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Measures of time series coupling based on generalized weighted multiple regression


Pascual-Marqui, Roberto D; Biscay, Rolando J; Bosch-Bayard, Jorge; Faber, Pascal; Kinoshita, Toshihiko; Kochi, Kieko; Milz, Patricia; Nishida, Keiichiro; Yoshimura, Masafumi (2017). Measures of time series coupling based on generalized weighted multiple regression. bioRxiv 235721, University of Zurich.

Abstract

The sharing and the transmission of information between cortical brain regions is carried out by mechanisms that are still not fully understood. A deeper understanding should shed light on how consciousness and cognition are implemented in the brain. Research activity in this field has recently been focusing on the discovery of non-conventional coupling mechanisms, such as all forms of cross-frequency couplings between diverse combinations of amplitudes and phases, applied to measured or estimated cortical signals of electric neuronal activity. However, all coupling measures that involve phase computation have poor statistical properties. In this work, the conventional estimators for the well-known phase-phase (phase synchronization or locking), phase-amplitude, and phase-amplitude-amplitude couplings are generalized by means of the weighted multiple regression model. The choice of appropriate weights produces estimators that bypass the need for computing the complex-valued phase. In addition, a new coupling, denoted as the inhibitory coupling (InhCo), is introduced and defined as the dependence of one complex-valued variable on the inverse and on the conjugate inverse of another complex-valued variable. A weighted version denoted as wInhCo is also introduced, bypassing the need for computing the inverse of a complex variable, which has very poor statistical properties. The importance of this form of inhibitory coupling is that it may capture well-known processes, such as the observed inverse alpha/gamma relation within the same cortical region, or the inverse alpha/alpha relation between distant cortical regions.

Abstract

The sharing and the transmission of information between cortical brain regions is carried out by mechanisms that are still not fully understood. A deeper understanding should shed light on how consciousness and cognition are implemented in the brain. Research activity in this field has recently been focusing on the discovery of non-conventional coupling mechanisms, such as all forms of cross-frequency couplings between diverse combinations of amplitudes and phases, applied to measured or estimated cortical signals of electric neuronal activity. However, all coupling measures that involve phase computation have poor statistical properties. In this work, the conventional estimators for the well-known phase-phase (phase synchronization or locking), phase-amplitude, and phase-amplitude-amplitude couplings are generalized by means of the weighted multiple regression model. The choice of appropriate weights produces estimators that bypass the need for computing the complex-valued phase. In addition, a new coupling, denoted as the inhibitory coupling (InhCo), is introduced and defined as the dependence of one complex-valued variable on the inverse and on the conjugate inverse of another complex-valued variable. A weighted version denoted as wInhCo is also introduced, bypassing the need for computing the inverse of a complex variable, which has very poor statistical properties. The importance of this form of inhibitory coupling is that it may capture well-known processes, such as the observed inverse alpha/gamma relation within the same cortical region, or the inverse alpha/alpha relation between distant cortical regions.

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Additional indexing

Item Type:Working Paper
Communities & Collections:04 Faculty of Medicine > Psychiatric University Hospital Zurich > Clinic for Psychiatry, Psychotherapy, and Psychosomatics
04 Faculty of Medicine > The KEY Institute for Brain-Mind Research
Dewey Decimal Classification:610 Medicine & health
Language:English
Date:18 December 2017
Deposited On:10 Jan 2018 15:07
Last Modified:19 Feb 2018 10:06
Series Name:bioRxiv
OA Status:Hybrid
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1101/235721

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