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Linear time-invariant Systems01:23

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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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In designing and analyzing filters, resonant circuits, or circuit analysis at large, working with standard element values like 1 ohm, 1 henry, or 1 farad can be convenient before scaling these values to more realistic figures. This approach is widely utilized by not employing realistic element values in numerous examples and problems; it simplifies mastering circuit analysis through convenient component values. The complexity of calculations is thereby reduced, with the understanding that...
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Related Experiment Video

Updated: Feb 2, 2026

Spiral Ganglion Neuron Explant Culture and Electrophysiology on Multi Electrode Arrays
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Scale-invariant structures of spiral waves.

Daniel Sohn1, Konstantinos Aronis1, Hiroshi Ashikaga2

  • 1Cardiac Arrhythmia Service, Johns Hopkins University School of Medicine, 600 N Wolfe Street, Carnegie 568, Baltimore, MD, USA.

Computers in Biology and Medicine
|November 22, 2018
PubMed
Summary
This summary is machine-generated.

Spiral waves, implicated in cardiac arrhythmias, exhibit scale-invariant structures. These hidden patterns of information flow within spiral waves persist across different spatial and temporal scales.

Keywords:
Coherent structuresFibrillationPattern formationRenormalizationSpiral wavesinformation theory

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Area of Science:

  • Computational biology
  • Cardiac electrophysiology
  • Nonlinear dynamics

Background:

  • Spiral waves are a key mechanism in complex cardiac arrhythmias like atrial and ventricular fibrillation.
  • Understanding the dynamics of spiral waves is crucial for developing treatments for these life-threatening conditions.

Purpose of the Study:

  • To quantify the complex dynamics of spiral waves.
  • To investigate spiral waves as organizing manifolds of information flow across multiple scales.

Main Methods:

  • Simulated cardiac excitation in a 2-D lattice to model spiral waves.
  • Employed renormalization group techniques by coarse-graining and re-scaling spatiotemporal data.
  • Quantified Lagrangian Coherent Structures (LCS) to analyze information flow.
  • Compared finite-time Lyapunov exponents across scales to identify scale-invariant structures.

Main Results:

  • Lagrangian coherent structures (LCS) exhibited changes across different spatial and temporal scales.
  • Identified specific LCS that were scale-invariant, meaning they were preserved across scales.
  • These scale-invariant patterns were not readily apparent from traditional voltage mapping of spiral wave trajectories.

Conclusions:

  • Certain Lagrangian coherent structures (LCS) representing information flow within spiral waves are preserved across multiple spatiotemporal scales.
  • These findings suggest underlying organizational principles in spiral wave dynamics that are robust to scale changes.