Corpus ID: 235421893

Estimating the interaction graph of stochastic neuronal dynamics by observing only pairs of neurons

  title={Estimating the interaction graph of stochastic neuronal dynamics by observing only pairs of neurons},
  author={E. D. Santis and A. Galves and G. Nappo and M. Piccioni},
Abstract. We address the questions of identifying pairs of interacting neurons from the observation of their spiking activity. The neuronal network is modeled by a system of interacting point processes with memory of variable length. The influence of a neuron on another can be either excitatory or inhibitory. To identify the existence and the nature of an interaction we propose an algorithm based only on the observation of joint activity of the two neurons in successive time slots. This reduces… Expand


Estimating the interaction graph of stochastic neural dynamics
In this paper we address the question of statistical model selection for a class of stochastic models of biological neural nets. Models in this class are systems of interacting chains with memory ofExpand
Metastable spiking networks in the replica-mean-field limit
This work extends the RMF computational framework to neural networks modeled by point processes with exponential stochastic intensities, and shows that metastable finite-size networks admit multistable RMF limits, which are fully characterized by stationary firing rates. Expand
The Pair-Replica-Mean-Field Limit for Intensity-based Neural Networks
The replica framework is extended to allow elementary replica constituents to be composite objects, namely, pairs of neurons, as they include pairwise interactions and exhibit non-trivial dependencies in their stationary dynamics, which cannot be captured by first-order replica models. Expand
The effect of graph connectivity on metastability in a stochastic system of spiking neurons
Abstract We consider a continuous-time stochastic model of spiking neurons originally introduced by Ferrari et al. in Ferrari et al. (2018). In this model, we have a finite or countable number ofExpand
A Result of Metastability for an Infinite System of Spiking Neurons.
In 2018, Ferrari et al. wrote a paper called "Phase Transition for Infinite Systems of Spiking Neurons" in which they introduced a continuous time stochastic model of interacting neurons. This modelExpand
Graphical Modeling for Multivariate Hawkes Processes with Nonparametric Link Functions
Hawkes (1971a) introduced a powerful multivariate point process model of mutually exciting processes to explain causal structure in data. In this article, it is shown that the Granger causalityExpand
Hydrodynamic Limit for Spatially Structured Interacting Neurons
We study the hydrodynamic limit of a stochastic system of neurons whose interactions are given by Kac Potentials that mimic chemical and electrical synapses and leak currents. The system consists ofExpand
Hydrodynamic Limit for Interacting Neurons
This paper studies the hydrodynamic limit of a stochastic process describing the time evolution of a system with N neurons with mean-field interactions produced both by chemical and by electricalExpand
On a toy model of interacting neurons
We continue the study of a stochastic system of interacting neurons introduced in De Masi-Galves-L\"ocherbach-Presutti (2014). The system consists of N neurons, each spiking randomly with rateExpand
Infinite Systems of Interacting Chains with Memory of Variable Length—A Stochastic Model for Biological Neural Nets
We consider a new class of non Markovian processes with a countable number of interacting components. At each time unit, each component can take two values, indicating if it has a spike or not atExpand