DUMONT, Grégory; HENRY, Jacques; TARNICERIU, Carmen Oana

doi:10.1016/j.jtbi.2016.06.022

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DUMONT, Grégory
Group for Neural Theory [Paris]

HENRY, Jacques
Modélisation et calculs pour l'électrophysiologie cardiaque [CARMEN]
Institut de Mathématiques de Bordeaux [IMB]

TARNICERIU, Carmen Oana
Faculty of Computer Science [Iași]

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Journal of Theoretical Biology. 2016, vol. 406, p. 31-41

Elsevier

Résumé en anglais

Identifying the right tools to express the stochastic aspects of neural activity has proven to be one of the biggest challenges in computational neuroscience. Even if there is no definitive answer to this issue, the most common procedure to express this randomness is the use of stochastic models. In accordance with the origin of variability, the sources of randomness are classified as intrinsic or extrinsic and give rise to distinct mathematical frameworks to track down the dynamics of the cell. While the external variability is generally treated by the use of a Wiener process in models such as the Integrate-and-Fire model, the internal variability is mostly expressed via a random firing process. In this paper, we investigate how those distinct expressions of variability can be related. To do so, we examine the probability density functions to the corresponding stochastic models and investigate in what way they can be mapped one to another via integral transforms. Our theoretical findings offer a new insight view into the particular categories of variability and it confirms that, despite their contrasting nature, the mathematical formalization of internal and external variability are strikingly similar.< Réduire

Mots clés en anglais

Fokker-Planck equation

Age structured model

Neural noise

Noisy Leaky Integrate-and-Fire model

Escape rate

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Theoretical connections between mathematical neuronal models corresponding to different expressions of noise

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