Fokker-Planck and Fortet equation-based parameter estimation for a leaky integrate-and-fire model with sinusoidal and stochastic forcing

DOI10.1186/2190-8567-4-4zbMath1431.92011OpenAlexW2148361269WikidataQ43010224 ScholiaQ43010224MaRDI QIDQ2251600

André Longtin, Alexandre Iolov, Susanne Ditlevsen

Publication date: 14 July 2014

Published in: The Journal of Mathematical Neuroscience (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/2190-8567-4-4

zbMATH Keywords

Fokker-Planck equationfirst-passage timesstochastic neuron modelsFortet integral equationparameter estimation from stopping times

Mathematics Subject Classification ID

PDEs in connection with biology, chemistry and other natural sciences (35Q92) Biomechanics (92C10) Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics (82C31) Fokker-Planck equations (35Q84)

Related Items (11)

How does transient signaling input affect the spike timing of postsynaptic neuron near the threshold regime: an analytical study ⋮ The gamma renewal process as an output of the diffusion leaky integrate-and-fire neuronal model ⋮ Reconstruction of the input signal of the leaky integrate-and-fire neuronal model from its interspike intervals ⋮ The First-passage Time of the Brownian Motion to a Curved Boundary: an Algorithmic Approach ⋮ A Reduced Order Modeling Framework for Strongly Perturbed Nonlinear Dynamical Systems Near Arbitrary Trajectory Sets ⋮ On Firing Rate Estimation for Dependent Interspike Intervals ⋮ Responses of leaky integrate-and-fire neurons to a plurality of stimuli in their receptive fields ⋮ A Fokker-Planck control framework for stochastic systems ⋮ Random quasi-periodic paths and quasi-periodic measures of stochastic differential equations ⋮ Optimal Design for Estimation in Diffusion Processes from First Hitting Times ⋮ Expected exit time for time-periodic stochastic differential equations and applications to stochastic resonance

Uses Software

• GSL
• SciPy

Cites Work

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• A review of the methods for signal estimation in stochastic diffusion leaky integrate-and-fire neuronal models
• Maximum likelihood analysis of spike trains of interacting nerve cells
• Bistability and the dynamics of periodically forced sensory neurons
• A first-passage-time analysis of the periodically forced noisy leaky integrate-and-fire model
• On the parameter estimation for diffusion models of single neuron's activities. I: Application to spontaneous activities of mesencephalic reticular formation cells in sleep and waking states
• A review of the integrate-and-fire neuron model: II. Inhomogeneous synaptic input and network properties
• Les fonctions aléatoires du type de Markoff associees à certaines équations linéaires aux dérivées partielles du type parabolique
• Estimating Parameters of Generalized Integrate-and-Fire Neurons from the Maximum Likelihood of Spike Trains
• Estimation of the input parameters in the Feller neuronal model
• Stochastic Processes for Physicists
• Maximum Likelihood Decoding of Neuronal Inputs from an Interspike Interval Distribution
• Stochastic Integrate and Fire Models: A Review on Mathematical Methods and Their Applications
• Maximum Likelihood Estimation of a Stochastic Integrate-and-Fire Neural Encoding Model
• Spiking Neurons and the First Passage Problem
• Representations of the First Hitting Time Density of an Ornstein-Uhlenbeck Process¹

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