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Mathematical relationships between resonances resolve key modes and novel definitions of ’thermodynamic’ state variables in human brain

Jennifer Goldman

11h — Site Sophia

A mechanistic understanding of the mind remains one of the most substantive problems in science, but the probabilistic nature of neural signals seems to oc- clude a deep understanding of brain activity. Between behavioral states and individual subjects, neural electromagnetic signals vary in magnitude, complex- ity, and spectral composition [1,2]. D.O. Hebb [3] posited that reverberations produced by transiently communicating cell assemblies could underpin neural network communication. G.M. Edelman [4] hypothesized that re-entrant, reit- erated activity in recurrent neural architectures (loops) could select communi- cating neural assemblies. W. Singer and others have shown cognition-dependent phase coherence of disparate neural networks on conserved frequencies [5] . How- ever, no consensus has been reached even regarding the spectral organization of human brain activity and organizing principles remain somewhat obscured in skewed, high-dimensional signals. Neural network activity is comprised of rhythmic and arrhythmic components. The arrhythmic component reflects fluc- tuation of brain activity at all discernible frequencies [1], described by power spectra of the form 1/f. Such heavy-tailed, power law distributions are often found in self-organizing, complex systems [6]. Deviating above the power law, resonant modes have particular time constants, representing rhythmic brain ac- tivity with relatively more energy than expected by their frequency position in the heavy-tailed distribution, however, the organization of modes has remained highly controversial [1,7–14]. Largely, this controversy rests on ad hoc definition of bandwidths (δ ≈ 1 : 4 Hz, θ ≈ 4 : 8 Hz, α ≈ 8 : 16 Hz, β ≈ 16 : 32 Hz, and γ ≥ 32 Hz) in which modes are assumed, perhaps erroneously, to be general- ized. In this lecture I will first outline the state of the field and relevant prior findings, then present my analyses of human magnetoencephalography (MEG) data. These analyses have led to the identification of cognitive state dependent, self-similar structures of neural resonance revealing keystone positions for es- pecially powerful modes with distinct mathematical relationships. Next, I will show how a natural definition of entropy and energy in the modes is consistent with ‘thermodynamic’ state variables, opening the possibility that definitions of ‘work’ and ‘order’ may also be useful for understanding basic functions of the brain.

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