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 …
many papers have appeared on single neuron description and specifically on stochastic …
RUL prediction of deteriorating products using an adaptive Wiener process model
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 …
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 …
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
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 …
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 …
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 …
motion crossing piecewise linear boundaries which can be discontinuous. Using this …
Fractionally integrated Gauss-Markov processes and applications
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 …
integral of order α∈(0, 1) of Gauss-Markov processes. The general expressions of the …
Integrated stationary Ornstein–Uhlenbeck process, and double integral processes
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 …
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 …
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 …
Because neurons nonperiodically emit spikes, examining spike timing can reveal …