Talk:Measures of neuronal signal synchrony

--- The article is focused on continuous time series, but synchrony is also defined for discrete signals. It would be good to clarify this at the beginning. Also maybe it would be better to say correlated rather than synchronous time series in the first paragraph.

• • • Rewritten correspondingly.

--- In the second paragraph, the synchronization of oscillatory systems could be mentioned.

• • • It did not really fit there (and I would like to stay as general as possible), however, in this paragraph I now added a link from the word “synchronization” to the Scholarpedia article by Pikovsky and Rosenblum which deals explicitly with synchronization of oscillatory systems.

--- In the next par, when citing nonlinear interdependences, the papers by Arnhold et al and Quian Quiroga et al could be cited.

• • • Done.

Cross-correlation: It should be added that anticorrelated signals give a value of -1.

• • • Done.

--- Coherence: the values of omega after equation 2 are not discrete frequencies (they don't have the right units).

• • • Removed altogether (not really needed anyway).

--- equation 3: Shouldn't it be C_xy instead of F_xy? Also, I think the square of F is incorrect.

• • • Corrected.

--- The line after 'to reduce the finite size effect'... I don't think this is correct. The data is partitioned to have some statistics.

• • • Welch’s method reduces noise in the estimated power spectra in exchange for reducing the frequency resolution. Due to the noise caused by imperfect and finite data, the noise reduction from Welch's method is often desired (see Proakis, J.G. and Manolakis, D.G. (1996) Digital Signal Processing, Upper Saddle River, NJ: Prentice-Hall, pp 910–913.).

--- Mutual Information: many variables are not defined/explained (at least at the point where they are first used). What is M_x and p_x? What is X? What's p_xy?

• • • Corrected.

--- There is a sentence with 2 equations (5 and 6) in between. Please edit the text.

• • • The sentence has been rewritten.

--- After eq. 6, instead of weights, I would say probability. You should also say how these probabilities are estimated and that they sum up to 1.

• • • The word has been exchanged. The estimation of the probabilities is described at the end of the Section. The word ‘normalized’ has been added

--- Just before transfer entropy: Paninski 2003 is not in the reference list.

• • • Reference included.

--- After equation 8, p_xy(.., .., ..) is not defined.

• • • Definition included.

--- 'Since transfer entropy can be expressed as the difference of mutual informations'... Please explain or give more details.

• • • Too complicated to explain in a few words, otherwise too distracting, thus left out.

--- 'density-adaptive' algorithm. I know what the author means, but it's not clear.

• • • Described in the previous Section (“Mutual Information”) but sentence has been removed (see last comment).

--- Granger causality: how are the coefficients (a) estimated? Please give more details.

• • • Rewritten. For more detailed information the link to the main article on “Granger causality” is provided.

--- Just before eq. 13. Instead of saying 'remaining vectors in x_n', do you mean remaining vectors x_j? Then, it would be clear what x_j is in the equation.

• • • Latex-problem. The {} to denote the set of vectors x_n were omitted. Corrected

--- 'Exchanging systems X and Y...' You could say what one could in principle get from the asymmetry.

• • • This is dealt with in the extra section “Comment on directional measures”. I wanted to deal with directionality just once.

--- The last sentence of this section is a bit out of the blue. Please explain better (or leave out).

• • • Difficult to explain in only a few words. Left out.

--- Phase synchronization: The main advantage of phase synchro is not only that it is restricted to some frequency bands (coherence is as well) but that the measure is time resolved; i.e. you get a phase value for each data point.

• • • Well, you get a phase (and a phase difference) for each data point, but all indices of phase synchronization (e.g. the mean phase coherence) average somehow over distributions of phase differences. Also the value of the phase difference does not tell you anything about synchronization, what is important is whether it remains more or less constant (consider also the random phase slips often found in noisy data).

[By the way, this is different for some new measures of spike train synchrony where you really get instantaneous values of synchrony.]

--- After eq. 16. Instead of 'this gives'... you could say: From Z we can obtain the Hilbert phase...

• • • Done.

--- After eq. 18 'This is proportional' (what are you referring to?)

• • • Answer: the decay rate. This part has been rewritten and the connection is now made unambiguous.

--- Equation 19: Isn't there a normalization factor?

• • • The normalization factor is hidden in Eq. 18: e^(-w_c^2 sigma^2 / 2)

--- Eq. 20: I would write Im(W_x) and Re(W_x) [add _x]

• • • Done.

--- next line: In QQ is was shown that the ***extraction of the phase from the*** wavelet transform... related to the ***one obtained with the*** Hilbert...

• • • Rewritten such the it is clear that the phases are related (not the transforms nor the extractions).

--- Last sentence of this paragraph: It is not clear to me why broadband phase definitions may be favorable. To me the estimation of a phase from a broadband signal is meaningless. Please explain better (or take out).

• • • Please have a look at Sect 7.2.1. and Fig. 11 of the reference which is provided (Frei et al., 2010). I think the key information from this reference is given, namely the fact that a broadband phase variable such as the unfiltered Hilbert phase generally reflects the dominant frequency in the spectral composition of a signal (which might change in time).

--- Next par: The mean phase coherence ***is*** an index... (Fig. 2). ***It*** is obtained...

• • • Rewritten.

--- You should explain the unwinding of the phase.

• • • Added “wrapped to the interval [0,2 \pi)” to the description of the mean phase coherence (I think it is at this point where it really becomes important).

--- Eq. 21 seems isolated from the text. Please edit. You could also mention other quantifications.

• • • Done.

--- 'For a renormalization accounting'... You could perhaps say a bit more about this.

• • • I think this is a technical detail and too many of these would distract and add unnecessary length. The interested reader can always refer to the citation which is provided.

--- Before the last sentence of the paper (...a common driver.). It is also possible that driver-response relationships just reflect the properties of the individual time series [for a reference see Quian Quiroga et al, 2000].

• • • Included.

--- You could also say a few words about surrogate tests.

• • • Also here I think this would be too distracting (I already have a couple of excursions and would really like to focus on the measures). ‘Surrogates’ should be a separate article to which I could then refer in a short sentence. As of now I would have to explain too much.