Detecting synchronization clusters in multivariate time series via coarse-graining of Markov chains

Synchronization cluster analysis is an approach to the detection of underlying structures in data sets of multivariate time series, starting from a matrix R of bivariate synchronization indices. A previous method utilized the eigenvectors of R for cluster identification, analogous to several recent attempts at group identification using eigenvectors of the correlation matrix. All of these approaches assumed a one-to-one correspondence of dominant eigenvectors and clusters, which has however been shown to be wrong in important cases. We clarify the usefulness of eigenvalue decomposition for synchronization cluster analysis by translating the problem into the language of stochastic processes, and derive an enhanced clustering method harnessing recent insights from the coarse-graining of finite-state Markov processes. We illustrate the operation of our method using a simulated system of coupled Lorenz oscillators, and we demonstrate its superior performance over the previous approach. Finally we investigate the question of robustness of the algorithm against small sample size, which is important with regard to field applications.Comment: Follow-up to arXiv:0706.3375. Journal submission 9 Jul 2007. Published 19 Dec 200

Inverse transformed encoding models - A solution to the problem of correlated trial-by-trial parameter estimates in fMRI decoding

Techniques of multivariate pattern analysis (MVPA) can be used to decode the discrete experimental condition or a continuous modulator variable from measured brain activity during a particular trial. In functional magnetic resonance imaging (fMRI), trial-wise response amplitudes are sometimes estimated from the measured signal using a general linear model (GLM) with one onset regressor for each trial. When using rapid event-related designs with trials closely spaced in time, those estimates are highly variable and serially correlated due to the temporally extended shape of the hemodynamic response function (HRF). Here, we describe inverse transformed encoding modelling (ITEM), a principled approach of accounting for those serial correlations and decoding from the resulting estimates, at low computational cost and with no loss in statistical power. We use simulated data to show that ITEM outperforms the current standard approach in terms of decoding accuracy and analyze empirical data to demonstrate that ITEM is capable of visual reconstruction from fMRI signals

Instantaneous oscillatory direction and phase for multivariate timeseries

This text describes a generalization of the analytic signal (Gabor, 1946) approach for the definition of instantaneous amplitude and phase to the case of multivariate signals. It was originally written as an appendix for another paper, where the determination of the locally dominant oscillatory direction (the instantaneous amplitude) described here is used as a preprocessing step for another kind of data analysis. The text is reproduced in a 'standalone' form because the procedure might prove useful in other contexts too, especially for the purpose of phase synchronization analysis (Rosenblum et al., 1996) between two (or more) multivariate sets of time series (Pascual-Marqui, 2007)

The hollow of being: What can we learn from Merleau-Ponty's ontology for a science of consciousness?

Representative for contemporary attempts to establish a science of consciousness we examine Chalmers' statement and resolution of the "hard problem of consciousness". Agreeing with him that in order to account for subjectivity it is necessary to expand the ontology of the natural sciences, we argue that it is not sufficient to just add conscious experience to the list of fundamental features of the world. Instead, we turn to phenomenology as the philosophy of conscious experience and give an outline of Merleau-Ponty's critique of the objectivist ontology underlying science which excludes subjectivity from the world. We reconstruct his proposal for a revised ontology in The Visible and the Invisible aiming at an extended understanding of Being including subjectivity, which takes on the form of a constellation of new ontological terms centered around the concept of the "flesh of the world". Trying to spell out the consequences of Merleau-Ponty's ontological considerations for scientific practice and especially the science of consciousness, we notice that his philosophy of subjectivity-in-the-world on its part is unable to connect to the insights of the natural sciences. The phenomenological critique of the "hard problem" reveals a deeper disparity which, at present, limits its practical implications

die Theorie selbstreferentieller Systeme und der Konstruktivismus

Einleitung I. Maturana 1\. Der Organismus als autopoietisches System 2\. Die Geschlossenheit des Nervensystems 3\. Kognition, Kommunikation, Beobachtung 4\. Erkenntnis II. Roth 1\. Verhältnis zu Maturana 2\. Neurobiologische Befunde und Konsequenzen 3\. Die Unwirklichkeit der »Realität« 4\. Die Konstruktivität des Wahrnehmungsapparats 5\. Physik als intendierte Realität III. Luhmann 1\. Systemtheorie 2\. Erkenntnistheoretische Überlegungen in den »Sozialen Systemen« 3\. »Operativer Konstruktivismus« Beobachtung–Differenz–Umwelt–Metatheorie Schluß: Konstruktivismus als naturale OntologieDas Thema der Arbeit ist die Frage, welche Konsequenzen im Bereich der Erkenntnistheorie sich aus denjenigen wissenschaftlichen Ansätzen ableiten lassen, die am Begriff des Systems orientiert sind. Ihr Inhalt besteht in der Darstellung systemtheoretischer Konzepte und ihrer erkenntnistheoretischen Konsequenzen bei Maturana, Roth und Luhmann, sowie in deren Kritik auf der Ebene der System- wie auch der Erkenntnistheorie, mit der Absicht, durch eigene Überlegungen einen Beitrag zur Klärung und Fortentwicklung einer systemtheoretisch angeleiteten Erkenntnistheorie zu leisten. Resultate sind, daß die überwiegend konstruktivistische erkenntnistheoretische Haltung der drei Autoren sich nur bedingt mit systemtheoretischen Argumenten rechtfertigen läßt, und daß die zugrundegelegte Theorie selbstreferentieller Systeme generell noch nicht den Stand erreicht hat, auf dem sich zuverlässig Schlüsse ziehen lassen. Abschließend wird kurz die Idee von Systemtheorie als einer »naturalen Ontologie« skizziert.Elektronische Version von 200

MACS - a new SPM toolbox for model assessment, comparison and selection

Background: In cognitive neuroscience, functional magnetic resonance imaging (fMRI) data are widely analyzed using general linear models (GLMs). However, model quality of GLMs for fMRI is rarely assessed, in part due to the lack of formal measures for statistical model inference. New Method: We introduce a new SPM toolbox for model assessment, comparison and selection (MACS) of GLMs applied to fMRI data. MACS includes classical, information-theoretic and Bayesian methods of model assessment previously applied to GLMs for fMRI as well as recent methodological developments of model selection and model averaging in fMRI data analysis. Results: The toolbox - which is freely available from GitHub - directly builds on the Statistical Parametric Mapping (SPM) software package and is easy-to-use, general-purpose, modular, readable and extendable. We validate the toolbox by reproducing model selection and model averaging results from earlier publications. Comparison with Existing Methods: A previous toolbox for model diagnosis in fMRI has been discontinued and other approaches to model comparison between GLMs have not been translated into reusable computational resources in the past. Conclusions: Increased attention on model quality will lead to lower false-positive rates in cognitive neuroscience and increased application of the MACS toolbox will increase the reproducibility of GLM analyses and is likely to increase the replicability of fMRI studies

Eigenvalue Decomposition as a Generalized Synchronization Cluster Analysis

Motivated by the recent demonstration of its use as a tool for the detection and characterization of phase-shape correlations in multivariate time series, we show that eigenvalue decomposition can also be applied to a matrix of indices of bivariate phase synchronization strength. The resulting method is able to identify clusters of synchronized oscillators, and to quantify their strength as well as the degree of involvement of an oscillator in a cluster. Since for the case of a single cluster the method gives similar results as our previous approach, it can be seen as a generalized Synchronization Cluster Analysis, extending its field of application to more complex situations. The performance of the method is tested by applying it to simulation data.Comment: Submitted Oct 2005, accepted Jan 2006, "published" Oct 2007, actually available Jan 200

Robust artifactual independent component classification for BCI practitioners

Objective. EEG artifacts of non-neural origin can be separated from neural signals by independent component analysis (ICA). It is unclear (1) how robustly recently proposed artifact classifiers transfer to novel users, novel paradigms or changed electrode setups, and (2) how artifact cleaning by a machine learning classifier impacts the performance of brain–computer interfaces (BCIs). Approach. Addressing (1), the robustness of different strategies with respect to the transfer between paradigms and electrode setups of a recently proposed classifier is investigated on offline data from 35 users and 3 EEG paradigms, which contain 6303 expert-labeled components from two ICA and preprocessing variants. Addressing (2), the effect of artifact removal on single-trial BCI classification is estimated on BCI trials from 101 users and 3 paradigms. Main results. We show that (1) the proposed artifact classifier generalizes to completely different EEG paradigms. To obtain similar results under massively reduced electrode setups, a proposed novel strategy improves artifact classification. Addressing (2), ICA artifact cleaning has little influence on average BCI performance when analyzed by state-of-the-art BCI methods. When slow motor-related features are exploited, performance varies strongly between individuals, as artifacts may obstruct relevant neural activity or are inadvertently used for BCI control. Significance. Robustness of the proposed strategies can be reproduced by EEG practitioners as the method is made available as an EEGLAB plug-in.EC/FP7/224631/EU/Tools for Brain-Computer Interaction/TOBIBMBF, 01GQ0850, Verbundprojekt: Bernstein Fokus Neurotechnologie - Nichtinvasive Neurotechnologie für Mensch-Maschine Interaktion - Teilprojekte A1, A3, A4, B4, W3, ZentrumDFG, 194657344, EXC 1086: BrainLinks-BrainTool

Exceedance Probabilities for the Dirichlet Distribution

We derive an efficient method to calculate exceedance probabilities (EP) for the Dirichlet distribution when the number of event types is larger than two. Also, we present an intuitive application of Dirichlet EPs and compare our method to a sampling approach which is the current practice in neuroimaging model selection

Kullback-Leibler Divergence for the Normal-Gamma Distribution

We derive the Kullback-Leibler divergence for the normal-gamma distribution and show that it is identical to the Bayesian complexity penalty for the univariate general linear model with conjugate priors. Based on this finding, we provide two applications of the KL divergence, one in simulated and one in empirical data