{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T07:25:54Z","timestamp":1740122754425,"version":"3.37.3"},"reference-count":47,"publisher":"Springer Science and Business Media LLC","issue":"5","license":[{"start":{"date-parts":[[2022,3,28]],"date-time":"2022-03-28T00:00:00Z","timestamp":1648425600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2022,3,28]],"date-time":"2022-03-28T00:00:00Z","timestamp":1648425600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100012166","name":"national key r&d program of china","doi-asserted-by":"crossref","award":["2019YFA0709502"],"award-info":[{"award-number":["2019YFA0709502"]}],"id":[{"id":"10.13039\/501100012166","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"national natural sciences foundation of china","doi-asserted-by":"crossref","award":["62072111"],"award-info":[{"award-number":["62072111"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100013314","name":"111 project","doi-asserted-by":"crossref","award":["B18015"],"award-info":[{"award-number":["B18015"]}],"id":[{"id":"10.13039\/501100013314","id-type":"DOI","asserted-by":"crossref"}]},{"name":"shanghai municipal science and technology major project","award":["2018SHZDZX01"],"award-info":[{"award-number":["2018SHZDZX01"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Neural Process Lett"],"published-print":{"date-parts":[[2022,10]]},"DOI":"10.1007\/s11063-022-10792-y","type":"journal-article","created":{"date-parts":[[2022,3,28]],"date-time":"2022-03-28T21:06:32Z","timestamp":1648501592000},"page":"3893-3911","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Analytic Investigation for Synchronous Firing Patterns Propagation in Spiking Neural Networks"],"prefix":"10.1007","volume":"54","author":[{"given":"Ning","family":"Hua","sequence":"first","affiliation":[]},{"given":"Xiangnan","family":"He","sequence":"additional","affiliation":[]},{"given":"Jianfeng","family":"Feng","sequence":"additional","affiliation":[]},{"given":"Wenlian","family":"Lu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2022,3,28]]},"reference":[{"issue":"3","key":"10792_CR1","doi-asserted-by":"publisher","first-page":"031126","DOI":"10.1103\/PhysRevE.86.031126","volume":"86","author":"B Barzel","year":"2012","unstructured":"Barzel B, Biham O (2012) Stochastic analysis of complex reaction networks using binomial moment equations. Phys Rev E 86(3):031126","journal-title":"Phys Rev E"},{"issue":"2","key":"10792_CR2","doi-asserted-by":"publisher","first-page":"026106","DOI":"10.1103\/PhysRevE.85.026106","volume":"85","author":"JP Gleeson","year":"2012","unstructured":"Gleeson JP, Melnik S, Ward JA, Porter MA, Mucha PJ (2012) Accuracy of mean-field theory for dynamics on real-world networks. Phys Rev E 85(2):026106","journal-title":"Phys Rev E"},{"volume-title":"Stochastic systems","year":"1983","key":"10792_CR3","unstructured":"Adomian G (ed) (1983) Stochastic systems. Academic Press, Cambridge, MA"},{"issue":"2","key":"10792_CR4","doi-asserted-by":"publisher","first-page":"102","DOI":"10.3390\/e20020102","volume":"20","author":"Z Xiao","year":"2018","unstructured":"Xiao Z, Wang B, Sornborger AT, Tao L (2018) Mutual information and information gating in synfire chains. Entropy 20(2):102","journal-title":"Entropy"},{"issue":"1","key":"10792_CR5","doi-asserted-by":"publisher","first-page":"52","DOI":"10.1049\/iet-syb:20070031","volume":"3","author":"CS Gillespie","year":"2009","unstructured":"Gillespie CS (2009) Moment-closure approximations for mass-action models. IET Syst Biol 3(1):52\u201358","journal-title":"IET Syst Biol"},{"issue":"2","key":"10792_CR6","doi-asserted-by":"publisher","first-page":"212","DOI":"10.2307\/3001852","volume":"9","author":"LA Goodman","year":"1953","unstructured":"Goodman LA (1953) Population growth of the sexes. Biometrics 9(2):212\u2013225","journal-title":"Biometrics"},{"issue":"2","key":"10792_CR7","doi-asserted-by":"crossref","first-page":"268","DOI":"10.1111\/j.2517-6161.1957.tb00263.x","volume":"19","author":"P Whittle","year":"1957","unstructured":"Whittle P (1957) On the use of the normal approximation in the treatment of stochastic processes. J Roy Stat Soc: Ser B (Methodol) 19(2):268\u2013281","journal-title":"J Roy Stat Soc: Ser B (Methodol)"},{"key":"10792_CR8","doi-asserted-by":"publisher","first-page":"253","DOI":"10.1007\/978-3-319-28028-8_13","volume-title":"Control of self-organizing nonlinear systems","author":"C Kuehn","year":"2016","unstructured":"Kuehn C (2016) Moment closure\u2014a brief review. In: Sch\u00f6ll E, Klapp S, H\u00f6vel P (eds) Control of self-organizing nonlinear systems. Springer, Cham, pp 253\u2013271"},{"issue":"2","key":"10792_CR9","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1007\/BF00288786","volume":"13","author":"HR Wilson","year":"1973","unstructured":"Wilson HR, Cowan JD (1973) A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue. Kybernetik 13(2):55\u201380","journal-title":"Kybernetik"},{"issue":"20","key":"10792_CR10","doi-asserted-by":"publisher","first-page":"5268","DOI":"10.1523\/JNEUROSCI.2542-07.2008","volume":"28","author":"A Kumar","year":"2008","unstructured":"Kumar A, Rotter S, Aertsen A (2008) Conditions for propagating synchronous spiking and asynchronous firing rates in a cortical network model. J Neurosci 28(20):5268\u20135280","journal-title":"J Neurosci"},{"key":"10792_CR11","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-57715-8","volume-title":"Time-space, spiking neural networks and brain-inspired artificial intelligence","author":"NK Kasabov","year":"2019","unstructured":"Kasabov NK (2019) Time-space, spiking neural networks and brain-inspired artificial intelligence. Springer, Cham"},{"issue":"2","key":"10792_CR12","doi-asserted-by":"publisher","first-page":"1675","DOI":"10.1007\/s11063-020-10322-8","volume":"52","author":"C Tan","year":"2020","unstructured":"Tan C, \u0160arlija M, Kasabov N (2020) Spiking neural networks: background, recent development and the NeuCube architecture. Neural Process Lett 52(2):1675\u20131701","journal-title":"Neural Process Lett"},{"issue":"5345","key":"10792_CR13","doi-asserted-by":"publisher","first-page":"1950","DOI":"10.1126\/science.278.5345.1950","volume":"278","author":"A Riehle","year":"1997","unstructured":"Riehle A, Gr\u00fcn S, Diesmann M, Aertsen A (1997) Spike synchronization and rate modulation differentially involved in motor cortical function. Science 278(5345):1950\u20131953","journal-title":"Science"},{"issue":"6","key":"10792_CR14","doi-asserted-by":"publisher","first-page":"1321","DOI":"10.1162\/089976603321780290","volume":"15","author":"Y Aviel","year":"2003","unstructured":"Aviel Y, Mehring C, Abeles M, Horn D (2003) On embedding synfire chains in a balanced network. Neural Comput 15(6):1321\u20131340","journal-title":"Neural Comput"},{"issue":"5","key":"10792_CR15","doi-asserted-by":"publisher","first-page":"052406","DOI":"10.1103\/PhysRevE.102.052406","volume":"102","author":"D Obeid","year":"2020","unstructured":"Obeid D, Zavatone-Veth JA, Pehlevan C (2020) Statistical structure of the trial-to-trial timing variability in synfire chains. Phys Rev E 102(5):052406","journal-title":"Phys Rev E"},{"issue":"6","key":"10792_CR16","doi-asserted-by":"publisher","first-page":"e1004979","DOI":"10.1371\/journal.pcbi.1004979","volume":"12","author":"Z Wang","year":"2016","unstructured":"Wang Z, Sornborger AT, Tao L (2016) Graded, dynamically routable information processing with synfire-gated synfire chains. PLoS Comput Biol 12(6):e1004979","journal-title":"PLoS Comput Biol"},{"issue":"1","key":"10792_CR17","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1038\/s41467-018-03261-5","volume":"9","author":"C Pehlevan","year":"2018","unstructured":"Pehlevan C, Ali F, \u00d6lveczky BP (2018) Flexibility in motor timing constrains the topology and dynamics of pattern generator circuits. Nat Commun 9(1):1\u201315","journal-title":"Nat Commun"},{"key":"10792_CR18","doi-asserted-by":"publisher","first-page":"312","DOI":"10.1016\/j.neunet.2020.03.019","volume":"126","author":"J Cabessa","year":"2020","unstructured":"Cabessa J, Tchaptchet A (2020) Automata complete computation with Hodgkin\u2013Huxley neural networks composed of synfire rings. Neural Netw 126:312\u2013334","journal-title":"Neural Netw"},{"issue":"24","key":"10792_CR19","doi-asserted-by":"publisher","first-page":"244102","DOI":"10.1103\/PhysRevLett.110.244102","volume":"110","author":"S Nkomo","year":"2013","unstructured":"Nkomo S, Tinsley MR, Showalter K (2013) Chimera states in populations of nonlocally coupled chemical oscillators. Phys Rev Lett 110(24):244102","journal-title":"Phys Rev Lett"},{"issue":"26","key":"10792_CR20","doi-asserted-by":"publisher","first-page":"10563","DOI":"10.1073\/pnas.1302880110","volume":"110","author":"EA Martens","year":"2013","unstructured":"Martens EA, Thutupalli S, Fourriere A, Hallatschek O (2013) Chimera states in mechanical oscillator networks. Proc Nat Acad Sci 110(26):10563\u201310567","journal-title":"Proc Nat Acad Sci"},{"key":"10792_CR21","doi-asserted-by":"publisher","first-page":"110061","DOI":"10.1016\/j.chaos.2020.110061","volume":"139","author":"AV Andreev","year":"2020","unstructured":"Andreev AV, Ivanchenko MV, Pisarchik AN, Hramov AE (2020) Stimulus classification using chimera-like states in a spiking neural network. Chaos Solitons Fractals 139:110061","journal-title":"Chaos Solitons Fractals"},{"issue":"3\u20134","key":"10792_CR22","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1016\/S0928-4257(97)81432-5","volume":"90","author":"A Aertsen","year":"1996","unstructured":"Aertsen A, Diesmann M, Gewaltig MO (1996) Propagation of synchronous spiking activity in feedforward neural networks. J Physiol-Paris 90(3\u20134):243\u2013247","journal-title":"J Physiol-Paris"},{"issue":"10","key":"10792_CR23","doi-asserted-by":"publisher","first-page":"3870","DOI":"10.1523\/JNEUROSCI.18-10-03870.1998","volume":"18","author":"MN Shadlen","year":"1998","unstructured":"Shadlen MN, Newsome WT (1998) The variable discharge of cortical neurons: implications for connectivity, computation, and information coding. J Neurosci 18(10):3870\u20133896","journal-title":"J Neurosci"},{"issue":"2","key":"10792_CR24","doi-asserted-by":"publisher","first-page":"022407","DOI":"10.1103\/PhysRevE.102.022407","volume":"102","author":"B Pietras","year":"2020","unstructured":"Pietras B, Gallice N, Schwalger T (2020) Low-dimensional firing-rate dynamics for populations of renewal-type spiking neurons. Phys Rev E 102(2):022407","journal-title":"Phys Rev E"},{"issue":"5","key":"10792_CR25","doi-asserted-by":"publisher","first-page":"463","DOI":"10.1038\/nn836","volume":"5","author":"ME Mazurek","year":"2002","unstructured":"Mazurek ME, Shadlen MN (2002) Limits to the temporal fidelity of cortical spike rate signals. Nat Neurosci 5(5):463\u2013471","journal-title":"Nat Neurosci"},{"issue":"6\u20137","key":"10792_CR26","doi-asserted-by":"publisher","first-page":"675","DOI":"10.1016\/S0893-6080(01)00065-X","volume":"14","author":"H C\u00e2teau","year":"2001","unstructured":"C\u00e2teau H, Fukai T (2001) Fokker-Planck approach to the pulse packet propagation in synfire chain. Neural Netw 14(6\u20137):675\u2013685","journal-title":"Neural Netw"},{"issue":"6","key":"10792_CR27","first-page":"487","volume":"7","author":"LG Nowak","year":"1997","unstructured":"Nowak LG, Sanchez-Vives MV, McCormick DA (1997) Influence of low and high frequency inputs on spike timing in visual cortical neurons. Cereb Cortex (New York, NY: 1991) 7(6):487\u2013501","journal-title":"Cereb Cortex (New York, NY: 1991)"},{"issue":"6","key":"10792_CR28","doi-asserted-by":"publisher","first-page":"593","DOI":"10.1038\/nn1056","volume":"6","author":"AD Reyes","year":"2003","unstructured":"Reyes AD (2003) Synchrony-dependent propagation of firing rate in iteratively constructed networks in vitro. Nat Neurosci 6(6):593\u2013599","journal-title":"Nat Neurosci"},{"issue":"6761","key":"10792_CR29","doi-asserted-by":"publisher","first-page":"529","DOI":"10.1038\/990101","volume":"402","author":"M Diesmann","year":"1999","unstructured":"Diesmann M, Gewaltig MO, Aertsen A (1999) Stable propagation of synchronous spiking in cortical neural networks. Nature 402(6761):529\u2013533","journal-title":"Nature"},{"issue":"5","key":"10792_CR30","doi-asserted-by":"publisher","first-page":"051904","DOI":"10.1103\/PhysRevE.64.051904","volume":"64","author":"H Sompolinsky","year":"2001","unstructured":"Sompolinsky H, Yoon H, Kang K, Shamir M (2001) Population coding in neuronal systems with correlated noise. Phys Rev E 64(5):051904","journal-title":"Phys Rev E"},{"issue":"7155","key":"10792_CR31","doi-asserted-by":"publisher","first-page":"802","DOI":"10.1038\/nature06028","volume":"448","author":"J De La Rocha","year":"2007","unstructured":"De La Rocha J, Doiron B, Shea-Brown E, Josi\u0107 K, Reyes A (2007) Correlation between neural spike trains increases with firing rate. Nature 448(7155):802\u2013806","journal-title":"Nature"},{"issue":"1","key":"10792_CR32","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1016\/S0006-3495(72)86068-5","volume":"12","author":"HR Wilson","year":"1972","unstructured":"Wilson HR, Cowan JD (1972) Excitatory and inhibitory interactions in localized populations of model neurons. Biophys J 12(1):1\u201324","journal-title":"Biophys J"},{"issue":"9","key":"10792_CR33","doi-asserted-by":"publisher","first-page":"615","DOI":"10.1038\/nrn2886","volume":"11","author":"A Kumar","year":"2010","unstructured":"Kumar A, Rotter S, Aertsen A (2010) Spiking activity propagation in neuronal networks: reconciling different perspectives on neural coding. Nat Rev Neurosci 11(9):615\u2013627","journal-title":"Nat Rev Neurosci"},{"key":"10792_CR34","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511815706","volume-title":"Spiking neuron models: single neurons, populations, plasticity","author":"W Gerstner","year":"2002","unstructured":"Gerstner W, Kistler WM (2002) Spiking neuron models: single neurons, populations, plasticity. Cambridge University Press, Cambridge"},{"issue":"9","key":"10792_CR35","doi-asserted-by":"publisher","first-page":"2057","DOI":"10.1162\/089976602320264015","volume":"14","author":"N Fourcaud","year":"2002","unstructured":"Fourcaud N, Brunel N (2002) Dynamics of the firing probability of noisy integrate-and-fire neurons. Neural Comput 14(9):2057\u20132110","journal-title":"Neural Comput"},{"issue":"4","key":"10792_CR36","doi-asserted-by":"publisher","first-page":"041906","DOI":"10.1103\/PhysRevE.73.041906","volume":"73","author":"J Feng","year":"2006","unstructured":"Feng J, Deng Y, Rossoni E (2006) Dynamics of moment neuronal networks. Phys Rev E 73(4):041906","journal-title":"Phys Rev E"},{"issue":"3","key":"10792_CR37","doi-asserted-by":"publisher","first-page":"913","DOI":"10.1016\/j.neuroimage.2010.02.075","volume":"52","author":"W Lu","year":"2010","unstructured":"Lu W, Rossoni E, Feng J (2010) On a Gaussian neuronal field model. NeuroImage 52(3):913\u2013933","journal-title":"NeuroImage"},{"key":"10792_CR38","volume-title":"Renewal theory","author":"DR Cox","year":"1962","unstructured":"Cox DR (1962) Renewal theory. Methuen Publishing, London"},{"key":"10792_CR39","doi-asserted-by":"publisher","DOI":"10.1201\/9780203494462","volume-title":"Computational neuroscience: a comprehensive approach","author":"J Feng","year":"2003","unstructured":"Feng J (2003) Computational neuroscience: a comprehensive approach. CRC Press, Boca Raton"},{"key":"10792_CR40","volume-title":"Spikes: exploring the neural code","author":"F Rieke","year":"1999","unstructured":"Rieke F (1999) Spikes: exploring the neural code. MIT Press, Cambridge"},{"issue":"3","key":"10792_CR41","doi-asserted-by":"publisher","first-page":"183","DOI":"10.1023\/A:1008925309027","volume":"8","author":"N Brunel","year":"2000","unstructured":"Brunel N (2000) Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons. J Comput Neurosci 8(3):183\u2013208","journal-title":"J Comput Neurosci"},{"issue":"6","key":"10792_CR42","doi-asserted-by":"publisher","first-page":"1321","DOI":"10.1162\/089976698300017214","volume":"10","author":"C Vreeswijk","year":"1998","unstructured":"Vreeswijk C, Sompolinsky H (1998) Chaotic balanced state in a model of cortical circuits. Neural Comput 10(6):1321\u20131371","journal-title":"Neural Comput"},{"issue":"46","key":"10792_CR43","doi-asserted-by":"publisher","first-page":"10786","DOI":"10.1523\/JNEUROSCI.3508-05.2005","volume":"25","author":"TP Vogels","year":"2005","unstructured":"Vogels TP, Abbott LF (2005) Signal propagation and logic gating in networks of integrate-and-fire neurons. J Neurosci 25(46):10786\u201310795","journal-title":"J Neurosci"},{"issue":"4","key":"10792_CR44","first-page":"349","volume":"3","author":"MC Mozer","year":"1989","unstructured":"Mozer MC (1989) A focused back-propagation algorithm for temporal pattern recognition. Complex Syst 3(4):349\u2013381","journal-title":"Complex Syst"},{"key":"10792_CR45","volume-title":"Random fields and geometry","author":"RJ Adler","year":"2009","unstructured":"Adler RJ, Taylor JE (2009) Random fields and geometry. Springer, Berlin"},{"key":"10792_CR46","doi-asserted-by":"publisher","first-page":"36","DOI":"10.1007\/s10548-021-00842-4","volume":"35","author":"A Byrne","year":"2021","unstructured":"Byrne A, Ross J, Nicks R, Coombes S (2021) Mean-field models for EEG\/MEG: from oscillations to waves. Brain Topogr 35:36\u201353","journal-title":"Brain Topogr"},{"key":"10792_CR47","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s13408-020-00086-9","volume":"10","author":"C Bick","year":"2020","unstructured":"Bick C, Goodfellow M, Laing CR, Martens EA (2020) Understanding the dynamics of biological and neural oscillator networks through exact mean-field reductions: a review. J Math Neurosci 10:1\u201343","journal-title":"J Math Neurosci"}],"container-title":["Neural Processing Letters"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11063-022-10792-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11063-022-10792-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11063-022-10792-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,9,21]],"date-time":"2024-09-21T04:25:43Z","timestamp":1726892743000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11063-022-10792-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,3,28]]},"references-count":47,"journal-issue":{"issue":"5","published-print":{"date-parts":[[2022,10]]}},"alternative-id":["10792"],"URL":"https:\/\/doi.org\/10.1007\/s11063-022-10792-y","relation":{},"ISSN":["1370-4621","1573-773X"],"issn-type":[{"type":"print","value":"1370-4621"},{"type":"electronic","value":"1573-773X"}],"subject":[],"published":{"date-parts":[[2022,3,28]]},"assertion":[{"value":"28 February 2022","order":1,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"28 March 2022","order":2,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}