dataesr/scientific-paragraphs-categorization huggingface dataset:
, 2012 )  that can be used for DTI-and HARDI-based modeling. Examples of tractographic output for a highresolution macaque dataset are shown in Fig. 7  B. These tools can be useful in performing network-based comparisons of structural properties  ( Taylor et al. , 2016b ) , possibly in conjunction with functional network studies. TORTOISE provides methods for group analysis based on separate comparisons of structural properties from diffeomorphic registrations (DR_TAMAS;  Irfanoglu et al. , 2016 ). Study design is important for all aspects of analysis, but the DWI acquisition method particularly affects how well distortion artifacts can be reduced. Acquiring sets of DWIs with opposite phase encoding has been shown important in reducing EPI inhomogeneity distortions  ( Irfanoglu et al. , 2019 ( Irfanoglu et al.
, , 2015)) , especially in the presence of subject motion  ( Taylor et al. , 2016a ). A T2-weighted structural volume with fat suppression can furthermore act as a useful reference for further reduction of geometric distortions. TORTOISE's tools have been designed to take advantage of such acquisitions. Multiple demos for TORTOISE and AFNI's FATCAT are available. The FATCAT_DEMO2 illustrates full single subject processing of a dual-phase encoded DWI dataset, including probabilistic tractography on gray matter parcellation. Each step of processing automatically generates QC images to help evaluate the data. These include alignment images, subject motion plots, directionally encoded color (DEC) maps, thresholded FA maps, and ROI overlays. The FAT_MVM_DEMO provides an example of combining FATCAT tractography results from a network of target ROIs with multivariate modeling (MVM) for a hierarchical group analysis: first, at the "network level" with an omnibus F-statistic, and then zooming in at the "ROI level" with post hoc t-tests.
Data sharing As an extension of the PRIME-DE consortium, which was established to openly share NHP neuroimaging data  ( Milham et al. , 2020 ( Milham et al. , , 2018)) , PRIME-RE also maintains a list of NHP neuroimaging data-sharing initiatives. Similar to the analytical resources described above, anyone can submit a (link to a) data resource for inclusion on PRIME-RE us-ing a simple submission form. The data sharing section of PRIME-RE currently lists PRIME-DE, OpenNeuro, and NeuroVault. The PRIME-DE initiative  ( Milham et al. , 2018 )  specifically focuses on NHP data and comprises data from 22 different sites all over the world. The database contains structural, functional and diffusion data; BOLD and contrastagent data; awake and anesthetized scans; resting-state and task-based fMRI.
OpenNeuro, previously known as OpenfMRI  ( Poldrack et al. , 2013 ; Poldrack and Gorgolewski, 2017 )  hosts MRI, MEG, EEG, iEEG, and ECoG data. Most of the data are from human subjects, but Open-Neuro is not restricted to human data and some NHP data-sets are now available as well. Neurovault  ( Gorgolewski et al. , 2015 )  specializes in sharing un-thresholded statistical maps, mask files, parcellation maps, and any other voxelwise data. Originally restricted to human imaging data, the framework was recently extended to allow non-human data as well  ( Fox et al. , 2020 ). For NHP data, volumetric data should be registered to the NMT, a processing step that can easily be done using several of the tools listed on PRIME-RE (see Section 3. 2. 2 ).
Discussion Neuroimaging with non-human primates requires highly specific experimental and analytical expertise. Recent initiatives such as PRIME-DE  ( Milham et al. , 2018 )  have made a wealth of shared NHP neuroimaging data openly available, but the analysis of these datasets demands appropriate analytical expertise, tools, and workflows. To facilitate the study of NHP neuroimaging data, PRIME-RE was established as an infrastructure for knowledge and resource sharing, collaboration and communication. The PRIME-RE website serves as a central knowledge hub for the NHP neuroimaging community. It is home to a structured dynamic overview of relevant analytical resources, and a continuously evolving wiki that describes the challenges and potential solutions of all facets of NHP neuroimaging. Both these knowledge bases are collectively curated by community-driven practices.
This content makes PRIME-RE a NHP-specific complement to more broadly oriented sites, such as the Neuroimaging Tools and Resources Collaboratory (NITRC, https://www. nitrc. org )  ( Kennedy et al. , 2016 ; Luo et al. , 2009  ) that cat-alogues data, tools and pipelines for all general aspects of neuroimaging. A common data structure to reference research resources, such as the RRID (Research Resource Identifier)  ( Bandrowski et al. , 2016 )  might allow seamless integration of the resources in PRIME-RE and NITRC in the future. It is common for development teams of broadly used neuroimaging packages to organize courses focused on the use of their specific package (e. g. , AFNI 1  , FSL 2  , or SPM 3  ). In recent years, open science initiatives such as Brainhack  ( Craddock et al. , 2016 )  and the NeuroHackademy, have led to a boost in the creation of tutorials, courses, demos and workshops that more generally cover different aspects of neuroimaging and open science practices.
While this content is often spread over various websites, some efforts are being made to curate this information (e. g, https://learn-neuroimaging. github. io/tutorials-and-resources ). Besides its community-curated wiki and links to tutorials and documentation for individual resources, PRIME-RE also hosts a list of links to external tutorial and resource collections that may be useful for the NHP neuroimaging community. The PRIME-DE/RE initiatives follow on prior large-scale human neuroimaging resources, such as the 1000 Functional Connectomes Project  ( Biswal et al. , 2010 ) , ADHD-200  ( Brown et al. , 2012 )  or ABIDE  ( Di Martino et al. , 2014 ). In these projects, data sharing was complemented by open source pipelines for preprocessing and analyzing the data (Configurable Pipeline for the Analysis of Connectomes)  ( Craddock et al.
, 2013 ). While these accompanying tools may be limited in resolving all potential issues, their early release lowers the barrier for users to engage with the shared data, and accelerates the development of novel analysis solutions. By focusing on community building, PRIME-RE aims to provide a broad dynamic framework to channel the efforts of the NHP neuroimaging community and evolve together. In the future, PRIME-RE may be expanded to include an even broader spectrum of resources involved in NHP neuroimaging. One can think of blueprints for hardware (e. g. , chairs, behavioral response devices, and coils), electronic schematics, models for 3-D printing or laser cutting; protocols for data acquisition (e. g. , sequences), animal care, housing, training and handling. Additional resource categories can be created for protocols and tools targeted at the combination of NHP neuroimaging with other experimental approaches such as brain perturbation techniques  ( Klink et al.
, this issue ) , electrophysiological recordings, and histology. The Wiki could furthermore be expanded to address task or experimental design, validation approaches, quality control, and different types of univariate and multivariate analysis methods, although some of these are not specific to NHP neuroimaging. PRIME-RE supports best practices of open science at every step from data acquisition, through data organization, to code structure and analysis. Contributors and users are encouraged to adhere to the FAIR principles  ( Wilkinson et al. , 2016 )  and both communicate and document their tools and data. Compared to human neuroimaging, NHP neuroimaging has been lagging behind in adopting such collaborative open science initiatives, and we can only speculate about the reasons why. It is conceivable, for instance, that due to the large amount of work involved in overcoming the challenges of NHP neuroimaging, the researchers involved might be a bit more protective of their solutions.
For instance, because they reside on a laboratory's internal servers or personal websites. However, people's attitudes towards openly sharing the resource solutions they have developed appear to be improving  ( Balbastre et al. , 2017 ; Tasserie et al. , 2020 )  and new developments in information technology promote such initiatives while simultaneously creating avenues to assign explicit credit to developers. A collaborative open approach to NHP neuroimaging will not only foster collaboration in the short term, but also guide future development efforts, enhance reproducibility, and benefit the whole community in the long term. The contribution template for PRIME-RE requires a minimum set of metadata to ensure a consistent and comprehensive resource index (see Table  1  ). The website provides a graphic interface that simplifies database navigation and makes it easy for researchers to discover relevant tools, data, and learning material.
Acknowledgements We would like to thank  Patrick Markwalter  for assistance with compiling references, editing and formatting. We thank the following people for their contributions to shared resources:  Richard C. Reynolds ,  Gang Chen , and  Robert Cox  (AFNI, esp. afni_proc. py); Konrad Wagstyl  and  Alan C. Evans  (CIVET);  Leslie Ungerleider  ( CIVET, NMT );  Cameron Craddock  (C-PAC);  David Meunier  and  Régis Trapeau  (Macapype);  Jochen Weber  (NeuroElf);  Jonathan Williford  ( NHP-BIDS );  Borja Ibañez  (precon_all);  Arun Garimella ,  Felipe Mendez , and  Luis Concha  ( PRE-EMACS );  Antoine Grigis  and  Béchir Jarraya  (Pypreclin);  Gabriel Devenyi ,  Nikos K. Logothetis , and  George Paxinos  (SARM); Afonso Silva  and  David Leopold  (MBM);  Lennart Verhagen  and members of the  Cognitive Neuroecology Lab (MrCat).
This research was supported in part by the  Intramural Research Program  of the  NIMH  and utilized the computational resources of the  NIH HPC  Biowulf cluster ( http://hpc. nih. gov ). Pypreclin work was supported by the  Fondation pour la Recherche Medicale  (FRM grant number  ECO20160736100  to JT),  Fondation de France ,  Human Brain Project  ( Corticity  project). RT and KH are supported by  ANR-19-DATA-0025-01  NeuroWebLab. RBM is supported by the  Biotechnology and Biological Sciences Research Council (BBSRC)   UK [BB/N019814/1 ]. The  Wellcome Centre for Integrative Neuroimaging  is supported by core funding from the  Wellcome Trust  [ 203129/Z/16/Z ].
Code and data availability Both the code for the PRIME-RE website ( https://prime-re. github. io ) and its Wiki pages are available on GitHub ( https://github. com/ PRIME-RE/prime-re. github. io ). All resources described in this paper and listed on PRIME-RE are freely available from their respective developers or maintainers. Every listing on PRIME-RE comes with a link to the actual resource and a brief statement on possible usage restrictions (e. g. , citing a specific paper). The list of more common software packages may contain packages that require users to purchase a license, but most are freely available as well.
Furthermore, datasets with a large number of adolescents diversely recruited across Europe have been provided as a result of the multicentric nature of the HELENA study. This fact allows researchers to focus their analysis on an age range which is rarely studied, the adolescence period, where early detection of adverse sedentary and dietary habits might influence health status in adulthood. Finally, little has been found in the literature considering the same interaction approach, where screen time plays an important role in the association of MD and adiposity among adolescents. As we have observed, the negative association between screen time and MD adherence on adiposity indices, joint public health implementation programs oriented to both, avoiding excessive screen time and promoting the MD dietary pattern for primary prevention of major chronic diseases, should be considered in the near future.
Recent research in data assimilation has led to the introduction of the parametric Kalman filter (PKF): an implementation of the Kalman filter, whereby the covariance matrices are approximated by a parameterized covariance model. In the PKF, the dynamics of the covariance during the forecast step rely on the prediction of the covariance parameters. Hence, the design of the parameter dynamics is crucial, while it can be tedious to do this by hand. This contribution introduces a Python package, SymPKF, able to compute PKF dynamics for univariate statistics and when the covariance model is parameterized from the variance and the local anisotropy of the correlations. The ability of SymPKF to produce the PKF dynamics is shown on a nonlinear diffusive advection (the Burgers equation) over a 1D domain and the linear advection over a 2D domain.
In the parametric Kalman filter (PKF)  (Pannekoucke et al. , 2016 (Pannekoucke et al. , , 2018b, a), a) , the covariance matrix is approximated by a parametric covariance model; the time evolution of the matrix is deduced from the time integration of the parameters' evolution equations. One of the major limitations for the PKF is the design of the parameter evolution equations. Although not difficult from a mathematical point of view, this step requires the calculation of many terms that are difficult to calculate by hand and may involve errors in the calculation. To facilitate the derivation of the parametric dynamics and certify the correctness of the resulting system a symbolic derivation of the dynamics would be welcome. The goal of the package SymPKF 1. 0 1 is to facilitate the computation of the PKF dynamics for a particular class of covariance model, the VLATcov model, which is parameterized by the variance and the anisotropy.
The symbolic computation of the PKF dynamics relies on a computer algebra system (CAS) able to handle abstract mathematical ex-O. Pannekoucke and P. Arbogast: SymPKF (v1. 0)  pressions. A preliminary version has been implemented with Maxima 2  (Pannekoucke, 2021a). However, in order to create an integrated framework that would include the design of the parametric system, as well as its numerical evaluation, the symbolic Python package SymPy  (Meurer et al. , 2017)  has been preferred for the present implementation. In particular, SymPKF comes with an automatic code generator to provide an end-to-end exploration of the PKF approach from the computation of the PKF dynamics to their numerical integration. The paper is organized as follows. The next section provides the background on data assimilation and introduces the PKF.
Section 3 focuses on the PKF for univariate VLATcov models in the perspective of symbolic computation by a CAS. Then, the package SymPKF is introduced in Sect. 4 from its use on the nonlinear diffusive advection (the Burgers equation) over a 1D domain. A numerical example illustrates the use of the automatic code generator provided in SymPKF. Then, the example of the linear advection over a 2D domain shows the ability of SymPKF to handle 2D and 3D domains. The section ends with a simple illustration of a multivariate situation, which also shows that SymPKF applies to a system of prognostic equations. The conclusion is given in Sect. 5.
Discussion and intermediate conclusion However, although the calculation of the system in Eq. (  16 ) is straightforward, as it is similar to the calculation of Reynolds equations  (Pannekoucke et al. , 2018a) , it is tedious because of the many terms involved, and there is a risk of introducing errors during the calculation by hand. Then, once the dynamics of the parameters are established, it remains to design a numerical code to test whether the uncertainty is effectively well represented by the PKF dynamics. Again, the design of a numerical code is not necessarily difficult, but with numerous terms the risk of introducing an error is important. To facilitate the design of the PKF dynamics and the numerical evaluation, the package SymPKF has been introduced to perform the VLATcov parameter dynamics and to generate a numerical code used for the investigations (Pannekoucke, 2021c).
Definition of the dynamics The definition of the dynamics relies on the formalism of SymPy as shown in Fig. 1. The coordinate system is first defined as instances of the class Symbols. Note that the time is defined as sympkf. t, while the spatial coordinate is left to the choice of the user, here x. Then, the function u is defined as an instance of the class Function as a function of (t, x). In this example, the dynamics consist of a single equation defined as an instance of the class Eq, but in the general situation in which the dynamics are given as a system of equations, the dynamics have to be represented as a Python list of equations. A preprocessing of the dynamics is then performed to determine several important quantities to handle the dynamics: the prognostic fields (functions for which a time derivative is present), the diagnostic fields (functions for which there is no time derivative in the dynamics), the constant functions (functions that only depend on the spatial coordinates), and the constants (pure scalar terms that are not a function of any coordinate).
Note that E[u(t, x, ω)] is a function of (t, x) only: the expectation operator converts a random variable into a deterministic variable. Then, the symbolic computation of the second-order fluctuation-mean interaction dynamics in Eq. (  16a ) is per-formed, thanks to SymPy, by following the steps as described in Sect. 2. 2. 1. In particular, the computation also leads to the tangent-linear dynamics of the error in Eq. (  6 ), from which it is possible to compute the dynamics of the variance in Eq. (16b) and of the metric tensor in Eq. (16c) (or its associated aspect tensor version). Applying these steps and the appropriate substitutions, this is achieved when calling the in_metric or in_aspect Python property of an instance of the class SymbolicPKF. This is shown for the Burgers equation in Fig.
5  for the term E[ε u ∂ 5 x ε u ]. Whatever closure has been obtained in an analytical or an empirical way, it remains to compute the closed PKF dynamics to assess their performance. To do so a numerical implementation of the system of partial differential equations has to be introduced. As for the computation of the PKF dynamics, the design of a numerical code can be tedious, with a risk of introducing errors in the implementation due to the numerous terms occurring in the PKF dynamics. To facilitate the research on the PKF, SymPKF comes with a Python numerical code generator, which provides an end-to-end investigation of the PKF dynamics. This code generator is now detailed.
Automatic code generation for numerical simulations While compiled language with appropriate optimization should be important for industrial applications, we chose to implement a pure Python code generator, which offers a https://doi. org/10. 5194/gmd-14-5957-2021 Geosci. Model Dev. , 14, 5957-5976, 2021 simple research framework for exploring the design of PKF dynamics. It would have been possible to use a code generator already based on SymPy (see, e. g. ,  Louboutin et al. , 2019) , but with such code generators being domain-specific, it was less adapted to the investigation of the PKF for arbitrary dynamics. Instead, we consider a finite-difference implementation of partial derivatives with respect to spatial coordinates. The default domain to perform the computation is the periodic unit square with the dimension of the number of spatial coordinates.
g. , F xxy = F 2 x • F y = F y • F 2 x. The finite difference of order α with respect to a single spatial coordinate is the centered finite difference based on α + 1 points. For instance, Fig. 6  shows how to close the PKF dynamics for the Burgers equation following P18 and how to build a code from an instance of the class sympkf. FDModelBuilder: it creates the class ClosedPKFBurgers. In this example, the code is rendered from templates thanks to Jinja 3 ; then it is executed at runtime. Note that the code can also be written in an appropriate Python module for adapting the code to a particular situation or to check the correctness of the generated code. At the end, the instance closed_pkf_burgers of the class ClosedPKFBurgers is created, raising a warning to indicate that the value of constant κ has to be specified before performing a numerical simulation.
Note that the code generator of SymPKF can be used for arbitrary dynamics, e. g. , the Burgers equation itself. Hence, a numerical code solving the Burgers equation is rendered from its symbolic definition. Then an ensemble of 1600 forecasts is computed starting from an ensemble of initial errors at time 0. The ensemble of initial errors is sampled from the Gaussian distribution N 0, P f h of zero mean and covariance matrix P f h. Note that the ensemble forecasting implemented in SymPKF as the method Model. ensemble_forecast (see Fig. 7 ) leverages the multiprocessing tools of Python to use the multiple cores of the CPU when present. On the computer used for the simulation, the forecasts are performed in parallel on eight cores. The ensemble estimation of the mean, the variance, and the length scale is shown in Fig.
8  (dashed lines). Since https://doi. org/10. 5194/gmd-14-5957-2021 Geosci. Model Dev. , 14, 5957-5976, 2021 the ensemble is finite, sampling noise is visible, e. g. , in the variance at the initial time that is not strictly equal to V h. In this simulation, it appears that the PKF (solid line) coincides with the ensemble estimation (dashed lines), which shows the ability of the PKF to predict the forecast error covariance dynamics. Note that the notebook corresponding to the Burgers experiment is available in the example directory of SymPKF. While this example shows an illustration of SymPKF in a 1D domain, the package also applies in 2D and 3D domains, as presented now.
(  31c ) is similar to the dynamics of the conformation tensor in viscoelastic flow  (Bird and Wiest, 1995; Hameduddin et al. , 2018). We do not introduce any numerical simulation of the PKF dynamics in Eq. (30) or Eq. (31), but interested readers are referred to the 2D numerical PKF assimilation cycles of Pannekoucke (2021b), which have been made thanks to SymPKF. This example illustrates a 2D situation and shows the multidimensional capabilities of SymPKF. Similarly to the simulation conducted for the Burgers equation, it is possible to automatically generate a numerical code able to perform numerical simulations of the dynamics in Eq. (31) (not shown here). Hence, this 2D domain example showed the ability of SymPKF to apply in dimensions larger than 1D. Before concluding, we would like to present a preliminary application of SymPKF in a multivariate situation.
Conclusions This contribution introduced the package SymPKF that can be used to conduct the research on the parametric Kalman filter prediction step for covariance models parameterized by the variance and the anisotropy (VLATcov models). SymPKF provides an end-to-end framework: from the equations of dynamics to the development of a numerical code. The package has been first introduced by considering the nonlinear diffusive advection dynamics in the Burgers equation. In particular, this example shows the ability of SymPKF to handle abstract terms, e. g. , the unclosed terms formulated with the expectation operator. The expectation operator implemented in SymPKF is a key tool for the computation of the PKF dynamics. Moreover, we showed how to handle a closure and how to automatically render numerical codes.
Acknowledgements. We would like to thank  Sylwester Arabas  and the two anonymous referees for their fruitful comments, which have contributed to improving the paper. The  UML  class diagram has been generated from UMLlet (Auer et al. , 2003). Financial support. This research has been supported by the  French national program LEFE/INSU (Étude du filtre de KAlman PAramétrique, KAPA). Review statement. This paper was edited by  Sylwester Arabas  and reviewed by two anonymous referees.