相关论文: Mean field system of a two-layers neural model in …

We consider spatially extended systems of interacting nonlinear Hawkes processes modeling large systems of neurons placed in Rd and study the associated mean field limits. As the total number of neurons tends to infinity, we prove that the…

Firing rate fluctuations in neural populations are observed experimentally over multiple time scales, in single neurons, across trials when elicited by stimuli, and across populations. In this work, we examine how firing rate fluctuations…

How does the brain predict physical outcomes while acting in the world? Machine learning world models compress visual input into latent spaces, discarding the spatial structure that characterizes sensory cortex. We propose isomorphic world…

Deep convolutional neural networks (CNNs) trained on objects and scenes have shown intriguing ability to predict some response properties of visual cortical neurons. However, the factors and computations that give rise to such ability, and…

We study the dynamics of a low-dimensional system of coupled model neurons as a step towards understanding the vastly complex network of neurons in the brain. We analyze the bifurcation structure of a system of two model neurons with…

A quantum model of neural network is introduced and its phase structure is examined. The model is an extension of the classical Z(2) gauged neural network of learning and recalling to a quantum model by replacing the Z(2) variables, $S_i =…

We study a purely inhibitory neural network model where neurons are represented by their state of inhibition. The study we present here is partially based on the work of Cottrell \cite{Cot} and Fricker et al. \cite{FRST}. The spiking rate…

We construct Markov processes for modeling the rupture of edges in a two-dimensional foam. We first describe a network model for tracking topological information of foam networks with a state space of combinatorial embeddings. Through a…

In this paper, we build a model for biological neural nets where the activity of the network is described by Hawkes processes having a variable length memory. The particularity of this paper is to deal with an infinite number of components.…

The experimental study of neural networks requires simultaneous measurements of a massive number of neurons, while monitoring properties of the connectivity, synaptic strengths and delays. Current technological barriers make such a mission…

Evolution and its intelligence element present thrill and challenges in its exploration. Yet, how species have memory, retrieve them and maintain continuity are the fundamental questions. Most of the phenomenon can only be hypothesised by…

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,…

The dynamics of neural networks is often characterized by collective behavior and quasi-synchronous events, where a large fraction of neurons fire in short time intervals, separated by uncorrelated firing activity. These global temporal…

The mean field (MF) theory of multilayer neural networks centers around a particular infinite-width scaling, where the learning dynamics is closely tracked by the MF limit. A random fluctuation around this infinite-width limit is expected…

Understanding the relation between cortical neuronal network structure and neuronal activity is a fundamental unresolved question in neuroscience, with implications to our understanding of the mechanism by which neuronal networks evolve…

Cortical neurons whose activity is recorded in behavioral experiments has been classified into several types such as stimulus-related neurons, delay-period neurons, and reward-related neurons. Moreover, the population activity of neurons…

In computer simulations of spiking neural networks, often it is assumed that every two neurons of the network are connected by a probability of 2\%, 20\% of neurons are inhibitory and 80\% are excitatory. These common values are based on…

This paper presents a two-phase method for learning interaction kernels of stochastic many-particle systems. After transforming stochastic trajectories of every particle into the particle density function by the kernel density estimation…

This paper studies a stochastic neural field model that is extended from our previous paper [14]. The neural field model consists of many heterogeneous local populations of neurons. Rigorous results on the stochastic stability are proved,…

A new model of two coupled neurons is presented by the partly diffusive Hindmarsh-Rose equations. The solution semiflow exhibits globally absorbing characteristics. As the main result, the self-synchronization of the coupled neurons at a…