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Extended Abstracts Spring 2016 pp 89–94Cite as

Birkhäuser

Nonlinear Estimation of Synaptic Conductances via Piecewise Linear Systems

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Part of the book series: Trends in Mathematics ((RPCRMB,volume 8))

Abstract

We use the piecewise linear McKean model to present a proof-of-concept to address the estimation of synaptic conductances when a neuron is spiking. Using standard techniques of non-smooth dynamical systems, we obtain an approximation of the period in terms of the parameters of the system which allows to estimate the steady synaptic conductance of the spiking neuron. The method gives also fairly good estimations when the synaptic conductances vary slowly in time.

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Acknowledgements

This work is partially supported by the Spanish Ministry of Economy and Competitiveness through project MTM2015-71509-C2-2-R (AG), by the MCYT/FEDER grant number MTM2014-54275-P (RP, AT and CV) and by the Government of Catalonia under grant 2014-SGR–504 (AG).

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Authors and Affiliations

  1. Departament de Matemàtiques-EPSEB, Universitat Politècnica de Catalunya, Barcelona, Spain

    Antoni Guillamon

  2. Departament de Matemàtiques i Informàtica, Universitat de les Illes Balears, Palma, Spain

    Rafel Prohens, Antonio E. Teruel & Catalina Vich

Authors
  1. Antoni Guillamon
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  2. Rafel Prohens
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  3. Antonio E. Teruel
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  4. Catalina Vich
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Corresponding author

Correspondence to Antoni Guillamon .

Editor information

Editors and Affiliations

  1. DEIB, Politecnico di Milano , Milano, Italy

    Alessandro Colombo

  2. Department of Engineering Mathematics, University of Bristol , BRISTOL, Avon, United Kingdom

    Mike Jeffrey

  3. Departament de Matemàtiques, Universitat Politècnica de Catalunya , Barcelona, Spain

    J. Tomàs Lázaro

  4. Departament de Matemàtiques, Universitat Politècnica de Catalunya, Barcelona, Spain

    Josep M. Olm

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Guillamon, A., Prohens, R., Teruel, A.E., Vich, C. (2017). Nonlinear Estimation of Synaptic Conductances via Piecewise Linear Systems. In: Colombo, A., Jeffrey, M., Lázaro, J., Olm, J. (eds) Extended Abstracts Spring 2016. Trends in Mathematics(), vol 8. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-55642-0_16

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