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arXiv · 1304.3002

Determination of the calcium channel distribution in the olfactory system

C. Conca·R. Lecaros·J. H. Ortega·L. Rosier
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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 func- tions, we obtain identifiability, stability and reconstruction results. Further- more, 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 invert- ibility 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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C. Conca, R. Lecaros, J. H. Ortega, L. Rosier. 2013-04-10. Determination of the calcium channel distribution in the olfactory system. https://arxiv.org/abs/1304.3002

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