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Determination of the calcium channel distribution in the olfactory system

Abstract : In this paper we study a linear inverse problem with a biological interpretation, which is modeled by a Fredholm integral equation of the first kind. When the kernel in the Fredholm equation is represented by step functions, we obtain identifiability, stability and reconstruction results. Furthermore, we provide a numerical reconstruction algorithm for the kernel, whose main feature is that a non-regular mesh has to be used to ensure the invertibility of the matrix representing the numerical discretization of the system. Finally, a second identifiability result for a polynomial approximation of degree less than nine of the kernel is also established.
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Contributor : François Chaplais Connect in order to contact the contributor
Submitted on : Monday, February 2, 2015 - 10:40:47 AM
Last modification on : Wednesday, November 17, 2021 - 12:31:01 PM

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Carlos Conca, Rodrigo Lecaros, Jaime Ortega, Lionel Rosier. Determination of the calcium channel distribution in the olfactory system. Journal of Inverse and Ill-posed Problems, De Gruyter, 2014, 22 (5), pp.671--711. ⟨10.1515/jip-2013-0033⟩. ⟨hal-01112038⟩



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