Related papers: Spatio-temporal spike trains analysis for large sc…
Understanding the interaction patterns among simultaneous recordings of spike trains from multiple neuronal units is a key topic in neuroscience. However, an optimal approach of assessing these interactions has not been established, as…
We present a simple Markov model of spiking neural dynamics that can be analytically solved to characterize the stochastic dynamics of a finite-size spiking neural network. We give closed-form estimates for the equilibrium distribution,…
Spiking activity in cortical networks is nonlinear in nature. The linear-nonlinear cascade model, some versions of which are also known as point-process generalized linear model, can efficiently capture the nonlinear dynamics exhibited by…
Neurons in the nervous system convey information to higher brain regions by the generation of spike trains. An important question in the field of computational neuroscience is how these sensory neurons encode environmental information in a…
Markov chain Monte Carlo methods are a powerful tool for sampling equilibrium configurations in complex systems. One problem these methods often face is slow convergence over large energy barriers. In this work, we propose a novel method…
Perceptions and actions, thoughts and memories result from coordinated activity in hundreds or even thousands of neurons in the brain. It is an old dream of the physics community to provide a statistical mechanics description for these and…
Although the spike-trains in neural networks are mainly constrained by the neural dynamics itself, global temporal constraints (refractoriness, time precision, propagation delays, ..) are also to be taken into account. These constraints are…
In this paper an alternative approach to statistical mechanics based on the maximum information entropy principle (MaxEnt) is examined, specifically its close relation with the Gibbs method of ensembles. It is shown that the MaxEnt…
In this article we focus on dynamic network data which describe interactions among a fixed population through time. We model this data using the latent space framework, in which the probability of a connection forming is expressed as a…
The paper explores the capability of continuous-time recurrent neural networks to store and recall precisely timed scores of spike trains. We show (by numerical experiments) that this is indeed possible: within some range of parameters, any…
Complex network states are characterized by the interplay between system's structure and dynamics. One way to represent such states is by means of network density matrices, whose von Neumann entropy characterizes the number of distinct…
Spiking Neural Networks (SNNs), models inspired by neural mechanisms in the brain, allow for energy-efficient implementation on neuromorphic hardware. However, SNNs trained with current direct training approaches are constrained to a…
We briefly review and highlight the consequences of rigorous and exact results obtained in \cite{cessac:10}, characterizing the statistics of spike trains in a network of leaky Integrate-and-Fire neurons, where time is discrete and where…
Over the brief time intervals available for processing retinal output, roughly 50 to 300 msec, the number of extra spikes generated by individual ganglion cells can be quite variable. Here, computer-generated spike trains were used to…
Spike-sorting techniques attempt to classify a series of noisy electrical waveforms according to the identity of the neurons that generated them. Existing techniques perform this classification ignoring several properties of actual neurons…
The brain is a highly complex system. Most of such complexity stems from the intermingled connections between its parts, which give rise to rich dynamics and to the emergence of high-level cognitive functions. Disentangling the underlying…
Recurrent neural networks have seen widespread use in modeling dynamical systems in varied domains such as weather prediction, text prediction and several others. Often one wishes to supplement the experimentally observed dynamics with…
Understanding the functioning of a neural system in terms of its underlying circuitry is an important problem in neuroscience. Recent developments in electrophysiology and imaging allow one to simultaneously record activities of hundreds of…
Information theoretic measures (entropies, entropy rates, mutual information) are nowadays commonly used in statistical signal processing for real-world data analysis. The present work proposes the use of Auto Mutual Information (Mutual…
Fitting network models to neural activity is an important tool in neuroscience. A popular approach is to model a brain area with a probabilistic recurrent spiking network whose parameters maximize the likelihood of the recorded activity.…