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Summary
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This study extends information dynamics to continuous time, revealing that active information storage diverges, preventing convergent predictive capacity. New measures quantify memory utilization in neural and other complex systems.

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Area of Science:

  • Complex Systems Science
  • Information Theory
  • Computational Neuroscience

Background:

  • Information dynamics quantifies intrinsic information processing in time series.
  • Current methods are limited to discrete-time formulations.
  • Previous work established continuous-time transfer entropy.

Purpose of the Study:

  • To provide a comprehensive framework for information processing in continuous time.
  • To incorporate information storage into continuous-time information dynamics.
  • To analyze the behavior of predictive capacity and its components.

Main Methods:

  • Formulating information processing measures in continuous time.
  • Decomposing active information storage into active memory utilization and instantaneous predictive capacity.
  • Developing measures for jump and neural spiking processes.

Main Results:

  • A convergent rate of predictive capacity does not exist in continuous time due to divergent active information storage rates.
  • Active information storage can be separated into active memory utilization and instantaneous predictive capacity.
  • Active memory utilization allows for pathwise and rate quantity definitions.

Conclusions:

  • The developed continuous-time information dynamics framework accounts for information storage.
  • Divergent rates of active information storage are identified as a key characteristic.
  • New measures for memory utilization are applicable to various continuous-time processes, including neural spiking models.