相关论文: Closed-form modeling of neuronal spike train stati…

Neurons perform computations, and convey the results of those computations through the statistical structure of their output spike trains. Here we present a practical method, grounded in the information-theoretic analysis of prediction, for…

This paper is devoted to establishing the full scaling limit theorems for multivariate Hawkes processes. Under some mild conditions on the exciting kernels, we develop a new way to prove that after a suitable time-spatial scaling, the…

We introduce a mathematical framework where the statistics of spikes trains, produced by neural networks evolving under synaptic plasticity, can be analysed.

Some recent papers relate the criticality of complex systems to their maximal capacity of information processing. In the present paper, we consider high dimensional point processes, known as age-dependent Hawkes processes, which have been…

Simultaneous recordings from multiple neural units allow us to investigate the activity of very large neural ensembles. To understand how large ensembles of neurons process sensory information, it is necessary to develop suitable…

Strongly coupled, recurrent, balanced network models have been successful in describing and predicting many phenomena observed in cortical neural recordings. However, most balanced network models use current-based synapse models in place of…

To understand the behavior of a neural circuit it is a presupposition that we have a model of the dynamical system describing this circuit. This model is determined by several parameters, including not only the synaptic weights, but also…

We consider a model of interacting neurons where the membrane potentials of the neurons are described by a multidimensional piecewise deterministic Markov process (PDMP) with values in ${\mathbb R}^N, $ where $ N$ is the number of neurons…

We consider a new class of non Markovian processes with a countable number of interacting components, both in discrete and continuous time. Each component is represented by a point process indicating if it has a spike or not at a given…

Bidimensional spiking models currently gather a lot of attention for their simplicity and their ability to reproduce various spiking patterns of cortical neurons, and are particularly used for large network simulations. These models…

A key difficulty that arises from real event data is imprecision in the recording of event time-stamps. In many cases, retaining event times with a high precision is expensive due to the sheer volume of activity. Combined with practical…

We introduce a novel and efficient simulation scheme for Hawkes processes on a fixed time grid, leveraging their affine Volterra structure. The key idea is to first simulate the integrated intensity and the counting process using Inverse…

Spatio-temporal Hawkes point processes are a particularly interesting class of stochastic point processes for modeling self-exciting behavior, in which the occurrence of one event increases the probability of other events occurring. These…

We propose a flexible Bayesian approach for estimating the joint density of a multivariate outcome of interest in the presence of categorical covariates. Leveraging a Gaussian copula framework, our method effectively captures the dependence…

Recurrent neural networks are powerful tools for understanding and modeling computation and representation by populations of neurons. Continuous-variable or "rate" model networks have been analyzed and applied extensively for these…

Hawkes processes are a class of self-exciting point processes that are used to model complex phenomena. While most applications of Hawkes processes assume that event data occurs in continuous-time, the less-studied discrete-time version of…

In this paper, we present a maximum likelihood method for estimating the parameters of a univariate Hawkes process with self-excitation or inhibition. Our work generalizes techniques and results that were restricted to the self-exciting…

Targeting a better understanding of credit market dynamics, the authors have studied a stochastic model named the Hawkes process. Describing trades arrival times, this kind of model allows for the capture of self-excitement and mutual…

Many events occur in the world. Some event types are stochastically excited or inhibited---in the sense of having their probabilities elevated or decreased---by patterns in the sequence of previous events. Discovering such patterns can help…

In this paper we introduce a new model named CARMA(p,q)-Hawkes process as the Hawkes model with exponential kernel implies a strictly decreasing behaviour of the autocorrelation function and empirically evidences reject the monotonicity…