Network Structure and Observability

Starting point of the assessment framework is the network structure that defines the number of neurons and their interactions. Alongside with the network some of its nodes are chosen to be observable, i.e. data can only be collected from these units. When these decisions are made, the size, topology, and observability of the artificial neural circuit are defined. The neural simulation is influenced by each of these three factors, which are therefore discussed in the following.

(Overall complexity) Compared to the enormous number of neurons in the

brain (e.g. 1011in humans [Kandel et al., 2000, p.19]) and their manifold of den- dritic wirings, it is obvious that the simulated network’s complexity is probably the most unrealistic component in the set-up. It only consists of a small num- ber of neurons, which are sparsely interconnected compared to 10,000–150,000 synaptic contacts a real neuron makes [Kandel et al., 2000, p.25]. Further, al- though only less than half of the simulated neurons have been chosen to be observable, this level of observability is chosen too high, compared to techno-

logical limits on data-collection, which do not facilitate such high coverage in monitoring. The constructed network and data-sampling capabilities thus do not correspond to a realistic neural circuit in three points: size, connectivity, and observability of the simulated system. The reason for using a compara- tively small network with sparse connectivity is that even rebuilding only small parts of the nervous system in a nearly realistic manner is accompanied by two problematic demands: A severe amount of data to build and parameterise such model, and extremely powerful computational resources are needed for its sim- ulation (e.g. [Markram, 2006, Bhalla, 2008]). Existing complex simulators are not freely accessible (yet) and setting such up is clearly beyond the scope of this PhD project. Investigations of the SSS therefore have to be done with highly simplified neural networks. Whether resulting observations also hold in more complex situations will therefore remain subject to speculations.

(Impact of Topology on Dynamics) Studies have shown that depending

on how neurons are interconnected with each other different pattern of activity can emerge [Sporns et al., 2000, Sporns and Tononi, 2002, Galan, 2008, Bull- more and Sporns, 2009]. The modelled neural circuitry used here is not complex enough to observe complex patterns, but network topology has still an effect on the activity of modelled neurons and especially on the impetus of their data. Before this is explained in detail, the practical implication of the relationship between network structure and impetus is mentioned: The SSS’s performance is positively correlated with the impetus and the length data; analysis of real recordings might thus depend on the origin of the data. Data from structures with feed-forward connections (like the visual system [Ganis and Kosslyn, 2007]) might show a lower impetus than those from circuits with significant recur- rent connections (e.g. hippocampus [Siegel and Sapru, 2007, pp.447]); different amounts of data may thus be required for successful network recovery. But how can network structure influence the impetus in the data? This is explained next for the simulated network, where links represent excitatory synaptic connec- tions.

The impetus of a node is affected by two factors: the number of converging connections in that node and its relative position in the network. The first point is obvious by noticing that the number of parents of a node correlates with the number of excitatory inputs this node can receive simultaneously. More spikes can thus be evoked in nodes with many parents, and it can therefore have a higher impetus than a node with fewer incoming connections. For one part the impetus of a node is thus influenced by local network properties like its parents, but the position of that node within the network (a rather global property) can also affect its impetus. This can be seen by considering the feed-forward

network used in the simulations (Fig. 7.1), where activity propagating through the network has a tendency to increase. In more detail, neurons on the input- side of the network (Fig. 7.1a, left) do not receive any or just few incoming connections. They do thus not receive significant excitatory inputs, but only the spontaneous baseline stimulation. Differently, nodes in the centre of the network (Fig. 7.1a, middle) exhibit more incoming connections through which excitatory potentials are received from neurons nearer to the input side. These centre-neurons are thus more likely to show spiking activity because, additional to stimulation spikes, they also spike due to excitations from neurons further upstream in the network. The activity and impetus of the centre neurons is therefore higher than that of neurons at the input side of the network. Moving further downstream towards the output side of the network (Fig. 7.1a, right), neurons receive excitatory inputs at even higher rates than the centre neurons before them. In this set-up, nodes on the output side of the network are thus likely to exhibit the highest activity and impetus, simply because activity slowly accumulates over neuron-layers. Whether the inclining impetus throughout the structure actually had an effect in the simulated network cannot be reliably assessed: Since most observable nodes are located in the output half of the net- work, only few plausible links exist within the other half. Although some of these are reliably inferred (Fig. 7.6), their small number prevents a significant comparison in order to show whether these are less likely to be revealed than those towards the output side of the network. Investigating this aspect would require varying observability of the network to ensure equal distribution of plau- sible links; however, this is subject to future work. Here, observable nodes are left unchanged in order to facilitate comparisons between different simulations shown (later).