相关论文: A Generalized Rate Model for Neuronal Ensembles

Neurons can code for multiple variables simultaneously and neuroscientists are often interested in classifying neurons based on their receptive field properties. Statistical models provide powerful tools for determining the factors…

As training data rapid growth, large-scale parallel training with multi-GPUs cluster is widely applied in the neural network model learning currently.We present a new approach that applies exponential moving average method in large-scale…

Fast Gradient Sign Method (FGSM) is a popular method to generate adversarial examples that make neural network models robust against perturbations. Despite its empirical success, its theoretical property is not well understood. This paper…

Networks of model neurons with balanced recurrent excitation and inhibition produce irregular and asynchronous spiking activity. We extend the analysis of balanced networks to include the known dependence of connection probability on the…

We present an analytical framework that allows the quantitative study of statistical dynamic properties of networks with adaptive nodes that have memory and is used to examine the emergence of oscillations in networks with response…

A large number of neural network models of associative memory have been proposed in the literature. These include the classical Hopfield networks (HNs), sparse distributed memories (SDMs), and more recently the modern continuous Hopfield…

Mathematical models of biological neural networks are associated to a rich and complex class of stochastic processes. In this paper, we consider a simple {\em plastic} neural network whose {\em connectivity/synaptic strength} $(W(t))$…

The time elapsed model describes the firing activity of an homogeneous assembly of neurons thanks to the distribution of times elapsed since the last discharge. It gives a mathematical description of the probability density of neurons…

The analysis of market correlations is crucial for optimal portfolio selection of correlated assets, but their memory effects have often been neglected. In this work, we analyse the mean market correlation of the S&P500 which corresponds to…

We construct a model that predicts the statistical properties of spike trains generated by a sensory neuron. The model describes the combined effects of the neuron's intrinsic properties, the noise in the surrounding, and the external…

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…

We investigate a one-dimensional model of active motion, which takes into account the effects of persistent self-propulsion through a memory function in a dissipative-like term of the generalized Langevin equation for particle swimming…

Various classes of neurons alternate between high-frequency discharges and silent intervals. This phenomenon is called burst firing. To analyze burst activity in an insect system, grasshopper auditory receptor neurons were recorded in vivo…

The principles of neural encoding and computations are inherently collective and usually involve large populations of interacting neurons with highly correlated activities. While theories of neural function have long recognized the…

We propose multirate training of neural networks: partitioning neural network parameters into "fast" and "slow" parts which are trained on different time scales, where slow parts are updated less frequently. By choosing appropriate…

Longitudinal binary or count functional data are common in neuroscience, but are often too large to analyze with existing functional regression methods. We propose one-step penalized generalized estimating equations that supports…

Modeling non-Markovian time series is a recent topic of research in many fields such as climate modeling, biophysics, molecular dynamics, or finance. The generalized Langevin equation (GLE), given naturally by the Mori-Zwanzig projection…

We study analytically the dynamics of a network of sparsely connected inhibitory integrate-and-fire neurons in a regime where individual neurons emit spikes irregularly and at a low rate. In the limit when the number of neurons N tends to…

In this study, we improve a neural network (NN) parameterization of deep convection in the global atmosphere model ARP-GEM. To take into account the sporadic nature of convection, we develop a NN parameterization that includes a triggering…

An associative memory has been discussed of neural networks consisting of spiking N (=100) Hodgkin-Huxley (HH) neurons with time-delayed couplings, which memorize P patterns in their synaptic weights. In addition to excitatory synapses…