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

Journal of Computational Neuroscience

Volumn 34, Issue 1, 2013, Pages 73-87

  Marmarelis, Vasilis Z ^a   Shin, Dae C ^a   Song, Dong ^a   Hampson, Robert E ^b   Deadwyler, Sam A ^b   Berger, Theodore W ^a  

^a UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

^b WAKE FOREST UNIVERSITY   (United States)

Author keywords

Dynamic modeling; Multi input multi output neuronal systems; Nonlinear modeling; Prefrontal cortex; Principal Dynamic Modes; Volterra modeling

Indexed keywords

MIMO SYSTEMS; NONLINEAR SYSTEMS;

DYNAMICS MODELS; MODE-BASED; MULTI-INPUT MULTI-OUTPUT; MULTI-INPUT MULTI-OUTPUT NEURONAL SYSTEM; MULTI-INPUT-MULTI-OUTPUT MODELS; NEURONAL SYSTEMS; NON-LINEAR MODELLING; PREFRONTAL CORTEX; PRINCIPAL DYNAMIC MODES; VOLTERRA MODEL;

NEURONS;

ARTICLE; CELL INTERACTION; CONTROLLED STUDY; ELECTRODE; MATHEMATICAL MODEL; MENTAL TASK; MOLECULAR DYNAMICS; NERVE CONDUCTION; NERVE FUNCTION; NERVOUS SYSTEM PARAMETERS; NONLINEAR SYSTEM; PREDICTION; PRINCIPAL DYNAMIC MODE; PRIORITY JOURNAL; TASK PERFORMANCE;

EID: 84873410685     PISSN: 09295313     EISSN: 15736873     Source Type: Journal    
DOI: 10.1007/s10827-012-0407-7     Document Type: Article

References (122)

1. Abbott, L. F. (1999). Lapique's introduction of the integrate-and-fire model neuron. Brain Research Bulletin, 50, 303-304.
2. Abeles, M. (1991). Corticonics: Neural Circuits of the Cerebral Cortex. Cambridge, UK: Cambridge University Press.
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.
4. Amit, D. J. (1989). Modeling Brain Function: The World of Attractor Neural Networks. Cambridge, UK: Cambridge University Press.
5. Anderson, J. A. (1996). An Introduction to Neural Networks. Cambridge, MA: MIT Press.
6. Anderson, C. H., & Eliasmith C. (2004). Neural Engineering: Computation, Representation, and Dynamics in Neurobiological Systems (Computational Neuroscience). Cambridge, MA: MIT Press.
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.
8. Arbib, M. A. (2003). The Handbook of brain Theory and Neural Networks. Cambridge, MA: MIT Press.
9. Atencio, C. A., & Schreiner, C. E. (2008). Spectrotemporal processing differences between auditory cortical fast-spiking and regularspiking neurons. Journal of Neuroscience, 28, 3897-3910.
10. Atencio, C. A., & Schreiner, C. E. (2010). Columnar connectivity and laminar processing in cat primary auditory cortex. PLoS One, 5 (3), e9521.
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.
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.
13. Berger, T.W., Eriksson, J. L., Ciarolla, D. A., & Sclabassi, R. J. (1988). Nonlinear systems analysis of the hippocampal perforant pathdentate system. II. Effects of random train stimulation. Journal of Neurophysiology, 60, 1077-1094.
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.
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.
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). Brainimplantable biomimetic electronics as the next era in neural prosthetics. Proceedings of the IEEE, 89, 993-1012.
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.
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.
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.
20. Borst, A., & Theunissen, F. E. (1999). Information theory and neural coding. Nature Neuroscience, 2, 947-957.
21. Brandenberger, G. (2003). The ulradien rhythm of sleep: Diverse relations with pituitary and adrenal hormones. Revue Neurologique, 159(11), S5-S10.
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.
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.
24. Buzsaki, G. (2002). Theta oscillations in the hippocampus. Neuron, 33, 325-340.
25. Buzsaki, G. (2005). Theta rhythm of navigation: Link between path integration and landmark navigation, episodic and semantic memory. Hippocampus, 15, 827-840.
26. Churchland, P. S., & Sejnowski, T. J. (1999). The Computational Brain. Cambridge, MA: MIT Press.
27. Citron,M. C., & Emerson, R. C. (1983). White noise analysis of cortical directional selectivity in cat. Brain Research, 279, 271-277.
28. Citron, M. C., Kroeker, J. P., & McCann, G. D. (1981). Nonlinear interactions in ganglion cell receptive fields. Journal of Neurophysiology, 46, 1161-1176.
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.
30. Cottaris, N. P., & De Valois, R. L. (1998). Temporal dynamics of chromatic tuning in macaque primary visual cortex. Nature, 395, 896-900.
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.
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.
33. David, S. V., & Gallant, J. L. (2005). Predicting neuronal responses during natural vision. Network, 16, 239-260.
34. Deadwyler, S. A., & Hampson, R. E. (1995). Ensemble activity and behavior: What's the code? Science, 270, 1316-1318.
35. Deadwyler, S. A., & Hampson, R. E. (2004). Differential but complementary mnemonic functions of the hippocampus and subiculum. Neuron, 42, 465-476.
36. Deadwyler, S. A., & Hampson, R. E. (2006). Temporal coupling between subicular and hippocampal neurons underlies retention of trialspecific events. Behavioural Brain Research, 174, 272-280.
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 multielectrode array technology. IEEE Transactions on Biomedical Engineering, 55, 693-702.
38. Dobson, A. J. (2002). An Introduction to Generalized Linear Models. Boca Raton, Florida: Chapman &Hall/CRC Press.
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.
40. Eeckman, F. H. (1992). Neural Systems: Analysis and Modeling.
41. Eggermont, J. J. (1993). Wiener and Volterra analyses applied to the auditory system. Hearing Research, 66, 177-201.
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.
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.
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.
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.
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.
47. FitzHugh, R. (1955). Mathematical models of threshold phenomena in the nerve membrane. Bulletin of Mathematical Biophysics, 17, 257-278.
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.
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.
50. Fries, P. (2005). A mechanism for cognitive dynamics: Neuronal communication through neuronal coherence. Trends in Cognitive Science, 9, 474-480.
51. Fries, P., Nikolic, D., & Singer,W. (2007). The gamma cycle. Trends in Neurosciences, 30, 309-316.
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.
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.
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.
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.
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.
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.
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.
59. Hertz, J., Krogh, A., & Palmer, R.G. (1991). Introduction to the theory of neural computation. Addison-Wesley.
60. Hille, B. (2001). Ionic Channels of Excitable Membranes (3rd ed.). Sinauer Associates.
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.
62. Hobson, J., & Pace-Schott, E. (2002). The cognitive neuroscience of sleep: Neuronal systems, consciousness and learning. Nature Reviews Neuroscience, 3, 679-693.
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.
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.
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.
66. Izhikevich, E. M. (2007). Dynamical systems in neuroscience: Geometry of excitability and bursting. Cambridge, MA: MIT Press.
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.
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.
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.
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.
71. Jensen, O., Kaiser, J., & Lachaux, J. P. (2007). Human gammafrequency oscillations associated with attention and memory. Trends in Neurosciences, 30, 317-324.
72. Johnston, D., & Wu, S. (1997). Foundations of cellular neurophysiology. Cambridge, MA: MIT Press.
73. Jones, M. W., & Wilson, M. A. (2005). Theta rhythms coordinate hippocampal-prefrontal interactions in a spatial memory task. PLoS Biology, 3, e402.
74. Kahana, M. J. (2006). The cognitive correlates of human brain oscillations. Journal of Neuroscience, 26, 1669-1672.
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.
76. Klimesch, W., et al. (1998). Induced alpha-band power changes in the human EEG and attention. Neuroscience Letters, 244, 73-76.
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.
78. Koch, C. (1999). Biophysics of computation: Information processing in single neurons. Oxford, UK: Oxford University Press.
79. Koch, C., & Segev, I. (1989). Methods in neuronal modeling: From synapses to networks. Cambridge, MA: MIT Press.
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.
81. Lewicki, M. S. (2008). Bayesian modeling and classification of neural signals. Neural Computation, 6, 1005-1030.
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.
83. Lytton, W. W. (2008). Computer modeling of epilepsy. Nature Reviews Neuroscience, 9, 626-637.
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.
85. Marmarelis, V. Z. (1993). Identification of nonlinear biological systems using Laguerre expansions of kernels. Annals of Biomedical Engineering, 21, 573.
86. Marmarelis, V. Z. (1997). Modeling methodology for nonlinear physiological systems. Annals of Biomedical Engineering, 25, 239.
87. Marmarelis, V. Z. (2004). Nonlinear dynamic modeling of physiological systems, Wiley Interscience & IEEE Press.
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.
89. Marmarelis, P. Z., & Marmarelis, V.Z. (1978). Analysis of physiological systems: The white-noise approach. Plenum Press.
90. Marmarelis, P. Z., & Naka, K.-I. (1972). White-noise analysis of a neuron chain: Application of the Wiener theory. Science, 175, 1276-1278.
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.
92. Marmarelis, P. Z., & Naka, K.-I. (1974). Identification of multi-input biological systems. IEEE Transactions on Biomedical Engineering, 21, 88-101.
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.
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.
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.
96. Morris, C., & Lecar, H. (1981). Voltage oscillations in the barnacle giant muscle fiber. Biophysical Journal, 35, 193-213.
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.
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.
99. Nagumo, J., Arimoto, S., & Yoshizawa, S. (1962). An active pulse transmission line simulating nerve axon. Proceedings of the IRE, 50, 2061-2070.
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.
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.
102. Rieke, F.,Warland, D., de Ruyter van Steveninck, R.,&Bialek,W. (1997). Spikes: Exploring the Neural Code. Cambridge, MA:MIT Press.
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.
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.
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.
106. Rosenblatt, F. (1962). Principles of neurodynamics. Spartan Books.
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.
108. Schwartz, E. (1990). Computational neuroscience. Cambridge, MA: MIT Press.
109. Siapas, A., Lubenov, E., & Wilson, M. (2005). Prefrontal phase locking to hippocampal theta oscillations. Neuron, 46, 141-151.
110. Singer, W. (1993). Synchronization of cortical activity and its putative role in information processing and learning. Annual Review of Physiology, 55, 349-374.
111. Singer, W. (1999). Neuronal synchrony: A versatile code for the definition of relations? Neuron, 24(49-65), 111-125.
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.
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.
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.
115. Vertes, R. P. (2005). Hippocampal theta rhythm: A tag for short term memory. Hippocampus, 15, 923-935.
116. Victor, J. D., & Brown, E. N. (2003). Information and statistical structure in spike trains. Network: Computation in Neural Systems, 14, 1-4.
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.
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.
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.
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.
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.
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.