dataesr/scientific-paragraphs-categorization huggingface dataset:
The homogeneous description of their constituting SBFs, entirely determined by their input weights, also allows expressing complexity scores for SBNs easier than with ordinary Boolean Networks or even Threshold Boolean Networks. We tested our method by computing the extension of 2-dimensional SBNs , S 1 , N d=3 , S). For each network (initial and extended), we also computed several characteristics including network and behavioral complexities, but also the number of attractors and the size of basins of attraction. The volume of data to process is then already huge when starting from dimension 2 for which only 7 SBFs and 101 SBNs exist. Our program running on a workstation with 32 CPU threads (2 x Intel(R) Xeon(R) CPU E5-2667 v4 @ 3. 20GHz) and 64Go RAM (ECC DDR4 2400MHz) took 20 minutes to complete.
There are several ways by which this can be done. In larger dimensions, a manner to save computational time is to use Monte Carlo approaches. Another manner to reduce the number of quadruplets to compute while allowing us to explore larger extensions, is to make thin slices in initial and extended behavior complexities (e. g. 3 slices along initial behavior complexities: small, moderate and large complexities, and 3 slices in extended behaviors also limited to small, moderate and large complexities). Finally, even the extension of very large specific networks (dozens of nodes) and for specific behaviors could be computed in a reasonable time using the same ASP modules. All these downgraded exploration methods will be evaluated on the benchmark that constitutes our full 2 to 3 dimension exploration.
A. 1 Overall software architecture We used a combination of two programming languages, Answer Set Programming (ASP)  [14] , a non-monotonic logical based programming language, and Java, a classical imperative language. The main software, written in Java, orchestrates the execution and uses multiple ASP modules when needed. Inference modules in ASP We first give here a very short introduction to ASP. This logical language allows to express facts and rules, like Prolog, with the help of logical literals. For example, the following rules p(1). p  (2). and c :-p(1), p  (2). mean that the two facts p(1) and p(2) are true and that their conjunction implies c. An ASP program infers all logical models (sets of literals) that comply with the facts and rules it specifies: they are called Answer Sets (AS).
We greatly benefit from a recent improvement based on  [16]  which uses a lazy approach for grounding and then allows the use of numerical variables with a very large range. In order to increase the flexibility and the re-usability of our ASP code, we cut it into several inference modules dedicated to specific tasks and compatible between each others. Each one introduces a main literal that can be set to configure its module : sbn(N, D) : implies literals describing a SBN N of dimension D. -composedSbn(N a , N b ) : constrains two given SBNs N a and N b so that one SBN is an extension of the other as defined in 2. 2. -sequencePlayedBySbn(N, S, I) : constrains a SBN N to play a given sequence S on his node of index I. -orderedSbn(N) : from a given SBN N, generates the equivalent ordered one by permutation of nodes (see section A.
2). Processing Pipeline The main software is organized as a pipeline of processors (called jobs): each job, programmed in Java, does its own part of the work, then furnishes its results to the next job, etc. Using a custom Java library  [8] , the workload is divided into tasks that we scatter across the different jobs, allowing to make the execution parallel on any number of CPU cores, thus enhancing the overall performances. An overview of this pipeline is given figure 4. The potential of the combination of an imperative language and inference modules lay in the facts that we can take advantages from both: efficiently find data sets by ASP inference, filter and enrich them in the Java pipeline. Moreover, those enriched data set can be used in return to configure other calls to inference modules.
This could not have been easily done using only ASP. The jobs use inference modules by generating literals that link the modules they need. In practice, such a job generates an ASP file that imports and configures the needed modules. Here is a casual example: a job knows a SBF f and aims to find all SBNs that contain f and play the sequence s = (100) *. This job configures the necessary inference modules this way: // i m p l i e s t h e g e n e r a t i o n o f a SBN n o f d i m e n s i o n 3 sbn ( n , 3 ). // c o n s t r a i n s n t o c o n t a i n f :-not s b f ( n , f ). // c o n s t r a i n n t o p l a y t h e s e q u e n c e s :-not sequencePlayedBySbn ( n , s ). // d e f i n e t h e b i t s o f s and t h e i r o r d e r s e q u e n c e ( s , 1 , 1 ). // t h e f i r s t e l e m e n t o f s i s 1.
Acknowledgements Sergiu Ivanov is partially supported by the Paris region via the project DIM RFSI n •  2018-03  " Modèles informatiques pour la reprogrammation cellulaire ". The authors would also like to thank the  IDEX program  of the  University Grenoble Alpes  for its support through the projects COOL : this work is supported by the  French National Research Agency  in the framework of the  Investissements d'Avenir program  ( ANR-15-IDEX-02 ). This work is also supported by the  Innovation in Strategic Research program  of the  University Grenoble Alpes. The authors would thanks  Ibrahim Cheddadi  for fruitful discussions.
Bootstrapping 'Bootstrapping' is when an original dataset is used to generate the new data sets. This process is possible because the distribution of collected samples approximates the distribution of all possible samples that could be collected. Therefore, a bootstrap sample of the same length as the original sample can be created by randomly selecting individual samples, with replacement. By using random selection with replacement, the distribution of the bootstrap samples approximates the distribution from which the samples are drawn. There are (2n-1)! n!(n-1)! possible bootstrap samples when sample order is unimportant, which for sample sizes greater than ten (92 378 possible bootstrap samples), means that exhaustive bootstrapping is often not feasible because of the associated computational expense  [16].
A method for the empirical determination of MPE In this section, we present the proposed method of MPE determination using fabricated synthetic data, to illustrate the various steps of the method. In section 4, we will then present a validation of the method using an example measurement system. The synthetic data was generated from a set of arbitrarily defined normal distributions, from which individual 'measurements' were randomly generated. For this fictitious measurement system and the associated synthetic data, the distributions for the measurement deviations were set up so that the analytically true value of the MPE was 1 arbitrary unit. Throughout this work, we have implemented this method in Matlab  [17]. Firstly, we assume that any MPE commonly specifies the expected error in a 'worst case' scenario for any measurement acquired by an instrument within its specification.
These final distributions are then, finally, randomly sampled to create the final ten sets of synthetic data with an analytically correct MPE of 1 arbitrary unit. While in this example, the implication from a visual assessment of the data is that measurement setup 3 is dominant, through examination of figure 2 alone we cannot quantify (or, consequently, automatically determine) which setup is most likely to dominate the MPE determination process. As such, each measurement setup dataset was quantified using a metric, calculated as the endpoint of the 99. 9% CI (using t-distributions with 49 degrees of freedom) and taking the maximal endpoint of each synthetic dataset. To calculate these values, a distribution is fitted to each dataset and the CI of that distribution calculated. We then record the absolute values of the endpoints of the CI to determine the dominant measurement setup.
Step 1-determining the 'worst' measurement setup To begin, 50 measurements were acquired of the calibrated sphere in each of the eight measurement setups. In each case, a minimum-zone spherical shell encompassing 100% of the data points was fitted to the acquired point cloud data and the probing form dispersion error was calculated as the thickness of these shells. Data acquisition was performed using the manufacturer's proprietary software, while sphere fitting and calculation of the probing form dispersion error was performed in Polyworks 2019  [21]. The probing form error calculated from each measurement is presented in figure  8. The plot of the maximal endpoint of the 99. 9% CIs for each measurement setup presented in figure  9  suggests that measurement setup 7 represents the worst measurement.
The Q-Q plots presented in figure  10  confirm that the assumption that measurements follow a generalised extreme value distribution is overall reasonable in this case, up to small-sample variability in setups 4 and 7. The specific type (I-III) of generalised extreme value distribution is automatically determined according to best fit using maximum likelihood estimation, on a dataset-by-dataset basis. (a) deviation from nominal value for 1000 measurements; (b) generalised extreme value distribution fitted to deviations; (c) PDF of the maximal endpoint of the 99. 9% CI for each bootstrap, with a generalised extreme value distribution fitted to infer the maximal endpoint of the 99. 9% CI of the population; and (d) convergence of the setup-specific MPE to the estimated maximal endpoint of the 99.
Step 2-determining the number of measurements required for each measurement setup With measurement setup 7 chosen as the measurement setup most likely to define the MPE, 1000 measurements were acquired in this setup, to determine the minimum number of measurements required in each of the other measurement setups. This information is presented in figure  11. By fitting a generalised extreme value distribution to the data (figure  11(b )), we calculate the maximal endpoint of the 99. 9% CI for this sample, which in this example takes the value of 0. 496 mm (represented by the dashed vertical line in figure  11(b) ). Using bootstrapping to simulate 10 000 samples, we then calculate the maximal endpoint of the 99. 9% CI for each of the bootstrap samples, plot these as a frequency plot (figure  11(c) ) and fit a generalised extreme value distribution to this plot to create a PDF.
e. by the statistical analysis of a series of observations  [9] ) for any scenario. If a new measurement routine and environment was developed for an existing measurement system, for e. g. the efficient collection of data would allow for robust error analyses for arbitrary measurement procedures and environments. Although the experimental data was collected manually, automation systems, such as robot arms and rotation stages would significantly reduce the need for required operator intervention. Due to the minimal requirement for operator decision making during the analysis process, it would be feasible for the MPE determination process to be automated. Automation would reduce the additional resource needed for MPE determination to just the measurement time required to collect sufficient data, which could potentially be carried out during planned idle periods.
Such a reduction would be relatively small and designing this prediction algorithm would be complex. As such, this exercise is beyond the scope of this work, but represents an interesting avenue for future refinement of this method. Additionally, we should note that throughout this work, bootstrap CI estimation has been performed without using a bias correction (despite being commonly employed). This approach has potential ramifications to the analytical accuracy of the method. However, bias correction is generally used when there is a significant skew in the data, which is not seen in the data we acquired throughout this work. When designing the implementation of the method in Matlab, the default distribution fitting function occasionally failed to fit an appropriate distribution to the synthetic data used to test the algorithm.
The first and only study to specifically focus on the Figure  1  Languages of Colombian Amazonia with Yukuna highlighted by a diamond shape  (Hammarström et al. 2019). Lemus-Serrano et al. Glossa: a journal of general linguistics DOI: 10. 5334/gjgl. 1276 word-prosodic system of Yukuna, and rightly describe it as a tonal language, is Robayo  Romero (2018). In this paper, we focus precisely on this latter issue. Our aims are three-fold: first, we propose a phonological analysis of the tonal system of the language that addresses the attested variations in tonal paradigms. Second, we assess the statistical validity of the proposed analysis by using machine learning techniques (classifiers) to detect the factors that predict (i. e. , statistically condition) with high accuracy the placement of H tones in a data set of verbal paradigms.
Third, we observe tendencies in the statistical study that could suggest cues for future research on the tonal system of the language. The structure of the paper is summarized as follows. Section 2 provides the qualitative analysis of the Yukuna tonal system, and discusses its contribution to previous literature on the language. Section 3 describes the corpus collection, annotation and dataset used for the quantitative analysis. Section 4 explains the functioning of the computational classifiers used for the analysis and show their results. Section 5 provides a discussion of the results generated by the computational classifiers and their implication for the qualitative analysis. The conclusion is given in Section 6.
The analysis presented here clearly aligns with previous studies in some respects, while also providing new insights into the prosodic system of the language. Our phonological proposal is based on two main empirical observations from our database. The first observation concerns the case of previously unmentioned tonal patterns, which cannot be accounted for in terms of tonal polarity, but which are present in our database. This is the case of surface H sequences across root-suffix boundary (as in [pal ̥á-káhe] 'lie-nmlz'), or exclusively on the suffixes (as in [ḭn̥ a-káhé] 'go-nmlz'). Our phonological proposal accounts for these instances in terms of the tonal spreading of a single underlying /H/ tone (either bound or floating). This proposal has the advantage of grouping together all surface H sequences, whether in cases of roots with toneless suffixes, or root-internally (/hápa/ [hápá] 'work'), following the OCP.
The second observation concerns the case of surface patterns which would be predicted by a process of tonal polarity (such as HL-H), but which are absent from our database (except in instances involving underlyingly H suffixes). For instance, /wâta/ 'want' has a root-final surface L tone, but toneless suffixes are not produced as H as in [wáta-kahe] 'want-nmlz', see Table  2 ). This is also captured by our phonological proposal, as the /HL/ tone in /wâta/ is simply produced as a single surface H on its corresponding TBU. Our phonological proposal thus accounts for the majority of patterns in the language, although some irregular patterns remain unexplained. We discuss these unexplained patterns in more detail in Section 5.
Materials This section describes the corpus and dataset used as the basis for this study. First, we discuss the corpus collection and annotation process (3. 1), then we introduce the variables of the dataset used for the statistical analysis (3. 2). 3 Despite this singularity, both /-ʧi /and /-ɾé/ are suffixes, and not clitics. There is both segmental and tonal evidence in favor of this analysis, in particular, the fact that these suffixes carry in some cases the single surface H tone in a root+suffix combination, as with the verb 'hear' in Table  3.
Corpus collection and annotation This study is based on a corpus containing the paradigms for a total of 80 verbal roots and stems. The verbal forms were obtained from two sources. The paradigms for 60 verbal roots and stems were obtained through direct elicitation with one consultant, a native speaker of Yukuna (anonymized in the current study), in Leticia, Colombia, between October 2017 and January 2018. During the elicitation sessions, the target words (individual root-plus-affix combinations per root) were recorded three times in non-final position within a frame sentence. The equipment used for the recording was a Zoom H4N audio recorder, with a Shure Beta 53 omnidirectional condenser head worn Microphone. The remaining 20 verbal paradigms were extracted from a corpus of Yukuna narratives collected by the first author, containing data from some 30 native Yukuna speakers.
Finally, the collected paradigms were further validated during follow-up fieldwork sessions by different speakers in order to avoid overgeneralizing the potential biases and idiosyncrasies of a particular speaker or groups of speakers. Each verbal paradigm includes a set of 30 different root-plus-affix combinations, including all of the most commonly used forms in the language corpora: person indexes (prefixes), inflectional suffixes (negation, tense), deranking suffixes (nominalizers, subordinators and gender markers). 4 The paradigm columns are the same for all verbal roots, but not all root-plusaffix combinations were possible for all verbs, nor attested in the corpus. Phonologically, the affixes in this dataset are monosyllabic and disyllabic, and they are inherently toneless, except for one suffix (the purposive subordinator /-tʃi ́/).
This is illustrated in Table  4  with a few tokens extracted from the paradigm of the verb /pal ̥á/ pajlá 'lie'. The annotation of surface H tones was done based on auditory impression for most tokens, but Praat was used to verify the pitch contours for the transcription of less common and/or problematic patterns. Figure  2  provides the pitch contours for tokens illustrating six different types of tonal patterns attested in the dataset. The six tonal patterns are coded as VH (one H tone on root, no suffix), VH_S (one H tone on root, toneless suffix), V_SH (toneless root, one H tone on suffix), VH_SH (one H tone on root, one H tone on suffix), VHH_S (two H tones on root, toneless suffix), and V_SHH (toneless root, two H tones on suffix). 6 As Figure  2  indicates, the pitch contours show a marked fall in pitch after the H syllables, unless of course the H syllables are in word-final position (as in the VH and V_SHH patterns).
6 Instances of root internal surface H tone sequences (VHH) are scarce in the dataset. These instances include two roots with underlying /H/ in root-medial position (/atʰúpa/ athúpá 'spit' and /am̥ úɾa/ ajmúrá 'sink'), as well as the irregular root kémá ~ i ḿá 'tell'. Other roots have been identified with this pattern in the language (such as /hápa/ jápá 'work') but they were not included in the dataset used in this study.
Dataset and variables In addition to the corpus of verbal paradigms, the dataset includes seven variables shown in Table  5  which were automatically extracted from the corpus using R (R-Core-Team 2020) and the tidyverse framework  (Wickham 2017). Most of the variables chosen are purely descriptive (i. e. automatically extracted from the corpus) and concern factors that are believed to be directly or indirectly relevant to the tonal system of the language. Tonal variables simply list the positions of surface tones in root-plusaffix combinations: RootTone states whether there is a surface H tone on the root when the root carries a suffix, and if so, in which position. KajeTone indicates the position of the H tones on the suffix -kaje, i. e. , initial, final, both syllables, or absent. Morpho-phonological variables pertain to the segmental and morphological make-up of the words.
Unlike other root types, Type 6 is the only one that does not display any internal coherence, as roots in this type display tonal irregularities in different ways. The mapping of the underlying lexical tones presented previously, into the categories of the RootType variable used in the database is summarized in Table  6. We expect the RootType variable to be significant for the statistical analysis of the dataset in order to assess the validity of the phonological proposal. Since the phonological analysis itself is based on data observation, we also expect this variable to correlate with descriptive variables (such as RootTone). However, the variable RootType does not perfectly correlate with descriptive variables, precisely because many roots in the language display different tonal patterns throughout their paradigm.
For instance, roots with floating tones (root types 3 to 6) display a VH tonal pattern (root-final H tone) when they are not carrying any suffixes due to H tone obligatoriness, but then, display V_SH, V_SHH or VH_SH when carrying suffixes. We also expect the RootType variable to be insufficient to account for all the surface patterns, and to be complemented by additional variables, given the diverse instances of irregularities in the dataset. For instance, roots included in Type 4 (floating /H/ tone) display both VH_SH as well as V_SHH patterns when combined with different suffixes. An example of the variables and the coding conventions used in the dataset is shown in   Lastly, a general look at the distribution of variables in the dataset reveals important tendencies. First, we note that the most frequent structures are Vx (root with one suffix) and xVxx (prefix, root and two suffixes), regardless of root type (Figure  3 ).
This is due to the fact that most forms in the paradigm are morphologically complex. Indeed, while it is possible for verbal roots to occur without any affixes as phonological words in Yukuna, the preferred phonological word contains at least a root and a person prefix. Second, we note that in terms of tonal patterns, the shares of the six main patterns are V_SH = 32. 9% (448), VH_S = 27. 7% (377), VH_SH = 14. 7% (  200 ), V_SHH = 13. 4% (182), VHH_S = 7. 3% (99), VH = 4% (55). 9 This is directly related to the number of roots per root type in the dataset. For instance, the V_SH and VH_S patterns are mostly associated with roots type 3 and 1 respectively, which together make up more than half of the roots in the dataset (root types 4, 5, and 6 are smaller). However, and importantly, these patterns also reveal a preference for only one surface H syllable per word in the language (roots with /HL/ tones, either bound or floating).
This category has thus been removed from the quantitative analysis. above), and used to evaluate the classifiers. Due to the stability of the results across the ten sampling processes (more details in subsection 4. 1), the results from the tenth sampling are reported in the current paper. For the tenth sampling, the training and the test sets have and 954 and 407 tokens respectively. We used three different standard metrics to evaluate the performance of the classifiers on the test set: first, we estimated the accuracy of the classification (equal to the proportion of the correctly classified cases) of the entire data set. Second, we estimated the f-score, defined as the combination of two other measures: precision and recall: precision measures how many cases are correctly classified within all the predictions on a category, while recall evaluates how many cases are correctly retrieved among all the expected correct output.