Related papers: On the spike train variability characterized by va…
Understanding the dynamics of neural networks is a major challenge in experimental neuroscience. For that purpose, a modelling of the recorded activity that reproduces the main statistics of the data is required. In a first part, we present…
Periodic neural activity not locked to the stimulus or to motor responses is usually ignored. Here, we present new tools for modeling and quantifying the information transmission based on periodic neural activity that occurs with…
Modern well-performing approaches to neural decoding are based on machine learning models such as decision tree ensembles and deep neural networks. The wide range of algorithms that can be utilized to learn from neural spike trains, which…
Spike correlations between neurons are ubiquitous in the cortex, but their role is at present not understood. Here we describe the firing response of a leaky integrate-and-fire neuron (LIF) when it receives a temporarily correlated input…
Learning and memory in the brain are implemented by complex, time-varying changes in neural circuitry. The computational rules according to which synaptic weights change over time are the subject of much research, and are not precisely…
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 at this precise moment. The system evolves as…
In this article, we primarily propose a novel Bayesian characterization of stationary and nonstationary stochastic processes. In practice, this theory aims to distinguish between global stationarity and nonstationarity for both parametric…
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…
An essential step toward understanding neural circuits is linking their structure and their dynamics. In general, this relationship can be almost arbitrarily complex. Recent theoretical work has, however, begun to identify some broad…
We consider a conductance based neural network inspired by the generalized Integrate and Fire model introduced by Rudolph and Destexhe. We show the existence and uniqueness of a unique Gibbs distribution characterizing spike train…
Advances in modern technology have enabled the simultaneous recording of neural spiking activity, which statistically can be represented by a multivariate point process. We characterise the second order structure of this process via the…
Whether, when, and how causal interactions between neurons can be meaningfully studied from observations of neural activity alone are vital questions in neural data analysis. Here we aim to better outline the concept of functional…
We model spontaneous cortical activity with a network of coupled spiking units, in which multiple spatio-temporal patterns are stored as dynamical attractors. We introduce an order parameter, which measures the overlap (similarity) between…
We describe an approximate statistical model for the sample variance distribution of the non-linear matter power spectrum that can be calibrated from limited numbers of simulations. Our model retains the common assumption of a multivariate…
We address the problem of finding patterns from multi-neuronal spike trains that give us insights into the multi-neuronal codes used in the brain and help us design better brain computer interfaces. We focus on the synchronous firings of…
In the option valuation literature, the shortcomings of one factor stochastic volatility models have traditionally been addressed by adding jumps to the stock price process. An alternate approach in the context of option pricing and…
Identifying the right tools to express the stochastic aspects of neural activity has proven to be one of the biggest challenges in computational neuroscience. Even if there is no definitive answer to this issue, the most common procedure to…
The spectrum and coherency are useful quantities for characterizing the temporal correlations and functional relations within and between point processes. This paper begins with a review of these quantities, their interpretation and how…
Nonstationarity of the event rate is a persistent problem in modeling time series of events, such as neuronal spike trains. Motivated by a variety of patterns in neurophysiological spike train recordings, we define a general class of…
The critical brain hypothesis posits that neural circuitry operates near criticality to reap the computational benefits of accessing a wide range of timescales. The theory of critical phenomena generally predicts heavy-tailed (power-law)…