Network properties

The methods that were introduced in this study provide an efficient way to discover structural patterns in neuronal networks. By first selecting sets of edges according to research question driven criteria, the homogeneity test enables the researcher to quickly assess differences of edge probabilities between different sets, while the Hamming distance test constitutes a powerful tool for the evaluation of similar- ity between networks defined by edge sets, either within the same experimental condition or between different conditions. Both tests, homogeneity and Hamming, are easily applicable to various kinds of networks, not only in the context of brain research. It is obvious that the larger the networks, the more reliable the test results will be. However, also for small networks, as in our example, the methods provide reasonably reliable results.

Homogeneity

Looking at the results on the homogeneity of edge probabilities (Figs. 3.33-3.35), it becomes clear that the number of graphs with more local than distant links clearly outweighs the number of graphs with more distant than local links. This is most pronounced for the phase of the moving stimulus. Similarly, there

are, in total, more graphs with a higher density among the units with a similar orientation preference as compared to those among units with different orientation preferences. Thus, with the application of the network analysis approaches to a sample data set, it was possible to reproduce a number of fundamental findings: the results of the analysis on homogeneity of edge probabilities suggest that spatial proximity is a better predictor for functional connectivity than common orientation preference, as it has been de- scribed by Engel et al. (1990) and Braitenberg and Schüz (1998). These findings are also in line with the assumption that the brain has a small-world property with a high local clustering, but relatively few long-range connections (Watts and Strogatz, 1998; Sporns and Zwi, 2004; Gerhard et al., 2011).

Looking at the different "Gamma groups" separately, the effects separate as well: for Low Initial Gamma Power (Fig. 3.33), spatial proximity and orientation preferences are the main indicators for con- nectivity. For Medium Initial Gamma Power (Fig. 3.34), spatial proximity becomes even more dominant than it was observed for the Low Initial Gamma Power group. For High Initial Gamma Power (Fig. 3.35), spatial proximity is even more strongly linked to the strength of connectivity between the units in the network than it became apparent for the other two Gamma groups. Stimulus direction preference shows a strong relation to the connection probabilites for High Initial Gamma Power. This is mainly apparent during the warm condition and only slightly reduced during contralateral deactivation (this effect is not apparent in the Low and Medium Initial Gamma groups). Interestingly, this observation also holds for the spontaneous activity and static grating phases, but is in these cases completely diminished with ipsilateral deactivation. This indicates that feedback primes these connections between units of similar direction preference, even in the absence of a stimulus. This priming disappears when the feedback from the ipsilateral pMS cortex is eliminated.

Since the Neuroxidence algorithm eliminates the influence of rate variations and only exhibits the effect of synchronous firing events, all effects that were observed were due to changes in synchrony. This means that there were some effects in the structure of the synchronisation patterns, while there was no change in firing rate. This supports the hypothesis that information in the brain is encoded by synchronously active cell assemblies.

Hamming Distance

A significantly small Hamming Distance indicates a strong resemblance between the compared graphs, revealing the existence of characteristic structures in the observed networks. During spontaneous ac- tivity and presentation of the stationary stimulus, the networks were sparse, which made it difficult to statistically assess their features. Also, the variability among the networks was high in these phases. Accordingly, for most cases of spontaneous activity, the Hamming distance was not significantly small. Kenet et al. (2003) showed that even if the eyes are not exposed to any visual stimulus, specific ac- tivity structures can be observed in visual cortex, which resemble stimulus-induced activity patterns. However, from the observations presented here, these spontaneous structures seem to become severely disrupted by the deactivation of feedback from pMS.

For the moving stimulus, fixed structures emerged, indicated by smaller Hamming distances among the networks obtained under this condition. Since the stimulus is dynamic in this phase, new incoming information has to be constantly processed. Thus, the workload for the visual areas is higher as compared to the other stimulation conditions. Assuming the validity of the assembly hypothesis, a higher degree of synchrony among the cells belonging to the same assembly would be expected in this case. The small Hamming distance for this phase indicates the repeated synchronous activity of the same groups of neurons, again speaking in favour of the assembly hypothesis.

When interpreting the Hamming distance one should bear the following in mind: a small Hamming distance could be due to the fact that two networks with a certain number of edges are very similar, but also that the two networks might only show a few number of connections at all. Thus, the results should be interpreted relative to the total number of edges. However, also the absence of an edge holds information and should possibly even be valued as much as the presence of an edge.

Density

For both the NeuroXidence and the GLM approach, decreases in density were observed for both ipsi- and bilateral deactivation, which is in line with the changes in gamma power under the same conditions, as observed in previous studies of the LFP (Ebisch, 2007; Geider, 2008; Barnes, 2014) (see sections 3.7.3 and 3.8.2). These differences in density were most pronounced for phases of spontaneous activity.

The graphs constructed on the basis of NeuroXidence results exhibited densities up to 30 %, while the graphs constructed on the basis of results from GLM analysis showed densities between around 40-60 %. Though densities around 50 % could be seen as suspicious and pointing to a random assignment of links in the network, significant differences between experimental conditions could be extracted from the data: densities decreased during ipsi- and bilateral deactivation as compared to the warm condition, and especially for the High Initial Gamma group, this effect was very consistent.

It is important to note that graph density did not follow the same trends as the spike rate and some- times even showed diametrical effects. This is, for example, visible for the High Initial Gamma group, for MUA rate vs. network density based on NeuroXidence: for static and moving grating, an increase in spike rate was observed during ipsilateral deactivation (Fig. 3.22). The graph density, in contrast, decreased for these conditions (Fig. 3.37). Similarly, for single-unit spike rates vs. network density based on the GLM, it was observed that for the Low Initial Gamma group, spike rates increased during ipsilateral deactivation for the phases of spontaneous activity and static stimulus (Fig. 3.23), but graph densities decreased (Fig. 3.41). This confirms that the functional and effective connectivity measures applied here to determine the density extracted effects that are independent from the rate.

Clustering Coefficient

The clustering coefficient showed similar tendencies for the NeuroXidence and GLM apporaches (see sections 3.7.3 and 3.8.2). However, for the graphs based on the NeuroXidence analysis, the median clus- tering coefficients were very low, often at 0. There was no clear overall trend for the deactivation effects. This could be due to the fact that the graphs based on the NeuroXidence analysis only exhibited densi- ties up to 20-30 % and, as a consequence, the graphs were not fully connected. For this reason, the low clustering coefficients might at least partly be due to a sampling effect, caused by spatial subsampling of the selected cells, and the size of the correlation windows. With this, some actually existing connec- tions might not be detected. The graphs constructed on the basis of the GLM analysis exhibit higher densities overall and thus might form fully connected graphs, so that the analysis of the clustering coef- ficient is able to pick up the tendencies towards weaker clustering during ipsi- and bilateral deactivation, especially for the moving stimulus.

Characteristic Path Length

For calculating the characteristic path length, different definitions can be found in the literature, some of them setting Li j := ∞ for two nodes i and j that are not connected. In this case, for any graph that is not completely connected, the average path length will be infinite. Thus, as the initial probing of the

networks already showed that many graphs exhibited disconnected components, Li j was set to∞ for any two disconnected nodes i and j, but not considered for the computation of the average path length. With this, it should be noted that many connections do not exist in the graphs. Since the computation of the characteristic path length only considers existing connections, these missing links are skipped. This could lead to a bias in the analysis and result in higher observed characteristic path lengths than actually present in the underlying network.

For the analysis based on NeuroXidence, the characteristic path length behaved in a similar way to the density and the clustering coefficient (see section 3.7.3). This is actually counter-intuitive, but again might be due to the sampling issues described above.

For the GLM graphs, the characteristic path length increased for ipsi- and bilateral deactivation (see 3.8.2), which fits the expectation and can be viewed as a further validation of the analysis approach, even with the observed densities of around 50 %. Here, in contrast to the NX analysis, the density might be high enough to allow for a better assessment of the deactivation effect on the characteristic path length. Longer path lengths during pMS deactivation might aggravate information processing on the local network level and disturb the accuracy in the timing of action potentials, which could be one reason for the impairments that can be observed during neglect.

Summary

The analyses in this study were performed on different levels of granularity (from coarse to detailed): • LFP

• MUA rates and tunings

• MUA cross correlations / PARAFAC • MUA / networks based on NeuroXidence • SUA rates and tunings

• SUA / networks based on GLM

It is likely that multiplexing is present in the brain, meaning that information processing might hap- pen at multiple time scales and frequencies in parallel. Depending on the selected methods and analysis windows, the measures at hand will usually only extract information on a certain time scale. In order to identify the relevant time scales that the system is operating at, it is advisable to probe multiple mea- sures at different temporal and spatial scales, this is why multiple methods were applied here.

While the NeuroXidence approach yielded results based on binary, undirected networks, the GLM method was utilized in order to obtain information about directional information flow. It was shown that plausible effects could be extracted from the datasets, confirming that the application of both approaches is suitable in this context.

The analysis of the networks based on the GLM approach revealed a tendency that with increasing stimulation strength (from a blank screen to a moving high contrast grating), the observed density and clustering coefficient increased and the average path length decreased. Therefore, a stronger stimulus leads to a higher level of correlated activity. At the same time, the graph-theoretical distances are shortened. This might facilitate signal propagation and increase processing speed, because a lower number of synapses must be overcome to reach the next unit of cells.

However, due to the length of the cross-history window, the effect that is extracted by the GLM method might partly be a population effect, linked to the LFP, because within the selected integration window of 70 ms, global rate changes might be captured. This could lead to the relatively high density of links, but at the same time conceal more specific effects.

Both the NeuroXidence method and the GLM models are rate-corrected, and, therefore, comparable. Still, the two approaches did not yield the exact same results, for example with regards to the charac- teristic path length. However, with both approaches, significant results could be obtained, which were in line with previous studies. Possible reasons for these deviances are the differences in the probed time scales and the fact that NeuroXidence observes joint-spike events, i.e. synchronous activity of pairs of units, while the GLM approach focuses on temporal patterns and considers the direction of informa- tion flow within the network. These two measures might actually behave differently, so that it is not necessarily expected that congruent observations are made.