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Shape Minimization of Dendritic Attenuation

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Abstract

What is the optimal shape of a dendrite? Of course, optimality refers to some particular criterion. In this paper, we look at the case of a dendrite sealed at one end and connected at the other end to a soma. The electrical potential in the fiber follows the classical cable equations as established by W. Rall. We are interested in the shape of the dendrite which minimizes either the attenuation in time of the potential or the attenuation in space. In both cases, we prove that the cylindrical shape is optimal.

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Authors and Affiliations

  1. Institut Élie Cartan de Nancy, UMR 7502 Nancy-Université-CNRS-INRIA, B.P. 239, Vandœuvre-lès-Nancy Cedex, France

    Antoine Henrot & Yannick Privat

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  1. Antoine Henrot
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  2. Yannick Privat
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Correspondence to Antoine Henrot.

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Henrot, A., Privat, Y. Shape Minimization of Dendritic Attenuation. Appl Math Optim 57, 1–16 (2008). https://doi.org/10.1007/s00245-007-9002-0

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