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<p class="ydp77d16cb1MsoNormal"><span style="font-size:12.0pt;line-height:107%;font-family:"Times New Roman",serif">Marius,</span></p>
<p class="ydp77d16cb1MsoNormal"><span style="font-size:12.0pt;line-height:107%;font-family:"Times New Roman",serif"> The ground
truth of the EEG and phase delays begins with the physics of the electrical
field potential (<span style="color: rgb(34, 34, 34); background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial;">or the
electrostatic </span>potential) defined as the
amount of work needed to move a unit positive charge from a reference point to
a specific point inside the field without producing any acceleration. When
the </span><a href="https://en.wikipedia.org/wiki/Curl_(mathematics)" title="Curl (mathematics)" rel="nofollow" target="_blank"><span style="color: rgb(11, 0, 128); background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial; text-decoration-line: none;">curl</span></a><span style="color: rgb(34, 34, 34); background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial;"> </span><span class="ydp77d16cb1nowrap"><span style="font-size: 12pt; line-height: 107%; font-family: "Cambria Math", serif; color: rgb(34, 34, 34); background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial;">∇</span><span class="ydp77d16cb1nowrap"><span style="font-size: 12pt; line-height: 107%; font-family: "Times New Roman", serif; color: rgb(34, 34, 34); background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial;"> × E</span></span></span><span style="font-size: 12pt; line-height: 107%; font-family: "Times New Roman", serif; color: rgb(34, 34, 34); background-image: initial; background-position: initial; background-size: initial; background-repeat: initial; background-attachment: initial; background-origin: initial; background-clip: initial;"> is zero then the electrical potential is determined by
the gradient of the electrical field. EEG
differential amplifiers are used to measure the difference or gradient of the
electrical field and therefore the electrical potential is the difference
between the two inputs to the amplifier.
If one measures the electrical field and then removes ICs and starts
with a smaller number of EEG channels to create a larger number of time series
to replace the original time series then this changes the gradients of the
electrical field produced by the brain and also distorts the time differences
between samples then the physics of the electrical field no longer applies.<span style="font-size: 12pt; line-height: 107%;"></span></span></p>
<div><span style="font-size:12.0pt;line-height:107%;font-family:"Times New Roman",serif">The majority of neuroscientists agree that the physiological
ground truth for the genesis of the EEG as being summated synaptic potentials
in groups of neurons that are connected by axons. The ground truth of phase differences
between separated scalp locations are physiological factors of the electrical
sources and the connections between sources (i.e., networks) such as axonal
conduction velocities, length of connecting axons, synaptic rise times, synaptic
delays and synaptic integration times, etc.
This is well established science and it was quite surprising to read
posts on this forum by individuals that claim that there is no ground truth of
the EEG, EEG is all noise and therefore this justified altering phase
differences using a small number of ICs to create different time series (i.e.,
reconstruction) to thereby decoupling the brain from the subject and the
physics of electrical fields. Like
Pedro Valdez I have also recorded EEG from the dura and pia surface and
simultaneously from the scalp. I also
have impaled neurons and correlated the intracellular EEG with field potentials
as a function of distance from the impaled neurons. These recordings were when I was a post doc
at Albert Einstein College of Medicine With E. Roy John we moved multiple micro-electrodes
through wide regions of the cat brain while also recording EEG from the
scalp. It was during this time that Roy
and myself and others quantified how phase differences increase or decrease as
a function of interelectrode distance.
At the University of Maryland myself and colleaques, while still
collaborating with Roy, did extensive studies that linked phase differences to the
cortical white matter with short distance ‘U’ shaped fibers vs long distance
fasciculi. These measures helped Paul
Nunez to use scalp EEG phase differences to estimate white matter conduction
velocities. Additional validation
studies of the network physiological ground truth of EEG phase differences was
when I worked at NIH with patients before and after craniotomy. Further validations also involved
correlations with MRI T2 relaxation time. </span></div><div><span style="font-size:12.0pt;line-height:107%;font-family:"Times New Roman",serif"><br></span></div><div><span style="font-size:12.0pt;line-height:107%;font-family:"Times New Roman",serif">Luckily ICA reconstruction was not invented in the 1960s because if it
had then today we would have no idea that there is a replicable and verifiable ground
truth of EEG nor know about the relationship between EEG phase differences and
the cerebral white matter. </span></div>
<p class="ydp77d16cb1MsoNormal"><span style="font-size:12.0pt;line-height:107%;font-family:"Times New Roman",serif"> </span></p>
<p class="ydp77d16cb1MsoNormal"><span style="font-size:12.0pt;line-height:107%;font-family:"Times New Roman",serif">As for volume conduction and phase delays between
separated sensors I think that there may be some confusion between the
instantaneous physics of the electrical potential and the volume conductor
model used for the inverse solution. The
volume conductor model pertains to a single instant of time where the accuracy
of the spatial localization of sources is affected by inhomogeneities of tissue
conductivities that primarily affect amplitudes and only negligibly time
differences which are near to the speed of light. A good book on this topic is Malmuvo and
Plonsey “Bioelectricity”, Oxford University, 1995 or a standard physics text
book, for example, Richard Feynman’s book.
Here is a url to a study where we evaluated phase differences as a
function of the Euclidean distance between Brodmann areas that comprise the
default network - see figure 6 at:</span></p>
<p class="ydp77d16cb1MsoNormal"><span style="font-size:12.0pt;line-height:107%;font-family:"Times New Roman",serif">http://www.appliedneuroscience.com/Default_Network_LORETA_Phase_Reset-Thatcher_et_al.pdf</span></p>
<p class="ydp77d16cb1MsoNormal"><span style="font-size:12.0pt;line-height:107%;font-family:"Times New Roman",serif"> </span></p>
<p class="ydp77d16cb1MsoNormal"><span style="font-size:12.0pt;line-height:107%;font-family:"Times New Roman",serif">We have also evaluated the distortion of effective
connectivity by ICA reconstruction. For
example, we computed the phase slope index before and after ICA reconstruction
and 100% of the effective connectivity between 171 electrode pairs for all
frequencies is adulterated. This is
another example of decoupling the “ground truth” of the physiology of the brain
from the subject. We recently published a study that correlated
intelligence with effective connectivity where we found significant differences
between low and high I.Q. subjects. If
we had used ICA reconstruction then because phase differences are scrambled and
distorted and thereby decoupled from the brain it is unlikely that there would
have been any significant differences. </span></p>
<p class="ydp77d16cb1MsoNormal"><span style="font-size:12.0pt;line-height:107%;font-family:"Times New Roman",serif">Here is a url to this study: http://www.appliedneuroscience.com/Intelligence%20&%20information%20flow-Thatcher%20et%20al%202016.pdf</span></p>
<p class="ydp77d16cb1MsoNormal"><span style="font-size:12.0pt;line-height:107%;font-family:"Times New Roman",serif"> </span></p>
<p class="ydp77d16cb1MsoNormal"><span style="font-size:12.0pt;line-height:107%;font-family:"Times New Roman",serif">For those interested, here is a url to a book that E.
Roy John and myself published in 1977 that reviews the history of how the
ground truth of EEG was discovered. The ICA replacement violates the electricity and physiology of the brain and contradicts this history: http://www.appliedneuroscience.com/FuncNeuro_v1n.pdf</span></p>
<p class="ydp77d16cb1MsoNormal"><span style="font-size:12.0pt;line-height:107%;font-family:"Times New Roman",serif"> </span></p>
<p class="ydp77d16cb1MsoNormal"><span style="font-size:12.0pt;line-height:107%;font-family:"Times New Roman",serif">Best wishes,</span></p>
<p class="ydp77d16cb1MsoNormal"><span style="font-size:12.0pt;line-height:107%;font-family:"Times New Roman",serif"> </span></p>
<p class="ydp77d16cb1MsoNormal"><span style="font-size:12.0pt;line-height:107%;font-family:"Times New Roman",serif">Robert</span></p>
<!--EndFragment--></div><div><br></div><div><br></div></div><div id="ydpbeb3a7e6yahoo_quoted_2151849709" class="ydpbeb3a7e6yahoo_quoted"><div style="font-family:'Helvetica Neue', Helvetica, Arial, sans-serif;font-size:13px;color:#26282a;"><div>On Friday, August 4, 2017, 1:10:52 PM EDT, Marius Klug <marius.s.klug@gmail.com> wrote:</div><div><br></div><div><br></div><div><div id="ydpbeb3a7e6yiv0625967697"><div><div dir="ltr"><div><div>Hi everyone!<br clear="none"><br clear="none"></div><div>One thing after the other...:<br clear="none"></div><div><br clear="none"><br clear="none"></div>Georges, sure, feel free to use the example, I'm always happy to contribute :-) <br clear="none"><br clear="none"></div>A comparison of high to low density ICA cleaning would definitely be interesting and my hypothesis is that the ICA decomposition might be significantly worse (meaning more changes in the posterior channels) in the 19-channels set. If I have some spare time I might do that and post the results. Will take a while, though, I won't have time until end of September I think...<br clear="none"><br clear="none"><br clear="none"><div><br clear="none"></div><div>Robert, if you read again my very first email on the topic, I have not changed my mind the slightest bit... I have said from the beginning that ICA does indeed change the data, which is rather obvious. It's only about the question where this change is a positive or a negative one. However, as I said, it might be that 19 channels is not a sufficiently high number for a decent ICA decomposition for cleaning. It sure is not for working on the source level, but by now I did indeed assume that the eye components are so strong that even 19 channels are enough to cleanly take them out. If that's not the case, it's an important information and everyone needs to decide for themselves if they want to use ICA and risk losing a slight bit of brain data or other cleaning methods which might prove to be better in the low-density segment. I would, however still HIGHLY encourage you to test whether or not the results with the ICA-based cleaning are significantly better or worse than without. As long as you have not tested this, you keep rejecting a method that might prove useful for you.<br clear="none"><br clear="none"></div><div>The as you call it false belief of continuous artifacts has in my opinion already been adressed enough and I guess you just must have special means of keeping eye and neck muscles and heart beats from continuous signals in the EEG, since in ordinary participants eye components seem to correlate highly with eye tracker signals and I can still see the heart beats of my subjects in their EEG. As I've stated elsewhere, there are many means of increasing signal-to-noise ratio, ICA just being one of them (one other would for example be the averaging of ERPs). Many other published sources just tell us that those other means work as well and that the signal had been strong enough for statistically significant results. It does not say there are no continuous artifacts, that's a logical fallacy.<br clear="none"><br clear="none"></div><div>As for the statistically independent sources in ICA and connected brain regions: This is an interesting thing to think about, that's true. One answer would be that ICA has no temporal knowledge while separating the sources, it just works with point clouds, but the brain connections are temporal. One other might be that ICA doesn't separate based on correlation but more complex measures of the data set. I must admit I didn't have the time yet to fully understand the different ICA algorithms, though. My last answer to this is the fact that ICA gets nicely dipolar components which can be projected back to the brain, and this also works in simulations where the true sources are known. So for me, at least with sufficiently high density (64 at least, better 128) ICA components that have a neat separation from other components are brain sources. This has to be taken with a grain of salt though, since one needs to be experienced in understanding inhowfar a component might still be mixed sources. For example residual variance of the component gives at least a hint about this question. Unless proven otherwise, I will keep my working definition of ICA
components as sources, and especially dipolar sources as brain sources,
since I work on the source level anyway... <br clear="none"><br clear="none"></div><div>Be it as it may, the 18-19 bitcoin example still doesn't hold true, you can just replace "sources" with "components". You made another strawman argument which I answered because it's an interesting question, not because it's an actual counter argument against my case.<br clear="none"><br clear="none"></div><div>Also, I think exactly the central-limit theorem is being used in ICA. A singular source is always less gaussian than mixed sources, so a de-mixing matrix which maximizes non-gaussianity of components would maximize the separation of the components from each other. I think your argument here goes exactly where the basic ICA argument goes so I don't see your point. See <a shape="rect" href="http://arnauddelorme.com/ica_for_dummies/" rel="nofollow" target="_blank">http://arnauddelorme.com/ica_for_dummies/</a><br clear="none"></div><div><br clear="none"><br clear="none"><br clear="none"></div><div>Makoto, yes, the dipole model is definitely far from perfect. We also attempt to create a head model including the eyes and neck muscles, since the head movements are vitally important for us. Blood vessels is an interesting point though, we hadn't thought about this, as far as I know at least. This would definitely improve localization of the muscle artifacts and simplify the discrimination of eye and muscle, but of course muscles are complex in their electrical properties so it's going to be an interesting question if this is working as intended. The distributed source model does appeal to me in the sense that it's just more realistic than a single dipole creating the signal at the scalp, but I am not familiar with the assumptions that are held for this.<br clear="none"><br clear="none">Another big issue to me is that we don't get the same components for each subject. Clustering is a really bad way of combining the components, even though it's the best we have. In fact, I've realized that the clustering solution varies to a more-than-slight degree even if you re-cluster with the exact same parameters. I've thought of a method to do repeated clustering and compare the results to have a kind of probabilistic model slightly similar to Nima's Measure Projection, but it has proven to be more work than I had time. I might come back to it, though! As you said, a long way to go to make EEG a smoothly working brain imaging technique.. but all the more interesting and it's fascinating to be part of this!<br clear="none"><br clear="none"><br clear="none"><br clear="none"></div><div>Georges, I don't think anyone ever doubted that the data changes after one takes out eye components. It's obvious and I don't recall emails that state otherwise. The whole discussion was about the fact that the change in the data would increase the quality and make it closer to the actual brain data, that was even in Arno's very first post. It's reflected in the wording, for example you and robert use "distortion" or "adulteration", while Arno, Makoto and others from this ist use simply "change", because this implies no negative impact.<br clear="none"><br clear="none"></div><div>I think an important thing to keep in mind is that we can not really make any meaningful conclusions from sensor level activity as to where this activity originated from. Sensor-level connectivity will always have this drawback, plus the mixing in of artifactual sources, which is why Johanna has said a while ago that she performs only high-density EEG source-level connectivity analysis, nothing on the sensor-level at all. It obviously depends on your data set and application, but to me, 19 channel surface EEG is always to be treated with extra care as to any interpretations.<br clear="none"><br clear="none"><br clear="none"><br clear="none"></div><div>Tarik, yes, it seems to me that there is tons of method research to be done and paper to be written. We soon will have a synchronized data set containing high-density EEG with 28 as EMG on the neck, together with motion capture of the head, shoulders, hands and feet in position and orientation and eye tracking while moving around in virtual reality. This might provide useful for investigating the continuous artifacts, since we have eye movement, muscle activity, and (if we record this in addition) ECG all synchronized and we can look for it's connections to the EEG data. Well, the things to come! It all needs time and resources... Anyways, I would be glad to contribute to some of the papers if I can, since investigating the EEG methods is one of my main interests as a researcher.<br clear="none"><br clear="none"><br clear="none"></div><div>All the best,<br clear="none"></div><div>Marius<br clear="none"></div><div><br clear="none"><div><div class="ydpbeb3a7e6yiv0625967697gmail_extra"><div class="ydpbeb3a7e6yiv0625967697gmail_quote">2017-07-28 20:23 GMT+02:00 Tarik S Bel-Bahar <span dir="ltr"><<a shape="rect" href="mailto:tarikbelbahar@gmail.com" rel="nofollow" target="_blank">tarikbelbahar@gmail.com</a>></span>:<br clear="none"><blockquote class="ydpbeb3a7e6yiv0625967697gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex;"><div class="ydpbeb3a7e6yiv0625967697yqt0999110055" id="ydpbeb3a7e6yiv0625967697yqt77448"><div dir="ltr"><div><font color="#000000">Greetings, it's great to see a more congenial future-focused discussion </font><div style="display:inline;">building</div> here.<div style="display:inline;"> We all have knowledge we consider as true, biases that impact our perceptions and expectations, and this all sometimes gets in the way of (needed) discussion on research topics and assumptions. It seems we often need less "fixed ideas and assumptions" and to be more open to "new published data-based findings addressing specific topics". </div>Overall, kudos for keeping the <div style="display:inline;">human </div>conversation going<div style="display:inline;">, it may eventually lead to positive impacts for the EEG field.</div></div><div><div style="display:inline;"><font color="#000000"><br clear="none"></font></div></div><div><font color="#000000">From my perspective,</font><div style="display:inline;"> </div>argument<div style="display:inline;">s</div> or point of view, whether based on theory<div style="display:inline;">, math,</div> or experience,</div><div><font color="#000000">will </font><div style="display:inline;">remain</div> <div style="display:inline;">un</div>satisfactory until th<div style="display:inline;">ey</div> are <div style="display:inline;">in 1) </div>multiple published new high-quality<div style="display:inline;"> empirical</div><div style="display:inline;"> </div>papers <div style="display:inline;">that 2) examine a </div>range of topics related to the discussion here about ICA, EEG, <div style="display:inline;">phase metrics, </div>artifacts, etc... from a <div style="display:inline;">3) </div>data-and assessment-focused point of view. <div style="display:inline;">It's important to have conversations, but it's new peer-reviewed publications that will truly clarify things.</div></div><div><font color="#000000"></font><div style="display:inline;"><br clear="none"></div></div><div><font color="#000000"></font><div style="display:inline;">I may be too optimistic, but more collaboration amongst the discussants here could generate a half-dozen papers over the next year or two focused on these issues. These are opportunities for both young flexible researchers, as well as more mature researchers and clinicians. </div></div><div><font color="#000000"><br clear="none"></font></div><div><font color="#000000">One thing that has struck me is that the conversation has reflected </font><div style="display:inline;">1) </div>a divide between low-density and high-density EEG systems users, <div style="display:inline;">2) the differences in researcher and clinician values, </div>and <div style="display:inline;">that 3) </div>there is enough data <div style="display:inline;">already </div>out there to provide data-based publications addressing these topics. Further, the I think there is a lot of room for theoretical and methodological consolidation in the EEG field, but this will take time and effort, just as a clear understanding of the nature of true neural sources will take time and effort. </div><div><font color="#000000"><br clear="none"></font></div><div><font color="#000000">Below, a resend of my earlier list of topics that future articles can consider</font><div style="display:inline;"> or that we can add to/clarify</div>, and a list of articles (and authors) that <div style="display:inline;">can</div> be consulted regarding current use/opinions of ICA, EEG, phase, and con<div style="display:inline;">n</div>ectivity<div style="display:inline;"> analyses</div>.</div><div><font color="#000000"><br clear="none"></font></div><div><font color="#000000"><br clear="none"></font></div><div><font color="#000000"><br clear="none"></font></div><div><b><font color="#000000">Possible dimensions/constraints to consider or compare?</font></b></div><font color="#000000"><br clear="none">Channel density and relative total-head coverage</font><div><font color="#000000"><br clear="none"></font><div><div><font color="#000000">Low-density vs. moderate-density vs high-density</font></div><div><font color="#000000"><br clear="none"></font></div><div><font color="#000000">With and without EOG and/or EMG recording ?<br clear="none"></font></div><font color="#000000"><br clear="none">Number/type of artifact</font><div style="display:inline;">ual detected, number/type of</div> ICs removed<div><font color="#000000"><br clear="none"></font></div><div><div><font color="#000000">IC-based vs. non-IC based artifact removal</font></div><div><font color="#000000"><br clear="none"></font></div><div><font color="#000000">Number/type of artifact visible in channel record</font><div style="display:inline;"></div><br clear="none"><br clear="none">Clarity/robustness of artifact<div style="display:inline;">ual ICs </div>(e.g., ICs that are mixed vs. ICs that<br clear="none">are mixed (containing both artifact and neural info)<br clear="none"><br clear="none">Channel-level vs. ICA-level vs. source<div style="display:inline;">-estimated</div> connectivity metrics<br clear="none"><br clear="none">Length of epochs/trials<br clear="none"><br clear="none">Type of source analysis<br clear="none"><br clear="none">Type of reference (e.g., Chella et al., 2016)<br clear="none"><br clear="none">Type of ICA/blind source separation (e.g., Bridwell et al., 2016;<br clear="none">Brain Topography)<br clear="none"><br clear="none">Event-related or resting data<br clear="none"><br clear="none">Signal quality (e.g., gel versus saline, very noisy vs. quite clean)<br clear="none"><br clear="none">Reliability of particular metric<br clear="none"><br clear="none">Type of connectivity metric (e.g., various kinds of phase measures,<br clear="none">and the plethora of other connectivity and graph theoretical measures)<br clear="none"><br clear="none">MEG vs. EEG ?<br clear="none"><br clear="none">Sampling rate?<div><font color="#000000"><br clear="none"></font></div><div><font color="#000000">Type of population ?</font><div style="display:inline;"> Rate of artifacts per population/sample?</div></div><div><font color="#000000"></font><div style="display:inline;"><br clear="none"></div></div><div><font color="#000000"></font><div style="display:inline;">Individual differences in cleanness or clarity of EEG signal?</div></div><div><font color="#000000"></font><div style="display:inline;"><br clear="none"></div></div><div><font color="#000000"><br clear="none"><br clear="none"><br clear="none"><br clear="none">Sample articles that seem to use ICA in relation to connectivity<br clear="none">metrics are listed below.</font><div style="display:inline;"> </div>Moving forward, it may be beneficial to survey these authors and their findings.</div><div><font color="#000000"><br clear="none">de Pasquale, F., Della Penna, S., Sporns, O., Romani, G. L., &<br clear="none">Corbetta, M. (2015). A dynamic core network and global efficiency in<br clear="none">the resting human brain. Cerebral Cortex, bhv185.<br clear="none"><br clear="none">Lai, M., Demuru, M., Hillebrand, A., & Fraschini, M. (2017). A<br clear="none">Comparison Between Scalp-And Source-Reconstructed EEG Networks.<br clear="none">bioRxiv, 121764.<br clear="none"><br clear="none">Colclough, G. L., Woolrich, M. W., Tewarie, P. K., Brookes, M. J.,<br clear="none">Quinn, A. J., & Smith, S. M. (2016). How reliable are MEG<br clear="none">resting-state connectivity metrics?. NeuroImage, 138, 284-293.<br clear="none"><br clear="none">Kuntzelman, K., & Miskovic, V. (2017). Reliability of graph metrics<br clear="none">derived from resting‐state human EEG. Psychophysiology, 54(1), 51-61.<br clear="none"><br clear="none">Siems, M., Pape, A. A., Hipp, J. F., & Siegel, M. (2016). Measuring<br clear="none">the cortical correlation structure of spontaneous oscillatory activity<br clear="none">with EEG and MEG. NeuroImage, 129, 345-355.<br clear="none"><br clear="none">Toppi, J., Astolfi, L., Poudel, G. R., Innes, C. R., Babiloni, F., &<br clear="none">Jones, R. D. (2016). Time-varying effective connectivity of the<br clear="none">cortical neuroelectric activity associated with behavioural<br clear="none">microsleeps. NeuroImage, 124, 421-432.<br clear="none"><br clear="none">Farahibozorg, S. R., Henson, R. N., & Hauk, O. (2017). Adaptive<br clear="none">Cortical Parcellations for Source Reconstructed EEG/MEG Connectomes.<br clear="none">bioRxiv, 097774.<br clear="none"><br clear="none">Rueda-Delgado, L. M., Solesio-Jofre, E., Mantini, D., Dupont, P.,<br clear="none">Daffertshofer, A., & Swinnen, S. P. (2016). Coordinative task<br clear="none">difficulty and behavioural errors are associated with increased<br clear="none">long-range beta band synchronization, NeuroImage.<br clear="none"><br clear="none">Cooper, P. S., Wong, A. S., Fulham, W. R., Thienel, R., Mansfield, E.,<br clear="none">Michie, P. T., & Karayanidis, F. (2015). Theta frontoparietal<br clear="none">connectivity associated with proactive and reactive cognitive control<br clear="none">processes. Neuroimage, 108, 354-363.<br clear="none"><br clear="none">Nayak, C. S., Bhowmik, A., Prasad, P. D., Pati, S., Choudhury, K. K.,<br clear="none">& Majumdar, K. K. (2017). Phase Synchronization Analysis of Natural<br clear="none">Wake and Sleep States in Healthy Individuals Using a Novel Ensemble<br clear="none">Phase Synchronization Measure. Journal of Clinical Neurophysiology,<br clear="none">34(1), 77-83.<br clear="none"><br clear="none">Vecchio, F., Miraglia, F., Piludu, F., Granata, G., Romanello, R.,<br clear="none">Caulo, M., ... & Rossini, P. M. (2017). “Small World” architecture in<br clear="none">brain connectivity and hippocampal volume in Alzheimer’s disease: a<br clear="none">study via graph theory from EEG data. Brain imaging and behavior,<br clear="none">11(2), 473-485.<br clear="none"><br clear="none">Ranzi, P., Freund, J. A., Thiel, C. M., & Herrmann, C. S. (2016).<br clear="none">Encephalography Connectivity on Sources in Male Nonsmokers after<br clear="none">Nicotine Administration during the Resting State. Neuropsychobiology,<br clear="none">74(1), 48-59.<br clear="none"><br clear="none">Vecchio, F., Miraglia, F., Curcio, G., Della Marca, G., Vollono, C.,<br clear="none">Mazzucchi, E., ... & Rossini, P. M. (2015). Cortical connectivity in<br clear="none">fronto-temporal focal epilepsy from EEG analysis: a study via graph<br clear="none">theory. Clinical Neurophysiology, 126(6), 1108-1116.<br clear="none"><br clear="none">Smit, D. J., de Geus, E. J., Boersma, M., Boomsma, D. I., & Stam, C.<br clear="none">J. (2016). Life-span development of brain network integration assessed<br clear="none">with phase lag index connectivity and minimum spanning tree graphs.<br clear="none">Brain connectivity, 6(4), 312-325.<br clear="none"><br clear="none">Chung, Jae W., Edward Ofori, Gaurav Misra, Christopher W. Hess, and<br clear="none">David E. Vaillancourt. "Beta-band activity and connectivity in<br clear="none">sensorimotor and parietal cortex are important for accurate motor<br clear="none">performance." NeuroImage 144 (2017): 164-173.<br clear="none"><br clear="none">Shou, G., & Ding, L. (2015). 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