Journal of Computational Neuroscience

, Volume 34, Issue 1, pp 73–87

Nonlinear modeling of dynamic interactions within neuronal ensembles using Principal Dynamic Modes

  • Vasilis Z. Marmarelis
  • Dae C. Shin
  • Dong Song
  • Robert E. Hampson
  • Sam A. Deadwyler
  • Theodore W. Berger


A methodology for nonlinear modeling of multi-input multi-output (MIMO) neuronal systems is presented that utilizes the concept of Principal Dynamic Modes (PDM). The efficacy of this new methodology is demonstrated in the study of the dynamic interactions between neuronal ensembles in the Pre-Frontal Cortex (PFC) of a behaving non-human primate (NHP) performing a Delayed Match-to-Sample task. Recorded spike trains from Layer-2 and Layer-5 neurons were viewed as the “inputs” and “outputs”, respectively, of a putative MIMO system/model that quantifies the dynamic transformation of multi-unit neuronal activity between Layer-2 and Layer-5 of the PFC. Model prediction performance was evaluated by means of computed Receiver Operating Characteristic (ROC) curves. The PDM-based approach seeks to reduce the complexity of MIMO models of neuronal ensembles in order to enable the practicable modeling of large-scale neural systems incorporating hundreds or thousands of neurons, which is emerging as a preeminent issue in the study of neural function. The “scaling-up” issue has attained critical importance as multi-electrode recordings are increasingly used to probe neural systems and advance our understanding of integrated neural function. The initial results indicate that the PDM-based modeling methodology may greatly reduce the complexity of the MIMO model without significant degradation of performance. Furthermore, the PDM-based approach offers the prospect of improved biological/physiological interpretation of the obtained MIMO models.


Multi-input multi-output neuronal systems Pre-frontal cortex Dynamic modeling Nonlinear modeling Principal Dynamic Modes Volterra modeling 


  1. Abbott, L. F. (1999). Lapique’s introduction of the integrate-and-fire model neuron. Brain Research Bulletin, 50, 303–304.PubMedCrossRefGoogle Scholar
  2. Abeles, M. (1991). Corticonics: Neural Circuits of the Cerebral Cortex. Cambridge, UK: Cambridge University Press.Google Scholar
  3. Aftanas, L. I., & Golocheikine, S. A. (2001). Human anterior and frontal midline theta and lower alpha reflect emotionally positive state and internalized attention: high-resolution EEG investigation of meditation. Neuroscience Letters, 310, 57–60.PubMedCrossRefGoogle Scholar
  4. Amit, D. J. (1989). Modeling Brain Function: The World of Attractor Neural Networks. Cambridge, UK: Cambridge University Press.Google Scholar
  5. Anderson, J. A. (1996). An Introduction to Neural Networks. Cambridge, MA: MIT Press.Google Scholar
  6. Anderson, C. H., & Eliasmith C. (2004). Neural Engineering: Computation, Representation, and Dynamics in Neurobiological Systems (Computational Neuroscience). Cambridge, MA: MIT Press.Google Scholar
  7. Anderson, C., & Horne, J. A. (2003). Prefrontal cortex: links between low frequency delta EEG in sleep and neuropsychological performance in healthy, older people. Psychophysiology, 40, 349–357.PubMedCrossRefGoogle Scholar
  8. Arbib, M. A. (2003). The Handbook of brain Theory and Neural Networks. Cambridge, MA: MIT Press.Google Scholar
  9. Atencio, C. A., & Schreiner, C. E. (2008). Spectrotemporal processing differences between auditory cortical fast-spiking and regular-spiking neurons. Journal of Neuroscience, 28, 3897–3910.PubMedCrossRefGoogle Scholar
  10. Atencio, C. A., & Schreiner, C. E. (2010). Columnar connectivity and laminar processing in cat primary auditory cortex. PLoS One, 5(3), e9521.PubMedCrossRefGoogle Scholar
  11. Baker, S. N., Kilner, J. M., Pinches, E. M., & Lemon, R. N. (1999). The role of synchrony and oscillations in the motor output. Experimental Brain Research, 128, 109–117.CrossRefGoogle Scholar
  12. Barbieri, R., Quirk, M. C., Frank, L. M., Wilson, M. A., & Brown, E. N. (2001). Construction and analysis of non-Poisson stimulus response models of neural spike train activity. Journal of Neuroscience Methods, 105, 25–37.PubMedCrossRefGoogle Scholar
  13. Berger, T. W., Eriksson, J. L., Ciarolla, D. A., & Sclabassi, R. J. (1988). Nonlinear systems analysis of the hippocampal perforant path-dentate system. II. Effects of random train stimulation. Journal of Neurophysiology, 60, 1077–1094.Google Scholar
  14. Berger, T. W., & Glanzman, D. L. (2005). Toward replacement parts for the brain: Implantable biomimetic electronics as the next era in neural prosthetics. Cambridge, MA: MIT Press.Google Scholar
  15. Berger, T. W., Chauvet, G., & Sclabassi, R. J. (1994). A biological based model of functional properties of the hippocampus. Neural Networks, 7, 1031–1064.CrossRefGoogle Scholar
  16. Berger, T. W., Baudry, M., Brinton, R. D., Liaw, J. S., Marmarelis, V. Z., Park, A. Y., Sheu, B. J., & Tanguay, A. R. (2001). Brain-implantable biomimetic electronics as the next era in neural prosthetics. Proceedings of the IEEE, 89, 993–1012.Google Scholar
  17. Berger, T. W., Song, D., Chan, R. H., & Marmarelis, V. Z. (2010). The neurobiological basis of cognition: identification by multi-input, multi-output nonlinear dynamic modeling. Proceedings of the IEEE, 98, 356–374.PubMedCrossRefGoogle Scholar
  18. Berger, T. W., Hampson, R. E., Song, D., Goonawardena, A., Marmarelis, V. Z., & Deadwyler, S. A. (2011). A cortical neural prosthesis for restoring and enhancing memory. Journal of Neural Engineering, 8, 046017.PubMedCrossRefGoogle Scholar
  19. Berger, T. W., Song, D., Chan, R. H. M., Marmarelis, V. Z., Hampson, R. E., Deadwyler, S. A., LaCoss, J., Wills, J., & Granacki, J. J. (2012). A hippocampal cognitive prosthesis: Multi-Input. Multi-Output nonlinear modeling and VLSI implementation. IEEE Transactions Neural Systems and Rehabilitation Engineering, 20(2), 198–211.CrossRefGoogle Scholar
  20. Borst, A., & Theunissen, F. E. (1999). Information theory and neural coding. Nature Neuroscience, 2, 947–957.PubMedCrossRefGoogle Scholar
  21. Brandenberger, G. (2003). The ulradien rhythm of sleep: diverse relations with pituitary and adrenal hormones. Revue Neurologique, 159(11), S5–S10.Google Scholar
  22. Brockwell, A. E., Rojas, A. L., & Kass, R. E. (2004). Recursive Bayesian decoding of motor cortical signals by particle filtering. Journal of Neurophysiology, 91, 1899–1907.PubMedCrossRefGoogle Scholar
  23. Brown, E. N., Kass, R. E., & Mitra, P. P. (2004). Multiple neural spike train data analysis: state-of-the-art and future challenges. Nature Neuroscience, 7, 456–461.PubMedCrossRefGoogle Scholar
  24. Buzsaki, G. (2002). Theta oscillations in the hippocampus. Neuron, 33, 325–340.PubMedCrossRefGoogle Scholar
  25. Buzsaki, G. (2005). Theta rhythm of navigation: link between path integration and landmark navigation, episodic and semantic memory. Hippocampus, 15, 827–840.PubMedCrossRefGoogle Scholar
  26. Churchland, P. S., & Sejnowski, T. J. (1999). The Computational Brain. Cambridge, MA: MIT Press.Google Scholar
  27. Citron, M. C., & Emerson, R. C. (1983). White noise analysis of cortical directional selectivity in cat. Brain Research, 279, 271–277.PubMedCrossRefGoogle Scholar
  28. Citron, M. C., Kroeker, J. P., & McCann, G. D. (1981). Nonlinear interactions in ganglion cell receptive fields. Journal of Neurophysiology, 46, 1161–1176.PubMedGoogle Scholar
  29. Citron, M., Emerson, R. C., & Levick, W. R. (1988). Nonlinear measurement and classification of receptive fields in cat retinal ganglion cells. Annals of Biomedical Engineering, 16, 65–77.PubMedCrossRefGoogle Scholar
  30. Cottaris, N. P., & De Valois, R. L. (1998). Temporal dynamics of chromatic tuning in macaque primary visual cortex. Nature, 395, 896–900.PubMedCrossRefGoogle Scholar
  31. Courtemanche, R., Fujii, N., & Graybiel, A. M. (2003). Synchronous, focally modulated beta-band oscillations characterize Local Field Potential activity in the striatum of awake behaving monkeys. Journal of Neuroscience, 23, 11741–11752.PubMedGoogle Scholar
  32. Dan, Y., Alonso, J. M., Usrey, W. M., & Reid, R. C. (1998). Coding of visual information by precisely correlated spikes in the lateral geniculate nucleus. Nature Neuroscience, 1, 501–507.PubMedCrossRefGoogle Scholar
  33. David, S. V., & Gallant, J. L. (2005). Predicting neuronal responses during natural vision. Network, 16, 239–260.PubMedCrossRefGoogle Scholar
  34. Deadwyler, S. A., & Hampson, R. E. (1995). Ensemble activity and behavior: What's the code? Science, 270, 1316–1318.Google Scholar
  35. Deadwyler, S. A., & Hampson, R. E. (2004). Differential but complementary mnemonic functions of the hippocampus and subiculum. Neuron, 42, 465–476.PubMedCrossRefGoogle Scholar
  36. Deadwyler, S. A., & Hampson, R. E. (2006). Temporal coupling between subicular and hippocampal neurons underlies retention of trial-specific events. Behavioural Brain Research, 174, 272–280.PubMedCrossRefGoogle Scholar
  37. Dimoka, A., Courellis, S. H., Gholmieh, G., Marmarelis, V. Z., & Berger, T. W. (2008). Modeling the nonlinear properties of the in vitro hippocampal perforant path-dentate system using multi-electrode array technology. IEEE Transactions on Biomedical Engineering, 55, 693–702.PubMedCrossRefGoogle Scholar
  38. Dobson, A. J. (2002). An Introduction to Generalized Linear Models. Boca Raton, Florida: Chapman &Hall/CRC Press.Google Scholar
  39. Donoghue, J. P., Sanes, J. N., Hatsopoulos, N. G., & Gaal, G. (1998). Neural discharge and local field potential oscillations in primate motor cortex during voluntary movements. Journal of Neurophysiology, 79, 159–173.PubMedGoogle Scholar
  40. Eeckman, F. H. (1992). Neural Systems: Analysis and Modeling.Google Scholar
  41. Eggermont, J. J. (1993). Wiener and Volterra analyses applied to the auditory system. Hearing Research, 66, 177–201.PubMedCrossRefGoogle Scholar
  42. Eggermont, J. J., Aertsen, A. M. H. J., & Johannesma, P. I. M. (1983). Quantitative characterization procedure for auditory neurons based on the spectro-temporal receptive field. Hearing Research, 10, 167–190.PubMedCrossRefGoogle Scholar
  43. Ekstrom, A. D., Caplan, J., Ho, E., Shattuck, K., Fried, I., & Kahana, M. (2005). Human hippocampal theta activity during virtual navigation. Hippocampus, 15, 881–889.PubMedCrossRefGoogle Scholar
  44. Emerson, R. C., Citron, M. C., Vaughn, W. J., & Klein, S. A. (1987). Nonlinear directionally selective subunits in complex cells of cat striate cortex. Journal of Neurophysiology, 58, 33–65.PubMedGoogle Scholar
  45. Emerson, R. C., Bergen, J. R., & Adelson, E. H. (1992). Directionally selective complex cells and the computation of motion energy in cat visual cortex. Vision Research, 32, 203–218.PubMedCrossRefGoogle Scholar
  46. Fetz, E. E., Chen, D., Murthy, V. N., & Matsumura, M. (2000). Synaptic interactions mediating synchrony and oscillations in primate sensorimotor cortex. Journal of Physiology, Paris, 94, 323–331.PubMedCrossRefGoogle Scholar
  47. FitzHugh, R. (1955). Mathematical models of threshold phenomena in the nerve membrane. Bulletin of Mathematical Biophysics, 17, 257–278.CrossRefGoogle Scholar
  48. FitzHugh, R. (1969). Mathematical models of excitation and propagation in nerve. Chapter 1 (pp. 1–85 in H.P. Schwan, ed. Biological Engineering, New York, NY: McGraw-Hill.Google Scholar
  49. Fox, S. E., Wolfson, S., & Ranck, J. B. J. (1986). Hippocampal theta rhythm and the firing of neurons in walking and urethane anesthetized rats. Experimental Brain Research, 62, 495–508.CrossRefGoogle Scholar
  50. Fries, P. (2005). A mechanism for cognitive dynamics: neuronal communication through neuronal coherence. Trends in Cognitive Science, 9, 474–480.CrossRefGoogle Scholar
  51. Fries, P., Nikolic, D., & Singer, W. (2007). The gamma cycle. Trends in Neurosciences, 30, 309–316.PubMedCrossRefGoogle Scholar
  52. Gabor, S., Hangya, B., Hernadi, I., Winkler, I., Lakatos, P., & Ulbert, I. (2010). Phase entrainment of human delta oscillations can mediate the effects of expectation on reaction speed. Journal of Neuroscience, 30, 13578–13585.CrossRefGoogle Scholar
  53. Gale, J. T., Martinez-Rubio, C., Sheth, S. A., & Eskandar, E. N. (2011). Intra-operative behavioral tasks in awake humans undergoing deep brain stimulation surgery. Journal of Visualized Experiments. Google Scholar
  54. Hampson, R. E., & Deadwyler, S. A. (2003). Temporal firing characteristics and the strategic role of subicular neurons in short-term memory. Hippocampus, 13, 529–541.PubMedCrossRefGoogle Scholar
  55. Hampson, R. E., Pons, T. P., Stanford, T. R., & Deadwyler, S. A. (2004). Categorization in the monkey hippocampus: a possible mechanism for encoding information into memory. Proceedings of the National Academy of Sciences, 101, 3184–3189.CrossRefGoogle Scholar
  56. Hampson, R. E., Simeral, J. D., Berger, T. W., Song, D., Chan, R. H. M., & Deadwyler, S. A. (2011). Cognitively relevant recording in hippocampus: Beneficial feedback of ensemble codes in a closed loop paradigm. In R. P. Vertes & R. W. Stackman (Eds.), Electrophysiological Recording Techniques (pp. 215–240). New York: Humana Press.CrossRefGoogle Scholar
  57. Hampson, R. E., Song, D., Chan, R. H. M., Sweatt, A. J., Fuqua, J., Gerhardt, G. A., Shin, D., Marmarelis, V. Z., Berger, T. W., & Deadwyler, S. A. (2012). A nonlinear model for hippocampal cognitive prosthesis: memory facilitation by hippocampal ensemble stimulation. IEEE Transactions Neural Systems and Rehabilitation Engineering, 20(2), 184–197.CrossRefGoogle Scholar
  58. Hasselmo, M. E., Bodelon, C., & Wyble, B. P. (2002). A proposed function for hippocampal theta rhythm: separate phases of encoding and retrieval enhance reversal of prior learning. Neural Computation, 14, 793–817.PubMedCrossRefGoogle Scholar
  59. Hertz, J., Krogh, A., & Palmer, R.G. (1991). Introduction to the theory of neural computation. Addison-Wesley.Google Scholar
  60. Hille, B. (2001). Ionic Channels of Excitable Membranes (3rd ed.). Sinauer Associates.Google Scholar
  61. Hindmarsh, J. L., & Rose, R. M. (1984). A model of neuronal bursting using three coupled first order differential equations. Proceedings of the Royal Society of London, Series B: Biological Sciences, 221, 87–102.CrossRefGoogle Scholar
  62. Hobson, J., & Pace-Schott, E. (2002). The cognitive neuroscience of sleep: neuronal systems, consciousness and learning. Nature Reviews Neuroscience, 3, 679–693.PubMedCrossRefGoogle Scholar
  63. Hodgkin, A., & Huxley, A. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. The Journal of Physiology, 117, 500–544.PubMedGoogle Scholar
  64. Hopfield, J. J. (1982). Neural networks and physical systems with emergent collective computational abilities. Proceedings of the National Academy of Sciences of the United States of America, 79(8), 2554–2558.CrossRefGoogle Scholar
  65. Hyman, J., Zilli, E., Paley, A., & Hasselmo, M. (2005). Medial prefrontal cortex cells show dynamic modulation with the hippocampal theta rhythm dependent on behavior. Hippocampus, 15, 739–749.PubMedCrossRefGoogle Scholar
  66. Izhikevich, E. M. (2007). Dynamical systems in neuroscience: Geometry of excitability and bursting. Cambridge, MA: MIT Press.Google Scholar
  67. Izhikevich, E. M., & Edelman, G. M. (2008). Large-scale model of mammalian thalamocortical systems. Proceedings of the National Academy of Science, 105, 3593–3598.CrossRefGoogle Scholar
  68. Jacobs, J., Hwang, G., Curran, T., & Kahana, M. J. (2006). EEG oscillations and recognition memory: theta correlates of memory retrieval and decision making. NeuroImage, 15, 978–987.CrossRefGoogle Scholar
  69. Jacobs, J., Kahana, M. J., Ekstrom, A. D., & Fried, I. (2007). Brain oscillations control timing of single-neuron activity in Humans. Journal of Neuroscience, 27, 3839–3844.PubMedCrossRefGoogle Scholar
  70. Jensen, O., et al. (2002). Oscillations in the alpha band increase with memory load during retention in a short-term memory task. Cerebral Cortex, 12, 877–882.PubMedCrossRefGoogle Scholar
  71. Jensen, O., Kaiser, J., & Lachaux, J. P. (2007). Human gamma-frequency oscillations associated with attention and memory. Trends in Neurosciences, 30, 317–324.PubMedCrossRefGoogle Scholar
  72. Johnston, D., & Wu, S. (1997). Foundations of cellular neurophysiology. Cambridge, MA: MIT Press.Google Scholar
  73. Jones, M. W., & Wilson, M. A. (2005). Theta rhythms coordinate hippocampal-prefrontal interactions in a spatial memory task. PLoS Biology, 3, e402.PubMedCrossRefGoogle Scholar
  74. Kahana, M. J. (2006). The cognitive correlates of human brain oscillations. Journal of Neuroscience, 26, 1669–1672.PubMedCrossRefGoogle Scholar
  75. Kiss, T., Hoffmann, W. E., & Hajós, M. (2011). Delta oscillation and short-term plasticity in the rat medial prefrontal cortex: modelling NMDA hypofunction of schizophrenia. International Journal of Neuropsychopharmacology, 14, 29–42.PubMedCrossRefGoogle Scholar
  76. Klimesch, W., et al. (1998). Induced alpha-band power changes in the human EEG and attention. Neuroscience Letters, 244, 73–76.PubMedCrossRefGoogle Scholar
  77. Knill, D. C., & Pouget, A. (2004). The Bayesian brain: the role of uncertainty in neural coding and computation. Trends in Neurosciences, 27, 712–719.PubMedCrossRefGoogle Scholar
  78. Koch, C. (1999). Biophysics of computation: Information processing in single neurons. Oxford, UK: Oxford University Press.Google Scholar
  79. Koch, C., & Segev, I. (1989). Methods in neuronal modeling: From synapses to networks. Cambridge, MA: MIT Press.Google Scholar
  80. Lebedev, M. A., & Nelson, R. J. (1995). Rhythmically firing (20–50 Hz) neurons in monkey primary somatosensory cortex: activity patterns during initiation of vibratory-cued hand movements. Journal of Comparative Neuroscience, 2, 313–334.CrossRefGoogle Scholar
  81. Lewicki, M. S. (2008). Bayesian modeling and classification of neural signals. Neural Computation, 6, 1005–1030.CrossRefGoogle Scholar
  82. Lewis, E. R., & van Dijk, P. (2004). New variations on the derivation of spectro-temporal receptive fields for primary auditory afferent axons. Hearing Research, 189, 120–136.PubMedCrossRefGoogle Scholar
  83. Lytton, W. W. (2008). Computer modeling of epilepsy. Nature Reviews Neuroscience, 9, 626–637.PubMedCrossRefGoogle Scholar
  84. MacKay, D. J. C. (1995). Probable networks and plausible predictions—a review of practical Bayesian methods for supervised neural networks. Network: Computation in Neural Systems, 6(3), 469–505.CrossRefGoogle Scholar
  85. Marmarelis, V. Z. (1993). Identification of nonlinear biological systems using Laguerre expansions of kernels. Annals of Biomedical Engineering, 21, 573.PubMedCrossRefGoogle Scholar
  86. Marmarelis, V. Z. (1997). Modeling methodology for nonlinear physiological systems. Annals of Biomedical Engineering, 25, 239.PubMedCrossRefGoogle Scholar
  87. Marmarelis, V. Z. (2004). Nonlinear dynamic modeling of physiological systems, Wiley Interscience & IEEE Press.Google Scholar
  88. Marmarelis, V. Z., & Berger, T. W. (2005). General methodology for nonlinear modeling of neural systems with Poisson point-process inputs. Mathematical Biosciences, 196, 1–13.PubMedCrossRefGoogle Scholar
  89. Marmarelis, P. Z., & Marmarelis, V.Z. (1978). Analysis of physiological systems: The white-noise approach. Plenum Press.Google Scholar
  90. Marmarelis, P. Z., & Naka, K.-I. (1972). White-noise analysis of a neuron chain: application of the Wiener theory. Science, 175, 1276–1278.PubMedCrossRefGoogle Scholar
  91. Marmarelis, P. Z., & Naka, K.-I. (1973). Nonlinear analysis and synthesis of receptive-field responses in the catfish retina. Parts I, II and III. Journal of Neurophysiology, 36, 605–648.PubMedGoogle Scholar
  92. Marmarelis, P. Z., & Naka, K.-I. (1974). Identification of multi-input biological systems. IEEE Transactions on Biomedical Engineering, 21, 88–101.PubMedCrossRefGoogle Scholar
  93. Marmarelis, V. Z., & Orme, M. E. (1993). Modeling of neural systems by use of neuronal modes. IEEE Transactions on Biomedical Engineering, 40, 1149–1158.PubMedCrossRefGoogle Scholar
  94. Marmarelis, V. Z., Zanos, T. P., & Berger, T. W. (2009). Boolean modeling of neural systems with point-process inputs and outputs. Part I: theory and simulations. Annals of Biomedical Engineering, 37, 1654–1667.PubMedCrossRefGoogle Scholar
  95. Marmarelis, V. Z., Shin, D. C., Song, D., Hampson, R. E., Deadwyler, S. A., & Berger T.W. (2011). Dynamic nonlinear modeling of interactions between neuronal ensembles using Principal Dynamic Modes. Proc. 33rd Intern. IEEE-EMBS Conf., paper 920, Boston.Google Scholar
  96. Morris, C., & Lecar, H. (1981). Voltage oscillations in the barnacle giant muscle fiber. Biophysical Journal, 35, 193–213.PubMedCrossRefGoogle Scholar
  97. Murthy, V. N., & Fetz, E. E. (1992). Coherent 25- to 35-Hz oscillations in the sensorimotor cortex of awake behaving monkeys. Proceedings of the National Academy of Sciences of the United States of America, 89, 5670–5674.PubMedCrossRefGoogle Scholar
  98. Murthy, V. N., & Fetz, E. E. (1996). Oscillatory activity in sensorimotor cortex of awake monkeys: synchronization of local field potentials and relation to behavior. Journal of Neurophysiology, 76, 3949–3982.PubMedGoogle Scholar
  99. Nagumo, J., Arimoto, S., & Yoshizawa, S. (1962). An active pulse transmission line simulating nerve axon. Proceedings of the IRE, 50, 2061–2070.CrossRefGoogle Scholar
  100. Opris, I., Hampson, R. E., Stanford, T. R., Gerhardt, G. A., & Deadwyler, S. A. (2011). Neural activity in frontal cortical cell layers: evidence for columnar sensorimotor processing. Journal of Cognitive Neuroscience, 23, 1507–1521.PubMedCrossRefGoogle Scholar
  101. Pack, C. C., Conway, B. R., Born, R. T., & Livingstone, M. S. (2006). Spatiotemporal structure of nonlinear subunits in macaque visual cortex. Journal of Neuroscience, 26, 893–907.PubMedCrossRefGoogle Scholar
  102. Rieke, F., Warland, D., de Ruyter van Steveninck, R., & Bialek, W. (1997). Spikes: Exploring the Neural Code. Cambridge, MA: MIT Press.Google Scholar
  103. Rigosa, J., Weber, D. J., Prochazka, A., Stein, R. B., & Micera, S. (2011). Neuro-fuzzy decoding of sensory information from ensembles of simultaneously recorded dorsal root ganglion neurons for functional electrical stimulation applications. Journal of Neural Engineering, 8, 046019.PubMedCrossRefGoogle Scholar
  104. Rizzuto, D. S., Madsen, J. R., Bromfield, E. B., Schulze-Bonhage, A., Seelig, D., Aschenbrenner-Scheibe, R., & Kahana, M. J. (2003). Reset of human neocortical oscillations during a working memory task. Proceedings of the National Academy of Sciences of the United States of America, 100, 7931–7936.PubMedCrossRefGoogle Scholar
  105. Roopun, A. K., Cunningham, M. O., Racca, C., Alter, K., Traub, R. D., & Whittington, M. A. (2008). Region-specific changes in Gamma and Beta2 rhythms in NMDA receptor dysfunction models of schizophrenia. Schizophrenia Bulletin, 34, 962–973.PubMedCrossRefGoogle Scholar
  106. Rosenblatt, F. (1962). Principles of neurodynamics. Spartan Books.Google Scholar
  107. Sanes, J. N., & Donoghue, J. P. (1993). Oscillations in local field potentials of the primate motor cortex during voluntary movement. Proceedings of the National Academy of Sciences of the United States of America, 90, 4470–4474.PubMedCrossRefGoogle Scholar
  108. Schwartz, E. (1990). Computational neuroscience. Cambridge, MA: MIT Press.Google Scholar
  109. Siapas, A., Lubenov, E., & Wilson, M. (2005). Prefrontal phase locking to hippocampal theta oscillations. Neuron, 46, 141–151.PubMedCrossRefGoogle Scholar
  110. Singer, W. (1993). Synchronization of cortical activity and its putative role in information processing and learning. Annual Review of Physiology, 55, 349–374.PubMedCrossRefGoogle Scholar
  111. Singer, W. (1999). Neuronal synchrony: a versatile code for the definition of relations? Neuron, 24(49–65), 111–125.Google Scholar
  112. Song, D., Chan, R. H., Marmarelis, V. Z., Hampson, R. E., Deadwyler, S. A., & Berger, T. W. (2007). Nonlinear dynamic modeling of spike train transformations for hippocampal-cortical prostheses. IEEE Transactions on Biomedical Engineering, 54, 1053–1066.PubMedCrossRefGoogle Scholar
  113. Song, D., Chan, R. H. M., Marmarelis, V. Z., Hampson, R. E., Deadwyler, S. A., & Berger, T. W. (2009). Nonlinear modeling of neural population dynamics for hippocampal prostheses. Neural Networks, 22, 1340–1351.PubMedCrossRefGoogle Scholar
  114. Theunissen, F., Roddey, J. C., Stufflebeam, S., Clague, H., & Miller, J. P. (1996). Information theoretic analysis of dynamical encoding by four identified interneurons in the cricket cercal system. Journal of Neurophysiology, 75, 1345–1364.PubMedGoogle Scholar
  115. Vertes, R. P. (2005). Hippocampal theta rhythm: a tag for short term memory. Hippocampus, 15, 923–935.PubMedCrossRefGoogle Scholar
  116. Victor, J. D., & Brown, E. N. (2003). Information and statistical structure in spike trains. Network: Computation in Neural Systems, 14, 1–4.CrossRefGoogle Scholar
  117. von Stein, A., & Sarnthein, J. (2000). Different frequencies for different scales of cortical integration: from local gamma to long range alpha/theta synchronization. International Journal of Psychophysiology, 38, 301–313.CrossRefGoogle Scholar
  118. Widrow, B., & Lehr, M. A. (1990). 30 years of adaptive neural networks: perceptron, madaline, and backpropagation. Proceedings of the IEEE, 78(9), 1415–1442.CrossRefGoogle Scholar
  119. Wu, M. C., David, S. V., & Gallant, J. L. (2006). Complete functional characterization of sensory neurons by system identification. Annual Review of Neuroscience, 29, 477–505.PubMedCrossRefGoogle Scholar
  120. Zanos, T. P., Courellis, S. H., Berger, T. W., Hampson, R. E., Deadwyler, S. A., & Marmarelis, V. Z. (2008). Nonlinear modeling of causal interrelationships in neuronal ensembles. IEEE Transactions on Neural Systems and Rehabilitation Engineering, 16, 336–352.PubMedCrossRefGoogle Scholar
  121. Zanos, T. P., Hampson, R. E., Deadwyler, S. A., Berger, T. W., & Marmarelis, V. Z. (2009). Boolean modeling of neural systems with point-process inputs and outputs. Part II: application to the rat hippocampus. Annals of Biomedical Engineering, 37, 1668–1682.PubMedCrossRefGoogle Scholar
  122. Zhang, Y., Chen, Y., Bressler, S. L., & Ding, M. (2008). Response preparation and inhibition: the role of the cortical sensorimotor beta rhythm. Neuroscience, 156, 238–246.PubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Vasilis Z. Marmarelis
    • 1
  • Dae C. Shin
    • 1
  • Dong Song
    • 1
  • Robert E. Hampson
    • 2
  • Sam A. Deadwyler
    • 2
  • Theodore W. Berger
    • 1
  1. 1.University of Southern CaliforniaLos AngelesUSA
  2. 2.Wake Forest UniversityWinston-SalemUSA

Personalised recommendations