References and models cited by this paper

References and models that cite this paper

Abramowitz M, Stegun IA (1972) Stegun Handbook of Mathematical Functions

Badel L, Lefort S, Brette R, Petersen CC, Gerstner W, Richardson MJ (2008) Dynamic I-V curves are reliable predictors of naturalistic pyramidal-neuron voltage traces. J Neurophysiol 99:656-66 [Journal] [PubMed]

Bena I (2006) Dichotomous Markov noise: exact results for out-of-equilibrium systems International Journal of Modern Physics 20(20):2825-2888

Boucsein C, Tetzlaff T, Meier R, Aertsen A, Naundorf B (2009) Dynamical response properties of neocortical neuron ensembles: multiplicative versus additive noise. J Neurosci 29:1006-10 [Journal] [PubMed]

Brunel N (2000) Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons. J Comput Neurosci 8:183-208 [PubMed]

Brunel N, Chance FS, Fourcaud N, Abbott LF (2001) Effects of synaptic noise and filtering on the frequency response of spiking neurons. Phys Rev Lett 86:2186-9 [Journal] [PubMed]

Brunel N, Latham PE (2003) Firing rate of the noisy quadratic integrate-and-fire neuron. Neural Comput 15:2281-306 [Journal] [PubMed]

Brunel N, Sergi S (1998) Firing frequency of leaky intergrate-and-fire neurons with synaptic current dynamics. J Theor Biol 195:87-95 [Journal] [PubMed]

de la Rocha J, Doiron B, Shea-Brown E, Josic K, Reyes A (2007) Correlation between neural spike trains increases with firing rate. Nature 448:802-6 [Journal] [PubMed]

Doose J, Doron G, Brecht M, Lindner B (2016) Noisy Juxtacellular Stimulation In Vivo Leads to Reliable Spiking and Reveals High-Frequency Coding in Single Neurons. J Neurosci 36:11120-11132 [Journal] [PubMed]

Droste F (2015) Signal transmission in stochastic neuron models with non-white or non-Gaussian noise Humboldt-Universitat zu Berlin: PhD thesis

Droste F, Lindner B (2014) Integrate-and-fire neurons driven by asymmetric dichotomous noise. Biol Cybern 108:825-43 [Journal] [PubMed]

Droste F,Lindner B (2017) Exact results for power spectrum and susceptibility of a leaky integrate-and-fire neuron with two-state noise Physical Review E 95:012-411

Felch AC, Granger RH (2008) The hypergeometric connectivity hypothesis: divergent performance of brain circuits with different synaptic connectivity distributions. Brain Res 1202:3-13 [Journal] [PubMed]

Fourcaud N, Brunel N (2002) Dynamics of the firing probability of noisy integrate-and-fire neurons. Neural Comput 14:2057-110 [Journal] [PubMed]

Fourcaud-Trocmé N, Hansel D, van Vreeswijk C, Brunel N (2003) How spike generation mechanisms determine the neuronal response to fluctuating inputs. J Neurosci 23:11628-40 [PubMed]

Gardiner C (1985) Handbook of Stochastic Methods

GERSTEIN GL, MANDELBROT B (1964) RANDOM WALK MODELS FOR THE SPIKE ACTIVITY OF A SINGLE NEURON. Biophys J 4:41-68 [PubMed]

Helias M, Deger M, Diesmann M, Rotter S (2010) Equilibrium and Response Properties of the Integrate-and-Fire Neuron in Discrete Time. Front Comput Neurosci 3:29 [Journal] [PubMed]

Helias M, Deger M, Rotter S, Diesmann M (2010) Instantaneous non-linear processing by pulse-coupled threshold units. PLoS Comput Biol [Journal] [PubMed]

Helias M, Deger M, Rotter S, Diesmann M (2011) Finite post synaptic potentials cause a fast neuronal response. Front Neurosci 5:19 [Journal] [PubMed]

Ikegaya Y, Sasaki T, Ishikawa D, Honma N, Tao K, Takahashi N, Minamisawa G, Ujita S, Matsuki N (2013) Interpyramid spike transmission stabilizes the sparseness of recurrent network activity. Cereb Cortex 23:293-304 [Journal] [PubMed]

Ilin V, Malyshev A, Wolf F, Volgushev M (2013) Fast computations in cortical ensembles require rapid initiation of action potentials. J Neurosci 33:2281-92 [Journal] [PubMed]

Jacobsen M,Jensen AT (2007) Exit times for a class of piecewise exponential Markov processes with two-sided jumps Stochastic Processes and their Applications 117(9):1330-1356

Lefort S, Tomm C, Floyd Sarria JC, Petersen CC (2009) The excitatory neuronal network of the C2 barrel column in mouse primary somatosensory cortex. Neuron 61:301-16 [Journal] [PubMed]

Lindner B, Longtin A, Bulsara A (2003) Analytic expressions for rate and CV of a type I neuron driven by white gaussian noise. Neural Comput 15:1760-87 [Journal] [PubMed]

Lindner B, Schimansky-Geier L (2001) Transmission of noise coded versus additive signals through a neuronal ensemble. Phys Rev Lett 86:2934-7 [Journal] [PubMed]

Lindner B, Schimansky-Geier L, Longtin A (2002) Maximizing spike train coherence or incoherence in the leaky integrate-and-fire model. Phys Rev E Stat Nonlin Soft Matter Phys 66:031916 [Journal] [PubMed]

Loebel A, Silberberg G, Helbig D, Markram H, Tsodyks M, Richardson MJ (2009) Multiquantal release underlies the distribution of synaptic efficacies in the neocortex. Front Comput Neurosci 3:27 [Journal] [PubMed]

Ly C, Tranchina D (2007) Critical analysis of dimension reduction by a moment closure method in a population density approach to neural network modeling. Neural Comput 19:2032-92 [Journal] [PubMed]

Mankin R, Ainsaar A, Reiter E (1999) Trichotomous noise-induced transitions. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 60:1374-80 [PubMed]

Markram H, Lübke J, Frotscher M, Roth A, Sakmann B (1997) Physiology and anatomy of synaptic connections between thick tufted pyramidal neurones in the developing rat neocortex. J Physiol 500 ( Pt 2):409-40 [PubMed]

Masoliver J (1987) First-passage times for non-Markovian processes: Shot noise. Phys Rev A Gen Phys 35:3918-3928 [PubMed]

Moreno R, de la Rocha J, Renart A, Parga N (2002) Response of spiking neurons to correlated inputs. Phys Rev Lett 89:288101 [Journal] [PubMed]

Moreno-Bote R, Renart A, Parga N (2008) Theory of input spike auto- and cross-correlations and their effect on the response of spiking neurons. Neural Comput 20:1651-705 [Journal] [PubMed]

Novikov A,Melchers R,Shinjikashvili E,Kordzakhia N (2005) First passage time of filtered Poisson process with exponential shape function Probabilistic Engineering Mechanics 20(1):57-65

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 [PubMed]

Ostojic S, Szapiro G, Schwartz E, Barbour B, Brunel N, Hakim V (2015) Neuronal morphology generates high-frequency firing resonance. J Neurosci 35:7056-68 [Journal] [PubMed]

Ricciardi LM, Sacerdote L (1979) The Ornstein-Uhlenbeck process as a model for neuronal activity. I. Mean and variance of the firing time. Biol Cybern 35:1-9 [PubMed]

Richardson MJ (2004) Effects of synaptic conductance on the voltage distribution and firing rate of spiking neurons. Phys Rev E Stat Nonlin Soft Matter Phys 69:051918 [Journal] [PubMed]

Richardson MJ, Gerstner W (2005) Synaptic shot noise and conductance fluctuations affect the membrane voltage with equal significance. Neural Comput 17:923-47 [Journal] [PubMed]

Richardson MJ, Gerstner W (2006) Statistics of subthreshold neuronal voltage fluctuations due to conductance-based synaptic shot noise. Chaos 16:026106 [Journal] [PubMed]

Richardson MJ, Swarbrick R (2010) Firing-rate response of a neuron receiving excitatory and inhibitory synaptic shot noise. Phys Rev Lett 105:178102 [Journal] [PubMed]

Rosenbaum R, Josic K (2011) Mechanisms that modulate the transfer of spiking correlations. Neural Comput 23:1261-305 [Journal] [PubMed]

Schwalger T, Droste F, Lindner B (2015) Statistical structure of neural spiking under non-Poissonian or other non-white stimulation. J Comput Neurosci 39:29-51 [Journal] [PubMed]

Siegert AJF (1951) On the first passage time probability problem Phys Rev 81:617-623

Sirovich L (2003) Dynamics of neuronal populations: eigenfunction theory; some solvable cases. Network 14:249-72 [PubMed]

Sirovich L, Knight BW, Omurtag A (2000) Dynamics of neuronal populations: The equilibrium solution. Siam J Applied Math 60:2009-2028

Song S, Sjöström PJ, Reigl M, Nelson S, Chklovskii DB (2005) Highly nonrandom features of synaptic connectivity in local cortical circuits. PLoS Biol 3:e68 [Journal] [PubMed]

STEIN RB (1965) A THEORETICAL ANALYSIS OF NEURONAL VARIABILITY. Biophys J 5:173-94 [PubMed]

Stein RB, French AS, Holden AV (1972) The frequency response, coherence, and information capacity of two neuronal models. Biophys J 12:295-322 [Journal] [PubMed]

Tchumatchenko T, Malyshev A, Wolf F, Volgushev M (2011) Ultrafast population encoding by cortical neurons. J Neurosci 31:12171-9 [Journal] [PubMed]

Thomson AM, Deuchars J, West DC (1993) Large, deep layer pyramid-pyramid single axon EPSPs in slices of rat motor cortex display paired pulse and frequency-dependent depression, mediated presynaptically and self-facilitation, mediated postsynaptically. J Neurophysiol 70:2354-69 [Journal] [PubMed]

Tsurui A,Osaki S (1976) On a first-passage problem for a cumulative process with exponential decay Stochastic Processes and their Applications 4(1):79-88

Tuckwell HC (1988) Introduction to Theoretical Neurobiology. Volume 2: Nonlinear and Stochastic Theories

Van den Broeck C (1983) On the relation between white shot noise, Gaussian white noise, and the dichotomic Markov process Journal of Statistical Physics 31(3):467-483

Vilela RD, Lindner B (2009) Comparative study of different integrate-and-fire neurons: spontaneous activity, dynamical response, and stimulus-induced correlation. Phys Rev E Stat Nonlin Soft Matter Phys 80:031909 [Journal] [PubMed]

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 257:90-9 [Journal] [PubMed]

Wolff L, Lindner B (2008) Method to calculate the moments of the membrane voltage in a model neuron driven by multiplicative filtered shot noise. Phys Rev E Stat Nonlin Soft Matter Phys 77:041913 [Journal] [PubMed]

Wolff L, Lindner B (2010) Mean, variance, and autocorrelation of subthreshold potential fluctuations driven by filtered conductance shot noise. Neural Comput 22:94-120 [Journal] [PubMed]

Wright JJ, Kydd RR, Lees GJ (1987) Gross electrocortical activity as a linear wave phenomenon with variable temporal damping, regulated by ascending catecholamine neurones. Int J Neurosci 33:1-13 [PubMed]