Information-devoid routes for scale-free neurodynamics
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Information-devoid routes for scale-free neurodynamics Arturo Tozzi1 · James F. Peters2,3,4,5 Received: 18 April 2020 / Accepted: 26 September 2020 © Springer Nature B.V. 2020
Abstract Neuroscientists are able to detect physical changes in information entropy in the available neurodata. However, the information paradigm is inadequate to describe fully nervous dynamics and mental activities such as perception. This paper suggests explanations to neural dynamics that provide an alternative to thermodynamic and information accounts. We recall the Banach–Tarski paradox (BTP), which informally states that when pieces of a ball are moved and rotated without changing their shape, a synergy between two balls of the same volume is achieved instead of the original one. We show how and why BTP might display this physical and biological synergy meaningfully, making it possible to model nervous activities. The anatomical and functional structure of the central nervous system’s nodes and edges makes it possible to perform a sequence of moves inside the connectome that doubles the amount of available cortical oscillations. In particular, a BTP-based mechanism permits scale-invariant nervous oscillations to amplify and propagate towards widely separated brain areas. Paraphrasing the BTP’s definition, we could state that: when a few components of a self-similar nervous oscillation are moved and rotated throughout the cortical connectome, two self-similar oscillations are achieved instead of the original one. Furthermore, based on topological structures, we illustrate how, counterintuitively, the amplification of scale-free oscillations does not require information transfer.
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Arturo Tozzi [email protected]; [email protected] James F. Peters [email protected]
1
Center for Nonlinear Science, University of North Texas, 1155 Union Circle, #311427, Denton, TX 76203-5017, USA
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Department of Electrical and Computer Engineering, University of Manitoba, 75A Chancellor’s Circle, Winnipeg, MB R3T 5V6, Canada
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Department of Mathematics, Adıyaman University, 02040 Adıyaman, Turkey
4
Department of Mathematics, Faculty of Arts and Sciences, Adıyaman University, 02040 Adıyaman, Turkey
5
Computational Intelligence Laboratory, University of Manitoba, Winnipeg, MB R3T 5V6, Canada
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Keywords Banach–tarski paradox · Brain · Power law · Fractal · Oscillations · Information Broadly successful information theory permits the appraisal of general features of physical/biological systems, suggesting that our world (including ourselves) is made up of a fundamental physical assembly termed information (Shannon 1948; Bekenstein 2003). Over time, numerous information-related perspectives have been portrayed: e.g., information theory has been correlated with statistical thermodynamics, Renyi entropy, Bekenstein–Hawking entropy, quantum mechanics, and so on (Jaynes 1957; Lloyd 2000; Marzuoli and Rasetti 2005; Bromiley et al. 2010; Cafaro et al. 2016; Tozzi et al. 2018). After the launch of the slogan “it from bit” (Whee
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