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Stochastic neural activity: A theoretical investigation. Nijmegen: Faculteit der Wiskunde en Natuurwetenschappen; 1969."},{"issue":"6","key":"ref4","doi-asserted-by":"crossref","first-page":"734","DOI":"10.1085\/jgp.59.6.734","article-title":"Dynamics of encoding in a population of neurons","volume":"59","author":"BW Knight","year":"1972","journal-title":"The Journal of general physiology"},{"issue":"1","key":"ref5","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1023\/A:1008964915724","article-title":"On the simulation of large populations of neurons","volume":"8","author":"A Omurtag","year":"2000","journal-title":"Journal of Computational Neuroscience"},{"issue":"3","key":"ref6","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1023\/A:1008925309027","article-title":"Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons","volume":"8","author":"N Brunel","year":"2000","journal-title":"Journal of computational neuroscience"},{"issue":"1","key":"ref7","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1162\/089976600300015899","article-title":"Population dynamics of spiking neurons: fast transients, asynchronous states, and locking","volume":"12","author":"W Gerstner","year":"2000","journal-title":"Neural computation"},{"issue":"2","key":"ref8","doi-asserted-by":"crossref","first-page":"360","DOI":"10.1162\/neco.2008.03-08-743","article-title":"Spike train statistics and dynamics with synaptic input from any renewal process: a population density approach","volume":"21","author":"C Ly","year":"2009","journal-title":"Neural Computation"},{"issue":"1","key":"ref9","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1023\/A:1008912914816","article-title":"A population density approach that facilitates large-scale modeling of neural networks: Analysis and an application to orientation tuning","volume":"8","author":"DQ Nykamp","year":"2000","journal-title":"Journal of computational neuroscience"},{"issue":"9","key":"ref10","doi-asserted-by":"crossref","first-page":"2129","DOI":"10.1162\/089976603322297322","article-title":"A simple and stable numerical solution for the population density equation","volume":"15","author":"M de Kamps","year":"2003","journal-title":"Neural computation"},{"issue":"10","key":"ref11","doi-asserted-by":"crossref","first-page":"e1003248","DOI":"10.1371\/journal.pcbi.1003248","article-title":"The influence of synaptic weight distribution on neuronal population dynamics","volume":"9","author":"R Iyer","year":"2013","journal-title":"PLoS computational biology"},{"key":"ref12","unstructured":"de Kamps M. A generic approach to solving jump diffusion equations with applications to neural populations. arXiv preprint arXiv:13091654. 2013."},{"issue":"5","key":"ref13","doi-asserted-by":"crossref","first-page":"051917","DOI":"10.1103\/PhysRevE.66.051917","article-title":"Population dynamics of interacting spiking neurons","volume":"66","author":"M Mattia","year":"2002","journal-title":"Physical Review E"},{"issue":"5","key":"ref14","doi-asserted-by":"crossref","first-page":"052903","DOI":"10.1103\/PhysRevE.70.052903","article-title":"Finite-size dynamics of inhibitory and excitatory interacting spiking neurons","volume":"70","author":"M Mattia","year":"2004","journal-title":"Physical Review E"},{"issue":"6","key":"ref15","doi-asserted-by":"crossref","first-page":"e1005545","DOI":"10.1371\/journal.pcbi.1005545","article-title":"Low-dimensional spike rate models derived from networks of adaptive integrate-and-fire neurons: comparison and implementation","volume":"13","author":"M Augustin","year":"2017","journal-title":"PLoS computational biology"},{"issue":"9","key":"ref16","doi-asserted-by":"crossref","first-page":"e1005045","DOI":"10.1371\/journal.pcbi.1005045","article-title":"The computational properties of a simplified cortical column model","volume":"12","author":"N Cain","year":"2016","journal-title":"PLoS computational biology"},{"issue":"4","key":"ref17","doi-asserted-by":"crossref","first-page":"e1005507","DOI":"10.1371\/journal.pcbi.1005507","article-title":"Towards a theory of cortical columns: From spiking neurons to interacting neural populations of finite size","volume":"13","author":"T Schwalger","year":"2017","journal-title":"PLoS computational biology"},{"issue":"8","key":"ref18","doi-asserted-by":"crossref","first-page":"2032","DOI":"10.1162\/neco.2007.19.8.2032","article-title":"Critical analysis of dimension reduction by a moment closure method in a population density approach to neural network modeling","volume":"19","author":"C Ly","year":"2007","journal-title":"Neural computation"},{"issue":"5","key":"ref19","doi-asserted-by":"crossref","first-page":"957","DOI":"10.1162\/089976602753633349","article-title":"A population study of integrate-and-fire-or-burst neurons","volume":"14","author":"ARR Casti","year":"2002","journal-title":"Neural Computation"},{"issue":"4","key":"ref20","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1080\/09548980601069787","article-title":"Population density methods for stochastic neurons with realistic synaptic kinetics: Firing rate dynamics and fast computational methods","volume":"17","author":"F Apfaltrer","year":"2006","journal-title":"Network: Computation in Neural Systems"},{"issue":"5","key":"ref21","doi-asserted-by":"crossref","first-page":"051918","DOI":"10.1103\/PhysRevE.69.051918","article-title":"Effects of synaptic conductance on the voltage distribution and firing rate of spiking neurons","volume":"69","author":"MJ Richardson","year":"2004","journal-title":"Physical Review E"},{"key":"ref22","article-title":"Dynamical systems in neuroscience","author":"EM Izhikevich","year":"2007"},{"issue":"6","key":"ref23","doi-asserted-by":"crossref","first-page":"062125","DOI":"10.1103\/PhysRevE.95.062125","article-title":"Population density equations for stochastic processes with memory kernels","volume":"95","author":"YM Lai","year":"2017","journal-title":"Physical Review E"},{"issue":"1","key":"ref24","doi-asserted-by":"crossref","first-page":"e84626","DOI":"10.1371\/journal.pone.0084626","article-title":"Emergence of connectivity motifs in networks of model neurons with short-and long-term plastic synapses","volume":"9","author":"E Vasilaki","year":"2014","journal-title":"PloS one"},{"issue":"37","key":"ref25","doi-asserted-by":"crossref","first-page":"11628","DOI":"10.1523\/JNEUROSCI.23-37-11628.2003","article-title":"How spike generation mechanisms determine the neuronal response to fluctuating inputs","volume":"23","author":"N Fourcaud-Trocm\u00e9","year":"2003","journal-title":"The Journal of neuroscience"},{"issue":"5","key":"ref26","doi-asserted-by":"crossref","first-page":"3637","DOI":"10.1152\/jn.00686.2005","article-title":"Adaptive exponential integrate-and-fire model as an effective description of neuronal activity","volume":"94","author":"R Brette","year":"2005","journal-title":"Journal of neurophysiology"},{"issue":"2","key":"ref27","doi-asserted-by":"crossref","first-page":"719","DOI":"10.1073\/pnas.94.2.719","article-title":"The neural code between neocortical pyramidal neurons depends on neurotransmitter release probability","volume":"94","author":"MV Tsodyks","year":"1997","journal-title":"Proceedings of the National Academy of Sciences"},{"issue":"6","key":"ref28","doi-asserted-by":"crossref","first-page":"445","DOI":"10.1016\/S0006-3495(61)86902-6","article-title":"Impulses and physiological states in theoretical models of nerve membrane","volume":"1","author":"R FitzHugh","year":"1961","journal-title":"Biophysical journal"},{"issue":"4","key":"ref29","doi-asserted-by":"crossref","first-page":"880","DOI":"10.1063\/1.166460","article-title":"Threshold, excitability and isochrones in the Bonhoeffer\u2013van der Pol system","volume":"9","author":"A Rabinovitch","year":"1999","journal-title":"Chaos: An Interdisciplinary Journal of Nonlinear Science"},{"key":"ref30","doi-asserted-by":"crossref","first-page":"1572","DOI":"10.1103\/PhysRevE.50.1572","article-title":"Forced Bonhoeffer\u02d8van der Pol oscillator in its excited mode","volume":"50","author":"A Rabinovitch","year":"1994","journal-title":"Phys Rev E"},{"issue":"2132","key":"ref31","doi-asserted-by":"crossref","first-page":"2404","DOI":"10.1098\/rspa.2011.0053","article-title":"Canards and curvature: the \u2018smallness of <italic>\u03f5<\/italic>\u2019 in slow\u2013fast dynamics","volume":"467","author":"M Desroches","year":"2011","journal-title":"Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences"},{"issue":"1","key":"ref32","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1137\/100809866","article-title":"Canard-Like Explosion of Limit Cycles in Two-Dimensional Piecewise-Linear Models of FitzHugh\u2013Nagumo Type","volume":"11","author":"HG Rotstein","year":"2012","journal-title":"SIAM Journal on Applied Dynamical Systems"},{"issue":"2","key":"ref33","doi-asserted-by":"crossref","first-page":"026204","DOI":"10.1103\/PhysRevE.83.026204","article-title":"Reduced representations of heterogeneous mixed neural networks with synaptic coupling","volume":"83","author":"RA Stefanescu","year":"2011","journal-title":"Physical Review E"},{"key":"ref34","doi-asserted-by":"crossref","first-page":"35","DOI":"10.3389\/fninf.2011.00035","article-title":"Meeting the memory challenges of brain-scale network simulation","volume":"5","author":"S Kunkel","year":"2012","journal-title":"Frontiers in Neuroinformatics"},{"issue":"2","key":"ref35","doi-asserted-by":"crossref","first-page":"021028","DOI":"10.1103\/PhysRevX.5.021028","article-title":"Macroscopic description for networks of spiking neurons","volume":"5","author":"E Montbri\u00f3","year":"2015","journal-title":"Physical Review X"},{"issue":"1","key":"ref36","doi-asserted-by":"crossref","first-page":"e1002872","DOI":"10.1371\/journal.pcbi.1002872","article-title":"Dynamic finite size effects in spiking neural networks","volume":"9","author":"MA Buice","year":"2013","journal-title":"PLoS computational biology"},{"key":"ref37","unstructured":"Sch\u00fccker J, Goedeke S, Dahmen D, Helias M. Functional methods for disordered neural networks. arXiv preprint arXiv:160506758. 2016."},{"key":"ref38","unstructured":"Dahmen D, Gr\u00fcn S, Diesmann M, Helias M. Two types of criticality in the brain. arXiv preprint arXiv:171110930. 2017."},{"issue":"1","key":"ref39","doi-asserted-by":"crossref","first-page":"10","DOI":"10.1186\/2190-8567-2-10","article-title":"Mean-field description and propagation of chaos in networks of Hodgkin-Huxley and FitzHugh-Nagumo neurons","volume":"2","author":"J Baladron","year":"2012","journal-title":"The Journal of Mathematical Neuroscience"},{"issue":"3","key":"ref40","first-page":"237","article-title":"Model of global spontaneous activity and local structured activity during delay periods in the cerebral cortex","volume":"7","author":"DJ Amit","year":"1997","journal-title":"Cerebral cortex (New York, NY: 1991)"},{"key":"ref41","doi-asserted-by":"crossref","first-page":"11","DOI":"10.3389\/fnsys.2016.00011","article-title":"Stimuli reduce the dimensionality of cortical activity","volume":"10","author":"L Mazzucato","year":"2016","journal-title":"Frontiers in systems neuroscience"},{"key":"ref42","doi-asserted-by":"crossref","first-page":"75","DOI":"10.3389\/fninf.2017.00075","article-title":"Perfect detection of spikes in the linear sub-threshold dynamics of point neurons","volume":"11","author":"J Krishnan","year":"2017","journal-title":"Frontiers in neuroinformatics"}],"updated-by":[{"DOI":"10.1371\/journal.pcbi.1006729","type":"new_version","label":"New version","source":"publisher","updated":{"date-parts":[[2019,3,14]],"date-time":"2019-03-14T00:00:00Z","timestamp":1552521600000}}],"container-title":["PLOS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/dx.plos.org\/10.1371\/journal.pcbi.1006729","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,5,9]],"date-time":"2020-05-09T05:14:07Z","timestamp":1589001247000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.1006729"}},"subtitle":[],"editor":[{"given":"Boris S.","family":"Gutkin","sequence":"first","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2019,3,4]]},"references-count":42,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2019,3,4]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.1006729","relation":{"has-preprint":[{"id-type":"doi","id":"10.1101\/275412","asserted-by":"object"}]},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,3,4]]}}}