A statistical modeling framework for detecting nonlinear synchronization

Abstract

Event Abstract Back to Event A statistical modeling framework for detecting nonlinear synchronization Johannes Schumacher1*, Gordon Pipa1 and Robert Haslinger2 1 University of Osnabrück, Germany 2 MIT, United States During sensory processing, the cortex exhibits complex dynamics that can lead to nonlinear dependencies in the data, defying detection by linear methods. In studies with coupled chaotic systems, analytical concepts have been found to describe such interactions. These include phase, lag, or generalized synchronization, which can be expressed by a nonlinear functional relationship y = H(x) between two systems x(t) and y(t) that explicitly allows time-delays. We present a method to detect nonlinear synchronization between time series x(t) and y(t) in a framework of generative statistical modeling. Volterra series are used to approximate the functional H. The kernels are modeled using cubic splines. Maximum likelihood regression with elastic net regularization fits the model to the data and enforces sparse parameter distributions. The method is computationally efficient and allows to determine the goodness-of-fit, as well as model comparison. To detect nonlinear interaction, an auxiliary signal y' is created by the model and compared to the target signal y. In addition to detection, a high goodness-of-fit yields a fully predictive model that allows decoding and the generation of new data. We evaluated the method on coupled chaotic systems. Presented are results for generalized synchronized rings of delay-coupled Mackey-Glass systems, as well as 1:1 phase synchronized coupled Rössler systems. Furthermore, we show experimentally that m:n synchronization is in principle detectable by the method, while analytically full Volterra series models are limited to 1:m synchronization. As work in progress, the applicability to neuroscientific data is demonstrated using monkey V1 single cell recordings obtained during presentation of natural scene movies. Funding: Supported by European project PHOCUS funded by the Emerging Technologies (FET) program within the Seventh Framework Program for Research of the European Commission. Keywords: Brain Signals, synchronization Conference: XI International Conference on Cognitive Neuroscience (ICON XI), Palma, Mallorca, Spain, 25 Sep - 29 Sep, 2011. Presentation Type: Poster Presentation Topic: Poster Sessions: Modeling and Analysis of Brain Signals Citation: Schumacher J, Pipa G and Haslinger R (2011). A statistical modeling framework for detecting nonlinear synchronization. Conference Abstract: XI International Conference on Cognitive Neuroscience (ICON XI). doi: 10.3389/conf.fnhum.2011.207.00178 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 18 Nov 2011; Published Online: 28 Nov 2011. * Correspondence: Ms. Johannes Schumacher, University of Osnabrück, Osnabrück, Germany, joschuma@uos.de Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Johannes Schumacher Gordon Pipa Robert Haslinger Google Johannes Schumacher Gordon Pipa Robert Haslinger Google Scholar Johannes Schumacher Gordon Pipa Robert Haslinger PubMed Johannes Schumacher Gordon Pipa Robert Haslinger Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.