Talk:Population measures of spike train synchrony

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    Reviewer A (Dr. Thomas Kreuz)

    Given the increasing availability of multi-unit recordings, the article addresses a very timely approach to data analysis, population measures of spike train synchrony. I think that it is a very nice contribution which is fully suitable for publication in Scholarpedia. Here is a list with just a few (mostly minor) issues.

    General comment:

    Do you have one or more figures that you could add to illustrate some of the methods? That might make it more accessible to some of the general and less mathematical readers.

    >>> It is hoped to illustrate the entry at a future point when multi-neuronal versions of the ISI and SPIKE distance have appeared.


    I would reverse the first sentence in order to start with the topic that is defined in this article (this will increase its visibility in web searches): “A population measure of spike train synchrony estimates the similarity of a pair of population responses in the same way as a measure of spike train synchrony estimates the similarity of a pair of spike trains.” The sentence after that is very long. Could you split it? This is particularly important because the first two paragraphs (intro) should be as broadly accessible as possible.

    >>> The first sentence has been changed much along the lines suggested and the subsequence sentence has been split.

    Section 1 (Measures of spike train synchrony):

    Maybe mention that u1,… are the spike times?

    >>> done

    Maybe mention quickly (in brackets) the three requirements for a metric?

    >>> mentioned, though not in brackets

    This sentence I would put right after the definitions of the bivariate measures: “Broadly speaking, population measures come in two varieties, those that measure the over-all synchrony of a set of responses and are calculated by averaging single-neuron measures of synchrony, and those which measure the similarity or dissimilarity between two sets of responses.”

    >>> This sentence has been placed after the introduction of the bivariate measures.

    “Since they will be useful” is maybe a bit too weak. The population measures are based on them so I would suggest to use a formulation that reflects this.

    >>> changed to "Since they form the base on which the population measures in this article are built, three different single-neuron distance measures are described here."

    Section 1.1 (The Victor-Purpura metric):

    Aren’t these three edit types (it is a matter of definition but also Victor always speaks of three)?

    >>> done

    Maybe replace ‘cheapest’ somehow by ‘minimum cost’? Would be a bit more formal.

    >>> done

    Section 1.2 (The van Rossum metric):

    If possible avoid starting sentences with variable (Heaviside sentence).

    >>> done

    Maybe write “Θ(t)=1 otherwise” (once you have a real number (0) and once the written number (one)).

    >>> done

    “The timescale τ, like 2/q in the Victor-Purpura metric it determines” --> “The timescale τ, like 2/q in the Victor-Purpura metric, determines”

    >>> done

    Section 1.3 (The ISI- and the SPIKE-distance):

    “they emphasis” --> “they emphasize”

    >>> done

    Section 2 (Measures of overall synchrony):

    Why not use u_1, u_2, … instead of t_1, t_2, …. I think this would stress the single population case more than introducing a new variable t.

    >>> done

    n --> N in formulas (above the sum symbol)

    >>> done

    Section 3 (Measures of the synchrony of two population responses):

    Maybe somehow stress ‘summed population code’ and ‘labelled-line code’ (italics?) the first time they appear.

    >>> done (italics!)

    Section 3.1 (The population Victor-Purpura metric):

    When talking about the complexity: “for spike trains with average length n” --> “for N spike trains with average length n.” (repeat the N).

    >>> done

    Here the number of spikes is denoted as n, in Section 1.2 you use m (above the sum symbol). Well, here it is the average number…

    >>> m changed to n in 1.2

    Section 3.2 (The population van Rossum metric):

    “To extend this idea to populations to embedding space” --> “To extend this idea to populations the embedding space”

    >>> fixed

    Edit “Here θ</theta>corresponds to the angle between<math>e1” (incorrect use of math mode)

    >>> fixed

    Here you use w to label spike trains, in Section 2 you use i and j. But maybe you want to distinguish the two cases (intra vs. inter)? Maybe also add upper bounds for sum symbols. And you use a different notation for sums over pairs than in Section 2 (but here you add over both half matrices so it is different?). But still the N could help.

    >>> w->i and added limits, made sums consistient

    “The directions of the individual unit vectors ew serves to parameterize this metric.” Here it is not really clear that the angle (between 0 and 90) or cos angle (between 1 and 0) is the parameter. By writing ‘parallel’ and ‘orthogonal’ you imply it but maybe it would be clearer if you would state it explicitly, maybe even in the equations: d(angle; U, V).

    >>> any improvement I tried were confusing in their own way.

    In the end you speak of a van Rossum ‘distance’, before you always used ‘metric’.

    >>> done

    You say ‘as with the single-neuron van Rossum metric’ but you did not mention this cost reduction for the single-neuron case before.

    >>> "as with . . metric" deleted.

    Section 4 (Example Applications):

    “used to analysis” --> “used to analyze”

    >>> fixed

    Section 5 (References):

    Please check pages. Often the ‘-‘ seems to be missing.

    >>> fixed. Phys Rev. pages don't have -s.

    Section 6 (Further reading):

    Please check title. Year right after authors.

    In addition I have already corrected directly some rather minor issues (typos etc). These corrections can be tracked and verified via the ‘View history’ function.

    Reviewer B (Dr. Daniel Chicharro)

    First review and reply

    The only general comment I have has been also suggested by Reviewer A and regards the description of which populations are compared. This is important because not all the population measures described can be equally used for all setups. I can imagine different scenarios. First, the intra-population measure of similarity. This can be used 1) as a measure of how similar are the responses of different cells in the same trial of a stimulus, or 2) to quantify the reliability of a single cell for different trials of the same stimulus. Second, the population measure can be used 3) to quantify the similarity of the responses of a single population across stimuli, or 4) across stimuli. Third, it can be used 5) to quantify the similarity of the responses to the same stimulus of two different multi-neural populations. In this cases the nature of the population is different and the requirements to apply the measures change:

    1) Diversity of single cells responses: There is a unique multi-neural population, a unique stimulus, and a unique trial (or an average across trials can be also done). Only the measures of overall synchrony (the average of bivariate measures) can be applied to get a quantification of the diversity of the responses of the cells.

    2) Reliability of single cell responses: There is a single cell, the population is considered as a population of trials of the same stimulus. What is quantified is the reliability of the response of this cell. ). Only the measures of overall synchrony (the average of bivariate measures) can be applied.

    3) Reliability of multi-neural population responses: There is a unique multi-neural population and the responses but now one examines the reliability as a population, so the question of population or single-neuron coding appears and the measures described in section “measures of synchrony of two population responses ” should be used (while they cannot for 1) and 2)). In this case the average of bivariate measures can also be used but it is less natural, since one would need to calculate the distance of a single cell response for trial 1 with each of the cell responses of trial 2 and so on.

    4) Population versus single cell coding of stimuli: There is a unique multi-neural population and different stimuli are presented. Again each cell is identifiable and there is a comparison of coding strategies. The multi Victor or Van Rossum should be used and the average of bivariate is less natural.

    5) Comparison of two multi-neural population responses: The last case is when one has two populations of cells instead of one and there is a way to map each cell to a single cell in the other population. This maybe is more difficult for real experiments, but one possible setup is in simulations when one wants to compare the sipke trains in two networks with the same structure but different single neuron components (integrate-and-fire versus Hodgkin Huxley)

    In cases 1) and 2) the multi-neuron Victor and VanRossum cannot be applied because it is not suited to assign labels to the neurons. In cases 3,4,5) the average bivariate measure can be used but it implies calculating a lot of combinations. In cases 1) 3) and 4) there is a unique multineural population, in case 2) there is a single neuron and a population of trials, and in case 5) there are two multi-neural populations.

    Even if not with all these details it should be clear in which cases it is possible to apply the multi Victor or Van Rossum and in which setup this is not possible. And similarly it should be clear in which cases it is natural to use the average bivariate measure or when it becomes too cumbersome.

    >>> This is a very good suggestion, I have tried to include some of this in the new paragraph

    "A measure of overall synchrony gives a single quantity describing how spread out a set of responses are. These might be multiple responses from a single neuron, for example multiple trials with the same stimulus, in which case overall synchrony measures quantifies the reliability of the response, or they might be responses to a corpus of stimuli, in which case the overall synchrony measure how strongly modulated the neuron is by the stimulus. Alternatively, the responses might be spike trains from multiple neurons with a single stimulus; in this case the overall synchrony measures is small if the role of the population is to reduce noise, or large if different neurons respond preferentially to different aspects of the stimulus. In contrast the measures of the synchrony of two population responses, which will be examined next, measure a distance between two equally-sized sets of spike trains, most typically, two different population responses or, in principle though not in practise, responses from two different sets of neurons where each neuron from one set has an equivalent neuron in the other set, or perhaps, reponses from real neurons and a model of the same network."

    Smaller comments:

    At the Intro: data sets are increasing recorded, should that be increasingly?

    >>> done

    At “the Victor-Purpura metric”: “each has a different cost” maybe better “each has a cost” because adding, deleting have the same cost.

    >>> done

    The use of Conversely is to me not completely correct. There is a sentence referring to small value of q. Then there is another sentence which is a general explanation but starts with Conversely. The Conversely would make sense linking the sentence of small value with the one of high value which is the subsequent. I suggest:

    "" It is never worthwhile to move a spike more than 2/q since doing so would have a higher cost than deleting the spike at one location and adding it at the other. For a small value of q spikes can be moved with little cost, and the distance is substantially determined by the difference in the number of spikes. Conversely, as q becomes larger, the metric becomes increasingly sensitive to spike times.""

    >>> done

    At “Measures of the synchrony of two population responses”: When it is said “In each case there is an extra parameter”. In fact for the van Rossum extension there are N(N-1)/2 extra parameters, but of course they can be taken as equal considering the angles of projection to be all the same.

    >>> added

    "Here, a single cost, $k$ has been used for the change of spike label. In principle, there could be a different cost for every possible change of label, giving $N(N-1)/2$ $k$-like parameters in all, in practice the metric is simplified, as here, by assuming all label changes have the same cost."


    "It is possible to reduce the number of parameters by making all the $\theta_{ij}$ as having the same value. This is analogous to the population Victor-Purpura metric where the cost of changing a spike label is always $k$ irrespective of which labels are involved."

    and made some other minor adjustments.

    At Example applications: Aranov --> Aronov

    >>> done

    Second review

    There is a part of the new paragraph which I do not fully understand:

    "Alternatively, the responses might be spike trains from multiple neurons with a single stimulus; in this case the overall synchrony measure is small if the role of the population is to reduce noise, or large if different neurons respond preferentially to different aspects of the stimulus"

    I think it would be better to contrast responding to similar aspects of the stimulus with responding to different aspects of the stimulus. I understand that the role of the population is to reduce noise means that they answer to the same aspect, but this is less explicit.

    Furthermore, the sentence was at first contradictory to me because the idea of overall synchrony is just the opposite of how the measure is defined, that is, from the meaning of overall synchrony one expects low synchrony for responses to different aspects, but the measure is high. Maybe it would be good to avoid this misunderstanding adding: "overall synchrony measure D is small (high synchrony) if the ...."

    >>> Thanks! I have changed it to

    "Alternatively, the responses might be spike trains from multiple neurons with a single stimulus. In this case, if the role of the population is to reduce noise, the individual neurons will respond in the same way to a single aspect of the stimulus and will be highly synchronized with a small distance $D$ and, conversely, if different neurons respond preferentially to different aspects of the stimulus the neurons will not be synchronized the $D$ will be large."


    I just went through the article and copy-edited it for language and readability. I don't think I actually changed the meaning of anything, other than deleting one sentence that I thought didn't serve any purpose. One thing I did that you might find obnoxious was to change the spelling of "labelled" to "labeled" -- I think that's better style, but if you don't like it I won't be offended if you change it back. Best regards, William Skaggs 16:35, 25 July 2013 (UTC)

    >> Thanks for your extensive and careful proofreading. Conor Houghton

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