Richard A, Orio P, Tanré E. (2018). An integrate-and-fire model to generate spike trains with long-range dependence Journal of Computational Neuroscience.

See more from authors: Richard A · Orio P · Tanré E

References and models cited by this paper

Baddeley R et al. (1997). Responses of neurons in primary and inferior temporal visual cortices to natural scenes. Proceedings. Biological sciences. 264 [PubMed]

Bair W, Koch C, Newsome W, Britten K. (1994). Power spectrum analysis of bursting cells in area MT in the behaving monkey. The Journal of neuroscience : the official journal of the Society for Neuroscience. 14 [PubMed]

Bhattacharya J, Edwards J, Mamelak AN, Schuman EM. (2005). Long-range temporal correlations in the spontaneous spiking of neurons in the hippocampal-amygdala complex of humans. Neuroscience. 131 [PubMed]

Bhattacharya RN, Gupta VK, Waymire E. (1983). The Hurst effect under trends Journal of Applied Probability. 20(3)

Brunel N, Sergi S. (1998). Firing frequency of leaky intergrate-and-fire neurons with synaptic current dynamics. Journal of theoretical biology. 195 [PubMed]

Cardinali A, Nason GP. (2010). Costationarity of locally stationary time series Journal of Time Series Econometrics. 2(2)

Cardinali A, Nason GP. (2018). Practical powerful wavelet packet tests for second-order stationarity Applied and Computational Harmonic Analysis. 44(3)

Carmona P, Coutin L, Montseny G. (2000). Approximation of some Gaussian processes Statistical Inference for Stochastic Processes. 3(1-2)

Chacron MJ, Pakdaman K, Longtin A. (2003). Interspike interval correlations, memory, adaptation, and refractoriness in a leaky integrate-and-fire model with threshold fatigue. Neural computation. 15 [PubMed]

Churilla AM et al. (1996). Membrane potential fluctuations of human T-lymphocytes have fractal characteristics of fractional Brownian motion. Annals of biomedical engineering. 24 [PubMed]

Coeurjolly JF. (2000). Simulation and identification of the fractional brownian motion: a bibliographical and comparative study Journal of Statistical Software. 5(1)

Dar FH, Meakin JR, Aspden RM. (2002). Statistical methods in finite element analysis. Journal of biomechanics. 35 [PubMed]

De Oliveira RC et al. (2006). Long-term correlation in single calcium-activated potassium channel kinetics Physica A: Statistical Mechanics and its Applications. 364

Decreusefond L, Nualart D. (2008). Hitting times for Gaussian processes The Annals of Probability. 36(1)

Delorme M, Wiese KJ. (2015). Maximum of a Fractional Brownian Motion: Analytic Results from Perturbation Theory. Physical review letters. 115 [PubMed]

Destexhe A, Rudolph M, Paré D. (2003). The high-conductance state of neocortical neurons in vivo. Nature reviews. Neuroscience. 4 [PubMed]

Ding M, Rangarajan G. (2003). Processes with long-range correlations: theory and applications Lecture Notes in Physics. 621

Doukhan P. (1994). Mixing: Properties and examples.

Drew PJ, Abbott LF. (2006). Models and properties of power-law adaptation in neural systems. Journal of neurophysiology. 96 [PubMed]

Fairhall AL, Lewen GD, Bialek W, de Ruyter Van Steveninck RR. (2001). Efficiency and ambiguity in an adaptive neural code. Nature. 412 [PubMed]

Flandrin P, Abry P, Gonçalvès P. (1995). Wavelets, spectrum analysis and 1/f processes.

GERSTEIN GL, MANDELBROT B. (1964). RANDOM WALK MODELS FOR THE SPIKE ACTIVITY OF A SINGLE NEURON. Biophysical journal. 4 [PubMed]

HODGKIN AL, HUXLEY AF. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. The Journal of physiology. 117 [PubMed]

Hammond A, Sheffield S. (2013). Power law Pólya’s urn and fractional Brownian motion Probability Theory and Related Fields. 157(3-4)

Jackson BS. (2004). Including long-range dependence in integrate-and-fire models of the high interspike-interval variability of cortical neurons. Neural computation. 16 [PubMed]

Lewis CD, Gebber GL, Larsen PD, Barman SM. (2001). Long-term correlations in the spike trains of medullary sympathetic neurons. Journal of neurophysiology. 85 [PubMed]

Lindner B. (2004). Interspike interval statistics of neurons driven by colored noise. Physical review. E, Statistical, nonlinear, and soft matter physics. 69 [PubMed]

Liu SC, Chang S. (1997). Dimension estimation of discrete-time fractional Brownian motion with applications to image texture classification. IEEE transactions on image processing : a publication of the IEEE Signal Processing Society. 6 [PubMed]

Lowen SB, Cash SS, Poo M, Teich MC. (1997). Quantal neurotransmitter secretion rate exhibits fractal behavior. The Journal of neuroscience : the official journal of the Society for Neuroscience. 17 [PubMed]

Lowen SB, Ozaki T, Kaplan E, Saleh BE, Teich MC. (2001). Fractal features of dark, maintained, and driven neural discharges in the cat visual system. Methods (San Diego, Calif.). 24 [PubMed]

Lundstrom BN, Higgs MH, Spain WJ, Fairhall AL. (2008). Fractional differentiation by neocortical pyramidal neurons. Nature neuroscience. 11 [PubMed]

Mandelbrot BB. (1965). Une classe de processus stochastiques homothetiquesa soi: Application a loi climatologique de H. E. Hurst Comptes Rendus Del academie Des Sciences De Paris. 240

Mandelbrot BB. (1975). Limit theorems on the self-normalized range for weakly and strongly dependent processes Z. Wahrscheinlichkeitstheorie und Verw. Gebiete. 31

Mandelbrot BB, Wallis JR. (1968). Noah, Joseph and operational hydrology Water Resources Research. 4

Metzler R, Klafter J. (2004). The restaurant at the end of random walk: recent developments in the description of anomalous transport by fractional dynamics J Phys A: Math Gen. 37

Middleton JW, Chacron MJ, Lindner B, Longtin A. (2003). Firing statistics of a neuron model driven by long-range correlated noise. Physical review. E, Statistical, nonlinear, and soft matter physics. 68 [PubMed]

Nason . (2013). A test for second-order stationarity and approximate confidence intervals for localized autocovariances for locally stationary time series Journal of the Royal Statistical Society. Series B. Statistical Methodology. 75(5)

Peng C-K et al. (1993). Long-range anticorrelations and non-Gaussian behavior of the heartbeat. Physical review letters. 70 [PubMed]

Peng CK et al. (1992). Long-range correlations in nucleotide sequences. Nature. 356 [PubMed]

Peng CK et al. (1994). Mosaic organization of DNA nucleotides. Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics. 49 [PubMed]

Pozzorini C, Naud R, Mensi S, Gerstner W. (2013). Temporal whitening by power-law adaptation in neocortical neurons. Nature neuroscience. 16 [PubMed]

Priestley MB, Subba Rao T. (1969). A test for non-stationarity of time-series Journal of the Royal Statistical Society. Series B. Methodological. 31

Sacerdote L, Giraudo MT. (2013). Stochastic integrate and fire models: a review on mathematical methods and their applications Stochastic biomathematical models. 2058

Samorodnitsky G. (2016). Stochastic processes and long range dependence Springer Series in Operations Research and Financial Engineering.

Schwalger T, Droste F, Lindner B. (2015). Statistical structure of neural spiking under non-Poissonian or other non-white stimulation. Journal of computational neuroscience. 39 [PubMed]

Schwalger T, Fisch K, Benda J, Lindner B. (2010). How noisy adaptation of neurons shapes interspike interval histograms and correlations. PLoS computational biology. 6 [PubMed]

Schwalger T, Schimansky-Geier L. (2008). Interspike interval statistics of a leaky integrate-and-fire neuron driven by Gaussian noise with large correlation times. Physical review. E, Statistical, nonlinear, and soft matter physics. 77 [PubMed]

Segev R et al. (2002). Long term behavior of lithographically prepared in vitro neuronal networks. Physical review letters. 88 [PubMed]

Shin Y, Kwiatkowski D, Phillips PC, Schmidt P. (1992). Testing the null hypothesis of stationarity against the alternative of a unit root Journal of Econometrics. 54(1)

Siegel R, Teich M, Turcott R. (1996). Temporal correlation in cat striate-cortex neural spike trains IEEE Trans Eng Med Biol. 15

Sobie C, Babul A, de Sousa R. (2011). Neuron dynamics in the presence of 1/f noise. Physical review. E, Statistical, nonlinear, and soft matter physics. 83 [PubMed]

Sottinen T. (2001). Fractional Brownian motion, random walks and binary market models Finance and Stochastics. 5(3)

Talay D, Richard A. (2016). Hölder continuity in the Hurst parameter of functionals of Stochastic Differential Equations driven by fractional Brownian motion arXiv 1605.03475.

Taqqu MS. (1975). Weak convergence to fractional Brownian motion and to the Rosenblatt process Z. Wahrscheinlichkeitstheorie und Verw. Gebiete. 31

Taqqu MS, Willinger W, Sherman R, Wilson DV. (1997). Self-similarity through high-variability: Statistical analysis of ethernet LAN traffic at the source level IEEE ACM Trans Networking. 5

Taqqu MS, Willinger W, Teverovsky V. (1995). Estimators for long-range dependence: an empirical study Fractals. 03(04)

Teich MC. (1992). Fractal neuronal firing patterns Single neuron computation.

Teich MC, Heneghan C, Lowen SB, Ozaki T, Kaplan E. (1997). Fractal character of the neural spike train in the visual system of the cat. Journal of the Optical Society of America. A, Optics, image science, and vision. 14 [PubMed]

Teka W, Marinov TM, Santamaria F. (2014). Neuronal spike timing adaptation described with a fractional leaky integrate-and-fire model. PLoS computational biology. 10 [PubMed]

Weron R. (2002). Estimating long-range dependence: finite sample properties and confidence intervals Physica A. Statistical Mechanics and its Applications. 312(1-2)

Zilany MS, Bruce IC, Nelson PC, Carney LH. (2009). A phenomenological model of the synapse between the inner hair cell and auditory nerve: long-term adaptation with power-law dynamics. The Journal of the Acoustical Society of America. 126 [PubMed]

References and models that cite this paper
This website requires cookies and limited processing of your personal data in order to function. By continuing to browse or otherwise use this site, you are agreeing to this use. See our Privacy policy and how to cite and terms of use.