Related papers: Some theoretical results on neural spike train pro…

We consider a spike-generating stationary Markov process whose transition probabilities are known. We show that there is a canonical potential whose Gibbs distribution, obtained from the Maximum Entropy Principle (MaxEnt), is the…

The metrization of the space of neural responses is an ongoing research program seeking to find natural ways to describe, in geometrical terms, the sets of possible activities in the brain. One component of this program are the {\em spike…

Spiking neural networks (SNNs) offer a promising pathway to implement deep neural networks (DNNs) in a more energy-efficient manner since their neurons are sparsely activated and inferences are event-driven. However, there have been very…

The ability to record from increasingly large numbers of neurons, and the increasing attention being paid to large scale neural network simulations, demands computationally fast algorithms to compute relevant statistical measures. We…

Experimental neuroscience increasingly requires tractable models for analyzing and predicting the behavior of neurons and networks. The generalized linear model (GLM) is an increasingly popular statistical framework for analyzing neural…

We present a method for the real time prediction of punctate events in neural activity, based on the time-frequency spectrum of the signal, applicable both to continuous processes like local field potentials (LFP) as well as to spike…

Our knowledge of the sensory world is encoded by neurons in sequences of discrete, identical pulses termed action potentials or spikes. There is persistent controversy about the extent to which the precise timing of these spikes is relevant…

A temporal point process is a mathematical model for a time series of discrete events, which covers various applications. Recently, recurrent neural network (RNN) based models have been developed for point processes and have been found…

This paper proposes a neuronal circuitry layout and synaptic plasticity principles that allow the (pyramidal) neuron to act as a "combinatorial switch". Namely, the neuron learns to be more prone to generate spikes given those combinations…

This paper studies a stochastic neural field model that is extended from our previous paper [14]. The neural field model consists of many heterogeneous local populations of neurons. Rigorous results on the stochastic stability are proved,…

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…

Spiking Neural P systems, SNP systems for short, are biologically inspired computing devices based on how neurons perform computations. SNP systems use only one type of symbol, the spike, in the computations. Information is encoded in the…

We study pairwise Ising models for describing the statistics of multi-neuron spike trains, using data from a simulated cortical network. We explore efficient ways of finding the optimal couplings in these models and examine their…

While Multiple Instance (MI) data are point patterns -- sets or multi-sets of unordered points -- appropriate statistical point pattern models have not been used in MI learning. This article proposes a framework for model-based MI learning…

The paper discusses multivariate self- and cross-exciting processes. We define a class of multivariate point processes via their corresponding stochastic intensity processes that are driven by stochastic jumps. Essentially, there is a jump…

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…

We demonstrate that the information contained in the spike occurrence times of a population of neurons can be broken up into a series of terms, each of which reflect something about potential coding mechanisms. This is possible in the…

Although recent neurophysiological experiments suggest that synchronous neural activity is involved in some perceptual and cognitive processes, the functional role of such coherent neuronal behavior is not well understood. As a first step…

We introduce a nonlinear modification of the classical Hawkes process, which allows inhibitory couplings between units without restrictions. The resulting system of interacting point processes provides a useful mathematical model for…

We consider a wide class of spiking neuron models, defined by rather general set of conditions typical for basic models like leaky integrate and fire, or binding neuron model. A neuron is fed with a point renewal process. A relation between…