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The Wald-Wolfowitz test, also known as the runs test, is a nonparametric statistical test used to assess the randomness of a sequence of two different types of elements (e.g., positive/negative values, successes/failures). It examines whether the order of the elements in a sequence is random or if there is a pattern or trend present. This nonparametric test applies to any ordered data despite the population and sample data distribution, even if a higher sample size is available.
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The Wald-Wolfowitz runs test, commonly referred to as the runs test, is a nonparametric test used to assess the randomness of ordered data. The test evaluates the number of runs, which are consecutive sequences of similar elements within the data. If the number of runs is significantly higher or lower than expected, the data is considered non-random, indicating a detectable pattern or structure.
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Time-dependent Increase in the Network Response to the Stimulation of Neuronal Cell Cultures on Micro-electrode Arrays
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Random walks on complex networks under time-dependent stochastic resetting.

Hanshuang Chen1, Yanfei Ye1

  • 1School of Physics and Optoelectronic Engineering, Anhui University, Hefei 230601, China.

Physical Review. E
|November 18, 2022
PubMed
Summary

We explore random walks on networks with time-dependent resetting. Time-modulated protocols accelerate target search more than constant resetting.

Area of Science:

  • Complex Systems
  • Statistical Physics
  • Network Science

Background:

  • Random walks are fundamental processes on networks.
  • Stochastic resetting modifies random walks by periodically returning the walker to a specific state.
  • Time-dependent resetting introduces a novel layer of control over random walk dynamics.

Purpose of the Study:

  • To investigate discrete-time random walks on networks with time-dependent stochastic resetting.
  • To analyze how resetting probability, dependent on walker age, influences network exploration.
  • To compare the efficiency of time-modulated resetting against constant resetting for search processes.

Main Methods:

  • Utilizing the renewal approach for analyzing resetting processes.
  • Employing spectral decomposition of the transition matrix for analytical solutions.

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  • Formulating stationary occupation probabilities and mean first passage times.
  • Considering step-shaped and rational function-based resetting protocols.

    • Main Results:

    • Exact solutions derived for stationary occupation probabilities and mean first passage times.
    • Demonstrated theoretical results on various network structures.
    • Validated findings through numerical simulations.
    • Identified specific time-dependent resetting protocols that outperform constant resetting.

    Conclusions:

    • Time-modulated stochastic resetting offers enhanced control over random walks on networks.
    • These protocols can significantly accelerate target search processes compared to static resetting.
    • The age-dependent resetting strategy provides a powerful tool for optimizing network exploration dynamics.