For citation:
Rabinovich M. I., Varona P. . Mathematics of mind. Izvestiya VUZ. Applied Nonlinear Dynamics, 2017, vol. 25, iss. 3, pp. 5-51. DOI: 10.18500/0869-6632-2017-25-3-5-51
Mathematics of mind
In this slide-lecture we formulate a novel paradigm for the mathematical description of mental functions such as consciousness, creativity, decision making and prediction of the future based on the past. Such cognitive functions are described in the framework of canonical nonlinear dynamical models that form joint global hierarchical networks. Subnetworks cooperate and compete with each other by inhibition. The suggested approach uses heteroclinic dynamics to represent transitivity and sequential interaction of different cognitive modalities at all levels of network hierarchy. For the first time we build a model of global network dynamics based on a set of kinetic ecological equations describing the interaction with emotion at each level of the hierarchy. This makes the model applicable for the description and understanding of perception, creativity and other complex cognitive processes. We discuss the creativity phenomenon, for example, in a joint «human-robot mind» considering the approximation in which the artificial partner is responsible for the binding and retrieving of multimodal perception information. The formation of chunks and the creation of working memory is a joint effort – human-robot mind. The human mind is responsible for the evaluation of the information in working memory. Creativity is estimated by Kolmogorov–Sinai entropy. As an example, we discuss joint human-robot musical improvisation, which can be generalized for many applications, in particular, in the context of artificial intelligence applications and to address several psychiatric disorders.
- Rabinovich M.I., Simmons A.N., Varona P. Dynamical bridge between brain and mind. Trends in Cognitive Sciences. 2015. Vol. 19(8). Pp. 453–461.
- Stokes M., Kusunoki M., Sigala N., Nili H., Gaffan D., Duncan J. Dynamic coding for cognitive control in prefrontal cortex. Neuron. 2013. Vol.78(2). Pp. 364–375.
- Rabinovich M, Huerta R, Laurent G. Transient dynamics for neural processing. Science. 2008. Vol. 321(5885). Pp. 48–50.
- Cunningham J.P., Yu B.M. Dimensionality reduction for large-scale neural recordings. Nature Neuroscience. 2014. DOI: 10.1038. nn.3776.
- Rabinovich M., Volkovskii A., Lecanda P., Huerta R., Abarbanel H.D.I.; Laurent G. Dynamical encoding by networks of competing neuron groups: Winnerless competition. Physical Review Letters. 2001. Vol. 87(6): 068102.
- Afraimovich V.S, Zhigulin V.P, Rabinovich M.I. On the origin of reproducible sequential activity in neural circuits. Chaos. 2004. Vol. 14(4). Pp. 1123–1129
- Jones L.M., Fontanini A., Sadacca B.F., Miller P., Katz D. B. Natural stimuli evoke dynamic sequences of states in sensory cortical ensembles. PNAS. 2007. Vol. 104(47).
- Limb C.J., Braun A.R. Neural substrates of spontaneous musical performance: An fMRI study of jazz improvisation. PLoS ONE. 2008. 3(2). doi:10.1371/journal.pone.0001679.
- Fox M.D., Snyder A.Z., Vincent J.L., Corbetta M., Van Essen D.C., Raichle M.E. The human brain is intrinsically organized into dynamic, anticorrelated functional net-works. PNAS. 2005. Vol. 102. Pp. 9673–9678.
- Yuste R., Fairhall A.L. Temporal dynamics in fMRI resting state activity. PNAS. 2015. Vol. 112(17).
- Spreng R.N, Sepulcre J., Turner G.R., Stevens W.D., Schacter D.L. Intrinsic architecture underlying the relations among the default, dorsal attention, and frontoparietal control networks of the human brain. J. Cogn. Neuroscience. 2013. Vol. 25. Pp. 74–86.
- Barttfeld P., Uhrig L., Sitt J.D., Sigman M., Jarraya B., Dehaene S. Signature of consciousness in the dynamics of resting-state brain activity. PNAS. 2015. Vol. 112(3). Pp. 887–892.
- Rabinovich M.I., Varona P., Tristan I., Afraimovich V.S. Chunking dynamics: Heteroc- linics in mind. Frontiers in Computational Neuroscience. 2014. Vol. 8(22).
- Rabinovich MI, Afraimovich VS, Varona P. Heteroclinic binding. Dynamical Systems. 2010. Vol. 25(3). Pp. 433–442.
- Rabinovich M.I., Muezzinoglu M.K., Strigo I., Bystritsky A. Dynamical principles of emotion-cognition interaction: mathematical images of mental disorders. PLOS ONE. 2010. Vol. 5(9): e12547.
- Rabinovich M.I., Muezzinoglu M.K. Nonlinear dynamics of the brain: Emotion and cognition. Physics-Uspekhi. 2010. Vol. 53(4). Pp. 357–372.
- Muezzinoglu M.K., Tristan I., Huerta R., Afraimovich V.S., Rabinovich M.I. Transient versus attractors in complex networks. International Journal of Bifurcation and Chaos. 2010. Vol. 20(6). Pp. 1–23.
- Muezzinoglu M.K., Vergara A., Huerta R., Rabinovich M.I. A sensor conditioning principle for odor identification. Sensors and Actuators B-Chemical. 2010. Vol. 146. Pp. 472–476.
- Bick C., Rabinovich M.I. On the occurrence of stable heteroclinic channels in Lotka-Volterra models. Dynamical Systems. 2010. Vol. 25. Pp. 95–110.
- Rabinovich M.I., Tristan I., Varona P. Hierarchical nonlinear dynamics of human attention. Neuroscience and Biobehavioral Reviews. 2015. Vol. 55. Pp. 18–35.
- Rabinovich M.I., Tristan I., Varona P. Neural dynamics of attentional cross-modality control. PLOS ONE. 2013. Vol. 8(5): e64406.
- Varona P., Rabinovich M.I. Hierarchical dynamics of informational patterns and decision-making. Proceedings of the Royal Society of London B: Biological Sciences. 2016. Vol. 283 (1832): 20160475. DOI: 10.1098/rspb.2016.0475.
- Lu J., Yang H., Zhang X., He H., Lu C., Yao D. The brain functional state of music creation: an fMRI study of composers. Scientific Reports. 2015. Vol. 5:12277
- Rabinovich M.I., Huerta R., Afraimovich V.I. Dynamics of sequential decision making. Phys. Rev Lett. 2006. Vol. 97(18): 188103.
- Rabinovich M.I., Huerta R., Varona P. Heteroclinic synchronization: ultrasubharmonic locking. Phys Rev Lett. 2006. Vol. 96(1): 014101.
- Rabinovich M.I., Varona P. Frontiers in neuroscience-neuroprosthetic. 2016 (paper submitted.)
- Rabinovich M.I., Afraimovich V.S., Bick C., Varona P. Information flow dynamics in the brain. Physics of Life Reviews. 2012. Vol. 9(1). Pp. 51–73.
- Rabinovich M.I., Afraimovich V.S., Bick C., Varona P. Instability, semantic dynamics and modeling brain data. Physics of Life Reviews. 2012. Vol. 9(1). Pp. 80–83.
- Jun Tani. Exploring Robotic Minds: Actions, Symbols, and Consciousness as Self Organizing Dynamic Phenomena. Oxford University Press, 2017.
- Barron A.B., Klein C. What insects can tell us about the origins of consciousness. PNAS. 2016. May 3. Vol. 113, No. 184900-4908.
- Key B., Arlinghaus R., Browman H.I. Insects cannot tell us anything about subjective experience or the origin of consciousness. PNAS. 2016. July 5. Vol.113, No. 27E3813.
- Koch C., Massimini M., Boly M., Tononi G. Neural correlates of consciousness: Progress and problems. Nat. Rev. Neurosci. 2016. Apr. Vol. 17, No. 5, Pp. 307–321.
- Dehaene S., Consciousness and the Brain: Deciphering How the Brain Codes Our Thoughts. Penguin, 2014.
- Dehaene S., Charles L., King J.R., Marti S. Toward a computational theory of conscious processing. Curr. Opin. Neurobiol. 2014. Vol. 25. Pp. 76-84.
- Varona P., Rabinovich M.I. Hierarchical dynamics of informational patterns and decision making. Proc. R. Soc. B. 2016. Vol. 283. P. 20160475.
- Beaty R.E., Benedek M., Silvia P.J., Schacter D.L. Creative cognition and brain network Dynamics. Trends Cogn. Sci. 2016. Vol. 20, No. 2. Pp. 87–95.
- Schurger A., Gale S., Gozel Olivia, Blanke Olaf. Performance monitoring for brain-computer-interface actions. Brain and Cognition. 2017. Feb. Vol. 111. Pp. 44–50.
- Sharma Shivani, Babu Nandita. Interplay between creativity, executive function and working memory in middle-aged and older adults. Creativity Research Journal. 2017. Vol 29. Pp. 71–77.
- Silva Rui, Louro Luis, Malheiro Tiago, Erlhagen Wolfram, Bicho Estela. Combining intention and emotional state inference in a dynamic neural field architecture for human-robot joint action. Adaptive Behavior. 2016. Vol. 24(5). Pp. 350–372.
- Beaty R.E., Silvia P.J., Benedek M. Brain networks underlying novel metaphor production. Brain and Cognition. 2017. Vol. 111. Pp. 163–170.
- First M., Williams J., Karg R., Spitzer R. Structured clinical interview for DSM-5. Research Version. SCID-5 for DSM-5, Research Version (SCID-5-RV). American Psychiatric Association. Arlington, VA, 2015.
- Rabinovich M.I., Simmons A.N., Varona P. Dynamical bridge between brain and mind. Trends Cogn. Sci. 2015. Vol. 19, No. 8. Pp. 453–461.
- Rabinovich M.I., Sokolov Y., Kozma R. Robust sequential working memory recall in heterogeneous cognitive networks. Front. Syst. Neurosci. 2014. Jan. Vol. 8. P. 220.
- Rabinovich M.I., Varona P. Functional dynamical networks in joint human-robot creativity. Front. Comput. Neurosci. 2017 (paper submitted).
- Barttfeld P., Uhrig L., Sitt J.D., Sigman M., Jarraya B., Dehaene S. Signature of consciousness in the dynamics of resting-state brain activity. Proc. Natl. Acad. Sci. U.S.A. 2015. Jan. Vol. 112, No. 3. Pp. 887–892.
- Lu J., Yang H., Zhang X., He H., Luo C., Yao D. The brain functional state of music creation: An fMRI study of composers. Sci. Rep. 2015. Jan. Vol. 5. P. 12277.
- Bajaj S., Adhikari B. M., Friston K. J., Dhamala M. Bridging the gap: Dynamic causal modeling and granger causality analysis of resting state functional magnetic resonance imaging. Brain Connect. 2016. Jan. Vol. 6, No. 8. Pp. 652–661.
- Andrews-Hanna J.R., Smallwood J., Spreng R.N. The default network and self-generated thought: Component processes, dynamic control, and clinical relevance. Ann. N.Y. Acad. Sci. 2014. 1316. Pp. 29–52.
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