A comment on paper of Kim et al. on mechanisms of hysteresis in human brain networks: comparing with theoretical m-adic model
aa r X i v : . [ q - b i o . N C ] J a n A comment on paper of Kim et al. onmechanisms of hysteresis in human brainnetworks: comparing with theoretical m -adicmodel Giuseppe Iurato and Andrei KhrennikovInternational Center for Mathematical Modelingin Physics, Engineering, Economics and Cognitive ScienceLinnaeus University, S-35195, V¨axj¨o, Sweden
Abstract
This comment is aimed to point out that the recent work due to Kim,et al. in which the clinical and experiential assessment of a brain networkmodel suggests that asymmetry of synchronization suppression is the keymechanism of hysteresis has coupling with our theoretical hysteresis modelof unconscious-conscious interconnection based on dynamics on m -adictrees. This is a comment on the recent work [22]. In this paper, the clinical andexperiential assessment of a brain network model suggests that asymmetryof synchronization suppression is the key mechanism of hysteresis observedduring loss and recovery of consciousness in general anesthesia. This studyhas indirectly provided empirical confirmation of the theoretical modeloutlined in [8] based on a possible implementation of an hysteretic patterninto a formal model of unconscious-conscious interconnection worked outon the basis of representations of mental entities by m -adic numbers.One of the main assumptions done by the authors of [22], is that(physical) hysteresis (of their brain network model took into account)observed during anesthetic state transitions shares the same underlyingmechanism as that observed in non-biological networks. This makes licitto put into comparative relations [8] and [22]. M -adic (ultrametric) model of conscious-unconscious interrelation First, rigorous attempts to formalize, through p -adic mathematics, theconstruct pair conscious-unconscious of psychology have been undertakenby Andrei Yu. Khrennikov since the late 1990s ([6], [12]-[20]). This for-malization via p -adic analysis was based on the use of concepts, tools andtechniques drawn from dynamical systems theory and this route is verypromising. One of the central points of this theoretical framework, whichlays out the basic concepts and notions of psychology and psychoanalysis,is the use of p -adic dynamical systems and related theory, thanks to whichit has been possible to take into account the chief elements of Freudian psy-choanalysis, among which the crucial relationships conscious-unconscious,which may be formalized through discrete dynamical system theory andrepresent the nodal points of the whole psychoanalytic framework.Mathematically, it is fruitful to proceed with the fields of p -adic num-bers, where p > p -adicnumbers, where p > p -adic and more generally ultrametric anal-ysis, have been used in modeling cognition and unconscious processing ofinformation by R. Lauro-Grotto ([24]) and F. Murtagh ([25]-[28]).Therefore, the psychological construct pair conscious-unconscious, say C − UC , is the keystone of every formalization attempt of psychoanaly-sis. In [8], the authors have simply taken into account a first elementaryformal model of hysteretic phenomena (regarding physical context), im-plemented into the p -adic dynamical model of the C − UC pair. In doingso, the authors of [8] have tried to use hysteretic phenomena (belongingto physics) to analogically transfer memory retaining effects into the phe-nomenology involved in the pair
C − UC . Indeed, hysteretic effects havebeen considered in attempts to mechanically formalize memory featuresof implicit memories of neurophysiology ([7], [23]), so the authors of [8]have thought to extend this idea to
C − UC pair, trying to shed light upona formal issue raised by the m -adic dynamical model. The model outlinedin [8] has been then applied to formalize other aspects of human psyche([9]) as well as to deduce a p -adic version of the Weber-Fechner law ([10])and some of its possible applications to economics and sociology ([11]). Hysteresis has a large range phenomenology, and may be understood fromeither the psychological and the physical standpoint. A possible concep- ion of hysteresis belonging to psychological context may be drawn fromthe APA Dictionary of Psychology which defines hysteresis as an effectin which the perception of a stimulus is influenced by any other stimulusimmediately preceding such a perception. It can be detected, for instance,in experiments making successive changes to a certain stimulus which isvarying along some dimension, hence asking to the participant to describeher or his perception. When such values along the given dimension aresteadily increased, then it will be reached a point in which the participantwill begin to place the related percept into a different category (e.g., asound is loud rather than quiet ), but, when values along the dimensionare decreased, then the crossover point will occur at a different point alongsuch a dimension. In particular, in vision, hysteresis may stand out withthe tendency for a perceptual state to persist under gradually changingconditions: this is, for example, the case when stereoscopic fusion maypersist, so producing the appearance of depth even when binocular dis-parity (i.e., the slight difference between the right and left retinal images)between the two images becomes so great that they would normally notbe able to be merged together.This last phenomenology of hysteresis (to be meant according to psy-chology) related to vision may be also correlated analogically ([3]) withcertain aspects of the physical phenomenology discussed first in [21], anddealing with conscious-unconscious visual recognition, hence reconsideredin [3] where the authors have then pointed out the possible analogical iden-tification of hysteresis effects in visual recognition experiments performedin [2]. Indeed, in such a context, H. von Helmholtz unconscious inferences,which play a crucial role in the passage from sensation to perception, areconsidered in relation to a quantum-like pattern of sensation-perceptiondynamics – quantically treated, in that not based on classical logics –so providing a concrete model for unconscious and consciousness process-ing of information and their interaction. To be precise, in the cognitivemodeling worked out in [21] and [3], if S represents the unconscious infor-mation processing and S ′ the conscious one, then, in the concrete instanceof von Helmholtz’s unconscious inference, S represents just the process-ing of sensation (its unconscious nature having been emphasized as earlyby Hermann von Helmholtz) and S ′ represents processing of perception-conscious representation of sensation. The related experiment performedin [2], then theoretically analyzed in [21] and [3], concerned the bistableperception (of the type S → S ′ ) of the rotation of an ambiguous figure(i.e., the Schr¨oder stair ), which turned out to be different, for each of thethree groups of persons chosen to form statistical test samples, due tothe diversity of data’s contextuality (suitably treatable just by quantumformalism) entailing optical illusions affected by memory biases, and putinto relation with hysteresis effects in [3].On the other hand, following [22], there already existed a wide lit-erature on computational biology works which, since the late of 1990sand the beginnings of 2000s, have put attention to possible hysteresisphenomena (to be meant according to physics and network systems) oc- This just resembles that typical phenomenology involved in sound experiences called intoquestion in explaining Weber-Fechner law ([10]). urring in a large-scale brain network modelled with simple oscillatorypatterns, in particular during state transitions of consciousness and un-consciousness (like in general anesthesia and sleep), with hysteresis ob-served during the loss and recovery of consciousness mediated by patternsof synchronization meant, according to general network systems, as apathway discontinuous transition between incoherent (unconsciousness)and synchronized (consciousness) states of a network that is, the asym-metry between the synchronization and desynchronization paths is justthe key network mechanism of hysteresis. The decreasing/increasing oflong-range network synchronization is considered as a basic neural mech-anism during the loss/recovery of consciousness . Furthermore, networkmechanism of hysteresis is not as a regional brain activity but rather is aglobally conceived mechanism ([22]). This is an remarkable outcome as itproves that (physical) hysteresis is a phenomenon concerning the generalpsychic mechanisms of human brain. In particular, in [22], it has beenproved that hysteresis occurs above all during state transitions around alower lever of consciousness. This justifies the theoretical implementationof a formal model of hysteretic phenomena (regarding physical context)into the p -adic dynamical model of the C − UC pair, as done in [8], wherethe authors have supposed that hysteresis mechanism roles functionallyunconscious realm and the related consciousness processes coming fromit. References [1] S. Albeverio, R. Cianci, A.Yu. Khrennikov, ” P -adic valued quanti-zation”, P-Adic Numbers, Ultrametric Analysis, and Applications, (2), 91-104 (2009).[2] M. Asano, A.Yu. Khrennikov, M. Ohya, Y. Tanaka, I. Yamato,”Violation of contextual generalization of the Leggett-Gargin equal-ity for recognition of ambiguous figures”, Physica Scripta (2014),https://doi.org/10.1088/00318949/2014/t163/014006[3] M. Asano, A. Khrennikov, M. Ohya, Y. Tanakahttps, ”A Hystere-sis Effect on Optical Illusion and Non-Kolmogorovian ProbabilityTheory”, White Noise Analysis and Quantum Information, 201-213(2017), https://doi.org/10.1142/97898132254660015 As authors themselves point out in [22], consciousness and unconsciousness cannot betrivially reduced to, respectively, synchronized and incoherent networks, as it is temporalcoordination, rather than synchrony, to be critical for consciousness. This is also in agreementwith (and provides partial empirical evidence to) what we have stated in [9]. Indeed, in [22], it has been ascertained that functional brain networks become more mod-ular during general anesthesia, in that coordinated and synchronized interactions across thecerebral cortex break down. So, for the aims of large-scale modeling, authors of [22] assumethat the conscious brain will have, in aggregate, more synchronized interactions with respectto the unconscious brain. This is in agreement with the hypothesis, assumed in [22], for which a stronger anesthetics(hence, a deeper unconscious state) induces a larger hysteresis.
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