The dual interpretation of edge time series: Time-varying connectivity versus statistical interaction.

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[1] § STAR★Methods › Quantification and statistical analysis › Prewhitening ↔ fit_models.m, lines 34 to 120 · score 0.55 · regression coefficients, node pairs, residuals, ij, matrix · Report a mismatch

Paper

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The authors' code

MATLAB · 120 lines · 3.4 KB · no license · 1 match

clear all
close all
clc
%% Description
%
% In this script, we read in time series data -- parcel-level Ca++
% imaging data and behavioral time courses. The goals is to fit lineaer
% models that explain the behavioral data in terms of:
%
% 1. the z-scored activity of parcel i,
% 2. the z-scored activity of parcel j,
% 3. the element-wise product of those z-scored time series (referred
% to in our previous work as an 'edge time series').
%
% This procedure is repeated for all unique {i,j} pairs, populating
% matrices of regression coefficients.
%
% We repeat this entire procedure for seven behavioral time courses. For
% reference, these data come from 'subject 18' in this paper:
%
% Chen, X., Mu, Y., Hu, Y., Kuan, A. T., Nikitchenko, M.,
% Randlett, O., ... & Ahrens, M. B. (2018). Brain-wide organization
% of neuronal activity and convergent sensorimotor transformations in
% larval zebrafish. Neuron, 100(4), 876-890.
%
% If you use this code in your own work, please cite the original data
% source, but also our paper:
%
% Merritt, H., Mejia, A., & Betzel, R. (2024). The dual
% interpretation of edge time series: Time-varying connectivity
% versus statistical interaction. bioRxiv, 2024-08.
%% Analysis
% load data
load data
z = zscore(z); % z-score time series
[nt,n] = size(z); % number of frames, number of parcels
[u,v] = find(triu(ones(n),1)); % upper triangle indices
% outer loop - over behavioral measures
for j = 1:size(b,2)
% behavior time series
y = b(:,j);
% constants
nobs = length(y);
dft = nobs - 1;
dfe = nobs - 4;
p = 4;
% more constants
ybar = mean(y);
sst = norm(y - ybar)^2;
% preallocate arrays for rsquared, regression coefficients, and pvalues
rsqu = zeros(length(u),1);
betas = zeros(length(u),p);
pvals = zeros(length(u),p);
% loop over all node pairs
for i = 1:length(u)
% update
if mod(i,round(length(u)/51)) == 0
fprintf('behavioral measure %i, %.2f percent complete (%i of %i edges)\n',j,100*i/length(u),i,length(u));
end
% matrix of explanatory values
x = ones(nt,4);
x(:,1) = z(:,u(i));
x(:,2) = z(:,v(i));
x(:,3) = z(:,u(i)).*z(:,v(i));
% get betas and pvalues
[Q,R] = qr(x,0);
% regression coefficients -- could stop here if we didn't want to
% do states
beta = R\(Q'*y);
% behavior predicted by model + residuals
yhat = x*beta;
residuals = y - yhat;
sse = norm(residuals)^2;
mse = sse./dfe;
ri = R\eye(p);
xtxi = ri*ri';
covb = xtxi*mse;
se = sqrt(diag(covb));
% t-statistic, pvalue (from distribution)
t = beta./se;
pval = 2*(tcdf(-abs(t),dfe));
% keep rsquared, betas, and pvalues
rsqu(i) = 1 - sse./sst;
betas(i,:) = beta;
pvals(i,:) = pval;
end
% plot the three matrices -- here, we only show upper triangle
s = zeros(1,3);
tnames = {'beta_i','beta_j','beta_{ij}'};
figure;
for i = 1:3
m = zeros(n);
m(triu(ones(n),1) > 0) = betas(:,i);
s(i) = subplot(1,3,i); imagesc(m); title(tnames{i}); xlabel('parcels'); ylabel('parcels');
end
set(s,'clim',[-max(abs(m(:))),max(abs(m(:)))]*0.25);
drawnow;
end

fit_models.m at commit f9f6238, no license · at the source

Overview

Authors: Haily Merritt^1,2, Amanda Mejia³, Richard Betzel^1,4,5,6

ORCID iDs: Richard Betzel

Cognitive Science Program, Indiana University, Bloomington, IN, USA
School of Informatics, Computing, and Engineering, Indiana University, Bloomington, IN, USA
Department of Statistics, Indiana University, Bloomington, IN, USA
Department of Neuroscience, University of Minnesota, Minneapolis, MN, USA
Masonic Institute for the Developing Brain, University of Minnesota, Minneapolis, MN, USA
Department of Psychological and Brain Sciences, Indiana University, Bloomington, IN, USA

Institutions: Indiana University Bloomington (United States); Indiana University (United States); University of Minnesota (United States)

Journal: iScience, volume 29, issue 6, article 115949

Dates: received 19 September 2024; accepted 27 April 2026; published online 22 May 2026

Type: Research article · Language: English

License: CC BY-NC-ND

Identifiers: DOI 10.1016/j.isci.2026.115949 · PMID 42231974 · PMCID PMC13224015 · OpenAlex W4402098305

Open access: gold, a free copy (OpenAlex)

Preprint: doi:10.1101/2024.08.29.609259

Status: code verified (how the code is found and verified)

Methods: Spectral & time-frequency, Statistics, Preprocessing, Graphs, Single-unit activity, calcium imaging, Smoothing, state filtering, decompositions

Keywords: natural sciences, biological sciences, neuroscience, systems neuroscience, techniques in neuroscience

Topic: Complex Systems and Time Series Analysis (Economics and Econometrics, Economics, Econometrics and Finance), according to OpenAlex

Funding: Neighborhood Coalition for Shelter; National Science Foundation; National Institute on Aging; National Science Foundation Division of Information and Intelligent Systems (2023985)

Citations: cited by 1 paper (Europe PMC); 96 references in the paper

Research resources: NiLearn RRID:SCR_001362http, MATLAB RRID:SCR_001622https, Freesurfer RRID:SCR_001847https, Brain Connectivity Toolbox RRID:SCR_004841https, fMRIPrep RRID:SCR_016216https

Abstract

The abstract is not reproduced here: the paper's license (CC BY-NC-ND) does not allow it. Read it in the paper, at the publisher or on Europe PMC.

Repositories

Its files are read in the Code ↔ Paper reader above, with 1 match between paragraphs and lines of code.

Zenodo 18377915

License: MIT

State: the link answers, verified on 28 September 2026

Evidence: files inventoried

Size: 1 file

Software Heritage: not checked

Found in: “Data and code availability”

Not found: README, license file, CITATION.cff, environment file, tests, continuous integration, documentation

Tools: Statistics and Machine Learning Toolbox (3 files)

Availability: 1 check, the latest on 28 September 2026: the link answers (HTTP 200)

28 September 2026: the link answers (HTTP 200)

8 files

example_code.m, MATLAB, 98 lines
fcn/fcn_cmaphot.m, MATLAB, 7 lines
fcn/fcn_edgets.m, MATLAB, 33 lines
fcn/fcn_edgets2edgecorr.m, MATLAB, 21 lines
fcn/fcn_node_entropy.m, MATLAB, 26 lines
fcn/fcn_profilesim.m, MATLAB, 21 lines
LICENSE, License, 21 lines
README.md, Text, 19 lines

At the source: doi.org/10.5281/zenodo.18377915

Zenodo 18377883

License: CC-BY-4.0

State: the link answers, verified on 28 September 2026

Evidence: files inventoried

Size: 1 file

Software Heritage: not checked

Found in: “Data and code availability”

Not found: README, license file, CITATION.cff, environment file, tests, continuous integration, documentation

Tools: Statistics and Machine Learning Toolbox (1 file)

Availability: 1 check, the latest on 28 September 2026: the link answers (HTTP 200)

28 September 2026: the link answers (HTTP 200)

2 files

fit_models.m, MATLAB, 120 lines
README.md, Text, 34 lines

At the source: doi.org/10.5281/zenodo.18377883

brain-networks/ets_glms

License: none: the authors keep all their rights

State: the link answers, verified on 28 September 2026

Evidence: files inventoried

Commit: f9f6238da55c6121880a412c901db56888a95f2b, 14 November 2025

Languages: MATLAB (1)

Size: 3 files, 1 script

Software Heritage: not archived

Found in: the Zenodo archive record

Holds: README

Not found: license file, CITATION.cff, environment file, tests, continuous integration, documentation

Tools: Statistics and Machine Learning Toolbox (1 file)

Availability: 1 check, the latest on 28 September 2026: the link answers

28 September 2026: the link answers

2 files

fit_models.m, MATLAB, 120 lines, 1 match
README.md, Text, 34 lines

At the source: github.com/brain-networks/ets_glms/tree/v0.1

brain-networks/edge-centric_demo

License: MIT

State: the link answers, verified on 28 September 2026

Evidence: files inventoried

Commit: 87f1b65890274f63b97dc62e647bd730321d58a9, 6 November 2020

Languages: MATLAB (6)

Size: 12 files, 6 scripts

Software Heritage: archived

Found in: the Zenodo archive record

Holds: README, license file

Not found: CITATION.cff, environment file, tests, continuous integration, documentation

Tools: Statistics and Machine Learning Toolbox (3 files)

Availability: 1 check, the latest on 28 September 2026: the link answers

28 September 2026: the link answers

8 files

example_code.m, MATLAB, 98 lines
fcn/fcn_cmaphot.m, MATLAB, 7 lines
fcn/fcn_edgets.m, MATLAB, 33 lines
fcn/fcn_edgets2edgecorr.m, MATLAB, 21 lines
fcn/fcn_node_entropy.m, MATLAB, 26 lines
fcn/fcn_profilesim.m, MATLAB, 21 lines
LICENSE, License, 21 lines
README.md, Text, 19 lines

At the source: github.com/brain-networks/edge-centric_demo/tree/v0.1

The paper's code and data availability statement is in the Data section.

Tracing map

Proposed by the machine: these links were found in the paper and verified at the source, without human review. The map will receive a Zenodo DOI once one of the paper's authors has validated it with their ORCID.

What the map holds:

4 repositories of the authors' code, each at its verified commit, with its license and how the link was found in the paper;
14 scripts, each with its path and the digest of its content;
1 match between paragraphs of the paper and lines of the code (method lexical-v1);
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

Datasets cited

data.mendeley.com/datasets/922xsfxh2g, at Mendeley Data; found in “Data and code availability”
figshare:7272617, at figshare; found in “Data and code availability”
humanconnectome.org/study/hcp-young-adult, at Human Connectome Project; found in the text, “Functional preprocessing”

Availability statements

The paper has a code and data availability statement and a code and data availability statement. Its license (CC BY-NC-ND) does not allow reproducing them here; in short, from what the harvester recognized in them:

they point to 2 datasets: data.mendeley.com/datasets/922xsfxh2g, figshare 7272617
they point to the authors' code: Zenodo 18377883, Zenodo 18377915
they say that the data are available on request

Read them in the paper: doi.org/10.1016/j.isci.2026.115949.

Versions

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Version 2, 28 September 2026

Authors: added Richard Betzel (0000-0001-9200-1681); removed Richard Betzel

Version 1, 28 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 3 authors, 5 keywords, 4 funders, 89 references, 5 RRIDs.

Cite

This paper

Merritt, H., Mejia, A., & Betzel, R. (2026). The dual interpretation of edge time series: Time-varying connectivity versus statistical interaction. iScience, 29(6), 115949. https://doi.org/10.1016/j.isci.2026.115949

BibTeX

@article{merritt2026dual, author = {Merritt, Haily and Mejia, Amanda and Betzel, Richard}, title = {{The dual interpretation of edge time series: Time-varying connectivity versus statistical interaction}}, journal = {iScience}, year = {2026}, month = may, volume = {29}, number = {6}, pages = {115949}, publisher = {Elsevier}, issn = {2589-0042}, doi = {10.1016/j.isci.2026.115949}, url = {https://doi.org/10.1016/j.isci.2026.115949}, pmid = {42231974}, pmcid = {PMC13224015} }

RIS

TY - JOUR AU - Merritt, Haily AU - Mejia, Amanda AU - Betzel, Richard TI - The dual interpretation of edge time series: Time-varying connectivity versus statistical interaction T2 - iScience J2 - iScience PY - 2026 DA - 2026/05/22 VL - 29 IS - 6 SP - 115949 SN - 2589-0042 PB - Elsevier DO - 10.1016/j.isci.2026.115949 UR - https://doi.org/10.1016/j.isci.2026.115949 LA - en ER -

CSL-JSON

{ "id": "10.1016/j.isci.2026.115949", "type": "article-journal", "title": "The dual interpretation of edge time series: Time-varying connectivity versus statistical interaction", "container-title": "iScience", "author": [ { "family": "Merritt", "given": "Haily" }, { "family": "Mejia", "given": "Amanda" }, { "family": "Betzel", "given": "Richard" } ], "container-title-short": "iScience", "volume": "29", "issue": "6", "page": "115949", "DOI": "10.1016/j.isci.2026.115949", "PMID": "42231974", "PMCID": "PMC13224015", "ISSN": "2589-0042", "publisher": "Elsevier", "URL": "https://doi.org/10.1016/j.isci.2026.115949", "language": "en", "issued": { "date-parts": [ [ 2026, 5, 22 ] ] } }

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The dual interpretation of edge time series: Time-varying connectivity versus statistical interaction.

Code ↔ Paper

Paper

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Overview

Abstract

Repositories

Zenodo 18377915

Zenodo 18377883

brain-networks/ets_glms

brain-networks/edge-centric_demo

Tracing map

Data

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Availability statements

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Version 2, 28 September 2026

Version 1, 28 September 2026: the first record

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