{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,17]],"date-time":"2026-07-17T05:23:41Z","timestamp":1784265821037,"version":"3.55.0"},"reference-count":62,"publisher":"Public Library of Science (PLoS)","issue":"1","license":[{"start":{"date-parts":[[2007,1,19]],"date-time":"2007-01-19T00:00:00Z","timestamp":1169164800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["www.ploscompbiol.org"],"crossmark-restriction":false},"short-container-title":["PLoS Comput Biol"],"DOI":"10.1371\/journal.pcbi.0020165","type":"journal-article","created":{"date-parts":[[2007,1,17]],"date-time":"2007-01-17T13:42:21Z","timestamp":1169041341000},"page":"e165","update-policy":"https:\/\/doi.org\/10.1371\/journal.pcbi.corrections_policy","source":"Crossref","is-referenced-by-count":186,"title":["Computational Aspects of Feedback in Neural Circuits"],"prefix":"10.1371","volume":"3","author":[{"given":"Wolfgang","family":"Maass","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Prashant","family":"Joshi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Eduardo D","family":"Sontag","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"340","published-online":{"date-parts":[[2007,1,19]]},"reference":[{"key":"pcbi-0020165-b001","doi-asserted-by":"crossref","first-page":"981","DOI":"10.1126\/science.7638624","article-title":"Recurrent excitation in neocortical circuits.","volume":"269","year":"1995","journal-title":"Science"},{"key":"pcbi-0020165-b002","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1177\/1534582303002001003","article-title":"How does the cerebral cortex work? Development, learning, attention, and 3D vision by laminar circuits of visual cortex.","volume":"2","year":"2003","journal-title":"Behav Cogn Neurosci Rev"},{"key":"pcbi-0020165-b003","doi-asserted-by":"crossref","first-page":"1028","DOI":"10.1126\/science.7863330","article-title":"Temporal information transformed into a spatial code by a neural network with realistic properties.","volume":"267","year":"1995","journal-title":"Science"},{"key":"pcbi-0020165-b004","doi-asserted-by":"crossref","first-page":"1743","DOI":"10.1162\/089976600300015123","article-title":"Neural systems as nonlinear filters.","volume":"12","year":"2000","journal-title":"Neural Computation"},{"key":"pcbi-0020165-b005","doi-asserted-by":"crossref","first-page":"2531","DOI":"10.1162\/089976602760407955","article-title":"Real-time computing without stable states: A new framework for neural computation based on perturbations.","volume":"14","year":"2002","journal-title":"Neural Computation"},{"key":"pcbi-0020165-b006","doi-asserted-by":"crossref","unstructured":"H\u00e4uslerSMaassW 2007 A statistical analysis of information processing properties of lamina-specific cortical microcircuit models. Cerebral Cortex epub. Available: http:\/\/www.igi.tugraz.at\/maass\/psfiles\/162.pdf. Accessed 1 December 2006.","DOI":"10.1093\/cercor\/bhj132"},{"key":"pcbi-0020165-b007","doi-asserted-by":"crossref","first-page":"789","DOI":"10.1038\/nature03011","article-title":"Plasticity in single neuron and circuit computations.","volume":"431","year":"2004","journal-title":"Nature"},{"key":"pcbi-0020165-b008","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1016\/j.jphysparis.2005.09.020","article-title":"Fading memory and kernel properties of generic cortical microcircuit models.","volume":"98","year":"2004","journal-title":"J Physiol (Paris)"},{"key":"pcbi-0020165-b009","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1016\/S0896-6273(03)00185-5","article-title":"Representation of time by neurons in the posterior parietal cortex of the macaque.","volume":"38","year":"2003","journal-title":"Neuron"},{"key":"pcbi-0020165-b010","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1093\/cercor\/10.3.263","article-title":"Delay activity of orbital and lateral prefrontal neurons of the monkey varying with different rewards.","volume":"10","year":"2000","journal-title":"Cerebral Cortex"},{"key":"pcbi-0020165-b011","doi-asserted-by":"crossref","first-page":"1877","DOI":"10.1152\/jn.2000.83.4.1877","article-title":"Modifications of reward expectation\u2013related neuronal activity during learning in primate orbitofrontal cortex.","volume":"83","year":"2000","journal-title":"J Neurophysiol"},{"key":"pcbi-0020165-b012","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1016\/S0166-2236(03)00122-X","article-title":"Changes in behavior-related neuronal activity in the striatum during learning.","volume":"26","year":"2003","journal-title":"Trends Neurosci"},{"key":"pcbi-0020165-b013","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1016\/S0166-2236(00)01868-3","article-title":"Synaptic reverberation underlying mnemonic persistent activity.","volume":"24","year":"2001","journal-title":"Trends Neurosci"},{"key":"pcbi-0020165-b014","doi-asserted-by":"crossref","first-page":"1257","DOI":"10.1093\/cercor\/bhg097","article-title":"A role for neural integrators in perceptual decision making.","volume":"13","year":"2003","journal-title":"Cerebral Cortex"},{"key":"pcbi-0020165-b015","doi-asserted-by":"crossref","first-page":"7739","DOI":"10.1073\/pnas.0401970101","article-title":"Plasticity and tuning by visual feedback of the stability of a neural integrator.","volume":"101","year":"2004","journal-title":"Proc Natl Acad Sci U S A"},{"key":"pcbi-0020165-b016","unstructured":"ShadlenMNGoldJI 2005 The neurophysiology of decision-making as a window on cognition. In GazzanigaMS The cognitive neurosciences. 3rd edition Cambridge (Massachusetts) MIT Press 1229 1241"},{"key":"pcbi-0020165-b017","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1126\/science.1091277","article-title":"Harnessing nonlinearity: Predicting chaotic systems and saving energy in wireless communication.","volume":"304","year":"2004","journal-title":"Science"},{"key":"pcbi-0020165-b018","doi-asserted-by":"crossref","first-page":"1715","DOI":"10.1162\/0899766054026684","article-title":"Movement generation with circuits of spiking neurons.","volume":"17","year":"2005","journal-title":"Neural Computation"},{"key":"pcbi-0020165-b019","doi-asserted-by":"crossref","unstructured":"WhiteEL 1989 Cortical circuits Boston Birkhaeuser 223","DOI":"10.1007\/978-1-4684-8721-3"},{"issue":"11","key":"pcbi-0020165-b020","first-page":"1910","article-title":"Motifs in brain networks.","volume":"2","year":"2004","journal-title":"PLoS Biol"},{"key":"pcbi-0020165-b021","unstructured":"RiekeRWarlandDvan SteveninckRRDBialekW 1997 SPIKES: Exploring the neural code Cambridge (Massachusetts) MIT Press 416"},{"key":"pcbi-0020165-b022","doi-asserted-by":"crossref","unstructured":"CowanJD 1968 Statistical mechanics of neural nets. In CaianielloER Neural networks Berlin Springer 181 188","DOI":"10.1007\/978-3-642-87596-0_17"},{"key":"pcbi-0020165-b023","first-page":"815","article-title":"Absolute stability of global pattern formation and parallel memory storage by competitive neural networks.","volume":"13","year":"1983","journal-title":"IEEE Trans Sys Man Cyber"},{"key":"pcbi-0020165-b024","doi-asserted-by":"crossref","first-page":"3088","DOI":"10.1073\/pnas.81.10.3088","article-title":"Neurons with graded response have collective computational properties like those of two-state neurons.","volume":"81","year":"1984","journal-title":"Proc Natl Acad Sci U S A"},{"key":"pcbi-0020165-b025","unstructured":"DayanPAbbottLF 2001 Theoretical neuroscience: Computational and mathematical modeling of neural systems Cambridge (Massachusetts) MIT Press"},{"key":"pcbi-0020165-b026","unstructured":"SavageJE 1998 Models of computation: Exploring the power of computing Reading (Massachusetts) Addison-Wesley 698"},{"key":"pcbi-0020165-b027","doi-asserted-by":"crossref","unstructured":"MaassWMarkramH 2006 Theory of the computational function of microcircuit dynamics. In GrillnerSGraybielAM The interface between neurons and global brain function. Dahlem Workshop Report 93 Cambridge (Masschusetts) MIT Press 371 390","DOI":"10.7551\/mitpress\/4596.003.0020"},{"key":"pcbi-0020165-b028","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1016\/0304-3975(94)00147-B","article-title":"Universal computation and other capabilities of hybrid and continuous dynamical systems.","volume":"138","year":"1995","journal-title":"Theor Comput Sci"},{"key":"pcbi-0020165-b029","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1016\/0304-3975(94)90178-3","article-title":"Analog computation via neural networks.","volume":"131","year":"1994","journal-title":"Theor Comput Sci"},{"key":"pcbi-0020165-b030","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1006\/jcss.1995.1013","article-title":"On the computational power of neural nets.","volume":"50","year":"1995","journal-title":"J Comput Syst Sci"},{"key":"pcbi-0020165-b031","doi-asserted-by":"crossref","unstructured":"OrponenP 1997 A survey of continuous-time computation theory. In DuDZKoKI Advances in algorithms, languages, and complexity Berlin Kluwer\/Springer 9 224","DOI":"10.1007\/978-1-4613-3394-4_11"},{"key":"pcbi-0020165-b032","unstructured":"SlotineJJELiW 1991 Applied nonlinear control Upper Saddle River (New Jersey) Prentice Hall 352"},{"key":"pcbi-0020165-b033","unstructured":"SontagED 1999 Mathematical control theory Berlin Springer-Verlag 531"},{"key":"pcbi-0020165-b034","unstructured":"HaykinS 1999 Neural networks: A comprehensive foundation. 2nd edition Upper Saddle River (New Jersey) Prentice Hall 842"},{"key":"pcbi-0020165-b035","doi-asserted-by":"crossref","first-page":"1071","DOI":"10.1162\/089976698300017359","article-title":"On the effect of analog noise in discrete-time analog computations.","volume":"10","year":"1998","journal-title":"Neural Computation"},{"key":"pcbi-0020165-b036","doi-asserted-by":"crossref","first-page":"771","DOI":"10.1162\/089976699300016656","article-title":"Analog neural nets with Gaussian or other common noise distribution cannot recognize arbitrary regular languages.","volume":"11","year":"1999","journal-title":"Neural Computation"},{"key":"pcbi-0020165-b037","doi-asserted-by":"crossref","first-page":"593","DOI":"10.1016\/j.jcss.2004.04.001","article-title":"On the computational power of recurrent circuits of spiking neurons.","volume":"69","year":"2004","journal-title":"J Comput Syst Sci"},{"key":"pcbi-0020165-b038","unstructured":"Sch\u00f6lkopfBSmolaAJ 2002 Learning with kernels Cambridge (Massachusetts) MIT Press"},{"key":"pcbi-0020165-b039","doi-asserted-by":"crossref","first-page":"2554","DOI":"10.1073\/pnas.79.8.2554","article-title":"Neural networks and physical systems with emergent collective computational abilities.","volume":"79","year":"1982","journal-title":"Proc Natl Acad Sci U S A"},{"key":"pcbi-0020165-b040","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1093\/cercor\/7.3.237","article-title":"Model of global spontaneous activity and local structured activity during delay periods in the cerebral cortex.","volume":"7","year":"1997","journal-title":"Cerebral Cortex"},{"key":"pcbi-0020165-b041","doi-asserted-by":"crossref","first-page":"204","DOI":"10.1016\/S0959-4388(03)00050-3","article-title":"Basic mechanisms for graded persistent activity: Discrete attractors, continuous attractors, and dynamic representations.","volume":"13","year":"2003","journal-title":"Curr Opin Neurobiol"},{"key":"pcbi-0020165-b042","doi-asserted-by":"crossref","first-page":"739","DOI":"10.1038\/nrn1198","article-title":"The high-conductance state of neocortical neurons in vivo.","volume":"4","year":"2003","journal-title":"Nat Rev Neurosci"},{"key":"pcbi-0020165-b043","doi-asserted-by":"crossref","first-page":"5323","DOI":"10.1073\/pnas.95.9.5323","article-title":"Differential signaling via the same axon of neocortical pyramidal neurons.","volume":"95","year":"1998","journal-title":"Proc Natl Acad Sci U S A"},{"key":"pcbi-0020165-b044","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1126\/science.287.5451.273","article-title":"Organizing principles for a diversity of GABAergic interneurons and synapses in the neocortex.","volume":"287","year":"2000","journal-title":"Science"},{"key":"pcbi-0020165-b045","doi-asserted-by":"crossref","first-page":"7745","DOI":"10.1073\/pnas.0401992101","article-title":"Plasticity and tuning of the time course of analog persistent firing in a neural integrator.","volume":"101","year":"2004","journal-title":"Proc Natl Acad Sci U S A"},{"key":"pcbi-0020165-b046","doi-asserted-by":"crossref","first-page":"2337","DOI":"10.1162\/0899766054796888","article-title":"What can a neuron learn with spike-timing\u2013dependent plasticity?","volume":"17","year":"2005","journal-title":"Neural Computation"},{"key":"pcbi-0020165-b047","unstructured":"WickensJK\u00f6tterR 1998 Cellular models of reinforcement. In HoukJCDavisJLBeiserDG Models of information processing in the basal ganglia Cambridge (Massachusetts) MIT Press"},{"key":"pcbi-0020165-b048","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1016\/S0306-4522(01)00344-X","article-title":"Fluctuating synaptic conductances recreate in vivo\u2013like activity in neocortical neurons.","volume":"107","year":"2001","journal-title":"Neuroscience"},{"key":"pcbi-0020165-b049","doi-asserted-by":"crossref","first-page":"1531","DOI":"10.1152\/jn.1999.81.4.1531","article-title":"Impact of network activity on the integrative properties of neocortical pyramidal neurons in vivo. J.","volume":"81","year":"1999","journal-title":"Neurophysiol"},{"key":"pcbi-0020165-b050","doi-asserted-by":"crossref","first-page":"869","DOI":"10.1038\/43119","article-title":"K+ channel regulation of signal propagation in dendrites of hippocampal pyramidal neurons.","volume":"387","year":"1997","journal-title":"Nature"},{"issue":"Part 1","key":"pcbi-0020165-b051","first-page":"67","article-title":"Characterization of single voltage\u2013gated Na+ and Ca2+ channels in apical dendrites of rat CA1 pyramidal neurons.","volume":"487","year":"1995","journal-title":"J Physiol"},{"key":"pcbi-0020165-b052","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1146\/annurev.physiol.60.1.327","article-title":"Electrical and calcium signaling in dendrites of hippocampal pyramidal neurons.","volume":"60","year":"1998","journal-title":"Annu Rev Physiol"},{"key":"pcbi-0020165-b053","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1038\/367069a0","article-title":"Active propagation of somatic action potentials into neocortical pyramidal cell dendrites.","volume":"367","year":"1994","journal-title":"Nature"},{"key":"pcbi-0020165-b054","unstructured":"TraubRDMilesR 1991 Neuronal networks of the hippocampus Cambridge (United Kingdom) Cambridge University Press 301"},{"key":"pcbi-0020165-b055","doi-asserted-by":"crossref","first-page":"1427","DOI":"10.1016\/0896-6273(95)90020-9","article-title":"A model of spike initiation in neocortical pyramidal neurons.","volume":"15","year":"1995","journal-title":"Neuron"},{"key":"pcbi-0020165-b056","doi-asserted-by":"crossref","first-page":"778","DOI":"10.1152\/jn.1988.59.3.778","article-title":"Developmental changes in Na+ conductances in rat neocortical neurons: Appearance of a slowly inactivating component.","volume":"59","year":"1988","journal-title":"J Neurophysiol"},{"key":"pcbi-0020165-b057","doi-asserted-by":"crossref","first-page":"617","DOI":"10.1038\/75797","article-title":"Stimulus dependence of two-state fluctuations of membrane potential in cat visual cortex.","volume":"3","year":"2000","journal-title":"Nature Neuroscience"},{"key":"pcbi-0020165-b058","doi-asserted-by":"crossref","first-page":"369","DOI":"10.1038\/30735","article-title":"Visual input evokes transient and strong shunting inhibition in visual cortical neurons.","volume":"393","year":"1998","journal-title":"Nature"},{"key":"pcbi-0020165-b059","doi-asserted-by":"crossref","first-page":"9517","DOI":"10.1523\/JNEUROSCI.18-22-09517.1998","article-title":"Synaptic integration in striate cortical simple cells.","volume":"18","year":"1998","journal-title":"J Neurosci"},{"key":"pcbi-0020165-b060","doi-asserted-by":"crossref","first-page":"155","DOI":"10.1016\/S0893-6080(01)00144-7","article-title":"Synapses as dynamic memory buffers.","volume":"15","year":"2002","journal-title":"Neural Networks"},{"key":"pcbi-0020165-b061","doi-asserted-by":"crossref","unstructured":"Natschl\u00e4gerTMarkramHMaassW 2003 Computer models and analysis tools for neural microcircuits. In K\u00f6tterR Neuroscience databases. A practical guide Boston Kluwer 123 138","DOI":"10.1007\/978-1-4615-1079-6_9"},{"key":"pcbi-0020165-b062","doi-asserted-by":"crossref","unstructured":"LegensteinRAMaassW 2007 Edge of chaos and prediction of computational performance for neural microcircuit models. Neural Networks. In press","DOI":"10.1016\/j.neunet.2007.04.017"}],"container-title":["PLoS Computational Biology"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.0020165","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,10]],"date-time":"2024-02-10T07:12:00Z","timestamp":1707549120000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pcbi.0020165"}},"subtitle":[],"editor":[{"given":"Rolf","family":"Kotter","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"editor"}]}],"short-title":[],"issued":{"date-parts":[[2007,1,19]]},"references-count":62,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2007,1,19]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pcbi.0020165","relation":{},"ISSN":["1553-7358"],"issn-type":[{"value":"1553-7358","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,1,19]]}}}