The amplitude-amplitude cross-frequency coupling method: a step-by-step guide to quantifying physiological network interactions.

Code ↔ Paper

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[1] § Methods › Inter-muscular coupling and network interactions › Global measures of inter-muscular coupling › Additional control analyses for global measures of inter-muscular coupling ↔ allguis/guis/bayesian/Functions/surrogate.m, lines 6–64 · score 0.60 · Fourier phase, amplitude distribution, randomization, nonlinear, surrogate, correlations

Paper

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The authors' code

MATLAB · 398 lines · 12 KB · GPL-3.0 · 1 match

%funcion generating surrogates: read further for different methods,
%most common is random permutation 'RP' or phase shuffle 'FT'.
%N= munber of surrogates to generate
function [surr,varargout] = surrogate(signal,N,varargin)
[m,L]=size(signal);
surr=zeros(N,L);
if nargin>2
method=varargin{1};
else
method='RP';
end
if strcmp(method,'RP') % Random Permutation surrogates
%New data are created simply by random permutations of the original series.
% The permutations guarantee the same amplitude distribution than the original series,
% but destroy any linear correlation. This method is associated to the null hypothesis of the
% data being uncorrelated noise (possibly Gaussian and measured by a static nonlinear function
for k=1:N
surr(k,:)=signal(randperm(L));
end
elseif strcmp(method,'FT') % FT surrogates
% Random Phases; also known as FT, for Fourier Transform):
% In order to preserve the linear correlation (the periodogram) of the series,
% surrogate data are created by the inverse Fourier Transform of the modules of Fourier Transform
% of the original data with new (uniformly random) phases. If the surrogates must be real,
% the Fourier phases must be antisymmetric with respect to the central value of data.
ll=ceil(L/2);
ftsig=fft(signal,L);
for k=1:N
surr(k,1)=ftsig(1); randph=2*pi*randgen(1,ll-1);
surr(k,2:ll)=ftsig(2:ll).*exp(1i*randph);
surr(k,2+L-ll:L)=conj(fliplr(surr(k,2:ll)));
surr(k,:)=real(ifft(surr(k,:),L));
endnono
end
elseif strcmp(method,'AAFT') % AAFT surrogates Amplitude Adjusted Fourier Transform):
% This method has approximately the advantages of the two previous ones: it tries to
% preserve both the linear structure and the amplitude distribution.
ll=ceil(L/2);
sigma=std(signal);
[sortsig,sortind]=sort(signal); rankind(sortind)=1:L;
rescrank=zeros(1,L);
for k=1:N
rgs=sort(randgen(1,L,0,sigma));
rescsig=rgs(rankind);
ftresc=fft(rescsig,L);
surr(k,1)=ftresc(1); randph=2*pi*randgen(1,ll-1);
%surr(k,2:ll)=abs(ftresc(2:ll)).*exp(1i*randph); % should we randomize all phases, since there might be some bias?
surr(k,2:ll)=ftresc(2:ll).*exp(1i*randph);
surr(k,2+L-ll:L)=conj(fliplr(surr(k,2:ll)));
surr(k,:)=real(ifft(surr(k,:),L));
[~,rescind]=sort(surr(k,:)); rescrank(rescind)=1:L;
surr(k,:)=sortsig(rescrank);
end
elseif strcmp(method,'AAFTFT') % AAFT with FT distribution instead of noise
ll=ceil(L/2);
ftsig=fft(signal,L);
[sortsig,sortind]=sort(signal); rankind(sortind)=1:L;
rescrank=zeros(1,L);
for k=1:N
surr(k,1)=ftsig(1); randph=2*pi*randgen(1,ll-1);
surr(k,2:ll)=ftsig(2:ll).*exp(1i*randph);
surr(k,2+L-ll:L)=conj(fliplr(surr(k,2:ll)));
surr(k,:)=real(ifft(surr(k,:),L));
rgs=sort(surr(k,:));
rescsig=rgs(rankind);
ftresc=fft(rescsig,L);
surr(k,1)=ftresc(1); randph=2*pi*randgen(1,ll-1);
surr(k,2:ll)=ftresc(2:ll).*exp(1i*randph);
surr(k,2+L-ll:L)=conj(fliplr(surr(k,2:ll)));
surr(k,:)=real(ifft(surr(k,:),L));
[~,rescind]=sort(surr(k,:)); rescrank(rescind)=1:L;
surr(k,:)=sortsig(rescrank);
end
elseif strcmp(method,'IAAFT') % IAAFT2 (exact spectrum), PS first seed
% Iterative Amplitude Adjusted Fourier Transform): This algorithm is an iterative version of AAFT.
% The steps are repeated until the autocorrelation function is sufficiently similar to the original,
% or until there is no change in the amplitudes.
maxitn=1000; % maximum number of iterations
[sortsig,sortind]=sort(signal); rankind(sortind)=1:L;
ftsig=fft(signal,L);
ovitn=0;
for k=1:N
surr(k,:)=signal(randperm(L));
itn=1; iterrank=rankind; olditrank=zeros(1,L);
while (max(abs(olditrank-iterrank))~=0 & itn<maxitn)
olditrank=iterrank;
iterf=real(ifft(abs(ftsig).*exp(1i*angle(fft(surr(k,:),L))))); % replace Fourier amplitudes (real() since makes mistakes of order \epsilon)
[~,iterind]=sort(iterf); iterrank(iterind)=1:L;
surr(k,:)=sortsig(iterrank);
itn=itn+1;
end
ovitn=ovitn+itn;
surr(k,:)=iterf;
end
ovitn=ovitn/N;
elseif strcmp(method,'IAAFT1') % IAAFT1 (exact distribution), PS first seed
maxitn=1000; % maximum number of iterations
[sortsig,sortind]=sort(signal); rankind(sortind)=1:L;
ftsig=fft(signal,L);
ovitn=0;
for k=1:N
surr(k,:)=signal(randperm(L));
itn=1; iterrank=rankind; olditrank=zeros(1,L);
while (max(abs(olditrank-iterrank))~=0 & itn<maxitn)
olditrank=iterrank;
iterf=real(ifft(abs(ftsig).*exp(1i*angle(fft(surr(k,:)))))); % replace Fourier amplitudes
[~,iterind]=sort(iterf); iterrank(iterind)=1:L;
surr(k,:)=sortsig(iterrank);
itn=itn+1;
end
ovitn=ovitn+itn;
end
ovitn=ovitn/N; % overall number of iterations
elseif strcmp(method,'TS') % TS: twin surrogates
% %this technique generates surrogates which correspond to an inde-pendent copy
% of the underlying system, i. e. they induce a trajectory of the underlying
% systemstarting at di?erent initial conditions. We show that these surrogates are
% well suited to test forcomplex synchronisation
if nargin>3
dL=varargin{2};
else
dL=L;
end
alpha=0.1;
Rij=zeros(L,L);
for k=2:L
Rij(k,1:k-1)=max(abs(signal(:,1:k-1)-signal(:,k)*ones(1,k-1)));
end
Rij=Rij+Rij';
[~,pl]=min(Rij(1:round(L/2),L));
Sij=sort(Rij(:)); delta=Sij(round(alpha*L^2)); clear Sij;
Rij(Rij<delta)=-1; Rij(Rij>delta)=0; Rij=abs(Rij);
ind=cell(L,1); eln=zeros(L,1); twind=1:L;
remp=1; % remaining points
while ~isempty(remp)
twn=remp(1);
ind{twn}=remp(max(abs(Rij(:,remp)-Rij(:,twn)*ones(1,numel(remp))))==0);
ind(ind{twn})=ind(twn);
eln(ind{twn})=length(ind{twn});
twind(ind{twn})=0;
remp=twind(twind>0);
end
clear Rij twind;
for sn=1:N
kn=randi(L,1)-1;
for j=1:dL
kn=kn+1;
surr(sn,j)=signal(1,kn);
kn=ind{kn}(randi(eln(kn),1));
if kn==L
kn=pl;
end
end
end
elseif strcmp(method,'PPS') % PPS surrogates
% can distinguish between a noisy periodic
% orbit and deterministic non-periodic inter-cycle dynamics. Possible origins of deterministic nonperiodic
% inter-cycle dynamics include: non-periodic linear or nonlinear dynamics, or chaos. This
% new algorithm is based on mimicking the large-scale dynamics with a local model, but obliterating
% the fine scale features with dynamic noise.
if nargin>3
dL=varargin{2};
else
dL=L;
end
ssig=zeros(1,L); mind=zeros(1,L);
for k=1:L
matr=max(abs(signal(:,:)-signal(:,k)*ones(1,L)));
[ssig(k),mind(k)]=min(matr(matr>0));
end
[~,pl]=min(matr(1:round(L/2))); rho=0.7*mean(ssig); clear mind ssig;
if m==1
for sn=1:N
kn=randi(L,1)-1;
for j=1:dL
kn=kn+1;
surr(sn,j)=signal(1,kn);
sigdist=abs(signal-(signal(kn)+randgen(1,1,0,rho)));
[~,kn]=min(sigdist);
if kn==L
kn=pl;
end
end
end
else
%bt=0; flag=0;
for sn=1:N
kn=randi(L,1)-1;
for j=1:dL
kn=kn+1;
%knold=kn;
surr(sn,j)=signal(1,kn);
sigdist=max(abs(signal(:,:)-(signal(:,kn)+randgen(m,1,0,rho))*ones(1,L)));
[~,kn]=min(sigdist);
if kn==L
kn=pl;
end
%{
if knold==kn
flag=flag+1;
else
if flag==1
bt=bt+1;
end
flag=0;
end
%}
end
end
end
elseif strcmp(method,'CPP') % cycle phase permutation surrogates
signal=mod(signal,2*pi);
dcpoints=find(signal(2:end)-signal(1:end-1)<-pi);
NC=length(dcpoints)-1;
if NC>0
cycles=cell(NC,1);
for k=1:NC
cycles{k}=signal(dcpoints(k)+1:dcpoints(k+1));
end
stcycle=signal(1:dcpoints(1));
endcycle=signal(dcpoints(k+1)+1:end);
for sn=1:N
surr(sn,:)=unwrap(horzcat(stcycle,cycles{randperm(NC)},endcycle));
end
else
for sn=1:N
surr(sn,:)=unwrap(signal);
end
end
elseif strcmp(method,'MCPP') % cycle phase permutation surrogates
signal=mod(signal,2*pi);
dcpoints=find(signal(2:end)-signal(1:end-1)<-pi);
fcpoints=find(signal(2:end)-signal(1:end-1)>pi);
NC=length(dcpoints)-1;
if NC>1
cycles=cell(NC+1,1);
cycles{1}=signal(1:dcpoints(1));
cn=1;
for k=1:NC
if isempty(fcpoints(fcpoints>dcpoints(k) & fcpoints<dcpoints(k+1)))
cn=cn+1;
cycles{cn}=signal(dcpoints(k)+1:dcpoints(k+1));
else
cycles{cn}=horzcat(cycles{cn},signal(dcpoints(k)+1:dcpoints(k+1)));
end
end
stcycle=cycles{1};
endcycle=signal(dcpoints(end)+1:end);
cycles=cycles(2:cn);
for sn=1:N
surr(sn,:)=unwrap(horzcat(stcycle,cycles{randperm(cn-1)},endcycle));
end
else
for sn=1:N
surr(sn,:)=unwrap(signal);
end
end
elseif strcmp(method,'tshift') % time shift permutation surrogates
for sn=1:N
if nargin>3
startp=varargin{2};
else
startp=randi(L-1,1);
end
surr(sn,:)=horzcat(signal(1+startp:L),signal(1:startp));
if nargout>1
varargout{1}(sn)=startp;
end
end
elseif strcmp(method,'tshift2') % time shift permutation surrogates
cutp=ceil(L/2);
surr=zeros(N,cutp);
for sn=1:N
if nargin>3
startp=varargin{2};
else
startp=randi(L-cutp,1);
end
surr(sn,:)=signal(1+startp:startp+cutp);
end
elseif strcmp(method,'CAAFT') % CAAFT (or STAP with m=1)
ll=ceil(L/2);
ms=mean(signal); sigma=std(signal);
[sortsig,sortind]=sort(signal); rankind(sortind)=1:L;
rescrank=zeros(1,L);
tmax=floor(L/4); p=tmax; K=N; % parameters of CAAFT
y=zeros(1,L); yft=zeros(1,L); z=zeros(1,L);
rx=zeros(1,tmax+1); ry=zeros(1,tmax+1); rz=zeros(1,tmax+1); % autocorrelations
ar=zeros(1,L); arrank=zeros(1,L); arcf=zeros(K,p+1); arstd=zeros(K,1); rw=zeros(K,tmax+1);
for tn=0:tmax % let us take without normalization
rx(tn+1)=mean((signal(1:L-tn)-ms).*(signal(1+tn:L)-ms));
end
for k=1:K
rgs=sort(randgen(1,L,0,sigma));
y=rgs(rankind);
ftresc=fft(y,L);
yft(1)=ftresc(1); randph=2*pi*randgen(1,ll-1);
yft(2:ll)=ftresc(2:ll).*exp(1i*randph);
yft(2+L-ll:L)=conj(fliplr(yft(2:ll)));
yft=ifft(yft,L);
[~,rescind]=sort(yft); rescrank(rescind)=1:L;
z=sortsig(rescrank);
my=mean(y); mz=mean(z);
for tn=0:tmax % let us take without normalization
ry(tn+1)=mean((y(1:L-tn)-my).*(y(1+tn:L)-my));
rz(tn+1)=mean((z(1:L-tn)-mz).*(z(1+tn:L)-mz));
end
cf=polyfit(rz,ry,1);
ru=cf(2)+cf(1)*rx;
[arcf(k,:),arstd(k)]=levinson(ru,p); arstd(k)=sqrt(arstd(k)); arcf(k,:)=-arcf(k,:);
for fn=1:p
for kn=1:fn-1
ar(fn)=ar(fn)+arcf(k,kn+1)*ar(fn-kn);
end
ar(fn)=ar(fn)+randgen(1,1,0,arstd(k));
end
for arn=1+p:L
ar(arn)=ar(arn-p:arn-1)*flipud(arcf(k,2:end)')+randgen(1,1,0,arstd(k));
end
[~,indar]=sort(ar); arrank(indar)=1:L;
w=sortsig(arrank); mw=mean(w);
for tn=0:tmax
rw(k,tn+1)=mean((w(1:L-tn)-mw).*(w(1+tn:L)-mw));
end
end
[~,indm]=min(std(rw-ones(K,1)*rx,0,2));
arcf=arcf(indm,:); arstd=arstd(indm); rw=rw(indm,:);
for k=1:N
for fn=1:p
for kn=1:fn-1
ar(fn)=ar(fn)+arcf(kn+1)*ar(fn-kn);
end
ar(fn)=ar(fn)+randgen(1,1,0,arstd);
end
for arn=1+p:L
ar(arn)=ar(arn-p:arn-1)*flipud(arcf(2:end)')+randgen(1,1,0,arstd);
end
[~,indar]=sort(ar); arrank(indar)=1:L;
surr(k,:)=signal(arrank);
end
end
end

surrogate.m at commit 400ae6b, under GPL-3.0 · at the source

Overview

Authors: Sergi Garcia-Retortillo¹, Óscar Abenza², Yaopeng J X Ma³, Plamen Ch Ivanov^3,4,5

ORCID iDs: Sergi Garcia-Retortillo, Óscar Abenza, Yaopeng J X Ma, Plamen Ch Ivanov

College of Nursing, University of Central Florida, Orlando, FL, United States
Faculty of Medicine and Health Sciences, University of Barcelona, Barcelona, Spain
Keck Laboratory for Network Physiology, Department of Physics, Boston University, Boston, MA, United States
Department of Neurosurgery, Boston University Chobanian and Avedisian School of Medicine, Boston, MA, United States
Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, Sofia, Bulgaria

Institutions: University of Central Florida (United States); Universitat de Barcelona (Spain); Boston University (United States); Bulgarian Academy of Sciences (Bulgaria); Institute of Biophysics and Biomedical Engineering (Bulgaria)

Journal: Frontiers in network physiology, volume 6, article 1784539

Dates: received 9 January 2026; accepted 16 March 2026; published online 10 April 2026

Type: Methods article · Language: English

License: CC BY

Identifiers: DOI 10.3389/fnetp.2026.1784539 · PMID 42039922 · PMCID PMC13105945 · OpenAlex W7153059861

Open access: gold, a free copy (OpenAlex)

Status: code verified

Categories: methods / tools (subfield)

Methods: Spectral & time-frequency, Preprocessing, Machine learning, Connectivity, Complexity, Smoothing, state filtering, decompositions, Evoked potentials, Physiology & signal measures

Keywords: complex systems, dynamic networks, electrocardiography, electromyography, electrophysiology, exercise, network physiology

Topic: Heart Rate Variability and Autonomic Control (Cardiology and Cardiovascular Medicine, Medicine), according to OpenAlex

Citations: cited by 2 papers (Europe PMC); 80 references in the paper

Abstract

The human organism operates as an integrated network in which multiple physiological systems dynamically coordinate across spatial and temporal scales. Quantifying these interactions requires analytical frameworks that move beyond single-system measures and capture multisystem coordination. Here, we present a detailed, step-by-step description of the Amplitude-Amplitude Cross-Frequency Coupling (ACFC) method, a network-based approach designed to quantify coordination among skeletomuscular, cardiovascular, and respiratory systems using simultaneous electrophysiological recordings. ACFC evaluates how the amplitudes of oscillatory components across specific frequency bands co-vary over time, producing three network-based markers: inter-muscular, cardio-muscular, and respiratory-muscular coupling. The method combines spectral decomposition, cross-correlation analyses, and network dynamics to characterize global network organization and coupling strength for distinct physiological states, and the temporal variability in systems coordination and network interactions at short timescales. Beyond quantifying average coupling and network link strength over extended period of time associated with a given physiological state, ACFC enables probing the temporal coordination of physiological rhythms embedded in systems dynamics, as well as the variability and evolution of their network interactions across timescales and states in response to internal and external demands. Using a bodyweight squat protocol as an illustrative example, we outline all analytical steps, parameter choices, and practical considerations required to implement the ACFC method to quantify physiological systems coupling and network interactions. This Methods article provides a reproducible guide for applying ACFC analyses and is intended to facilitate the adoption, adaptation, and extension of network-based approaches to study multisystem coordination in exercise, aging, and broader physiological or clinical contexts in Network Physiology.

Reproduced under the paper's license (CC BY), from the paper cited above.

Repository

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

luphysics/MODA

License: GPL-3.0

State: the link answers, verified on 29 September 2026

Evidence: files inventoried

Commit: 400ae6b8ea8310a24bce02558e3bb242f27bf558, 30 April 2020

Languages: MATLAB (69), Python (1)

Size: 135 files, 70 scripts

Software Heritage: not archived

Found in: the text, “Breathing rate time series”

Holds: README, license file, documentation

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

Tools: Signal Processing Toolbox (8 files), Statistics and Machine Learning Toolbox (8 files)

Availability: 1 check, the latest on 29 September 2026: the link answers

29 September 2026: the link answers

72 files

MODA.m, MATLAB, 111 lines
allguis/codes/Graphics/clear_axes_lines.m, MATLAB, 9 lines
allguis/codes/Graphics/clear_axes_points.m, MATLAB, 14 lines
allguis/codes/Graphics/fillsig.m, MATLAB, 55 lines
allguis/codes/Universal/MODATFAcalc.m, MATLAB, 200 lines
allguis/codes/Universal/MODAclose.m, MATLAB, 23 lines
allguis/codes/Universal/MODAcsvsave.m, MATLAB, 135 lines
allguis/codes/Universal/MODAload.m, MATLAB, 8 lines
allguis/codes/Universal/MODAread.m, MATLAB, 136 lines
allguis/codes/Universal/MODAreadcheck.m, MATLAB, 22 lines
allguis/codes/Universal/MODAsave.m, MATLAB, 13 lines
allguis/codes/Universal/MODAsettings.m, MATLAB, 51 lines
allguis/codes/Universal/imodwt.m, MATLAB, 314 lines
allguis/codes/Universal/matchRotation.m, MATLAB, 27 lines
allguis/codes/Universal/modwt.m, MATLAB, 350 lines
allguis/codes/Universal/newid.m, MATLAB, 568 lines
allguis/codes/Universal/wsurr.m, MATLAB, 42 lines
allguis/codes/cell2csv/cell2csv.m, MATLAB, 115 lines
allguis/codes/ginputc/ginputc.m, MATLAB, 421 lines
allguis/codes/ginputc/ginputc_original.m, MATLAB, 420 lines
allguis/codes/reading/csv_to_mvar.m, MATLAB, 5 lines
allguis/codes/reading/read_from_csv.m, MATLAB, 7 lines
allguis/codes/reading/read_from_mat.m, MATLAB, 7 lines
allguis/guis/bayesian/Bayesian.m, MATLAB, 1,110 lines
allguis/guis/bayesian/Bayesian_old.m, MATLAB, 1,064 lines
allguis/guis/bayesian/Functions/CFprint.m, MATLAB, 64 lines
allguis/guis/bayesian/Functions/MODAbayes_intdelete.m, MATLAB, 114 lines
allguis/guis/bayesian/Functions/MODAbayes_loadfilt.m, MATLAB, 108 lines
allguis/guis/bayesian/Functions/bandpass_butter.m, MATLAB, 18 lines
allguis/guis/bayesian/Functions/bayesPhs.m, MATLAB, 192 lines
allguis/guis/bayesian/Functions/bayes_main.m, MATLAB, 122 lines
allguis/guis/bayesian/Functions/dirc.m, MATLAB, 49 lines
allguis/guis/bayesian/Functions/full_bayesian.m, MATLAB, 52 lines
allguis/guis/bayesian/Functions/loop_butter.m, MATLAB, 44 lines
allguis/guis/bayesian/Functions/surrogate.m, MATLAB, 398 lines, 1 match
allguis/guis/bayesian/Functions/sync_map.m, MATLAB, 164 lines
allguis/guis/bispectrum/Bispectrum.m, MATLAB, 1,607 lines
allguis/guis/bispectrum/Functions/biphaseWavMod.m, MATLAB, 70 lines
allguis/guis/bispectrum/Functions/biphaseWavNew.m, MATLAB, 31 lines
allguis/guis/bispectrum/Functions/bispecWavMod.m, MATLAB, 208 lines
allguis/guis/bispectrum/Functions/bispecWavNew.m, MATLAB, 122 lines
allguis/guis/bispectrum/Functions/bispectrum_analysis.m, MATLAB, 59 lines
allguis/guis/bispectrum/Functions/compareMatrix.m, MATLAB, 14 lines
allguis/guis/bispectrum/Functions/myWt.m, MATLAB, 137 lines
allguis/guis/bispectrum/Functions/python/biphaseWavPython.m, MATLAB, 38 lines
allguis/guis/bispectrum/Functions/python/bispecWavPython.m, MATLAB, 133 lines
allguis/guis/bispectrum/Functions/python/wtAtf2Python.m, MATLAB, 123 lines
allguis/guis/bispectrum/Functions/surrogate.m, MATLAB, 92 lines
allguis/guis/bispectrum/Functions/wavsurrogate.m, MATLAB, 44 lines
allguis/guis/bispectrum/Functions/wtAtf2.m, MATLAB, 123 lines
allguis/guis/bispectrum/Functions/wtAtfMod.m, MATLAB, 103 lines
allguis/guis/coherence/CoherenceMulti.m, MATLAB, 1,757 lines
allguis/guis/coherence/Functions/MODAwpc.m, MATLAB, 332 lines
allguis/guis/coherence/Functions/surrcalc.m, MATLAB, 402 lines
allguis/guis/coherence/Functions/tlphcoh.m, MATLAB, 38 lines
allguis/guis/coherence/Functions/wphcoh.m, MATLAB, 30 lines
allguis/guis/filtering/Filtering.m, MATLAB, 1,390 lines
allguis/guis/filtering/Functions/Fourier.m, MATLAB, 21 lines
allguis/guis/filtering/Functions/MODAridge_filter.m, MATLAB, 172 lines
allguis/guis/filtering/Functions/bandpass_butter.m, MATLAB, 18 lines
allguis/guis/filtering/Functions/ecurve.m, MATLAB, 927 lines
allguis/guis/filtering/Functions/loop_butter.m, MATLAB, 50 lines
allguis/guis/filtering/Functions/rectfr.m, MATLAB, 328 lines
allguis/guis/filtering/Functions/ridge_extraction.m, MATLAB, 22 lines
allguis/guis/tfa/Functions/testwt.m, MATLAB, 6 lines
allguis/guis/tfa/Functions/wft.m, MATLAB, 1,373 lines
allguis/guis/tfa/Functions/wt.m, MATLAB, 1,505 lines
allguis/guis/tfa/Functions/wtwrapper.m, MATLAB, 76 lines
allguis/guis/tfa/TimeFrequencyAnalysis.m, MATLAB, 1,326 lines
scripts/fontsize.py, Python, 81 lines
LICENSE, License, 674 lines
README.md, Text, 124 lines

At the source: github.com/luphysics/MODA

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:

1 repository of the authors' code, each at its verified commit, with its license and how the link was found in the paper;
70 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

No dataset and no data link were found in the paper.

Data availability statement

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Version 1, 29 September 2026: the first record

Recorded: type, language, journal, volume, pages, dates, 4 authors, 7 keywords, 78 references.

Cite

This paper

Garcia-Retortillo, S., Abenza, Ó., Ma, Y. J. X., & Ivanov, P. C. (2026). The amplitude-amplitude cross-frequency coupling method: a step-by-step guide to quantifying physiological network interactions. Frontiers in network physiology, 6, 1784539. https://doi.org/10.3389/fnetp.2026.1784539

BibTeX

@article{garciaretortillo2026amplitude, author = {Garcia-Retortillo, Sergi and Abenza, Óscar and Ma, Yaopeng J X and Ivanov, Plamen Ch}, title = {{The amplitude-amplitude cross-frequency coupling method: a step-by-step guide to quantifying physiological network interactions}}, journal = {Frontiers in network physiology}, year = {2026}, month = apr, volume = {6}, pages = {1784539}, publisher = {Frontiers Media SA}, issn = {2674-0109}, doi = {10.3389/fnetp.2026.1784539}, url = {https://doi.org/10.3389/fnetp.2026.1784539}, pmid = {42039922}, pmcid = {PMC13105945} }

RIS

TY - JOUR AU - Garcia-Retortillo, Sergi AU - Abenza, Óscar AU - Ma, Yaopeng J X AU - Ivanov, Plamen Ch TI - The amplitude-amplitude cross-frequency coupling method: a step-by-step guide to quantifying physiological network interactions T2 - Frontiers in network physiology J2 - Front Netw Physiol PY - 2026 DA - 2026/04/10 VL - 6 SP - 1784539 SN - 2674-0109 PB - Frontiers Media SA DO - 10.3389/fnetp.2026.1784539 UR - https://doi.org/10.3389/fnetp.2026.1784539 LA - en ER -

CSL-JSON

{ "id": "10.3389/fnetp.2026.1784539", "type": "article-journal", "title": "The amplitude-amplitude cross-frequency coupling method: a step-by-step guide to quantifying physiological network interactions", "container-title": "Frontiers in network physiology", "author": [ { "family": "Garcia-Retortillo", "given": "Sergi" }, { "family": "Abenza", "given": "Óscar" }, { "family": "Ma", "given": "Yaopeng J X" }, { "family": "Ivanov", "given": "Plamen Ch" } ], "container-title-short": "Front Netw Physiol", "volume": "6", "page": "1784539", "DOI": "10.3389/fnetp.2026.1784539", "PMID": "42039922", "PMCID": "PMC13105945", "ISSN": "2674-0109", "publisher": "Frontiers Media SA", "URL": "https://doi.org/10.3389/fnetp.2026.1784539", "language": "en", "issued": { "date-parts": [ [ 2026, 4, 10 ] ] } }

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