dataesr/scientific-paragraphs-categorization huggingface dataset:
• We introduced several dFC random walk metrics. First, dFC speed analyses extract the distribution of the timeresolved rate of reconfiguration of FC along time. These distributions have a clear peak (typical dFC speed, that can already serve as a biomarker) and fat tails (denoting deviations from Gaussianity that can be detected by suitable scaling analyses of FC network streams). • Second, meta-connectivity (MC) analyses identify groups of functional links whose fluctuations co-vary in time and that define veritable dFC modules organized along specific dFC meta-hub controllers (differing from conventional FC modules and hubs). The decomposition of whole-brain dFC by MC allows performing dFC speed analyses separately for each of the detected dFC modules. • We present here blocks and pipelines for dFC random walk analyses that are made easily available through a dedicated MATLAB R toolbox (dFCwalk), openly downloadable.
A tool suitable for the scaling analysis of random walk paths is Detrended Fluctuation Analysis (DFA;  [39 , 46 , 50]  ), which we have adapted to dFC walks in Battaglia et al. [5]. Such analysis provides an estimation of the fractal geometry of dFC paths, in terms of a DFA exponent, α DFA = 0. 5 for memoryless walks, and α DFA > 0. 5 ( α DFA < 0. 5) for walks with positive (negative) sequential correlations in flight lengths. Exactly as typical static (time-averaged) FC analysis ignore time, the previously mentioned dFCwalk analyses introduced in Battaglia et al. [5]  ignore space. However, FC reconfiguration may occur at different speeds for different sets of links. Furthermore, the fluctuations of certain FC links may covary with the fluctuation of other FC links -forming a dFC module -but be relatively independent from the fluctuation of other sets of links.
Therefore, it may make sense to compute a different dFC speed distribution for different dFC modules ( modular dFC speeds ), since each of these modules performs its own specific random walk. A third aim of the dFCwalk framework will thus be the identification of these eventual dFC modules fluctuating in parallel according to independent random walks. To do so, we have introduced in Lombardo et al. [34]  and edge-covariance-based method which we called Meta-Connectivity (MC) analysis, and which is strongly related (although not identical) to other edge-centric functional connectivity approaches introduced elsewhere  [4 , 10 , 20]. In this approach, dFC modules are extracted applying conventional modular decomposition algorithms -as the Louvain method-to the MC matrix. Indeed, if we consider FC links as nodes of a new network, dual (see e.
Therefore, meta-hubs are localized controllers of non-localized functional systems and are in this sense very different from conventional FC hubs (see  [34]  for a detailed discussion). Altogether, in the two manuscripts by Battaglia et al. [5]  and Lombardo et al. [34]  we have forged a rich toolbox of interdependent analyses and metrics that have proved to be able to track changes of dFC properties across aging or in relation with variations of cognitive performance. We have now made this toolbox available in the form of a collection of MATLAB R functions ( dFCwalk toolbox , download link: https://github. com/FunDyn/dFCwalk. git , under Creative Commons Zero v1. 0 Universal license (CC0)) that allow coding complex analysis designs such as the ones of Battaglia et al. [5]  and Lombardo et al.
g. tstochastic neighbourhood embedding  [26]  , accessible in the standard MATLAB R Statistical toolbox via the function tsne. For the sake of computing speed, all computations are always performed in the compact 'vector' format even when inputs are provided in 'matrix' format (an automatic conversion to 'vector' format is performed by the dFCwalk toolbox functions). The dFCwalk toolbox functions Matrix2Vec can be called to perform conversions from 2D FC matrices in N × N matrix format to 1D vector FCs of size L × 1 or from 3D dFC streams in N × N × F tensor format to 2D dFC streams of size L × F.
Beyond smoothing histograms, window pooling also allows reduce the number of independent multiple comparisons to perform when sample size is small -as in Lombardo et al. [34]  -and to blur eventual spurious peaks of dFC speed resulting from artefactual aliasing due to fixed-size window filtering (cf. [31]  ). Concretely, there are no rules for choosing which window size to pool together and the scientist must take a decision which is ultimately arbitrary and dependent on dataset and study needs. Therefore, a pooled windows analysis should always be validated by a set of single-window analyses to show that the results of interest hold tendentially also for a majority of individual windows over the range of window sizes pooled together. This is, for instance, what we did in Supporting Figures of both Battaglia et al.
For instance, we find that α DFA exponents are generally closer to 0. 5 and thus denoting more "randomness" and less complexity for elder subjects (cf. here Fig. 2 D ). Finally, even if α DFA exponents must be evaluated separately for different windows, they could be averaged over different W 's with similar values of α DFA , or their distributions pooled for different W' s to reinstate a form of "smoothing by window pooling". Such procedure once again is only pragmatic, not rigorous, and should be cross-checked by evaluating the stability of results for single window estimations over the considered range to pool. In the dFCwalk toolbox, the function dFC_Speeds can be used to evaluate instantaneous dFC increments as well: [ ∼, Increments ] = dFC _ Speeds ( dFCstream2dFC ( TS , W , 1 ) , 1 ) We also copy in the toolbox a function DFA_fun from an open MATLAB R repository  [35]  for a fast "quick-and-dirty" evaluation of the DFA exponent.
Groups of covarying links are called dFC modules. Differences in the inter-modular meta-connectivity between the 'younger' and the 'older' group appear visually evident. (B) Two meta-connected links converging on a common root node form what we call a meta-connectivity trimer. We call then meta-hubs nodes serving as root to many strong trimers (or, equivalently, displaying a strong trimer meta-strength MC(i)). In panel B brain regions -defined in a Desikan et al. [19]  parcellationare colored according to their meta-strength MC( i ), restricted to each of the five dFC modules identified by the modular decomposition of the MC matrices in panel A. Many of these modules have meta-hubs resembling the ones of dFC modules discussed for a different dataset in Lombardo et al. [34]. of two links incident on a common root region a trimer , with the existence of inter-link covariance represented diagrammatically by a small spring between the meta-connected links (see Fig.
Second, differences between the MCs for the two groups are visually evident (with negative meta-link strengths emerging between the dFC modules in the MC for the 'older' group). Third, different dFC modules are centered around different meta-hubs (as visible by the meta-strength plots in Fig. 3 B ), distributed along a characteristic anteroposterior gradient. Remarkably the 5 dFC modules obtained here for the Battaglia et al. [5]  datasets are remarkably reminiscent of the 5 dFC modules also identified in the datasets of Lombardo et al. [34]  (notably the occipital, fronto-parietal and frontal modules have a good degree of overlap, although the used parcellations are different). Once a modular partition of the MC matrix into dFC modules α, β, γ … (obtained with whatever method) is fixed, several analyses of the dFCwalk framework can be restricted to just one dFC module of interest.
For instance, meta-strengths of regions can be computed by summing uniquely over metalinks between links belonging to a given dFC module α. Such restriction of the sum will provide dFC module-restricted meta-strengths: M C ( α) ( i ) = kl | ik,il∈ α M C ik,il To compute dFC module -restricted meta-strengths, the function ExtractTrimerStrengths can take as second optional input a list of the indices of the FC links included in the module of interest. For instance, if the Brain Connectivity Toolbox  [41]  is used to extract modules from MC via the function C = modularity_louvain_und_sign(MC) (note the use of a community extraction algorithm for signed and undirected graphs, since MC can be positive or negative and is symmetric), then the vector C will contain the M community labels (allegiance to a dFC module) for each one of the M links whose meta-connections are compiled into the MC matrix.
The command Strengths_alpha = ExtractTrimerStrengths(MC, find( C == alpha)) will then return a vector with N dFC module restricted meta-strengths. Any other dFC analysis (e. g. dFC speed or DFA) can be analogously restricted to a specific dFC module, by filtering in the dFC stream only the time-series associated to the included links. Let us suppose having a 2D or 3D format dFC stream variable dFCstream. Then the dFCwalk toolbox command SubgraphStream = Pick_SubgraphStream(dFCstream, links) will return a dFC stream restricted just to the links associated to the provided list of indices links. Any other function that can be applied to the original dFCstream can then also be applied to the restricted dFC stream. For instance: [ typSpeed, Speeds ] = dFC _ Speeds ( Pick _ SubgraphStream ( dFCstream , find ( C == alpha ) ) will compute the modular dFC speeds (see  [34]  ) for the dFC module with label alpha.
Surrogate dFC streams It may be needed to assess statistically whether a certain dFC feature measured on an empirical dataset significantly differs from the value that such feature would be expected to assume under some null hypothesis. In order to test differences of empirical dFC streams ( Fig. 4  A) from chance expectations, it is important to define suitable surrogate dFC stream, corresponding to different possible null hypotheses, so that confidence intervals for null hypothesis expectations can be constructed by evaluating the feature of interest over a large number of surrogate dFC streams. In Battaglia et al. [5]  we introduced two types of surrogate dFC streams, corresponding: either to fluctuations around an underlying "order" described by an unchanging, static FC ( FC stationarity ); or to a "disordered" complete lack of sequential correlations in the dFC stream ( temporally shuffled dFC).
To perform these manipulations, MATLAB code kindly provided by the first author of Hindriks et al. [25]  have been embedded in our dFCwalk toolbox and is accessible via the function PhaseRand_surrogates. To probe then the second "disorder" scenario, one can construct time-shuffled surrogates ( Fig. 4 C ). After constructing a dFC stream on the actual empirical data, a time-shuffled version of it can be computed by randomly permuting the order of the FC (t) timeframes but maintaining them individually unchanged. By this, the mean and variance of each of the FC connections independently are preserved but any sequential correlations are disrupted. Time-shuffled surrogates are thus compatible with a null hypothesis of absence of sequential correlations in the dFC stream. Standard MATLAB R functions can be used to generate such time-shuffled surrogates, e.
Conclusion We interpret dynamic Functional Connectivity (dFC) as a random walk in the space of possible FC networks performed with a quantifiable "speed". Meta-connectivity provides a static representation of the spatial coordination structure underlying dynamic fluctuations of FC. A toolbox of "dFCwalk" functions naturally stems from our conceptual framework. We have illustrated the use of such a toolbox on resting state fMRI datasets, but our approaches can be applied to generic multivariate time-series of neural activity (or even to non-neural signals). The high sensitivity of dFC analyses, in particular in their module-restricted versions, bear promise of future applications to the early detection and longitudinal characterization of neuro-pathologies associated with cognitive impairment, such as Alzheimer's disease.
Acknowledgements DB acknowledges support from the  Mission for Interdisciplinarity of the CNRS  ( Infiniti program 2017-2018, "BrainTime" ) and from the  EU Innovative Training Network "i-CONN"  ( H2020 ITN 859937 ). DL has been funded by the  Agency of Research of innovation (ANII, Uruguay , grant  POS EXT 2015 1 123495 ). VJ acknowledges funding by the  European Union 's  Horizon 2020 Framework Program  for We thank our coworkers  Randy McIntosh ,  Petra Ritter ,  Andreas Daffertshof er ,  Annette Witt ,  Gustavo Deco ,  Andrea Brovelli ,  Alain Barrat ,  Dionysios Perdikis ,  Emmanuel Daucé ,  Maxime Guye ,  Jonathan Wirsich  and  Jean-Philippe Ranjeva  for useful discussions that led us to the current conceptualization of dFCwalk.
They are of good quality in summer and autumn in most European regions, but tend to overestimate precipitation in winter and spring. PRIMAVERA show improvements in the latter bias by reducing mid-rain rate biases in Central and Eastern Europe. Moreover, CORDEX simulate less light rainfall than PRIMAVERA in most regions and seasons, which improves this common GCM bias. Finally, PRIMAVERA simulate less heavy precipitation than CORDEX in most regions and seasons, especially in summer. PRIMAVERA appear to be closer to observations. However, when we apply an averaged precipitation undercatch error of 20%, CORDEX become closer to these synthetic datasets.
Section 2 presents the data used as well as the method employed to evaluate the daily precipitation distribution. Section 3 presents the results and includes various sensitivity tests related to the impact of resolution and the effect of regridding model data on coarser grids. Section 4 presents several sensitivity tests regarding the method itself. Section 5 discusses the results and concludes with an opening towards the need for RCM and GCM communities to strengthen collaboration and communication. 2 Method and data.
CORDEX RCMs Over Europe, we use the CMIP5-driven EUR-44 and EUR-11 CORDEX simulations (please refer to the EURO-CORDEX simulation list here: https://euro-cordex. net/imperia/md/content/csc/cordex/20180130-eurocordex-simulations. pdf) run at 0. 44° (about 50 km) and 0. 11° (about 12 km) resolution. Daily precipitation model data have been extracted from the Earth System Grid Federation (ESGF) servers (as summarised in Table  2 ). We focus our analysis on the EUR-44 simulations because their resolution roughly corresponds to the resolutions used by PRIMAVERA GCMs, which allows a clean comparison between the two ensembles. However, we evaluate the roles of resolution, regridding, and ensemble size in daily precipitation distribution with equivalent pairs from EUR-11.
Observations Over Europe, we make use of the best available observational datasets (Fig. S1 ). These are mostly national datasets, such as SAFRAN-V2 (France;  Vidal et al. , 2010) , UKCPobs (British Isles;  Perry et al. , 2009) , ALPS-EURO4M (Alps;  Isotta et al. , 2014) , CARPACLIM (Carpathian region;  Szalai et al. ). To cover the Iberian Peninsula, we combine Spain02 v2  (Herrera et al. , 2012) and PT02 v2 (Belo-Pereira et al. , 2011). For other regions, we considered E-OBS v17  (Cornes et al. , 2018). E-OBS use the complete observational stations network for Scandinavia, Netherlands, Germany (Gerard van der Schrier, personal communication). E-OBS is therefore expected to have good quality over these regions. For the remaining regions, such as the Mediterranean region and the Eastern Europe, we also make use of E-OBS, although the quality is most likely lower  (Prein and Gobiet, 2017).
All the observation datasets used are listed in Table  3. The advantage of using such national datasets are that they are available at high resolutions (5-20 km) and they contain a very dense stations network, which minimizes the effect of precipitation undersampling  (Prein and Gobiet, 2017). These data are therefore considered to be the best available over Europe. Nevertheless, there are drawbacks, particularly related to the lack of precipitation undercatch correction. This issue can be particularly important for falling snow over mountains but also in other places when associated with strong winds (rain does not fall vertically in the gauges, which creates an error depending on wind speed and drop size). The lack of correction can include errors of 3-20% on average and up to 40-80% in high latitudes and mountainous regions  (Prein and Gobiet, 2017).
To overcome this problem, we use a method similar to  Kotlarski et al. (2014)  and  Rajczak and Schär (2017) , and assume a mean estimate of the undercatch error of 20% over all regions. All observations are therefore scaled by a factor of 1. 2 over all grid points and over the entire time series, which gives us a rough estimate of observational uncertainties. We refer to it as a synthetic observational dataset. Moreover,  Prein and Gobiet (2017)  advised to consider as many observational datasets as possible for regional analyses. Most datasets, however, are available either at much lower resolution than 50 km and therefore cannot be used for evaluating the ensembles at such resolution, or they are not available at daily timescales. We have done a test using GPCP v2 available daily at 1 degree resolution.
These results are summarised in the pie plot (right panel of Fig. 1 ) for all seasons (DJF, MAM, JJA, SON). The intercomparison of the model ensembles is performed as follows: 1) All datasets are regridded on the EUR-44 rotated pole grid, using a first-order conservative remapping. Then the precipitation data is pooled from each region and season. This step is repeated for every model and observational dataset. 2) The ensemble mean is calculated for each bin and a bootstrap resampling is used 1000 times on each model ensemble (CORDEX and PRIMAVERA) to establish a confidence interval around the ensemble mean (the 10% confidence interval is plotted with shaded colours around the ensemble mean in Fig. 1 ). For the observations, the bootstrap resampling is done on single years, therefore reflecting inter-annual variability.
2 3 ). CMIP5 model ensemble show rather different distributions, particularly shifted to smaller precipitation intensities, as expected from their coarse grids. PRIMAVERA and CORDEX ensembles are of good quality in summer and autumn (except in the CA region), but tend to overestimate precipitation in winter and spring. However, there are some precipitation intervals, seasons and regions for which the two ensembles significantly differ. A large difference between the two ensembles is found for heavy precipitation (in all regions in summer, and in some regions in other seasons). PRIMAVERA have less heavy rainfall than EUR-44, and tend to agree better with raw observations, while EUR-44 are closer to synthetic observational datasets when a 20% undercatch error is considered. Moreover, EUR-11 partially correct this overestimation of heavy precipitation seen in EUR-44.
For studies at the local scale or over orography, however, a higher resolution model dataset, such as EUR-11, would inevitably give more detailed spatial information (e. g. Kotlarski et al. , 2014; Prein et al. , 2015). The performance of PRIMAVERA was not logically expected because these GCMs were developed at a coarser resolution, and only their resolution was increased. The tuning was performed on their low-resolution counterparts, so little additional tuning was performed at these high resolutions (see  Roberts et al. , in revision, for changes in models when increasing resolution), as opposed to RCMs which are developed at a higher resolution and potentially tuned at each resolution. The added value of RCMs to CMIP5 GCMs is also an important result, and it emphasizes the importance of a well designed, well evaluated model chain when using dynamical downscaling as a method to obtain higher resolution climate data.
We show here that considering climate information from various sources is crucial. We have also taken into account the issue associated with observational uncertainty. To try to reduce as much as possible uncertainties linked to observations, we have used national gridded observational datasets. Although of very high quality, these are still not fit for a thorough evaluation of climate models at the regional scale, particularly over orography, and we had to roughly correct the observations by adding an averaged 20% to account for precipitation undercatch. This is not ideal but believed to be fairer when evaluating higher resolution models. In this study, we have only focused on present-day simulations. Assessing future climate projections between the two ensembles may be more difficult because the results would depend on other parameters independent of the models themselves, such as the lack of a common protocol (e.
Data availability All PRIMAVERA and CORDEX model data used in this study can be obtained from the Earth System Grid Federation nodes, such as esgf-data. dkrz. de, esgf-index1. ceda. ac. uk, cordexesg. dmi. dk, esgf-node. ipsl. fr, and esg-dn1. nsc. liu. se. Note that the simulations are still being produced, so the ensembles presented in this article may not cover the whole ensembles available on the ESGF archive. For a complete list of EURO-CORDEX simulations, please refer to the EURO-CORDEX homepage (www. euro-cordex. net). Details about PRIMAVERA data availability can be found in  Roberts et al. (2017) ,  Roberts (2018) ,  Scoccimarro et al. (2018) , von Storch et al. (2018), EC-Earth Consortium (2019), Voldoire (2019). PRIMAVERA Persistent Identifiers (PID) and CORDEX file tracking IDs are listed in the Data folder of https://github.
com/PRIMAVERA-H2020/PrecipDistribution (DOI: 10. 5281/zenodo. 3666302). Spain02 are available at http://www. meteo. unican. es/datasets/spain02; PT02 are available at http://www. ipma. pt/pt/produtoseservicos/index. jsp?page=dataset. pt02. xml. EURO4M-APGD are available at https://www. meteoswiss. admin. ch/home/search. subpage. html/en/data/products/2015/alpine-precipitation. html (doi: 10. 18751/Climate/Griddata/APGD/1. 0). CARPATCLIM are available at http://surfobs. climate. copernicus. eu/dataaccess/access_carpatclim. php. The E-OBS data are obtained through the ECA&D project: https://www. ecad. eu.
25° (18km) Tco399 (25km, horizontal output at 50km) resolution (in km at 50N) Ocean resolution 25km 25km 25km 40km 25km 25km (km) Simulation hist-1950 hist-1950 hist-1950 hist-1950 hist-1950 hist-1950 Ensemble r1i1p1f1 r1i1p2f1 r1i1p1f2 r1i1p1f1 r1i1p1f1 r1i1p1f1 member available under the terms of the Apache 2. 0 license from https://github. com/PRIMAVERA-H2020/PrecipDistribution (DOI: 10. 5281/zenodo. 3666302). This code uses the method that computes precipitation histograms of the contributions of specific intensity bins to the total precipitation based on the ASoP1 diagnostics developed by Klingaman et al. (2017) and available under the terms of the Apache 2. 0 license from https://github. com/nick-klingaman/ASoP. https://doi. org/10. 5194/gmd-2019-370 Preprint. Discussion started: 4 March 2020 c Author(s) 2020.
13. 9 cal kBP. Beyond this a variety of data are used, including marine records which require an initial transformation to an atmospheric equivalent. To achieve this, a preliminary Δ 14 C history is estimated based upon Hulu Cave speleothems  (Southon et al. 2012; Cheng et al. 2018). This preliminary Δ 14 C curve is used to drive the LSG OGCM and provide prior, first-order, estimates of regional MRAs  (Butzin et al. 2020  in this issue) for each IntCal20 marine dataset, with the exception of the Cariaco Basin which is adjusted adaptively during curve construction  (Hughen and Heaton 2020  in this issue). The adjusted marine data are then combined with speleothems, macrofossils from Lake Suigetsu, and floating tree-ring sequences to constitute a mixed, atmospheric and atmospheric-adjusted, dataset extending from ca.