Counting Pattern:
JSpattern detection
Toydata were analyzed to illustrate that NeuroXidence identifies all JSEs and derives their exact frequency of occurrence. The toydataset contained different JSEs with given frequencies of occurrence and JSEs that were isolated as well as overlapping. The complexity of the induced JSpattern varied between 2–10, based on a set of neurons varying between 2–8. NeuroXidence detected in each toydataset all induced JSpatterns as well as their subpatterns, and it derived the frequencies of occurrence correctly.
The determination of the total frequency of occurrences of one particular JSpattern in the dataset involves the sum of two pattern frequencies. One is the frequency of JSEs that are identical to the JSpattern of interest. The other is the frequency of all suprapatterns in which the JSpattern is included as a subpattern. NeuroXidence identifies these suprapatterns using an ANDoperation between the JSpattern of interest and any other detected JSpattern. Only if the resulting JSpattern is equal to the JSpattern of interest, is the frequency of the suprapattern considered (Supplemental Fig. 1).
Supplementary Figure 1: Deriving the frequency of occurrence of a testpattern requires accounting for the frequency of occurrence of subpatterns included in other JSEs. (A, C) To determine if a JSE is a subpattern of the testpattern, an AND operation between the testpattern and each JSE is applied. (B, D) The frequency of occurrence of the resulting pattern is considered only if it is identical to the testpattern. The total frequency of occurrence of the testpattern is given by the sum of all frequencies of all qualifying resulting patterns.
Destroying Patterns by Jittering:
Testpower for individual JSpatterns was derived from correlated Poisson processes, generated by a singleinteraction 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 JSpattern of interest beyond chancelevel. To demonstrate that NeuroXidence is capable of detecting JSEs that are jittered less than the allowed jitter, τc, we produced two sets of toydata with τc = 5 ms. The first toydataset 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 testpower for both datasets across different complexities, slidingwindow lengths, and frequencies of JSEs demonstrates that NeuroXidence detects jittered JSEs and precise JSEs equally well (Supplemental Fig. 4).
Supplementary Figure 2: Comparisons of testpower in relation to the frequency of excess jointspike events (JSEs). Subfigures show the testpower (yaxis) of NeuroXidence (blue, dashed red, dashed orange). The toydata 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 singleinteraction process. The excess rate of JSEs beyond the chance level is given on the xaxis. The blue curve indicates the testpower of NeuroXidence in both cases, the JSEs were absolutely synchronous (dataset 1). The dashed red curve shows the testpower 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 testpattern was the same as the maximal imprecision considered by NeuroXidence. The yellow curve indicates a testpattern with a jitter of 15 ms, which was three times larger (η = 3) than the maximal jitter considered by NeuroXidence (dataset 3). The latter testpattern was used to describe H0. The complexities of the testpatterns are changing down the columns (14), and the lengths of the analysis windows are changing across the rows (13).
Influence of multiple surrogates S on the distribution of JSE:
Supplementary Figure 3: Probability distributions forand 20 surrogates of. (A) Estimated distribution (10^{6} samples) of the frequency of jointspike 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 yaxis gives the time needed to analyze the data on one JSpattern with a complexity equal to the number of neurons in the dataset. The data consisted of one 800 ms sliding window and 20 trials. Spiketrains were modeled by a homogeneous gamma process (shape factor = 10) with a spike rate of 10 ap/s. The xaxis gives the complexity of the analyzed JSpattern. The color of the individual curves corresponds to the maximallyallowed jitter τ_{c} 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.
Receptive Fields
Supplementary Figure 5 Orientation tuning of recorded channels from cat area 17. Squares indicate the size of the receptive fields for each recorded channel. Midlines represent orientation preferences.
PSTH
Supplementary Figure 6: Peristimulus 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 simultaneouslyrecorded channels.
Video Files explaining the Preprocessing
