dataesr/scientific-paragraphs-categorization huggingface dataset:
Curation of the tractogram. The quality of the GT prevented the creation of ROIs. We found looping streamlines (Fig. 3 ) in 12 bundles (out of 25). We visually rejected broken streamlines not reaching expected  regions. The biggest changes included 8% rejection in the CC, 24% and 23% rejection in both ILF and 12% and 6% for both OR. CC and right ILF included a substantial number of looping streamlines. CC had many halfstreamlines stopping mid-line. ILF and OR were too similar, preventing a good segmentation; some streamlines were rejected manually. In other bundles, less than 1% of streamlines were discarded. The final clean tractogram contains 190,065 streamlines (5% rejection). We used the initial scoring system to score this curated data as a way to assess the intensity of the changes. We obtained 94% OL, 9% OR gt , and a Dice score of 92%.
-Bundle coverage: Fig. 5  (top section) compares the bundle dispersion in OL and OR gt between the two scoring systems. Main changes are reported in Table  3. Overall, f1 score was improved, particularly for the two BPS bundles and for the left OR, for which modifications have been brought in the GT data. Bottom section in Fig. 5  compares the submissions dispersion for these metrics. Overall, previous conclusions still hold: probabilistic tracking may help generate highest OL, but with highest OR gt. Submissions 9. 1 and 9. 2 (best OL) only obtain Dice scores of 45% and 46%, placing them in 43 rd and 38 th rank. Usage on new data. We successfully used the Tractoflow pipeline  13  with the noisy data using both the particle filtering tractography (PFT tracking) and the local tracking algorithms to obtain two full tractograms that were scored with the new system.
Discussion We have developed an enhanced Tractometer scoring system for the ISMRM 2015 Tractography Challenge data. It uses carefully determined regions of interest. It offers more reliable results because the segmentation now depends only on the quality of the ROIs. It does not depend on other aspects that were important in the Recobundles segmentation, such as the ordering of the bundles, quality of the reference tractogram (recovered bundles could hide broken/looping streamlines because the GT data itself contained such streamlines), and threshold values for the MDF. In short, our new segmentation is strict enough to prevent the inclusion of noisy streamlines but flexible enough to allow scoring submissions of varied streamline lengths, curvature, fanning, and tracking masks. Overall, the new segmentation offers similar rankings as before when using averaged values over all bundles and all teams, but scores for some bundles were strongly modified.
2. The associated simulated T1 data, however, was not realistic enough to obtain good results in segmentation software such as Freesurfer  24  or FSL FAST  25  for instance. We suggest that future work should include a list of potentially interesting masks, particularly a WM mask that could be used as a tracking mask. 3. The quality of individual streamlines, not only of bundles as whole entities, should be verified, both in the GT and during scoring. 4. Developers should specify a way that users may verify their tractogram format to prevent shifts (ex: ± 0. 5 when the origin of a voxel coordinate is considered at the center or at the corner of the voxel) or swapping of axes during interpretation (ex, specifying the orientation). 5. Developers should specify in which space the final scoring will be performed.
Soft robotics has been a trending topic within the robotics community for almost two decades. However, the available tools for the community to model and analyze soft robotics artifacts are still limited. This paper presents the development of a user-friendly MATLAB ® toolbox, SoRoSim, that integrates the Geometric Variable Strain model to facilitate the modeling, analysis, and simulation of hybrid rigid-soft open-chain robotic systems. The toolbox implements a recursive, two-level nested quadrature scheme to solve the model. We demonstrate several examples and applications to validate the toolbox and explore the toolbox's capabilities to efficiently model a vast range of robotic systems, considering different actuators and external loads, including the fluid-structure interactions. We think that the soft-robotics research community will benefit from the SoRoSim toolbox for a wide variety of applications.
Finally, the MATLAB package, TMTDyn by Saditi et al. ,  11  which uses discretized lumped systems and reduced-order models, is also an example in this direction. However, the majority of the available software for soft robotics modeling uses a theoretically simple but computationally heavy approach, with a lot of nodes and DOFs, designed for a general purpose simulation, instead of analysis and control. Within this scenario, we present the SoRoSim, which is a MATLAB toolbox based on the geometrically exact variable strain (GVS) approach. 12, 13   he approach directly extends the rigid robot modeling to soft and hybrid systems and bridges their gap. It allows the modelling, simulation, analysis, and control of rigid, soft and hybrid open-chain structures within the same framework. Moreover, as a MATLAB toolbox, it can be used together with other MATLAB addons such as the Optimization Toolbox  14  and the Control System Toolbox  15  to further facilitate the analysis and control process.
OOP also allows re-usability, once an object is defined and saved in MATLAB's work space the user can perform multiple manipulations without having to re-define the object. The SoRoSim toolbox consists of three classes, namely Link, Twist, and Linkage, that work together to form a powerful simulation tool that employs the geometrical variable strain model to analyze soft, rigid, and hybrid openchain manipulators. The toolbox was validated by comparing results with verified static models from Renda et al. ,  12  and dynamic models such as those in Boyer et al. 13  Experiments were also set up and used to validate the dynamic and static analysis results of the toolbox. In this section, we discuss the properties and methods of each class and demonstrate an example for using the toolbox.
They include the number of cross sections (per division) of the link (n_l), the number of radial points (n_r, applicable only for a circular cross section), and the color of the link (color). The user can choose a color that follows the MATLAB color code. The default values of n_l, n_r and color are '10', '18', and 'b' (blue) respectively. To create a Link, the syntax is LinkName = Link. Then the user needs to follow the dialog boxes that appear. Default values are provided for all properties if the user do not wish to change. Figure  4  shows the step by step process for creating a soft and a rigid link. Once a Link is created, the 'dot' indexing allows to access or modify its properties. For instance, to change the color of the link L1 to red, the syntax is L1. color='r'. Changing a property of the Link class will affect all its dependent properties.
External Force Properties We organize all properties used to apply external forces or moments on the linkage as External Force Properties. The Linkage class use properties called Gravity and G to define distributed external forces such as gravity. We can enable or disabled the gravity by typing S1. Gravity=1 or S1. Gravity=0. To update the magnitude and direction of the gravity, we can change the gravity wrench vector (G). Similar to Gravity, the Linkage class uses a property called PointForce to enable or disable the application of point forces and moments. np, Fp_loc, and , Fp_vec are Linkage class properties that determine the number of point forces, cell element of piece numbers corresponding to the application of point wrenches, and cell element with the magnitudes of point wrenches. Note that if we choose a rigid piece, the program will apply the point wrench at the center of mass provided by the cx of the Link.
While, if we choose a soft piece, the program will apply the same at the tip of the piece. Hence, the user needs to divide the soft link appropriately to adjust the point of application of the wrench. During the creation of a Linkage, the program prompts users to enter the value of these properties. Apart from these, the user can also apply a customized external wrench to the linkage. To do that, firstly, the user needs to enable the custom external force property called, CEFP by typing, S1. CEFP=1. The default value of CEFP is 0. Secondly, the user needs to modify a MAT-LAB function given by 'CustomExtForce. m' inside a folder, namely 'Custom. ' The MATLAB function CustomExtForce. m lets the user apply a customized external wrench as a function of the Linkage class element, time, q, q, g, J , η, and J.
Here, g, J , η, and J are transformation matrices, Jacobians, screw velocities, and time derivatives of Jacobians evaluated at every significant point. Using the MATLAB function, the user can apply a point wrench on rigid links and a distributed wrench on soft links. The user can also modify a property called added mass (M_added) to simulate an external wrench that depends on η. In section 6, we show an example of how we can use the customized external force to model the underwater propagation of a flagellate soft robot.
m' inside the folder, namely 'Custom. ' In the file, the user has access to the Linkage class element, time, q, q, g, J , η, and J. This opens up the possibility of simulating a closedloop control for the linkage. In addition to this, the user can also add a customized actuation on soft links. An Actuation Property called CAP is used to enable (value 1) or disable (value 0) customized actuation. CAP has a default value of 0. The process is similar to adding the customized external wrench. The user needs to modify a MATLAB function given by 'CustomActuation. m' inside the folder, namely 'Custom. ' Similar to the 'CustomExtForce. m' and 'CustomActuatorStrength. m', in the file 'Custom-Actuation. m', the user has access to the Linkage class element, time, q, q, g, J , η, and J. Using the MATLAB function and these inputs, the user can simulate other kinds of soft actuators.
Elastic and Other Properties Constant parameters such as generalized stiffness matrix and generalized damping matrix are pre-computed and saved as properties of the Linkage, namely, K and D. The class uses a property called Damped to enable (value 1) or disable (value 0) the elastic damping of soft links. The default value of Damped is 1. We reserve three customizable properties, CP1, CP2, and CP3, which can be used to save constant properties of the linkage for applying a custom external force or actuation. The Linkage class also has two other properties, namely CablePoints and PlotParameters. The class uses CablePoints for plotting the actuator path, and PlotParameters is a struct element of MATLAB with parameters for changing the output plot of the simulation. The user can access the plot parameters by typing S1.
Once the user enters the initial guess, the toolbox estimates the equilibrium state of the linkage using the nonlinear solver of MATLAB called, 'fsolve' and displays the output. Figure. 10 compares the equilibrium state of the linkage with its reference state. The toolbox also saves the results of the static simulation, value of joint coordinates (with a variable name 'q'), and actuator forces (with a variable name 'u'), in a MATLAB file called 'StaticsSolution. mat'. [Figure  10  about here. ] Similarly, to perform the dynamic simulation of the linkage, the syntax is S1. dynamics. Subsequently, the toolbox prompts the user to enter the actuation parameters for the dynamic simulation as a function of 't' (time). As an example, we can input the revolute joint angle as a periodic function (pi/2 * sin(2 * pi * t)) and the actuator strength as a ramp input that goes from 0 to -200 N in one second and stays at -200 N after that (-200 * t + (200 * t-200) * heaviside(t-1)).
After this, a dialog box pops up asking for the initial condition of the simulation, which includes the initial value of joint coordinates and their time derivatives, and the simulation time. We simulate this example by keeping the default values. The toolbox uses the differential solver of MATLAB called ode45 to solve dynamic problems. Once the dynamic simulation is complete, another dialog box appears and asks if the user needs the output video of the simulation. If the user chooses 'Yes', the toolbox plots the linkage states and generates an output video in '. avi' format. The toolbox saves the video as 'Dynamics. avi' on the folder from which we run the simulation. It also saves the dynamic simulation results in a MATLAB file called 'Dynamic-sSolution. mat'. The MATLAB file will have a (N dyn × 1) array of time (with a variable name 't') and a (N dyn × 2ndof ) matrix of joint coordinates and their derivatives (with a variable name 'qqd', which represents q and q).
Conclusion This paper presented SoRoSim, a MATLAB toolbox that uses the Geometric Variable Strain (GVS) approach to provide a unified framework for modeling, analysis, and simulation of soft, rigid, and hybrid soft-rigid open-chain manipulators. The paper discussed the theory and the computational implementation behind the toolbox in detail. The paper can be used as a user manual of the toolbox as it covers the overview of the toolbox and provides instructions on using the toolbox features. We validated the toolbox simulation results via numerical tests and provided a substantial number of toolbox applications. The SoRoSim version 2. 32 is an initial version of the toolbox. We will be constantly improving the toolbox by enhancing its performance, features, and GUIs. For instance, we can update the toolbox to handle branched-chain robots and closed-chain robots.
An implicit time integrator can be included to improve the speed of dynamic simulations. We can also include customizable cross sections for the links to simulate a random tube like geometries. Methods can be added to the Linkage class to simulate inverse kinematics and dynamics. As a result, the properties and methods of the toolbox classes may change in future versions. The limitations associated with the toolbox at this stage are that it simulates ideal problems. Simulation cases where external dissipative forces such as friction are critical will see a slight deviation due to the ideal assumption. However, we could add friction models in future editions of the toolbox to tackle this limitation. As the toolbox is developed in a MATLAB environment, there are plenty of ways to use the output data with the existing MATLAB packages and user-written MATLAB codes.
For example, the user can combine the SoRoSim toolbox with an optimization package of MATLAB to develop an optimal robot design for applications. We hope that the users of the SoRoSim toolbox find it userfriendly and will use it for research and engineering applications. Appendix: Formulae ad ξ(X) = k 0 3×3 p k ∈ R 6×6 , ad η(X) = w 0 3×3 v w ∈ R 6×6 , Adjoint operator of se(3). ad * ξ(X) = k p 0 3×3 k ∈ R 6×6 , ad * η(X) = w v 0 3×3 w ∈ R 6×6 , Coadjoint operator of se(3). Ad g(X) = R 0 3×3 rR R ∈ R 6×6 , Adjoint map of SE(3). Ad * g(X) = R rR 0 3×3 R ∈ R 6×6 , Coadjoint map of SE(3). exp Ω(X) = I 4 + Ω + 1 θ 2 (1 -cos (θ)) Ω 2 + 1 θ 3 (θ -sin (θ)) Ω 3 , Exponential map where θ is the magnitude of Ω. T Ω (X) = Step for entering the stiffness value of revolute and prismatic joints and the final image of the linkage.
Acknowledgements. This study has been supported by  ADEME (Agence de l'Environnement et de la Maitrise de l'Énergie)  under grant  ESCALAIR. 23  https: // doi. org/10. 5194/gmd-2023-78  Preprint. Discussion started: 25 May 2023 c Author(s) 2023. CC BY 4. 0  License.
Data availability. No dataset has been used for this study. Code availability. This study has been performed using ToyCTM v1. 0  (Mailler and Pennel, 2023). All the Python scripts used to launch the model and to perform the post-processing of model outputs to obtain the figures in this paper and the numbers in Table  4  are available from https://doi. org/10. 5281/zenodo. 7956919.
Analysis of simulated data Simulated contact frequency maps. To predict chromatin contact frequency maps for comparison with Hi-C data, we used ensembles of simulated polymer conformations as follows. For simulations of 300 kb loops or larger, we generated 2500 independent simulations and randomly picked 80 polymer conformations per trajectory, yielding 200 000 single conformations in total. For 150 and 228 kb loops, we randomly picked 50 conformations from 4000 independent simulations, also resulting in 200 000 single conformations in total. Predicting a contact map from an ensemble of polymer conformations requires to define a capture radius (i. e. a threshold for the spatial distance between bead centers below which any pair of beads generates a contact event). To determine this radius, we first computed contact maps at 3 kb resolution for various radii, then calculated the average contact frequency along each diagonal of the contact map as function of genomic separation, P(s).
Fitting theoretical distance models. In the Results section 'Estimating the fraction of loop states from static imaging data', we used the theoretical model from (Eq. 2) above to estimate the three state fractions A closed , A open and A extruding = 1 -A closed -A open from simulated anchoranchor vectors. We randomly picked N anchor-anchor vectors from 4000 independent simulation trajectories, each containing 3000 time points and fitted the analytical model to these data. Because the covariance of P( R) = P x (δx)P y (δy)P z (δz) is zero, rather than fitting this 3D function to the anchor-anchor vectors R, we simultaneously fitted the three 1D probability densities P x (δx), P y (δy) and P z (δz) (Eq. 2) to the three axial projections of anchoranchor vectors (δx,δy and δz), respectively. We performed these fits using a Python script that employs the curve fit function of the scipy package  (55) , with the three proportions initialized to 1/3 each ( A closed = A open = A extruding = 1 3 ).
Analysis of experimental data Analysis of ChIP-Seq and Hi-C data. For all genomic analyses, we used the hg19 reference genome. For ChIP-Seq data of CTCF, SMC1 and RAD21, we used publicly available data from Rao et al. (16). Raw reads were qualitychecked with FastQC  (60). Reads from different replicates were first mapped independently using bowtie2 v2. 2. 6. 2  (61)  with default parameters, and the correlation between replicates was computed using wigCorrelate  (62). Replicates with correlations larger than 0. 9 were pooled together and mapped again. We removed blacklisted regions  (63)  and called peaks using MACS2 v2. 1  (64)  with default parameters. CTCF motifs were identified genome-wide using FIMO  (65)  with the flags -max-stored-scores 50 000 000 and -thresh 0. 001. We then mapped CTCF sites identified with a P-value < 1 × 10 -5 onto CTCF ChIP-Seq peaks.
We then binned the aggregated map to 15 kb resolution. Analysis of imaging data. In the Results section 'Comparing polymer simulations to imaging data', we considered data from two experimental studies (Supplementary Figure  S4 ). First, we used multiplexed DNA FISH data in mouse embryonic stem cells (mESC) from replicates 1 and 2 of Takei et al. (31). This dataset covered one genomic region on each of the 20 chromosomes at 25 kb resolution, each region comprising 60 consecutive loci and spanning at least 1. 5 Mb, from which we extracted pairs of genomic loci. We removed from the analysis all cells where more than two identical chromosomes were detected. The pair-wise distances from all chromosomes were pooled together. Second, we considered live-cell imaging data from Gabriele et al. (35).
We assumed that 3D imaging data are obtained from cells in which extrusion can be abolished, e. g. by depleting cohesin. The two anchors of a loop are fluorescently labeled in two different colors (here, red and green) and imaged either at a fixed time point (static imaging) or tracked using time-lapse microscopy (dynamic imaging). This allows to determine the approximate 3D coordinates of the two anchors and the anchor-anchor distances (d) in a population of cells, either as a single snapshot or as function of time in single cells. Hi-C data shown on top are from Rao et al. (16). (B) Polymer simulations were used to model the dynamics of a generic chromatin segment with or without loop extrusion. The chromatin loop was assumed to transition between three different states, in the following order: open (the polymer is free of loops), extruding (the loop is actively extended) and closed (the loop is fully formed and the two anchors are kept close to each other).
Second, we compared simulated contact maps to available Hi-C data in order to determine plausible ranges for the fractions of loops in each state (open, extruding or closed) within a population of cells. Third, we used the same simulations to predict distributions of anchor-anchor distances for different biological and experimental parameters. We then used a statistical test to determine (for each set of parameters), whether and to what extent the presence of loop extrusion can be detected from distance distributions. Fourth, we proposed and tested a method to estimate the fractions of the open, closed, or extruding states based on distance distributions from static imaging data. Fifth, we analyzed how live-cell anchor trajectories can be used to estimate the duration (lifetime) of closed states and the speed of loop extrusion.
Comparing polymer simulations to Hi-C data Since TADs and loops were primarily defined from Hi-C data (4,5,16), realistic simulations must be able to account for these features in simulated contact frequency maps. In order to generate contact frequency maps from simulations, we used a capture radius of 150 nm, which provided the best match between simulated and experimental P(s) curves (Supplementary Figure  S2B ). We first verified that our simulations, in which extrusion was assumed to start at random genomic locations between the anchors, can qualitatively reproduce blocks of enriched contacts with corner peaks on the contact map diagonal, consistent with TADs and loops (Supplementary Figure  S2C ). Note that if extrusion was instead initiated at one of the two anchors or at the mid-point between them, the contact maps exhibited different features, namely stripes  (18, 52, 72) , and hairpins  (73)  or jets  (50) , respectively (Supplementary Figure  S2C ).
However, we excluded such structures from our analyses to focus on canonical TADs and loops instead. The strength of contact blocks and/or corner peaks in Hi-C data is expected to depend on the fractions of cells in which the anchors are in an open, closed, or extruding state. Obviously, these fractions also strongly determine the dynamics of tracked anchors and the expected distribution of anchor-anchor distances, and therefore impact the feasibility of detecting and/or characterizing loop extrusion  (37). For example, a high fraction of cells in a closed state could give rise to a bimodal distribution of anchor-anchor distances (one mode at small distances corresponding to closed states and a second mode at larger distances corresponding to open or extruding states), whereas a low fraction might not.
These fractions are poorly known -one aim of imagingbased approaches is precisely to estimate them. Nonetheless, to determine a realistic range of state fractions, we proceeded to vary them in our polymer simulations and compared simulated contact maps to a selection of experimental loops in Hi-C data (Figure  2 , Supplementary Figures  S2E, F  and S3 ). Below, we describe (i) the Hi-C data set considered, (ii) the simulations and the range of parameters explored, (iii) the metric we used to compare data to simulation predictions and (iv) the results of this comparison. We started from the Hi-C data (  16 ) of RAD21-mAID-GFP tagged HCT-116 cells, in which addition of auxin depletes RAD21  (69). We computationally identified 4470 loops in the 5 kb resolution Hi-C maps of cells without auxin treatment.