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Related Experiment Video

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Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns

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Published on: August 30, 2013

Geometric and projection effects in Kramers-Moyal analysis.

Steven J Lade¹

¹Nonlinear Physics Centre, Research School of Physics and Engineering, The Australian National University, Australian Capital Territory 0200, Australia. steven.lade@anu.edu.au

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|November 13, 2009

Summary

Kramers-Moyal coefficients offer a visual method for analyzing nonlinear stochastic time series. Geometric projection effects can influence coefficient estimation, but the method remains useful even for non-Markovian systems.

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Area of Science:

Physics
Mathematics
Computational Biology

Background:

Nonlinear stochastic time series analysis is crucial in many scientific fields.
Kramers-Moyal coefficients offer a powerful tool for characterizing such systems.
Geometric projection effects can introduce complexities in coefficient estimation.

Purpose of the Study:

To investigate the impact of geometric projection effects on Kramers-Moyal coefficient estimation.
To explore these effects in biologically inspired systems.
To assess the utility of the Kramers-Moyal method under projection effects.

Main Methods:

Utilized a nonstochastic projection operator method to predict geometric projection effects.
Employed direct numerical simulation of Langevin equations for comparison.
Analyzed general features and characteristics of the projection effects.

Main Results:

Geometric projection effects were found to influence Kramers-Moyal coefficient estimation.
The Kramers-Moyal method demonstrated utility even when projections introduced non-Markovian behavior.
The studied biological examples showed behavior close to Markovian.

Conclusions:

Kramers-Moyal coefficients remain a valuable tool for analyzing projected stochastic time series.
Understanding projection effects is important for accurate analysis of complex systems.
The method's robustness extends to systems with near-Markovian properties.