Stochastic integrate and fire models: a review on mathematical methods and their applications

L Sacerdote, MT Giraudo - … models: with applications to neuronal modeling, 2013 - Springer
Mathematical models are an important tool for neuroscientists. During the last 30 years
many papers have appeared on single neuron description and specifically on stochastic …

RUL prediction of deteriorating products using an adaptive Wiener process model

Q Zhai, ZS Ye - IEEE Transactions on Industrial Informatics, 2017 - ieeexplore.ieee.org
Degradation modeling plays an important role in system health diagnosis and remaining
useful life (RUL) prediction. Recently, a class of Wiener process models with adaptive drift …

Neurodynamics

S Coombes, KCA Wedgwood - Texts in applied mathematics, 2023 - Springer
This is a book about 'Neurodynamics'. What we mean is that this is a book about how ideas
from dynamical systems theory have been developed and employed in recent years to give …

Average beta burst duration profiles provide a signature of dynamical changes between the ON and OFF medication states in Parkinson's disease

B Duchet, F Ghezzi, G Weerasinghe… - PLoS computational …, 2021 - journals.plos.org
Parkinson's disease motor symptoms are associated with an increase in subthalamic
nucleus beta band oscillatory power. However, these oscillations are phasic, and there is a …

A phase transition in the first passage of a Brownian process through a fluctuating boundary with implications for neural coding

T Taillefumier, MO Magnasco - Proceedings of the National …, 2013 - National Acad Sciences
Finding the first time a fluctuating quantity reaches a given boundary is a deceptively simple-
looking problem of vast practical importance in physics, biology, chemistry, neuroscience …

First passage time for Brownian motion and piecewise linear boundaries

Z Jin, L Wang - Methodology and Computing in Applied Probability, 2017 - Springer
We propose a new approach to calculating the first passage time densities for Brownian
motion crossing piecewise linear boundaries which can be discontinuous. Using this …

Fractionally integrated Gauss-Markov processes and applications

M Abundo, E Pirozzi - … in Nonlinear Science and Numerical Simulation, 2021 - Elsevier
We investigate the stochastic processes obtained as the fractional Riemann-Liouville
integral of order α∈(0, 1) of Gauss-Markov processes. The general expressions of the …

Integrated stationary Ornstein–Uhlenbeck process, and double integral processes

M Abundo, E Pirozzi - Physica A: Statistical Mechanics and its Applications, 2018 - Elsevier
We find a representation of the integral of the stationary Ornstein–Uhlenbeck (ISOU) process
in terms of Brownian motion B t; moreover, we show that, under certain conditions on the …

[PDF][PDF] Successive spike times predicted by a stochastic neuronal model with a variable input signal

G D'Onofrio, E Pirozzi - Mathematical Biosciences and Engineering, 2016 - iris.unito.it
Two different stochastic processes are used to model the evolution of the membrane voltage
of a neuron exposed to a time-varying input signal. The first process is an inhomogeneous …

Estimating nonstationary input signals from a single neuronal spike train

H Kim, S Shinomoto - Physical Review E—Statistical, Nonlinear, and Soft …, 2012 - APS
Neurons temporally integrate input signals, translating them into timed output spikes.
Because neurons nonperiodically emit spikes, examining spike timing can reveal …