Graph Models of Neurodynamics to Support Oscillatory Associative Memories

Recent advances in brain imaging techniques require the development of advanced models of brain networks and graphs. Previous work on percolation on lattices and random graphs demonstrated emergent dynamical regimes, including zero- and non-zero fixed points, and limit cycle oscillations. Here we introduce graph processes using lattices with excitatory and inhibitory nodes, and study conditions leading to spatio-temporal oscillations. Rigorous mathematical analysis provides insights on the possible dynamics and, of particular concern to this work, conditions producing cycles with very long periods. A systematic parameter study demonstrates the presence of phase transitions between various regimes, including oscillations with emergent metastable patterns. We studied the impact of external stimuli on the dynamic patterns, which can be used for encoding and recall in robust associative memories.

[1]  Rodrigo Quian Quiroga,et al.  Imaging Brain Function With EEG , 2013, Springer New York.

[2]  Robert Kozma,et al.  Hierarchical random cellular neural networks for system-level brain-like signal processing , 2013, Neural Networks.

[3]  W. Marsden.  I and J , 2012 .

[4]  Kunihiko Kaneko,et al.  Associative memory model with spontaneous neural activity , 2012 .

[5]  A. Grinvald,et al.  Spontaneously emerging cortical representations of visual attributes , 2003, Nature.

[6]  Günther Palm,et al.  Neural associative memories and sparse coding , 2013, Neural Networks.

[7]  Karl J. Friston,et al.  CHAPTER 2 – Statistical parametric mapping , 2007 .

[8]  A. Grinvald,et al.  Dynamics of Ongoing Activity: Explanation of the Large Variability in Evoked Cortical Responses , 1996, Science.

[9]  James A. Reggia,et al.  Self-organizing maps based on limit cycle attractors , 2015, Neural Networks.

[10]  D. Ruelle,et al.  Recurrence Plots of Dynamical Systems , 1987 .

[11]  Karl J. Friston,et al.  Statistical parametric mapping , 2013 .

[12]  A Grinvald,et al.  Coherent spatiotemporal patterns of ongoing activity revealed by real-time optical imaging coupled with single-unit recording in the cat visual cortex. , 1995, Journal of neurophysiology.

[13]  A. Holroyd.  Sharp metastability threshold for two-dimensional bootstrap percolation , 2002, math/0206132.

[14]  J J Hopfield,et al.  Neurons with graded response have collective computational properties like those of two-state neurons. , 1984, Proceedings of the National Academy of Sciences of the United States of America.

[15]  Thomas K. Berger,et al.  Brief Bursts Self-Inhibit and Correlate the Pyramidal Network , 2010, PLoS biology.

[16]  W. Freeman.  The physiology of perception. , 1991, Scientific American.

[17]  Norio Matsuki,et al.  Metastability of Active CA 3 Networks , 2007 .