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Evaluating Areas Under Curves with DiscontinuitiesA definite integral is considered improper when the integrand is discontinuous at one of the limits of integration. This occurs when the function is undefined or becomes infinite at an endpoint, making the corresponding region under the curve unbounded. Such behavior is commonly associated with vertical asymptotes at the boundary of the interval. To properly define and evaluate these integrals, a limiting process is used to determine whether a...
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A method to detect discontinuities in census data.

Chris Barichievy1,2, David G Angeler3, Tarsha Eason4

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Summary
This summary is machine-generated.

This study introduces a new, simple method for detecting discontinuities in complex systems. The approach uses resampling of a neutral model, offering a transparent way to analyze ecological data and improve resilience research.

Keywords:
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Area of Science:

  • Ecology
  • Complex Systems Analysis
  • Statistical Modeling

Background:

  • Discontinuities in complex systems are crucial for understanding resilience.
  • Current discontinuity detection methods are often subjective, complex, or outdated.
  • A need exists for a simple, transparent method for discontinuity detection.

Purpose of the Study:

  • To present a novel, simple, and transparent method for detecting discontinuities in census data.
  • To provide R code for implementing the discontinuity detection analysis.
  • To facilitate advancements in basic and applied ecological research.

Main Methods:

  • Developed a discontinuity detection method based on resampling of a neutral model.
  • Applied the method to census data.
  • Included R code for reproducibility and application.

Main Results:

  • The proposed method successfully detects discontinuities in complex systems.
  • The approach offers an objective means of identifying scales and hierarchical patterns.
  • The R code is provided for practical implementation.

Conclusions:

  • The new discontinuity detection method is simple, transparent, and effective.
  • This method can enhance the quantitative analysis of resilience in complex systems.
  • It holds potential for advancing ecological research and applications.