10,166 research outputs found
Multiscale Analysis of Information Dynamics for Linear Multivariate Processes
In the study of complex physical and physiological systems represented by
multivariate time series, an issue of great interest is the description of the
system dynamics over a range of different temporal scales. While
information-theoretic approaches to the multiscale analysis of complex dynamics
are being increasingly used, the theoretical properties of the applied measures
are poorly understood. This study introduces for the first time a framework for
the analytical computation of information dynamics for linear multivariate
stochastic processes explored at different time scales. After showing that the
multiscale processing of a vector autoregressive (VAR) process introduces a
moving average (MA) component, we describe how to represent the resulting VARMA
process using state-space (SS) models and how to exploit the SS model
parameters to compute analytical measures of information storage and
information transfer for the original and rescaled processes. The framework is
then used to quantify multiscale information dynamics for simulated
unidirectionally and bidirectionally coupled VAR processes, showing that
rescaling may lead to insightful patterns of information storage and transfer
but also to potentially misleading behaviors
Assessing Transfer Entropy in cardiovascular and respiratory time series: A VARFI approach
In the study of complex biomedical systems represented by multivariate stochastic processes, such as the cardiovascular and respiratory systems, an issue of great relevance is the description of the system dynamics spanning multiple temporal scales. Recently, the quantification of multiscale complexity based on linear parametric models, incorporating autoregressive coefficients and fractional integration, encompassing short term dynamics and long-range correlations, was extended to multivariate time series. Within this Vector AutoRegressive Fractionally Integrated (VARFI)
framework formalized for Gaussian processes, in this work we propose to estimate the Transfer Entropy, or equivalently Granger Causality, in the cardiovascular and respiratory systems. This allows to quantify the information flow and assess directed interactions accounting for the simultaneous presence of short-term dynamics and long-range correlations. The proposed approach is first tested on simulations of benchmark VARFI processes where the transfer entropy could be computed from the known model parameters. Then, it is applied to experimental data consisting of heart period, systolic arterial pressure and respiration time series measured in healthy subjects monitored at rest and during mental and postural stress. Both simulations and real data analysis revealed that the proposed method
highlights the dependence of the information transfer on the balance between short-term and longrange correlations in coupled dynamical systems
Multiscale Information Decomposition: Exact Computation for Multivariate Gaussian Processes
Exploiting the theory of state space models, we derive the exact expressions
of the information transfer, as well as redundant and synergistic transfer, for
coupled Gaussian processes observed at multiple temporal scales. All of the
terms, constituting the frameworks known as interaction information
decomposition and partial information decomposition, can thus be analytically
obtained for different time scales from the parameters of the VAR model that
fits the processes. We report the application of the proposed methodology
firstly to benchmark Gaussian systems, showing that this class of systems may
generate patterns of information decomposition characterized by mainly
redundant or synergistic information transfer persisting across multiple time
scales or even by the alternating prevalence of redundant and synergistic
source interaction depending on the time scale. Then, we apply our method to an
important topic in neuroscience, i.e., the detection of causal interactions in
human epilepsy networks, for which we show the relevance of partial information
decomposition to the detection of multiscale information transfer spreading
from the seizure onset zone
Multiscale Granger causality
In the study of complex physical and biological systems represented by
multivariate stochastic processes, an issue of great relevance is the
description of the system dynamics spanning multiple temporal scales. While
methods to assess the dynamic complexity of individual processes at different
time scales are well-established, multiscale analysis of directed interactions
has never been formalized theoretically, and empirical evaluations are
complicated by practical issues such as filtering and downsampling. Here we
extend the very popular measure of Granger causality (GC), a prominent tool for
assessing directed lagged interactions between joint processes, to quantify
information transfer across multiple time scales. We show that the multiscale
processing of a vector autoregressive (AR) process introduces a moving average
(MA) component, and describe how to represent the resulting ARMA process using
state space (SS) models and to combine the SS model parameters for computing
exact GC values at arbitrarily large time scales. We exploit the theoretical
formulation to identify peculiar features of multiscale GC in basic AR
processes, and demonstrate with numerical simulations the much larger
estimation accuracy of the SS approach compared with pure AR modeling of
filtered and downsampled data. The improved computational reliability is
exploited to disclose meaningful multiscale patterns of information transfer
between global temperature and carbon dioxide concentration time series, both
in paleoclimate and in recent years
Multiscale Granger causality analysis by \`a trous wavelet transform
Since interactions in neural systems occur across multiple temporal scales,
it is likely that information flow will exhibit a multiscale structure, thus
requiring a multiscale generalization of classical temporal precedence
causality analysis like Granger's approach. However, the computation of
multiscale measures of information dynamics is complicated by theoretical and
practical issues such as filtering and undersampling: to overcome these
problems, we propose a wavelet-based approach for multiscale Granger causality
(GC) analysis, which is characterized by the following properties: (i) only the
candidate driver variable is wavelet transformed (ii) the decomposition is
performed using the \`a trous wavelet transform with cubic B-spline filter. We
measure GC, at a given scale, by including the wavelet coefficients of the
driver times series, at that scale, in the regression model of the target. To
validate our method, we apply it to publicly available scalp EEG signals, and
we find that the condition of closed eyes, at rest, is characterized by an
enhanced GC among channels at slow scales w.r.t. eye open condition, whilst the
standard Granger causality is not significantly different in the two
conditions.Comment: 4 pages, 3 figure
Measuring center of pressure signals to quantify human balance using multivariate multiscale entropy by designing a force platform
Copyright @ 2013 by the authors; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).To assess the improvement of human body balance, a low cost and portable measuring device of center of pressure (COP), known as center of pressure and complexity monitoring system (CPCMS), has been developed for data logging and analysis. In order to prove that the system can estimate the different magnitude of different sways in comparison with the commercial Advanced Mechanical Technology Incorporation (AMTI) system, four sway tests have been developed (i.e., eyes open, eyes closed, eyes open with water pad, and eyes closed with water pad) to produce different sway displacements. Firstly, static and dynamic tests were conducted to investigate the feasibility of the system. Then, correlation tests of the CPCMS and AMTI systems have been compared with four sway tests. The results are within the acceptable range. Furthermore, multivariate empirical mode decomposition (MEMD) and enhanced multivariate multiscale entropy (MMSE) analysis methods have been used to analyze COP data reported by the CPCMS and compare it with the AMTI system. The improvements of the CPCMS are 35% to 70% (open eyes test) and 60% to 70% (eyes closed test) with and without water pad. The AMTI system has shown an improvement of 40% to 80% (open eyes test) and 65% to 75% (closed eyes test). The results indicate that the CPCMS system can achieve similar results to the commercial product so it can determine the balance.National Science Council (NSC) of Taiwan and the Center for Dynamical Biomarkers and Translational Medicine, National Central University, Taiwan (which is sponsored by the NSC)
Detecting single-trial EEG evoked potential using a wavelet domain linear mixed model: application to error potentials classification
Objective. The main goal of this work is to develop a model for multi-sensor
signals such as MEG or EEG signals, that accounts for the inter-trial
variability, suitable for corresponding binary classification problems. An
important constraint is that the model be simple enough to handle small size
and unbalanced datasets, as often encountered in BCI type experiments.
Approach. The method involves linear mixed effects statistical model, wavelet
transform and spatial filtering, and aims at the characterization of localized
discriminant features in multi-sensor signals. After discrete wavelet transform
and spatial filtering, a projection onto the relevant wavelet and spatial
channels subspaces is used for dimension reduction. The projected signals are
then decomposed as the sum of a signal of interest (i.e. discriminant) and
background noise, using a very simple Gaussian linear mixed model. Main
results. Thanks to the simplicity of the model, the corresponding parameter
estimation problem is simplified. Robust estimates of class-covariance matrices
are obtained from small sample sizes and an effective Bayes plug-in classifier
is derived. The approach is applied to the detection of error potentials in
multichannel EEG data, in a very unbalanced situation (detection of rare
events). Classification results prove the relevance of the proposed approach in
such a context. Significance. The combination of linear mixed model, wavelet
transform and spatial filtering for EEG classification is, to the best of our
knowledge, an original approach, which is proven to be effective. This paper
improves on earlier results on similar problems, and the three main ingredients
all play an important role
Reduction of dynamical biochemical reaction networks in computational biology
Biochemical networks are used in computational biology, to model the static
and dynamical details of systems involved in cell signaling, metabolism, and
regulation of gene expression. Parametric and structural uncertainty, as well
as combinatorial explosion are strong obstacles against analyzing the dynamics
of large models of this type. Multi-scaleness is another property of these
networks, that can be used to get past some of these obstacles. Networks with
many well separated time scales, can be reduced to simpler networks, in a way
that depends only on the orders of magnitude and not on the exact values of the
kinetic parameters. The main idea used for such robust simplifications of
networks is the concept of dominance among model elements, allowing
hierarchical organization of these elements according to their effects on the
network dynamics. This concept finds a natural formulation in tropical
geometry. We revisit, in the light of these new ideas, the main approaches to
model reduction of reaction networks, such as quasi-steady state and
quasi-equilibrium approximations, and provide practical recipes for model
reduction of linear and nonlinear networks. We also discuss the application of
model reduction to backward pruning machine learning techniques
- âŠ