Clustering promotes switching dynamics in networks of noisy neurons

Franović, Igor; Klinshov, Vladimir

doi:10.1063/1.5017822

Cited by 13 publications

(5 citation statements)

References 58 publications

(105 reference statements)

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“…Mathematical models of probabilistic neural coding that incorporate random noise have proven useful in predicting cortical activity at both the cellular level and the systems level [51, 52]. And yet, the mechanisms by which cortical neurons regularly select a statistically unlikely but advantageous system state, in the context of a noisy dataset, are not well-understood [5, 6, 52]. The most optimal system state must somehow be selected from a probability distribution, in accordance with thermodynamical laws.…”

Section: Resultsmentioning

confidence: 99%

Random electrical noise drives non-deterministic computation in cortical neural networks

Stoll

2022

Preprint

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In cortical neurons, spontaneous membrane potential fluctuations affect the likelihood of firing an action potential. Yet despite retaining sensitivity to random electrical noise in gating signaling outcomes, these cells achieve highly accurate computations with extraordinary energy efficiency. A new approach models the inherently probabilistic nature of cortical neuron firing as a thermodynamic process of non-deterministic computation. Typically, the cortical neuron is modeled as a binary computational unit, in either an off-state or an on-state, but here, the cortical neuron is modeled as a two-state quantum system, with some probability of switching from an off-state to an on-state. This approach explicitly takes into account the contribution of random electrical noise in gating signaling outcomes, particularly during cortical up-states. In this model, the membrane potential is described as the mixed sum of all component microstates, or the quantity of von Neumann entropy encoded by the computational unit. This distribution of macrostates is given by a density matrix, which undergoes a unitary change of basis as each unit, System A, interacts with its surrounding environment, System B. Any linear correlations reduce the number of distinguishable pure states, leading to the selection of an optimal system state in the present context. This process of information compression is shown to be equivalent to the extraction of predictive value from a thermodynamic quantity of information. Calculations demonstrate that estimated coulomb scattering profiles and decoherence timescales in cortical neurons are consistent with a quantum system, with random electrical noise driving signaling outcomes.

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Section: Resultsmentioning

confidence: 99%

Random electrical noise drives non-deterministic computation in cortical neural networks

Stoll

2022

Preprint

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“…As shown in [44], the mean-field dynamics of a homogeneous neural network may be sometimes approximated by a one-dimensional equation similar to the one describing a single node of (10). Therefore the network (10) may be interpreted as a population of connected sub-networks, or an inhomogeneous neural network with incorporated clusters [45] (see also [46,47]). For illustrative purposes we again consider the network with a ring structure where each of N=10 nodes is connected to its nearest neighbors from each side with the same coupling strength K ij =K (see figure 9(a)).…”

Section: Resultsmentioning

confidence: 99%

Interval stability for complex systems

et al. 2018

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Stability of dynamical systems against strong perturbations is an important problem of nonlinear dynamics relevant to many applications in various areas. Here, we develop a novel concept of interval stability, referring to the behavior of the perturbed system during a finite time interval. Based on this concept, we suggest new measures of stability, namely interval basin stability (IBS) and interval stability threshold (IST). IBS characterizes the likelihood that the perturbed system returns to the stable regime (attractor) in a given time. IST provides the minimal magnitude of the perturbation capable to disrupt the stable regime for a given interval of time. The suggested measures provide important information about the system susceptibility to external perturbations which may be useful for practical applications. Moreover, from a theoretical viewpoint the interval stability measures are shown to bridge the gap between linear and asymptotic stability. We also suggest numerical algorithms for quantification of the interval stability characteristics and demonstrate their potential for several dynamical systems of various nature, such as power grids and neural networks.

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“…The name of the effect should be taken cum grano salis, because in contrast to stochastic resonance, it involves no additional external signal: one rather observes a non-monotonous dependence of the spiking rate on noise variance, whereby the oscillation frequency becomes minimal at a preferred noise level. Such an inhibitory effect of noise has recently been shown for cerebellar Purkinje cells [11], having explicitly demonstrated how the lifetimes of the spiking ("up") and the silent ("down") states [13][14][15] are affected by the noise variance. ISR has been indicated to play important functional roles in neuronal systems, including the reduction of spiking frequency in the absence of neuromodulators, suppression of pathologically long short-term memories, triggering of on-off tonic spiking activity and even optimization of information transfer along the signal propagation pathways [3,7,9,11].…”

mentioning

confidence: 88%

Inverse stochastic resonance in a system of excitable active rotators with adaptive coupling

Bačić¹,

Klinshov²,

Nekorkin³

et al. 2018

EPL

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Inverse stochastic resonance is a phenomenon where an oscillating system influenced by noise exhibits a minimal oscillation frequency at an intermediate noise level. We demonstrate a novel generic scenario for such an effect in a multi-timescale system, considering an example of emergent oscillations in two adaptively coupled active rotators with excitable local dynamics. The impact of plasticity turns out to be twofold. First, at the level of multiscale dynamics, one finds a range of intermediate adaptivity rates that give rise to multistability between the limit cycle attractors and the stable equilibria, a condition necessary for the onset of the effect. Second, applying the fast-slow analysis, we show that the plasticity also plays a facilitatory role on a more subtle level, guiding the fast flow dynamics to parameter domains where the stable equilibria become focuses rather than nodes, which effectively enhances the influence of noise. The described scenario persists for different plasticity rules, underlying its robustness in the light of potential applications to neuroscience and other types of cell dynamics.

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Clustering promotes switching dynamics in networks of noisy neurons

Cited by 13 publications

References 58 publications

Random electrical noise drives non-deterministic computation in cortical neural networks

Random electrical noise drives non-deterministic computation in cortical neural networks

Interval stability for complex systems

Inverse stochastic resonance in a system of excitable active rotators with adaptive coupling

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