Hierarchical modular structure enhances the robustness of self-organized criticality in neural networks

Abstract

One of the most prominent architecture properties of neural networks in the brain is the hierarchical modular structure. How does the structure property constrain or improve brain function? It is thought that operating near criticality can be beneficial for brain function. Here, we find that networks with modular structure can extend the parameter region of coupling strength over which critical states are reached compared to non-modular networks. Moreover, we find that one aspect of network function-dynamical range-is highest for the same parameter region. Thus, hierarchical modularity enhances robustness of criticality as well as function. However, too much modularity constrains function by preventing the neural networks from reaching critical states, because the modular structure limits the spreading of avalanches. Our results suggest that the brain may take advantage of the hierarchical modular structure to attain criticality and enhanced function.

Near-Critical Dynamics in Stimulus-Evoked Activity of the Human Brain and Its Relation to Spontaneous Resting-State Activity

“…Then, positive and negative excursions beyond a chosen threshold of 3 SDs for each sensor were identified. The 3 SDs threshold was shown previously to amount to ϳ0.1% false-positive detection probability (Shriki et al, 2013). This was derived using an receiver operating characteristic analysis to compare the measured signal distribution and the best-fit Gaussian distribution, representing the noise attributable to uncorrelated sources.…”

“…The timescale of the analysis, ⌬t ϭ 3.93 ms, was four times ⌬t min , which is the inverse of the data acquisition sampling rate. This timescale was chosen according to previous findings (Shriki et al, 2013) and at a very close proximity to the mean of interevent interval (IEI) across subjects (͗IEI͘ ϭ 3.96 Ϯ 0.59 and 3.98 Ϯ 0.63 for stimulus-evoked and rest, respectively; Fig. 2A).…”

“…Because for neuronal avalanches the probability density function (PDF) of cascades x follows a power law with slope ␣ ϭ Ϫ1.5 (Beggs and Plenz, 2003;Shriki et al, 2013), the corresponding cumulative density function (CDF) for cascade sizes, F NA (␤), which specifies the fraction of measured cascade sizes x Ͻ ␤, is a Ϫ 1 ⁄2 power-law function,…”

“…To date, criticality in humans as indicated by the neuronal avalanche analysis has been studied mostly in the context of resting activity (Tagliazucchi et al, 2012;Palva et al, 2013;Priesemann et al, 2013;Shriki et al, 2013). As opposed to spontaneous resting-state activity, stimulus-evoked activity comprises time-locked activity induced by the specific sensory stimuli or motor responses.…”

Cooperation in neural systems: Bridging complexity and periodicity

“…[13][14][15]. Neural avalanches, with scale-free distribution in both size and time duration, are another significant manifestation of natural complexity emerging from criticality [16][17][18][19][20][21]. The hypothesis of criticality affords an attractive way of explaining the intelligent global behavior of cooperative systems.…”