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<span style="font-size: 12pt;">Dear Dr. Schoffelen, </span></div>
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<span style="font-size: 12pt;">Thank you very much for your reply. </span></div>
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<span style="font-size: 12pt; font-family: Arial, Helvetica, sans-serif;">I hope to clarify some questions that probably needed more description and context. </span></div>
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<span style="font-size: 12pt; font-family: Arial, Helvetica, sans-serif;">I also hope this thread might be useful to someone else in the future and help to support the use of Fieldtrip for EEG connectivity analyses.</span></div>
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<div style="margin-top:0px; margin-bottom:0px; margin-top:0; margin-bottom:0"><span style="font-size: 12pt; font-family: Arial, Helvetica, sans-serif;">I computed the complex fourier spectrum as follows:</span>
</div>
<div style="margin-top:0px; margin-bottom:0px; margin-top:0; margin-bottom:0"><br>
</div>
<div style="margin-top:0px; margin-bottom:0px; margin-top:0; margin-bottom:0">
<p class="p1" style="margin:0px;font:10px Courier">f_o_i=1:0.5:55;</p>
<p class="p1" style="margin:0px;font:10px Courier">cycles=3:10;</p>
<p class="p1" style="margin:0px;font:10px Courier">t_o_i= [-40:100]/40<span class="Apple-converted-space"> </span></p>
<p class="p1" style="margin:0px;font:10px Courier">cfg=[];</p>
<p class="p1" style="margin:0px;font:10px Courier">cfg.method=<span class="s2" style="color: rgb(170, 4, 249);">'wavelet'</span>;</p>
<p class="p1" style="margin:0px;font:10px Courier">cfg.output=<span class="s2" style="color: rgb(170, 4, 249);">'fourier'</span>;</p>
<p class="p1" style="margin:0px;font:10px Courier">cfg.channel=<span class="s2" style="color: rgb(170, 4, 249);">'all'</span> </p>
<p class="p2" style="margin: 0px; font: 10px Courier; color: rgb(2, 128, 9);"><span class="s3" style="color: rgb(0, 0, 0);">cfg.trials=</span><span class="s2" style="color: rgb(170, 4, 249);">'all'</span><span class="s3" style="color: rgb(0, 0, 0);"> </span></p>
<p class="p1" style="margin:0px;font:10px Courier">cfg.keeptrials=<span class="s2" style="color: rgb(170, 4, 249);">'yes'</span>;</p>
<p class="p1" style="margin:0px;font:10px Courier">cfg.keeptapers=<span class="s2" style="color: rgb(170, 4, 249);">'yes'</span>;</p>
<p class="p1" style="margin:0px;font:10px Courier">cfg.foi=f_o_i;</p>
<p class="p1" style="margin:0px;font:10px Courier">cfg.toi=t_o_i;</p>
<p class="p1" style="margin:0px;font:10px Courier">cfg.width=ceil(f_o_i/(size(cycles,2)-1))+2</p>
<p class="p3" style="margin:0px;font:10px Courier;min-height:12px"><span class="Apple-converted-space"> </span></p>
<p class="p1" style="margin:0px;font:10px Courier">[freq] = ft_freqanalysis(cfg, data);</p>
<p class="p1" style="margin:0px;font:10px Courier"><br>
</p>
<p class="p1" style="margin:0px;font:10px Courier"><br>
</p>
</div>
<div style="margin-top:0px; margin-bottom:0px; margin-top:0; margin-bottom:0"><span style="color: rgb(0, 0, 0); background-color: rgb(255, 255, 255); display: inline !important; font-family: Arial, Helvetica, sans-serif;">The output is a 4-D fourier spectrum
with this dimension: 98x180x109x141 (trials x chan x freq x time)</span><br>
</div>
<div style="margin-top:0px; margin-bottom:0px; margin-top:0; margin-bottom:0"><span style="color: rgb(0, 0, 0); background-color: rgb(255, 255, 255); display: inline !important;"><br>
</span></div>
<div style="margin-top:0px; margin-bottom:0px; margin-top:0; margin-bottom:0"><span style="color: rgb(0, 0, 0); background-color: rgb(255, 255, 255); display: inline !important; font-family: Arial, Helvetica, sans-serif;">The modulation index is computed as
follows:</span></div>
<div style="margin-top:0px; margin-bottom:0px; margin-top:0; margin-bottom:0"><span style="color: rgb(0, 0, 0); background-color: rgb(255, 255, 255); display: inline !important;"><br>
</span></div>
<div style="margin-top:0px; margin-bottom:0px; margin-top:0; margin-bottom:0"><span style="color: rgb(0, 0, 0); background-color: rgb(255, 255, 255); display: inline !important;"></span></div>
</div>
</div>
</div>
<p class="p1" style="margin:0px;font:10px Courier;min-height:12px"><span class="Apple-converted-space"> </span></p>
<p class="p2" style="margin:0px;font:10px Courier">cfg= []</p>
<p class="p3" style="margin: 0px; font: 10px Courier; color: rgb(2, 128, 9);"><span class="s1" style="color: rgb(0, 0, 0);">cfg.freqlow<span class="Apple-converted-space">
</span>= [4 8]</span>%%scalar or vector, selection of frequencies for the low frequency data</p>
<p class="p3" style="margin: 0px; font: 10px Courier; color: rgb(2, 128, 9);"><span class="s1" style="color: rgb(0, 0, 0);">cfg.freqhigh
<span class="Apple-converted-space"> </span>= [30 55] </span>%%scalar or vector, selection of frequencies for the high frequency data</p>
<p class="p3" style="margin: 0px; font: 10px Courier; color: rgb(2, 128, 9);"><span class="s1" style="color: rgb(0, 0, 0);">cfg.channel<span class="Apple-converted-space">
</span>= </span><span class="s2" style="color: rgb(170, 4, 249);">'all'</span></p>
<p class="p2" style="margin:0px;font:10px Courier">cfg.method <span class="Apple-converted-space">
</span>= <span class="s2" style="color: rgb(170, 4, 249);">'mi'</span> <span class="s3" style="color: rgb(2, 128, 9);">
%%string, can be</span></p>
<p class="p3" style="margin: 0px; font: 10px Courier; color: rgb(2, 128, 9);">% %
<span class="Apple-converted-space"> </span>'coh' - coherence</p>
<p class="p3" style="margin: 0px; font: 10px Courier; color: rgb(2, 128, 9);">% %
<span class="Apple-converted-space"> </span>'plv' - phase locking value</p>
<p class="p3" style="margin: 0px; font: 10px Courier; color: rgb(2, 128, 9);">% %
<span class="Apple-converted-space"> </span>'mvl' - mean vector length</p>
<p class="p3" style="margin: 0px; font: 10px Courier; color: rgb(2, 128, 9);">% %
<span class="Apple-converted-space"> </span>'mi'<span class="Apple-converted-space">
</span>- modulation index</p>
<p class="p3" style="margin: 0px; font: 10px Courier; color: rgb(2, 128, 9);"><span class="s1" style="color: rgb(0, 0, 0);">cfg.keeptrials =
</span><span class="s2" style="color: rgb(170, 4, 249);">'no'</span><span class="s1" style="color: rgb(0, 0, 0);">
</span>%%string, can be 'yes' or 'no'</p>
<p class="p4" style="margin: 0px; font: 10px Courier; color: rgb(2, 128, 9); min-height: 12px;">
<span class="Apple-converted-space"> </span></p>
<p class="p2" style="margin:0px;font:10px Courier">crossfreq = ft_crossfrequencyanalysis(cfg, freq)</p>
<p class="p2" style="margin:0px;font:10px Courier"><br>
</p>
<p class="p2" style="margin:0px;font:10px Courier"><br>
</p>
<p class="p2" style="margin:0px;font:10px Courier"><span style="font-family: Arial, Helvetica, sans-serif; font-size: 12pt;">In response to your reply:</span></p>
<p class="p2" style="margin:0px;font:10px Courier"><span style="font-family: Arial, Helvetica, sans-serif; font-size: 11pt;"><br>
</span></p>
<p class="p2" style="margin: 0px; font-variant: normal; font-weight: normal; font-stretch: normal; font-size: 10px; line-height: normal; font-family: Courier;">
<span style="font-family: Arial, Helvetica, sans-serif; font-size: 11pt;"><i>Last but not least, is there a physiological or computational explanation for the impossibility of computing PAC on different electrodes?</i></span></p>
<p class="p2" style="margin: 0px; font-variant: normal; font-weight: normal; font-stretch: normal; font-size: 10px; line-height: normal; font-family: Courier;">
<span style="font-family: Arial, Helvetica, sans-serif; font-size: 11pt;"><i><br>
I don’t understand the question underlying this question: given some data, and a function, one could most of the time produce a result. In that sense it is always possible. Whether or not that result is interpretable, that’s a different question, but it probably
does not depend on whether it was computed on electrode O1, or on electrode P6</i><br>
</span></p>
<p class="p2" style="margin:0px;font:10px Courier"><br>
</p>
<div class="p2" style="margin:0px;font:10px Courier"><span style="font-family: Arial, Helvetica, sans-serif; font-size: 12pt;">The code of ft_crossfrequencyanalysis states that computation for different channels is not supported: </span></div>
<div class="p2" style="margin:0px;font:10px Courier"><br>
</div>
<div class="p2" style="margin:0px;font:10px Courier"><span style="font-family: Arial, Helvetica, sans-serif; font-size: 12pt;">Lines 85-86:</span><span style="font-size: 12pt;">
</span><br>
</div>
<p class="p2" style="margin:0px;font:10px Courier"><br>
</p>
<p class="p2" style="margin:0px;font:10px Courier"></p>
<p class="p1" style="margin: 0px; color: rgb(2, 128, 9);"><span style="font-size: 12pt;">% prior to 19 Jan 2017 this function had input options cfg.chanlow and cfg.chanhigh,</span></p>
<p class="p1" style="margin: 0px; color: rgb(2, 128, 9);"><span style="font-size: 12pt;">% but nevertheless did not support between-channel CFC computations</span></p>
<p class="p2" style="margin:0px;font:12px Courier;min-height:14px"><br>
</p>
<div class="p2" style="margin:0px;font:10px Courier"><span style="color: rgb(0, 0, 0); font-family: Arial, Helvetica, sans-serif; font-size: 12pt; background-color: rgb(255, 255, 255); display: inline !important;"> I was wondering the reason behind this since
I have found some toolboxes for PAC that allow computing the MI with a different selection of channels (e.g. occipital chans for phase and frontal chans for amplitude). </span><br>
</div>
<p class="p2" style="margin:0px;font:10px Courier"><br>
</p>
<p class="p2" style="margin:0px;font:10px Courier"><br>
</p>
<p class="p2" style="margin:0px;font:10px Courier"><br>
</p>
<p class="p2" style="margin:0px;font:10px Courier"></p>
<div><span style="font-family: Arial, Helvetica, sans-serif; font-size: 10pt;"><i>Q.2 When computing PAC with Fieldtrip, I get the same value for the entire frequency band of the phase (i.e. same number from 4 to 8 Hz). This is despite the resulting MI matrix
being N.channel*N.freqphase*N.freqAmplitude.</i></span></div>
<div><span style="font-family: Arial, Helvetica, sans-serif; font-size: 10pt;"><i>Since I would like to explore which theta frequency phase is mostly coupled with the higher frequency power, I would like to know why I get the same values and how to fix this
as I could not find any configuration about averaging frequencies (e.g. cfg.averageoverfreq = 'yes'/'no').</i></span></div>
<div><i><br>
</i></div>
<div><span style="font-family: Arial, Helvetica, sans-serif; font-size: 10pt;"><i>This I don’t understand. I cannot comment on this without knowing more about the exact parameters used for the generation of the input data into the ft_crossfrequencyanalysis
function.</i></span></div>
<div><i><br>
</i></div>
<p class="p2" style="margin:0px;font:10px Courier"><span style="font-family: Arial, Helvetica, sans-serif; font-size: 12pt;">I asked this question because, despite the output of <span style="color: rgb(0, 0, 0); background-color: rgb(255, 255, 255); display: inline !important;">ft_crossfrequencyanalysis</span>
being chanxfreqlowxfreqhigh (180x24x51), the value is the same for all the frequencies of the phase (4-8 Hz). There is no parameter in the function to configure this option and it is indeed limiting any explorative analysis. Is there a way to get a PAC estimate
for every frequency of the phase?</span></p>
<p class="p2" style="margin:0px;font:10px Courier"><br>
</p>
<p class="p2" style="margin:0px;font:10px Courier"><span style="font-family: Arial, Helvetica, sans-serif; font-size: 11pt;"><br>
</span></p>
<p class="p2" style="margin:0px;font:10px Courier"><span style="font-family: Arial, Helvetica, sans-serif; font-size: 12pt;">Q3. The last question about the statistics was because, with other PAC toolboxes, a statistic against a surrogate comodulogram with
no coupling is computed and a pvalue is generated to assess whether the PAC index is reliable or not. </span></p>
<p class="p2" style="margin:0px;font:10px Courier"><span style="font-family: Arial, Helvetica, sans-serif; font-size: 11pt;"><br>
</span></p>
<p class="p2" style="margin:0px;font:10px Courier"><span style="font-family: Arial, Helvetica, sans-serif; font-size: 12pt;">It seems that Fieldtrip does not have a function for this purpose. Also, the standard permutation statistics would require changing
the structure of the data to match it with the inputs required by spectral or time statistical analysis functions. Thus, I was wondering how to compute proper statistical testing on PAC data with Fieldtrip. </span></p>
<p class="p2" style="margin:0px;font:10px Courier"><span style="font-family: Arial, Helvetica, sans-serif; font-size: 12pt;"><br>
</span></p>
<p class="p2" style="margin:0px;font:10px Courier"><span style="font-family: Arial, Helvetica, sans-serif; font-size: 12pt;">In conclusion, if I understood your response correctly, Fieldtrip's function for computing PAC with Tort's Modulation index is not appropriate
for tasks with event-related modulation of oscillatory activity. Thus, PAC analysis should only be run on time windows where no event-related activity takes place or on resting-state data. Is that correct?</span></p>
<p class="p2" style="margin:0px;font:10px Courier"><br>
</p>
<p class="p2" style="margin:0px;font:10px Courier"><span style="font-family: Arial, Helvetica, sans-serif; font-size: 11pt;"><br>
</span></p>
<p class="p2" style="margin:0px;font:10px Courier"><span style="font-family: Arial, Helvetica, sans-serif; font-size: 12pt;">Thank you for taking the time to read my questions and responses. </span></p>
<p class="p2" style="margin:0px;font:10px Courier"><span style="font-family: Arial, Helvetica, sans-serif; font-size: 11pt;"><br>
</span></p>
<p class="p2" style="margin:0px;font:10px Courier"><span style="font-family: Arial, Helvetica, sans-serif; font-size: 11pt;"><br>
</span></p>
<p class="p2" style="margin:0px;font:10px Courier"><span style="font-family: Arial, Helvetica, sans-serif; font-size: 12pt;">Best wishes and happy Easter,</span></p>
<p class="p2" style="margin:0px;font:10px Courier"><span style="font-family: Arial, Helvetica, sans-serif; font-size: 11pt;"><br>
</span></p>
<p class="p2" style="margin:0px;font:10px Courier"><span style="font-family: Arial, Helvetica, sans-serif; font-size: 12pt;">Elisa</span></p>
<p class="p2" style="margin:0px;font:10px Courier"><span style="font-family: Arial, Helvetica, sans-serif; font-size: 11pt;"><br>
</span></p>
<p class="p2" style="margin:0px;font:10px Courier"><span style="font-family: Arial, Helvetica, sans-serif; font-size: 11pt;"><br>
</span></p>
<p class="p2" style="margin:0px;font:10px Courier"><span style="font-family: Arial, Helvetica, sans-serif; font-size: 11pt;"><br>
</span></p>
<p class="p2" style="margin:0px;font:10px Courier"><span style="font-family: Arial, Helvetica, sans-serif; font-size: 11pt;"> </span><br>
</p>
<p class="p2" style="margin:0px;font:10px Courier"><br>
</p>
<p class="p2" style="margin:0px;font:10px Courier"></p>
<p class="p2" style="margin:0px;font:10px Courier"><span style="font-family: Arial, Helvetica, sans-serif; font-size: 12pt;"></span></p>
<p class="p2" style="margin:0px;font:12px Courier;min-height:14px"><br>
</p>
<p></p>
<div style="font-family: Arial, Helvetica, sans-serif; font-size: 12pt; color: rgb(0, 0, 0);">
<br>
</div>
<hr tabindex="-1" style="display:inline-block; width:98%">
<div id="divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" color="#000000" style="font-size: 11pt;"><b>From:</b> fieldtrip <fieldtrip-bounces@science.ru.nl> on behalf of Schoffelen, J.M. (Jan Mathijs) via fieldtrip <fieldtrip@science.ru.nl><br>
<b>Sent:</b> Wednesday, April 13, 2022 07:59<br>
<b>To:</b> FieldTrip discussion list <fieldtrip@science.ru.nl><br>
<b>Cc:</b> Schoffelen, J.M. (Jan Mathijs) <janmathijs.schoffelen@donders.ru.nl><br>
<b>Subject:</b> Re: [FieldTrip] PAC analysis with ft_crossfrequencyanalysis</font>
<div> </div>
</div>
<div class="" style="word-wrap:break-word; line-break:after-white-space">Hi Elisa,
<div class=""><br class="">
</div>
<div class="">Your questions are not decorated with any insights about code/data, so it’s a bit guessing as to how to compile an answer to your questions that might help you further. I’ll try anyhow:</div>
<div class="">
<div>
<blockquote type="cite" class="">
<div class="">
<div class="" style="font-family:Helvetica; font-size:14px; font-style:normal; font-variant-caps:normal; font-weight:normal; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none">
<div class="" style="font-family:Arial,Helvetica,sans-serif; font-size:12pt">
<ol class="">
<li class=""><span class=""><span class="" style="background-color: rgb(255, 255, 255); display: inline !important;"><span class=""> What is the minimum epoch length required to compute PAC (is 1s enough to compute the phase of 4 Hz)? <br class="">
</span></span></span></li></ol>
</div>
</div>
</div>
</blockquote>
<div>The sliding time window (which is not necessarily the same as the epoch length) should be sufficiently long to get a decent estimate of the phase at 4Hz. Thus, a cfg.t_ftimwin for the low frequency oscillation, to be used in ft_freqanalysis to compute
the freqlo should be sufficient. </div>
<div><br class="">
</div>
<blockquote type="cite" class="">
<div class="">
<div class="" style="font-family:Helvetica; font-size:14px; font-style:normal; font-variant-caps:normal; font-weight:normal; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none">
<div class="" style="font-family:Arial,Helvetica,sans-serif; font-size:12pt">
<ol class="">
<li class="" style="display:block"><span class=""><span class="" style="background-color: rgb(255, 255, 255); display: inline !important;"><span class=""><br class="">
</span></span></span></li><li class=""><span class=""><span class="" style="background-color: rgb(255, 255, 255); display: inline !important;"><span class="">Is this computation suitable for tasks with a strong event-related synchronization? I read that ERPs should be subtracted from
this analysis to avoid confounding effects but here I have reaching movements.</span></span></span></li></ol>
</div>
</div>
</div>
</blockquote>
<div>No, and subtraction of an ERP is not going to be very useful in my opinion. See: <a href="https://www.fieldtriptoolbox.org/faq/evoked_vs_induced/" data-auth="NotApplicable" class="">https://www.fieldtriptoolbox.org/faq/evoked_vs_induced/</a></div>
<div><br class="">
</div>
<blockquote type="cite" class="">
<div class="">
<div class="" style="font-family:Helvetica; font-size:14px; font-style:normal; font-variant-caps:normal; font-weight:normal; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none">
<div class="" style="font-family:Arial,Helvetica,sans-serif; font-size:12pt">
<ol class="">
<li class=""><span class=""><span class="" style="background-color: rgb(255, 255, 255); display: inline !important;"><span class="">When computing PAC with Fieldtrip, I get the same value for the entire frequency band of the phase (i.e. same number from 4 to
8 Hz). This is d<span class="" style="background-color: rgb(255, 255, 255); display: inline !important;">espite the resulting MI matrix being N.channel*N.freqphase*N.freqAmplitude.</span></span></span></span></li><li class="" style="display:block"><span class=""><span class="" style="background-color: rgb(255, 255, 255); display: inline !important;"><span class="">Since I would like to explore which theta frequency phase is mostly coupled with the higher frequency power,
I would like to know why I get the same values and how to fix this as I could not find any configuration about averaging frequencies (e.g. cfg.averageoverfreq = 'yes'/'no').</span></span></span></li></ol>
</div>
</div>
</div>
</blockquote>
<div>This I don’t understand. I cannot comment on this without knowing more about the exact parameters used for the generation of the input data into the ft_crossfrequencyanalysis function.</div>
<div><br class="">
</div>
<blockquote type="cite" class="">
<div class="">
<div class="" style="font-family:Helvetica; font-size:14px; font-style:normal; font-variant-caps:normal; font-weight:normal; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none">
<div class="" style="font-family:Arial,Helvetica,sans-serif; font-size:12pt">
<ol class="">
<li class="">If I manage to compute a meaningful MI, how do I statistically test whether it is significant?</li></ol>
</div>
</div>
</div>
</blockquote>
<div>‘Significant’ is always related to a null hypothesis. What’s your null hypothesis?</div>
<div><br class="">
</div>
<blockquote type="cite" class="">
<div class="" style="font-family:Helvetica; font-size:14px; font-style:normal; font-variant-caps:normal; font-weight:normal; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none">
<div class="" style="font-family:Arial,Helvetica,sans-serif; font-size:12pt">
<ol class="">
<li class="">Last but not least, is there a physiological or computational explanation for the impossibility of computing PAC on different electrodes?</li></ol>
</div>
</div>
</blockquote>
<div>I don’t understand the question underlying this question: given some data, and a function, one could most of the time produce a result. In that sense it is always possible. Whether or not that result is interpretable, that’s a different question, but it
probably does not depend on whether it was computed on electrode O1, or on electrode P6</div>
<div><br class="">
</div>
<div>Best wishes,</div>
<div>Jan-Mathijs</div>
<div><br class="">
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<div class="" style="margin:0in 0in 0.0001pt">Thank you very much for taking the time to read my questions. I really hope to get some answers from you.</div>
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<div class="" style="margin:0in 0in 0.0001pt">Best wishes.</div>
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<div class="" style="margin:0in 0in 0.0001pt">Elisa </div>
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<div class="" style="margin:0in 0in 0.0001pt"><span class="" style="margin: 0px; font-size: 11pt; color: rgb(102, 102, 102); font-family: Raavi, "Nirmala UI", "Gurmukhi MN", sans-serif;">Elisa Tatti, Ph.D.</span></div>
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mailing list</span><br class="" style="font-family:Helvetica; font-size:14px; font-style:normal; font-variant-caps:normal; font-weight:normal; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none">
<a href="https://mailman.science.ru.nl/mailman/listinfo/fieldtrip" data-auth="NotApplicable" class="" style="font-family:Helvetica; font-size:14px; font-style:normal; font-variant-caps:normal; font-weight:normal; letter-spacing:normal; orphans:auto; text-align:start; text-indent:0px; text-transform:none; white-space:normal; widows:auto; word-spacing:0px">https://mailman.science.ru.nl/mailman/listinfo/fieldtrip</a><br class="" style="font-family:Helvetica; font-size:14px; font-style:normal; font-variant-caps:normal; font-weight:normal; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none">
<a href="https://urldefense.com/v3/__https://doi.org/10.1371/journal.pcbi.1002202__;!!HJOPV4FYYWzcc1jazlU!5LW3HBBoemUPEhg6a_oAvt1CgyxKXM4ht3E-09jq5qNQLSuUAwlDJ4wg-LQfRQyUez2tPhThigXKwdpfytysP0iAbbWWxNcf__bmiQ$" data-auth="NotApplicable" class="" style="font-family:Helvetica; font-size:14px; font-style:normal; font-variant-caps:normal; font-weight:normal; letter-spacing:normal; orphans:auto; text-align:start; text-indent:0px; text-transform:none; white-space:normal; widows:auto; word-spacing:0px">https://urldefense.com/v3/__https://doi.org/10.1371/journal.pcbi.1002202__;!!HJOPV4FYYWzcc1jazlU!5LW3HBBoemUPEhg6a_oAvt1CgyxKXM4ht3E-09jq5qNQLSuUAwlDJ4wg-LQfRQyUez2tPhThigXKwdpfytysP0iAbbWWxNcf__bmiQ$</a><span class="" style="font-family:Helvetica; font-size:14px; font-style:normal; font-variant-caps:normal; font-weight:normal; letter-spacing:normal; text-align:start; text-indent:0px; text-transform:none; white-space:normal; word-spacing:0px; text-decoration:none; float:none; display:inline!important"></span></blockquote>
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