相关论文: Generalized Rate-Code Model for Neuron Ensembles w…

This paper considers estimating the parameters in a regime-switching stochastic differential equation(SDE) driven by Normal Inverse Gaussian(NIG) noise. The model under consideration incorporates a continuous-time finite state Markov chain…

Longitudinal voice biomarkers provide a non-invasive source of information for monitoring Parkinson's disease progression, but their statistical analysis is difficult because repeated measurements from the same subject are correlated,…

We study the effects of noise on stationary pulse solutions (bumps) in spatially extended neural fields. The dynamics of a neural field is described by an integrodifferential equation whose integral term characterizes synaptic interactions…

Deployment of machine learning models in real high-risk settings (e.g. healthcare) often depends not only on the model's accuracy but also on its fairness, robustness, and interpretability. Generalized Additive Models (GAMs) are a class of…

We study the design and implementation of numerical methods to solve the generalized Langevin equation (GLE) focusing on canonical sampling properties of numerical integrators. For this purpose, we cast the GLE in an extended phase space…

In two recent papers, Rudolph and Destexhe (Neural Comp. {\bf 15}, 2577-2618, 2003; Neural Comp. in press, 2005) studied a leaky integrator model (i.e. an RC-circuit) driven by correlated (``colored'') Gaussian conductance noise and…

Systems neuroscience relies on two complementary views of neural data, characterized by single neuron tuning curves and analysis of population activity. These two perspectives combine elegantly in neural latent variable models that…

To evaluate the nature of the neural code in the cerebral cortex, we have used a combination of theory and experiment to assess how information is represented in a realistic cortical population response. We have shown how a sensory stimulus…

Dynamic mode decomposition (DMD) is an efficient tool for decomposing spatio-temporal data into a set of low-dimensional modes, yielding the oscillation frequencies and the growth rates of physically significant modes. In this paper, we…

We study the stochastic system of interacting neurons introduced in De Masi et al. (2015) and in Fournier and L\"ocherbach (2016) in a diffusive scaling. The system consists of $N$ neurons, each spiking randomly with rate depending on its…

Recurrent networks of non-linear units display a variety of dynamical regimes depending on the structure of their synaptic connectivity. A particularly remarkable phenomenon is the appearance of strongly fluctuating, chaotic activity in…

A main concern in cognitive neuroscience is to decode the overt neural spike train observations and infer latent representations under neural circuits. However, traditional methods entail strong prior on network structure and hardly meet…

Stochastic bistable systems whose stationary distributions belong to the q-exponential family are investigated using two approaches: (i) the Langevin model subjected to additive and quadratic multiplicative noise, and (ii) the…

We asymptotically derive a non-linear Langevin-like equation with non-Gaussian white noise for a wide class of stochastic systems associated with multiple stochastic environments, by developing the expansion method in our previous paper [K.…

The goal of a generative model is to capture the distribution underlying the data, typically through latent variables. After training, these variables are often used as a new representation, more effective than the original features in a…

Neurons in the nervous system are submitted to distinct sources of noise, such as ionic-channel and synaptic noise, which introduces variability in their responses to repeated presentations of identical stimuli. This motivates the use of…

Continuously monitored atomic spin-ensembles allow, in principle, for real-time sensing of external magnetic fields beyond classical limits. Within the linear-Gaussian regime, thanks to the phenomenon of measurement-induced spin-squeezing,…

In large-scale excitatory neuronal networks, rapid synchronization manifests as {multiple firing events (MFEs)}, mathematically characterized by a finite-time blow-up of the neuronal firing rate in the mean-field Fokker-Planck equation.…

We study a stochastic nonlocal PDE, arising in the context of modelling spatially distributed neural activity, which is capable of sustaining stationary and moving spatially-localized ``activity bumps''. This system is known to undergo a…

We present a deep recurrent neural network architecture to solve a class of stochastic optimal control problems described by fully nonlinear Hamilton Jacobi Bellmanpartial differential equations. Such PDEs arise when one considers…