An efficient algorithm for continuous time cross correlogram of spike trains

We propose an efficient algorithm to compute the smoothed correlogram for the detection of temporal relationship between two spike trains. Unlike the conventional histogram-based correlogram estimations, the proposed algorithm operates on continuous time and does not bin either the spike train nor the correlogram. Hence it can be more precise in detecting the effective delay between two recording sites. Moreover, it can take advantage of the higher temporal resolution of the spike times provided by the current recording methods. The Laplacian kernel for smoothing enables efficient computation of the algorithm. We also provide the basic statistics of the estimator and a guideline for choosing the kernel size. This new technique is demonstrated by estimating the effective delays in a neuronal network from synthetic data and recordings of dissociated cortical tissue.

[1]  R. Kass,et al.  Multiple neural spike train data analysis: state-of-the-art and future challenges , 2004, Nature Neuroscience.

[2]  Pieter R. Roelfsema,et al.  How Precise is Neuronal Synchronization? , 1995, Neural Computation.

[3]  Kohyu Fukunishi,et al.  Dendrite classification in rat hippocampal neurons according to signal propagation properties Observation by multichannel optical recording in cultured neuronal networks , 1998, Experimental Brain Research.

[4]  Richard H. R. Hahnloser.  Cross-intensity functions and the estimate of spike-time jitter , 2007, Biological Cybernetics.

[5]  M K Habib,et al.  Dynamics of neuronal firing correlation: modulation of "effective connectivity". , 1989, Journal of neurophysiology.

[6]  Wulfram Gerstner,et al.  Coding properties of spiking neurons: reverse and cross-correlations , 2001, Neural Networks.

[7]  J. Marron,et al.  Equivalence of Smoothing Parameter Selectors in Density and Intensity Estimation , 1988 .

[8]  G. P. Moore,et al.  Neuronal spike trains and stochastic point processes. I. The single spike train. , 1967, Biophysical journal.

[9]  T. Sejnowski,et al.  Reliability of spike timing in neocortical neurons. , 1995, Science.

[10]  G. P. Moore,et al.  Neuronal spike trains and stochastic point processes. II. Simultaneous spike trains. , 1967, Biophysical journal.

[11]  Pieter R. Roelfsema,et al.  How precise is neural synchronization , 1995 .

[12]  E. Parzen.  On Estimation of a Probability Density Function and Mode , 1962 .

[13]  Thomas Hofmann,et al.  A recipe for optimizing a time-histogram , 2007 .

[14]  G. Ramakers,et al.  Conditional firing probabilities in cultured neuronal networks: a stable underlying structure in widely varying spontaneous activity patterns , 2007, Journal of neural engineering.

[15]  Danko Nikolic,et al.  Non-parametric detection of temporal order across pairwise measurements of time delays , 2007, Journal of Computational Neuroscience.

[16]  Peter Dayan,et al.  Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems , 2001 .

[17]  Wofgang Maas,et al.  Networks of spiking neurons: the third generation of neural network models , 1997 .

[18]  Iman H. Brivanlou,et al.  Mechanisms of Concerted Firing among Retinal Ganglion Cells , 1998, Neuron.

[19]  W G Regehr,et al.  Timing of synaptic transmission. , 1999, Annual review of physiology.

[20]  Stefan Rotter,et al.  Single-trial estimation of neuronal firing rates: From single-neuron spike trains to population activity , 1999, Journal of Neuroscience Methods.

[21]  Bruno A. Olshausen,et al.  Book Review , 2003, Journal of Cognitive Neuroscience.

[22]  S. Thorpe,et al.  Spike times make sense , 2005, Trends in Neurosciences.

[23]  A. Aertsen,et al.  On the significance of correlations among neuronal spike trains , 2004, Biological Cybernetics.

[24]  Steve M. Potter,et al.  A new approach to neural cell culture for long-term studies , 2001, Journal of Neuroscience Methods.

[25]  R. Kass,et al.  Statistical smoothing of neuronal data. , 2003, Network.

[26]  Donald L. Snyder,et al.  Random Point Processes in Time and Space , 1991 .

[27]  Duane Q. Nykamp,et al.  Revealing Pairwise Coupling in Linear-Nonlinear Networks , 2005, SIAM J. Appl. Math..

[28]  Carlos D. Brody,et al.  Correlations Without Synchrony , 1999, Neural Computation.

[29]  R. Reid,et al.  Temporal Coding of Visual Information in the Thalamus , 2000, The Journal of Neuroscience.

[30]  C. Knox,et al.  Cross-correlation functions for a neuronal model. , 1974, Biophysical journal.