This title appears in the Scientific Report :
2015
The transfer function of the LIF model: A reduction from colored to white noise
The transfer function of the LIF model: A reduction from colored to white noise
The assessment of the stability of neuronal networks, the emergence of oscillations and correlated activity rely on the response properties of a neuron to a modulation of its input, i.e. the transfer function. For the leaky integrate-and-fire neuron model exposed to white noise the transfer function...
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Personal Name(s): | Schücker, Jannis (Corresponding Author) |
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Diesmann, Markus / Helias, Moritz | |
Contributing Institute: |
Computational and Systems Neuroscience; INM-6 Computational and Systems Neuroscience; IAS-6 |
Published in: | 2015 |
Imprint: |
2015
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Conference: | Eleventh Goettingen Meeting of German Neuroscience Community, Goettingen (Germany), 2015-03-18 - 2015-03-21 |
Document Type: |
Poster |
Research Program: |
The Human Brain Project Brain-inspired multiscale computation in neuromorphic hybrid systems Theory of multi-scale neuronal networks Supercomputing and Modelling for the Human Brain Theory, modelling and simulation |
Publikationsportal JuSER |
The assessment of the stability of neuronal networks, the emergence of oscillations and correlated activity rely on the response properties of a neuron to a modulation of its input, i.e. the transfer function. For the leaky integrate-and-fire neuron model exposed to white noise the transfer function has been derived analytically [1,2]. The decay time of a few milliseconds for a postsynaptic current amounts to the synaptic noise not being white, but rather having higher power at low frequencies. The effect of such colored noise on the response properties has been studied intensively at the beginning of the last decade [3,4]. Analytical results were derived in the low as well as in the high frequency limit. The main finding is that the linear response amplitude of model neurons exposed to filtered synaptic noise does not decay to zero in the high frequency limit. A numerical method has also been developed to study the influence of synaptic noise on the response properties [5]. Here we first revisit the transfer function for neuron models without synaptic filtering and simplify the derivation exploiting analogies between the one dimensional Fokker-Planck equation and the quantum harmonic oscillator. Synaptic filtering comes along with considerable difficulties, since it adds a dimension to the governing Fokker-Planck equation. We overcome these complications by developing a general method of reduction to a lower dimensional effective system, respecting the details of the noise in the boundary conditions [6]. Static boundary conditions were derived earlier by a perturbative treatment of the arising boundary layer problem [4]. Here we extend this study to the dynamic case. Finally we compare the analytical results to direct simulations (Fig.1) and observe that the approximations are valid up to moderate frequencies. Deviations are explained by the nature of the made approximations.References: [1] Brunel N, Hakim V: Fast global oscillations in networks of integrate-and-fire neurons with low firing rates. Neural Comput 1999, 11(7):1621–1671. [2] Lindner B, Schimansky-Geier L: Transmission of noise coded versus additive signals through a neuronal ensemble. Phys Rev Lett 2001, 86:2934–2937. [3] Brunel N, Chance FS, Fourcaud N, Abbott, LF: Effects of synaptic noise and filtering on the frequency response of spiking neurons. Phys Rev Lett 2001, 86(10):2186–2189. [4] Fourcaud N, Brunel N: Dynamics of the firing probability of noisy integrate-and-fire neurons. Neural Comput 2002, 14:2057–2110. [5] Richardson, MJE: Firing-rate response of linear and nonlinear integrate-and-fire neurons to modulated current-based and conductance-based synaptic drive. Phys Rev E 2007, 76(2 Pt 1):021919. [6] Klosek MM, Hagan PS: Colored noise and a characteristic level crossing problem. J Math Phys 1998, 39:931–953. |