Journal ArticleDOI

# Reconstructing Plant Connectivity using Directed Spectral Decomposition

01 Jan 2012-IFAC Proceedings Volumes (Elsevier)-Vol. 45, Iss: 15, pp 481-486

TL;DR: In this article, the authors developed a methodology for reconstruction of plant connectivity from dynamic data using directional spectral analysis, a novel adaptation of ideas from neurosciences and econometrics.

AbstractProcess connectivity is a key information that is sought in a diverse set of applications ranging from design to fault diagnosis of engineering and biological processes. The present work develops a methodology for reconstruction of plant connectivity from dynamic data using directional spectral analysis, a novel adaptation of ideas from neurosciences and econometrics. The method is based on the concept of Granger causality while the procedure rests on the directional decomposition of power spectrum into direct and indirect energy transfers. The quantification of effective connectivity is obtained using a structural vector auto-regressive (SVAR) representation of the process. Results from simulation studies demonstrate the potential of the proposed method.

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TL;DR: A new frequency-domain approach to describe the relationships (direction of information flow) between multivariate time series based on the decomposition of multivariate partial coherences computed from multivariate autoregressive models is introduced.
Abstract: Abstract. This paper introduces a new frequency-domain approach to describe the relationships (direction of information flow) between multivariate time series based on the decomposition of multivariate partial coherences computed from multivariate autoregressive models. We discuss its application and compare its performance to other approaches to the problem of determining neural structure relations from the simultaneous measurement of neural electrophysiological signals. The new concept is shown to reflect a frequency-domain representation of the concept of Granger causality.

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Proceedings ArticleDOI
, Fan Yang1, Wei Wang1
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Proceedings ArticleDOI
01 Apr 2017
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### Cites background from "Reconstructing Plant Connectivity u..."

• ...For a link connecting source xj to sink xi, the normalized connectivity strength is defined as [3]...

[...]

• ...gene regulatory networks), neurosciences (for understanding neural connections of the brain), econometrics, climatology [1],[2],[3] etc....

[...]

##### References
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Journal ArticleDOI
TL;DR: In this article, the cross spectrum between two variables can be decomposed into two parts, each relating to a single causal arm of a feedback situation, and measures of causal lag and causal strength can then be constructed.
Abstract: There occurs on some occasions a difficulty in deciding the direction of causality between two related variables and also whether or not feedback is occurring. Testable definitions of causality and feedback are proposed and illustrated by use of simple two-variable models. The important problem of apparent instantaneous causality is discussed and it is suggested that the problem often arises due to slowness in recording information or because a sufficiently wide class of possible causal variables has not been used. It can be shown that the cross spectrum between two variables can be decomposed into two parts, each relating to a single causal arm of a feedback situation. Measures of causal lag and causal strength can then be constructed. A generalisation of this result with the partial cross spectrum is suggested.

14,541 citations

### "Reconstructing Plant Connectivity u..." refers methods in this paper

• ...Connectivity analysis using Granger causality [Granger, 1969] has emerged as a major tool for examining information flow between brain regions [Smith et al., 2011, Baccala and Sameshima, 2001]....

[...]

• ...Granger [1969] adopted Wiener’s ideas to give rise to a practically implementable definition of causality, now known as Granger causality [Granger, 1969]....

[...]

Book ChapterDOI
01 Jan 2001
TL;DR: In this article, it is shown that the cross spectrum between two variables can be decomposed into two parts, each relating to a single causal arm of a feedback situation, and measures of causal lag and causal strength can then be constructed.
Abstract: There occurs on some occasions a difficulty in deciding the direction of causality between two related variables and also whether or not feedback is occurring. Testable definitions of causality and feedback are proposed and illustrated by use of simple two-variable models. The important problem of apparent instantaneous causality is discussed and it is suggested that the problem often arises due to slowness in recordhag information or because a sufficiently wide class of possible causal variables has not been used. It can be shown that the cross spectrum between two variables can be decomposed into two parts, each relating to a single causal arm of a feedback situation. Measures of causal lag and causal strength can then be constructed. A generalization of this result with the partial cross spectrum is suggested.The object of this paper is to throw light on the relationships between certain classes of econometric models involving feedback and the functions arising in spectral analysis, particularly the cross spectrum and the partial cross spectrum. Causality and feedback are here defined in an explicit and testable fashion. It is shown that in the two-variable case the feedback mechanism can be broken down into two causal relations and that the cross spectrum can be considered as the sum of two cross spectra, each closely connected with one of the causations. The next three sections of the paper briefly introduce those aspects of spectral methods, model building, and causality which are required later. Section IV presents the results for the two-variable case and Section V generalizes these results for three variables.

10,077 citations

### "Reconstructing Plant Connectivity u..." refers methods in this paper

• ...Connectivity analysis using Granger causality [Granger, 1969] has emerged as a major tool for examining information flow between brain regions [Smith et al....

[...]

• ...Connectivity analysis using Granger causality [Granger, 1969] has emerged as a major tool for examining information flow between brain regions [Smith et al., 2011, Baccala and Sameshima, 2001]....

[...]

• ...Granger [1969] adopted Wiener’s ideas to give rise to a practically implementable definition of causality, now known as Granger causality [Granger, 1969]....

[...]

Journal Article
21 Mar 1991
TL;DR: In this article, the authors introduce the concept of Stationary Random Processes and Spectral Analysis in the Time Domain and Frequency Domain, and present an analysis of Processes with Mixed Spectra.
Abstract: Preface. Preface to Volume 2. Contents of Volume 2. List of Main Notation. Basic Concepts. Elements of Probability Theory. Stationary Random Processes. Spectral Analysis. Estimation in the Time Domain. Estimation in the Frequency Domain. Spectral Analysis in Practice. Analysis of Processes with Mixed Spectra.

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BookDOI
04 Oct 2007
TL;DR: This reference work and graduate level textbook considers a wide range of models and methods for analyzing and forecasting multiple time series, which include vector autoregressive, cointegrated, vector Autoregressive moving average, multivariate ARCH and periodic processes as well as dynamic simultaneous equations and state space models.
Abstract: This reference work and graduate level textbook considers a wide range of models and methods for analyzing and forecasting multiple time series. The models covered include vector autoregressive, cointegrated, vector autoregressive moving average, multivariate ARCH and periodic processes as well as dynamic simultaneous equations and state space models. Least squares, maximum likelihood, and Bayesian methods are considered for estimating these models. Different procedures for model selection and model specification are treated and a wide range of tests and criteria for model checking are introduced. Causality analysis, impulse response analysis and innovation accounting are presented as tools for structural analysis. The book is accessible to graduate students in business and economics. In addition, multiple time series courses in other fields such as statistics and engineering may be based on it. Applied researchers involved in analyzing multiple time series may benefit from the book as it provides the background and tools for their tasks. It bridges the gap to the difficult technical literature on the topic.

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Book
01 Jan 1997
TL;DR: Getting Started with DSPs 30: Complex Numbers 31: The Complex Fourier Transform 32: The Laplace Transform 33: The z-Transform Chapter 27 Data Compression / JPEG (Transform Compression)
Abstract: In early 1980s, DSP was taught as a graduate level course in electrical engineering. A decade later, DSP had become a standart part of the ungraduate curriculum.

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