Fast and Accurate Langevin Simulations of Stochastic Hodgkin-Huxley Dynamics

Stochastic shielding and edge importance for Markov chains with timescale separation

(2018) Deena R. Schmidt et al.   PLoS Computational Biology

Effects of ion channel noise on neural circuits: an application to the respiratory pattern generator to investigate breathing variability

(2017) Haitao Yu et al.   JOURNAL OF NEUROPHYSIOLOGY

Dynamics of Gamma Bursts in Local Field Potentials

(2015) Priscilla E. Greenwood et al.   NEURAL COMPUTATION

Spontaneous Action Potentials and Neural Coding in Unmyelinated Axons

(2015) Cian O’Donnell et al.   NEURAL COMPUTATION

Stochastic representations of ion channel kinetics and exact stochastic simulation of neuronal dynamics

(2014) David F. Anderson et al.   JOURNAL OF COMPUTATIONAL NEUROSCIENCE

Measuring Edge Importance: A Quantitative Analysis of the Stochastic Shielding Approximation for Random Processes on Graphs

(2014) Deena R Schmidt et al.   Journal of Mathematical Neuroscience

An Investigation of the Stochastic Hodgkin-Huxley Models Under Noisy Rate Functions

(2013) Marifi Güler   NEURAL COMPUTATION

Channel-based Langevin approach for the stochastic Hodgkin-Huxley neuron

(2013) Yandong Huang et al.   PHYSICAL REVIEW E

Breakdown of Fast-Slow Analysis in an Excitable System with Channel Noise

(2013) Jay M. Newby et al.   PHYSICAL REVIEW LETTERS

Stochastic Hodgkin-Huxley Equations with Colored Noise Terms in the Conductances

(2012) Marifi Güler   NEURAL COMPUTATION

Modeling ion channel dynamics through reflected stochastic differential equations

(2012) Ciara E. Dangerfield et al.   PHYSICAL REVIEW E

Stochastic-Shielding Approximation of Markov Chains and its Application to Efficiently Simulate Random Ion-Channel Gating

(2012) Nicolaus T. Schmandt et al.   PHYSICAL REVIEW LETTERS

Simple, Fast and Accurate Implementation of the Diffusion Approximation Algorithm for Stochastic Ion Channels with Multiple States

(2012) Patricio Orio et al.   PLoS One

Stochastic differential equation models for ion channel noise in Hodgkin-Huxley neurons

(2011) Joshua H. Goldwyn et al.   PHYSICAL REVIEW E

Accurate and Fast Simulation of Channel Noise in Conductance-Based Model Neurons by Diffusion Approximation

(2011) Daniele Linaro et al.   PLoS Computational Biology

The What and Where of Adding Channel Noise to the Hodgkin-Huxley Equations

(2011) Joshua H. Goldwyn et al.   PLoS Computational Biology

Encoding and decoding amplitude-modulated cochlear implant stimuli—a point process analysis

(2010) Joshua H. Goldwyn et al.   JOURNAL OF COMPUTATIONAL NEUROSCIENCE

Comparison of Langevin and Markov channel noise models for neuronal signal generation

(2010) B. Sengupta et al.   PHYSICAL REVIEW E

Invariant Manifolds of Binomial-Like Nonautonomous Master Equations

(2010) Berton A. Earnshaw et al.   SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS

Global Asymptotic Stability of Solutions of Nonautonomous Master Equations

(2010) Berton A. Earnshaw et al.   SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS

Evaluation of Stochastic Differential Equation Approximation of Ion Channel Gating Models

(2009) Ian C. Bruce   ANNALS OF BIOMEDICAL ENGINEERING

Stochastic Population Model for Electrical Stimulation of the Auditory Nerve

(2009) N.S. Imennov et al.   IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING

Exact reductions of Markovian dynamics for ion channels with a single permissive state

(2009) James P. Keener   JOURNAL OF MATHEMATICAL BIOLOGY

Simulation of the Electrically Stimulated Cochlear Neuron: Modeling Adaptation to Trains of Electric Pulses

(2008) Jihwan Woo et al.   IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING

Invariant manifold reductions for Markovian ion channel dynamics

(2008) James P. Keener   JOURNAL OF MATHEMATICAL BIOLOGY

Construction of Equivalent Stochastic Differential Equation Models

(2008) Edward J. Allen et al.   STOCHASTIC ANALYSIS AND APPLICATIONS