Related papers: Interval Timing: Modeling the break-run-break patt…
In the mean field integrate-and-fire model, the dynamics of a typical neuron within a large network is modeled as a diffusion-jump stochastic process whose jump takes place once the voltage reaches a threshold. In this work, the main goal…
In the mean field integrate-and-fire model, the dynamics of a typical neuron within a large network is modeled as a diffusion-jump stochastic process whose jump takes place once the voltage reaches a threshold. In this work, the main goal…
A random walk (or a Wiener process), possibly with drift, is observed in a noisy or delayed fashion. The problem considered in this paper is to estimate the first time \tau the random walk reaches a given level. Specifically, the p-moment…
In this paper we extend the encounter-based model of diffusion-mediated surface absorption to the case of an unbiased run-and-tumble particle (RTP) confined to a finite interval $[0,L]$ and switching between two constant velocity states…
Recently, the SPIKE-distance has been proposed as a parameter-free and time-scale independent measure of spike train synchrony. This measure is time-resolved since it relies on instantaneous estimates of spike train dissimilarity. However,…
We explore a mechanism of pattern formation arising in processes described by a system of a single reaction-diffusion equation coupled with ordinary differential equations. Such systems of equations arise from the modeling of interactions…
Identifying the instances of jumps in a discrete-time-series sample of a jump diffusion model is a challenging task. We have developed a novel statistical technique for jump detection and volatility estimation in a return time series data…
Fluctuations of the human heart beat constitute a complex system that has been studied mostly under resting conditions using conventional time series analysis methods. During physical exercise, the variability of the fluctuations is…
In this paper, we study a distributed parameter estimation problem with an asynchronous communication protocol over multi-agent systems. Different from traditional time-driven communication schemes, in this work, data can be transmitted…
Activity of inhibitory neuron with delayed feedback is considered in the framework of point stochastic processes. The neuron receives excitatory input impulses from a Poisson stream, and inhibitory impulses from the feedback line with a…
Spike generation in neurons produces a temporal point process, whose statistics is governed by intrinsic phenomena and the external incoming inputs to be coded. In particular, spike-evoked adaptation currents support a slow temporal process…
A well-known stochastic model for intermittent fluctuations in physical systems is investigated. The model is given by a super-position of uncorrelated exponential pulses, and the degree of pulse overlap is interpreted as an intermittency…
Permutation Invariant Training (PIT) has long been a stepping stone method for training speech separation model in handling the label ambiguity problem. With PIT selecting the minimum cost label assignments dynamically, very few studies…
This paper is concerned with the development of rigorous approximations to various expectations associated with Markov chains and processes having non-stationary transition probabilities. Such non-stationary models arise naturally in…
The mutual information between stimulus and spike-train response is commonly used to monitor neural coding efficiency, but neuronal computation broadly conceived requires more refined and targeted information measures of input-output joint…
We consider a reaction-diffusion process with retardation. The particles, immersed in traps initially, remain inactive until another particle is annihilated spontaneously with a rate $\lambda$ at a certain point $\vec x$. In that case the…
Often in sequential trials additional data become available after a stopping boundary has been reached. A method of incorporating such information from overrunning is developed, based on the ``adding weighted Zs'' method of combining…
We analyze phase transitions in the conditional entropy of a sequence caused by a change in the conditional variables. Such transitions happen, for example, when training to learn the parameters of a system, since the transition from the…
We study the limiting behavior of continuous time trawl processes which are defined using an infinitely divisible random measure of a time dependent set. In this way one is able to define separately the marginal distribution and the…
We consider a stochastic process driven by a diffusion and jumps. We devise a technique, which is based on a discrete record of observations, for identifying the times when jumps larger than a suitably defined threshold occurred. The…