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A complex interplay of single-neuron properties and the recurrent network structure shapes the activity of cortical neurons. The single-neuron activity statistics differ in general from the respective population statistics, including…
Strong inhibitory input to neurons, which occurs in balanced states of neural networks, increases synaptic current fluctuations. This has led to the assumption that inhibition contributes to the high spike-firing irregularity observed in…
The Bayesian view of the brain hypothesizes that the brain constructs a generative model of the world, and uses it to make inferences via Bayes' rule. Although many types of approximate inference schemes have been proposed for hierarchical…
We study a problem of designing ``robust'' external excitations for control and synchronization of an assembly of homotypic harmonic oscillators representing so-called theta neurons. The model of theta neurons (Theta model) captures, in…
The spiking activity of neocortical neurons exhibits a striking level of variability, even when these networks are driven by identical stimuli. The approximately Poisson firing of neurons has led to the hypothesis that these neural networks…
Competitive balance model has been proposed as an extension to the balance model to address the conflict of interests in signed networks arXiv:2001.04664 . In this model two different paradigms compete with each other due to the competitive…
In this study, we apply a mean field theory to the neural network model with two periodic inputs in order to clarify the conditions of synchronies. This mean field theory yields a self-consistent condition for the synchrony and enables us…
Mean-field game theory relies on approximating games that are intractable to model due to a very large to infinite population of players. While these kinds of games can be solved analytically via the associated system of partial…
This article studies the dynamics of the mean-field approximation of continuous random networks. These networks are stochastic integrodifferential equations driven by Gaussian noise. The kernels in the integral operators are realizations of…
Mean field models (MFMs) of cortical tissue incorporate salient features of neural masses to model activity at the population level. One of the common aspects of MFM descriptions is the presence of a high dimensional parameter space…
We analyze the dynamics of networks of spiking neural oscillators. First, we present an exact linear stability theory of the synchronous state for networks of arbitrary connectivity. For general neuron rise functions, stability is…
We present a Statistical Mechanics (SM) model of deep neural networks, connecting the energy-based and the feed forward networks (FFN) approach. We infer that FFN can be understood as performing three basic steps: encoding, representation…
We introduce a system of self-propelled agents (active Brownian particles) with velocity alignment in two spatial dimensions and derive a mean-field theory from the microscopic dynamics via a nonlinear Fokker-Planck equation and a moment…
In a generic neuron model, we present the linear response theory for the firing rate in response to both time dependent input currents and noise amplitudes. In both cases the signal transmission is strongly attenuated for frequencies above…
We revisit the problem of characterising the mean-field limit of a network of Hopfield-like neurons. Building on the previous works of Ben Arous and Guionnet we establish for a large class of networks of Hopfield-like neurons, i.e. rate…
A fundamental problem in neuroscience is understanding how working memory -- the ability to store information at intermediate timescales, like 10s of seconds -- is implemented in realistic neuronal networks. The most likely candidate…
Recent experimental and computational evidence suggests that several dynamical properties may characterize the operating point of functioning neural networks: critical branching, neutral stability, and production of a wide range of firing…
Given a large number of homogeneous players that are distributed across three possible states, we consider the problem in which these players have to control their transition rates, while minimizing a cost. The optimal transition rates are…
This work is part of an effort to understand the neural basis for our visual system's ability, or failure, to accurately track moving visual signals. We consider here a ring model of spiking neurons, intended as a simplified computational…
The steady-state firing rate and firing-rate response of the leaky and exponential integrate-and-fire models receiving synaptic shot noise with excitatory and inhibitory reversal potentials is examined. For the particular case where the…