title: Theoretical connections between mathematical neuronal models corresponding to different expressions of noise.
abstract: 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 is strikingly similar.
authors.affiliation: École Normale Supérieure, Group for Neural Theory, Paris, France. Electronic address: gregory.dumont@ens.fr.
authors.forename: Grégory
authors.initials: G
authors.lastname: Dumont
authors.affiliation: INRIA team Carmen, INRIA Bordeaux Sud-Ouest, 33405 Talence cedex, France. Electronic address: Jacques.Henry@inria.fr.
authors.forename: Jacques
authors.initials: J
authors.lastname: Henry
authors.affiliation: Intersdisciplinary Research Department - Field Sciences, Alexandru Ioan Cuza University of Iaşi, Lascăr Catargi nr. 54, Iaşi, Romania. Electronic address: tarniceriuoana@yahoo.co.uk.
authors.forename: Carmen Oana
authors.initials: CO
authors.lastname: Tarniceriu
mesh_terms: D003198:Computer Simulation; D008959:Models, Neurological; D009474:Neurons / Q000502:physiology*; D013269:Stochastic Processes
keywords: Age structured model; Escape rate; Fokker–Planck equation; Neural noise; Noisy Leaky Integrate-and-Fire model