Synchronization and redundancy: Implications for robustness of neural learning and decision making

Neural Computation

Volumn 23, Issue 11, 2011, Pages 2915-2941

  Bouvrie, Jake ^a   Slotine, Jean Jacques ^b  

^a DUKE UNIVERSITY   (United States)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHM; ANIMAL; BIOLOGICAL MODEL; BRAIN; COMPUTER SIMULATION; DECISION MAKING; HUMAN; LEARNING; LETTER; NONLINEAR SYSTEM; PHYSIOLOGY;

ALGORITHMS; ANIMALS; BRAIN; COMPUTER SIMULATION; DECISION MAKING; HUMANS; LEARNING; MODELS, NEUROLOGICAL; NONLINEAR DYNAMICS;

EID: 80053987470     PISSN: 08997667     EISSN: 1530888X     Source Type: Journal    
DOI: 10.1162/NECO_a_00183     Document Type: Letter

References (55)

1. Adams, P. (1998). Hebb and Darwin. Journal of Theoretical Biology, 195(4), 419-438.
2. Bennett, M., & Zukin, R. (2004). Electrical coupling and neuronal synchronization in the mammalian brain. Neuron, 41(4), 495-511.
3. Bollobas, B. (2001). Random graphs (2nd ed.).Cambridge: Cambridge University Press.
4. Cao, M., Stewart, A., & Leonard, N. (2010). Convergence in human decision-making dynamics. Systems and Control Letters, 59, 87-97.
5. Chechik, G., Anderson, M., Bar-Yosef, O., Young, E., Tishby, N., & Nelken, I. (2006). Reduction of information redundancy in the ascending auditory pathway. Neuron, 51(3), 278-280.
6. Clay, J. R., & DeHaan, R. L. (1979). Fluctuations in interbeat interval in rhythmic heart-cell clusters: Role of membrane voltage noise. Biophysical Journal, 28(3), 377-389.
7. Croner, L. J., Purpura, K., & Kaplan, E. (1993). Response variability in retinal ganglion cells of primates. Proceedings of the National Academy of Sciences of the United States of America, 90(17), 8128-8130.
8. Doukhan, P. (1994). Mixing: Properties and examples. Berlin: Springer-Verlag.
9. Eliasmith, C., & Anderson, C. (2004). Neural engineering: Computation, representation, and dynamics in neurobiological systems. Cambridge, MA: MIT Press.
10. Enright, J. (1980). Temporal precision in circadian systems: A reliable neuronal clock from unreliable components? Science, 209(4464), 1542-1545.
11. Faisal, A., Selen, L., & Wolpert, D. (2008). Noise in the nervous system. Nat. Rev. Neu-rosci., 9,292-303.
12. Fernando, C., Goldstein, R., & Szathmary, E. (2010). The neuronal replicator hypothesis. Neural Computation, 22(11), 2809-2857.
13. Friedrich, R. W., Habermann, C. J., & Laurent, G. (2004). Multiplexing using synchrony in the zebrafish olfactory bulb. Nature Neurosci., 7, 862-871.
14. Fukuda, T., Kosaka, T., Singer, W., & Galuske, R. (2006). Gap junctions among dendrites of cortical Gabaergic neurons establish a dense and widespread inter-columnar network. J. Neurosci., 26(13), 3434-3443.
15. Georgopoulos, A., Kalaska, J., Caminiti, R., & Massey, J. (1982). On the relations between the direction of two-dimensional arm movements and cell discharge in primate motor cortex. J. Neurosci., 2(11), 1527-1537.
16. Gigante, G., Mattia, M., Braun, J., & Del Giudice, P. (2009). Bistable perception modeled as competing stochastic integrations at two levels. PLoS Comput Biol., 5(7), e1000430.
17. Grammont, F., & Riehle, A. (1999). Precise spike synchronization in monkey motor cortex involved in preparation for movement. Exp. Brain. Res., 128,118-122.
18. Grandhe, S., Abbas, J., & Jung, R. (1999). Brain-spinal cord interactions stabilize the locomotor rhythm to an external perturbation. Biomed. Sci. Instrum., 35,175-180.
19. Hahnloser, R., Douglas, R. J., Mahovald, M., & Hepp, K. (1999). Feedback interactions between neuronal pointers and maps for attentional processing. Nat. Neurosci., 2, 746-752.
20. Hertz, J., Krogh, A. S., & Palmer, R. (1991). Introduction to the theory of neural computation. Reading, MA: Addison-Wesley.
21. Hung, C., Kreiman, G., Poggio, T., & DiCarlo, J. (2005). Fast readout of object identity from macaque inferior temporal cortex. Science, 310(5749), 863-866.
22. Itti, L., & Koch, C. (2001). Computational modelling of visual attention. Nat. Rev. Neu-rosci., 2(3), 194-203.
23. Jadbabaie, A., Lin, J., & Morse, A. S. (2003). Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Transactions on Automatic Control, 48(6), 988-1001.
24. Kandel, E., Schwartz, J., & Jessell, T. (2000). Principles of neural science (4th ed.). New York: McGraw-Hill.
25. Kiani, R., & Shadlen, M. N. (2009). Representation of confidence associated with a decision by neurons in the parietal cortex. Science, 324(5928), 759-764.
26. Kiemel, T., Gormley, K. M., Guan, L., Williams, T. L., & Cohen, A. H. (2003). Estimating the strength and direction of functional coupling in the lamprey spinal cord. J. Comput. Neurosci., 15(2), 233-245.
27. Kopell, N. (2000). We got rhythm: Dynamical systems of the nervous system. Notices of the AMS, 47 6-16.
28. Kopell, N., & Ermentrout, G. (1986). Symmetry and phase-locking in chains of weakly coupled oscillators. Communications on Pure and Applied Mathematics, 39, 623-660.
29. LeDoux, J. (2000). Emotion circuits in the brain. Annu. Rev. Neurosci., 23,155-184.
30. Lee, T., & Mumford, D. (2003). Hierarchical bayesian inference in the visual cortex. J. Opt. Soc. Am. A: Opt. Image. Sci. Vis., 20(7), 1434-1448.
31. Lohmiller, W., & Slotine, J. (1998). On contraction analysis for non-linear systems. Automatica, 34, 683-696.
32. Maren, S. (2001). Neurobiology of Pavlovian fear conditioning. Annu. Rev. Neurosci., 24, 897-931.
33. Masuda, N., Kawamura, Y., & Kori, H. (2010). Collective fluctuations in networks of noisy components. New Journal of Physics, 12(9), 093007.
34. Mumford, D. (1992). On the computational architecture of the neocortexII: The role of cortico-cortical loops. Biol. Cyb., 66,241-251.
35. Needleman, D. J., Tiesinga, P. H., & Sejnowski, T. J. (2001). Collective enhancement of precision in networks of coupled oscillators. Physica D: Nonlinear Phenomena, 155(3-4), 324-336.
36. Pham, Q.-C., & Slotine, J.-J. (2007). Stable concurrent synchronization in dynamic system networks. Neural Networks, 20(1), 62-77.
37. Pham, Q.-C., Tabareau, N., & Slotine, J.-J. (2009). A contraction theory approach to stochastic incremental stability. IEEE Transactions on Automatic Control, 54(4), 816-820.
38. Pouget, A., & Sejnowski, T. (1997). Spatial transformations in the parietal cortex using basis functions. Journal of Cognitive Neuroscience, 9(2), 222-237.
39. Poulakakis, I., Scardovi, L., & Leonard, N. (2010). Coupled stochastic differential equations and collective decision making in the two-alternative forced-choice task. In Proc. American Control Conference. Piscataway, NJ: IEEE.
40. Puchalla, J. L., Schneidman, E., Harris, R. A., & Berry, M. J. (2005). Redundancy in the population code of the retina. Neuron, 46(3), 493-504.
41. Rao, R., & Ballard, D. (1999). Predictive coding in the visual cortex: A functional interpretation of some extra-classical receptive-field effects. Nat. Neurosci., 2, 79-87.
42. Russo, G., & Slotine, J.-J. (2010). Global convergence of quorum sensing networks. Physical Review E, 28.
43. Schnitzler, A., & Gross, J. (2005). Normal and pathological oscillatory communication in the brain. Nature Reviews Neuroscience, 6,285-296.
44. Scholz, J., & Schoner, G. (1999). The uncontrolled manifold concept: Identifying control variables for a functional task. Exp. Brain Res., 126(3), 289-306.
45. Sherman, A., & Rinzel, J. (1991). Model for synchronization of pancreatic beta-cells by gap junction coupling. Biophysical Journal, 59(3), 547-559.
46. Slotine, J.-J. E., & Li, W. (1991). Applied nonlinear control. Upper Saddle River, NJ.
47. Prentice Hall. Tabareau, N., Slotine, J.-J., & Pham, Q.-C. (2010). How synchronization protects from noise. PLoS Comput Biol, 6(1), e1000637.
48. Taylor, A., Tinsley M. R., Wang, F., Huang, Z., & Showalter, K. (2009). Dynamical quorum sensing and synchronization in large populations of chemical oscillators. Science, 323(5914), 614-617.
49. Ting, L. (2007). Dimensional reduction in sensorimotor systems: A framework for understanding muscle coordination of posture. P. Cisek, T. Drew, & J. Kalaska (Eds.), Computational neuroscience: Theoretical insights into brain function (pp. 301-325).
50. Todorov, E. (2008). Recurrent neural network trained in the presence of noise give rise to mixed muscle-movement representations. http://www.cs.washington.edu/homes/todorov/papers/mixed.pdf.
51. Varier, S., & Kaiser, M. (2011). Neural development features: Spatio-temporal development of the Caenorhabditis elegans neuronal network. PLoS Computational Biology, 7(1), 1-9.
52. Wang, W., & Slotine, J. (2005). On partial contraction analysis for coupled nonlinear oscillators. Biological Cybernetics, 92(1), 38-53.
53. Yang, T., & Shadlen, M. N. (2007). Probabilistic reasoning by neurons. Nature, 447(7148), 1075-1080.
54. Yao, Y., Rosasco, L., & Caponnetto, A. (2007). On early stopping in gradient descent learning. Constructive Approximation, 26(2), 289-315.
55. Robustness of noisy consensus dynamics with directed communication