Related papers: A Generalized Rate Model for Neuronal Ensembles
In order to describe the firing activity of a homogenous assembly of neurons, we consider time elapsed models, which give mathematical descriptions of the probability density of neurons structured by the distribution of times elapsed since…
We introduce a machine learning-based approach called ab initio generalized Langevin equation (AIGLE) to model the dynamics of slow collective variables in materials and molecules. In this scheme, the parameters are learned from atomistic…
Neural network dynamics emerge from the interaction of spiking cells. One way to formulate the problem is through a theoretical framework inspired by ideas coming from statistical physics, the so-called mean-field theory. In this document,…
The focus of our study in this paper is on the active dynamics and a fractional generalized Langevin equation with a memory kernel K(t). The Fokker-Planck equation is obtained by deriving it from a second-order differential equation. The…
We study a pulse-coupled dynamics of excitable elements in uncorrelated scale-free networks. Regimes of self-sustained activity are found for homogeneous and inhomogeneous couplings, in which the system displays a wide variety of behaviors,…
Neuronal models based on the Hodgkin-Huxley equation form a fundamental framework in the field of computational neuroscience. While the neuronal state is often modeled deterministically, experimental recordings show stochastic fluctuations,…
We address the problem of identifying functional interactions among stochastic neurons with variable-length memory from their spiking activity. The neuronal network is modeled by a stochastic system of interacting point processes with…
Consider a compound Poisson process with jump measure $\nu$ supported by finitely many positive integers. We propose a method for estimating $\nu$ from a single, equidistantly sampled trajectory and develop associated statistical…
Neural encoding is a field in neuroscience that focuses on characterizing how information from stimuli is encoded in the spiking activity of neurons. When more than one stimulus is present, a theory known as multiplexing posits that neurons…
The generalized Langevin equation is a model for the motion of coarse-grained particles where dissipative forces are represented by a memory term. The numerical realization of such a model requires the implementation of a stochastic…
The problem of neural coding is to understand how sequences of action potentials (spikes) are related to sensory stimuli, motor outputs, or (ultimately) thoughts and intentions. One clear question is whether the same coding rules are used…
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…
A gauge model of neural network is introduced, which resembles the Z(2) Higgs lattice gauge theory of high-energy physics. It contains a neuron variable $S_x = \pm 1$ on each site $x$ of a 3D lattice and a synaptic-connection variable…
Modelling the dynamics of interactions in a neuronal ensemble is an important problem in functional connectivity research. One popular framework is latent factor models (LFMs), which have achieved notable success in decoding neuronal…
The synergy between spiking neural networks and neuromorphic hardware holds promise for the development of energy-efficient AI applications. Inspired by this potential, we revisit the foundational aspects to study the capabilities of…
This paper extends the Transmission Neural Network model proposed by Gao and Caines in [1]-[3] to incorporate inhibitory connections and neurotransmitter populations. The extended network model contains binary neuronal states, transmission…
It is often of interest to perform clustering on longitudinal data, yet it is difficult to formulate an intuitive model for which estimation is computationally feasible. We propose a model-based clustering method for clustering objects that…
A generalized Langevin equation with fluctuating diffusivity (GLEFD) is proposed, and it is shown that the GLEFD satisfies a generalized fluctuation-dissipation relation. If the memory kernel is a power law, the GLEFD exhibits anomalous…
Most of animal and human behavior occurs on time scales much longer than the response times of individual neurons. In many cases, it is plausible that these long time scales emerge from the recurrent dynamics of electrical activity in…
This paper focuses on the outline of some computational methods for the approximate solution of the integral equations for the neuronal firing probability density and an algorithm for the generation of sample-paths in order to construct…