dataesr/scientific-paragraphs-categorization huggingface dataset:
Different loci were selected depending on which criterion (bipartition support or clock-likeness) was implemented first in SortaDate, so we used both orders. The best four and eight loci were selected with the get_good_genes. py module based on these rankings to yield a total of four matrices, which were then used for divergence time estimation in PhyloBayes using the CAT-GTR PhyloBayes majority-rule consensus tree for the 75% TreSpEx-and-BaCoCa-filtered data matrix as a fixed topology. For the matrix comprising the top four loci based on 'clock-likeness' first and bipartition support second, we estimated divergence times using two clock models-autocorrelated lognormal  (Thorne, Kishino, & Painter, 1998)   In all analyses, calibrations for the divergence between Branchiobdellida and Hirudinida (201 mya) and the divergence of Capitellidae from Opheliidae (307 mya) were treated as hard upper bounds, with the lower bound modelled as a truncated Cauchy distribution (p =.
| RESULTS Sixty-nine transcriptomes from 60 clitellates and 9 polychaetes were generated for this study (Table  1 ) and can be downloaded from the SRA at NCBI (BioProject accession PRJNA603081). We added publicly available transcriptome/ genome data for four additional clitellates (Eisenia andrei, Helobdella robusta, Hormogaster elisae and Pristina leidyi) and one polychaete (Capitella teleta) for a total of 74 transcriptomes. Three gene sets from these transcriptomes were analysed, reflecting different levels of gene occupancy (Table  S1 ). We saw no signs of host contamination of the two leech sequences of concern. When top vertebrate blast matches were added to the loci that contained a sequence from these taxa, all but four of the 167 trees showed reciprocally monophyletic Annelida and Vertebrata.
Ignoring the position of Randiella for the moment, Parvidrilus is consistently recovered as sister to a large clade comprising two subclades: Capilloventer (representing Capilloventridae) and the rest of Clitellata. In most cases, we recover Randiella as sister to Parvidrilus with moderate-to-strong support (Figure  1 , Table  S2 ). In the 25% and 50% MARE-filtered trees, however, Randiella is sister to Capilloventer, with weak-to-moderate bootstrap support (Table  S2 , Figures  S1  and S2 ). The 15 species analysed represent six of the ten naidid subfamilies recognized by the WoRMS database (www. marin espec ies. org), that is, excluding Opistocystinae, Telmatodrilinae and Rhyacodriloidinae, as well as the enigmatic Branchiura (Branchiurinae, likely to be Tubificinae; see  Erséus, Envall, Marchese, & Gustavsson, 2010; Martin, Martínez-Ansemil, & Sambugar, 2010)  and Paranadrilus, the latter of which with unsettled classification.
, 1999; Borda & Siddall, 2004; Siddall & Burreson, 1998)  or Oceanobdelliformes (e. g. Glyptonotobdella and Piscicolidae sp. ) as sister to all other leeches  (Tessler et al. , 2018). However, it is concordant with traditional taxonomy and cladistic analysis of morphological data  (Siddall & Burreson, 1995)  (though unlike Siddall and Burreson, we recover a monophyletic Piscicolidae, as do  Williams & Burreson, 2006). This conflict over the status of Rhynchobdellida appears to be a rooting problem. If on our phylogeny, Hirudinida had been rooted on the branch leading to Piscicolidae sp. and Glyptonotobdella instead of on the branch between Arhynchobdellida (Erpobdella, Haemopis and Cylicobdellidae sp. ) and Rhynchobdellida (Helobdella, Theromyzon, Piscicolidae sp. and Glyptonotobdella), our leech topology would match that of Tessler et al.
(2017)  attributed to Pangaean break-up in the Jurassic. The estimated dates of that split recovered in this study (ranging from 113 to 157 mya across data sets and analyses for node J; Table  S3 , Figure  3 ) are somewhat more recent than the dates reported by  Anderson et al. (2017). This may be an artefact of lower taxon sampling within Crassiclitellata in this study; this discrepancy merits further investigation.
ACKNOWLEDGEMENTS We would like to thank  Ainara Achurra ,  Marie Bartz ,  Nicolas Bekkouche ,  Egil Boräng ,  Marcel Bouché ,  George Brown ,  Csaba Csuzdi ,  Sharmishtha Dattagupta ,  Narcisse Giani ,  Richard Marchant ,  Patrick Martin ,  Svante Martinsson ,  Manuel Kleiner ,  Marcel Koken ,  Adrian Pinder ,  Danuta Plisko ,  Malalatiana Razafindrakoto ,  Dan Shain ,  Bruce Snyder ,  Gerusa Steffen ,  Per Sundberg ,  Marcus Svensson  and  Cecilia Wentrup , for providing specimens or assisting in fieldwork. We also thank  Pamela Brannock  and  Damien Waits  for laboratory and bioinformatics assistance. This is Molette Biology Laboratory contribution 101 and  Auburn University Marine Biology  Program contribution 200. The authors convey special thanks to  Mark Miller  and the  CIPRES Science Gateway  for access to XSEDE computational resources and assistance with analyses.
(Brinkhurst, 1984)019ellidae. Unfortunately, we were unable to obtain properly preserved tissue from Narapidae, Acanthobdellida (but seePhillips et al. , 2019, who used ethanol-fixed material unsuitable for our transcriptomic approach) and Alluroididae during the course of this study. Important representatives of the likely polyphyletic family Haplotaxidae s. lat. (Brinkhurst, 1984)are also missing. T A B L E 1 (Continued) Taxon Locality SRA # Museum Rhyacodrilus pigueti Achurra & Martinsson, 2013 SRR8799323 SMNH 174296 26 Jan 2011) Transcriptomes for nine of the ten polychaete outgroups and all but four ingroup taxa were generated during the course Parvidrilidae Parvidrilus meyssonnieri Des Châtelliers & Martin, 2012 France, Thurins, Galerie de la Martinière, 45. 681°N, of this project; those for Eisenia andrei (DRX021555), Hormogaster elisae (PRJNA196484) and Pristina leidyi 4.
Bioinformatics The maximum likelihood phylogenetic analysis of CHS (protein sequences) was obtained with several CHSs from the following fungi: D. teres, Aspergillus nidulans  [22] , Alternaria alternata, Botrytis cinerea  [23] , Blumeria graminis  [24] , Fusarium graminearum, Tuber melanosporum  [25]  and Magnaporthe grisea  [9]. The tree was generated with PhyML  [26]  and available at http://www. phylogeny. fr. The tree was visualized with the online software iTOL (http://itol. embl. de). The CHS sequences from D. teres, A. alternata, B. graminis, F. graminearum, T. melanosporum and M. grisea were obtained by blasting the A. nidulans CHSs (National Center for Biotechnology Information (NCBI)  [27]. The identification of CHS domains was carried out with Motif Scan  [28]. Sequences were aligned with Clustal Omega  [29].
Species of Fungi Protein Id Accession Number Drechslera teres DtCHS1 EFQ95838 DtCHS2 EFQ92549 DtCHS3 EFQ88914 DtCHS4 EFQ93986 DtCHS5 EFQ92060 DtCHS7 EFQ96223 Aspergillus nidulans AnCHS1 P30583 AnCHS2 P30584 AnCHS3 XP_660127 AnCHS4 P78611 AnCHS5 XP_663922 AnCHS7 XP_658650 Alternaria alternata AaCHS1 XP_018390769 AaCHS2 XP_018389428 AaCHS3 XP_018384374 AaCHS4 XP_018387091 AaCHS5 XP_018384599 AaCHS7 XP_018384594 Table 1. Cont.
Species of Fungi Protein Id Accession Number Botrytis cinerea BcCHS1 XP_024550705 BcCHS2 XP_001550325 BcCHS3 XP_001557191 BcCHS4 XP_024546183 BcCHS5 XP_001545514 BcCHS7 XP_024549635 Blumeria graminis BgCHS1 EPQ66343 BgCHS2 EPQ67341 BgCHS3 EPQ67743 BgCHS4 CCU76828 BgCHS5 AAF04279 BgCHS7 CCU74227 Fusarium graminearum FgCHS1 CAC41025 FgCHS2 XP_011318411 FgCHS3 PCD18709 FgCHS4 XP_011317052 FgCHS5 XP_011317820 FgCHS7 XP_011317804 Tuber melanosporum TmCHS1 XP_002842229 TmCHS2 XP_002840530 TmCHS3 XP_002837735 TmCHS4 XP_002840095 TmCHS5 XP_002839897 TmCHS7 XP_002835817 Magnaporthe grisea MgCHS2 CAA65275 MgCHS3 CAA65276 MgCHS4 AAB71411 MgCHS5 BAA74449 MgCHS7 ACH58563 2. 3. RNA Extraction and cDNA Synthesis D. teres mycelium was crushed with liquid nitrogen using a mortar and a pestle. Spore suspensions, stored at -80 • C, were lyophilized (Freeze Dryer Alpha 1/ 2-4 Christ) for 12 h at -55 • C, then milled using a ball mill MM400 (Retsch) for 2 min at 20 Hz.
A one-way ANOVA with Tukey's post-hoc test was performed with IBM SPSS Statistics v19 (IBM SPSS, Chicago, IL, USA) to determine the statistically significant differences among groups. A hierarchical clustering using uncentered absolute correlation and complete linkage was performed with Cluster 3. 0 (Pearson correlation coefficient threshold = 0. 83)  [37]. The heat map was visualized with Java TreeView (http://jtreeview. sourceforge. net/) [38].
nidulans encoding CHSs of Classes I, II, III, IV, V VI and VII  [22]. The presence of multiple CHSs in many fungi suggests that several CHSs can be used for chitin production at different stages of the fungal life-cycle  [10]. According to the classification proposed by Chigira et al. [55]  and Choquer et al. [56] , in our study, DtCHS1, DtCHS2, DtCHS3, DtCHS4, DtCHS5 and DtCHS7 encode CHSs from Class I, Class II, Class III, Class IV, Class V and Class VII, respectively  [55, 56]. These enzymes are localized in the plasma membrane  [9]. BLASTp analysis carried out using the CHS protein sequences of A. nidulans identified six CHSs in D. teres (hereafter referred to as DtCHS1, 2, 3, 4, 5 and 7 for the protein sequences and DtCHS1, 2, 3, 4, 5 and 7 for the genes) (Table  1 ). The maximum likelihood phylogenetic analysis carried out using CHS full-length protein sequences from several classes of fungi, notably Dothideomycetes, Sordariomycetes and Leotiomycetes, allowed assigning a phylogenetic relatedness for the D.
Expression Analysis of Cell Wall-Related Genes in D. teres The software geNorm PLUS  [67]  was used to analyze gene expression stability across different samples of D. teres: spores and mycelium on BOA (+), mycelium on MP (-), and mycelium on PDA (+/-) in the presence or absence of the bacterium. The stability and transcript levels of the eleven candidate reference genes actin, ApsC, Cos4, GlkA, PfkA, PgiA, SarA, IsdA, H2B, GAPDH and RS14 were investigated with geNorm PLUS. Cos4 and PgiA were identified as the best two transcripts for use in normalization of the data (Supplementary Figure  S1 ). The attention was focused on key genes involved in fungal cell wall biosynthesis. Besides CHSs, genes coding for enzymes involved in β-(1,3;1,4)-glucan and β-(1,3)-glucan synthesis were investigated.
Acknowledgements We are grateful to  Gautam Reddy  and  Huy Tran  for multiple relevant discussions. This work was supported by the  National Science Foundation ,  Program PoLS , Grant  1411313. JD was partially supported by the  NSF-Simons Center for Quantitative Biology  ( Simons Foundation   SFARI/597491-RWC  and the  National Science Foundation   17764421 ). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
INTRODUCTION Discovering what subsets X of our descriptive variables X allow for an exact or approximate reconstruction of a given target variable Y is a core task in exploratory data mining  [10, 12]. The example applications of approximate functional dependency discovery are many, as the presence of significant dependencies can provide valuable insight in the data generating process  [4, 6] , while the absence of such dependencies allows us to verify that the target cannot be reconstructed and is hence private within the data. Approximate functional dependency discovery is related, but different from three well known applications, namely key discovery in databases  [9, 13] , feature selection in machine learning  [7] , and Markov blanket discovery in Bayesian networks  [21]. Unlike key discovery, we do not operate under a closed world assumption  [5] , and unlike feature selection, we are explicitly interested in discovering the top-K strongest joint dependencies, rather than pairwise associations and mostly greedy answers  [2].
In sum, the main contributions of this paper are as follows. We (1) propose the use of uniform priors to address the reliability problem and arrive at SMI as a score to mine statistically sound functional dependencies,  (2)  show that computing the exact upper bound of SMI leads to an NP-hard problem,  (3)  show how to instantiate a branch-and-bound algorithm that allows to efficiently discover the top-k dependencies scored by SMI thanks to an admissible, tight, yet tractable upper bound for SMI, and (4) empirically evaluate our approach in terms of runtime and statistical efficiency. For readability and conciseness we postpone all proofs to the appendix. We make all code and data available in the supplementary. Although we are not the first to consider estimation of mutual information using Bayesian approaches  [17, 18] , we are to the best of our knowledge the first to consider smoothing for reliable functional dependency discovery.
e D X = 1≤k ≤j D X i k. Given two sets of features X and Z such that X ⊆ Z and given some value x ∈ D X , D Z/x is the set of values z ∈ D Z matching x, i. e. whose restriction on variables of X is x. The number |D Z/x | of these values is denoted N x Z. Given some probability space, probability mass function of a random vector Z of features is denoted P Z. Its associated entropy is H(Z) def = E log 1 P Z = - z∈D Z xlogx (P Z (z)) , (1) where xlogx denotes function x → x log(x), introduced for conciseness and log(x) refers to logarihm of x to an arbitrary base. Entropy computed from a set of counts N = (n i ) is also denoted h(N) = - n ∈N xlogx n n ′ ∈N n ′. (2) Mutual information shared between X and Y is then I(X; Y ) def = H(Y ) + H(X) -H(X, Y ). = H(Y ) -H(Y |X) (3) Given a dataset and a set X of features, we denote by n x the number of samples for which X is equal to x.
Laplace Smoothing Laplace smoothing is a well-known shrinkage technique to reduce variance when estimating categorical distributions from samples: given a variable Z following a categorical distribution P Z of unknown probabilities p 1 ,. , p N Z and given a dataset of n iid samples, let n 1 ,. , n N Z be the histogram of corresponding values of Z occurring in the dataset. Then the α-smoothed estimator P(α ) Z of distribution P Z for some α ≥ 0 is defined by P(α ) Z (z) = n z + α n + N Z × α. ( 5 ) Setting α = 0 gives the standard maximum likelihood estimator (MLE) which equates probabilities of events with their frequencies of occurrence in data. The parameter α is called pseudocount since when α is an integer, it simulates the occurrence of α extra samples for each possible value of Z. The larger α, the smaller the variance of the estimator but the larger its bias.
Problem statement With the above definition and preliminary analysis of SMI, we can now formally state the problem at hand. Problem 1 (Top-K Functional Dependency Discovery). Given a dataset D over descriptive variables Z and target variable Y , a coefficient α and a number K, find the K sets {X i } 1≤i ≤K ⊆ Z of descriptive variables that achieve the highest α-smoothed mutual information ˜I(α ) (X; Y ) with Y. To solve this problem, we first derive the exact expression of ˜I(α ) (X; Y ). Given some smoothed joint distribution and its contingency table illustrated on Tab. 1 , we first observe that rows and columns (i. e. marginal distributions) sum up pseudocounts the same way they sum up real samples. We formalize this as follows. Property 1. Smoothed marginals P(N Y α ) X (x) = y ∈D Y P(α ) X,Y (x, y) P(N X α ) Y (y) = x∈D X P(α ) X,Y (x, y).
Introduction Because of smoothing, SMI sadly has no structure-such as convexity, monotonicity, modularity-that we can exploit for efficient optimization. To illustrate the difference in behavior between SMI and standard mutual information, let us consider a dataset over arbitrarily many features Z, of a finite set of n samples. It is easy to see that when we increase the number of selected features X ⊆ Z, the product N X α tends to +∞ for any α > 0. In other words, the smoothed distribution over X and Y , P(N X α ) Y tends to the uniform distribution, and by an argument of continuity, the smoothed entropy H(N X α ) (Y ) tends to log (N Y ). As we can rewrite conditional entropy, H(α ) (Y |X), as an average of smoothed entropy terms H(α ) (Y |X) = x n x + N Y α n + N X N Y α H(α ) (Y |X = x) , and the relative number of "real counts" of P(α ) Y |X=x gets smaller and smaller relative to the (uniformly spread) pseudocounts α, H(α ) (Y |X) also tends to log (N Y ).
Each constraint here has a variable number N x Z ≥ 1 of unknowns such that N Z = x N x Z. Because each value x is mapped to N Y constraints that only relate to part of the dataset matching x, the term H(α ) (Y |Z) is better decomposed in a way that makes the partition of the dataset induced by the different values of X explicit. H(α ) (Y |Z) = x n x + N x Z N Y α n + N Z N Y α H(α ) (Y |Z, X = x) (7) with H(α ) (Y |Z, X = x) def = z∈D Z/x n z + N Y α n x + N x Z N Y α H(α ) (Y |Z = z). These latter terms H(α ) (Y |Z, X = x) are "local" in the sense that H(α ) (Y |Z, X = x) only depends on counts n z,y for z ∈ D Z/x and on the subset of the N Y previous constraints mapped to value x. In other words, it only depends on the subset of samples matching value x. Therefore the initial optimization problem can be decomposed in two nested layers where the inner layer consists of "local" optimization problems mapped to each value x of X and where the outer layer is a single "global" optimization problem merging solutions of the inner layer.
,20 , and for each such model, we then sample 100 datasets D (i) n, j of size n. That is, every point (P, n) we report is an average over 2 000 datasets. As here we are interested in evaluating the quality of each estimator τ , we determine the top-1 maximizer X * i, j,n,τ for each dataset D (i) n, j. As our evaluation metric in this experiment we use the normalized intersection between the ground truth and the discovered set. Formally, it is defined as I (P,n) (τ ) = E |X * i ∩ X * i, j,n,τ | max{|X * i |, |X * i, j,n,τ |} , where X * i represents the true maximizer of model p (i) and the expected value is with respect to i ∈  [1, 20]  and j ∈  [1, 100]. We also consider precision P and recall R, which are defined as P (P,n) (τ ) = E |X * i ∩ X * i, j,n,τ | |X * i, j,n,τ | and R (P,n) (τ ) = E |X * i ∩ X * i, j,n,τ | |X * i |.
Computational Efficiency Next, we study the computational efficiency of SMI and its competitors on real data. To make sure that we fairly compare scores and bound efficiencies rather than the quality of their implementation, we implemented all scores in the same optimized branch-and-bound framework described in Sec. 3. 5. To obtain upper bounds of scores Î χ,α and ÎS , we replace term Î (X; Y ) with H(Y ) in Eq. 16 and Eq. 17. For Î0 , we use the improved bound proposed by Mandros et al. [11]. To allow for easy comparison, we evaluate on the same datasets used and further described by Mandros et al. [10] , reporting on all those that take more than 10 seconds for at least one of the scores. We give the wall-clock run times in Tab. 3. We make the code and all data available for reproducibility.
, X P } as the true maximizer. (3) We compute the average scores I (P,n) (τ ), P (P,n) (τ ) and R (P,n) (τ ) for each estimator τ over all 20 × 100 datasets. 6. 1. 2 Experiment on computational efficiency (Sec. 4. 2). All tests have been run on Intel i7-8700 CPU (3. 20GHz) with 16GB RAM. Bounds used for the different estimators are given below: • For the smoothed mutual information (SMI), the bound given in Sec. 3. 4 of the present article. • For the reliable fraction of information (RFI), we use the improved bound given in Mandros et al  [11]. • For the adjusted fraction of information proposed by Vinh et al. [12] , the bound is Î χ,α (X; Y ) = H (Y ) - 1 2n χ α,l (X,Y ). • For the MDL score proposed by Suzuki  [20] , the bound is ÎS (X; Y ) = H (Y ) - (N X -1)(N Y -1) 2n log(n). We limited the processing time of each run to one hour.
X P as the parent variables of Y. (b) Then for each tuple x P = (x 1 ,. , x P ) of values of X P = {X 1 ,. , X P }, we draw uniformly a sample distribution P(Y |X P = x p ) on the 3-simplex thanks to a symmetric Dirichlet distribution Dir(1) of order N Y = 4. (c) We reject the model while mutual information I(X; Y ) is outside the interval [0. 2, 0. 4]. (d) Then for each feature X k for 1 ≤ k ≤ 10, we draw uniformly a sample distribution P(X k ) on the 3-simplex thanks to a symmetric Dirichlet distribution Dir(1) of order N X K = 4. (e) Given each model, we sample 100 datasets of size n applying ancestral sampling on the joint distribution: P(Y , X) = P(Y |X 1 ,. , X P ) × 10 k =1 P(X k ).
X 1 to 1 X P as the parent variables of Y. (b) Then for each tuple x P = (x 1 ,. , x P ) of values of X P = {X 1 ,. , X P }, we draw uniformly a sample distribution P(Y |X P = x p ) on the 3-simplex thanks to a symmetric Dirichlet distribution Dir(1) of order N Y = 4. (c) We reject the model while mutual information I(X; Y ) is outside the interval [0. 2, 0. 4]. (d) Then for each feature X k for 1 ≤ k ≤ 10, we draw uniformly a sample distribution P(X k ) on the 3-simplex thanks to a symmetric Dirichlet distribution Dir(1) of order N X K = 4. (e) Given each model, we sample 100 datasets of size n applying ancestral sampling on the joint distribution: P(Y , X) = P(Y |X 1 ,. , X P ) × 10 k =1 P(X k ).
Simulation Setup For this study, we consider a planar robot arm that rigidly grasps one end of an elastic cable, whose other end is static; We assume that the total motion of this composed cable-robot system remains on the plane. A monocular vision sensor observes the manipulated cable and measures its 2D contour in real-time. The dynamic behaviour of the elastic cable is simulated as in  [52]  by using the minimum energy principle  [53] , whose solution is computed using the CasADi framework  [54]. The cable is assumed to have negligible plastic behaviour. All numerical simulation algorithms are implemented in MATLAB. The cable simulation code is publicly available at https://github. com/Jihong-Zhu/cableModelling2D. Let the long vector s t ∈ R 2α represents the 2D profile of the cable, which is simulated using a resolution of α = 100 data points.
Experiments To validate the proposed theory, we developed an experimental platform composed of a three degrees-of-freedom serial robotic manipulator (DOBOT Magician), a Linux-based motion control system (Ubuntu 16. 04), and a USB Webcam (Logitech C270); Image processing is performed by using the OpenCV libraries  [58]. A sampling time of dt ≈ 0. 04 seconds is used in our Linux-based control system. In this setup, the robot rigidly grasps an elastic piece of pneumatic air tubing, whose other end is attached to the ground. The 3-DOF mechanism has a double parallelogram structure that enables to control the gripper's x-y-z position while keeping a constant orientation. For this experimental study, we only control 2-DOF of the robot such it manipulates the tubing with plane motions. Figure  11  depicts the setup.
Funding This research work is supported in part by the  Research Grants Council (RGC) of Hong Kong  under grant number  14203917 , in part by  PROCORE-France/Hong Kong Joint Research Scheme  sponsored by the  RGC  and the  Consulate General of France in Hong Kong  under grant  F-PolyU503/18 , in part by the  Chinese National Engineering Research Centre for Steel Construction (Hong Kong Branch ) at  PolyU  under grant  BBV8 , in part by the  Key-Area Research and Development Program of Guangdong Province 2020  under project  76  and in part by  The Hong Kong Polytechnic University  under grant G-YBYT.