IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i6p1011-d374107.html
   My bibliography  Save this article

Revealing Spectrum Features of Stochastic Neuron Spike Trains

Author

Listed:
  • Simone Orcioni

    (DII, Department of Information Engineering, Università Politecnica delle Marche, 60131 Ancona, Italy)

  • Alessandra Paffi

    (DIET, Department of Information Engineering, Electronics and Telecommunications, Università Sapienza, 00185 Rome, Italy)

  • Francesca Apollonio

    (DIET, Department of Information Engineering, Electronics and Telecommunications, Università Sapienza, 00185 Rome, Italy)

  • Micaela Liberti

    (DIET, Department of Information Engineering, Electronics and Telecommunications, Università Sapienza, 00185 Rome, Italy)

Abstract

Power spectra of spike trains reveal important properties of neuronal behavior. They exhibit several peaks, whose shape and position depend on applied stimuli and intrinsic biophysical properties, such as input current density and channel noise. The position of the spectral peaks in the frequency domain is not straightforwardly predictable from statistical averages of the interspike intervals, especially when stochastic behavior prevails. In this work, we provide a model for the neuronal power spectrum, obtained from Discrete Fourier Transform and expressed as a series of expected value of sinusoidal terms. The first term of the series allows us to estimate the frequencies of the spectral peaks to a maximum error of a few Hz, and to interpret why they are not harmonics of the first peak frequency. Thus, the simple expression of the proposed power spectral density (PSD) model makes it a powerful interpretative tool of PSD shape, and also useful for neurophysiological studies aimed at extracting information on neuronal behavior from spike train spectra.

Suggested Citation

  • Simone Orcioni & Alessandra Paffi & Francesca Apollonio & Micaela Liberti, 2020. "Revealing Spectrum Features of Stochastic Neuron Spike Trains," Mathematics, MDPI, vol. 8(6), pages 1-13, June.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:6:p:1011-:d:374107
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/6/1011/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/6/1011/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ayala Matzner & Izhar Bar-Gad, 2015. "Quantifying Spike Train Oscillations: Biases, Distortions and Solutions," PLOS Computational Biology, Public Library of Science, vol. 11(4), pages 1-21, April.
    2. Alberto Mazzoni & Frédéric D Broccard & Elizabeth Garcia-Perez & Paolo Bonifazi & Maria Elisabetta Ruaro & Vincent Torre, 2007. "On the Dynamics of the Spontaneous Activity in Neuronal Networks," PLOS ONE, Public Library of Science, vol. 2(5), pages 1-12, May.
    3. I. Goychuk & P. Hänggi, 2009. "Nonstationary stochastic resonance viewed through the lens of information theory," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 69(1), pages 29-35, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Lev Ryashko & Irina Bashkirtseva, 2022. "Stochastic Bifurcations and Excitement in the ZS-Model of a Thermochemical Reaction," Mathematics, MDPI, vol. 10(6), pages 1-11, March.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Bershadskii, A. & Ikegaya, Y., 2011. "Chaotic neuron clock," Chaos, Solitons & Fractals, Elsevier, vol. 44(4), pages 342-347.
    2. Bashkirtseva, Irina A. & Ryashko, Lev B. & Pisarchik, Alexander N., 2020. "Ring of map-based neural oscillators: From order to chaos and back," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).
    3. Marc Benayoun & Jack D Cowan & Wim van Drongelen & Edward Wallace, 2010. "Avalanches in a Stochastic Model of Spiking Neurons," PLOS Computational Biology, Public Library of Science, vol. 6(7), pages 1-13, July.
    4. Sinisa Pajevic & Dietmar Plenz, 2009. "Efficient Network Reconstruction from Dynamical Cascades Identifies Small-World Topology of Neuronal Avalanches," PLOS Computational Biology, Public Library of Science, vol. 5(1), pages 1-20, January.
    5. Hollerbach, Rainer & Kim, Eun-jin & Mahi, Yanis, 2019. "Information length as a new diagnostic in the periodically modulated double-well model of stochastic resonance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1313-1322.
    6. Protachevicz, Paulo R. & Batista, Antonio M. & Caldas, Iberê L. & Baptista, Murilo S., 2024. "Analytical solutions for the short-term plasticity," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    7. Matthias Rybarsch & Stefan Bornholdt, 2014. "Avalanches in Self-Organized Critical Neural Networks: A Minimal Model for the Neural SOC Universality Class," PLOS ONE, Public Library of Science, vol. 9(4), pages 1-8, April.
    8. Guido Gigante & Gustavo Deco & Shimon Marom & Paolo Del Giudice, 2015. "Network Events on Multiple Space and Time Scales in Cultured Neural Networks and in a Stochastic Rate Model," PLOS Computational Biology, Public Library of Science, vol. 11(11), pages 1-23, November.
    9. Kensuke Arai & Robert E Kass, 2017. "Inferring oscillatory modulation in neural spike trains," PLOS Computational Biology, Public Library of Science, vol. 13(10), pages 1-31, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:8:y:2020:i:6:p:1011-:d:374107. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.