dataesr/scientific-paragraphs-categorization huggingface dataset:
Data sample Raw neuroimaging data from the ADNI GO/2 studies  (Wyman et al. , 2013; Beckett et al. , 2015)  were downloaded for 244 subjects. These included T1w images for all subjects, as well as DWI and resting-state fMRI (rsfMRI) images for separate cohorts of subjects. An additional 12 subjects for which both DWI and rsfMRI were acquired in the same session were identified and their data also downloaded. A volumetric 96-ROI parcellation was defined on the MNI template and consisted of 82 cortical ROIs from the regional map parcellation  (Kötter and Wanke, 2005)  and an additional 14 subcortical ROIs spanning the thalamus and basal ganglia. Details on the construction of the 96-ROI parcellation can be found in  Bezgin et al. (2017). Among the 244 subjects we downloaded, 74 were control subjects, while the others were patients at different stages of the pathology progression.
In this study, we performed a rough coarse-graining of the original ADNI labels indicating the stage or type of pathology. We thus overall labeled 119 patients as MCI (grouping together the labels four patients as MCI, 64 as EMCI and 41 as LMCI) and 51 patients as AD (overall 170 patients for the simple classification experiments of Fig. 6 ). Overall, T1 and DTI were jointly available for 88 subjects (allowing to reconstruct SC matrix), and T1 and fMRI for 178 (allowing to reconstruct FC). However, among the 244 subjects we downloaded, only 12 subjects (referred to as the SC emp 1 FC emp subset) had a complete set of structural and functional images (T1, DTI, fMRI), hinting at how urgently needed is data completion.
Data preprocessing Neuroimaging data preprocessing was done using a custom Nipype pipeline implementation  (Gorgolewski et al. , 2011). First, raw neuroimaging data were reconstructed into NIFTI format using the dcm2nii software package (https://www. nitrc. org/projects/dcm2nii/). Skull stripping was performed using the Brain Extraction Tool (BET) from the FMRIB Software Library package  (FSL v5)  for all image modalities before all other preprocessing steps. Brain extraction of T1w images using BET was generally suboptimal and was supplemented by optiBET  (Lutkenhoff et al. , 2014) , an iterative routine that improved brain extractions substantially by applying transformations and back-projections between the native brain mask and MNI template space. Segmentation of the T1w images was performed using FSL's FAT tool with bias field correction to obtain into three distinct tissue classes.
To improve the registration of the ROI parcellation to native space, the parcellation was first nonlinearly registered to a publicly-available older adult template (aged 70-74 years;  Fillmore et al. , 2015)  using the Advanced Normalization Tools (ANTS;  Avants et al. , 2011)  software package before subsequent registrations. Diffusion-weighted images were preprocessed using FSL's eddy and bedpostx tools. The ROI parcellation was first nonlinearly registered to each subject's T1w structural image and then linearly registered to the DWI image using ANTS. rsfMRI data were preprocessed using FSL's FEAT toolbox. Preprocessing included motion correction, high-pass filtering, registration, normalization, and spatial smoothing (FWHM: 5 mm). Subjects with excessive motion were excluded from our sample.
Data sample Forty-nine healthy subjects between the ages of 18 and 80 (mean 42. 16 6 18. 37; 19 male/30 female) were recruited as volunteers. Subjects with a self-reported history of neurologic, cognitive, or psychiatric conditions were excluded from the experiment. Research was performed in compliance with the Code of Ethics of the World Medical Association (Declaration of Helsinki). Written informed consent was provided by all subjects with an understanding of the study before data collection, and was approved by the local ethics committee in accordance with the institutional guidelines at Charité Hospital, Berlin.
Acquisition procedures Acquisition procedures for these data (magnetic resonance acquisition procedure, dwMRI data preprocessing and tractography, fMRI data preprocessing, computation of SC and FC connectome matrices) have been described by  Zimmermann et al. (2016) , where we redirect the reader interested in full detail. Briefly, functional and structural image acquisition was performed on a 3T Siemens Tim Trio Scanner MR equipped with a 12-channel Siemens head coil. After anatomic and dwMRI measurements, subjects were removed from the scanner and again put in later for the functional measurements. Data were obtained from subjects at resting state; subjects were asked to close their eyes, relax, and avoid falling asleep. Anatomical and diffusion images were preprocessed using a fully automated open-source pipeline for extraction of functional and structural connectomes  (Schirner et al.
, 2015). The pipeline performed the following steps. Using the FreeSurfer software toolbox (http://surfer. nmr. mgh. harvard. edu/), anatomic T1-weighted images were motion corrected and intensity normalized, nonbrain tissue was removed, and a brain mask was generated. White matter and subcortical segmentation was performed, and a cortical parcellation based on the probabilistic Desikan-Killiany FreeSurfer atlas divided the gray matter into 68 ROIs (regions of interest, 34 per hemisphere;  Desikan et al. , 2006). The diffusion data were further corrected (for head movement, eddy current distortions, etc. ). Probabilistic fiber tracking was performed using MRTrix streamtrack algorithm. The fMRI resting-state preprocessing was performed using the FEAT (fMRI Expert Analysis Tool) version 6. 0 first-level analysis software tool from the FMRIB (fMRI of the brain) Software Library (www.
, 2015)  that the best match (max of Pearson correlation between the upper-triangular parts of the empirical and virtual FCs) is obtained at a slightly subcritical point for G* = G critic -e. Linear SC-to-FC and FC-to-SC completion To infer FC SLM from SC emp, we chose to always use a common value G* ref = 0. 83, which is the median of G* for all 12 FC emp 1 SC emp subjects in the ADNI and healthy ageing dataset (the error made in doing this approximation is estimated to be ,1% in Extended Data Fig. 3-1C ). When the connectome FC emp is not known, Equations 2, 3 can directly be used to evaluate the covariance matrix C (setting s = 1 and G = G* ref ). We then estimate the regional fluctuation covariance from these inferences and normalize it into a Pearson correlation matrix to infer FC SLM (see pseudo-code in Extended Data Table  1-1 ).
Linear FC SLM completions for our ADNI dataset and for the healthy aging dataset can be downloaded as MATLAB workspace within Extended Data 1 FC_SLM. mat (available at the address https://github. com/FunDyn/VirtualCohorts). To infer SC SLM from FC emp , we invert the analytical expressions of Equations 2, 3 and always set s = 1 and G = G* ref leading to: W p ¼ ÀC À1 =G p ref (4) ,where C is the covariance matrix estimated from empirical BOLD time series. The linearly completed SC SLM is then set to be identical to W* setting its diagonal to zero to avoid offsets, which would be meaningless given the conventional choice of noise s which we have made (see Extended Data Table  2-1 ). Note that all the free parameters of the SLM model appear uniquely as scaling factors and do not affect the (normalized) correlation of the inferred SC SLM with the SC emp.
However, the absolute strengths of inferred structural connections remain arbitrary, with only the relative strengths between different connections being reliable (since unaffected by arbitrary choices of scaling parameters; see pseudo-code in Extended Data Table  2-1 ). Linear SC SLM completions for the ADNI dataset and for the healthy aging dataset can be downloaded as MATLAB workspace within Extended Data 1 SC_SLM. mat (available at the address https:// github. com/FunDyn/VirtualCohorts).
5) computed by taking the coefficient of variation of BOLD MFM time series. By computing the Pearson correlation coefficient of upper-triangular between FC MFM and FC emp for every subject from SC emp 1 FC emp subset in the ADNI dataset (see Table  1 , line 2. 3), we obtained a best-fitting zone in a narrow concave stripe (see Fig. 3A  for one subject), (G*, t *) parameter set, bring the system to this best-fitting zone and values lower than this is ðG À ; t À Þ set and higher values are ðG 1 ; t 1 Þ. Qualitatively analogous results are found for the healthy aging dataset. This non-monotonic behavior of yellow zone in G/t plane occurs where three criteria are jointly met; the second criterion is the clustering coefficient of time-average FC MFM matrices (see Table  1 , line 2. 6) and finally, the third criterion is the clustering coefficient of dFC MFM matrices (see Table  1 , line 2.
6), where the dFC matrices were computed for an arbitrary window using the dFCwalk toolbox  (Arbabyazd et al. , 2020;  https://github. com/FunDyn/dFCwalk. git). By knowing the optimal working point of the system where all three criteria are jointly optimum (see Table  1 , line 2), we freeze the algorithm and finally run a last simulation with the chosen parameters to perform nonlinear SCto-FC data completion (see Table  1 , lines 3-5). Nonlinear FC MFM completions for our ADNI dataset and for the healthy aging dataset can be downloaded as a MATLAB workspace within Extended Data 1 FC_MFM. mat (available at the address https://github. com/ FunDyn/VirtualCohorts).
Nonlinear SC MFM completions for our ADNI and healthy aging datasets can be downloaded as a MATLAB workspace within Extended Data 1 SC_MFM. mat (available at the address https://github. com/ FunDyn/VirtualCohorts). Trivial completion using the "other connectome" In the case in which one of the two connectomes is missing (e. g. , just SC available but not FC) one may think to use the available connectome (in this example, SC) as a "good guess" for the missing one (in this example, FC). We refer to this trivial procedure as a completion using the other connectome. If the match quality between surrogate connectomes obtained via more complex procedures and the target empirical connectome to reconstruct happened to be comparable with the one that one can get via the trivial completion, then it would not be worth using more sophisticated methods.
We assessed then, for comparison with other strategies, the performance of such trivial completion approach on the SC emp 1 FC emp subset of the ADNI dataset and on the whole healthy aging dataset. In order for a completion approach to be considered viable, it is necessary that it outperforms significantly this trivial completion via the "other type" connectome, which can be quantified by a relative improvement coefficient: D trivial ¼CC½VirtualConnectome;ActualConnectome ÀCC½OtherConnectome;Actualconnectome CC½OtherConnectome;Actualconnectome%:.
Bivirtual data completion The pipelines for data completion described above can be concatenated, by performing. e. g. , FC-to-SC completion on a virtually FC or SC-to-FC completion on a virtual SC (rather than actual FC emp or SC emp , respectively). In this way, one can create bivirtual dual counterparts SC bi-MFM (FC bi-MFM ) or SC bi-SLM (FC bi-SLM ) for any of the available empirical SC emp (FC emp ) by applying in sequence nonlinear MFM-based or linear SLM-based procedures for SC-to-FC and then FC-to-SC completion (or, conversely, FC-to SC followed by SC-to-FC completions). Linear and nonlinear bivirtual completions for our ADNI and healthy aging datasets can be downloaded as MATLAB workspaces within Extended Data 1 SC_bivirt. mat and FC_bivirt. mat (available at the address https:// github.
Analogously, we define CC generic = group average of CC[Connectome virt (same subject), Connectome emp (a different subject)]. The Improvement by personalization coefficient is then defined as D Pers = (CC personalized -CC generic )/CC generic. This coefficient significantly larger than zero denotes that completion pipelines get to improved results when completion is personalized. At least for FC, we can estimate from empirical data how much the improvement by personalization could be expected to be in the case in which a first FC extraction for a given subject had to be replaced by a second one coming from a second scan from the same subject versus a scan for another generic subject. To obtain such an estimate, we focus on a dataset mediated from the Human Connectome Project and conceived to probe test/retest variability  (Termenon et al.
, 2016). In this dataset, 100 subjects underwent two resting state scans, so that two FC emp can be extracted for each of them. If we redefine CC personalized = CC[FC emp (same subject first scan), FC emp (same subject second scan)] and CC generic = Group average of CC[FC emp (same subject, first scan), FC emp (a different subject, first scan)], then we can evaluate an empirical D Pers = (CC personalized -CC generic )/CC generic. For empirical FCs from the Termenon et al. (  2016 ) dataset we obtain an improvement by personalization of ;122%, to be used as a comparison level when looking at improvements by personalization in virtual and bivirtual connectomes.
Note that the number of network nodes were different for connectomes in the ADNI and in the healthy aging datasets, since the used reference parcellations included a different number of regions in the two cases. However, graph theoretical metrics can be computed in precisely the same way and we perform in this study uniquely within-dataset analyses. In Figure  8 , we show point clouds for all subjects of the ADNI dataset pooled together. Analogous plots for the healthy aging dataset are shown in Extended Data Figure  8-1. We then computed correlations between vectors of graph-theoretical features over the different brain regions within specific subjects. This analysis is an important probe of the personalization quality in data completion, since every subject may have a different spectrum of graph-theoretical properties across the different regions and that it is important that information about these topological specificities is maintained by completion.
These within-subject correlations, often higher than global population correlations, since not disturbed by variations of mean feature values across subjects, are summarized in Table  3  for the ADNI dataset and in Extended Data Table  3 -1 for the healthy aging dataset. In these tables, we provide both absolute correlation values and the indication of how each correlation is improved by computing it within subjects rather than across the whole sample. Correlations were evaluated over data points belonging to the interquartile range of empirical data and then extrapolated to the whole range to avoid estimation to be fully dominated by cloud tails of extreme outliers. We extracted then the community structure of empirical and bivirtual dual connectomes using the Louvain algorithm  (Blondel et al.
Supervised subject classification To show the possibility to extract personalized information relevant for subject characterization, we performed different machine-learning supervised classification tasks using as input features derived from empirical and (bi)virtual connectomes. The input and target features to predict were different for the ADNI and the healthy aging datasets. Concerning the ADNI dataset, we separated subjects in two subgroups: controls and patients (MCI or AD). Subjects (the actual ones or their associated virtual counterparts) are thus labeled as "positive" when belonging to the patient subgroup or negative otherwise. Note that our classifiers were not sufficiently powerful to reliably discriminate subjects in three classes (control, MCI, and AD) on this dataset, at least under the simple classification strategies we used.
For illustration, we constructed classifiers predicting subject category from input vectors compiling the total connectivity strengths (in either SC or FC connectomes, real, virtual, or bivirtual) of different brain regions. The dimension of the input space was thus limited to the number of regions in the used 96-ROIs parcellation, which is of the same order of the number of available subjects in the overall dataset. 23 6 2  4 5 6 10%  260 6 6  47 6 8%  12 6 6%  Indicated values for real/bivirtual dual correlations (for strength, clustering, and centrality coefficients) or relative mutual information (for communities) are mean 6 SD of the mean over subjects. Concerning the healthy aging dataset, we separated subjects in four age classes with 13 subjects in Class I (age = 18-25), and 12 subjects in Classes II (age = 26-39), III (age = 40-57), and IV (age = 58-80) and used as target labels for classification the ordinal of the specific age class of each subject.
As input vectors we used in this case the top 10 PCA of upper-triangular of connectome. In both cases, we chose as classifier a boosted ensemble of 50 shallow decision trees. For the ADNI dataset, we trained it using the RUSBoost algorithm  (Seiffert et al. , 2010) , particularly adapted to data in which the number of input features is large with respect to the training dataset size and in which positive and negative labels are unbalanced. For the healthy aging dataset, we used a standard random forest method  (Breiman, 2001). For both datasets, for training and testing we split the dataset into five folds, each of them with a proportion of labels maintained identical to the one of the full dataset and performed training on three of the five folds and testing on the remaining two folds (generalization performance).
We measured performance based on confusion matrices between predicted and actual class labels and, just for the binary classification problem on the ADNI dataset, on the receiver operator curve (ROC) analysis as well. For ROC analysis, we quantified fractions of true and false positives (numbers of true or false positives over the total number of actual positives) during generalization, which depend on an arbitrary threshold to be applied to the classifier ensemble output to decide for positivity of not of the input data. ROCs are generated by smoothly growing this threshold. An area under the curve (AUC) was then evaluated as a summary performance indicator, being significantly larger than 50% in the case of performance above chance level. The ROC curves plotted in Figure  7B ,C, as well as their associated 95% confidence range of variation are smoothed using a cubic smoothing spline based on the cloud of TP and FP values at different thresholds over the 1000 individual training and testing classification runs.
Virtual cohorts To generate virtual cohorts, i. e. , synthetic datasets made of a multitude of virtual connectomes beyond individual subject or patient data completion, we artificially boosted the size of the original dataset by generating a much larger number of virtual subjects with multiple alternative (but all equally valuable) completions of the missing connectomic data. Concretely, to generate the virtual cohort dataset illustrated in Figure  9A , we took the 88 subjects in the SC emp only plus the 12 subjects in the SC emp 1 FC emp subsets of the ADNI dataset (including 21 AD subjects, 35 MCI, and 32 control subjects) and run for each of them the nonlinear SC-to-FC completion algorithm 100 times, using each time a different random seed. The net result was a group of 100 alternative FC MFM instances for each of the subjects, yielding in total a virtual cohort of 8800 FC MFM matrices to be potentially used for classifier training.
Such a cohort can be downloaded as a MATLAB workspace within Extended Data 1 FC_cohort. mat (available at the address https://github. com/FunDyn/ VirtualCohorts). To generate Figure  9A , showing a dimensionally reduced representation of the relative distances between these 8800 virtual matrices, we used an exact t-SNE projection  (Maaten and Hinton, 2008)  of the vectors of upper-triangular parts of the different FC MFM s toward a two-dimensional space, using a default perplexity value of 30 and no-exaggeration. On the same t-SNE projection, beyond the FC MFM connectomes within the virtual cohort connectomes we show as well additional FC connectomes, for the sake of comparison (using the same t-SNE neural network adopted for projecting the virtual cohort connectomes on the Euclidean plane).
Connectomic data may have gaps: the example of ADNI The first dataset we have chosen to focus in the framework of this study corresponds to one of the earliest and most popular available datasets in AD research, including a substantial amount of structural and functional connectomic information, i. e. , the ADNI database (adni. loni. usc. edu). ADNI is impressive for the variety of features it aimed at systematically gathering (Fig. 1A ). Importantly, based on the T1, DTI and rsBOLD fMRI images available through the ADNI datasets, state-of-the-art processing pipelines can be used to extract subject-specific structural and resting-state functional connectomes, compiled into connectivity matrices adapted to the brain parcellation of choice (Fig. 1B ; for details, see Materials and Methods). We had access to 244 overall subjects (119 labeled as MCI and 51 as AD, thus 170 patients, in addition to 74 control subjects, see Materials and Methods) for which MRI data had been gathered.
Control dataset: healthy aging To confirm the robustness of all following analyses performed on the first ADNI dataset, we also consider in the following comparisons with analogous analyses conducted on a second control dataset. In this previously analyzed dataset  (Zimmermann et al. , 2016; Battaglia et al. , 2020) , we considered 49 healthy adult subjects covering an age-span from 18 to 80 years that we split in four age classes (for details, see Materials and Methods). For all these 49 subjects, both FC emp and SC emp are simultaneously available, thus extending the number of subjects for which a ground truth connectome against which evaluate the performance of each tested completion pipeline is possible. We also note that connectomes in the two ADNI and healthy aging datasets were defined in terms of different brain parcellations, involving a different number of regions.
, 2016 (Gilson et al. , , 2018)). We will show later that these algorithms, although initially designed to identify changes of effective connectivity occurring between resting state and task conditions, have the potential to cope with the actual problem of MFM inversion, providing reasonably good ansatz for SC inference. As linear approaches are significantly faster than nonlinear approaches, it is important to study their performance alongside nonlinear approaches to confirm the actual justification of the use of more complicated algorithms. We will see that for one of the two considered datasets, the ADNI one, nonlinear methods are superior for the data completion applications we are interested in. However, performance of completion happened to be slightly superior for the SLM-based than for the MFM-based methods in the case of the second healthy aging dataset (hence the interest of exploring and benchmarking both linear and nonlinear completion strategies).
When the input SC (or FC) connectomes used as input for FC simulation (or SC inverse inference) correspond to empirical connectomes SC emp (or FC emp ), derived from T1 and DTI (fMRI) images, then model simulation (inversion) can be used to complete gaps in the dataset, whenever FC emp (or SC emp ) is missing. We refer then to these operations as (B) SC-to-FC completion and (C) FC-to-SC completion. Both exist in linear and nonlinear versions. from  Gilson et al. (2016 Gilson et al. ( , 2018)) , to infer a surrogate SC MFM starting from a random initial guess (see section Non-linear FC-to-SC completion). When connectomic data are incomplete (only SC emp or only FC emp are available, but not both simultaneously), computational simulation or inference procedures can be used to fill these gaps: by using FC MFM or FC SLM as virtual replacements for a missing FC emp (Fig.