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## Frequency Domain Connectivity Identification: An Application of Partial Directed Coherence in fMRI

SATO, Joao R.; TAKAHASHI, Daniel Y.; ARCURI, Silvia M.; Sameshima, Koichi; MORETTIN, Pedro A.; Baccala, Luiz Antonio
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
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Functional magnetic resonance imaging (fMRI) has become an important tool in Neuroscience due to its noninvasive and high spatial resolution properties compared to other methods like PET or EEG. Characterization of the neural connectivity has been the aim of several cognitive researches, as the interactions among cortical areas lie at the heart of many brain dysfunctions and mental disorders. Several methods like correlation analysis, structural equation modeling, and dynamic causal models have been proposed to quantify connectivity strength. An important concept related to connectivity modeling is Granger causality, which is one of the most popular definitions for the measure of directional dependence between time series. In this article, we propose the application of the partial directed coherence (PDC) for the connectivity analysis of multisubject fMRI data using multivariate bootstrap. PDC is a frequency domain counterpart of Granger causality and has become a very prominent tool in EEG studies. The achieved frequency decomposition of connectivity is useful in separating interactions from neural modules from those originating in scanner noise, breath, and heart beating. Real fMRI dataset of six subjects executing a language processing protocol was used for the analysis of connectivity. Hum Brain Mapp 30:452-461...

## Analyzing the connectivity between regions of interest: An approach based on cluster Granger causality for NRI data analysis

SATO, Joao R.; FUJITA, Andre; CARDOSO, Elisson F.; THOMAZ, Carlos E.; BRAMMER, Michael J.; AMARO JR., Edson
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
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The identification, modeling, and analysis of interactions between nodes of neural systems in the human brain have become the aim of interest of many studies in neuroscience. The complex neural network structure and its correlations with brain functions have played a role in all areas of neuroscience, including the comprehension of cognitive and emotional processing. Indeed, understanding how information is stored, retrieved, processed, and transmitted is one of the ultimate challenges in brain research. In this context, in functional neuroimaging, connectivity analysis is a major tool for the exploration and characterization of the information flow between specialized brain regions. In most functional magnetic resonance imaging (fMRI) studies, connectivity analysis is carried out by first selecting regions of interest (ROI) and then calculating an average BOLD time series (across the voxels in each cluster). Some studies have shown that the average may not be a good choice and have suggested, as an alternative, the use of principal component analysis (PCA) to extract the principal eigen-time series from the ROI(s). In this paper, we introduce a novel approach called cluster Granger analysis (CGA) to study connectivity between ROIs. The main aim of this method was to employ multiple eigen-time series in each ROI to avoid temporal information loss during identification of Granger causality. Such information loss is inherent in averaging (e.g....

## Functional clustering of time series gene expression data by Granger causality

Fujita, André; Severino, Patricia ; Kojima, Kaname ; Sato, João ; Patriota, Alexandre Galvão; Miyano, Satoru
Fonte: BioMed Central; London Publicador: BioMed Central; London
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
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Background: A common approach for time series gene expression data analysis includes the clustering of genes with similar expression patterns throughout time. Clustered gene expression proﬁles point to the joint contribution of groups of genes to a particular cellular process. However, since genes belong to intricate networks, other features, besides comparable expression patterns, should provide additional information for the identiﬁcation of functionally similar genes. Results: In this study we perform gene clustering through the identiﬁcation of Granger causality between and within sets of time series gene expression data. Granger causality is based on the idea that the cause of an event cannot come after its consequence. Conclusions: This kind of analysis can be used as a complementary approach for functional clustering, wherein genes would be clustered not solely based on their expression similarity but on their topological proximity built according to the intensity of Granger causality among them.; The supercomputing resource was provided by Human Genome Center (Univ. of Tokyo). This work was supported by FAPESP and CNPq - Brazil and RIKEN - Japan.

## O efeito de contágio (spill-over) entre os mercados bolsistas

Costa, Ana Sofia Casimiro da
Fonte: Instituto Universitário de Lisboa Publicador: Instituto Universitário de Lisboa
Relevância na Pesquisa
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## Analyzing Information Flow in Brain Networks with Nonparametric Granger Causality

Dhamala, Mukeshwar; Rangarajan, Govindan; Ding, Mingzhou
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
46.91%
Multielectrode neurophysiological recording and high-resolution neuroimaging generate multivariate data that are the basis for understanding the patterns of neural interactions. How to extract directions of information flow in brain networks from these data remains a key challenge. Research over the last few years has identified Granger causality as a statistically principled technique to furnish this capability. The estimation of Granger causality currently requires autoregressive modeling of neural data. Here, we propose a nonparametric approach based on widely used Fourier and wavelet transforms to estimate Granger causality, eliminating the need of explicit autoregressive data modeling. We demonstrate the effectiveness of this approach by applying it to synthetic data generated by network models with known connectivity and to local field potentials recorded from monkeys performing a sensorimotor task.

## Assessing and Compensating for Zero-lag Correlation Effects in Time-lagged Granger Causality Analysis of fMRI

Deshpande, Gopikrishna; Sathian, K.; Hu, Xiaoping
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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Effective connectivity in brain networks can be studied using Granger causality analysis which is based on temporal precedence, while functional connectivity is usually derived using zero-lag correlation. Due to the smoothing of the neuronal activity by the hemodynamic response inherent in the functional magnetic resonance imaging (fMRI) acquisition process, Granger causality, as normally computed from fMRI data, may be contaminated by zero-lag correlation. Simulations performed in this work showed that the zero-lag correlation does “leak” into estimates of time-lagged causality. To eliminate this leak, we introduce a method in which the zero-lag influences are explicitly modeled in the vector autoregressive model but omitted while calculating Granger causality. The effectiveness of this method is demonstrated using fMRI data obtained from healthy humans performing a verbal working memory task.

## Granger Causality Analysis of Steady-State Electroencephalographic Signals during Propofol-Induced Anaesthesia

Barrett, Adam B.; Murphy, Michael; Bruno, Marie-Aurélie; Noirhomme, Quentin; Boly, Mélanie; Laureys, Steven; Seth, Anil K.
Fonte: Public Library of Science Publicador: Public Library of Science
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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Changes in conscious level have been associated with changes in dynamical integration and segregation among distributed brain regions. Recent theoretical developments emphasize changes in directed functional (i.e., causal) connectivity as reflected in quantities such as ‘integrated information’ and ‘causal density’. Here we develop and illustrate a rigorous methodology for assessing causal connectivity from electroencephalographic (EEG) signals using Granger causality (GC). Our method addresses the challenges of non-stationarity and bias by dividing data into short segments and applying permutation analysis. We apply the method to EEG data obtained from subjects undergoing propofol-induced anaesthesia, with signals source-localized to the anterior and posterior cingulate cortices. We found significant increases in bidirectional GC in most subjects during loss-of-consciousness, especially in the beta and gamma frequency ranges. Corroborating a previous analysis we also found increases in synchrony in these ranges; importantly, the Granger causality analysis showed higher inter-subject consistency than the synchrony analysis. Finally, we validate our method using simulated data generated from a model for which GC values can be analytically derived. In summary...

## Upsampling to 400-ms Resolution for Assessing Effective Connectivity in Functional Magnetic Resonance Imaging Data with Granger Causality

McFarlin, Daniel R.; Kerr, Deborah L.; Nitschke, Jack B.
Fonte: Mary Ann Liebert, Inc. Publicador: Mary Ann Liebert, Inc.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.91%
Granger causality analysis of functional magnetic resonance imaging (fMRI) blood-oxygen-level-dependent signal data allows one to infer the direction and magnitude of influence that brain regions exert on one another. We employed a method for upsampling the time resolution of fMRI data that does not require additional interpolation beyond the interpolation that is regularly used for slice-timing correction. The mathematics for this new method are provided, and simulations demonstrate its viability. Using fMRI, 17 snake phobics and 19 healthy controls viewed snake, disgust, and neutral fish video clips preceded by anticipatory cues. Multivariate Granger causality models at the native 2-sec resolution and at the upsampled 400-ms resolution assessed directional associations of fMRI data among 13 anatomical regions of interest identified in prior research on anxiety and emotion. Superior sensitivity was observed for the 400-ms model, both for connectivity within each group and for group differences in connectivity. Context-dependent analyses for the 400-ms multivariate Granger causality model revealed the specific trial types showing group differences in connectivity. This is the first demonstration of effective connectivity of fMRI data using a method for achieving 400-ms resolution without sacrificing accuracy available at 2-sec resolution.

## Multivariate Granger causality: an estimation framework based on factorization of the spectral density matrix

Wen, Xiaotong; Rangarajan, Govindan; Ding, Mingzhou
Fonte: The Royal Society Publishing Publicador: The Royal Society Publishing
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.91%
Granger causality is increasingly being applied to multi-electrode neurophysiological and functional imaging data to characterize directional interactions between neurons and brain regions. For a multivariate dataset, one might be interested in different subsets of the recorded neurons or brain regions. According to the current estimation framework, for each subset, one conducts a separate autoregressive model fitting process, introducing the potential for unwanted variability and uncertainty. In this paper, we propose a multivariate framework for estimating Granger causality. It is based on spectral density matrix factorization and offers the advantage that the estimation of such a matrix needs to be done only once for the entire multivariate dataset. For any subset of recorded data, Granger causality can be calculated through factorizing the appropriate submatrix of the overall spectral density matrix.

## Increasing fMRI Sampling Rate Improves Granger Causality Estimates

Lin, Fa-Hsuan; Ahveninen, Jyrki; Raij, Tommi; Witzel, Thomas; Chu, Ying-Hua; Jääskeläinen, Iiro P.; Tsai, Kevin Wen-Kai; Kuo, Wen-Jui; Belliveau, John W.
Fonte: Public Library of Science Publicador: Public Library of Science
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.96%
Estimation of causal interactions between brain areas is necessary for elucidating large-scale functional brain networks underlying behavior and cognition. Granger causality analysis of time series data can quantitatively estimate directional information flow between brain regions. Here, we show that such estimates are significantly improved when the temporal sampling rate of functional magnetic resonance imaging (fMRI) is increased 20-fold. Specifically, healthy volunteers performed a simple visuomotor task during blood oxygenation level dependent (BOLD) contrast based whole-head inverse imaging (InI). Granger causality analysis based on raw InI BOLD data sampled at 100-ms resolution detected the expected causal relations, whereas when the data were downsampled to the temporal resolution of 2 s typically used in echo-planar fMRI, the causality could not be detected. An additional control analysis, in which we SINC interpolated additional data points to the downsampled time series at 0.1-s intervals, confirmed that the improvements achieved with the real InI data were not explainable by the increased time-series length alone. We therefore conclude that the high-temporal resolution of InI improves the Granger causality connectivity analysis of the human brain.

## Increasing fMRI Sampling Rate Improves Granger Causality Estimates

Lin, Fa-Hsuan; Ahveninen, Jyrki; Raij, Tommi; Witzel, Thomas; Chu, Ying-Hua; Jääskeläinen, Iiro P.; Tsai, Kevin Wen-Kai; Kuo, Wen-Jui; Belliveau, John W.
Fonte: Public Library of Science Publicador: Public Library of Science
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
46.96%
Estimation of causal interactions between brain areas is necessary for elucidating large-scale functional brain networks underlying behavior and cognition. Granger causality analysis of time series data can quantitatively estimate directional information flow between brain regions. Here, we show that such estimates are significantly improved when the temporal sampling rate of functional magnetic resonance imaging (fMRI) is increased 20-fold. Specifically, healthy volunteers performed a simple visuomotor task during blood oxygenation level dependent (BOLD) contrast based whole-head inverse imaging (InI). Granger causality analysis based on raw InI BOLD data sampled at 100-ms resolution detected the expected causal relations, whereas when the data were downsampled to the temporal resolution of 2 s typically used in echo-planar fMRI, the causality could not be detected. An additional control analysis, in which we SINC interpolated additional data points to the downsampled time series at 0.1-s intervals, confirmed that the improvements achieved with the real InI data were not explainable by the increased time-series length alone. We therefore conclude that the high-temporal resolution of InI improves the Granger causality connectivity analysis of the human brain.

## Short and long run causality measures: theory and inference

Dufour, Jean-Marie; Taamouti, Abderrahim
Tipo: info:eu-repo/semantics/workingPaper; info:eu-repo/semantics/workingPaper Formato: application/pdf
Relevância na Pesquisa
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The concept of causality introduced by Wiener (1956) and Granger (1969) is defined in terms of predictability one period ahead. This concept can be generalized by considering causality at a given horizon h, and causality up to any given horizon h [Dufour and Renault (1998)]. This generalization is motivated by the fact that, in the presence of an auxiliary variable vector Z, it is possible that a variable Y does not cause variable X at horizon 1, but causes it at horizon h > 1. In this case, there is an indirect causality transmitted by Z. Another related problem consists in measuring the importance of causality between two variables. Existing causality measures have been defined only for the horizon 1 and fail to capture indirect causal effects. This paper proposes a generalization of such measures for any horizon h. We propose nonparametric and parametric measures of unidirectional and instantaneous causality at any horizon h. Parametric measures are defined in the context of autoregressive processes of unknown order and expressed in terms of impulse response coefficients. On noting that causality measures typically involve complex functions of model parameters in VAR and VARMA models, we propose a simple method to evaluate these measures which is based on the simulation of a large sample from the process of interest. We also describe asymptotically valid nonparametric confidence intervals...

## Carbonomics of the Bangladesh agricultural output: Causality and long-run equilibrium

Fonte: Emerald Group Publishing Ltd Publicador: Emerald Group Publishing Ltd
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.84%

## Kernel Granger causality and the analysis of dynamical networks

Marinazzo, Daniele; Pellicoro, Mario; Stramaglia, Sebastiano
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
46.96%
We propose a method of analysis of dynamical networks based on a recent measure of Granger causality between time series, based on kernel methods. The generalization of kernel Granger causality to the multivariate case, here presented, shares the following features with the bivariate measures: (i) the nonlinearity of the regression model can be controlled by choosing the kernel function and (ii) the problem of false-causalities, arising as the complexity of the model increases, is addressed by a selection strategy of the eigenvectors of a reduced Gram matrix whose range represents the additional features due to the second time series. Moreover, there is no {\it a priori} assumption that the network must be a directed acyclic graph. We apply the proposed approach to a network of chaotic maps and to a simulated genetic regulatory network: it is shown that the underlying topology of the network can be reconstructed from time series of node's dynamics, provided that a sufficient number of samples is available. Considering a linear dynamical network, built by preferential attachment scheme, we show that for limited data use of bivariate Granger causality is a better choice w.r.t methods using $L1$ minimization. Finally we consider real expression data from HeLa cells...

## Synergy, redundancy and unnormalized Granger causality

Stramaglia, Sebastiano; Angelini, Leonardo; Cortés, Jesus M.; Marinazzo, Daniele
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
47.01%
We analyze by means of Granger causality the effect of synergy and redundancy in the inference (from time series data) of the information flow between subsystems of a complex network. Whilst fully conditioned Granger causality is not affected by synergy, the pairwise analysis fails to put in evidence synergetic effects. We show that maximization of the total Granger causality to a given target, over all the possible partitions of the set of driving variables, puts in evidence redundant multiplets of variables influencing the target, provided that an {\it unnormalized} definition of Granger causality is adopted. Along the same lines we also introduce a pairwise index of synergy (w.r.t. to information flow to a third variable) which is zero when two independent sources additively influence a common target, differently from previous definitions of synergy.; Comment: 2 figures

## Kernel method for nonlinear Granger causality

Marinazzo, Daniele; Pellicoro, Mario; Stramaglia, Sebastiano
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
46.85%
Important information on the structure of complex systems, consisting of more than one component, can be obtained by measuring to which extent the individual components exchange information among each other. Such knowledge is needed to reach a deeper comprehension of phenomena ranging from turbulent fluids to neural networks, as well as complex physiological signals. The linear Granger approach, to detect cause-effect relationships between time series, has emerged in recent years as a leading statistical technique to accomplish this task. Here we generalize Granger causality to the nonlinear case using the theory of reproducing kernel Hilbert spaces. Our method performs linear Granger causality in the feature space of suitable kernel functions, assuming arbitrary degree of nonlinearity. We develop a new strategy to cope with the problem of overfitting, based on the geometry of reproducing kernel Hilbert spaces. Applications to coupled chaotic maps and physiological data sets are presented.; Comment: Revised version, accepted for publication on Physical Review Letters

## Frequency decomposition of conditional Granger causality and application to multivariate neural field potential data

Chen, Yonghong; Bressler, Steven L.; Ding, Mingzhou
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
47.01%
It is often useful in multivariate time series analysis to determine statistical causal relations between different time series. Granger causality is a fundamental measure for this purpose. Yet the traditional pairwise approach to Granger causality analysis may not clearly distinguish between direct causal influences from one time series to another and indirect ones acting through a third time series. In order to differentiate direct from indirect Granger causality, a conditional Granger causality measure in the frequency domain is derived based on a partition matrix technique. Simulations and an application to neural field potential time series are demonstrated to validate the method.; Comment: 18 pages, 6 figures, Journal published

## Granger Causality: Basic Theory and Application to Neuroscience

Ding, Mingzhou; Chen, Yonghong; Bressler, Steven L.
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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Multi-electrode neurophysiological recordings produce massive quantities of data. Multivariate time series analysis provides the basic framework for analyzing the patterns of neural interactions in these data. It has long been recognized that neural interactions are directional. Being able to assess the directionality of neuronal interactions is thus a highly desired capability for understanding the cooperative nature of neural computation. Research over the last few years has shown that Granger causality is a key technique to furnish this capability. The main goal of this article is to provide an expository introduction to the concept of Granger causality. Mathematical frameworks for both bivariate Granger causality and conditional Granger causality are developed in detail with particular emphasis on their spectral representations. The technique is demonstrated in numerical examples where the exact answers of causal influences are known. It is then applied to analyze multichannel local field potentials recorded from monkeys performing a visuomotor task. Our results are shown to be physiologically interpretable and yield new insights into the dynamical organization of large-scale oscillatory cortical networks.

## Validity of time reversal for testing Granger causality

Winkler, Irene; Panknin, Danny; Bartz, Daniel; Müller, Klaus-Robert; Haufe, Stefan
Tipo: Artigo de Revista Científica
This paper seeks to examine the dynamic causal relations between the two major financial assets, stock prices of the US and South Africa and the rand/US$exchange rate. The study uses a mixed bag of time series approaches such as cointegration, Granger causality, impulse response functions and forecasting error variance decompositions. The paper identifies a bi-directional causality from the Standard & Poor's 500 stock price index to the rand/US$ exchange rate in the Granger sense. It was also found that the Standard & Poor's stock price index accounts for a significant portion of the variations in the Johannesburg Stock Exchange's All Share index. Thus, while causality in the Granger sense could not be established for the relationship between the price indices of the two stock exchanges it can argued that there is some relationship between them. The results of the study have implications for both business and Government.