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Updated: May 29, 2026
10:19
Three-Dimensionally Printed Microfluidic Cross-flow System for Ultrafiltration/Nanofiltration Membrane Performance Testing
Published on: February 13, 2016
Filtrations indexed by attracting levels and their applications.
Yusuke Imoto1, Tomoo Yokoyama2
1Institute for the Advanced Study of Human Biology, Kyoto University, Yoshida Konoe-cho, Sakyo-ku, Kyoto 606-8501, Japan.
Chaos (Woodbury, N.Y.)
|May 28, 2026
Summary
We developed new filtrations for dynamical systems, enhancing topological data analysis. This method reveals trajectory sensitivity and breakdown points, with applications in weather forecasting.
Area of Science:
- Dynamical Systems and Topological Data Analysis
Background:
- Topological Data Analysis (TDA) methods like persistent homology are powerful for analyzing complex data.
- Dynamical systems generate data where understanding trajectory behavior and stability is crucial.
Purpose of the Study:
- Introduce a novel class of filtrations for dynamical systems.
- Provide new inputs for persistent homology and TDA.
- Quantify trajectory sensitivity and attraction breakdown under perturbations.
Main Methods:
- Filtrations indexed by attracting levels in dynamical systems.
- Construction applicable to metric spaces and general partial maps with cost functions.
- Filtration-theoretic framework with connections to algebraic topology.
Main Results:
- Filtrations quantify forward trajectory sensitivity to attractors.
- Filtrations quantify backward perturbation magnitude at which attraction fails.
- General framework yields complementary filtrations and natural space decompositions.
Conclusions:
- The new filtration framework offers a versatile tool for TDA in dynamical systems.
- Demonstrated application to tropical cyclone ensemble forecasts identifies sensitive regions.
- Highlights potential for improved analysis of complex dynamic processes.
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