Gibbs distribution analysis of temporal correlations structure in retina ganglion cells

Journal of Physiology Paris

Volumn 106, Issue 3-4, 2012, Pages 120-127

  Vasquez, J C ^a   Marre, O ^b   Palacios, A G ^c   Berry, M J ^b   Cessac, B ^a  

^a UNIVERSITÉ DE NICE SOPHIA ANTIPOLIS   (France)

^b PRINCETON UNIVERSITY   (United States)

^c UNIVERSIDAD DE VALPARAÍSO   (Chile)

Author keywords

Gibbs distributions; Higher order correlation; Maximum entropy; Spike train analysis; Statistical physics

Indexed keywords

ANIMAL CELL; ANIMAL TISSUE; ARTICLE; CONTROLLED STUDY; GIBBS DISTRIBUTION ANALYSIS; HIDDEN MARKOV MODEL; NERVE CELL; NONHUMAN; RETINA; RETINA GANGLION CELL; SALAMANDER; SPATIOTEMPORAL SPIKE; SPIKE; STATISTICS; STIMULUS RESPONSE; VISUAL STIMULATION;

ALGORITHMS; ANIMALS; MODELS, NEUROLOGICAL; MODELS, STATISTICAL; PHOTIC STIMULATION; RETINAL GANGLION CELLS; URODELA; WAVELET ANALYSIS;

EID: 84862201186     PISSN: 09284257     EISSN: 17697115     Source Type: Journal    
DOI: 10.1016/j.jphysparis.2011.11.001     Document Type: Article

References (44)

1. Abeles M., Gerstein G.L. Detecting spatiotemporal firing patterns among simultaneously recorded single neurons. J. Neurophys. 1988, 60(3):909-924.
2. Abeles M., Vaadia E., Bergman H., Prut Y., Haalman I., Slovin H. Dynamics of neuronal interactions in the frontal cortex of behaving monkeys. Concepts Neurosci. 1993, 4:131-158.
3. Amari S.-I. Information geometry of multiple spike trains. Springer Series in Computational Neuroscience, Part 11 2010, vol. 7:221-253. Springer. 10.1007/978-1-4419-5675. S. Grün, S. Rotter (Eds.).
4. Bowen R. Equilibrium states and the ergodic theory of Anosov diffeomorphisms. Lect. Notes Math. 1975, vol. 470. Springer-Verlag, New York.
5. Brown E.N., Kass R.E., Mitra P.P. Multiple neural spike train data analysis: state-of-the-art and future challenges. Nat. Neurosci. 2004, 7(5):456-461. . 10.1038/nn1228.
6. Cessac B. A discrete time neural network model with spiking neurons II. Dynamics with noise. J. Math. Biol. 2011, 62:863-900. http://lanl.arxiv.org/abs/1002.3275. 10.1007/s00285-010-0358-4.
7. Cessac B. Statistics of spike trains in conductance-based neural networks: rigorous results. J. Comput. Neurosci. 2011, 1(8). 10.1186/2190-8567-1-8.
8. Cessac B., Palacios A. Spike train statistics from empirical facts to theory: the case of the retina. Current Mathematical Problems in Computational Biology and Biomedicine 2011, Springer.
9. Chazottes J., Keller G. Pressure and equilibrium states in ergodic theory. Mathematics of Complexity and Dynamical Systems 2011, 1422-1437. Springer. 10.1007/978-1-4614-1806-1-90.
10. Ganmor E., Segev R., Schneidman E. The architecture of functional interaction networks in the retina. J. Neurosci. 2011, 31(8):3044-3054.
11. Ganmor E., Segev R., Schneidman E. Sparse low-order interaction network underlies a highly correlated and learnable neural population code. PNAS 2011, 108(23):9679-9684.
12. Gantmacher F.R. The Theory of Matrices 1998, AMS Chelsea Publishing, Providence, RI.
13. Gao Y., Kontoyiannis I., Bienenstock E. Estimating the entropy of binary time series: methodology, some theory and a simulation study. Entropy 2008, 10(2):71-99.
14. Georgii, H.-O., 1988. Gibbs Measures and Phase Transitions. De Gruyter Studies in Mathematics, vol. 9, Berlin; New York.
15. Grassberger P. Estimating the information content of symbol sequences and efficient codes. IEEE Trans. Inform. Theory 1989, 35.
16. Grün S., Diesmann M., Aertsen A. Unitary events in multiple single-neuron spiking activity: I. Detection and significance. Neural Comput. 2002, 14(1):43-80. 10.1162/089976602753284455.
17. Jaynes E. Information theory and statistical mechanics. Phys. Rev. 1957, 106(620).
18. Kass R.E., Ventura V., Brown E.N. Statistical issues in the analysis of neuronal data. J. Neurophys. 2005, 94(1):8-25. . 10.1152/jn.00648.2004.
19. Keller G. Equilibrium States in Ergodic Theory 1998, Cambridge University Press.
20. Kravchuk, K., Vidybida, A., 2010. Delayed feedback causes non-Markovian behavior of neuronal firing statistics. J. Phys. A., submitted for publication, arXiv:. arxiv:1012.6019.
21. Lindsey B., Morris K., Shannon R., Gerstein G. Repeated patterns of distributed synchrony in neuronal assemblies. J. Neurophys. 1997, 78:1714-1719.
22. Marre O., Boustani S.E., Frégnac Y., Destexhe A. Prediction of spatiotemporal patterns of neural activity from pairwise correlations. Phys. Rev. Lett. 2009, 102(13):4. 10.1103/PhysRevLett.102.138101.
23. Meyer D. The Ruelle-Araki Transfer Operator in Classical Statistical Mechanics 1980, vol. 123. Springer-Verlag.
24. Nagaev A.V. An asymptotic formula for the Neyman-Pearson risk in discriminating between two Markov chains. J. Math. Sci. 2002, 111(3):3582-3591. ISSN 1072-3374/1573-8795. 10.1023/A:1016151602853.
25. Ohiorhenuan I.E., Mechler F., Purpura K.P., Schmid A.M., Hu Q., Victor J.D. Sparse coding and high-order correlations in fine-scale cortical networks. Nature 2010, 466(7):617-621.
26. Pouzat, C., Chaffiol, A., 2009. On Goodness of Fit Tests For Models of Neuronal Spike Trains Considered as Counting Processes. http://arxiv.org/abs/0909.2785v1.
27. Roudi, Y., Hertz, J., 2010. Mean field theory for non-equilibrium network reconstruction 11 arXiv:. arxiv:1009.5946v1.
28. Roudi, Y., Hertz, J., 2011. Mean field theory for non-equilibrium network reconstruction. Phys. Rev. Lett. 106 (048702), arXiv:. arxiv:1009.5946v1.
29. Ruelle D. Statistical Mechanics: Rigorous Results 1969, Benjamin, New York.
30. Ruelle D. Thermodynamic Formalism 1978, Addison-Wesley, Reading, Massachusetts.
31. Schaub, M.T., Schultz, S.R., 2010. The Ising decoder: reading out the activity of large neural ensembles, arXiv:. arxiv:1009.1828.
32. Schneidman E., Berry M., Segev R., Bialek W. Weak pairwise correlations imply string correlated network states in a neural population. Nature 2006, 440:1007-1012.
33. Schürmann T., Grassberger P. Entropy estimation of symbol sequences. Chaos 1996, 6(3):414-427.
34. Segev R., Baruchi I., Hulata E., Ben-Jacob E. Hidden neuronal correlations in cultured networks. Phys. Rev. Lett. 2004, 92:118102.
35. Segev R., Goodhouse J., Puchalla J., Berry M.J. Recording spikes from a large fraction of the ganglion cells in a retinal patch. Nat. Neurosci. 2004, 7:1155-1162.
36. Seneta E. Non-negative Matrices and Markov Chains 2006, Springer.
37. Shlens J., Field G.D., Gauthier J.L., Grivich M.I., Petrusca D., Sher A., Litke A.M., Chichilnisky E.J. The structure of multi-neuron firing patterns in primate retina. J. Neurosci. 2006, 26(32):8254-8266.
38. Stevenson I.H., Kording K.P. How advances in neural recording affect data analysis. Nat. Neurosci. 2011, 14(2).
39. Strong S., Koberle R., de Ruyter van Steveninck R., Bialek W. Entropy and information in neural spike trains. Phys. Rev. Lett. 1998, 80(1):197-200.
40. Tang A., Jackson D., Hobbs J., Chen W., Smith J.L., Patel H., Prieto A., Petrusca D., Grivich M.I., Sher A., Hottowy P., Dabrowski W., Litke A.M., Beggs J.M. A maximum entropy model applied to spatial and temporal correlations from cortical networks in vitro. J. Neurosci. 2008, 28(2):505-518. 10.1523/JNEUROSCI.3359-07.2008.
41. Tkačik, G., Schneidman, E., Berry II, M.J., Bialek, W., 2009. Spin glass models for a network of real neurons 15, arXiv:. arxiv:0912.5409v1.
42. Tkačik G., Prentice J.S., Balasubramanian V., Schneidman E. Optimal population coding by noisy spiking neurons. PNAS 2010, 107(32):14419-14424.
43. Vasquez, J.-C., Viéville, T., Cessac, B., 2010. Entropy-based Parametric Estimation of Spike Train Statistics, INRIA Research Report. http://arxiv.org/abs/1003.3157.
44. Villa A.E.P., Tetko I.V., Hyland B., Najem A. Spatiotemporal activity patterns of rat cortical neurons predict responses in a conditioned task. Proc. Natl. Acad. Sci. USA 1999, 96(3):1106-1111.