Toy-data were analyzed to illustrate that NeuroXidence identifies all JSEs and derives their exact frequency of occurrence. The toy-dataset contained different JSEs with given frequencies of occurrence and JSEs that were isolated as well as overlapping. The complexity of the induced JS-pattern varied between 2–10, based on a set of neurons varying between 2–8. NeuroXidence detected in each toy-dataset all induced JS-patterns as well as their sub-patterns, and it derived the frequencies of occurrence correctly.
The determination of the total frequency of occurrences of one particular JS-pattern in the dataset involves the sum of two pattern frequencies. One is the frequency of JSEs that are identical to the JS-pattern of interest. The other is the frequency of all supra-patterns in which the JS-pattern is included as a sub-pattern. NeuroXidence identifies these supra-patterns using an AND-operation between the JS-pattern of interest and any other detected JS-pattern. Only if the resulting JS-pattern is equal to the JS-pattern of interest, is the frequency of the supra-pattern considered (Supplemental Fig. 1).
Supplementary Figure 1: Deriving the frequency of occurrence of a test-pattern requires accounting for the frequency of occurrence of sub-patterns included in other JSEs. (A, C) To determine if a JSE is a sub-pattern of the test-pattern, an AND operation between the test-pattern and each JSE is applied. (B, D) The frequency of occurrence of the resulting pattern is considered only if it is identical to the test-pattern. The total frequency of occurrence of the test-pattern is given by the sum of all frequencies of all qualifying resulting patterns.
Destroying Patterns by Jittering:
Test-power for individual JS-patterns was derived from correlated Poisson processes, generated by a single-interaction process . Thus, correlated spike trains were characterized by a background rate, corresponding to the independent spiking of neurons, and by a JSE rate, defining the expected frequency of the JS-pattern of interest beyond chance-level. To demonstrate that NeuroXidence is capable of detecting JSEs that are jittered less than the allowed jitter, τc, we produced two sets of toy-data with τc = 5 ms. The first toy-dataset contained exact JSEs (Supplementary Fig. 4, solid blue line), while the second was derived from the first by the random jittering of individual spikes by τc (Supplementary Fig. 2, dashed red line). The agreement of the test-power for both datasets across different complexities, sliding-window lengths, and frequencies of JSEs demonstrates that NeuroXidence detects jittered JSEs and precise JSEs equally well (Supplemental Fig. 4).
Supplementary Figure 2: Comparisons of test-power in relation to the frequency of excess joint-spike events (JSEs). Subfigures show the test-power (y-axis) of NeuroXidence (blue, dashed red, dashed orange). The toy-data model consisted of 50 trials, each with 5 ‘simultaneous’ spike trains with a spike rate of 10 ap/s. Synchronization of spike trains was modeled by a single-interaction process. The excess rate of JSEs beyond the chance level is given on the x-axis. The blue curve indicates the test-power of NeuroXidence in both cases, the JSEs were absolutely synchronous (dataset 1). The dashed red curve shows the test-power for the same data as used before, but each spike was jittered randomly by an allowed maximum of 5 ms (dataset 2). Thus, the jitter of spikes in the test-pattern was the same as the maximal imprecision considered by NeuroXidence. The yellow curve indicates a test-pattern with a jitter of 15 ms, which was three times larger (η = 3) than the maximal jitter considered by NeuroXidence (dataset 3). The latter test-pattern was used to describe H0. The complexities of the test-patterns are changing down the columns (1-4), and the lengths of the analysis windows are changing across the rows (1-3).
Influence of multiple surrogates S on the distribution of JSE:
Supplementary Figure 3: Probability distributions forand 20 surrogates of. (A) Estimated distribution (106 samples) of the frequency of joint-spike events per trial given a Poisson distribution with an expected value of 0.3 JSEs per trial. (B) Estimated distribution based on averaging S = 20 surrogates of the distribution in (A). (C) Probability distribution of the difference .
Scaling of computation effort:
Supplementary Figure 4: Computational complexity of NeuroXidence as a function of the number of neurons that were analyzed. The y-axis gives the time needed to analyze the data on one JS-pattern with a complexity equal to the number of neurons in the dataset. The data consisted of one 800 ms sliding window and 20 trials. Spike-trains were modeled by a homogeneous gamma process (shape factor = 10) with a spike rate of 10 ap/s. The x-axis gives the complexity of the analyzed JS-pattern. The color of the individual curves corresponds to the maximally-allowed jitter τc in units of the bin length (blue = 3, red = 5, green = 7). Each curve represents the average computational complexity measured for 15 independent realization of the same data model. The dashed curves give the expected computational complexity if complexity were an exponential function of number of neurons.
Supplementary Figure 5 Orientation tuning of recorded channels from cat area 17. Squares indicate the size of the receptive fields for each recorded channel. Mid-lines represent orientation preferences.
Supplementary Figure 6: Peri-stimulus time histograms of 6 single units in 20 trials recorded in cat area 17. The PSTHs were based on a bin width of 25 ms. Channels were selected to be representative for 48 simultaneously-recorded channels.
Video Files explaining the Preprocessing