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Hi Francesco,
<div><br>
</div>
<div>In summary, you would like to do statistical inference using a cluster-based permutation test, using (delta-Z)coherence as a test statistic, computed between a fixed reference channel (hopefully not an EEG channel) and all other channels.</div>
<div><br>
</div>
<div>With the current state of the fieldtrip code, this will not work out-of-the-box.</div>
<div>The functionality that you require has not been well developed in FieldTrip, see for instance this thread: <a href="https://eur01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fmailman.science.ru.nl%2Fpipermail%2Ffieldtrip%2F2014-September%2F021278.html&data=05%7C02%7Cfieldtrip%40science.ru.nl%7C655b34ee04f344990d3b08ddd4cea6bf%7C084578d9400d4a5aa7c7e76ca47af400%7C1%7C0%7C638900706234576769%7CUnknown%7CTWFpbGZsb3d8eyJFbXB0eU1hcGkiOnRydWUsIlYiOiIwLjAuMDAwMCIsIlAiOiJXaW4zMiIsIkFOIjoiTWFpbCIsIldUIjoyfQ%3D%3D%7C0%7C%7C%7C&sdata=7Qiqa1X8k4Kjs3ciq7jAZ4fqE0s%2FRrEWq086JBhrME0%3D&reserved=0" originalsrc="https://mailman.science.ru.nl/pipermail/fieldtrip/2014-September/021278.html">https://mailman.science.ru.nl/pipermail/fieldtrip/2014-September/021278.html</a></div>
<div><br>
</div>
<div>Given the lack of interest in general for this specific way of doing statistical inference, there has been little incentive to ensure that the data bookkeeping is consistent (i.e. reshaping vectors back into appropriately sized matrices etc). An added
complication in your case, is the fact that the black-box operation that currently converts the input data into a mass-bivariate test-statistic (ft_statfun_indepsamplesZcoh) blows up the dimensionality (going from Nchan to Nchan x Nchan), which indeed makes
it challenging to come up with a good way to interpret (and create) clusters.</div>
<div><br>
</div>
<div>Part of the challenges would go away, if you were to create a version of ft_statfun_indepsampesZcoh that allows for an additional input argument that lists the index of the channel that is to be used as a reference channel, so that the output of the adjusted
’statfun’ will be reshapeable into a Nchan x Nfreq x Ntime matrix, thus subsequently allowing for ’traditional’ spatial clustering. What would be needed in addition, is some ‘glue code’ in the higher level functions: ft_statistics_montecarlo/analytic/etc +
possibly ft_freqstatistics to translate a meaningfully named cfg option (e.g.: cfg.refchannel, which as a default value could be defined as ‘all’) into a vector/scalar of indices that is then passed as input into ft_statfun_indepsamplesZcoh)</div>
<div><br>
</div>
<div>I think I tried something like this once in the past, but I don’t remember why this did not make it into FT. </div>
<div><br>
</div>
<div>See below (with no guarantee that it works, nor that it - if it works - the results are correct) for some inspiration. Note that the example code probably will not treat data with more than a singleton time point in a correct way.</div>
<div><br>
</div>
<div>If you decide to pursue this, please feel free to submit an improved version of the code as a PR on our github repo.</div>
<div><br>
</div>
<div>Best wishes,</div>
<div>Jan-Mathijs</div>
<div><br>
</div>
<div><br>
</div>
<div><br>
</div>
<div>===============================</div>
<div><br>
</div>
<div>
<div>function [s,cfg] = statfun_indepsamplesZcoh(cfg, dat, design);</div>
<div><br>
</div>
<div>% STATFUN_indepsamplesZcoh calculates the independent samples coherence Z-statistic </div>
<div>% on the biological data in dat (the dependent variable), using the information on </div>
<div>% the independent variable (iv) in design.</div>
<div>%</div>
<div>% The external interface of this function has to be</div>
<div>% [s,cfg] = statfun_indepsamplesT(cfg, dat, design);</div>
<div>% where</div>
<div>% dat contains the biological data, Nsamples x Nreplications</div>
<div>% dat must contain fourier representations. </div>
<div>% design contains the independent variable (iv), Nfac x Nreplications</div>
<div>%</div>
<div>% Configuration options:</div>
<div>% cfg.computestat = 'yes' or 'no', calculate the statistic (default='yes')</div>
<div>% cfg.computecritval = 'yes' or 'no', calculate the critical values of the test statistics (default='no')</div>
<div>% cfg.computepval = 'yes' or 'no', calculate the p-values (default='no')</div>
<div>%</div>
<div>% The following options are relevant if cfg.computecritval='yes' and/or</div>
<div>% cfg.computepval='yes'.</div>
<div>% cfg.alpha = critical alpha-level of the statistical test (default=0.05)</div>
<div>% cfg.tail = -1, 0, or 1, left, two-sided, or right (default=1)</div>
<div>% cfg.tail in combination with cfg.computecritval='yes'</div>
<div>% determines whether the critical value is computed at</div>
<div>% quantile cfg.alpha (with cfg.tail=-1), at quantiles</div>
<div>% cfg.alpha/2 and (1-cfg.alpha/2) (with cfg.tail=0), or at</div>
<div>% quantile (1-cfg.alpha) (with cfg.tail=1).</div>
<div>%</div>
<div><br>
</div>
<div>% Copyright (C) 2006, Eric Maris</div>
<div>%</div>
<div>% $Log: statfun_indepsamplesZcoh.m,v $</div>
<div>% Revision 1.3 2006/05/17 11:59:55 erimar</div>
<div>% Corrected bugs after extensive checking of the properties of this</div>
<div>% statfun.</div>
<div>%</div>
<div>% Revision 1.2 2006/05/12 15:32:40 erimar</div>
<div>% Added functionality to calculate one- and two-sided critical values and</div>
<div>% p-values.</div>
<div>%</div>
<div>% Revision 1.1 2006/05/05 13:06:47 erimar</div>
<div>% First version of statfun_indepsamplesZcoh.</div>
<div>%</div>
<div><br>
</div>
<div>% set defaults</div>
<div>if ~isfield(cfg, 'computestat'), cfg.computestat ='yes'; end;</div>
<div>if ~isfield(cfg, 'computecritval'), cfg.computecritval ='no'; end;</div>
<div>if ~isfield(cfg, 'computepval'), cfg.computepval ='no'; end;</div>
<div>if ~isfield(cfg, 'alpha'), cfg.alpha =0.05; end;</div>
<div>if ~isfield(cfg, 'tail'), cfg.tail =1; end;</div>
<div>if ~isfield(cfg, 'ivar'), cfg.ivar =1; end;</div>
<div><br>
</div>
<div>% perform some checks on the configuration</div>
<div>if strcmp(cfg.computepval,'yes') & strcmp(cfg.computestat,'no')</div>
<div> error('P-values can only be calculated if the test statistics are calculated.');</div>
<div>end;</div>
<div><br>
</div>
<div>% original data</div>
<div>nsgn = cfg.dim(1);</div>
<div>if length(cfg.dim)>1,</div>
<div> nfrq = cfg.dim(2);</div>
<div>else</div>
<div> nfrq = 1;</div>
<div>end</div>
<div>if length(cfg.dim)>2,</div>
<div> ntim = cfg.dim(3);</div>
<div>else</div>
<div> ntim = 1;</div>
<div>end</div>
<div><br>
</div>
<div>if ~isfield(cfg, 'cmbindx'), </div>
<div> cmb1 = 1:nsgn;</div>
<div> cmb2 = 1:nsgn;</div>
<div> cmbindx = reshape(1:(length(cmb1)*length(cmb2)),[length(cmb1) length(cmb2)]);</div>
<div> cmbindx = tril(cmbindx, -1);</div>
<div> cmbindx = cmbindx(:);</div>
<div> cmbindx(find(cmbindx==0)) = [];</div>
<div> ncmb = length(cmbindx);</div>
<div>else</div>
<div> cmb1 = unique(cfg.cmbindx(:,1));</div>
<div> cmb2 = unique(cfg.cmbindx(:,2)); </div>
<div> ncmb = size(cfg.cmbindx,1);</div>
<div> tmpcmbindx = reshape(1:(length(cmb1)*length(cmb2)),[length(cmb1) length(cmb2)]);</div>
<div> for kk = 1:ncmb</div>
<div> cmbindx(kk, 1) = tmpcmbindx(find(cmb1==cfg.cmbindx(kk,1)), ...</div>
<div> find(cmb2==cfg.cmbindx(kk,2)));</div>
<div> end</div>
<div>end</div>
<div><br>
</div>
<div>% perform some checks on the design</div>
<div>selc1 = find(design(cfg.ivar,:)==1);</div>
<div>selc2 = find(design(cfg.ivar,:)==2);</div>
<div>nreplc1 = length(selc1);</div>
<div>nreplc2 = length(selc2);</div>
<div>nrepl = nreplc1 + nreplc2;</div>
<div>if nrepl<size(design,2)</div>
<div> error('Invalid specification of the independent variable in the design array.');</div>
<div>end;</div>
<div>if nreplc1<2 | nreplc2<2</div>
<div> error('Every condition must contain at least two trials/tapers.');</div>
<div>end;</div>
<div>dfc1 = nreplc1*2;</div>
<div>dfc2 = nreplc2*2;</div>
<div><br>
</div>
<div>if strcmp(cfg.computestat, 'yes')</div>
<div> tmpstat = zeros(ncmb, nfrq);</div>
<div> for j = 1:nfrq</div>
<div> tmpdat = dat([j-1]*nsgn+1:j*nsgn, :); </div>
<div> % compute the statistic </div>
<div> </div>
<div> %---condition 1</div>
<div> csdc1 = tmpdat(cmb1,selc1)*tmpdat(cmb2,selc1)'/nreplc1;</div>
<div> powerc11 = mean(abs(tmpdat(cmb1,selc1)).^2,2);</div>
<div> powerc12 = mean(abs(tmpdat(cmb2,selc1)).^2,2)';</div>
<div> csdc1 = csdc1./sqrt(powerc11*powerc12);</div>
<div> </div>
<div> %---condition 2</div>
<div> csdc2 = tmpdat(cmb1,selc2)*tmpdat(cmb2,selc2)'/nreplc2;</div>
<div> powerc21 = mean(abs(tmpdat(cmb1,selc2)).^2,2);</div>
<div> powerc22 = mean(abs(tmpdat(cmb2,selc2)).^2,2)';</div>
<div> csdc2 = csdc2./sqrt(powerc21*powerc22);</div>
<div> </div>
<div> %---bias-correction</div>
<div> biasc1 = 1./(dfc1-2);</div>
<div> biasc2 = 1./(dfc2-2);</div>
<div> denomZ = sqrt(1./(dfc1-2) + 1./(dfc2-2));</div>
<div> tmp = (atanh(abs(csdc1))-biasc1-atanh(abs(csdc2))+biasc2)./denomZ;</div>
<div> tmp = tmp(:);</div>
<div> tmpstat(:,j) = tmp(cmbindx);</div>
<div> end</div>
<div> s.stat = tmpstat;</div>
<div>end</div>
<div><br>
</div>
<div>if strcmp(cfg.computecritval,'yes')</div>
<div> % also compute the critical values</div>
<div> if cfg.tail==-1</div>
<div> s.critval = norminv(cfg.alpha);</div>
<div> elseif cfg.tail==0</div>
<div> s.critval = [norminv(cfg.alpha/2),norminv(1-cfg.alpha/2)];</div>
<div> elseif cfg.tail==1</div>
<div> s.critval = norminv(1-cfg.alpha);</div>
<div> end;</div>
<div>end</div>
<div><br>
</div>
<div>if strcmp(cfg.computepval,'yes')</div>
<div> % also compute the p-values</div>
<div> if cfg.tail==-1</div>
<div> s.pval = normcdf(s.stat);</div>
<div> elseif cfg.tail==0</div>
<div> s.pval = 2*normcdf(-abs(s.stat));</div>
<div> elseif cfg.tail==1</div>
<div> s.pval = 1-normcdf(s.stat);</div>
<div> end;</div>
<div>end</div>
</div>
<div><br>
</div>
<div><br>
</div>
<div>===============================</div>
<div><br>
</div>
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<blockquote type="cite">
<div>On 18 Jul 2025, at 15:23, Francesco Torricelli via fieldtrip <fieldtrip@science.ru.nl> wrote:</div>
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<p class="MsoNormal" style="margin:12pt 0cm 8pt;text-align:justify;line-height:115%;font-size:12pt;font-family:Aptos,sans-serif">
<span lang="EN-US" style="font-size:10pt;line-height:115%;font-family:Arial,sans-serif">Dear FieldTrip Community,</span></p>
<div style="margin: 12pt 0cm 8pt; text-align: justify; line-height: 115%; font-size: 12pt; font-family: Aptos, sans-serif;">
<span lang="EN-US" style="font-size:10pt;line-height:115%;font-family:Arial,sans-serif"> </span><br class="webkit-block-placeholder">
</div>
<p class="MsoNormal" style="margin:12pt 0cm 8pt;text-align:justify;line-height:115%;font-size:12pt;font-family:Aptos,sans-serif">
<span lang="EN-US" style="font-size:10pt;line-height:115%;font-family:Arial,sans-serif">We would like to test differences in coherence at the single-subject level (i.e., with trial as unit-of-observation) with cluster-based permutation test. To do this, we
thought we could use the function </span><span lang="EN-US" style="font-size:10pt;line-height:115%;font-family:Consolas">ft_freqstatistics</span><span lang="EN-US" style="font-size:10pt;line-height:115%;font-family:Arial,sans-serif"> combined with
</span><span lang="EN-US" style="font-size:10pt;line-height:115%;font-family:Consolas">statfun_indepsamplesZcoh</span><span lang="EN-US" style="font-size:10pt;line-height:115%;font-family:Arial,sans-serif">. However, when running the code, we get an error,
which is probably due to the fact that </span><span lang="EN-US" style="font-size:10pt;line-height:115%;font-family:Consolas">statfun_indepsamplesZcoh</span><span lang="EN-US" style="font-size:10pt;line-height:115%;font-family:Arial,sans-serif"> works on channels
combinations. It is therefore non-obvious how to form clusters in the spatial dimension.
</span><span lang="EN-US" style="font-size:10pt;line-height:115%;font-family:Arial,sans-serif">Since we are interested in computing coherence between just one channel <i>j</i> and all the other channels <i>N-j</i>, we would like to form clusters in the spatial
dimension across the <i>N-j</i> channels (plus the frequency and time dimensions). Has anyone in this community ever dealt with this kind of issue before? And, if so, how did you manage to solve the problem?</span></p>
<p class="MsoNormal" style="margin:12pt 0cm 8pt;text-align:justify;line-height:115%;font-size:12pt;font-family:Aptos,sans-serif">
<span lang="EN-US" style="font-size:10pt;line-height:115%;font-family:Arial,sans-serif">Here is a more detailed description of how the input data looks like (</span><span lang="EN-US" style="font-size:10pt;line-height:115%;font-family:Consolas">data1</span><span lang="EN-US" style="font-size:10pt;line-height:115%;font-family:Arial,sans-serif">
and </span><span lang="EN-US" style="font-size:10pt;line-height:115%;font-family:Consolas">data2</span><span lang="EN-US" style="font-size:10pt;line-height:115%;font-family:Arial,sans-serif">, one for each condition):</span></p>
</div>
<div><span id="cid:ii_md8tig3a0"><structure.png></span></div>
<div><span lang="EN-US" style="text-align:justify;font-size:10pt;line-height:115%;font-family:Arial,sans-serif">Both
</span><span lang="EN-US" style="text-align:justify;font-size:10pt;line-height:115%;font-family:Consolas">data1</span><span lang="EN-US" style="text-align:justify;font-size:10pt;line-height:115%;font-family:Arial,sans-serif"> and
</span><span lang="EN-US" style="text-align:justify;font-size:10pt;line-height:115%;font-family:Consolas">data2</span><span lang="EN-US" style="text-align:justify;font-size:10pt;line-height:115%;font-family:Arial,sans-serif"> structures are the output of
</span><span lang="EN-US" style="text-align:justify;font-size:10pt;line-height:115%;font-family:Consolas">ft_freqanalysis</span><span lang="EN-US" style="text-align:justify;font-size:10pt;line-height:115%;font-family:Arial,sans-serif">.</span><br>
</div>
<p class="MsoNormal" style="margin:12pt 0cm 8pt;text-align:justify;line-height:115%;font-size:12pt;font-family:Aptos,sans-serif">
<span lang="EN-US" style="font-size:10pt;line-height:115%;font-family:Arial,sans-serif">What follows is the code we used:</span></p>
<p class="MsoNormal" style="margin:12pt 0cm 0cm;line-height:normal;font-size:12pt;font-family:Aptos,sans-serif">
<span lang="EN-US" style="font-size:10pt;font-family:Consolas">cfg = [];</span></p>
<div style="margin: 0cm; line-height: normal; font-size: 12pt; font-family: Aptos, sans-serif;">
<span lang="EN-US" style="font-size:10pt;font-family:Consolas">cfg.method =
<span style="color:rgb(167,9,245)">'montecarlo'</span>;</span></div>
<div style="margin: 0cm; line-height: normal; font-size: 12pt; font-family: Aptos, sans-serif;">
<span lang="EN-US" style="font-size:10pt;font-family:Consolas">cfg.parameter =
<span style="color:rgb(167,9,245)">'fourierspctrm'</span>;</span></div>
<div style="margin: 0cm; line-height: normal; font-size: 12pt; font-family: Aptos, sans-serif;">
<span lang="EN-US" style="font-size:10pt;font-family:Consolas">cfg.statistic =
<span style="color:rgb(167,9,245)">'indepsamplesZcoh'</span>;</span></div>
<div style="margin: 0cm; line-height: normal; font-size: 12pt; font-family: Aptos, sans-serif;">
<span lang="EN-US" style="font-size:10pt;font-family:Consolas">cfg.correctm =
<span style="color:rgb(167,9,245)">'cluster'</span>;</span></div>
<div style="margin: 0cm; line-height: normal; font-size: 12pt; font-family: Aptos, sans-serif;">
<span lang="EN-US" style="font-size:10pt;font-family:Consolas">cfg.clusteralpha = 0.05;</span></div>
<div style="margin: 0cm; line-height: normal; font-size: 12pt; font-family: Aptos, sans-serif;">
<span lang="EN-US" style="font-size:10pt;font-family:Consolas">cfg.clusterstatistic =
<span style="color:rgb(167,9,245)">'maxsum'</span>;</span></div>
<div style="margin: 0cm; line-height: normal; font-size: 12pt; font-family: Aptos, sans-serif;">
<span lang="EN-US" style="font-size:10pt;font-family:Consolas">cfg.minnbchan = 2;</span></div>
<div style="margin: 0cm; line-height: normal; font-size: 12pt; font-family: Aptos, sans-serif;">
<span lang="EN-US" style="font-size:10pt;font-family:Consolas">cfg.neighbours = neighbours;</span></div>
<div style="margin: 0cm; line-height: normal; font-size: 12pt; font-family: Aptos, sans-serif;">
<span lang="EN-US" style="font-size:10pt;font-family:Consolas">cfg.tail = 0;</span></div>
<div style="margin: 0cm; line-height: normal; font-size: 12pt; font-family: Aptos, sans-serif;">
<span lang="EN-US" style="font-size:10pt;font-family:Consolas">cfg.clustertail = 0;</span></div>
<div style="margin: 0cm; line-height: normal; font-size: 12pt; font-family: Aptos, sans-serif;">
<span lang="EN-US" style="font-size:10pt;font-family:Consolas">cfg.alpha = 0.025;</span></div>
<div style="margin: 0cm; line-height: normal; font-size: 12pt; font-family: Aptos, sans-serif;">
<span lang="EN-US" style="font-size:10pt;font-family:Consolas">cfg.numrandomization = 100;</span></div>
<div style="margin: 0cm; line-height: normal; font-size: 12pt; font-family: Aptos, sans-serif;">
<span lang="EN-US" style="font-size:10pt;font-family:Consolas">n_M1_categ1 = size(data1.fourierspctrm, 1);</span></div>
<div style="margin: 0cm; line-height: normal; font-size: 12pt; font-family: Aptos, sans-serif;">
<span lang="EN-US" style="font-size:10pt;font-family:Consolas">n_M1_categ2 = size(data2.fourierspctrm, 1);</span></div>
<div style="margin: 0cm; line-height: normal; font-size: 12pt; font-family: Aptos, sans-serif;">
<span lang="EN-US" style="font-size:10pt;font-family:Consolas">cfg.design = [ones(1,n_M1_categ1), ones(1,n_M1_categ2)*2]';
</span></div>
<p class="MsoNormal" style="line-height:normal;margin:0cm 0cm 8pt;font-size:12pt;font-family:Aptos,sans-serif">
<span lang="EN-US" style="font-size:10pt;font-family:Consolas">cfg.ivar = 1;</span></p>
<div style="margin: 12pt 0cm 8pt; text-align: justify; line-height: 115%; font-size: 12pt; font-family: Aptos, sans-serif;">
<span lang="EN-US" style="font-size:10pt;line-height:115%;font-family:Arial,sans-serif"></span><br class="webkit-block-placeholder">
</div>
<p class="MsoNormal" style="margin:12pt 0cm 8pt;line-height:115%;font-size:12pt;font-family:Aptos,sans-serif">
<span lang="EN-US" style="font-size:10pt;line-height:115%;font-family:Consolas">[stat] = ft_freqstatistics(cfg, data1, data2)</span><span lang="EN-US" style="font-size:10pt;line-height:115%">;</span></p>
<div>
<p class="MsoNormal" style="margin:12pt 0cm 8pt;text-align:justify;line-height:115%;font-size:12pt;font-family:Aptos,sans-serif">
<span lang="EN-US" style="font-size:10pt;line-height:115%;font-family:Arial,sans-serif">It may be helpful to report also that, when running the same code without performing cluster-based correction (i.e.,
</span><span lang="EN-US" style="font-size:10pt;line-height:115%;font-family:Consolas">cfg.correctm =
<span style="color:rgb(167,9,245)">'no'</span></span><span lang="EN-US" style="font-size:10pt;line-height:115%;font-family:Arial,sans-serif">), the
</span><span lang="EN-US" style="font-size:10pt;line-height:115%;font-family:Consolas">stat</span><span lang="EN-US" style="font-size:10pt;line-height:115%;font-family:Arial,sans-serif"> output that we obtain is a row vector with length equal to the number
of channels pairs (</span><span lang="EN-US" style="font-size:10pt;line-height:115%;font-family:Arial,sans-serif">reported in
</span><span lang="EN-US" style="font-size:10pt;line-height:115%;font-family:Consolas">stat.cfg.chancmbindx</span><span lang="EN-US" style="font-size:10pt;line-height:115%;font-family:Arial,sans-serif">) multiplied by the frequency dimension and the time dimension.
This output shape does not correspond to the </span><span lang="EN-US" style="font-size:10pt;line-height:115%;font-family:Consolas">dimord</span><span lang="EN-US" style="font-size:10pt;line-height:115%;font-family:Arial,sans-serif"> field reported in the
</span><span lang="EN-US" style="font-size:10pt;line-height:115%;font-family:Consolas">stat</span><span lang="EN-US" style="font-size:10pt;line-height:115%;font-family:Arial,sans-serif"> structure (i.e.,
</span><span lang="EN-US" style="font-size:10pt;line-height:115%;font-family:Consolas">'</span><span lang="EN-US" style="font-size:10pt;line-height:115%;font-family:Consolas">chancmb_freq_time</span><span lang="EN-US" style="font-size:10pt;line-height:115%;font-family:Consolas">'</span><span lang="EN-US" style="font-size:10pt;line-height:115%;font-family:Arial,sans-serif">).</span></p>
<p class="MsoNormal" style="margin:12pt 0cm 8pt;text-align:justify;line-height:115%;font-size:12pt;font-family:Aptos,sans-serif">
<span lang="EN-US" style="font-size:10pt;line-height:115%;font-family:Arial,sans-serif">Thank you very much for your attention.</span></p>
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<span lang="EN-US" style="font-size:10pt;line-height:115%;font-family:Arial,sans-serif">Best,</span></p>
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<span lang="EN-US" style="font-size:10pt;line-height:115%;font-family:Arial,sans-serif"><br>
</span></p>
<p class="MsoNormal" style="margin:12pt 0cm 8pt;text-align:justify;line-height:115%;font-size:12pt;font-family:Aptos,sans-serif">
<span lang="EN-US" style="font-size:10pt;line-height:115%;font-family:Arial,sans-serif">Francesco Torricelli</span></p>
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<span class="gmail_signature_prefix">-- </span><br>
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<div style="text-align:right"><span style="font-size:large">Francesco Torricelli, MSc, PhD</span><br>
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<div style="text-align:right"><i>Section of Physiology,</i><br>
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<div style="text-align:right"><i>Department of Neuroscience and Rehabilitation,</i></div>
<div style="text-align:right"><i>University of Ferrara</i></div>
<div style="text-align:right"><font size="1">Via Fossato di Mortara 19, </font><span style="font-size:x-small">44121 Ferrara (Italy)</span></div>
<div style="text-align:right"><span style="font-size:x-small">Tel: +39 347 980 9976</span></div>
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https://doi.org/10.1371/journal.pcbi.1002202<br>
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