dataesr/scientific-paragraphs-categorization huggingface dataset:
c-e Whisker plot comparing, for tested conditions: L max parameter (c), estimated RHs growth rate (d), the length between d 50 ± 2δ _2 and distance from RT at d 50 -2δ _2 (f). Crosses indicate mean value of the corresponding data, dots present outliers according to Tukey method. Data were obtained from two biological replicates, using 7 to 8 M. truncatula roots per replicate. For RH growth rate estimation using root growth rate, see "Material and methods". Letters present the significative groups obtained from a one-way ANOVA test with Bonferroni multiple comparison post-test (p < 0. 05) (Fig. 3c ). IAA treatment, as expected for a treatment at 10 µM  [26] , induced a strong reduction in RH length. Provided that the root growth rate is known (statistics and root growth rate provided in "Materials and methods"), the model also offers the possibility to estimate RH growth rate (Eq.
Transfer of the method to other species In order to explore further the possibilities of the algorithm, RHs of two different species were measured. As for Medicago, the monocotyledon Brachypodium presents a dense population of root hairs, with a light opaque root corpus (Additional file 2: Fig. S5a ). Hence the algorithm required only slight modifications to be adapted to the pictures analysed, mainly by adjusting radius or iteration parameters from the steps 3. 1, 3. 2, 4. 1, 4. 2, 8. 4 and 10 described in Table  1  (Additional file 3: Script 3, see details of adjustable settings in "Materials and methods" section). The sigmoidal fit applied at the region 0 to 6000 µm from the root tip described well the data obtained with RHS (Additional file 2: Fig. S5a ). Alternatively, Arabidopsis roots have a very different profile.
3 ). We accurately measure maximal RH lengths L max and detect experimentally induced changes in length. Hence, this method allows standardizing RH maximal length measured in different physiological conditions, with the robustness deriving from the fit of > 100 data points per root. In addition, the distance from the root tip to the d 50 -2δ point allows a definition of the end of the root elongation zone, corresponding approximately to the first emerging RHs  [21, 22]. Therefore, the region between the root tip and the d 50 -2δ point is a convenient and accurate estimate of the cumulated length of the cell division and elongation zones, and changes in its length reflect changes in one or both of these processes. Similarly, the region defined by the d 50 -2δ to d 50 + 2δ zone reflects the length of the RH growth region.
Image acquisition Before describing in detail the different steps of the method, the whole pipeline depicting the entire process that encompass Imaging, Fiji Script analysis, data sorting and sigmoid fit is summarized in Additional file 2: Figure  S6. Three days after transfer into the growth chamber (that is to say 18 h after specific treatments if applicable), roots were excised from aerial organs and placed between slide and coverslip in liquid Fahareus medium. A bright field microscope (Leica DMI6000 with motorized stage x, y, z. LAS software, Halogen Leica lamp, 5× Dry objective with 0. 15 numerical aperture, Hamamatsu Orca ER-1395 Camera) was used to acquire images with a resolution of 19,703 ppi. RH width is on average covered by 10 pixels. The motorized stage of the microscope and the mosaic reconstitution facilities of LAS software were used to acquire and reconstitute all the analysed images (analogous tools are freely available in ImageJ and Fiji  [24] ).
The effect of varying this parameter, which regulates the amount of data points retained versus data variability due to e. g. "holes" in RH profile, is illustrated in Additional file 2: Fig. S8 ). Root Hair Sizer also proposes to annotate the image if some parts of the root need to be removed from the analysis. The position of these comments along the root are recovered in the final table through the annotation of each data point as 1 and 0 (respectively the presence and absence of the comment at this point) on separated columns. Furthermore, at several steps RHS allows the user to check and eventually manually correct the automatic process achieved by the algorithm. All automatic definitions and manual corrections are recorded and saved as region of interest (ROI). After running RHS a first time, it is possible to analyse another region of the root while using ROI associated with the original image by employing the script presented in Additional file 6: Script 2.
Then, we settle the limits for the second fit between d 50_1 ± 5δ _1. Sigmoidal adjustment was achieved using GraphPad Prism software. Data obtained from each image were treated separately. A least squares fitting has been applied using the following rules to define the fit's initial values for each considered image: with L absolute min and L absolute max respectively the minimal and maximal RH length measured in all data obtained along the whole root of the considered image.
Root growth rate measurement This measurement was done on separate batches of roots in the same condition than for RH length measurement. After 1 h of root immersion in the treatment solution, boxes were emptied, then closed, and the RT position was marked on the box cap with a marker. After 18 h of incubation, the new RT position was marked and the box was scanned. The distance between two consecutive points was then measured using Fiji software. The root growth rate can be measured as the ratio of this distance by the time between the two measures. Root growth was measured from two biological replicates giving the.
Acknowledgements We acknowledge  Fabienne Maillet  ( Laboratoire des Interactions Plantes-Microorganismes-INRA, Toulouse ), for providing us with NF. We acknowledge also  Aylin Haas  ( Center for Organismal Studies-Heidelberg University ) for providing us with Brachypodium images. The authors thanks  Joni Frederick  ( LadHyX, Ecole Polytechnique, France ) for language editing corrections.
Funding MG benefits from a doctoral fellowship provided by the French Ministère de l'Enseignement Supérieur, de la Recherche et de l'Innovation, through the Science du Végétal doctoral school (ED567), and from a postdoctoral fellowship financially supported by a research group grant of the Excellence Cluster CellNetworks to Guido Grossmann, COS Heidelberg. This study was supported by the grant ANR-11-BSV7-010-02 from the Agence Nationale de la Recherche (ANR, project CAROLS) and benefits from the support of the LabEx Saclay Plant Sciences-SPS (ANR-10-LABX-0040-SPS).
By constructing a graph intermediary, redundant information can be merged or discarded, producing substantially compressed input -small enough to be fully encoded by Seq2Seq models. Such a method can be seen as merging previous work on symbolic knowledge bases for information extraction with newer approaches using deep neural networks to encode knowledge. Our approach, shown in Figure  1 , takes a query and its corresponding multi-document web search results and builds for each query a specific local knowledge graph. We present several modeling contributions to effectively encode the entire graph as a sequence and attend to the most relevant portions within this linearization. We demonstrate the effectiveness of this approach on two large-scale generative tasks with both long and noisy multi-document web input and paragraph length output: long-form question answering on the ELI5 dataset  (Fan et al.
Multi-Document Input Previous work in multi-document summarization  (Barzilay et al. , 1999)  applies various techniques to handle long input, including clustering to find similar information  (Honarpisheh et al. , 2008) , extractive methods to select relevant sentences  (Daumé III and Marcu, 2002; Gillick and Favre, 2009; Berg-Kirkpatrick et al. , 2011; Di Fabbrizio et al. , 2014; Bing et al. , 2015; Cao et al. , 2017)  including maximal marginal relevance  (Fabbri et al. , 2019) , and incorporating queries  (Baumel et al. , 2018)  and graphs  (Ganesan et al. , 2010; Yasunaga et al. , 2017). However, there are few large scale multi-document summarization datasets and many approaches have focused on extractive selection or hybrid extractive-abstractive models. In this work, we use graph construction to re-structure multidocument input for abstractive generation.
Advancements in question answering have examined performance on datasets with multidocument input, such as TriviaQA  (Joshi et al. , 2017). Various approaches have been proposed, including leveraging TF-IDF and bigram hashing with an RNN to find relevant information  (Chen et al. , 2017) , models that score individual paragraphs for sub-selection  (Clark and Gardner, 2017) , and nearest neighbor search with paragraph re-ranking  (Das et al. , 2018a). However, these approaches have been applied to extractive question answering tasks that require span identification, rather than abstractive text generation in an information synthesis setting.
Scaling to Encode the Graph Recent progress has improved the ability of language models to process longer sequences  (Sukhbaatar et al. , 2019; Dai et al. , 2019) , but models remain limited in their capacity to encode long documents. The multi-document results of query-based web search have hundreds of thousands of tokens, beyond the limit of current Seq2Seq models to handle. For example, the ELI5 dataset provides an average of 200K tokens of web search input. However, by compressing the web search results into a knowledge graph, we significantly reduce the number of tokens by an order of magnitude and make it possible for a model to access the entirety of the search information. To represent the full graph, models must scale to encode around 10K input tokens. The attention mechanism in Transformer architectures becomes computationally expensive for sequences of this length.
Datasets and Evaluation ELI5 First, we experiment with the Explain Like I'm Five (ELI5)  (Fan et al. , 2019)  question answering dataset of 270K complex questions paired with multi-sentence, explanatory answers (130 words on average). To facilitate question answering, the dataset provides the top 100 web search hits from querying the question, which results in 200K words on average. See Appendix for examples. Previous work  (Fan et al. , 2019)  used TF-IDF to find sentences in the web search that have the largest overlap with the question and created a TF-IDF extraction of about 850 words as input for Seq2Seq models. Instead, we construct a local knowledge graph for each question from the 100 web search hits. Following the average length of the TF-IDF support document constructed in  (Fan et al.
, 2019) , we experiment with modeling the first N = 850 tokens of the linearized graph, then scale to encode the entire graph using E-MCA. WikiSum Second, we experiment on the Wik-iSum CommonCrawl  (Liu et al. , 2018b)  summarization dataset 4  with 1. 5 million examples. This task formulates Wikipedia lead paragraph generation as a multi-document summarization problem, where the paragraph must be generated using the cited article references and other queried content from web search. The query used is the title of the Wikipedia article. See Appendix for examples. Previous work  (Liu et al. , 2018b)  applied TF-IDF Ranking to order the paragraphs of web search given a query. Models receive the reordered paragraphs ranked by TF-IDF as input. Liu et al. (2018b)  model the first N = 500 words of this re-ranking and then N = 11, 000 using MCA.
We construct the knowledge graph for each Wikipedia article from the first 200K words of the ranked web search results 5 , and experiment with encoding 500 and 11, 000 tokens. Evaluation Both tasks evaluate the multisentence generation output against the gold output using F1 ROUGE. On WikiSum, we report only ROUGE-L following  (Liu et al. , 2018b). We conduct a comparative human evaluation on the ELI5 dataset. We use crowdworkers to examine the responses of two models on 300 different questions from the test set. For each question, 3 evaluators are shown two answers and asked to choose the one they prefer. To reduce variance, answers are standardized at 150 words each.
Training and Generation To reduce the vocabulary size of varied web document content, we apply byte-pair encoding  (Sennrich et al. , 2016)  to generate 40K codes for each dataset. We implement our models in fairseqpy  (Ott et al. , 2019)  using the Transformer Big architecture and training schedule described in  (Vaswani et al. , 2017). Detailed parameters are listed in the Appendix. For generation, we use beam search with beam size 5 and tune a minimum and maximum length on the validation set.
Linearized Graph Improves Performance In Table  1 , we compare our methods to various baselines on the ELI5 dataset. Using MMR to select the most relevant non-redundant input is similar to the TF-IDF baseline from  Fan et al. (2019). The Seq2Seq Multi-task Triples baseline standardizes the input by forming triples but does not remove redundant triples. It produces marginally better results compared to the baseline Multi-Task model. Sub-selecting to the Top 20 Triples is harmful, as similar text has high TF-IDF overlap with the query so redundant information is selected. Creating the graph structure brings an improvement of around 0. 6 ROUGE-1. Similar trends are seen for the WikiSum dataset in Table  2 , where graph construction improves the Multi-task model by 0. 5 ROUGE-1. These improvements are statistically significant at the 95% confidence level.
For both datasets, a further improvement is seen by using the hierarchical attention mechanism to attend to only the most relevant information in the linearized graph input. For ELI5, it brings an additional 0. 2 ROUGE-1 improvement and on Wik-iSum a 0. 3 ROUGE-1 improvement. By using MCA to scale Seq2Seq models to encode the entire graph, further gains can be seen. Particularly in information synthesis tasks, prior work has shown the importance of reading more information. Liu et al. (2018b)  achieved a 2-point ROUGE improvement by reading 11K tokens instead of 500. In our setting, E-MCA improves our results around 0. 3 ROUGE on ELI5 and 1. 3 ROUGE on WikiSum. We display random generations from both datasets in the Appendix. We use human evaluation to compare the Multitask baseline to the Multi-task Graph + Top-k Attention model.
Graph Improves Answer Token Coverage Despite Compression Figure  6  displays the distribution of the number of nodes, edges, and the largest node weight for each local graph built on the ELI5 dataset. The 100 web search results are compressed to a few hundred nodes. By merging redundancy and trimming irrelevant triples from the graph, the input is reduced by an order of magnitude (Figure  7 , left). Despite compression, the graph retains more answer tokens than TF-IDF subselection. Figure 7 (right)  displays the percentage of answer tokens not present in the input. The TF-IDF Extraction from  (Fan et al. , 2019)  is missing 38% of tokens. The graph constructed on all 100 web search results is only missing 8. 7% of tokens, but has around 10K words. When analyzing just the first 850 tokens to match the average length of the TF-IDF extraction, the graph is better (only missing 35% of tokens).
Felez  40  develops a software program that models multibody systems using bond graphs. To manage derivative causalities with this software, he proposes introducing Lagrange multipliers into the system to eliminate derivative causality. Van Dijk and Breedveld present different methods for simulating bond graph models  41. Simulations were conducted with a predecessor of the 20-sim software, and numerically compared on the basis of computing time and accuracy. The potential to use multibond graphs was mentioned, but the difficulty of implementing bond graphs with vector bonds was not detailed. This point will be discussed later in this paper. Marquis-Favre and Scavarda  42  propose a method to simplify bond graph models for multibody systems with kinematic loops. Nevertheless, few complex multibody systems with closed kinematic loops have been simulated directly from dedicated software.
It would have a practical operation as a flow source but with effort-out causality instead of a flow-out causality. The constitutive laws of the controlled effort sources are as follows: -the usual constitutive law for an effort source, -the constraint: effort = e such that flow(e)=f. Figure  16  illustrates the implementation of this constraint. The effort e(t) applied iteratively to the system is determined so that the difference ε(t) between the flow measurement f (t) and its set point fc(t) tends to zero. This implementation uses the constraint() function in 20-Sim. At every simulation step, this function induces an iterative procedure to find the force that keeps the velocity offset at zero within a given error margin. This iterative procedure is only supported by the Modified Backward Differentiation Formulation in 20-Sim software.
Data production This work is based on data collected with CUPID-0 between June 2017 and December 2018, for a total exposure of 9. 95 kg yr (Zn 82 Se). Two of the enriched crystals, not properly working, and the two with natural Se are not included in this analysis. The collected data are processed offline using a C++ based analysis framework originally developed by the CUORE-0 and CUORE collaborations  [19]. The specific analysis tools developed for scintillating calorimeters in the framework of CUPID-0 are presented in Ref. [20, 21]. Table  1  Measurements and limits on contaminations of CUPID-0 detector components. Ge-LD radiopurity is certified by UMICORE company. The contaminations of VIKUITI TM foils have been measured via Inductively Coupled Plasma Mass Spectrometry (ICPMS) at LNGS  [9]  and with a BiPo detector  [12]  (private communication).
The corrected amplitude is converted into energy by fitting a parabolic function with zero intercept to the energy of the most intense peaks produced by a 232 Th source periodically positioned close to the cryostat external shield  [20]. The heat released by α and β/γ of the same energy is slightly different because of the different energy spent in the light channel. To re-calibrate the α events, we identify the most intense α peaks produced by 238 U and 232 Th internal contaminations (see Fig. 2 ), and convert the amplitude to energy using a parabolic function. Data acquired between two calibrations are grouped in a DataSet and processed together through the analysis chain. We compute time coincidences between detectors within a ±20 ms window, optimized by studying the time distribution of physical coincident events collected during calibrations.
Monte Carlo simulations The background sources identified through data analysis are simulated with a Monte Carlo toolkit, called Arby, based on the Geant4 toolkit  [28] , version 4. 10. 02. The radioactive decays from the various background sources can be generated in any volume or surface of the CUPID-0 detector, cryostat and shielding implemented in Arby. The primary and any secondary particles are then propagated through the CUPID-0 geometry using the Livermore physics list. The energy deposited in ZnSe crystals is recorded in the Monte Carlo output together with the time at which the interaction occurred. The fraction of energy released by any particle type is also recorded to allow particle identification. Radioactive decays are implemented using the G4RadioactiveDecay database. The decay chains of 232 Th, 238 U, and 235 U can be simulated completely or in part, to reproduce breaks of secular equilibrium.
These data are collected in dedicated runs in which the heater is used to generate pulses with variable amplitudes (then converted into particle equivalent energies) and the efficiency is calculated, for each pulse amplitude, as the ratio between triggered and generated pulses. Exactly as done in experimental data production, events depositing energy in different crystals within ±20 ms window are combined into multiplets and pile-up events (see Section 2) in the same crystal are discarded. Finally, exploiting the information about the type of particle depositing energy, we reproduce in the Monte Carlo data the same event selection applied in the experimental data to produce the M 1α and M 1β/γ spectra. Particularly, we include in the M 1α spectrum (with efficiency > 99. 9% at E> 2 MeV) not only the α events, but also the heterogeneous β/γ + α events due to Bi-Po decay sequences, that in the experimental data are tagged as α events (see Fig.
External sources The external sources are contaminations in the holder, in the cryostat and in the shields. These sources produce events in the M 1β/γ , M 2 , and Σ 2 spectra. The γ lines that can be used to identify these sources, besides being few, have limited statistics and, thus, cannot be exploited to directly extract information about the position of contaminations. For this reason, we take as reference the background model of the CUORE-0 experiment, that was operated in the same cryostat as CUPID-0. Given the lower statistics of CUPID-0 data and the higher 2νββ rate, we have to apply further approximations with respect to the CUORE-0 model. Particularly, we cannot disentangle 232 Th, 238 U and 40 K contaminations in CryoExt from the ones in ExtPb, because their spectra are degenerate.
Results We perform a simultaneous Bayesian fit of M 1α , M 1β/γ , M 2 and Σ 2 spectra with a linear combination of 33 background sources, to evaluate their activities. We use the JAGS (Just Another Gibbs Sampler) software  [33]  to define the Bayesian statistical model and to sample the joint posterior Probability Density Function (PDF) of the fit parameters (i. e. the normalization coefficients of the Monte Carlo spectra). More details about the JAGS-based analysis tool for background model fit can be found in Ref. [10]. We use non-negative uniform priors for all fit parameters, with a few exceptions discussed in Section 5. We choose a variable step size binning to minimize the effect of not ideal detector response which manifests itself in line shapes of complicated modeling, especially in the α region.
Conclusion and perspectives In this paper we fit the CUPID-0 data using 33 radioactive sources, modeled via Monte Carlo simulations. We identify the contribution of the various background sources to the ROI bkg counting rate and we perform an analysis of the corresponding systematic uncertainties. Excluding the 2νββ decay contribution (which is negligible at the Q-value of 82 Se ββ decay), we obtain that ∼44% of background rate in the ROI bkg is produced by cosmic muon showers, while the remaining fraction is due to radioactive decays in Crystals (∼33%), in Reflectors & Holder (∼6%), and in Cryostat & Shields (∼17%). Based on these results, an upgrade of the CUPID-0 detector has been scheduled in order to reduce the background level in the ROI and to further improve the comprehension of background sources.
Acknowledgments This work was partially supported by the  European Research Council  (FP7/2007-2013) under contract  LU-CIFER no. 247115. We thank  M. Iannone  for his help in all the stages of the detector assembly,  A. Pelosi  for constructing the assembly line,  M. Guetti  for the assistance in the cryogenic operations,  R. Gaigher  for the mechanics of the calibration system,  M. Lindozzi  for the cryostat monitoring system,  M. Perego  for his invaluable help in many tasks, the mechanical workshop of LNGS ( E. Tatananni ,  A. Rotilio ,  A. Corsi , and  B. Romualdi ) for the continuous help in the overall setup design. We acknowledge the  Dark Side Collaboration  for the use of the low-radon clean room. This work makes use of the DIANA data analysis and APOLLO data acquisition software which has been developed by the  CUORICINO, CUORE ,  LUCIFER  and  CUPID-0  collaborations.