Interactions of large numbers of spiking neurons give rise to complex neural dynamics with
fluctuations occurring at multiple scales. Understanding the dynamical mechanisms …

Fractional-order derivatives have been widely used to describe the spiking patterns of
neurons, without considering their self-similar dendritic structures. In this study, a self-similar …

This paper reviews our recent work addressing the role of both synaptic-input and
connectivity-architecture fluctuations in coarse-grained descriptions of integrate-and-fire …

A coarse-grained representation of neuronal network dynamics is developed in terms of
kinetic equations, which are derived by a moment closure, directly from the original large …

We present a detailed theoretical framework for statistical descriptions of neuronal networks
and derive (1+ 1)-dimensional kinetic equations, without introducing any new parameters …

The neural dynamics generating sensory, motor, and cognitive functions are commonly
understood through field theories for neural population activity. Classic neural field theories …

All vertebrate brains contain a dense matrix of thin fibers that release serotonin (5-
hydroxytryptamine), a neurotransmitter that modulates a wide range of neural, glial, and …

The multiple activities of neurons frequently generate several spiking-bursting variations
observed within the neurological mechanism. We show that a discrete fractional-order …

A range of perceptual and cognitive processes have been characterized from the
perspective of probabilistic representations and inference. To understand the neural circuit …

We present a detailed analysis of the dynamical regimes observed in a balanced network of
identical quadratic integrate-and-fire neurons with sparse connectivity for homogeneous and …