Abstract
Biocognitive phenomena are inherently unstable and, under normal conditions, must be constantly controlled by embedding regulators. The canonical models are blood pressure and the stream of consciousness that require persistent delicate regulation in higher organisms. Here, using the Rate Distortion Theorem of information theory, we derive a form of the Data Rate Theorem of control theory that characterizes such instability for adiabatically stationary nonergodic systems and uncover novel forms of cognitive dynamics under stochastic challenge. These range from aperiodic stochastic amplification to Yerkes-Dodson signal transduction and outright system collapse. The analysis leads toward new statistical tools for data analysis, again uncovering groupoid symmetry-breaking phase transition analogs to Fisher Zeros in physical systems.
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References
Adler, M., A. Mayo, and U. Alon, 2014. Logarithmic and power law input-output relations in sensory systems with fold-change detection. PLOS Computational Biology https://doi.org/10.1371/journal.pcbi.1003781.
Appleby, J., X. Mao, and A. Rodkina, 2008. Stabilization and destabilization of nonlinear differential equations by noise. IEEE Transactions on Automatic Control 53:126–132.
Atlan H., and I. Cohen, 1998. Immune information, self-organization, and meaning. International Immunology 10:711–718.
Cover, T., and J. Thomas, 2006. Elements of Information Theory, 2nd ed. New York: Wiley.
de Groot, S., and P. Mazur, 1984. Nonequilibrium Thermodynamics. New York: Dover.
Diamond, D., A. Campbell, C. Park, J. Halonen, and P. Zoladz, 2007. The Temporal Dynamics Model of Emotional Memory Processing Neural Plasticity. https://doi.org/10.1155/2007/60803.
Dolan, B., W. Janke, D. Johnston, and M. Stathakopoulos, 2001. Thin Fisher zeros. Journal of Physics A 34:6211–6223.
Dunkel, J., S. Hilbert, L. Schimansky-Geier, and P. Hanggi, 2004. Stochastic resonance in biological nonlinear evolution models. Physical Review E 69:056118.
Effros, M., P. Chou, and R. Gray, 1994. Variable-rate source coding theorems for stationary nonergodic sources. IEEE Transactions on Information Theory 40:1920–1925.
Einstein, A., 1905/1956. Investigations on the Theory of the Brownian Motion. New York: Dover Publications.
Feynman, R., 2000. Lectures on Computation. New York: Westview Press.
Fisher, M., 1965. Lectures in Theoretical Physics, Vol. 7. Boulder: University of Colorado Press.
Jackson, D., A. Kempf, and A. Morales, 2017. A robust generalization of the Legendre transform for QFT. Journal of Physics A 50:225201.
Kang, Y., R. Liu, and X. Mao, 2020. Aperiodic stochastic resonance in neural information processing with Gaussian colored noise. Cognitive Neurodynamics https://doi.org/10.1007/s11571-020-09632-3.
Khinchin, A., 1957. Mathematical Foundations of Information Theory. New York: Dover.
Laidler, K., 1987. Chemical Kinetics, 3rd ed. New York: Harper and Row.
Maturana, H., and F. Varela, 1980. Autopoiesis and Cognition: The Realization of the Living. Boston: Reidel.
Moss, F., L. Ward, and W. Sannita, 2004. Stochastic resonance and sensory information processing: a tutorial and review of application. Clinical Neurophysiology 115:267–281.
Nair, G., F. Fagnani, S. Zampieri, and R. Evans, 2007. Feedback control under data rate constraints: an overview. Proceedings of the IEEE 95, 108138.
Protter, P., 2005. Stochastic Integration and Dierential Equations, 2nd ed. New York: Springer.
Ruelle, D., 1964. Cluster property of the correlation functions of classical gases. Reviews of Modern Physics, April:580–584.
Shields, P., D. Neuhoff, L. Davisson, and F. Ledrappier, 1978. The Distortion-Rate function for nonergodic sources. The Annals of Probability 6:138–143.
van der Groen, O., M. Tang, N. Wenderoth, and J. Mattingley, 2018. Stochastic resonance enhances the rate of evidence accumulation during combined brain stimulation and perceptual decision-making. PLOS Computational Biology 14:e1006301. https://doi.org/10.1371/journal.pcbi.1006301.
Vazquez-Rodriguez, B., A. Avena-Koenigsberger, O. Sporns, A. Griffa, P. Hagmann, and H. Larralde, 2017. Stochastic resonance at criticality in a network model of the human brain. Scientific Reports 7:13020 https://doi.org/10.1038/s41598-017-13400-5.
Wallace, R., 2005. Consciousness: A Mathematical Treatment of the Global Neuronal Workspace Model. New York: Springer.
Wallace, R., 2012. Consciousness, crosstalk, and the mereological fallacy: an evolutionary perspective. Physics of Life Reviews 9:426–453.
Wallace, R., 2016. Subtle noise structures as control signals in high-order biocognition. Physics Letters A 380:726–729.
Wallace, R., 2020. On the variety of cognitive temperatures and their symmetry-breaking dynamics. Acta Biotheoretica. https://doi.org/10.1007/s10441-019-09375-8.
Wallace, R., 2021. Toward a formal theory of embodied cognition. BioSystems 202:104356.
Wallace, R., 2022a. Consciousness, Cognition and Crosstalk: The Evolutionary Exaptation of Nonergodic Groupoid Symmetry-Breaking. New York: Springer.
Wallace, R., 2022b. Formal perspectives on shared interbrain activity in social communication. Cognitive Neurodynamics. https://doi.org/10.1007/s11571-022-09811-4.
Wallace, R., 2022c. Deception and Delay in Organized Conflict: Essays on the Mathematical Theory of Maskirovka. New York: Springer.
Weinstein, A., 1996. Groupoids: unifying internal and external symmetry. Notices of the American Mathematical Association 43:744–752.
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Wallace, R. (2023). On Regulation. In: Essays on the Extended Evolutionary Synthesis. SpringerBriefs in Evolutionary Biology. Springer, Cham. https://doi.org/10.1007/978-3-031-29879-0_3
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DOI: https://doi.org/10.1007/978-3-031-29879-0_3
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