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Analyzing and modeling fractal intensity point processes

A R Kumar1, D H Johnson

  • 1Department of Electrical and Computer Engineering, Rice University, Houston, Texas 77251-1892.

The Journal of the Acoustical Society of America
|June 1, 1993
PubMed
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This study introduces fractal intensity point processes to model neural discharge patterns. These processes use fractal dimension and fractal time to capture self-similar characteristics, aiding in understanding auditory and visual system data.

Area of Science:

  • Computational Neuroscience
  • Signal Processing
  • Statistical Physics

Background:

  • Discharge patterns in auditory and visual systems exhibit complex self-similar characteristics.
  • Doubly stochastic point processes are needed to model these intricate patterns.
  • Fractal intensity processes offer a framework for describing such complex temporal dynamics.

Purpose of the Study:

  • To introduce and characterize fractal intensity point processes for neural data.
  • To define and utilize fractal dimension and fractal time as key descriptors.
  • To establish methods for generating and selecting appropriate fractal intensity processes.

Main Methods:

  • Utilized the Fano factor to quantify self-similar intensity characteristics.
  • Defined fractal dimension as the exponent of Fano factor power-law behavior.

Related Experiment Videos

  • Defined fractal time to distinguish long-term from short-term fractal dynamics.
  • Employed nonlinear transformations of fractional Gaussian noise to generate fractal intensity point processes.

    • Main Results:

    • Fractal dimension and fractal time effectively capture self-similar intensity features.
    • Various factors including average rate, refractory effects, and serial dependence influence fractal time.
    • A methodology was developed to select the best transformation based on amplitude distribution and Fano factor.

    Conclusions:

    • Fractal intensity point processes provide a robust model for neural discharge patterns.
    • Fractal dimension and fractal time are crucial parameters for analyzing self-similarity in neural data.
    • The developed generation and selection methods facilitate the application of these processes to real-world data.