Functional connectivity is linked to symbolic BOLD patterns: Replication, extension, and clinical application of the human "Complexome".
The 12 matches · 7 of them tie a paragraph to a whole file, not to given lines: weak matches, whose lines are not tinted
- [1] § RESULTS › Extending the “Complexome”: Complexity Cofluctuations and Pattern Incongruency ↔ analysis_code/main_functions/calc_wpe_cofluctuations.m, lines 1–112 · score 0.84 · root sum square, downward cofluctuations, drop coincidence, sliding window, edge timeseries, metric
- [2] § MATERIALS AND METHODS › WPE Calculation ↔ analysis_code/main_functions/permEntropy_motif_distribution.m, lines 123–211 · score 0.80 · Shannon entropy, weighting factor, weighted pattern frequency, factorial, log2, unity
- [3] § MATERIALS AND METHODS › WPE Calculation ↔ Code/permEntropy.m, lines 104–169 · score 0.79 · Shannon entropy, weighting factor, weighted pattern frequency, factorial, log2, unity
- [4] § RESULTS › Extending the “Complexome”: Complexity Cofluctuations and Pattern Incongruency ↔ analysis_code/main_functions/calc_wpe_cofluctuations.m, lines 1–112 · score 0.79 · root sum square, downward cofluctuation, cofluctuation timeseries, sliding window, edge timeseries, BOLD timeseries
- [5] § MATERIALS AND METHODS › Complexity Timeseries Cofluctuation ↔ analysis_code/main_functions/calc_wpe_cofluctuations.m, lines 149–228 · score 0.68 · temporal unwrapping procedure, frame, edge timeseries, fluctuate, pairwise, cofluctuations
- [6] § RESULTS › FC Is Linked to Complexity Dynamics and BOLD Signal Patterns ↔ Code/demo_complexity_timeseries.m, the whole file · a weak match · score 0.62 · Young Adults, window parameters, HCP, BOLD timeseries, scan, brain regions
- [7] § MATERIALS AND METHODS › WPE Calculation ↔ analysis_code/wrapper_functions/wrapper_wpe_coflux_ipi.m, the whole file · a weak match · score 0.61 · slide length, WPE timeseries, sliding window, segmented, BOLD timeseries, ROI
- [8] § MATERIALS AND METHODS › Complexity Timeseries Cofluctuation ↔ analysis_code/main_functions/calc_dynamic_wpe.m, the whole file · a weak match · score 0.56 · spatiotemporal complexity architecture, brain activity, brain regions, dynamics, windows, WPE
- [9] § MATERIALS AND METHODS › Complexity Timeseries Cofluctuation ↔ analysis_code/main_functions/timeresolved_permEntropy_motifs.m, the whole file · a weak match · score 0.55 · spatiotemporal complexity architecture, brain activity, dynamics, signals, windows, Timeseries
- [10] § MATERIALS AND METHODS › WPE Calculation ↔ analysis_code/main_functions/timeresolved_permEntropy_motifs.m, the whole file · a weak match · score 0.54 · slide length, sliding window, overlapping, BOLD timeseries, TR, dynamic
- [11] § MATERIALS AND METHODS › Index of Pattern Incongruency ↔ analysis_code/main_functions/calc_ipi.m, the whole file · a weak match · score 0.54 · Euclidean distance, pattern incongruency, brain regions, scalar, symbolic, windows
- [12] § RESULTS › FC Is Linked to Complexity Dynamics and BOLD Signal Patterns ↔ analysis_code/wrapper_functions/wrapper_wpe_coflux_ipi.m, the whole file · a weak match · score 0.53 · sliding window parameters, slide lengths, segmentation, BOLD timeseries, brain regions, AUC SCD
Paper
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The authors' code
MATLAB · 322 lines · 16 KB · no license · 3 matches
- function [wpe_ts_zscore_i, ets_wpe_i_vec, rms_wpe_i_vec, mean_ets_wpe_i_vec, corr_wpe_ts_i_vec, ...
- count_bidirect_coflux_i, auc_scd, idx_auc_scd, rms_scd, rms_auc_zeroed, scd_count, ...
- rms_scd_count, linear_ind] = calc_wpe_cofluctuations(WPE_norm, n_edges, nr_windows, n_rois)
- % CALC_WPE_COFLUCTUATIONS
- %
- % Estimate cofluctuations between WPE timeseries using temporal dot product
- % and root sum square of resultant (i.e., like edge timeseries but not on BOLD data).
- % Subsequently, find instances of simultaneous complexity decrease (SCD) and
- % downward cofluctation of WPE timeseries. The temporal union of these
- % instances serves as an alternative to the original 'drop coincidence'
- % measure from Krohn et al. (2023).
- %
- % Finally, the area under the curve (AUC) of the cofluctuation timeseries,
- % indexed for these instances (i.e., AUC-SCD), serves as a summary measure of
- % the magnitude and number of SCD over time, between a pair of brain regions.
- %
- % See Esfahliani et al. (2020) for introduction to temporal unwrapping procedure
- % applied to product-moment correlations between BOLD timeseries, used to generate 'edge timeseries':
- %
- % F. Z. Esfahlani, Y. Jo, J. Faskowitz, L. Byrge, D. P. Kennedy, O. Sporns, and R. F. Betzel,
- % “High-amplitude cofluctuations in cortical activity drive functional connectivity,”
- % Proc. Natl. Acad. Sci., vol. 117, no. 45, pp. 28393–28401, Nov. 2020, doi: 10.1073/pnas.2005531117.
- %
- %
- % INPUTS:
- %
- % WPE_norm (matrix) - Numeric array containing weighted permutation entropy values in bits,
- % for every window and brain region, normalized to [0,1].
- % (i.e., the WPE timeseries)
- % Dimensions: nr_windows -by- n_rois.
- %
- %
- %
- % n_edges (scalar) - Number of edges in the whole brain network.
- % Here, 29646 - i.e., (n_rois*n_rois - n_rois)/2
- % nr_windows (scalar) - Number of consecutive sliding windows per BOLD TS.
- % Calculated in single_wpe_coflux_ipi.m from n_tps, window_size, and slide_samples.
- % n_rois (scalar) - Number of brain regions in atlas.
- % Here, 244 (Romanello et al., 2026)
- %
- % OUTPUTS:
- %
- % wpe_ts_zscore_i (matrix) - Z-scored WPE_norm.
- % Numeric array, dimensions: nr_windows -by- n_rois,
- %
- % ets_wpe_i_vec (matrix) - Temporal, element-wise dot product between a pair of z-scored WPE timeseries.
- % Numeric array, dimensions: n_edges -by- nr_windows.
- % Analogous to "edge timeseries" between pair of z-scored BOLD timeseries.
- %
- % rms_wpe_i_vec (matrix) - Root-sum-squared of "edge timeseries" between a pair of z-scored WPE timeseries.
- % Numeric array, dimensions: n_edges -by- nr_windows.
- % Analogous to amplitude of cofluctuation between pair of z-scored BOLD timeseries.
- %
- % mean_ets_wpe_i_vec (vector) - Mean over windows of WPE 'edge timeseries'.
- % Numeric vector of length n_edges.
- %
- % corr_wpe_ts_i_vec (vector) - Each element contains product-moment correlation over windows of edge
- % timeseries for a given edge. Should be approximately equal to
- % mean_ets_wpe_i_vec.
- % Numeric vector of length n_edges.
- %
- % count_bidirect_coflux_i (vector) - Each element contains count of number bidirectional positive
- % cofluctuations (both WPE TS go up OR down).
- % Numeric vector of length n_edges.
- %
- % idx_auc_scd (matrix) - Each element indicates if regions of given edge at given window meet
- % criteria for simultaneous complexity decrease (1 = yes, 0 = no)
- % Logical matrix with dims: n_edges x nr_windows.
- %
- %
- % rms_scd (matrix) - Amplitude of cofluctuation in instances of SCD. Cell array of length n_edges.
- % Each cell contains a numeric vector whose length
- % corresponds to the number of windows where SCD criteria was met. Values contain
- % coflcutuation values for SCD windows.
- %
- % rms_auc_zeroed (matrix) - Each row contains root sum square of WPE 'edge timeseries', but non-SCD
- % windows are zeroes. Used for area-under-curve calculation.
- % Numeric matrix with dims n_edges x nr_windows
- %
- % auc_scd (vector) - Each element contains area-under-the-curve of indexed cofluctuation
- % timeseries (SCD instances) for a given edge. This value is our analogous drop coincidence
- % metric.
- % Numeric vector with length n_edges.
- %
- % scd_count (vector) - Each element contains count of number of windows in which both regions showed decreases in
- % complexity, relative to their previous window.
- % Numeric vector of length n_edges.
- %
- % rms_scd_count (vector) - Each element contains count of number of windows in which both regions
- % showed decreases in complexity AND downward cofluctuations (same direction).
- % Numeric vector of length n_edges.
- %
- % linear_ind (vector) - Used for transforming between matrix/vector (lower triangle) form of symmetrical data.
- % Numeric vector of length n_edges.
- %
- %
- % Note: there are additional local functions at the bottom of this file!
- % get_wpe_ets()
- % get_wpe_decrease_indices()
- % get_coflux_scd()
- %
- %------------------------------------------------------------------------------------------------------------------------------
- % Amy Romanello, 2026.
- %
- % Original publication:
- % A. Romanello, N. von Schwanenflug, M. Franka, F. Paul, H. Prüss, S. Krohn, and C. Finke,
- % “Functional connectivity is linked to symbolic BOLD patterns: Replication,
- % extension, and clinical application of the human ‘complexome,’” Netw. Neu-rosci.,
- % pp. 1–26, Apr. 2026, doi: 10.1162/NETN.a.572.
- %
- % Please cite the above publication when using or adapting this code for subsequent work.
- % ------------------------------------------------------------------------------------------------------------------------------
- %% Step 1: Set up and compute WPE 'edge timeseries' & root-sum-square of cofluctuations
- % This is a generalized application of the temporal unwrapping procedure described in Esfahlani et al. (2020).
- % Here, applied to the standardized covariance between WPE timeseries, instead of BOLD timeseries.
- % z-score wpe ts --> each col is zscored separately to have mean 0, sd 1
- wpe_ts_zscore_i = zscore(WPE_norm);
- % compute cofluctuations between all pairs of WPE TS
- % this is a local function at the bottom
- [ets_wpe_i_vec, rms_wpe_i_vec, mean_ets_wpe_i_vec, ...
- corr_wpe_ts_i_vec, linear_ind] = get_wpe_ets(wpe_ts_zscore_i, n_rois, nr_windows);
- %% Step 2: Get indices of decreases in WPE from window t to t+1
- [neg_delta_wpe_i] = get_wpe_decrease_indices(WPE_norm, nr_windows, n_rois);
- %% Step 3: Get indices of positive cofluctuation (= both(!) WPE TS go up or down in same window)
- idx_ets_pos_i = ets_wpe_i_vec>=0;
- % save number of positive cofluctuations per edge (for later)
- count_bidirect_coflux_i = sum(idx_ets_pos_i,2);
- %% Step 4: Get cofluctuations for instances of simultaneous complexity decreases (SCD) only
- [auc_scd, idx_auc_scd, rms_scd, rms_auc_zeroed, scd_count,...
- rms_scd_count] = get_coflux_scd(neg_delta_wpe_i, idx_ets_pos_i, ...
- rms_wpe_i_vec, n_edges, n_rois, nr_windows, linear_ind);
- %%%%%% LOCAL FUNCTIONS %%%%%%
- function [ets_wpe_i_vec, rms_wpe_i_vec, mean_ets_wpe_i_vec, ...
- corr_wpe_scale_i_vec, linear_ind] = get_wpe_ets(wpe_ts_zscore_i, n_rois, nr_windows)
- % Apply temporal unwrapping procedure to pairwise WPE timeseries. This includes z-scoring of
- % WPE timeseries, taking the element-wise dot product between them, and calculating the amplitude
- % of cofluctuation using the root-sum-squared.
- % pre-allocate vars
- ets_wpe_i = nan(n_rois, n_rois, nr_windows);
- fc_wpe_scalar_i = nan(n_rois, n_rois);
- mean_ets_wpe_i = nan(n_rois, n_rois); % should be a matrix now
- rms_wpe_i = nan(n_rois, n_rois, nr_windows);
- % loop over roi pairs
- for row = 1:n_rois
- for col = 1:n_rois
- % get pair of regions
- cofluct_roi1 = col ;
- cofluct_roi2 = row ;
- % - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
- % - - - - Cofluctuations / Edge timeseries of WPE timeseries
- % - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
- % grab for legibility purposes
- ts_wpe_roi1_2_z = wpe_ts_zscore_i(:,[cofluct_roi1 cofluct_roi2]);
- % get dimensions - output vars can be over-written on each iter
- [ntime_wpe,nnodes_wpe] = size(ts_wpe_roi1_2_z) ; % should be: nr windows, 2
- % calculate number of edges
- nedges_wpe = nnodes_wpe*(nnodes_wpe - 1)/2 ; % should always be 1 for us
- % indices of unique edges (upper triangle)
- [u_wpe,v_wpe] = find(triu(ones(nnodes_wpe),1));
- idx_wpe = (v_wpe - 1)*nnodes_wpe + u_wpe ;
- % calculate "static fc" - correlation b/t z-scored complexity time-series of 2 rois,
- % should be equivalent (or nearly) to the mean of the edge-time series between the 2 rois
- fc_wpe = corr(ts_wpe_roi1_2_z) ;
- % generate edge time series
- ets_wpe_i(row,col,:) = ts_wpe_roi1_2_z(:,u_wpe).*ts_wpe_roi1_2_z(:,v_wpe) ;
- % save for legibility
- ets_wpe = squeeze(ets_wpe_i(row, col, :));
- % sanity check?
- fc_wpe_scalar_i(row, col) = fc_wpe(u_wpe,v_wpe);
- mean_ets_wpe_i(row, col) = mean(ets_wpe);
- % calculate co-fluctuation amplitude at each frame
- rms_wpe_i(row,col,:) = sum(ets_wpe.^2,2).^0.5 ;
- end
- end
- % % sanity check
- % is_symmetric_ets = nan(nr_windows,1);
- % is_symmetric_rms = nan(nr_windows,1);
- % for s=1:nr_windows
- % is_symmetric_ets(s) = issymmetric(ets_wpe_i(:,:,s));
- % is_symmetric_rms(s) = issymmetric(rms_wpe_i(:,:,s));
- % end
- %
- % sum(is_symmetric_ets)==nr_windows
- % sum(is_symmetric_rms)==nr_windows
- % save just lower triangle of symmetric matrices
- ets_wpe_i_vec = icatb_mat2vec(ets_wpe_i);
- rms_wpe_i_vec = icatb_mat2vec(rms_wpe_i);
- mean_ets_wpe_i_vec = icatb_mat2vec(mean_ets_wpe_i);
- [corr_wpe_scale_i_vec, linear_ind] = icatb_mat2vec(fc_wpe_scalar_i); % save linear indices for later
- end
- function [neg_delta_wpe_i] = get_wpe_decrease_indices(WPE_norm, nr_windows, n_rois)
- % Compute delta wpe to indetify windows where wpe goes down from t to t+1
- % pre-allocate vars
- wpe_delta_i = nan(nr_windows, n_rois); % we want the first row to remain NaN
- % shift windows by 1 (rows)
- wpe_ts_2_end = WPE_norm(2:end,:);
- wpe_ts_1_endmin1 = WPE_norm(1:end-1,:);
- wpe_delta_i(2:end,:) = wpe_ts_2_end-wpe_ts_1_endmin1; % first row (win 1) remains NaN (no delta)
- % now binarize that matrix to get an index for negative delta wpe windows
- neg_delta_wpe_i = wpe_delta_i<0;
- end
- function [auc_scd, idx_auc_scd, rms_scd, rms_auc_zeroed, scd_count,...
- rms_scd_count] = get_coflux_scd(neg_delta_wpe_i, idx_ets_pos_i, rms_wpe_i_vec, n_edges, n_rois, nr_windows, linear_ind)
- % Using indices of complexity decrease in both WPE TS (SCD) + instances of downward coflucuations, find their intersection and
- % compute area-under-the-curve of the cofluctuation amplitude during those moments. Here, AUC-SCD serves as a continuous measure,
- % analogous to complexity "drop coincidence" in Krohn et al. (2023)
- % convert linear indices to subscripts
- [rows, cols] = ind2sub([n_rois, n_rois], linear_ind);
- % pre-allocate vars
- auc_scd = nan(n_edges,1);
- idx_auc_scd = nan(n_edges, nr_windows);
- rms_scd = cell(n_edges,1);
- rms_auc_zeroed = nan(n_edges, nr_windows);
- scd_count = nan(n_edges,1);
- rms_scd_count = nan(n_edges,1);
- for e=1:n_edges % loop over edges
- % get roi ids for edge e
- roi_1 = rows(e);
- roi_2 = cols(e);
- % get neg delta indices for these 2 rois (over all windows)
- neg_delta_roi_1 = neg_delta_wpe_i(:,roi_1);
- neg_delta_roi_2 = neg_delta_wpe_i(:,roi_2);
- % get positive poitions of ets for edge e, over all windows
- ets_wpe_pos_edge_e = idx_ets_pos_i(e,:)';
- % find windows where both WPE TS decrease - relative to previous
- % window (simultaneous complexity decrease = SCD)
- scd_idx = neg_delta_roi_1&neg_delta_roi_2;
- % save sum of SCD - sum over windows
- scd_count(e,1) = sum(scd_idx);
- % get indx for SCD = 1 AND ets_pos = 1
- idx_pos_coflux_pos_scd = ets_wpe_pos_edge_e&scd_idx;
- rms_scd_count(e,1) = sum(idx_pos_coflux_pos_scd);
- % now use that boolean to index into the rms vector
- rms_edge_e = rms_wpe_i_vec(e,:)';
- % rms where SCD + ETS = 1
- rms_scd_edge_e = rms_edge_e(idx_pos_coflux_pos_scd);
- % make vector for area-under-curve (auc) calculation - zero non-SCD windows
- rms_auc_vec = rms_edge_e; % copy
- rms_auc_vec(~idx_pos_coflux_pos_scd) = 0;
- % calc auc for edge e
- auc_scd_edge_e = trapz(rms_auc_vec);
- % store vars for later
- auc_scd(e) = auc_scd_edge_e;
- idx_auc_scd(e,:) = idx_pos_coflux_pos_scd';
- rms_scd{e} = rms_scd_edge_e;
- rms_auc_zeroed(e, :) = rms_auc_vec';
- end
- idx_auc_scd = logical(idx_auc_scd);
- end
- end
calc_wpe_cofluctuations.m, no license · at the source
Overview
- Department of Neurology and Experimental Neurology, Charité-Universitätsmedizin Berlin, corporate member of Freie Universität Berlin, Humboldt-Universität Berlin, Berlin, Germany
- Berlin School of Mind and Brain, Humboldt-Universität zu Berlin, Berlin, Germany
- Max Delbrück Center for Molecular Medicine in the Helmholtz Association, Berlin, Germany
- Experimental and Clinical Research Center, a cooperation between the Max Delbrück Center for Molecular Medicine in the Helmholtz Association and Charité-Universitätsmedizin Berlin, Berlin, Germany
- NeuroCure Clinical Research Center, Charité-Universitätsmedizin Berlin, corporate member of Freie Universität Berlin, Humboldt-Universität zu Berlin, and Berlin Institute of Health, Berlin, Germany
- German Center for Neurodegenerative Diseases (DZNE) Berlin, Berlin, Germany
Abstract
Functional connectivity (FC) quantifies the temporal coherence of blood-oxygen-level-depen
Reproduced under the paper's license (CC BY), from the paper cited above.
Repositories
Its files are read in the Code ↔ Paper reader above, with 12 matches between paragraphs and lines of code.
OSF mr8f7
Availability: 1 check, the latest on 27 September 2026: the link answers (HTTP 200)
- 27 September 2026: the link answers (HTTP 200)
4 files
- Code/
demo_complexity_timeseri , MATLAB, 78 lines, 1 matches.m - Code/
demo_state_metrics.m , MATLAB, 206 lines - Code/
permEntropy.m , MATLAB, 169 lines, 1 match - Code/
timeresolved_permEntropy , MATLAB, 82 lines.m
OSF wjua7
Availability: 1 check, the latest on 27 September 2026: the link answers (HTTP 200)
- 27 September 2026: the link answers (HTTP 200)
10 files
- analysis_code/
main_functions/ , MATLAB, 87 lines, 1 matchcalc_dynamic_wpe.m - analysis_code/
main_functions/ , MATLAB, 102 lines, 1 matchcalc_ipi.m - analysis_code/
main_functions/ , MATLAB, 322 lines, 3 matchescalc_wpe_cofluctuations. m - analysis_code/
main_functions/ , MATLAB, 80 lineseuclidean_dist_pd_v2.m - analysis_code/
main_functions/ , MATLAB, 41 linesicatb_mat2vec.m - analysis_code/
main_functions/ , MATLAB, 211 lines, 1 matchpermEntropy_motif_distri bution.m - analysis_code/
main_functions/ , MATLAB, 120 lines, 2 matchestimeresolved_permEntropy _motifs.m - analysis_code/
run_wpe_cofluctuations_i , MATLAB, 146 linespi.m - analysis_code/
wrapper_functions/ , MATLAB, 157 linessingle_wpe_coflux_ipi.m - analysis_code/
wrapper_functions/ , MATLAB, 118 lines, 2 matcheswrapper_wpe_coflux_ipi.m
The paper's code and data availability statement is in the Data section.
Tracing map
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What the map holds:
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- neither the text of the paper nor the code itself.
Its JSON (tracing-map.json) is deposited on Zenodo with its DOI once the map is validated.
Data
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Data and materials availability
Analysis code to reproduce the main findings of this study is made available on the Open Science Framework: https://
Reproduced under the paper's license (CC BY), from the paper cited above.
Versions
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Recorded: type, language, journal, volume, issue, pages, dates, 7 authors, 5 keywords, 2 funders, 27 references.
Cite
This paper
Romanello, A., von Schwanenflug, N., Franka, M., Paul, F., Prüss, H., Krohn, S., & Finke, C. (2026). Functional connectivity is linked to symbolic BOLD patterns: Replication, extension, and clinical application of the human "Complexome". Network neuroscience (Cambridge, Mass.), 10(3), 761-786. https://
BibTeX
@article{romanello2026fu
author = {Romanello, Amy and von Schwanenflug, Nina and Franka, Michelle and Paul, Friedemann and Prüss, Harald and Krohn, Stephan and Finke, Carsten},
title = {{Functional connectivity is linked to symbolic BOLD patterns: Replication, extension, and clinical application of the human "Complexome"}},
journal = {Network neuroscience (Cambridge, Mass.)},
year = {2026},
month = aug,
volume = {10},
number = {3},
pages = {761--786},
publisher = {MIT Press},
issn = {2472-1751},
doi = {10.1162/
url = {https://
pmid = {42730197},
pmcid = {PMC13569379}
}
RIS
TY - JOUR
AU - Romanello, Amy
AU - von Schwanenflug, Nina
AU - Franka, Michelle
AU - Paul, Friedemann
AU - Prüss, Harald
AU - Krohn, Stephan
AU - Finke, Carsten
TI - Functional connectivity is linked to symbolic BOLD patterns: Replication, extension, and clinical application of the human "Complexome"
T2 - Network neuroscience (Cambridge, Mass.)
J2 - Netw Neurosci
PY - 2026
DA - 2026/
VL - 10
IS - 3
SP - 761
EP - 786
SN - 2472-1751
PB - MIT Press
DO - 10.1162/
UR - https://
LA - en
ER -
CSL-JSON
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"type": "article-journal",
"title": "Functional connectivity is linked to symbolic BOLD patterns: Replication, extension, and clinical application of the human \"Complexome\"",
"container-title": "Network neuroscience (Cambridge, Mass.)",
"author": [
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"family": "Romanello",
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"family": "Finke",
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"container-title-short":
"volume": "10",
"issue": "3",
"page": "761-786",
"DOI": "10.1162/
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"ISSN": "2472-1751",
"publisher": "MIT Press",
"URL": "https://
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