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Related Concept Videos

Linear time-invariant Systems01:23

Linear time-invariant Systems

A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
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Time-Series Graph00:54

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A time-series graph is a line graph with repeated measurements taken at successive intervals of time. It is also called a time series chart. To construct a time-series graph, one must look at both pieces of a paired data set. The horizontal axis is used to plot the time increments, and the vertical axis is used to plot the values of the variable that one is measuring. By using the axes in this way, each point on the graph will correspond to time and a measured quantity. The points on the graph...
Multi-input and Multi-variable systems01:22

Multi-input and Multi-variable systems

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Classification of Systems-I01:26

Classification of Systems-I

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Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

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Related Experiment Video

Updated: May 30, 2026

Cross-Modal Multivariate Pattern Analysis
13:51

Cross-Modal Multivariate Pattern Analysis

Published on: November 9, 2011

Uniform approach to linear and nonlinear interrelation patterns in multivariate time series.

Christian Rummel1, Eugenio Abela, Markus Müller

  • 1Support Center for Advanced Neuroimaging, Institute of Diagnostic and Interventional Neuroradiology, Inselspital, Bern University Hospital, University of Bern, CH-3010 Bern, Switzerland. crummel@web.de

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 30, 2011
PubMed
Summary

This study introduces a novel surrogate-based method to distinguish linear and nonlinear interrelations in time series data. The approach reveals linear cross-correlations in resting-state fMRI and identifies significant nonlinear interrelations in epilepsy iEEG data.

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Area of Science:

  • Neuroscience
  • Data Analysis
  • Signal Processing

Background:

  • Multivariate time series analysis commonly uses linear and nonlinear measures to study spatiotemporal interrelations.
  • Existing methods may not effectively differentiate between linear and nonlinear interdependencies.

Purpose of the Study:

  • To develop and validate a uniform surrogate-based approach for disentangling linear and nonlinear interrelations in multivariate time series.
  • To apply this framework to real-world neuroimaging data, including resting-state fMRI and iEEG.

Main Methods:

  • Employed a surrogate-based framework to identify interrelations exceeding random effects and linear correlation.
  • Explored the bivariate version using a model with tunable coupling and nonlinearity.
  • Applied the method to resting-state fMRI data from healthy subjects and iEEG data from epilepsy patients.

Main Results:

  • Resting-state fMRI interrelations were predominantly characterized by linear cross-correlation.
  • Nonlinear interrelations in iEEG data were significantly detected, particularly in epileptogenic tissue and during seizures.
  • The null hypothesis of linear iEEG interrelation was rejected under specific conditions.

Conclusions:

  • The proposed surrogate-based method effectively distinguishes between linear and nonlinear interrelations in complex time series.
  • Findings suggest linear models suffice for rsfMRI, while nonlinear dynamics are crucial for understanding iEEG in epilepsy.
  • This approach offers a robust tool for analyzing neural dynamics and identifying pathological patterns.