Extended Anderson Criticality in Heavy-Tailed Neural Networks

Wardak, Asem; Gong, Pulin

doi:10.1103/physrevlett.129.048103

Cited by 7 publications

(2 citation statements)

References 55 publications

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“…Therefore, effect of modular hierarchical inhomogeneous structure on the critical behaviour of the system requires further investigation. Wardak and Gong (2022) heavy-tailed probabilty distribution for synaptic connections and reported extended critcal regimes between quiescent and active states. Kuśmierz et al (2020) showed a continuous transition to chaos in an excitatory network with power-law distributed synaptic weights.…”

Section: Discussionmentioning

confidence: 98%

Scale free avalanches in excitatory-inhibitory populations of spiking neurons with conductance based synaptic currents

Ehsani

Jost

2022

J Comput Neurosci

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We investigate spontaneous critical dynamics of excitatory and inhibitory (EI) sparsely connected populations of spiking leaky integrate-and-fire neurons with conductance-based synapses. We use a bottom-up approach to derive a single neuron gain function and a linear Poisson neuron approximation which we use to study mean-field dynamics of the EI population and its bifurcations. In the low firing rate regime, the quiescent state loses stability due to saddle-node or Hopf bifurcations. In particular, at the Bogdanov-Takens (BT) bifurcation point which is the intersection of the Hopf bifurcation and the saddle-node bifurcation lines of the 2D dynamical system, the network shows avalanche dynamics with power-law avalanche size and duration distributions. This matches the characteristics of low firing spontaneous activity in the cortex. By linearizing gain functions and excitatory and inhibitory nullclines, we can approximate the location of the BT bifurcation point. This point in the control parameter phase space corresponds to the internal balance of excitation and inhibition and a slight excess of external excitatory input to the excitatory population. Due to the tight balance of average excitation and inhibition currents, the firing of the individual cells is fluctuation-driven. Around the BT point, the spiking of neurons is a Poisson process and the population average membrane potential of neurons is approximately at the middle of the operating interval $$[V_{Rest}, V_{th}]$$ [ V Rest , V th ] . Moreover, the EI network is close to both oscillatory and active-inactive phase transition regimes.

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Section: Discussionmentioning

confidence: 98%

Scale free avalanches in excitatory-inhibitory populations of spiking neurons with conductance based synaptic currents

Ehsani

Jost

2022

J Comput Neurosci

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“…Many physical objects in nature, such as capillary distribution and leaf veins, are statistically self-similar: parts of them show the same statistical properties as the whole. An equivalent description of self-similarity is scale invariant, [25,26] where there is a smaller part that is similar to the proximate larger part at a certain amplitude. Thus, we can perform the contraction-expansion variations on the part of physical quantities of the system.…”

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confidence: 99%

Predicted Critical State Based on Invariance of the Lyapunov Exponent in Dual Spaces

Liu 刘,

Xia 夏

2024

Chinese Phys. Lett.

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The critical state in disordered systems, a fascinating and subtle eigenstate, has attracted a lot of research interest. However, the nature of the critical state is difficult to describe quantitatively, and in general, it cannot predict a system that hosts the critical state. In this work, we propose an explicit criterion that the Lyapunov exponent of the critical state should be 0 simultaneously in dual spaces, namely Lyapunov exponent remains invariant under the Fourier transform. With this criterion, we exactly predict a one-dimensional quasiperiodic model which is not self-duality, but hosts a large number of critical states. Then, we perform numerical verification of the theoretical prediction and display the self-similarity of the critical state. Due to computational complexity, higher dimensional models are not performed calculations, however, since the description of extended and localized states by the Lyapunov exponent is universal and dimensionless, utilizing the Lyapunov exponent of dual spaces to describe critical states should also be universal. Finally, we conjecture that there exists some kind of connection between the invariance of the Lyapunov exponent and conformal invariance, which can promote the research of critical phenomena.

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