相关论文: Closed-form modeling of neuronal spike train stati…

We derive rigorous results describing the asymptotic dynamics of a discrete time model of spiking neurons introduced in \cite{BMS}. Using symbolic dynamic techniques we show how the dynamics of membrane potential has a one to one…

Spiking neural network models characterize the emergent collective dynamics of circuits of biological neurons and help engineer neuro-inspired solutions across fields. Most dynamical systems' models of spiking neural networks typically…

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…

We study a multivariate Hawkes process as a model for time-continuous relational event networks. The model does not assume the network to be known, it includes covariates, and it allows for both common drivers, parameters common to all the…

In this paper, we address the problem of fitting multivariate Hawkes processes to potentially large-scale data in a setting where series of events are not only mutually-exciting but can also exhibit inhibitive patterns. We focus on…

Neuronal systems need to process temporal signals. We here show how higher-order temporal (co-)fluctuations can be employed to represent and process information. Concretely, we demonstrate that a simple biologically inspired feedforward…

The apparent stochasticity of in-vivo neural circuits has long been hypothesized to represent a signature of ongoing stochastic inference in the brain. More recently, a theoretical framework for neural sampling has been proposed, which…

In awake animals, the activity of the cerebral cortex is highly complex, with neurons firing irregularly with apparent Poisson statistics. One way to characterize this complexity is to take advantage of the high interconnectivity of…

In this article, we review a class of neuro-mimetic computational models that we place under the label of spiking predictive coding. Specifically, we review the general framework of predictive processing in the context of neurons that emit…

Computational modeling is becoming a widely used methodology in modern neuroscience. However, as the complexity of the phenomena under study increases, the analysis of the results emerging from the simulations concomitantly becomes more…

Maximum entropy models are the least structured probability distributions that exactly reproduce a chosen set of statistics measured in an interacting network. Here we use this principle to construct probabilistic models which describe the…

Quantification of neuronal correlations in neuron populations helps us to understand neural coding rules. Such quantification could also reveal how neurons encode information in normal and disease conditions like Alzheimer's and…

Cortical neurons include many sub-cellular processes, operating at multiple timescales, which may affect their response to stimulation through non-linear and stochastic interaction with ion channels and ionic concentrations. Since new…

In this paper we construct a mathematical model for excitable membranes by introducing circuit characteristics for ion pump, ion current activation, and voltage-gating. The model is capable of reestablishing the Nernst resting potentials,…

We examine a previouly introduced attractor neural network model that explains the persistent activities of neurons in the anterior ventral temporal cortex of the brain. In this model, the coexistence of several attractors including…

Point process modeling is gaining increasing attention, as point process type data are emerging in numerous scientific applications. In this article, motivated by a neuronal spike trains study, we propose a novel point process regression…

The Hawkes process (HP) has been widely applied to modeling self-exciting events including neuron spikes, earthquakes and tweets. To avoid designing parametric triggering kernel and to be able to quantify the prediction confidence, the…

With rapid development of techniques to measure brain activity and structure, statistical methods for analyzing modern brain-imaging play an important role in the advancement of science. Imaging data that measure brain function are usually…

Sparse sequences of neural spikes are posited to underlie aspects of working memory, motor production, and learning. Discovering these sequences in an unsupervised manner is a longstanding problem in statistical neuroscience. Promising…

We develop flexible multivariate spatio-temporal Hawkes process models to analyze patterns of terrorism. Previous applications of point process methods to political violence data mainly utilize temporal Hawkes process models, neglecting…