{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,22]],"date-time":"2024-08-22T16:40:27Z","timestamp":1724344827610},"reference-count":65,"publisher":"MIT Press","issue":"6","content-domain":{"domain":["direct.mit.edu"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2024,5,10]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Biological neural networks are notoriously hard to model due to their stochastic behavior and high dimensionality. We tackle this problem by constructing a dynamical model of both the expectations and covariances of the fractions of active and refractory neurons in the network\u2019s populations. We do so by describing the evolution of the states of individual neurons with a continuous-time Markov chain, from which we formally derive a low-dimensional dynamical system. This is done by solving a moment closure problem in a way that is compatible with the nonlinearity and boundedness of the activation function. Our dynamical system captures the behavior of the high-dimensional stochastic model even in cases where the mean-field approximation fails to do so. Taking into account the second-order moments modifies the solutions that would be obtained with the mean-field approximation and can lead to the appearance or disappearance of fixed points and limit cycles. We moreover perform numerical experiments where the mean-field approximation leads to periodically oscillating solutions, while the solutions of the second-order model can be interpreted as an average taken over many realizations of the stochastic model. Altogether, our results highlight the importance of including higher moments when studying stochastic networks and deepen our understanding of correlated neuronal activity.<\/jats:p>","DOI":"10.1162\/neco_a_01656","type":"journal-article","created":{"date-parts":[[2024,4,25]],"date-time":"2024-04-25T00:08:47Z","timestamp":1714003727000},"page":"1121-1162","update-policy":"http:\/\/dx.doi.org\/10.1162\/mitpressjournals.corrections.policy","source":"Crossref","is-referenced-by-count":0,"title":["The Determining Role of Covariances in Large Networks of Stochastic Neurons"],"prefix":"10.1162","volume":"36","author":[{"given":"Vincent","family":"Painchaud","sequence":"first","affiliation":[{"name":"Department of Mathematics and Statistics, McGill University, Montreal, Qu\u00e9bec H3A 0B6, Canada vincent.painchaud@mail.mcgill.ca"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Patrick","family":"Desrosiers","sequence":"additional","affiliation":[{"name":"Department of Physics, Engineering Physics, and Optics, Universit\u00e9 Laval, Quebec City, Qu\u00e9bec G1V 0A6, Canada"},{"name":"CERVO Brain Research Center, Quebec City, Qu\u00e9bec G1E 1T2, Canada"},{"name":"Centre interdisciplinaire en mod\u00e9lisation math\u00e9matique de l\u2019Universit\u00e9 Laval, Quebec City, Qu\u00e9bec G1V 0A6, Canada patrick.desrosiers@phy.ulaval.ca"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nicolas","family":"Doyon","sequence":"additional","affiliation":[{"name":"D\u00e9partment of Mathematics and Statistics, Universit\u00e9 Laval, Quebec City, Qu\u00e9bec G1V 0A6, Canada"},{"name":"CERVO Brain Research Center, Quebec City, Qu\u00e9bec G1E 1T2, Canada"},{"name":"Centre interdisciplinaire en mod\u00e9lisation math\u00e9matique de l\u2019Universit\u00e9 Laval, Quebec City, Qu\u00e9bec G1V 0A6, Canada nicolas.doyon@mat.ulaval.ca"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"281","published-online":{"date-parts":[[2024,5,10]]},"reference":[{"issue":"5","key":"2024082215382151700_bib1","doi-asserted-by":"publisher","first-page":"358","DOI":"10.1038\/nrn1888","article-title":"Neural correlations, population coding and computation","volume":"7","author":"Averbeck","year":"2006","journal-title":"Nature Reviews Neuroscience"},{"issue":"18","key":"2024082215382151700_bib2","doi-asserted-by":"publisher","first-page":"7681","DOI":"10.1523\/JNEUROSCI.3405-12.2013","article-title":"Refractoriness enhances temporal coding by auditory nerve fibers","volume":"33","author":"Avissar","year":"2013","journal-title":"Journal of Neuroscience"},{"issue":"1","key":"2024082215382151700_bib3","doi-asserted-by":"publisher","first-page":"403","DOI":"10.1146\/annurev-neuro-120320-082744","article-title":"The geometry of information coding in correlated neural populations","volume":"44","author":"Azeredo da Silveira","year":"2021","journal-title":"Annual Review of Neuroscience"},{"issue":"6","key":"2024082215382151700_bib4","doi-asserted-by":"publisher","first-page":"2200","DOI":"10.1523\/JNEUROSCI.18-06-02200.1998","article-title":"Refractoriness and neural precision","volume":"18","author":"Berry","year":"1998","journal-title":"Journal of Neuroscience"},{"issue":"669","key":"2024082215382151700_bib5","doi-asserted-by":"publisher","first-page":"55","DOI":"10.2307\/92540","article-title":"Properties of a mass of cells capable of regenerating pulses","volume":"240","author":"Beurle","year":"1956","journal-title":"Philosophical Transactions of the Royal Society of London. 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