Memory-induced resonancelike suppression of spike generation in a resonate-and-fire neuron model

Memory-induced absolute negative mobility

Non-Markovian systems form a broad area of physics that remains greatly unexplored despite years of intensive investigations. The spotlight is on memory as a source of effects that are absent in their Markovian counterparts. In this work, we dive into this problem and analyze a driven Brownian particle moving in a spatially periodic potential and exposed to correlated thermal noise. We show that the absolute negative mobility effect, in which the net movement of the particle is in the direction opposite to the average force acting on it, may be induced by the memory of the setup. To explain the origin of this phenomenon, we resort to the recently developed effective mass approach to dynamics of non-Markovian systems.

Fractional Spiking Neuron: Fractional Leaky Integrate-and-Fire Circuit Described with Dendritic Fractal Model

As dendrites are essential parts of neurons, they are crucial factors for neuronal activities to follow multiple timescale dynamics, which ultimately affect information processing and cognition. However, in the common SNN (Spiking Neural Networks), the hardware-based LIF (Leaky Integrate-and-Fire) circuit only simulates the single timescale dynamic of soma without relating dendritic morphologies, which may limit the capability of simulating neurons to process information. This study proposes the dendritic fractal model mainly for quantifying dendritic morphological effects containing branch and length. To realize this model, We design multiple analog fractional-order circuits (AFCs) which match their extended structures and parameters with the dendritic features. Then introducing AFC into FLIF (Fractional Leaky Integrate-and-Fire) neuron circuits can demonstrate the same multiple timescale dynamics of spiking patterns as biological neurons, including spiking adaptation, inter-spike variability with power-law distribution, first-spike latency, and intrinsic memory. By contrast, it further enhances the degree of mimicry of neuron models and provides a more accurate model for understanding neural computation and cognition mechanisms.

Statistical moments of the interspike intervals for a neuron model driven by trichotomous noise

The influence of a colored three-level input noise (trichotomous noise) on the spike generation of a perfect integrate-and-fire (PIF) model of neurons is studied. Using a first-passage-time formulation, exact expressions for the Laplace transform of the output interspike interval (ISI) density and for the statistical moments of the ISIs (such as the coefficient of variation, the skewness, the serial correlation coefficient, and the Fano factor) are derived. To model the anomalous subdiffusion that can arise from, e.g., the trapping properties of dendritic spines, the model is extended by including a random operational time in the form of an inverse strictly increasing Lévy-type subordinator, and exact formulas for ISI statistics are given for this case as well. Particularly, it is shown that at some parameter regimes, the ISI density exhibits a three-modal structure. The results for the extended model show that the ISI serial correlation coefficient and the Fano factor are nonmonotonic with respect to the input current, which indicates that at an intermediate value of the input current the variability of the output spike trains is minimal. Similarities and differences between the behavior of the presented models and the previously investigated PIF models driven by dichotomous noise are also discussed.

Effects of transient subordinators on the firing statistics of a neuron model driven by dichotomous noise

The behavior of a stochastic perfect integrate-and-fire (PIF) model of neurons is considered. The effect of temporally correlated random activity of synaptic inputs is modeled as a combination of an asymmetric dichotomous noise and a random operation time in the form of an inverse strictly increasing Lévy-type subordinator. Using a first-passage-time formulation, we find exact expressions for the output interspike interval (ISI) statistics. Particularly, it is shown that at some parameter regimes the ISI density exhibits a multimodal structure. Moreover, it is demonstrated that the coefficient of variation, the serial correlation coefficient, and the Fano factor display a nonmonotonic dependence on the mean input current μ, i.e., the ISI's regularity is maximized at an intermediate value of μ. The features of spike statistics, analytically revealed in our study, are compared with previously obtained results for a perfect integrate-and-fire neuron model driven by dichotomous noise (without subordination).