Analysis of spatiotemporal signals of complex systems

Uhl, Christian; Friedrich, Rudolf; Haken, Hermann

doi:10.1103/physreve.51.3890

Cited by 37 publications

(12 citation statements)

References 21 publications

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“…The number of nonzero eigenvalues of the matrix C ij represents the number of orthogonal components that can express the recorded 18-dimensional vector. The optimality of the K-L method reduces the amount of information about a signal down to a reasonable number of independent eigenvalues that represent important characteristic features of the signal (Broomhead and King 1986;Uhl et al 1995;Haken 1996). The first principal eigenvalue is taken to be along the direction with the maximum variance.…”

Section: Determining the Modesmentioning

confidence: 99%

Coordination modes in the multisegmental dynamics of hula hooping

Balasubramaniam

Turvey

2004

Biological Cybernetics

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In hula hooping, organized motions of the body keep the hoop in stable oscillatory motion parallel to the ground. We examined the hypothesis that the multiple degrees of freedom (DF) of the lower limbs in producing the oscillations are resolved into a few control DF. The Karhunen-Loève decomposition was applied to the kinematics of the lower limbs in three experiments in which oscillation amplitude and frequency were manipulated. Kinematic variance was accommodated by two modes whose relative contributions varied with task parameters. Complementary analyses of interjoint Hilbert relative phase suggested a lower-limb organization into a vertical suspension mode and an oscillatory fore-aft mode. These modes might stabilize the hoop's angular momentum by controlling, respectively, its vertical and horizontal components.

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Section: Determining the Modesmentioning

confidence: 99%

Coordination modes in the multisegmental dynamics of hula hooping

Balasubramaniam

Turvey

2004

Biological Cybernetics

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“…However, despite the great variety of methods that have been developed, they generally suffer from significant limitations because they adopt (sometimes explicitly but often implicitly) ad hoc procedures predicated on characteristics of the data that are often not true, such as Gaussianity and linearity, or unsupported, such as the independence of the signal sources. Other procedures based on very specific models of dynamical systems (such as least-squared with the assumption that a system is near a critical point [28, 29]) lack the generality that enables their use in other applications. These deficiencies become more acute as the capabilities of the instrumentation increases and the measurements become more sensitive to complex and subtle spatio-temporal variations in the observed physical systems.…”

Section: Introductionmentioning

confidence: 99%

Detecting spatio-temporal modes in multivariate data by entropy field decomposition

Frank

Galinsky

2016

J. Phys. A: Math. Theor.

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A new data analysis method that addresses a general problem of detecting spatio-temporal variations in multivariate data is presented. The method utilizes two recent and complimentary general approaches to data analysis, information field theory (IFT) and entropy spectrum pathways (ESP). Both methods reformulate and incorporate Bayesian theory, thus use prior information to uncover underlying structure of the unknown signal. Unification of ESP and IFT creates an approach that is non-Gaussian and non-linear by construction and is found to produce unique spatio-temporal modes of signal behavior that can be ranked according to their significance, from which space-time trajectories of parameter variations can be constructed and quantified. Two brief examples of real world applications of the theory to the analysis of data bearing completely different, unrelated nature, lacking any underlying similarity, are also presented. The first example provides an analysis of resting state functional magnetic resonance imaging (rsFMRI) data that allowed us to create an efficient and accurate computational method for assessing and categorizing brain activity. The second example demonstrates the potential of the method in the application to the analysis of a strong atmospheric storm circulation system during the complicated stage of tornado development and formation using data recorded by a mobile Doppler radar. Reference implementation of the method will be made available as a part of the QUEST toolkit that is currently under development at the Center for Scientific Computation in Imaging.

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“…The analysis problem presented by rsFMRI data is, in some sense, a classic example of a data analysis problem that has become ubiquitous with the advancement of modern scientific instruments and been addressed by a range of methods (Ghil et al, 2002; Christakos, 1991; Plis et al, 2007; Min & Wynter, 2011; Wallace, Smith, & Bretherton, 1992; Lamus, Haemaelaeinen, Temereanca, Brown, & Purdon, 2012; Bijma, de Munck, & Heethaar, 2005; Plaut & Vautard, 1994; Uhl, Friedrich, & Haken, 1995, 1993). These data consist of high spatial and temporal resolution noisy volumes within which non-linear and non-Gaussian processes produce complicated signal fluctuations.…”

Section: Discussionmentioning

confidence: 99%

Dynamic Multiscale Modes of Resting State Brain Activity Detected by Entropy Field Decomposition

Frank

Galinsky

2016

Neural Computation

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The ability of functional magnetic resonance imaging (FMRI) to non-invasively measure fluctuations in brain activity in the absence of an applied stimulus offers the possibility of discerning functional networks in the “resting state” of the brain. However, the reconstruction of brain networks from these signal fluctuations poses a significant challenge because they are generally non-linear, non-Gaussian, and can overlap in both their spatial and temporal extent. Moreover, because there is no explicit input stimulus there is no signal model with which to compare the brain responses. A variety of techniques have been devised to address this problem but the predominant approaches are based on the presupposition of statistical properties of complex brain signal parameters which are unprovable but facilitate the analysis. In this paper we address this problem with a new method called the entropy field decomposition for estimating structure within spatio-temporal data. This method is based upon a general information field theoretic formulation of Bayesian probability theory incorporating prior coupling information that allows the enumeration of the most probable parameter configurations without the need for unjustified statistical assumptions. This approach facilitates the construction of brain activation modes directly from the spatial-temporal correlation structure of the data. These modes and their associated spatial-temporal correlation structure can then be used to generate space-time activity probability trajectories called functional connectivity pathways which provide a characterization of functional brain networks.

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Analysis of spatiotemporal signals of complex systems

Cited by 37 publications

References 21 publications

Coordination modes in the multisegmental dynamics of hula hooping

Coordination modes in the multisegmental dynamics of hula hooping

Detecting spatio-temporal modes in multivariate data by entropy field decomposition

Dynamic Multiscale Modes of Resting State Brain Activity Detected by Entropy Field Decomposition

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