How does it relate to the -5/3 law?

The skill calculates the Kolmogorov energy spectrum where E(k) ~ k^(-5/3), which is the signature of the inertial range in fully developed turbulence.

What is the Kolmogorov-Onsager-Hurst triad?

It is a unified mathematical framework connecting energy cascades (Kolmogorov), regularity/dissipation thresholds (Onsager), and long-range memory (Hurst) in complex systems.

What is the advantage of using DFA over R/S analysis?

Detrended Fluctuation Analysis (DFA) is more robust for non-stationary data, as it removes local trends that could otherwise skew the estimation of the Hurst exponent.

How does this skill help with financial data?

It uses the Hurst exponent to determine if a market is trending (H > 0.5), mean-reverting (H < 0.45), or following a random walk (H ≈ 0.5), helping identify trading regimes.

Kolmogorov-Onsager-Hurst Scaling Analysis

Name: Kolmogorov-Onsager-Hurst Scaling Analysis
Author: plurigrid

byplurigrid

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Data Science & ML

Analyzes time-series data using scaling theory to identify turbulence regimes, persistence, and long-range dependencies.

About

This skill provides a comprehensive framework for scaling analysis based on the triad of Kolmogorov, Onsager, and Hurst theories. It allows developers and researchers to quantify the fractal nature of complex systems, ranging from fluid dynamics and network traffic to financial market regimes. By implementing robust algorithms like Rescaled Range (R/S) analysis and Detrended Fluctuation Analysis (DFA), the skill helps determine if a system is persistent, anti-persistent, or purely stochastic, while providing the mathematical bridge between spectral exponents, Hölder regularity, and fractal dimensions.

Key Features

Hurst exponent estimation via R/S and Detrended Fluctuation Analysis (DFA)
Kolmogorov -5/3 energy spectrum calculation for turbulence modeling
Computation of fractal dimensions and spectral exponents for system characterization
Validation of Onsager's anomalous dissipation thresholds and Hölder regularity
2 GitHub stars
Market regime classification (Trending vs. Mean-Reverting) for financial datasets

Use Cases

Bioinformatics researchers analyzing heartbeat intervals or neural spike trains for physiological health markers
Financial analysts classifying market volatility and trend persistence in price returns
Network engineers diagnosing long-range dependence and self-similarity in TCP/Ethernet traffic

About

Key Features

Hurst exponent estimation via R/S and Detrended Fluctuation Analysis (DFA)
Kolmogorov -5/3 energy spectrum calculation for turbulence modeling
Computation of fractal dimensions and spectral exponents for system characterization
Validation of Onsager's anomalous dissipation thresholds and Hölder regularity
2 GitHub stars
Market regime classification (Trending vs. Mean-Reverting) for financial datasets

Use Cases

Bioinformatics researchers analyzing heartbeat intervals or neural spike trains for physiological health markers
Financial analysts classifying market volatility and trend persistence in price returns
Network engineers diagnosing long-range dependence and self-similarity in TCP/Ethernet traffic