相关论文: Mean field theory for a balanced hypercolumn model…

Simple elastic models of spin-crossover compounds are known empirically to exhibit classical critical behavior. We demonstrate how the long-ranged interactions responsible for this behavior arise naturally upon integrating out mechanical…

Asynchronous irregular (AI) and critical states are two competing frameworks proposed to explain spontaneous neuronal activity. Here, we propose a mean-field model with simple stochastic neurons that generalizes the integrate-and-fire…

We present a simple Markov model of spiking neural dynamics that can be analytically solved to characterize the stochastic dynamics of a finite-size spiking neural network. We give closed-form estimates for the equilibrium distribution,…

In this paper we consider a measure-theoretical formulation of the training of NeurODEs in the form of a mean-field optimal control with $L^2$-regularization of the control. We derive first order optimality conditions for the NeurODE…

Electrical stimulation of neural systems is a key tool for understanding neural dynamics and ultimately for developing clinical treatments. Many applications of electrical stimulation affect large populations of neurons. However,…

Questions about information encoded by the brain demand statistical frameworks for inferring relationships between neural firing and features of the world. The landmark discovery of grid cells demonstrates that neurons can represent spatial…

Low-dimensional descriptions of neural network dynamics are an effective tool for bridging different scales of organization of brain structure and function. Recent advances in deriving mean-field descriptions for networks of coupled…

We analytically study the input-output properties of a neuron whose active dendritic tree, modeled as a Cayley tree of excitable elements, is subjected to Poisson stimulus. Both single-site and two-site mean-field approximations incorrectly…

Firing patterns in the central nervous system often exhibit strong temporal irregularity and heterogeneity in their time averaged response properties. Previous studies suggested that these properties are outcome of an intrinsic chaotic…

We consider optimizing two-layer neural networks in the mean-field regime where the learning dynamics of network weights can be approximated by the evolution in the space of probability measures over the weight parameters associated with…

The presence of correlated noise, arising from a mixture of independent fluctuations and a common noisy input shared across the neural population, is a ubiquitous feature of neural circuits, yet its impact on collective network dynamics…

Fourier Neural Operators (FNOs) have emerged as leading surrogates for solver operators for various functional problems, yet their stability, generalization and frequency behavior lack a principled explanation. We present a systematic…

Motivated by considerations from neuroscience (macroscopic behavior of large ensembles of interacting neurons), we consider a population of mean field interacting diffusions in $\mathbf {R}^m$ in the presence of a random environment and…

Although real-world complex systems typically interact through sparse and heterogeneous networks, analytic solutions of their dynamics are limited to models with all-to-all interactions. Here, we solve the dynamics of a broad range of…

We present a mean field solution of the dynamics of a Greenberg-Hastings neural network with both excitatory and inhibitory units. We analyse the dynamical phase transitions that appear in the stationary state as the model parameters are…

We consider a mean-field control problem in which admissible controls are required to be adapted to the common noise filtration. The main objective is to show how the mean-field control problem can be approximates by time consistent…

A common approach to interpreting spiking activity is based on identifying the firing fields---regions in physical or configuration spaces that elicit responses of neurons. Common examples include hippocampal place cells that fire at…

Distributions of neuronal activity within cortical circuits are often found to display highly skewed shapes with many neurons emitting action potentials at low or vanishing rates, while some are active at high rates. Theoretical studies…

The asymmetric simple exclusion process with random-force disorder is studied within the mean field approximation. The stationary current through a domain with reversed bias is analyzed and the results are found to be in accordance with…

A major goal of neuroscience, statistical physics and nonlinear dynamics is to understand how brain function arises from the collective dynamics of networks of spiking neurons. This challenge has been chiefly addressed through large-scale…