Self-organisation of small-world networks by adaptive rewiring in response to graph diffusion.

Complex networks emerging in natural and human-made systems tend to assume small-world structure. Is there a common mechanism underlying their self-organisation? Our computational simulations show that network diffusion (traffic flow or information transfer) steers network evolution towards emergence of complex network structures. The emergence is effectuated through adaptive rewiring: progressive adaptation of structure to use, creating short-cuts where network diffusion is intensive while annihilating underused connections. With adaptive rewiring as the engine of universal small-worldness, overall diffusion rate tunes the systems' adaptation, biasing local or global connectivity patterns. Whereas the former leads to modularity, the latter provides a preferential attachment regime. As the latter sets in, the resulting small-world structures undergo a critical shift from modular (decentralised) to centralised ones. At the transition point, network structure is hierarchical, balancing modularity and centrality - a characteristic feature found in, for instance, the human brain.

Dynamic effective connectivity in cortically embedded systems of recurrently coupled synfire chains.

As a candidate mechanism of neural representation, large numbers of synfire chains can efficiently be embedded in a balanced recurrent cortical network model. Here we study a model in which multiple synfire chains of variable strength are randomly coupled together to form a recurrent system. The system can be implemented both as a large-scale network of integrate-and-fire neurons and as a reduced model. The latter has binary-state pools as basic units but is otherwise isomorphic to the large-scale model, and provides an efficient tool for studying its behavior. Both the large-scale system and its reduced counterpart are able to sustain ongoing endogenous activity in the form of synfire waves, the proliferation of which is regulated by negative feedback caused by collateral noise. Within this equilibrium, diverse repertoires of ongoing activity are observed, including meta-stability and multiple steady states. These states arise in concert with an effective connectivity structure (ECS). The ECS admits a family of effective connectivity graphs (ECGs), parametrized by the mean global activity level. Of these graphs, the strongly connected components and their associated out-components account to a large extent for the observed steady states of the system. These results imply a notion of dynamic effective connectivity as governing neural computation with synfire chains, and related forms of cortical circuitry with complex topologies.

Donders is dead: cortical traveling waves and the limits of mental chronometry in cognitive neuroscience.

An assumption nearly all researchers in cognitive neuroscience tacitly adhere to is that of space-time separability. Historically, it forms the basis of Donders' difference method, and to date, it underwrites all difference imaging and trial-averaging of cortical activity, including the customary techniques for analyzing fMRI and EEG/MEG data. We describe the assumption and how it licenses common methods in cognitive neuroscience; in particular, we show how it plays out in signal differencing and averaging, and how it misleads us into seeing the brain as a set of static activity sources. In fact, rather than being static, the domains of cortical activity change from moment to moment: Recent research has suggested the importance of traveling waves of activation in the cortex. Traveling waves have been described at a range of different spatial scales in the cortex; they explain a large proportion of the variance in phase measurements of EEG, MEG and ECoG, and are important for understanding cortical function. Critically, traveling waves are not space-time separable. Their prominence suggests that the correct frame of reference for analyzing cortical activity is the dynamical trajectory of the system, rather than the time and space coordinates of measurements. We illustrate what the failure of space-time separability implies for cortical activation, and what consequences this should have for cognitive neuroscience.

Spatially constrained adaptive rewiring in cortical networks creates spatially modular small world architectures.

A modular small-world topology in functional and anatomical networks of the cortex is eminently suitable as an information processing architecture. This structure was shown in model studies to arise adaptively; it emerges through rewiring of network connections according to patterns of synchrony in ongoing oscillatory neural activity. However, in order to improve the applicability of such models to the cortex, spatial characteristics of cortical connectivity need to be respected, which were previously neglected. For this purpose we consider networks endowed with a metric by embedding them into a physical space. We provide an adaptive rewiring model with a spatial distance function and a corresponding spatially local rewiring bias. The spatially constrained adaptive rewiring principle is able to steer the evolving network topology to small world status, even more consistently so than without spatial constraints. Locally biased adaptive rewiring results in a spatial layout of the connectivity structure, in which topologically segregated modules correspond to spatially segregated regions, and these regions are linked by long-range connections. The principle of locally biased adaptive rewiring, thus, may explain both the topological connectivity structure and spatial distribution of connections between neuronal units in a large-scale cortical architecture.

Traveling waves and trial averaging: the nature of single-trial and averaged brain responses in large-scale cortical signals.

Analyzing single trial brain activity remains a challenging problem in the neurosciences. We gain purchase on this problem by focusing on globally synchronous fields in within-trial evoked brain activity, rather than on localized peaks in the trial-averaged evoked response (ER). We analyzed data from three measurement modalities, each with different spatial resolutions: magnetoencephalogram (MEG), electroencephalogram (EEG) and electrocorticogram (ECoG). We first characterized the ER in terms of summation of phase and amplitude components over trials. Both contributed to the ER, as expected, but the ER topography was dominated by the phase component. This means the observed topography of cross-trial phase will not necessarily reflect the phase topography within trials. To assess the organization of within-trial phase, traveling wave (TW) components were quantified by computing the phase gradient. TWs were intermittent but ubiquitous in the within-trial evoked brain activity. At most task-relevant times and frequencies, the within-trial phase topography was described better by a TW than by the trial-average of phase. The trial-average of the TW components also reproduced the topography of the ER; we suggest that the ER topography arises, in large part, as an average over TW behaviors. These findings were consistent across the three measurement modalities. We conclude that, while phase is critical to understanding the topography of event-related activity, the preliminary step of collating cortical signals across trials can obscure the TW components in brain activity and lead to an underestimation of the coherent motion of cortical fields.

High-capacity embedding of synfire chains in a cortical network model.

Synfire chains, sequences of pools linked by feedforward connections, support the propagation of precisely timed spike sequences, or synfire waves. An important question remains, how synfire chains can efficiently be embedded in cortical architecture. We present a model of synfire chain embedding in a cortical scale recurrent network using conductance-based synapses, balanced chains, and variable transmission delays. The network attains substantially higher embedding capacities than previous spiking neuron models and allows all its connections to be used for embedding. The number of waves in the model is regulated by recurrent background noise. We computationally explore the embedding capacity limit, and use a mean field analysis to describe the equilibrium state. Simulations confirm the mean field analysis over broad ranges of pool sizes and connectivity levels; the number of pools embedded in the system trades off against the firing rate and the number of waves. An optimal inhibition level balances the conflicting requirements of stable synfire propagation and limited response to background noise. A simplified analysis shows that the present conductance-based synapses achieve higher contrast between the responses to synfire input and background noise compared to current-based synapses, while regulation of wave numbers is traced to the use of variable transmission delays.

Detecting synfire chains in parallel spike data.

The synfire chain model of brain organization has received much theoretical attention since its introduction (Abeles, 1982, 1991). However there has been no convincing experimental demonstration of synfire chains due partly to limitations of recording technology but also due to lack of appropriate analytic methods for large scale recordings of parallel spike trains. We have previously published one such method based on intersection of the neural populations active at two different times (Schrader et al., 2008). In the present paper we extend this analysis to deal with higher firing rates and noise levels, and develop two additional tools based on properties of repeating firing patterns. All three measures show characteristic signatures if synfire chains underlie the recorded data. However we demonstrate that the detection of repeating firing patterns alone (as used in several papers) is not enough to infer the presence of synfire chains. Positive results from all three measures are needed.

Generalization of learning by synchronous waves: from perceptual organization to invariant organization.

From a few presentations of an object, perceptual systems are able to extract invariant properties such that novel presentations are immediately recognized. This may be enabled by inferring the set of all representations equivalent under certain transformations. We implemented this principle in a neurodynamic model that stores activity patterns representing transformed versions of the same object in a distributed fashion within maps, such that translation across the map corresponds to the relevant transformation. When a pattern on the map is activated, this causes activity to spread out as a wave across the map, activating all the transformed versions represented. Computational studies illustrate the efficacy of the proposed mechanism. The model rapidly learns and successfully recognizes rotated and scaled versions of a visual representation from a few prior presentations. For topographical maps such as primary visual cortex, the mechanism simultaneously represents identity and variation of visual percepts whose features change through time.