English

Determination of the calcium channel distribution in the olfactory system

Optimization and Control 2013-04-11 v1

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.

Keywords

Cite

@article{arxiv.1304.3002,
  title  = {Determination of the calcium channel distribution in the olfactory system},
  author = {C. Conca and R. Lecaros and J. H. Ortega and L. Rosier},
  journal= {arXiv preprint arXiv:1304.3002},
  year   = {2013}
}