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#### Variable critical exponents induced by topology-dependent coalescence in a branching network

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##### Citation

Buendia, V., Zeraati, R., Engel, T., & Levina, A. (2021). *Variable
critical exponents induced by topology-dependent coalescence in a branching network*. Poster presented at Bernstein
Conference 2021. doi:10.12751/nncn.bc2021.p139.

Cite as: https://hdl.handle.net/21.11116/0000-0009-2794-4

##### Abstract

Experimental evidence shows that resting neuronal activity consists of power-law distributed outbursts, known as avalanches, similar to avalanches observed in the branching process at criticality [1]. It has been suggested biological systems can benefit from operating near such critical points, enhancing their response to stimulus and computational capabilities [2]. The exponents of the power-law decay of such avalanches—called critical exponents—coincide with those of the branching process, which is often used to model activity propagation in the brain. However, such mapping implicitly relies on the assumption of a random connectivity structure, in contrast with the structured networks found in the cortex. The theory of critical phenomena states that structured lattices display a different set of critical exponents for avalanches than the mean-field case [3]. Then, how is it possible to observe the mean-field critical exponents in structured networks?

Here, we investigate how the changes in structured connectivity mimicking the spatial organization of the primate cortex affect the critical dynamics of finite branching networks. We vary network topology through two mechanisms: growing the radius of interactions, and randomly rewiring local connections (Fig. a). Both mechanisms can produce different finite-size scaling (FSS) in the avalanche-size distributions, with the critical exponents changing from the values expected in structured lattice to the mean-field ones (Fig. b), without losing all the network structure. In particular, we show that the finite-size nature of the networks can obscure the true scaling properties: the actual scaling happens only for very large avalanches—which are cut due to the finite-size—while small avalanches follow an apparent mean-field scaling. On the other hand, random rewiring directly changes the critical exponent. Moreover, we show that the dynamics of the structured network can be captured with an adaptive branching process based on the local coalescences (the concurrent excitation of a neuron from multiple sources [4], Fig. c). Therefore, our results indicate that accounting for the network topology is essential to uncover the dynamical state and correct exponents from empirical data. These findings are especially significant for studying neural dynamics based on the finite-size recordings from the primate cortex, where local inter-columnar connectivity plays an important role.