Output Stream of Binding Neuron with Threshold 2 Stimulated with Renewal Process
Keywords:binding neuron, Poisson process, renewal process, interspike interval, probability density function, moments of a distribution
Information is transmitted between neurons in a brain via typical electrical impulses, which are called spikes. Since the activity of biological neurons is random, the statistics of neuronal activity, namely, the time intervals between neuron-generated consecutive spikes, is studied. A neuron transforms a random stream of input impulses into another stream, the output one. The input stream is described in this paper as a renewal point process. As a neuronal model, a binding neuron with threshold 2 is considered. A relationship between the Laplace transforms of the probability density functions of the interspike intervals in the input stream of impulses and the output stream generated as a response to this stimulus has been obtained. The derived relationship enables the determination of the probability density function and all of its moments. The resulting formulas are applied to the case where the input process is the Erlang one. In the considered case, the dependence of the regularity of the neuronal activity on the input stream parameters and the physical parameters of the neuron model is found.
R. Brette. Philosophy of the spike: Rate-based vs. spikebased theories of the brain. Front. Syst. Neurosci. 9, 151 (2015).
G. Maimon, J.A. Assad. Beyond Poisson: Increased spiketime regularity across primate parietal cortex. Neuron 62, 426 (2009).
S. Shinomoto et al. Relating neuronal firing patterns to functional differentiation of cerebral cortex. PLoS Comput. Biol. 5, e1000433 (2009).
D.H. Johnson. Point process models of single-neuron discharges. J. Comput. Neurosci. 3, 275 (1996).
A.K. Vidybida. Inhibition as binding controller at the single neuron level. BioSystems 48, 263 (1998).
O.K. Vidybida. Output stream of a binding neuron. Ukr. Math. J. 59, 1819 (2007).
D. Cox. Renewal Theory. 1st Edition (Methuen and Co., 1962) [ISBN: 978-0412205705].
A.K. Dhawale, M.A. Smith, B.P. Olveczky. The role of variability in motor learning. Annu. Rev. Neurosci. 40, 479 (2017).
A. Compte, C. Constantinidis, J. Tegn'er, S. Raghavachari, M.V. Chafee, P.S. Goldman-Rakic, Xiao-Jing Wang. Temporally irregular mnemonic persistent activity in prefrontal neurons of monkeys during a delayed response task. J. Neurophysiol. 90, 3441 (2003).
V. Arunachalam, R. Akhavan-Tabatabaei, C. Lopez. Results on a binding neuron model and their implications for modified hourglass model for neuronal network. Comput. Math. Methods Med. 2013, 374878 (2013).
A. Vidybida. Relation between firing statistics of spiking neuron with instantaneous feedback and without feedback. Fluct. Noise Lett. 14, 1550034 (2015).
A.N. Burkitt. A review of the integrate-and-fire neuron model: I. Homogeneous synaptic input. Biol. Cybern. 95, 1 (2006).
A.K. Vidybida. Output stream of binding neuron with instantaneous feedback. Eur. Phys. J. B 65, 577 (2008).
P. Lansky, L. Sacerdote, C. Zucca. The Gamma renewal process as an output of the diffusion leaky integrate-andfire neuronal model. Biol. Cybern. 110, 193 (2016).
O. Shchur, A. Vidybida. Distribution of interspike intervals of a neuron with inhibitory autapse stimulated with a renewal process. Fluct. Noise Lett. 22, 2350003 (2023).
A.K. Vidybida. Output stream of leaky integrate-and-fire neuron without diffusion approximation. J. Stat. Phys. 166, 267 (2017).
A.K. Vidybida, O.V. Shchur. Moment-generating function of output stream of leaky integrate-and-fire neuron. Ukr. J. Phys. 66, 254 (2021).
K. Kravchuk. Leaky integrate-and-fire neuron under Poisson stimulation. In: Proceedings of the 2016 II International Young Scientists Forum on Applied Physics and Engineering (YSF), Kharkiv, Ukraine, October 10-14 (IEEE, 2016), p. 203.
How to Cite
License to Publish the Paper
The corresponding author and the co-authors (hereon referred to as the Author(s)) of the paper being submitted to the Ukrainian Journal of Physics (hereon referred to as the Paper) from one side and the Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, represented by its Director (hereon referred to as the Publisher) from the other side have come to the following Agreement:
1. Subject of the Agreement.
The Author(s) grant(s) the Publisher the free non-exclusive right to use the Paper (of scientific, technical, or any other content) according to the terms and conditions defined by this Agreement.
2. The ways of using the Paper.
2.1. The Author(s) grant(s) the Publisher the right to use the Paper as follows.
2.1.1. To publish the Paper in the Ukrainian Journal of Physics (hereon referred to as the Journal) in original language and translated into English (the copy of the Paper approved by the Author(s) and the Publisher and accepted for publication is a constitutive part of this License Agreement).
2.1.2. To edit, adapt, and correct the Paper by approval of the Author(s).
2.1.3. To translate the Paper in the case when the Paper is written in a language different from that adopted in the Journal.
2.2. If the Author(s) has(ve) an intent to use the Paper in any other way, e.g., to publish the translated version of the Paper (except for the case defined by Section 2.1.3 of this Agreement), to post the full Paper or any its part on the web, to publish the Paper in any other editions, to include the Paper or any its part in other collections, anthologies, encyclopaedias, etc., the Author(s) should get a written permission from the Publisher.
3. License territory.
The Author(s) grant(s) the Publisher the right to use the Paper as regulated by sections 2.1.1–2.1.3 of this Agreement on the territory of Ukraine and to distribute the Paper as indispensable part of the Journal on the territory of Ukraine and other countries by means of subscription, sales, and free transfer to a third party.
4.1. This Agreement is valid starting from the date of signature and acts for the entire period of the existence of the Journal.
5.1. The Author(s) warrant(s) the Publisher that:
– he/she is the true author (co-author) of the Paper;
– copyright on the Paper was not transferred to any other party;
– the Paper has never been published before and will not be published in any other media before it is published by the Publisher (see also section 2.2);
– the Author(s) do(es) not violate any intellectual property right of other parties. If the Paper includes some materials of other parties, except for citations whose length is regulated by the scientific, informational, or critical character of the Paper, the use of such materials is in compliance with the regulations of the international law and the law of Ukraine.
6. Requisites and signatures of the Parties.
Publisher: Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine.
Address: Ukraine, Kyiv, Metrolohichna Str. 14-b.
Author: Electronic signature on behalf and with endorsement of all co-authors.