메뉴 건너뛰기




Volumn 9, Issue 10, 2013, Pages

A Complex-Valued Firing-Rate Model That Approximates the Dynamics of Spiking Networks

Author keywords

[No Author keywords available]

Indexed keywords

COMPLEX NETWORKS; EIGENVALUES AND EIGENFUNCTIONS; ELECTROPHYSIOLOGY; FOKKER PLANCK EQUATION; NEURAL NETWORKS; SYNCHRONIZATION;

EID: 84887310609     PISSN: 1553734X     EISSN: 15537358     Source Type: Journal    
DOI: 10.1371/journal.pcbi.1003301     Document Type: Article
Times cited : (58)

References (36)
  • 1
    • 0015260274 scopus 로고
    • Excitatory and inhibitory interactions in localized populations of model neurons
    • Wilson HR, Cowan JD, (1972) Excitatory and inhibitory interactions in localized populations of model neurons. Biophysical Journal 12: 1-24.
    • (1972) Biophysical Journal , vol.12 , pp. 1-24
    • Wilson, H.R.1    Cowan, J.D.2
  • 2
    • 0000650934 scopus 로고
    • Reduction of conductance-based models with slow synapses to neural nets
    • Ermentrout B, (1994) Reduction of conductance-based models with slow synapses to neural nets. Neural Comput 6: 679-695.
    • (1994) Neural Comput , vol.6 , pp. 679-695
    • Ermentrout, B.1
  • 4
    • 0041324844 scopus 로고    scopus 로고
    • Rate models for conductance-based cortical neuronal networks
    • Shriki O, Hansel D, Sompolinsky H, (2003) Rate models for conductance-based cortical neuronal networks. Neural Comput 15: 1809-1841.
    • (2003) Neural Comput , vol.15 , pp. 1809-1841
    • Shriki, O.1    Hansel, D.2    Sompolinsky, H.3
  • 5
    • 79551566720 scopus 로고    scopus 로고
    • From spiking neuron models to linear-nonlinear models
    • Ostojic S, Brunel N, (2011) From spiking neuron models to linear-nonlinear models. PLoS Comput Biol 7: e1001056.
    • (2011) PLoS Comput Biol , vol.7
    • Ostojic, S.1    Brunel, N.2
  • 6
    • 0034180383 scopus 로고    scopus 로고
    • The approach of a neuron population firing rate to a new equilibrium: an exact theoretical result
    • Knight BW, Omurtag A, Sirovich L, (2000) The approach of a neuron population firing rate to a new equilibrium: an exact theoretical result. Neural Comput 12: 1045-55.
    • (2000) Neural Comput , vol.12 , pp. 1045-1055
    • Knight, B.W.1    Omurtag, A.2    Sirovich, L.3
  • 7
    • 0034076273 scopus 로고    scopus 로고
    • A population density approach that facilitates large-scale modeling of neural networks: analysis and an application to orientation tuning
    • Nykamp DQ, Tranchina D, (2000) A population density approach that facilitates large-scale modeling of neural networks: analysis and an application to orientation tuning. J Comput Neurosci 8: 19-50.
    • (2000) J Comput Neurosci , vol.8 , pp. 19-50
    • Nykamp, D.Q.1    Tranchina, D.2
  • 8
    • 33845394008 scopus 로고    scopus 로고
    • Population density methods for stochastic neurons with realistic synaptic kinetics: Firing rate dynamics and fast computational methods
    • Apfaltrer F, Ly C, Tranchina D, (2006) Population density methods for stochastic neurons with realistic synaptic kinetics: Firing rate dynamics and fast computational methods. Network 17: 373-418.
    • (2006) Network , vol.17 , pp. 373-418
    • Apfaltrer, F.1    Ly, C.2    Tranchina, D.3
  • 9
    • 0035289566 scopus 로고    scopus 로고
    • A population density approach that facilitates large-scale modeling of neural networks: extension to slow inhibitory synapses
    • Nykamp DQ, Tranchina D, (2001) A population density approach that facilitates large-scale modeling of neural networks: extension to slow inhibitory synapses. Neural Comput 13: 511-546.
    • (2001) Neural Comput , vol.13 , pp. 511-546
    • Nykamp, D.Q.1    Tranchina, D.2
  • 10
    • 6644226801 scopus 로고    scopus 로고
    • Effects of synaptic noise and filtering on the frequency response of spiking neurons
    • Brunel N, Chance F, Fourcaud N, Abbott LF, (2001) Effects of synaptic noise and filtering on the frequency response of spiking neurons. Phys Rev Lett 86: 2186-2189.
    • (2001) Phys Rev Lett , vol.86 , pp. 2186-2189
    • Brunel, N.1    Chance, F.2    Fourcaud, N.3    Abbott, L.F.4
  • 11
    • 34548099438 scopus 로고    scopus 로고
    • Firing-rate response of linear and nonlinear integrate-and-fire neurons to modulated current-based and conductance-based synaptic drive
    • Richardson MJE, (2007) Firing-rate response of linear and nonlinear integrate-and-fire neurons to modulated current-based and conductance-based synaptic drive. Phys Rev E Stat Nonlin Soft Matter Phys 76: 021919.
    • (2007) Phys Rev E Stat Nonlin Soft Matter Phys , vol.76 , pp. 021919
    • Richardson, M.J.E.1
  • 14
    • 59649129373 scopus 로고    scopus 로고
    • Are the input parameters of white noise driven integrate and fire neurons uniquely determined by rate and CV?
    • Vilela RD, Lindner B, (2009) Are the input parameters of white noise driven integrate and fire neurons uniquely determined by rate and CV? J Theor Biol 257: 90-99.
    • (2009) J Theor Biol , vol.257 , pp. 90-99
    • Vilela, R.D.1    Lindner, B.2
  • 15
    • 0347694858 scopus 로고    scopus 로고
    • How spike generation mechanisms determine the neuronal response to uctuating inputs
    • Fourcaud-Trocmé N, Hansel D, van Vreeswijk C, Brunel N, (2003) How spike generation mechanisms determine the neuronal response to uctuating inputs. J Neurosci 23: 11628-40.
    • (2003) J Neurosci , vol.23 , pp. 11628-11640
    • Fourcaud-Trocmé, N.1    Hansel, D.2    van Vreeswijk, C.3    Brunel, N.4
  • 16
    • 33646397012 scopus 로고    scopus 로고
    • How noise affects the synchronization properties of recurrent networks of inhibitory neurons
    • Brunel N, Hansel D, (2006) How noise affects the synchronization properties of recurrent networks of inhibitory neurons. Neural Comput 18: 1066-110.
    • (2006) Neural Comput , vol.18 , pp. 1066-1110
    • Brunel, N.1    Hansel, D.2
  • 17
    • 0030953157 scopus 로고    scopus 로고
    • Paradoxical effects of external modulation of inhibitory interneurons
    • Tsodyks MV, Skaggs WE, Sejnowski TJ, McNaughton BL, (1997) Paradoxical effects of external modulation of inhibitory interneurons. J Neurosci 17: 4382-8.
    • (1997) J Neurosci , vol.17 , pp. 4382-4388
    • Tsodyks, M.V.1    Skaggs, W.E.2    Sejnowski, T.J.3    McNaughton, B.L.4
  • 18
    • 0037213793 scopus 로고    scopus 로고
    • Cortical damping: analysis of thalamocortical response transformations in rodent barrel cortex
    • Pinto DJ, Hartings JA, Brumberg JC, Simons DJ, (2003) Cortical damping: analysis of thalamocortical response transformations in rodent barrel cortex. Cereb Cortex 13: 33-44.
    • (2003) Cereb Cortex , vol.13 , pp. 33-44
    • Pinto, D.J.1    Hartings, J.A.2    Brumberg, J.C.3    Simons, D.J.4
  • 19
    • 60449095959 scopus 로고    scopus 로고
    • Inhibitory stabilization of the cortical network underlies visual surround suppression
    • Ozeki H, Finn IM, Schaffer ES, Miller KD, Ferster D, (2009) Inhibitory stabilization of the cortical network underlies visual surround suppression. Neuron 62: 578-592.
    • (2009) Neuron , vol.62 , pp. 578-592
    • Ozeki, H.1    Finn, I.M.2    Schaffer, E.S.3    Miller, K.D.4    Ferster, D.5
  • 20
    • 0033210816 scopus 로고    scopus 로고
    • Fast global oscillations in networks of integrate-and-fire neurons with low firing rates
    • Brunel N, Hakim V, (1999) Fast global oscillations in networks of integrate-and-fire neurons with low firing rates. Neural Comput 11: 1621-71.
    • (1999) Neural Comput , vol.11 , pp. 1621-1671
    • Brunel, N.1    Hakim, V.2
  • 21
    • 0029835892 scopus 로고    scopus 로고
    • Chaos in neuronal networks with balanced excitatory and inhibitory activity
    • van Vreeswijk C, Sompolinsky H, (1996) Chaos in neuronal networks with balanced excitatory and inhibitory activity. Science 274: 1724-6.
    • (1996) Science , vol.274 , pp. 1724-1726
    • van Vreeswijk, C.1    Sompolinsky, H.2
  • 22
    • 0034006515 scopus 로고    scopus 로고
    • Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons
    • Brunel N, (2000) Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons. J Comput Neurosci 8: 183-208.
    • (2000) J Comput Neurosci , vol.8 , pp. 183-208
    • Brunel, N.1
  • 24
    • 0021279321 scopus 로고
    • On approximations of stein's neuronal model
    • Lánský P, (1984) On approximations of stein's neuronal model. J Theor Biol 107: 631-47.
    • (1984) J Theor Biol , vol.107 , pp. 631-647
    • Lánský, P.1
  • 25
    • 0038162289 scopus 로고    scopus 로고
    • What determines the frequency of fast network oscillations with irregular neural discharges? i. synaptic dynamics and excitation-inhibition balance
    • Brunel N, Wang XJ, (2003) What determines the frequency of fast network oscillations with irregular neural discharges? i. synaptic dynamics and excitation-inhibition balance. Journal of Neurophysiology 90: 415-430.
    • (2003) Journal of Neurophysiology , vol.90 , pp. 415-430
    • Brunel, N.1    Wang, X.J.2
  • 26
    • 69049105412 scopus 로고    scopus 로고
    • How connectivity, background activity, and synaptic properties shape the cross-correlation between spike trains
    • Ostojic S, Brunel N, Hakim V, (2009) How connectivity, background activity, and synaptic properties shape the cross-correlation between spike trains. J Neurosci 29: 10234-53.
    • (2009) J Neurosci , vol.29 , pp. 10234-10253
    • Ostojic, S.1    Brunel, N.2    Hakim, V.3
  • 28
    • 0035212197 scopus 로고    scopus 로고
    • Variability and information in a neural code of the cat lateral geniculate nucleus
    • Liu RC, Tzonev S, Rebrik S, Miller KD, (2001) Variability and information in a neural code of the cat lateral geniculate nucleus. J Neurophysiol 86: 2789-806.
    • (2001) J Neurophysiol , vol.86 , pp. 2789-2806
    • Liu, R.C.1    Tzonev, S.2    Rebrik, S.3    Miller, K.D.4
  • 29
    • 28044458279 scopus 로고    scopus 로고
    • Prediction and decoding of retinal ganglion cell responses with a probabilistic spiking model
    • Pillow JW, Paninski L, Uzzell VJ, Simoncelli EP, Chichilnisky EJ, (2005) Prediction and decoding of retinal ganglion cell responses with a probabilistic spiking model. J Neurosci 25: 11003-13.
    • (2005) J Neurosci , vol.25 , pp. 11003-11013
    • Pillow, J.W.1    Paninski, L.2    Uzzell, V.J.3    Simoncelli, E.P.4    Chichilnisky, E.J.5
  • 30
    • 33745176194 scopus 로고    scopus 로고
    • Cortex is driven by weak but synchronously active thalamocortical synapses
    • Bruno RM, Sakmann B, (2006) Cortex is driven by weak but synchronously active thalamocortical synapses. Science 312: 1622-7.
    • (2006) Science , vol.312 , pp. 1622-1627
    • Bruno, R.M.1    Sakmann, B.2
  • 31
    • 0034100736 scopus 로고    scopus 로고
    • Circuit dynamics and coding strategies in rodent somatosensory cortex
    • Pinto DJ, Brumberg JC, Simons DJ, (2000) Circuit dynamics and coding strategies in rodent somatosensory cortex. J Neurophysiol 83: 1158-66.
    • (2000) J Neurophysiol , vol.83 , pp. 1158-1166
    • Pinto, D.J.1    Brumberg, J.C.2    Simons, D.J.3
  • 32
    • 77954231844 scopus 로고    scopus 로고
    • Sensitivity to perturbations in vivo implies high noise and suggests rate coding in cortex
    • London M, Roth A, Beeren L, Häusser M, Latham PE, (2010) Sensitivity to perturbations in vivo implies high noise and suggests rate coding in cortex. Nature 466: 123-127.
    • (2010) Nature , vol.466 , pp. 123-127
    • London, M.1    Roth, A.2    Beeren, L.3    Häusser, M.4    Latham, P.E.5
  • 33
    • 78049285293 scopus 로고    scopus 로고
    • Cortical preparatory activity: Representation of movement or first cog in a dynamical machine?
    • Churchland M, Cunningham J, Kaufman M, Ryu S, Shenoy K, (2010) Cortical preparatory activity: Representation of movement or first cog in a dynamical machine? Neuron 68: 387-400.
    • (2010) Neuron , vol.68 , pp. 387-400
    • Churchland, M.1    Cunningham, J.2    Kaufman, M.3    Ryu, S.4    Shenoy, K.5
  • 34
    • 79959931689 scopus 로고    scopus 로고
    • Inter-spike interval distributions of spiking neurons driven by fluctuating inputs
    • Ostojic S, (2011) Inter-spike interval distributions of spiking neurons driven by fluctuating inputs. J Neurophysiol 106: 361-373.
    • (2011) J Neurophysiol , vol.106 , pp. 361-373
    • Ostojic, S.1
  • 35
    • 0022693272 scopus 로고
    • Parabolic bursting in an excitable system coupled with a slow oscillation
    • Ermentrout GB, Kopell N, (1986) Parabolic bursting in an excitable system coupled with a slow oscillation. Siam J Appl Math 46: 233-253.
    • (1986) Siam J Appl Math , vol.46 , pp. 233-253
    • Ermentrout, G.B.1    Kopell, N.2
  • 36
    • 48249155020 scopus 로고    scopus 로고
    • Stochastic synchrony of chaos in a pulse-coupled neural network with both chemical and electrical synapses among inhibitory neurons
    • Kanamaru T, Aihara K, (2008) Stochastic synchrony of chaos in a pulse-coupled neural network with both chemical and electrical synapses among inhibitory neurons. Neural Comput 20: 1951-72.
    • (2008) Neural Comput , vol.20 , pp. 1951-1972
    • Kanamaru, T.1    Aihara, K.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.