dataesr/scientific-paragraphs-categorization huggingface dataset:
Specifically ∆t i = C ∆x P i /M i , ( 44 ) where 0 < C < 1 is a free parameter, usually C ∼ 0. 25. While commonly used in the case of Vlasov-Poisson, we are not aware of explicit derivations of this value from stability criteria as in the case of hyperbolic conservation laws. A closely related criterion is ∆t i = C ∆x/ A i , where A i := -∇φ| Xi is the acceleration. This condition sets a global timestep that is commonly used in simulations where forces are computed via the PM algorithm (e. g. ,  Merz et al. 2005 ). Other criteria are also possible, for instance the ABACUS code  (Garrison et al. 2016) , in addition to Eq. 44, uses a heuristic condition based on the global maximum value of the RMS velocity over the maximum acceleration of particles in a volume element. In the case of tree or direct summation based methods, the scale played by the mesh grid resolution is taken over by the softening length.
This can effectively be written as a matrix inversion problem Aφ = f where the finite difference stencil gives rise to a sparse matrix A and the solution sought is φ = A -1 f. Efficient methods exist to solve such equations. A particularly powerful one, that can directly operate even on an AMR structure, is the adaptive multigrid method  (Brandt 1977; Trottenberg et al. 2001) , which is used e. g. , by the RAMSES code  (Teyssier 2002). It combines simple point relaxation (e. g. , Jacobi or Gauss-Seidel iterations) with a hierarchical coarsening procedure which spreads the residual correction exponentially fast across the domain. Some additional care is required at the boundaries of adaptively refined regions. Here the resolution of the mesh changes, typically by a linear factor of two, and interpolation from the coarser grid to the ghost zones of the fine grid is required.
It is then possible to rewrite Eq. (  64 ) employing the position of the nearest replica, which results into pairwise interactions with a modified gravitational potential. This potential needs to be computed numerically, thus, in GADGET3, for instance, it is tabulated and then interpolated at runtime, whereas in GADGET4, the code relies on a look-up table of a Taylor expansion with analytic derivatives of the Ewald potential. We summarise in more detail how this is achieved in Sect. 5. 3, where we discuss in particular how the FFT can be efficiently used to execute the Fourier summation. This direct summation of individual particle-particle forces is O(N 2 ), that is, quadratic in the number of particles and thus becomes quickly computationally prohibitive. In addition, since it is a highly non-local operation, it would require a considerable amount of inter-process communication.
In practice, this method is sometimes used to compute short-range interactions, where the operation is local and can exploit the large computational power provided by GPUs. This is, for instance, the approach followed by the HACC code  (Habib et al. 2016 ), when running one of the largest simulations to date with 3. 6 trillion particles; and also by the ABACUS code  (Garrison et al. 2018). Direct summation enabled by GPUs has also been adopted by  Rácz et al. (2019)  for compactified simulations, where there is an additional advantage that only a small subset of the volume has to be followed down to z = 0 (cf. Sect. 6. 3. 5).
( 65 ) The long-range contribution φ lr can be computed using the PM method on a relatively coarse mesh. On the other hand, the short-range contribution φ sr , can be computed from the direct force between particles only in their immediate vicinity -since the particles further away contribute through the PM part. Instead of the direct force, which gives then rise to the P 3 M method, modern codes often use a tree-method (see next section) for the short range force (this is e. g. , what is implemented in the GADGET2 code by  Springel (2005) , see also  Wang 2021). The splitting kernel effectively spreads the mass over a finite scale r s for the long range interaction, and corrects for the residual with the short range interaction on scales r s. Many choices are a priori possible,  Hockney and Eastwood (1981) , e.
Note that for a Cartesian expansion in monomials x l y m z n at a fixed order p = l + m + n, one has (p + 1)(p + 2)/2 multipole moments, i. e. (p + 1)(p + 2)(p + 3)/6 for all orders up to incl. p, i. e. memory needed for each node scales as O(p 3 ), and a standard implementation evaluating multipole pair interactions scales as O(p 6 ). For expansions in spherical harmonics, one can achieve O(p 3 ) scaling  (Dehnen 2014). Note that for higher order expansions one can rely on known recursion relations to obtain the kernel coefficients  (Visscher and Apalkov 2010)  allowing arbitrary order implementations. Recently, it was demonstrated that a trace-free reformulation of the Cartesian expansion has a slimmer memory footprint (Coles and Bieri 2020) (better than 50% for p ≥ 8). The same authors provide convenient Python scripts to auto-generate code for optimized expressions of the FMM operators symbolically.
Some special care must be taken when applying the transfer function convolution and resolution of the Poisson equation. Such approaches were pioneered by  Katz et al. (1994) ;  Bertschinger (2001) , and then extended to higher accuracy and 2LPT perturbation theory using a tree-based approach by  Jenkins (2010)  which is implemented in a non-public code used by the Virgo consortium, and using multi-grid techniques by  Hahn and Abel (2011)  in the publicly available MUSIC-1 code 18. A recent addition is the GENET-IC code 19   (Stopyra et al. 2021 ) that focuses on the application of constraints (cf. Sect. 6. 3. 7) to such zoom simulations but currently only supports first order LPT. An example of a particularly deep zoom simulation is the 'voids in voids' simulation shown in Fig. 13.
A possible constraint is e. g. , a Gaussian peak on scale R at position x i so that Hi (k) = exp -k 2 R 2 /2 + ik • x i , constraints on differentials and integrals of the field can be easily taken into account in the Fourier-space kernel. Using this algorithm, various simulations were able to reproduce the local distribution of galaxies and famous features of the local Universe such as the Local and Perseus-Pices Superclusters, and the Virgo and Coma clusters as well as the Great Attractor (e. g. ,  Sorce et al. 2014). This is illustrated in the top left panel of Fig. 11 , which displays a simulation from the CLUES collaboration 20   (Gottloeber et al. 2010; Carlesi et al. 2016). Traditionally, the observational constraints were mostly set by radial velocity data (which was assumed to be more linear than density, thus more directly applicable for constraining the primordial density field), for instance, from dataset such as the "Cosmic Flows 2"  (Tully et al.
Closing remark In this section we have reviewed several possible extensions to the physically simplest ΛCDM simulations. Some of these modifications are more speculative in nature, as e. g. , modified gravity, whereas others are strongly motivated by physical experiments, e. g. , massive neutrinos. For an adequate interpretation of future datasets it will be important to explore the interplay of such modifications and the possible degeneracies that arise among them when interpreting cosmological data. For instance, the power spectrum suppression that baryons display relative to CDM, could potentially be misinterpreted as a signature of massive neutrinos. In this direction, for instance,  Kuo et al. (2018)   2018 ) have performed simulations with this focus, where they consider cosmological scenarios with both modified gravity and warm dark matter, with modified gravity and massive neutrinos, and with primordial non-Gaussianities and interacting dark energy.
(2014)  demonstrated small differences in the global density profile but pronounced differences in the subhalo mass functions between AMR and tree-based codes consistent with the earlier found suppression of small haloes when conservative refinement criteria are used. Schneider et al. (2013)  carried out the "Euclid comparison project" -a more demanding test simulating a box of 500 h -1 Mpc per side with 2048 3 particles, which should have led to converged results with respect to boxsize and mass resolution. There were only three participant codes, GADGET-3, PKDGRAV-3, and RAMSES, which showed a remarkable agreement of < 5% for k ∼ 5h Mpc -1. An important feature of this code comparison was that the initial conditions were released publicly 22 , so that any N -body code could carry out the same simulation and compare their predictions.
In fact, subsequently, further codes have been added to this comparison as the initial conditions were run by several authors recently to include the codes ABACUS  (Garrison et al. 2019) , L-GADGET-3  (Angulo et al. 2020), and GADGET-4 (Springel et al. 2020). In Fig. 24  we show a recent comparison between four state-of-the-art codes. Remarkably, the power spectrum on large scales agrees between all of them to better than 0. 4% which extends up to k ∼ 2h Mpc -1 and somewhat degrades to 2% up to k ∼ 10h Mpc -1. Note that in the original comparison paper, GADGET-3 was an outlier, displaying systematic differences with respect to the other codes. However, the results of  Angulo et al. (2020)  and  Springel et al. (2020)  regarding the GADGET-3 code suggest that this run was probably carried out with poorer time integration or force accuracy compared to the other codes.
2009; Lawrence et al. 2017; DeRose et al. 2019; Euclid Collaboration et al. 2019; Angulo et al. 2020 ) even beyond ΛCDM  (Winther et al. 2019; Ramachandra et al. 2020; Arnold et al. 2021 ) and for baryonic effects  (Aricò et al. 2020a; Giri and Schneider 2021) , the galaxy power spectrum and correlation function  (Kwan et al. 2015; Zhai et al. 2019) , weak lensing peak counts and power spectra  (Liu et al. 2015; Petri et al. 2015) , the 21-cm power spectrum  (Jennings et al. 2019) , the halo mass function  (McClintock et al. 2019; Bocquet et al. 2020) , halo clustering statistics  (Nishimichi et al. 2019; Kobayashi et al. 2020). Traditionally, emulators have been built with Gaussian processes (GP), but more recently feed forward neural networks are gaining popularity as they allow to deal with larger datasets and a high number of dimensions.
2014)  in 2014. This simulation evolved a 10 240 3 particle distribution from redshift 93 down to redshift zero in a 8h -1 Gpc cubic volume. This simulation was carried out with 20,000 CPUs of the Titan Supercomputer at the Oak Ridge National Laboratory in USA. Gravitational forces were computed with the 2HOT code (Warren 2013) using a tree algorithm with multipole expansion, with a background subtraction to improve the performance at high redshifts, and a dual tree traversal specifying cell-cell interactions in which multiple particles share the same interaction list. A key aspect enabling this simulation was the usage of Graphic Processing Units (GPUs) and many optimisations via SSE or AVX vector instructions. Additionally, catalogues of dark matter halos as well as a light-cone were constructed during the runtime of the simulation.
2015; Yu et al. 2017a ). In the same year, 2017, the Euclid Flagship simulation  (Potter et al. 2017 ) was completedthe first multi-trillion particle simulation with high force and mass resolution. The simulation comprised 10 000 3 particles in a 3h -1 Gpc box aimed at the preparation for the EUCLID mission. This simulation employed the PKDGRAV-3 code  (Potter and Stadel 2016)  which uses a binary tree with FMM expansion for the force calculation. As for other large simulations, it was possible thanks to the use of GPUs speeding up the gravity calculation. The Outer Rim was another simulation that reached the trillion particle count. It simulated a region of 3h -1 Gpc across using the HACC code  (Habib et al. 2016 ) and a half million of cores of the Mira BG/Q supercomputer at the Argonne Leadership Computing Facility in the USA.
Another lesson learned from recent simulations is that I/O bandwidth and disk space is an important factor that could limit the usefulness of simulations. For instance, 200'000 CPU hours were needed only to read the initial conditions of the Outer Rim simulation. Perhaps more importantly, the large raw datasets generated (easily in the petabyte scale), restrict the use of these simulations to a limited number of people, which unavoidably hinders their scientific exploitation. For this reason, more and more of the post-processing, including the construction of light-cones, structure identification, merger trees, and even the creation of maps for various observables (e. g. gravitational lensing or of the Sunyaev-Zeldovich effect) are carried out during the simulation runtime. Despite the extraordinary combination of volume and mass resolution of the simulations listed in the previous section, none of these multi-trillion particle calculations is actually sufficient to adequately match the characteristics e.
Sharing simulation data is also important in the context of cross-validation of simulation codes and results, since it readily allows a comparison and assessment of the accuracy and potential sources of systematic errors. In principle, this extends also to the simulation codes themselves: a public code release strategy can leverage increased scrutiny of the methods employed in any single code, in terms of both correctness and economy. One of the pioneer efforts in the direction of data dissemination was that of the Virgo Consortium with the Millennium Database  (Lemson and Virgo Consortium 2006)   23. In the context of the German Virtual Observatory, and following the example of the SkyServer in the Sloan Sky Digital Server, the Millennium Database served halo and semi-analytic galaxy catalogues via a relational database accessed trough the standard Structured Query Language (SQL).
More recent examples are databases for the Bolshoi simulations 24  which have additionally served full particle data, the Australian Theoretical Virtual Observatory 25  which offers several post-processing and visualization tools  (Bernyk et al. 2016) , and the INDRA database 26  which provides access to a large ensemble of gravity-only simulations  (Falck et al. 2021). As an example of the significant value open data policies provide to simulation projects is the fact that even though the Millennium Simulation was carried out more than 15 years ago, it is still today being used in many research projects. SQL databases are extremely efficient and useful for mining large datasets, however, for many applications it is desirable to serve large catalogues for which SQL is not optimal. In such cases, the increase of worldwide network bandwidths and the web developments have made practical to provide data in excess of tens of Terabytes.
One example is http://skiesanduniverses. org/ where data from the Multidark  (Klypin et al. 2016) , Bolshoi  (Klypin et al. 2011) , GLAM  (Klypin and Prada 2018b) , and Uchuu  (Ishiyama et al. 2021)  simulations can be directly downloaded. Another interesting alternative approach adopted to serve the data of the 1-trillion particles DarkSky simulation 27  is to directly map data in a given URL to a Python virtual memory buffer. In this way, local Python sessions can directly access data stored in a remote server. The Outer Rim and Last Journey simulations data, instead, was shared directly trough the Globus technology 28. Globus is a non-profit research data management that allows triggering secure data transfers among different locations (e. g. personal computers, cloud storage, or supercomputer facilities) via GridFTP.
Acknowledgements We would like to thank the editor,  Thorsten Naab , for his invitation to write this article and his enormous patience during the process. We would also like to thank  Alexandre Barreira ,  Silvia Bonoli ,  Sergio Contreras ,  Baojiu Li ,  Go Ogiya ,  Aseem Paranjape ,  Cornelius Rampf ,  Jens Stücker , and  Matteo Zennaro , for comments and suggestions. REA acknowledges the support of the  ERC Starting -Grant  716151  (BACCO). O. H. acknowledges funding from the  European Research Council (ERC)  under the European Union's  Horizon 2020 research and innovation programme , Grant agreement No. 679145  ( COSMO -SIMS ).
Raul E. Angulo  and  Oliver Hahn Ali-Haïmoud Y , Bird S (2013) An efficient implementation of massive neutrinos in non-linear structure formation simulations. MNRAS428(4):3375-3389. https://doi. org/10. 1093/mnras/sts286. arXiv:1209. 0461 [astro-ph. CO]  Allys E ,  Marchand T ,  Cardoso JF ,  Villaescusa-Navarro F ,  Ho S ,  Mallat  S (2020) New interpretable statistics for large-scale structure analysis and generation. Phys. Rev. D102(10): 103506. https://doi. org/10. 1103/PhysRevD. 102. 103506. arXiv:2006. 06298 [astro-ph. CO] Alonso D (2012) CUTE solutions for two-point correlation functions from large cosmological datasets. arXiv e-prints arXiv:1210. 1833. arXiv:1210. 1833 [astro-ph. IM]  Alvarez M ,  Baldauf T ,  Bond JR ,  Dalal N ,  de Putter R ,  Doré O ,  Green D ,  Hirata C ,  Huang Z ,  Huterer D ,  Jeong D ,  Johnson MC ,  Krause E ,  Loverde M ,  Meyers J ,  Meerburg PD ,  Senatore L ,  Shandera S ,  Silverstein E ,  Slosar A ,  Smith K ,  Zaldarriaga M ,  Assassi V ,  Braden J ,  Hajian A ,  Kobayashi T ,  Stein G ,  van Engelen  A (2014) Testing Inflation with Large Scale Structure: Connecting Hopes with Reality.
Travail -Laboratoire de Ploufragan-Plouzané, Unité Génétique Virale de Biosécurité, Ploufragan, France 25 UMR 1161 Virology ANSES/INRAE/ENVA, ANSES Animal Health Laboratory, 94704 Maisons-Alfort, France *corresponding author Fátima Jorge: fatima. esperancajorge@otago. ac. nz The symbiont-associated (SA) environmental package is a new extension to the minimum information about any (x) sequence (MIxS) standards, established by the Parasite Microbiome Project (PMP) consortium, in collaboration with the Genomics Standard Consortium. The SA was built upon the host-associated MIxS standard, but reflects the nestedness of symbiontassociated microbiota within and across host-symbiont-microbe interactions. This package is designed to facilitate the collection and reporting of a broad range of metadata information that apply to symbionts such as life history traits, association with one or multiple host organisms, or the nature of host-symbiont interactions along the mutualism-parasitism continuum.
These standards have been integrated into large scale microbiome projects (e. g. Human Microbiome Project, https://www. hmpdacc. org/), Earth Microbiome Project (https://earthmicrobiome. org/), Microbiology of the Built Environment (MoBE, https://www. microbe. net), microbiome bioinformatics platforms (e. g. QIIME, Qiita, mothur, JGI GOLD, MG-RAST, EBI, NCBI) and are now required upon manuscript submission. A primary advantage of the MIxS standards is the collation of large aggregates of associated metadata that can be harnessed to uncover, and eventually comprehend, patterns of microbial diversity and ecology. The MIxS-SA package was initially drafted during the 1 st Parasite Microbiome project workshop that involved the contribution of members of the GSC in addition to microbial ecologists, parasitologists, pathologists and marine biologists  [14].
Participants rapidly identified the need to incorporate information on the nestedness of symbiont-associated systems, and the absence within the MIxS host-associated package of descriptors of complex life histories of mutualistic and parasitic symbionts. Until now, researchers have either omitted this information or added research-specific symbiont-associated annotations, limiting significantly the potential to compare, combine and/or reuse data from different systems and studies. Whereas the MIxS-SA package was initially designed for the study of parasite-microbes interaction, the scope of the package was expanded to include non-parasitic symbionts. This addition is a necessary expansion due to the context-dependent nature of symbiotic interactions and the ability of a given symbiont to interact differently with different organisms.
Notably, the resulting MIxS-SA package reduces the need to develop additional highly similar packages for different types of symbionts. Symbiotic associations are generally classified as mutualistic (mutually beneficial association), commensal (beneficial association to one of the partners, but not harmful to the other), or parasitic (detrimental association to one of the partners)  [15]. In the context of the symbiontassociated package, the term symbiont applies to macro and microorganisms that can establish a physical interaction with at least one other organism at some stage of their life cycle regardless of the nature and dependence of the interaction. As such, this definition also covers symbiotic organisms that establish facultative and accidental associations (e. g. dead-end hosts), not requiring evolutionary processes to explain their association, but excludes free-living organisms that establish a symbiotic relationship with another free-living organism (e.
g. flowers and bees). The MIxS-SA package presented herein has gone through an open and iterative review process engaging the GSC community and experts studying symbiotic organisms across various symbiont and host taxa. Here, we present the selected list of metadata descriptors for symbiont-associated microbiota studies, including a subset of mandatory (M) terms that underpin metadata compliance (Table  1 ; Supplementary Information SI-1 contains all MIxS-SA items). In order to allow comparative studies of the microbiota of, sometimes closely related, free-living and symbiotic organisms, the MIxS-SA includes terms already found in the MIxS host-associated package. Thus, in MixS-SA, the term ‶ host″ (when used alone) refers to the host of the biological sample which is the symbiotic organism.
New terms were created to characterise the ‶ host of the symbiotic host″. We provide symbiont-associated package specific "Expected values" and "Examples". Changes to the package (addition of terms, modification etc. ) can be proposed by the community by creating a ticket on the MIxS GitHub page (https://github. com/GenomicsStandardsConsortium/mixs). Given the diversity of symbiotic interactions and that the nature and dependence of such interactions can be context-dependent rather than a fixed trait, it was crucial to define terms and provide value syntax that were inclusive for diverse types of symbioses and also across the symbiont life histories and transmission processes. For example, the term "host dependence" (a mandatory item) and "type of symbiosis" (a conditional item) are discrete but complementary items.
While "host dependence" aims to provide a general characterization of the known type of host dependence for the symbiotic organism (e. g. facultative), "type of symbiosis" was specifically designed to further characterize the type of biological interaction established between the symbiotic organism and its respective host at the moment the biological sample was taken (e. g. mutualistic). As a result, the MIxS-SA package features mandatory and conditionally mandatory, and optional features that enable flexibility according to the knowledge of the study system at the time of sampling. Two examples of MIxS-SA-compliant metadata are provided in Supplementary information (SI-2), and the respective study designs are presented in Figure  1. The examples refer to 16S rRNA gene studies of (a) the bacterial communities of the parasite Coitocaecum parvum, a trematode, across four of its life stages: the sporocyst, the metacercaria and the adult, as well as the free-living cercaria  [16] , and (b) of the leaves and roots of the parasitic plant Orobanche hederae and its ivy host, Hedera spp.