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Assembly and Characterization of Biomolecular Memristors Consisting of Ion Channel-doped Lipid Membranes
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Memory traces in dynamical systems.

Surya Ganguli1, Dongsung Huh, Haim Sompolinsky

  • 1Sloan-Swartz Center for Theoretical Neurobiology, University of California, San Francisco, CA 94143, USA. surya@phy.ucsf.edu

Proceedings of the National Academy of Sciences of the United States of America
|November 21, 2008
PubMed
Summary
This summary is machine-generated.

Biological systems need short-term memory for real-time computation. Fisher information theory reveals dynamical systems can store input history, with capacity limits dependent on network structure and nonlinearities.

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Area of Science:

  • Computational neuroscience
  • Dynamical systems theory
  • Information theory

Background:

  • Biological systems require short-term memory for processing sensory input streams in real-time.
  • Dynamical systems, particularly high-dimensional ones, are proposed mechanisms for retaining memory traces of past inputs within their current state.
  • Fundamental limits and necessary properties of dynamical systems for effective memory retention remain key research questions.

Purpose of the Study:

  • To investigate the fundamental limits of memory traces in dynamical systems.
  • To identify the properties required for dynamical systems to achieve maximal memory capacity.
  • To apply Fisher information theory to quantify memory capacity in systems processing noisy, time-dependent signals.

Main Methods:

  • Application of Fisher information theory to dynamical systems driven by time-dependent, noisy signals.
  • Introduction of the Fisher Memory Curve (FMC) to measure the signal-to-noise ratio (SNR) in the dynamical state relative to the input SNR.
  • Analysis of memory capacity in linear neuronal networks (normal and nonnormal connectivity) and networks with saturating nonlinearities.

Main Results:

  • The integrated FMC quantifies the total memory capacity of a dynamical system.
  • Linear neuronal networks with normal connectivity have a memory capacity of 1; any network of N neurons has a maximum capacity of N.
  • Nonnormal networks achieving maximal capacity require specific feedforward architectures with superlinear amplification and optimal input connectivity.
  • Networks with saturating nonlinearities have limited memory capacity (≤√N), achievable with divergent feedforward structures to prevent saturation.
  • Memory retention in fluid systems can be facilitated by transient nonnormal amplification (e.g., convective instability, turbulence).

Conclusions:

  • Fisher information theory provides a framework to quantify memory capacity in dynamical systems.
  • Network architecture, connectivity properties (normal vs. nonnormal), and nonlinearities significantly constrain memory capacity.
  • Specific nonnormal network designs and feedforward architectures can approach theoretical memory limits, offering insights into efficient biological and artificial memory systems.