Abstract.
Systems driven by Poisson-distributed quantal inputs can be described as “shot noise” stochastic processes. This formalism can apply to neurons which receive a large number of Poisson-distributed synaptic inputs of similar quantal size. However, the presence of temporal correlations between these inputs destroys their quantal nature, and such systems can no longer be described by classical shot noise processes. Here, we show that explicit expressions for various statistical properties, such as the amplitude distribution and the power spectral density, can be deduced and investigated as functions of the correlation between input channels. The monotonic behavior of these expressions allows an one-to-one relation between temporal correlations and the statistics of fluctuations. Multi-channel shot noise processes, therefore, open a way to deduce correlations in input patterns by analyzing fluctuations in experimental systems. We discuss applications such as detecting correlations in networks of neurons from intracellular recordings of single neurons.
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References
N. Campbell, Proc. Cambr. Phil. Soc. 15, 117 (1909); 310 (1909)
W. Schottky, Ann. Phys. (Leipzig) 57, 541 (1918)
S.O. Rice, Bell Syst. Tech. J. 23, 282 (1944); S.O. Rice, Bell Syst. Tech. J. 24, 46 (1945)
M.B. Johnson, Phys. Rev. 29, 367 (1927); H. Nyquist, Phys. Rev. 32, 110 (1928)
A. Papoulis, Probability, random variables, and stochastic processes (McGraw-Hill, Boston, USA, 1991)
E.N. Gilbert, H.O. Pollak, Bell Syst. Tech. J. 39, 333 (1960)
A. Papoulis, J. Appl. Prob. 8, 118 (1971)
G.M. Morris, J. Opt. Soc. Amer. A 1, 482 (1984); A.O. Hero, IEEE Trans. Inform. Theory 37, 92 (1991)
T.T. Kadota, IEEE Trans. Inform. Theory 34, 1517 (1988); C.W. Helstrom, C.-L. Ho, IEEE Trans. Commun. 40, 1327 (1992)
L. Saminadayar et al., Phys. Rev. Lett. 79, 2526 (1997); R. de-Picciotto et al., Nature 389, 162 (1997)
M.J.M. de Jong, C.W.J. Beenakker, in Mesoscopic Electron Transport, edited by L.L. Sohn et al., 225 (Kluwer Academic Publishers, Dordrecht, 1997); Ya.M. Blanter, M. Büttiker, Phys. Rep. 336, 2 (2000)
J.C. Cuevas et al., Phys. Rev. Lett. 82, 4086 (1999); R. Cron et al., Phys. Rev. Lett. 86, 4104 (2001); J.C. Cuevas, M. Fogelström, Phys. Rev. Lett. 89, 227003 (2002)
J.C. Egues et al., in Quantum Noise in Mesoscopic Physics, NATO ASI Series II, Vol. 97 (Kluwer Academic Publishers, Dordrecht, 2003)
S.B. Lowen, M.C. Teich, IEEE Trans. Inform. Theory 36, 1302 (1990)
C.W.J. Beenakker, M. Patra, Mod. Phys. Lett. B 13, 337 (1999)
C. Klüppelberg, T. Mikosch, Bernoulli 1, 125 (1995); G. Samorodnitsky, in Proc. Intern. Conf. on App. Prob. and Time Series, edited by R.P. Heyde et al., p. 322 (Springer Verlag, 1995)
F. Baccelli, B. Blaszczyszyn, Adv. Appl. Probab. 33, 293 (2001)
M.C. Teich, B.E.A. Saleh, J. Opt. Soc. Am. 71, 771 (1981); B.E.A. Saleh, M.C. Teich, Biol. Cybern. 52, 101 (1985); M.C. Teich et al., J. Opt. Soc. Am. A 14, 529 (1997); M.A. Freed, J. Neurosci. 20, 3956 (2000); N. Hohn, A.N. Burkitt, Phys. Rev. E 63, 031902 (2001)
A. Destexhe, D. Paré, J. Neurophysiol. 81, 1531 (1999); M. Rudolph, A. Destexhe, Phys. Rev. Lett. 86, 3662 (2001)
R. Gütig et al., J. Neurosci. 23, 3697 (2003)
A. Destexhe, M. Rudolph, D. Paré, Nature, Rev. Neurosci. 4, 739 (2003)
H. Markram et al., J. Physiol. 500, 409 (1997); P. Salin, D.A. Prince, J. Neurophysiol. 75, 1573 (1996); P. Stern et al., J. Physiol. 449, 247 (1992)
A. Destexhe, M. Rudolph, J. Comput. Neurosci. 17, 327 (2004)
J. DeFelipe et al., Neurocytology 31, 299 (2003)
A. Destexhe et al., Neurosci. 107, 13 (2001)
M. Rudolph, A. Destexhe, Neural Comput. 17, 2301 (2005)
M. Rudolph et al., J. Neurophysiol. 94, 2805 (2005)
J.C. Magee, E.P. Cook, Nature Neurosci. 3, 895 (2000); B.K. Andrásfalvy, J.C. Magee, J. Neurosci. 21, 9151 (2001)
M. London, I. Segev, Nature Neurosci. 4, 853 (2001)
S.R. Williams, G.J. Stuart, Science 295, 1907 (2002)
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Rudolph, M., Destexhe, A. A multichannel shot noise approach to describe synaptic background activity in neurons. Eur. Phys. J. B 52, 125–132 (2006). https://doi.org/10.1140/epjb/e2006-00261-3
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DOI: https://doi.org/10.1140/epjb/e2006-00261-3


