbation of the dataset. Here, the perturbation is generated by the bootstrap resampling. Likewise, a cluster is considered isolated if two objects separated regarding this cluster remain separated after a perturbation. According to  Bertrand & Bel Mufti (2006)  and El Moubarki (2009), each stability measure is defined as the probabilistic measure of a quality rule. The rules for cohesion and isolation are defined as follows: -Rule for the cohesion of a cluster : If two objects are grouped together in cluster of partition , then they must be together in partition obtained after perturbation.
, 1993). Cohesion and isolation measures are computed for each cluster C of the partition. Subsequently, weighted sum of cluster's cohesion and isolation indices are used to estimate respectively the cohesion and the isolation of the global partition. Weights are introduced in order to take into account of the size of the different clusters, as reported in Appendix (Eq. (  4 ) and Eq. (  5 )). Further details are given in El Moubarki  (2009). As demonstrated by Bel  Mufti et al. (2012) , there is a tight connection between these indices and the Rand index. Indeed, the Rand index can be expressed on the basis of both cohesion and isolation measures. For more details, the equations defined by El Moubarki (2009) are reported in Appendix (Eq. (  6 )). In the context of free sorting data analysis, the Rand index is commonly used either to evaluate the agreement between two subjects' partitions or as the key criterion to determine a consensus partition of the objects from the various subjects' partitions  (Courcoux et al.
Investigating the degree of association of objects to clusters To obtain better insight into the partition , a deeper evaluation was made to analyze how strongly an object is related to the cluster it belongs to. For this purpose, the empirical degree of association of an object to a cluster has been computed, using the same rationale of the boostrapped partitions that reflect the perturbations of the dataset. Let us denote as * +,, % the estimation of the degree of association between the objects and ( -j , i. e. the frequency of merging together and across the partitions ( 1, …. These values are aggregated in reference to each cluster of the initial partition in order to compute the / +,0 criterion, defined as follows, for the 1 23 cluster of : / +,0 4 5 ∑ * +,, % ,∈ ,,8+ if ∉ (3a) / +,0 4 5 : ∑ * +,, % ,∈ ,,8+ if ∈ (3b) where 0 is the size of the 1 23 cluster of.
Discussion The first aim of this study was to introduce a versatile algorithm for determining a partition from an additive tree. This algorithm operates in a recursive way so that, for the tree/subtree under consideration at a given step, the edge corresponding to the highest LengthRatio value is cut and two new additive trees are then computed on the basis of the terms on either side of the cut. Overall, there were differences between the clusters formed by our algorithm (listed in Fig. 6 ) and the branching patterns of the original additive tree (Fig. 5 ). In other words, if the tree had been split only on the basis of its original branching pattern, the resulting clusters would have been different. We can notice that such a difference may be due to the size of the dataset considered in this study.
A threshold value of 80% was set herein but it is worth noting that this value can be adapted depending on the dataset and the context. Other stopping rules could also be considered, including the number or the size of the clusters. For example, in  Guénoche et al. (2012) , the number of clusters was defined a priori. Such a criterion could be integrated in a straightforward way in the proposed algorithm. A second objective was to assess the stability of the partition. Overall, the three measures proposed here-cohesion, isolation, and degree of association-generated complementary information that contributed to an improved assessment of the quality of the partition. The analysis of cohesion and isolation enabled us to assess the stability of the clusters: cohesion was a good indicator of a strong pattern within a cluster, and isolation yielded insight into other objects that might be related to a cluster.
(1984)  and  Lawless & Civille (2013) , the development of a lexicon serves the purposes of unifying the language used among stakeholders and of facilitating communication among winemakers, marketing personnel, wine researchers, and consumers. The choice of the subjects used to construct the structuration of sensory lexicon is also an important issue. In our case study, the inspection on the expertise led us to consider the whole panel of subjects as only minor differences occurred between different segments of expertise  (Koenig et al. , 2020). Moreover, these ones were mostly due to very specific terms such as 'English candy'. In light of these minor differences, we decided to deal with the whole dataset consisting in all the subjects. However, the choice of the subjects used is very important for the implementation of the method.
Conclusion Our aim was to propose a method of categorization that was adapted to both the semantic nature of the data set and the large number of terms under study. A partitioning procedure was developed to determine a set of clusters from an additive tree. Here, this algorithm was applied on a free sorting dataset corresponding to wine-odor terms. The algorithm relies on an additive tree representation of the data which appears to be more adapted when a large number of objects is considered. The approach proposed herein provide a partition of the objects from the additive tree representation. To better characterize the quality of the partition obtained, values of cohesion, isolation, and degree of association were computed using a bootstrapping strategy. The partition highlighted by our strategy, and the measures of stability associated with it, were largely consistent with the literature, in particular compared to the aroma wheel of  Noble et al.
Acknowledgments This work was carried out with the financial support of the regional program " Food for Tomorrow / Cap Aliment, Research ,  Education, and Innovation in Pays de la Loire" , which is supported by the  French Region Pays de la Loire  and the  European Regional Development Fund (FEDER) , as well as the financial support of the  Ecole Supérieure d'Agricultures in Angers. The study was carried out using the facilities of the  Senso'Veg platform. We would like to thank  Flore Lourtioux  and  Margaux Lecourtois , who participated in the recruitment of subjects and the acquisition of the data for the free-sorting task.
Behavioral responses Behavioral responses were labelled according to Reminsje et al. (Reminsje et al. , 2005)  (Fig. 1 ). During the acquisition phase, the correct answers (ACR) and erroneous answers (AE) were differentiated. During the reversal phase, the correct answers (RCR) and reversal errors (RE) were also identi ed following each switch of the rules. Among all reversal errors (RE) following the switch, the last error just prior to learning the new rule (i. e. the rst CR) was called the ' nal reversal error (FRE)'. After the rst CR, a false response, the 'no link to the switch (RENS)' was considered as the participant having learned the new rule. Data acquisition/analysis fNIRS Recording fNIRS signals were recorded with a portable continuous wave MEDELOPT® system (Seenel Imaging TM) using a 32-detector and 16-emitter design (Fig.
2A ). Optodes covered the prefrontal, frontal, and parietal lobes, with an emitter-detector distance of 2. 5 cm. The sampling rate was 2 Hz (500 ms each sample) and data were recorded at two wavelengths (660 and 850 nm). The position of the headgear was checked before and after the experiment; photos were taken to review placement and optode positions were digitalized for each subject using a 3D digitizer (NDI Medical Polaris Vega TM). No subject was excluded for an incorrect fNIRS sensor location. Optode positions (sources and detectors) were de ned according to the EEG 10-10 system coordinates to standardize the headgear position among the participants. The lower edge of electrode positions was located over the frontal area, with detector 2 (D2) centered above the highest point of the eyebrow (Fp2) (Fig.
2B ). The headgear covered the temporal area, with detector 27 (D27) above the C line (C1). The sensitivity of various con gurations was assessed using the AtlasViewer toolbox of Matlab to evaluate the best con guration of source and detector combinations for scanning the frontal and temporal lobes  (Aasted et al. , 2005)  (Fig. 2A  and 2B ). The fNIRS sensitivity map (Fig. 2C ) was modelled using AtlasViewer and freely available Monte-Carlo photon transport software (tMCimg routine, number of simulated photons = 10 6 ). The more optimal sensitivity con guration of the fNIRS source and detector positions is presented in Fig. 2A. [Insert Fig. 2  about here].
Data analysis The response of the participants associated with detection of the unexpected outcome for each trial following a switch of the parameters was assessed by the accuracy (the percent of correct answers) and reaction time (the time, in seconds, used by the participant to choose the animals). Each presentation following a switch was ordered for each trial: the rst presentation following a new rule was designated 1, the second presentation 2, etc. , until the new switch of rules. The average accuracy and reaction time were then computed for each numbered presentation. The various parameters were compared between the rst and following presentations for each condition to analyze the effect of repetition. The number of successive errors was also evaluated. These errors, called perseverative reversal errors, indicate that the former discrimination strategy, which is now obsolete, was still used, indicating that the participant had not yet updated his/her strategy.
Several studies have evaluated the effect of reward and punishment feedback on reversal learning by focusing on contrasting reversal learning with the acquisition phase  (Reminsje et al. , 2005; Budhani et al. , 2007; Ghahremani et al. , 2010; Xue et al. , 2017). Hemodynamic analysis was performed according to Reminsje (  2002 ). The reversal effect (i. e. unexpected outcome) was then characterized by contrasting the responses recorded during reversal learning and those during the acquisition phase: (FRE + RE) -(AE + RENS) (Fig. 1 ). Such a contrast was performed here for the reward and punishment conditions. Contrasts were performed at the single-subject level. Homer2 Matlab toolbox was used to analyze the fNIRS signal  (Huppert et al. , 2009). A band-pass lter between 0. 03 and 0. 1 Hz was applied to eliminate physiological noise (very low-frequency oscillations, respiration, and heartbeat).
A window from - 5 to 30 s around the onset of the stimulation (t = 0 s) was used to analyze the hemodynamic response to  RLT (Buxton, 2001). The xation-cross interstimulus interval throughout the whole task, served as the implicit baseline to allow the estimation of the hemodynamic response function by simple averaging  (Costantini et al. , 2013). The weighted arithmetic average cerebral hemodynamic response was then computed for each type of stimulation for all combined blocks and each subject. The data were z-score normalized for each subject to homogenize the data according to the individual characteristics. A baseline correction [-5, 0] s was nally applied to the normalized data.
Conclusion In this manuscript, we have successfully established the existence of a unique solution and stability result for an impulsive hybrid evolution system (1. 1) on time scales in a Banach space X. In addition, we have studied the exact controllability result for the hybrid evolution system (1. 2). These results have been established by using the evolution operator theory, nonlinear analysis and the Banach contraction theorem. Moreover. to illustrate the application of obtained analytical outcomes, we provided one theoretical and with the help of MATLAB, we have given a numerical example for the different time scales including T = R (case-1 of example 6. 2), T = P 1,1 (case-2 of example 6. 2) and T = [0, 3] 1 2 Z ∪ [4, 6] R (case-3 of example 6. 2).
The results of the third section are applied in the fourth section to the three proposed classes of detectors based on differences of empirical d. f. s. To do so, the consistency of a dependent multiplier bootstrap for the detectors is proven under strong mixing. The fifth section presents a summary of large-scale Monte-Carlo experiments demonstrating the good finite-sample properties of the resulting sequential testing procedures. An application on real financial data concludes the article. Auxiliary results and proofs are deferred to a sequence of appendices. A preliminary implementation of the studied tests is available in the package npcp  (Kojadinovic, 2020)  for the R statistical system (R Core Team, 2020).
Data examples To illustrate the use of the proposed sequential change-point detection tests, we considered two fictitious scenarios, the first (resp. second) of a univariate (resp. bivariate) nature based on closing quotes of the NASDAQ composite index (resp. Microsoft and Intel stocks) for the period 2019-01-02 -2020-04-11. The latter were obtained using the get. hist. quote() function of the tseries R package  (Trapletti and Hornik, 2019). In both scenarios, it was assumed that, on the last day of 2019, one wished to monitor the (univariate or bivariate) daily log-returns for a change in contemporary distribution possibly using the stretch of m = 251 (univariate of bivariate) log-returns of 2019 as learning sample. The latter decision was confirmed after the tests of  Bücher, Fermanian and Kojadinovic (2019)  implemented in the functions stDistAutocop() and cpDist() of the npcp R package  (Kojadinovic, 2020)  provided no evidence against stationarity for the two candidate learning samples.
Some of the fundamentals of these mathematical approaches and tools are summarized below. In the setting of the Arccos distribution, the MLE of α is obtained as α = argmax α L(α), where L(α) = n j=1 f (x j ; α) and x 1 ,. , x n denote the data. The SE corresponding to α is equal to [{-∂ 2 log L(α)/∂α 2 } -1 | α= α ] 1/2. We also have logL = log L( α), AIC = -2 logL + 2k, and BIC = -2 logL + k log(n), with k = 1 corresponding to the number of estimated parameter(s). The K-S statistic is specified by K-S = max j=1,. ,n j n -F(x ( j) ; α), F(x ( j) ; α) - j -1 n , where x (1) ,. , x  (2)  are the ordered values of x 1 ,. , x n. Based on the null hypothesis H 0 : "the dataset values are from the Arccos distribution", the corresponding p value is defined as p value = P(K ≥ K-S), where K is random variable following the appropriate K-S distribution.
Analysis Tables  2  and 3  provide the results of a descriptive summary for the fitted Arccos and power distributions for data sets 1 and 2, respectively. From the obtained results, the smallest -logL, AIC, BIC, K-S, A * , W * and the highest p values are acquired for the Arccos distribution. Therefore, the Arccos distribution gives significantly better fit to both datasets based on these measures and hence can be an adequate distribution for these data. Moreover, Figs. 3a and 4a present the estimated pdfs for data sets 1 and 2, respectively. In addition, Figs. 3b  and 4b  show the comparison of the estimated cdfs for the two distributions with the empirical cdfs. Apparently, for the two considered data sets, the Arccos distribution captures the general pattern of the histograms. The same holds for the estimated cdfs and the empirical cdfs.
Acknowledgements  Jiju Gillariose  is grateful to the  Department of Science and Technology (DST), Govt. of India  for the financial support under the  INSPIRE Fellowship. The authors are grateful to two referees for their valuable comments. Open Access This article is licensed under a Creative Commons Attribution 4. 0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.