优先级 60 · 方法 · 引力波数据 · 时间序列分析
MF-toolkit: A high-performance python library for multifractal analysis with automated crossover detection, source identification and application to gravitational waves data
MF-toolkit:面向多重分形分析的高性能Python库,具有自动交叉点检测、源辨识及引力波数据应用
✉ N. Mendez (Instituto Sabato, Universidad Nacional de San Martín; Facultad Regional Haedo, Universidad Tecnológica Nacional), M. Mariani (Department of Mathematical Science, UTEP), M. Beccar-Varela (Department of Mathematical Science, UTEP) et al.
原文摘要Abstract
Multifractal Detrended Fluctuation Analysis (MFDFA) is a powerful and widely used technique for characterizing the scaling properties and long-range correlations of complex time series. However, its application often involves significant practical challenges, such as the subjective identification of scaling regions (crossovers) and the disambiguation of the physical origins of multifractality. We introduce MF-toolkit, a high-performance, parallelized Python library designed to address these challenges. It integrates three key innovations: (1) fully automatic crossover detection algorithms (CDV-A and SPIC), which remove operator bias and enhance reproducibility; (2) a built-in implementation of the Iterative Amplitude Adjusted Fourier Transform (IAAFT) for generating surrogate data, enabling the robust identification of the source of multifractality; and (3) a comprehensive suite for generating synthetic time series for rigorous validation. We demonstrate the rigor and utility of MF-toolkit through its application to characterize the multifractal properties of non-stationary noise in gravitational wave (LIGO) data. The MF-toolkit library offers a robust, efficient, and user-friendly tool for advanced time series analysis, facilitating more rigorous and reproducible research across physics and other data-intensive fields. PROGRAM SUMMARY/NEW VERSION PROGRAM SUMMARY Program Title: MF-toolkit CPC Library link to program files:https://doi.org/10.17632/zwx686b23t.1 Developer's repository link:https://github.com/NahueMendez/mf-toolkit Licensing provisions: MIT Programming language: Python Supplementary material:https://app.readthedocs.org/projects/mf-toolkit/ Nature of problem: Applying multifractal detrended fluctuation analysis to a time series is a widely used process in complex system physics but the time computing and the resources needed strongly depends on the number of samples of the input signal. The method in its multifractal extension require to calculate the fluctuation function for every scale size s and every moment q. This issue escalates when it is needed to analyze a group of time series to asses statistically its multifractals parameters. Solution method: We address the bottleneck of MFDFA by computing the fluctuation functions using CPU-based plane parallelization and Numba's just-in-time compilation taking advantage of the independency of the calculations. This drastically reduces time computing, and it can be used for processing large datasets.
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AI 综述
AI-generated · 以原文为准
亮点将CDV-A与SPIC自动交叉检测、IAAFT代理数据源辨识集成到统一并行MFDFA流程,消除缩放区间选择的主观偏差;在LIGO数据中证实多重分形主要来自仪器噪声而非天体物理源。
预印本 2026-04-17 · 刊出 2026-06-18 · 收录 2026-08-20