Coexistence of scale-invariant and rhythmic behavior in self-organized criticality

Cognitive function: holarchy or holacracy?

Cognition is the most complex function of the brain. When exploring the inner workings of cognitive processes, it is crucial to understand the complexity of the brain's dynamics. This paper aims to describe the integrated framework of the cognitive function, seen as the result of organization and interactions between several systems and subsystems. We briefly describe several organizational concepts, spanning from the reductionist hierarchical approach, up to the more dynamic theory of open complex systems. The homeostatic regulation of the mechanisms responsible for cognitive processes is showcased as a dynamic interplay between several anticorrelated mechanisms, which can be found at every level of the brain's organization, from molecular and cellular level to large-scale networks (e.g., excitation-inhibition, long-term plasticity-long-term depression, synchronization-desynchronization, segregation-integration, order-chaos). We support the hypothesis that cognitive function is the consequence of multiple network interactions, integrating intricate relationships between several systems, in addition to neural circuits.

Spike-Timing-Dependent Plasticity With Axonal Delay Tunes Networks of Izhikevich Neurons to the Edge of Synchronization Transition With Scale-Free Avalanches

Critical brain hypothesis has been intensively studied both in experimental and theoretical neuroscience over the past two decades. However, some important questions still remain: (i) What is the critical point the brain operates at? (ii) What is the regulatory mechanism that brings about and maintains such a critical state? (iii) The critical state is characterized by scale-invariant behavior which is seemingly at odds with definitive brain oscillations? In this work we consider a biologically motivated model of Izhikevich neuronal network with chemical synapses interacting via spike-timing-dependent plasticity (STDP) as well as axonal time delay. Under generic and physiologically relevant conditions we show that the system is organized and maintained around a synchronization transition point as opposed to an activity transition point associated with an absorbing state phase transition. However, such a state exhibits experimentally relevant signs of critical dynamics including scale-free avalanches with finite-size scaling as well as critical branching ratios. While the system displays stochastic oscillations with highly correlated fluctuations, it also displays dominant frequency modes seen as sharp peaks in the power spectrum. The role of STDP as well as time delay is crucial in achieving and maintaining such critical dynamics, while the role of inhibition is not as crucial. In this way we provide possible answers to all three questions posed above. We also show that one can achieve supercritical or subcritical dynamics if one changes the average time delay associated with axonal conduction.

Proper spatial heterogeneities expand the regime of scale-free behavior in a lattice of excitable elements

Signatures of criticality, such as power law scaling of observables, have been empirically found in a plethora of real-life settings, including biological systems. The presence of critical states is believed to have many functional advantages and is associated with optimal operational abilities. Typically, critical dynamics arises in the proximity of phase transition points between absorbing disordered states (subcriticality) and ordered active regimes (supercriticality) and requires a high degree of fine tuning to emerge, which is unlikely to occur in real biological systems. In the present study we propose a rather simple, and biologically relevant mechanism that profoundly expands the critical-like region. In particular, by means of numerical simulation we show that incorporating spatial heterogeneities into the square lattice of map-based excitable oscillators broadens the parameter space in which the distribution of excitation wave sizes follows closely a power law. Most importantly, this behavior is only observed if the spatial profile exhibits intermediate-sized patches with similar excitability levels, whereas for large and small spatial clusters only marginal widening of the critical state is detected. Furthermore, it turned out that the presence of spatial disorder in general amplifies the size of excitation waves, whereby the relatively highest contributions are observed in the proximity of the critical point. We argue that the reported mechanism is of particular importance for excitable systems with local interactions between individual elements.