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BIBO stability of continuous and discrete -time systems01:24

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System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
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Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
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A unified method for assessing the observability of dynamic complex systems.

Juan G Diaz Ochoa1

  • 1PerMediQ GmbH, Pelargusstr. 2, D-70180, Stuttgart, Germany.

Computers in Biology and Medicine
|May 15, 2023
PubMed
Summary

A new method, the Φ-S diagram, assesses causal processes in biological systems by analyzing time series data. This tool helps identify mechanistic responses and understand system complexity, offering a more robust framework for biological systems analysis.

Keywords:
CausalityDynamic complex systemsGeometric information theoryObservabilityPersistent entropyPersistent topologyTime series

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Area of Science:

  • Systems biology
  • Complexity science
  • Geometric information theory

Background:

  • Systems theory in biology and medicine seeks predictive models of complex systems.
  • Current methods struggle to assess universal causal principles due to multi-scale information integration and inherent uncertainty in organisms.
  • Existing tools lack the ability to evaluate the stability and mechanistic nature of causal processes across different scales.

Purpose of the Study:

  • To develop a novel method for assessing the stability of causal processes in biological systems.
  • To introduce a complexity measure, the Φ-S diagram, for identifying mechanistic responses.
  • To provide a more robust framework for representing and analyzing complex biological systems.

Main Methods:

  • Analysis of time series patterns using geometric information theory and persistent homology.
  • Evaluation of information within phase space trajectories to detect stability of causal processes.
  • Development and application of the Φ-S diagram as a complexity measure.

Main Results:

  • The Φ-S diagram was successfully applied to deterministic and real-world health datasets (ICU repository).
  • The method confirmed the mechanistic nature of the analyzed biological data.
  • Individual variability was observed to potentially impact the detection of cardiac responses, highlighting the need for robust analytical frameworks.

Conclusions:

  • The Φ-S diagram offers a reliable method for evaluating causal relationships and mechanistic responses in biological systems.
  • This approach provides a more robust framework for understanding complex biological systems, addressing limitations in current methods.
  • The study demonstrates the potential of geometric information theory and persistent homology in advancing systems biology analysis.