dataesr/scientific-paragraphs-categorization huggingface dataset:
For example, the mass matrix is passed into the ODE solver as an optional parameter so as to avoid explicit matrix inversion. In addition, the ODE solution is guaranteed to stay within a user-requested residual tolerance. We believe this type of optimization and error control is clearly advantageous over simulation codes that do not have it. To mimic the phenomenon where the water molecules can enter and exit the computational domain, the pseudo-periodic boundary conditions were implemented in  [33] [34] [35]. At this stage, we have chosen not to implement this in SpinDoctor, instead, spins are not allowed to leave the computational domain. Implementing pseudo-periodic boundary conditions would make the code more complicated, and it remains to be seen if it is a desired feature among potential users.
If it is, then it could be part of a future development. The twising and bending of the canonical configuration is something unique to SpinDoctor. It removes many computational geometry difficulties by meshing first the canonical configuration before deforming the FE mesh via an analytical coordinate transformation. This is a way to simulate fibers that are not parallel, that bend, for example. For fibers that disperse, perhaps more complicated analytical coordinate transformations can be performed on the canonical configuration to mimic that situation. This is a possible future direction to explore. SpinDoctor depends on MATLAB for the ODE solve routines as well as for the computational geometry routines to produce the tight wrap ECS. To implement SpinDoctor outside of MATLAB would require replacing these two sets of MATLAB routines.
Other routines of SpinDoctor can be easily implemented in another programming language. SpinDoctor can be downloaded at https://github. com/jingrebeccali/SpinDoctor. In summary, we have validated SpinDoctor simulations using reference signals from the Matrix Formalism method, in particular in the case of permeable membranes. We then compared SpinDoctor with the Monte-Carlo simulations produced by the publicly available software package Camino Diffusion MRI Toolkit  [26]. We showed that the membrane permeability of SpinDoctor can be straightforwardly linked to the transmission probability in Monte-Carlo simulations. For numerous examples, it was seen that the SpinDoctor and the Camino simulations can be made close to each other if one increases the degrees of freedom (the finite element mesh size for SpinDoctor and the number of spins for Camino) and increase the accuracy of the time stepping (by tightening the ODE solve tolerances in SpinDoctor and by increasing the number of time steps in Camino).
With a finite element mesh of 100K nodes, SpinDoctor takes less than one minute per b-value. At 1 million finite element nodes, limited computer memory resulted in a computational time 4. 7 hours for b = 100 s/mm 2 and 8. 9 hours for b = 1000 s/mm 2. This issue will be taken into account in the future with high performance computing techniques in MATLAB and on other platforms. One of our recent works  [40]  is promising for this purpose. We also illustrated several extensions of SpinDoctor functionalities, including the incorporation of T 2 relaxation, the simulation of non-standard diffusion-encoding sequences. We note the dendrite branch example illustrates SpinDoctor's ability to import and use externally generated meshes provided by the user. This capability will be very useful given the most recent developments in simulating ultra-realistic virtual tissues  [65, 67].
Conclusion This paper describes a publicly available MATLAB toolbox called SpinDoctor that can be used to solve the BTPDE to obtain the dMRI signal and to solve the diffusion equation of the HADC model to obtain the ADC. SpinDoctor is a software package that seeks to reduce the work required to perform numerical simulations for dMRI for prototyping purposes. SpinDoctor provides built-in options of including spherical cells with a nucleus, cylindrical cells with a myelin layer, an extra-cellular space enclosed either in a box or in a tight wrapping around the cells. The deformation of canonical cells by bending and twisting is implemented via an analytical coordinate transformation of the FE mesh. Permeable membranes for the BTPDE is implemented using double nodes on the compartment interfaces.
Built-in diffusion-encoding pulse sequences include the Pulsed Gradient Spin Echo and the Ocsillating Gradient Spin Echo. Error control in the time stepping is done using built-in MATLAB ODE solver routines. User feedback to improve SpinDoctor is welcomed. The geometry is made of cylindrical cells, the myelin layer, and the ECS (see Figure  7 ). The diffusion coefficient in all compartments is 2 × 10 -3 mm 2 /s and the compartments do not experience spin exchange, with all permeability coefficients set to zero. The diffusion-encoding sequeces are PGSE (δ = 10ms, ∆ = 13ms) and dPGSE sequences (δ = 10ms, ∆ = 13ms, τ = δ + ∆), the diffusion-encoding direction is ug = [1, 1, 1].
Acknowledgment The authors gratefully acknowledge the  French-Vietnam Master in Applied Mathematics program  whose students (co-authors on this paper,  Van-Dang Nguyen ,  Try Nguyen Tran ,  Bang Cong Trang ,  Khieu Van Nguyen ,  Vu Duc Thach Son ,  Hoang An Tran ,  Hoang Trong An Tran, Thi Minh Phuong Nguyen ) have contributed to the SpinDoctor project during their internships in France in the past several years, as well as the  Vice-Presidency for Marketing and International Relations at Ecole Polytechnique  for financially supporting a part of the students' stay. Jan Valdman  was supported by the  Czech Science Foundation (GACR) , through the grant  GA17-04301S. Van-Dang Nguyen  was supported by the  Swedish Energy Agency, Sweden  with the project  ID P40435-1  and  MSO4SC  with the grant number  731063.
Since the samples were captured with the same probe set and assuming no vast differences in plasmid copy number, the ratios should be consistent over all positive samples independent of their genomic coverage. This is, however, not expected for false-positive samples. Therefore, we calculated the Mahalanobis distance (  22 ), a standard method for outlier detection in multivariate datasets, to find false-positive and authenticate low coverage true-positive samples (χ 2 = 5. 991, df = 2, P = 0. 05; SI Appendix, Table  S2 ). Five samples, EDI002. A, DIR002. A, LVC001. B, LVC001. C, and PEI001. A, were classified as outliers. Despite having chromosomal coverage, DIR002. A, EDI002. A, and PEI001. A had no or only a few reads mapping to the plasmids and were therefore considered as Y. pestis negative.
Third, mapping of short reads is more prone to mismapping and calling of false-positive SNPs generated at sites of genome rearrangement. Whereas the first source can be circumvented via in vitro protocols like UDG treatment  (25) , the latter two can be reduced but not eliminated with strict mapping parameters and exclusion of problematic regions  (26)  as applied here. A fourth source for false SNP assignments could result from multiple genetically distinct strains that would lead to a chimeric sequence. The latter was not observed in our data (SI Appendix, Fig. S1 ) and this phenomenon might be limited to chronic infections with pathogens such as Mycobacterium tuberculosis, where mixed infections have been previously documented  (27). The introduction of false-positive SNPs by sequencing errors is stochastically negligible as shown in simulated datasets (SI Appendix).
In metagenomic datasets, reads of related species map frequently to conserved regions in the reference genome. When the position is not covered by reads from the target organism (Y. pestis) but the genomic region is similar enough in other environmental organisms so that their reads can map, they might mimic a SNP in Y. pestis when the contaminant species carries a different allele in that position. (B) Excluding all SNPs for which heterozygous calls were identified in the surrounding regions. Heterozygous calls accumulate in conserved regions due to the abovedescribed effect. (C) Excluding all SNPs within regions that include positions that lack genomic coverage. Variants in genome architecture often appear as gaps in mapped data and are likely to cause mapping errors, potentially resulting in false-positive SNPs.
The performance of the presented tool and the validity of the selected criteria were assessed using simulated datasets, where each dataset consisted of both reads of a known Y. pestis genotype (CO92) with different coverages and reads from a captured sample previously determined as Y. pestis-negative (DIR002. A) for representation of an environmental background that is typical for ancient DNA datasets. The SNP evaluation on the artificial datasets-applied with the same criteria as for the First Pandemic genomes presented in this study-showed a maximum sensitivity (all false-positive CO92 SNPs detected) and a high specificity (3. 49-8. 57% of true-positive CO92 positions erroneously filtered out; SI Appendix, Figs. S2  and S3  and Tables S5, S6, and S7). This evaluation was applied to all nonshared SNPs within the First Pandemic lineage, totaling between 1 and 87 chromosomal SNPs per genome (SI Appendix, Table  S8 ).
2 μM indexing primer. Cycling conditions were as follows: 5 min at 94 °C, followed by 18 cycles of 30 s each at 94 °C, 60 °C, and 68 °C, with a final extension of 7 min at 72 °C. Amplified products were purified using MinElute columns and eluted in 35 μL of EB. Samples were quantified using Quant-iT PicoGreen dsDNA kit (P7589; Invitrogen Life Technologies) on the Synergy HT Multi-Mode Microplate Reader with Gen5 software. In-Solution Capture. For the in-solution capture, a probe set was generated using a fragment size of 52 bp and a tiling of 1 bp with the following genomes as templates: CO92 chromosome (NC_003143. 1), CO92 plasmid pMT1 (NC_003134. 1), CO92 plasmid pCD1 (NC_003131. 1), KIM 10 chromosome (NC_004088. 1), Pestoides F chromosome (NC_009381. 1), and Y. pseudotuberculosis IP 32953 chromosome (NC_006155.
1). The capture was performed as previously described (65) on 96-well plates with a maximum of two samples pooled per well and all blanks with unique index combinations in one well. Sequencing and Data Processing. All captured products were sequenced either on an Illumina NextSeq500 or HiSeq4000 platform at the Max Planck Institute for the Science of Human History in Jena, Germany. The non-UDG libraries of Edix Hill samples were sequenced on Illumina NextSeq500 at the University of Cambridge Biochemistry DNA Sequencing Facility, and the FastQ files were processed on the Estonian Biocenter server and screened with MALT (20) using a reference set including full bacterial and viral genomes with 85% identity. For all sequenced UDG libraries, de-multiplexed reads were processed with the EAGER pipeline (66) starting with Illumina adapter removal, sequencing quality filtering (minimum base quality of 20) and length filtering (minimum length of 30 bp).
1, with base pairs 3,000-4,200 masked (19)], to avoid overestimation of coverage due to homologous regions. For the verification of positive qPCR results, we normalized the number of reads mapping to each plasmid with reads mapping to the chromosome and calculated the Mahalanobis distance for each sample to detect outliers. Based on this, we excluded the samples PEI001. A and DIR002. A as false positives (SI Appendix, Table  S2 ). The raw data of the Aschheim and Altenerding genomes were processed identically, however considering only the A120 sample for Aschheim instead of the combined A120+A76 data  (7, 8). SNP Calling and Evaluation. All genomes recovered from UDG-libraries with higher than 4. 5-fold mean coverage including the Altenerding genome were assessed in the SNP analysis. Additionally, the sample WAG001.
S1 ). For the evaluation of unique and shared SNPs of First Pandemic genomes retrieved from UDG-treated libraries, we used the newly developed tool "SNPEvaluation" (https://github. com/andreasKroepelin/SNP_Evaluation) and a comparative mapping, using BWA with high stringent (-n 0. 1, -l 32) and low stringent (-n 0. 01, -l 32) mapping parameters, allowing for more mismatches in the latter. SNPs were called true positive when meeting the following criteria within a 50-bp window: (A) the ratio of mean coverage of low-stringent to high-stringent mapping is not higher than 1. 00, (B) no "heterozygous" positions, and (C) no noncovered positions (SI Appendix, Tables  S8  and S9 ). An assessment of this method is presented in SI Appendix, showing a maximal sensitivity (100% false positives detected) while accepting a high specificity (up to 3.
ACKNOWLEDGMENTS. We are grateful to  Aditya K. Lankapalli ,  Aida Andrades Valtueña , and all members of the  Department of Archaeogenetics, Max Planck Institute for the Science of Human History  for support and fruitful discussions, and  Raphaela Stahl ,  Marta Burri ,  Cäcilia Freund ,  Franziska Aron ,  Antje Wissgott , and  Guido Brandt  for their assistance in the laboratory. We thank the staff of the  State Collection for Anthropology  and  Palaeoanatomy Munich  for support during sample collection and  Ronny Friedrich  at the  Curt-Engelhorn-Centre Archaeometry gGmbH, Mannheim , for providing additional information on radiocarbon dates. Furthermore, we thank  Kyle Harper  and  Henry Gruber  for their correspondence. The excavation of  Saint-Doulchard Le Pressoir  was led by  Philippe Maçon ,  Service d'Archéologie Préventive de l'Agglomération de Bourges Plus , who initiated the archaeogenetic investigation together with D.
Various methods have been proposed for this, usually based on an analysis of variance (ANOVA). An important limitation of most existing ANOVA models applied to MMEs is due to the nature of climate projection datasets available for the analysis. Typically, given the high computational costs of GCMs and RCMs, a large number of possible scenario/GCM/ RCM combinations may be missing from the MMEs. For instance, in the EURO-CORDEX dataset  (Jacob et al. 2014; Kotlarski et al. 2014), 7  RCMs have been used to produce high-resolution projections over the European domain, from 5 CMIP5 GCMs and for 3 RCP scenarios  (Taylor et al. 2012). From the 7 3 5 3 3 5 105 possible scenario/GCM/RCM combinations, only 17 were actually available for the analysis of  Jacob et al. (2014). The number is increasing progressively but the matrix of GCM/ RCM combinations will probably not fill up entirely by the end of this generation of the EURO-CORDEX dataset.
It is thus not subject to the multiple-run constraint. In many MMEs configurations, especially when MMEs are noisy or when a small number of members is available, estimates of uncertainty components obtained with a time series approach are expected to be more precise than with the single-time approach  (Hingray et al. 2019). For both single-time and time series approaches, classical ANOVA methods cannot be applied with missing data (i. e. , when several scenario/GCM/RCM combinations are not available). A drastic solution would be to retain only scenario/GCM/RCM runs for which all combinations are available. However, this would lead to a dramatic waste of information, reducing the dataset to very few combinations (e. g. , 2 RCMs 3 4 GCMs for the EURO-CORDEX dataset; see  Verfaillie et al. 2018).
Missing-data methods have been developed to reduce biases and increase the efficiency of the estimation in such cases. They use, for instance, an ad hoc data reconstruction algorithm  (Déqué et al. 2007)  or likelihood-based techniques  (Little and Rubin 2014). Under the assumption that missing combinations follow the same decomposition of variance as the data actually at hand, Bayesian inference and data augmentation techniques  (Tanner and Wong 1987)  can be applied and present the advantage to propagate missingdata uncertainty. As an example,  Tingley (2012)  applies a Bayesian ANOVA method to infer climate anomalies and to handle missing spatial locations. In the present study, we introduce a method allowing for the characterization of multiple uncertainty sources, namely scenario, GCM, and RCM uncertainties, as well as internal variability, from an incomplete dataset of climate projections.
2017 (Verfaillie et al. , 2018) )  and the Système d'analyse fournissant des renseignements atmosphériques à la neige (SAFRAN) meteorological reanalysis as an observation dataset  (Durand et al. 2009). In this paper, we consider projections obtained at 1500 m, a typical elevation representative of the mountain environment, allowing comparison between all the four massifs used here, given that this elevation level is common to the four massifs chosen.
For all effects and for both temperature and precipitation, the estimation uncertainty roughly increases with time and directly follows, by construction, m(t) 1 a i (t) 6 1:645 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Var[Y * i,j,k (t)] q. This interval is subdivided into subintervals whose width is proportional to the fraction of total uncertainty variance explained by the different sources of uncertainties. (c) Fraction of total variance explained by each source of uncertainty. the evolution of the standard deviation s(t) obtained for the residual errors of the ANOVA model [see Fig. 5  and Eqs. (A2), (A9), (A11), and (A13) in the appendix]. The magnitude of the estimation uncertainty depends mostly on the size and setup of the dataset available for the estimation.
Conclusions and outlooks This work presents the development and application of a Bayesian approach, named QUALYPSO, which uses data augmentation to assess the different sources of uncertainty in incomplete multiscenario multimodel ensembles (MMEs) of climate experiments. In a first step, the climate response of each available simulation chain is estimated with a trend model (i. e. , cubic splines here) fitted to raw climate projections. Climate change responses can then be obtained and residuals from the climate change response are used to estimate the internal variability of the chain. The other uncertainty components of the projections (scenario uncertainty and climate model uncertainty) are estimated with a Bayesian ANOVA model applied to the climate change responses of available simulation chains.
For the Bayesian estimates, 95% credible intervals are shown. cubic splines. Many alternatives are possible and have been considered in previous works. For example,  Hawkins and Sutton (2009)  and  Hingray and Saïd (2014)  apply fourth-order polynomial functions to temperature changes. Cubic splines are expected to provide a flexible and robust fit of the climate response. This estimation can also be improved using multiple runs of each chain, if available (e. g. ,  Kendon et al. 2008; Deser et al. 2012; Hingray et al. 2019). In all cases, an improvement of the method would be to consider the estimated climate response of each chain as uncertain, and to account for this uncertainty in the Bayesian ANOVA approach. Acknowledgments. This work was supported by the French National program LEFE (Les Enveloppes Fluides et l'Environnement) and by the French National Research Agency, via the CDP-Trajectories project, in the framework of the ''Investissements d'avenir'' program (ANR-15-IDEX-02).
This study also benefited from the outcomes of the ADAMONT project (GICC program and ONERC) and of the Interreg project POCTEFA/Clim'Py. Irstea, IGE and CNRM/CEN are part of Labex OSUG@2020. Deborah Verfaillie's work has been funded by the European project EUCP (H2020-SC5-2016-776613). We also thank Matthieu Lafaysse (Univ. Grenoble Alpes, Université de Toulouse, Météo-France, CNRS, CNRM, CEN, Grenoble, France), Samuel Somot, Aurélien Ribes and Michel Déqué (CNRM, Météo-France, CNRS, Université de Toulouse, Toulouse, France) and Wilfried Thuiller (LECA, Grenoble, France) for interesting discussions on this subject. We also thank the editor and two anonymous reviewers for their constructive comments, which helped us to improve the manuscript.
Recently, several groups have coupled Hi-C (or another 3C derivative) to sequence capture with pools of oligonucleotides complementary to thousands of restriction fragment ends  [8] [9] [10] [11] [12]. Such "CHi-C" (Capture Hi-C) methods allow the simultaneous and higher resolution mapping of chromatin interactions for large subsets of the genome, such as all promoters or DNase hypersensitive sites. For example, promoter-centered interactomes have already been used to assign epigenomic status and follow enhancer looping dynamics throughout development, as well as to characterize disease-linked intergenic sequence polymorphisms  [13] [14] [15] [16] [17]. Despite being highly informative, CHi-C datasets have specific properties that set them apart from other 3C-like techniques, which require specialized analytical tools to take these aspects into account.
The majority of CHi-C strategies involve large numbers (thousands) of genomically dispersed baits for which interacting regions are detected. The asymmetry between the number of baits and the number of detected interacting regions leads to an asymmetry of CHi-C contact matrices, confounding standard Hi-C normalization approaches. In addition, individual baits have variable capture efficiencies which introduce additional technical biases. Depending on the bait design, CHi-C datasets will be more or less populated with ligation products between two bait fragments ("double-captured" interactions), as well as between bait and non-bait ("single-captured"), which may complicate bias assessment even further. As for all genome-wide datasets, the challenges for CHi-C analysis are in the appropriate definition of an expected background level, from which "significant" signal can be resolved, and in the development of correct normalization strategies to reduce the impact of non-biological biases.
CHiCAGO uses a statistical background model to account for different biases in promoter-CHi-C data, combining three factors to define the expected background interaction level: genomic distance, bait capture efficiency, and technical biases present in Hi-C and sequencing approaches  [20]. These parameters are fitted to the data to define an expected interaction strength for each individual restriction fragment, based on a combined negative binomial and Poisson variable. However, the treatment of each single fragment as an independent variable creates problems when accounting for biological replicates, since despite its improved coverage compared to Hi-C, current depths of CHi-C datasets still vastly sub-sample the possible space of ligation products. As a result, many reproducible chromatin loops observed at the resolution of larger bins of pooled restriction fragments are lost when scoring individual restriction fragments (Additional file 1: Figure  S1 ).
Related to this, it also follows that chromatin interactions comprising contiguous fragments of increased signal, centered on an interaction peak, are less likely to result from technical artifacts than isolated "spikes" of CHi-C signal. CHiCAGO utilizes the same geometric mean approach as DESeq2  [21]  to allow weighting for different read depths of different replicates, but this may not completely counter the problem, especially if there is a large discrepancy in numbers of sequence reads between replicates. We tried to overcome these existing limitations of CHi-C analysis methods and developed ChiCMaxima, which we applied to multiple published promoter CHi-C datasets, including mouse embryonic stem (mES) cells with different restriction enzyme and probe design strategies  [10, 11] , and nine different human primary hematopoietic cell types  [13].