{'fraction_non_alphanumeric': 0.03491608090661311, 'fraction_numerical': 0.016697747812365514, 'mean_word_length': 4.917826825127334, 'pattern_counts': {'":': 0, '<': 3, '<?xml version=': 0, '>': 2, 'https://': 0, 'lorem ipsum': 0, 'www.': 1, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 1, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
A positive-negative mode of population covariation links brain connectivity, demographics and behavior

We investigated the relationship between individual subjects’ functional connectomes and 280 behavioral and demographic measures, in a single holistic multivariate analysis relating imaging to non-imaging data from 461 subjects in the Human Connectome Project. We identified one strong mode of population co-variation; subjects were predominantly spread along a single “positive-negative” axis, linking lifestyle, demographic and psychometric measures to each other and to a specific pattern of brain connectivity.

to discover whether any specific patterns of brain connectivity are associated with specific sets of correlated demographics and behavior -as brain-behavior modes of population covariation.
We used resting-state functional MRI data from 461 HCP subjects, and network modeling tools from FSL (FMRIB Software Library). A population-average brain parcellation was estimated using independent component analysis 2 , giving 200 distinct brain regions; these constitute the nodes in our network modeling. The functional connections (edges) between these nodes were estimated using Tikhonov-regularised partial correlation, resulting in a 200×200 connectome for each subject. These connectomes were combined into a single large connectome matrix (containing all connectomes from all subjects; Supplementary Fig.  1). Separately, 158 behavioral and demographic non-imaging SMs from the same set of subjects were formed into a subject measure matrix. We regressed potential confounds (including brain size and head motion) out of both matrices. Redundancies among connectomes and SMs were reduced by (separately) keeping just the first 100 principal components of each matrix.
A natural choice of method for investigating underlying relationships between two sets of variables is canonical correlation analysis (CCA) 3 , a procedure that seeks maximal correlations between combinations of variables in both sets. Using CCA we estimated pairs of canonical variates along which sets of SMs and patterns of brain connectivity co-vary in a similar way across subjects. We refer to each such pair of variates as a mode of co-variation. Strict tests were applied to avoid over-fitting and false-positive inflation. Statistical significance was determined with a permutation test that accounted for the family structure of the HCP data 4 . This analysis revealed a single highly significant CCA mode that relates functional connectomes to subject measures (r=0.87, P<10 −5 corrected for multiple comparisons across all modes estimated). These analyses were driven by and report only correlations; inferring and interpreting the (presumably complex and diverse) causalities remains a challenging issue for the future.  Table 1). Also plotted (Fig. 1b) are the relationships of all subjects with this mode, i.e., individual subject scores in the SM canonical variate vs. subject scores in the connectome canonical variate (one point per subject). This mode of population co-variation resembles descriptions of a general intelligence g factor 5 , but extends it to include key aspects of real-life function, including years of education, income, and life satisfaction. Remarkably, this can be considered a onedimensional "positive-negative" axis, insofar as nearly all the positively correlated SMs are commonly considered as positive personal qualities or indicators (e.g., high performance on memory and cognitive tests, life satisfaction, years of education, income), and all negatively correlated SMs relate to negative traits (e.g., those related to substance use, rule breaking behavior, anger). One striking example is the strongly negative position of cannabis usage on the scale (though this is not on its own driving the overall results, which are almost unchanged if cannabis users are excluded from the CCA -see Online Methods). Highscoring subjects (top-right points in the scatter-plot) have high relative values for "positive" SMs (at the top of the SM list), and low relative values for "negative" SMs (at the bottom).
In low-scoring subjects (bottom-left points), the pattern is reversed, with high values for negative SMs and low values for positive ones.
We next investigated whether this one CCA mode is indeed unique in modeling a substantially larger fraction of the total population variance (in the connectome and SM matrices) than the other 99 modes estimated. It is clear (Fig. 1c) that the first CCA mode explains a much larger fraction of the total data than any other mode, and is the only one to fall far outside the null confidence interval. Using the null distributions to normalise the variance explained into z-scores, the primary CCA mode has Z=7.7 for connectomes (the largest of any of the other 99 modes is 2.7) and Z=9.2 for SMs (the largest of any other mode is 2.4). Red indicates stronger connections and blue weaker, for high-scoring subjects (and vice versa for low-scoring subjects). There is positive overall correlation (across edges, r=0.20) between the CCA connectome-modulation weights and the original population mean connectome shown in Supplementary Fig. 3, meaning that subjects that score highly in this CCA mode have stronger connectivity overall than lowscoring subjects -reflected in the dominance of red-colored edges.
When the data is summarised according to brain regions that most strongly contribute to these connections, a striking pattern emerges ( Fig. 2b and Supplementary Table 2) that includes bilaterally symmetric peaks in medial frontal and parietal cortex, in the temporoparietal junction and in anterior insula and frontal operculum. These areas, taken together, have high spatial overlap with the default mode network 6,7 . While precise anatomical dissociations and functional specialisations among these regions is the subject of debate in cognitive neuroscience, they have been associated with many higher-level aspects of human cognition, including episodic and semantic memory 7,8 , imagination and construction 8 , value-guided decision-making 9 , delay discounting 10 , spatial reasoning 11 and high order social process such as theory of mind 12 . With deference to the caution required when making reverse inferences 13 , it may be expected that these aspects of cognitive function would have an influence on life in a complex society. While there are peaks in dorsal prefrontal cortex, it is notable that the highest node strengths are not centered on the dorsolateral prefrontal regions often associated with fluid intelligence 14,15 .
An obvious exception to the positive-negative interpretation of SMs is peg-board dexterity (time-taken), where high-scoring subjects perform worse. That exception, however, is consistent with the connectome result ( Fig. 2) insofar as the within-early-visual connections are weaker in high-scoring subjects, as are connections with two sensory/motor nodes (23 and 26 -likely Brodmann areas 4 and 5 respectively).
In summary, we found one significant mode of population variation that links a specific pattern of brain connectivity to a specific pattern of covariance between many behavioral and demographic subject measures. The vast majority of the SMs that correlate positively with this mode are "positive" subject traits/measures (education, income, IQ, life-satisfaction); those that correlate negatively are mostly "negative" subject measures. However, while strongly resembling the known general intelligence g factor for many of the subject measures, this mode does not trivially map onto just the strongest single principal component of the subject measures (see Supplementary Fig. 4; the CCA mode maps strongly onto the top three SM principal components and not just the first). It is plausible that the CCA mode includes a neural correlate of g, but is a more general mode of positive brain function, and is more directly tied into to the underlying biology (specifically, connectivity between brain regions), given that it is driven both by structured population covariance in behavioral measures and by intrinsic brain connectivity. We note a common criticism of the g factor, that there could be many distinct uncorrelated neural systems underlying high-level cognitive function, and that different cognitive tasks will involve different but overlapping sets of these latent processes, resulting in "artificial" correlation between subject measures, and hence the appearance of a g factor 16 . In future work it will be important to determine whether this known "unresolvable" ambiguity in g factor interpretation might be resolved through more fine-grained analysis of the data source newly available -the subject-specific functional connectomes -potentially even allowing direct investigation of the latent neural systems 17 , which may help us understand the coordinated interactions among brain systems that give rise to a general mode of positive function in humans.

Data
We used resting-state functional magnetic resonance imaging (rfMRI) data from 461 subjects taking part in the Human Connectome Project. All subjects were healthy adults (ages 22-35 y, 271 females) scanned on a 3 T Siemens connectome-Skyra scanner (customised to achieve 100 mT/m gradient strength). For each subject there were 4 × 15minute runs of rfMRI timeseries data with temporal resolution 0.73 s and spatial resolution 2 mm isotropic. This high spatial and temporal resolution was made possible through the use of multiband echo-planar imaging, with a simultaneous-multi-slice acceleration factor of 8 18 . To aid in cross-subject registration and surface mapping, T1-weighted and T2-weighted structural images of resolution 0.7 mm isotropic were also acquired, and B0 field mapping was also carried out to aid in correcting EPI distortions. The original set of subject measures was all the behavioral, demographic and other measures reported in the "open access" and "restricted" subject information spreadsheets available from the HCP database website (http://humanconnectome.org/data).

Data pre-processing
Data pre-processing was carried out with tools from FSL 19 , FreeSurfer 20 and HCP workbench tools 21 . Each 15-minute run of each subject's rfMRI data was preprocessed according to 22 ; spatial preprocessing was applied 23 , and structured artefacts were then removed using ICA+FIX (independent component analysis followed by FMRIB's ICAbased X-noiseifier 24,25 ). FIX removes more than 99% of the artefactual ICA components found in each dataset. The rfMRI data was represented as a timeseries of grayordinates -a combination of cortical surface vertices and subcortical standard-space voxels 23 .

Group-ICA parcellation
Group-ICA was performed to generate a set of group-average nodes (or parcels). For this, 4 15-minute runs from 468 HCP subjects were temporally demeaned and had variance normalisation applied 2 . These were fed into the MIGP algorithm 26 , which carried out a 4500-dimensional principal component analysis (PCA) from the 4×468 timeseries. The output of MIGP is a very close approximation to PCA applied to temporal concatenation of the 4×486 timeseries, but can be calculated even when the full concatenated matrix is too large to form. The MIGP output (PCA spatial eigenvectors) was fed into group-ICA, run using FSL's MELODIC tool 2 , applying spatial-ICA at several different ICA dimensionalities (D = 25, 50, 100, 200, 300). The dimensionality determines the number of distinct ICA components (spatial maps); a higher dimensionality typically means that the regions within individual spatial component maps will be smaller. A set of ICA maps can be considered as a parcellation, though it lacks some properties often assumed for parcellations: ICA maps are not binary masks but contain a continuous range of weight values, and a given map can include multiple spatially separated peaks/regions.

Node timeseries (individual subjects)
For a given group-ICA parcellation, the set of ICA spatial maps was mapped onto each subject's rfMRI timeseries data to derive one timeseries per ICA component per subject. For these purposes we consider each ICA component as a network "node". For each subject, these 25 (or 50, 100, 200 or 300) timeseries can then be used in network analyses. The method used to estimate the node-timeseries was "dual-regression stage-1", in which the full set of ICA maps was used as spatial regressors against the full timeseries data, estimating one timeseries for each ICA map 27 . This results in 25-300 nodes' timeseries of 4800 timepoints for each subject.

Network matrices (individual subjects and group averages)
Network matrices (also referred to as netmats or parcellated connectomes) were then derived from the node-timeseries. For each subject, the D (25-300) node-timeseries were fed into network modeling, creating a D×D matrix of connectivity estimates. Network modeling was carried out using the FSLNets toolbox (fsl.fmrib.ox.ac.uk/fsl/fslwiki/FSLNets). Netmats were estimated for the 461 subjects that have fully complete timeseries of 4800 timepoints (7 subjects whose data were fed into the group-ICA were missing some timepoints, and so were excluded from the subsequent quantitative subject-level network modeling). We applied network modeling using partial temporal correlation between nodes' timeseries. This aims to estimate direct connection strengths more accurately than is achieved by full correlation 28 . To improve the stability of the estimates of partial correlation coefficients, a small amount of L2 regularization is applied (setting rho=0.01 in the Ridge Regression netmats option in FSLNets). Netmat values were converted from Pearson correlation scores (r-values) into z-statistics with Fisher's transformation. Partial correlation z-statistic netmats were estimated separately for each 15-minute dataset, and then averaged across the 4 runs for each subject, resulting in a single netmat (for a given group-ICA dimensionality) per subject. Group average partial and full correlation network matrices were estimates by averaging the z-statistic netmats across all subjects.

Europe PMC Funders Author Manuscripts
For display/interpretational purposes (Fig. 2, Supplementary Figs. 2, 3), hierarchical clustering of the group-average full correlation network matrix was carried out using Ward's method implemented in Matlab. This was applied to all 200 nodes (from the 200dimensional group-ICA). For more quantitative evaluation of specific connectivities (e.g., as used for our CCA), partial correlation is preferable, as it is more successful (than full correlation) in identifying the strengths of connections that are considered direct in a functional sense 28 . However, for display of hierarchical network matrix clustering, we consider full correlation to be useful because of the extra robustness in identifying densely connected clusters that is achieved by also considering indirect connections. Additionally, this approach can help interpretability of the hierarchy/clustering, because it better matches the information that drives a low-dimensional clustering (e.g., a low-dimensional ICA that identifies a small number of gross resting-state networks, where there is no equivalent process to partial correlation occurring in the within-cluster modeling); hence this helps relate the results to typical low-dimensional network representation in the literature. Because this is a hierarchical clustering (see Supplementary Fig. 3), there is no single dimensionality (number of clusters) identified, but rather a continuum of clustering levels. However, largescale clustering into 4 clusters allows simple interpretation relative to the literature: one cluster (blue) relates to sensory, motor and dorsal attention network ("task positive network") areas 6 ; the other dominant cortical cluster (yellow) identifies the default mode network 6 , and the two others (brown and red) relate to extended/secondary default-mode areas and subcortical/cerebellar areas.

The PTN data release
The above-described Parcellations, node Timeseries and Netmats (PTN) were publicly released via the central HCP ConnectomeDB database in late 2014. These same subjectspecific netmats were used for the current study.

CCA modeling of many SMs and functional connectomes
We carried out a single integrated multivariate analysis using CCA, to simultaneously coanalyse a full set of functional networks (from all subjects) along with a large subset of the SMs. This aims to identify symmetric linear relations between the two sets of variables. Each significant CCA component (or mode) identifies a linear combination of netmat-edges (connectome connections) and a linear combination of SMs, where the variation in strength of involvement across subjects is maximally correlated. That is, we used CCA to find modes that relate sets of functional brain connections to sets of subjects' demographics and behavioral measures.
In our main analysis, we used the netmats from the 200-dimensional group-ICA. This was a somewhat arbitrary choice, as all dimensionalities within reason are valid, but we also found that the other dimensionalities gave very similar CCA results (see below). As the parcellated network matrices (netmats) are symmetric, we only kept values on one side of the diagonal, resulting in 19900 unique edges (200×199/2). Combining across subjects resulted in a 461×19900 (s×edges) matrix N 1 .
From the original set of 478 SMs, we formed a 461×478 matrix S 1 . where each column was normalised (scaled) according to its mean value, removing resulting columns that were badly conditioned due to a very low (z<0.1) mean value. We then demeaned (columnwise) and globally variance-normalised (matrixwise, separately for the two matrices) N 1 and N 2 before concatenating them horizontally to give N 3 , a matrix that therefore includes both preferences. (Nevertheless, we show below that this gave almost identical CCA results to only using N 1 or N 2 .) We used a rank-based inverse Gaussian transformation 29 , to enforce Gaussianity for each of the SMs, producing S 2 . This transformation was used to avoid undue influence of potential outlier values, although we later confirmed that this normalisation made almost no difference to the final CCA results (see below).
We identified 9 confound SMs, whose potential effect we wished to remove from our main analysis:

1.
Acquisition reconstruction software version (as an improved MRI reconstruction method was implemented in the third quarter of acquisition year 1).

2.
A summary statistic quantifying average subject head motion during the resting-state fMRI acquisitions (this is the average, across all timepoints, of the timepoint-to-timepoint head motion, that measure being the linear distance moved, averaged across the head).

8.
The cube-root of total brain volume (including ventricles), as estimated by FreeSurfer.

9.
The cube-root of total intracranial volume, as estimated by FreeSurfer.
In addition to identifying these 9 confound SMs, we also demeaned and squared measures 2-9 (the first is a binary indicator), to create additional confound measures, to help account for potentially nonlinear effects of these confounds. All confounds were demeaned, and any missing data treated as zeros. We then regressed the 17 resulting confounds out of both data matrices (resulting in N 4 and S 3 ). (The CCA result was virtually unchanged if we did not regress the confounds out of N and S, or if we only regressed them out of N.) We excluded any SMs from any further consideration (including post-hoc reporting) where fewer than 60 subjects had valid measures (6 SMs). We also excluded race (partly because the race measure is not quantitative, but consists of several distinct categories).
To focus our primary CCA on core behavioral measures of most interest, we excluded from the CCA a further set of SMs (but did include these in the final post hoc testing):

2.
69 SMs, which were quantitatively poor measures according to one or more of the following criteria: a.
An SM contained very extreme outlier values, as measured by most extreme value from the median. Specifically, if x s is an SM value for subject s, and y s =(x s -median(x s )) 2 , we consider an SM to have extreme outliers if max(y s ) >100×mean(y s ) .

b.
Fewer than 250 subjects had valid measures (too much missing data).

c.
Discreteness with severe imbalance, defined as >95% of all subjects having the same SM value.

3.
191 supplied measures from the T1-weighted structural brain analysis using FreeSurfer (including volumes of subcortical structures, and average thickness and surface area of many cortical regions). These are of course imaging-derived, but are supplied along with all the other SMs in the HCP database. We did not want these to drive the CCA, as we wanted the only imaging-derived measures utilised to be the functional connectomes.

4.
45 variables considered undesirable to feed into the core CCA, in some cases because they are not sufficiently likely to be measures relating to brain function, and in some cases where "minor" measures are highly correlated with more major related measures. For example, some measures would not necessarily be considered a confound, but we did not want them to be driving the main CCA result, to avoid complicating later interpretation. Thus we removed: "Is the subject in college?"; "Is the subject in a live-in relationship?"; "Is the subject born in Missouri?"; BMI (body mass index) and BMI self-report (note that as height and weight are confounds, BMI is essentially a confound and already removed); To avoid overfitting in the CCA, we used PCA to reduce the dimensionality of both N 4 and S 4 to c=100, reducing each to size 461×100 (i.e., keeping the top 100 subject-weighteigenvectors N 5 and S 5 to feed into the CCA). In the case of applying PCA to S, we accounted for missing data in the SMs (4% of matrix entries) by estimating the subjects×subjects covariance matrix one element at a time, where, for any two subjects, SMs missing for either subject are ignored. This approximation to the covariance matrix was projected onto the nearest valid (positive-definite) covariance matrix using the nearestSPD (http://www.mathworks.com/matlabcentral/fileexchange/42885-nearestspd) matlab toolbox; this projection was extremely mild, with the correlation between the before vs after covariance values being very high (r=0.99996), but is important in order for the covariance matrix to be valid. The resulting covariance was therefore formed without any need to impute missing SM values. It was fed into an eigenvalue decomposition (of order 100) to estimate the top 100 subject-wise SM eigenvectors S 5 , for feeding into the CCA, which represented 98.5% of the total SMs variance in S 4 . The top 100 subject-wise connectome eigenvectors (N 5 ) represented 41.5% of the total connectomes population variance in N 4 .
CCA (via canoncorr in Matlab) estimated 100 components (modes), optimising de-mixing matrices A and B such that the resulting U=N 5 A and V=S 5 B (461×100) matrices were maximally similar to each other. The correlation between a corresponding pair of columns (one each from U and V) indicates the strength with which a mode of population variation is common to both brain networks and behavioral measures; significance was estimated via 100,000 permutations of the rows of one matrix relative to the other. CCA was then re-run after each permutation. There are many related subjects in the HCP data, and family structure was kept intact when permuting the data 4 , therefore building up a valid null distribution of CCA results.
We identified just one CCA mode that related functional connectomes to SMs with high significance (r=0.8723, P<10 −5 , corrected-p 5% critical r threshold = 0.840). This mode was by definition the one component (out of 100 estimated) whose correlation between the connectome-subject-weights and the SM-subject-weights was maximal, and as this is compared against the null distribution of maximal correlation values, the quoted p-value is explicitly corrected for multiple testing (searching across all CCA modes estimated). This CCA mode represents one significant mode of population co-variation, for which individual subjects' strength of involvement with this mode is highly similar for both a subset of the functional connectome and a subset of the SMs. The mode comprises 4 vectors: • U 1 , a 461×1 vector of individual subject weights derived from the connectomes matrix (in which each value describes the extent to which a given subject is positively or negatively correlated with this mode of population variation with respect to brain connectivity) • V 1 , a 461×1 vector, also of individual subject weights, derived from the SMs matrix (and which is highly correlated with U 1 , r=0.87) • A 1 , a 100×1 vector of CCA mode weights relating to the 100 connectome PCA components fed into the CCA (i.e., the extent to which combinations of edge strength relate to mode weights-vector U 1 ) • B 1 , a 100×1 vector describing the extent to which each SM PCA component relates to mode weights-vector V 1 .
CCA finds the A and B that maximise the correlation between U and V. To obtain relative weights (and signs) of involvement of the original sets of connectome edges and SMs, we correlated U 1 and V 1 respectively against N and S, even for those SMs not used for the CCA, resulting in "full length" edge/SM weight vectors A F1 and B F1 . This simple approach for mapping CCA modes onto the original data matrices (to get connectomes and SM weights) allows for the estimation of the same test statistic for those SMs included in the CCA and those that were excluded.
In order to generate the CCA edge strength "increase" and "decrease" maps shown in Figs. 2b and 2d, we carried out the following. Using vector A F1 (CCA edge modulation weights), we multiplied each element by the sign of the population mean edge connectivity, converting the modulation weights into measures of edge strength modulation. We reshaped the resulting vector into a square nodes×nodes matrix containing the same values (i.e., reversing the reshaping depicted top-left in Supplementary Fig. 1). For each column (node), we then estimated the average of the lowest 25% of values, and also the average of the highest 25% of values. This gave us estimates of the mean (across edges involving each node) strength decrease and increase, respectively. These values were then plotted spatially by multiplying each nodes' spatial map by its edge strength decrease/increase, and averaging across all nodes for a given grayordinate. Note that a given node could in theory have both strong edge strength decreases (i.e., for certain edges involving that node) as well as strong increases (for other edges), but in general the maps of decrease and increase show little overlap.

Additional CCA validation tests
Several additional analyses were performed to further increase confidence that the CCA mode is a, robust, interpretable, mode of variation associating factors internal to the brain and subject measures. In general each test is evaluated in terms of 4 correlations [1 2 3 4]:  We now list the additional tests carried out: • If we added age into the confounds, which subsumes the effect of removing all the age-adjusted SMs from feeding into the CCA, the results were almost unchanged [0.99 0.99 0.99 1.00].
• Similarly, in order to explicitly determine whether there was a strong effect of feeding in both age-adjusted and non-adjusted SMs into the CCA, we carried out two additional CCA tests. In the first we excluded all ageadjusted measures previously fed into the CCA, for which non-adjusted SMs were also being used; this removed 10 SMs. In a second test we did the opposite, removing 10 non-adjusted SMs. In both cases we re-ran the CCA and compared the 4 primary CCA weight vectors against the original vectors. The results were virtually unchanged, with the smallest correlation across the 8 new-old vector pairs (two CCA re-runs and 4 weight vectors) being r=0.997.
• THC is the strongest-involved negative SM; hence, we tested the effect of removing THC from feeding into the CCA. The result is virtually

•
In order to evaluate whether information similar to that in the connectomes might also be present in structural volume measures, we re-ran the CCA using the 47 FreeSurfer structural measures (volumes of individual tissue components and brain sub-structures) instead of the functional connectomes. Because this number of variables was much smaller, it was necessary to reduce the number of PCA components to 30. The correlation between U 1 and V 1 (from the resulting dominant CCA mode) was reduced to 0.56 (p=0.002). The correlations between the original V 1 and B F1 and the volumetric-feature-based estimates of these were 0.51 and 0.78 respectively, i.e., lower than the corresponding connectome-based correlations reported above when reducing the number of PCA components from 100 to 30 without making any other changes. Thus, while the relationship between "brain" and SMs is weaker when using volumetric brain measures instead of functional connectivity measures, the results are still partially present. We also re-ran the original CCA, but after adding the 47 FreeSurfer structural volumes as additional confounds (to be regressed out of the connectomes and SMs). The correlation between U 1 and V 1 was 0.86 (i.e., nearly as high as in the original result), and the CCA weight vectors were similar to the original results [0.59 0.63 0.70 0.81]; these values are quite similar to the those reported above when re-running the original analysis with a reduction of PCA components to 30. We conclude that there is some shared variance between brain sub-volumes and functional connectomes (and hence the primary CCA result is to a limited extent recapitulated when co-modeling structural volumes and SMs), but the original CCA result (using functional connectomes) is stronger, and is largely unchanged when regressing out the brain structure volumes.
• As a simple sanity check of the permutation scheme that respects family structure, we replaced all rows (in both connectomes and SMs matrices) from a given family with the average row across all family members, for each family, and re-ran the CCA. We reduced the number of PCA components kept to 40, given the greatly reduced new "subject" numbers (157). The result is virtually unchanged [--0.74 0.88], and the significance of this first CCA mode remains at p~1/N permutations .

•
Although we have no reason to doubt the validity of the permutation-based significance test (of the main CCA result), we carried out a separate traintest validation analysis in which the CCA was only run on a subset of the data, and the outputs tested against the rest. We randomly kept approximately 80% of the subjects in a "train" analysis, leaving the other 20% as a test validation subset, without splitting any families across the train/test subsets. We ran the CCA on the train dataset, and confirmed that the main CCA mode estimated was virtually the same as the main original result (with weight vector similarities in the range r=0.85:0.99). We then took the CCA SM and connectome weight vectors from the train dataset and multiplied those into the left-out test dataset SM and connectome matrices, in order to estimate subject weight vectors U 1 and V 1 for the test dataset. We correlated U 1 and V 1 , and carried out a (within the test dataset) permutation test (again respecting family structure, 1000 permutations) in order to measure the significance of the test dataset subject weight vectors' correlation. We ran this train-test process 10 times, each with a randomly different set of subjects in the train and test subjects. The mean correlation between the left-out (test) U 1 and V 1 was 0.25 (N subjects~9 0); the mean correlation in the null (permuted data) was 0.03 and the standard deviation was 0.1. In all 10 cases the correlation between the test dataset subject weight vectors was maximally significant at p=1/ N permutations (i.e., p=0.001). Hence the main CCA mode result is strongly supported by these train/test evaluations.

Supplementary Material
Refer to Web version on PubMed Central for supplementary material. (a) The set of SMs (subject measures) most strongly associated with the CCA mode of population variability. SMs included in the CCA are colored blue, while others (grey) were correlated with the CCA mode post-hoc. Vertical position is according to correlation with the CCA mode, while font size indicates SM variance explained by the CCA mode. Here we do not report "secondary" SMs that are highly redundant with those shown here (Supplementary Table 1 shows the complete set of SMs that correlate highly with the CCA mode). See wiki.humanconnectome.org/display/PublicData/HCP+Data+Dictionary+Public-+500+Subject+Release for details of the SMs. (b) The principal CCA mode -a scatter-plot of SM weights versus connectome weights, with one point per subject, and an example subject measure (fluid intelligence) indicated with different colors. The high correlation visualised here indicates significant co-variation between the two datasets. (c) The total variance explained of the original data matrices (shown separately for connectomes and subject measures) is plotted for the first 20 CCA modes. In black/grey is shown the mean and the 5 th to 95 th percentiles of the null distribution of the same measures, estimated via permutation testing. Using the null distributions to normalize variance explained accounts for the fact that the initial modes are expected to have higher correlations, even in the null scenario, but, as can be seen from the nulls, this is in any case a very small effect.  (a) The 30 brain connections most strongly associated with the CCA mode of population variability. To aid interpretation, the CCA edge modulation weights are multiplied by the sign of the population mean correlation; hence red indicates stronger connections and blue weaker, for high-scoring subjects (and vice versa for low-scoring subjects). (b) Map of CCA connection strength increases (each node's parcel map is weighted by CCA edge-strength increases, summed across edges involving the node). (c) Group-mean functional clustering: 4 clusters from a hierarchical analysis of all 200 nodes' population-average full correlation ( Supplementary Fig. 3). These fall into two groups: one cluster (blue) contains sensory, motor, insula and dorsal attention regions, and a group of 3 correlated clusters (brown, red, yellow) primarily covering the default mode network and subcortical/cerebellar areas.