In the first phase of the project, computational methods for analyzing nonlinear time series based on state-transition networks (STNs) were developed and evaluated. The activities focused both on the theoretical foundations of the method and on testing it on real and synthetic data representative of complex systems.
Two main procedures for time-series symbolization—phase-space partitioning and ordinal patterns—were implemented, and the corresponding code was integrated into an open-source platform. An extensive dataset was constructed, including periodic and chaotic dynamics, white and colored noise, as well as experimental recordings (e.g., robotic locomotion data and EEG signals). This dataset enabled a systematic comparison of the two symbolization approaches and of a broad set of network- and entropy-based measures used to characterize dynamical regimes.
From a theoretical perspective, we analyzed the relationship between STN-derived measures and the topological and metric entropies from dynamical-systems theory, demonstrating their consistency for prototype systems. We also investigated a recently introduced quantity, the Lyapunov measure, showing that it is related to the derivative of the Rényi entropy spectrum and can serve as a sensitive indicator of critical transitions.
The results were disseminated through presentations at prestigious international conferences (SIAM DS 2025 in Denver, USA; Dynamics Days Europe 2025 in Thessaloniki, Greece; ENACS 2025 in Dresden, Germany) and through articles published in specialized journals, including Physical Review Research and STAR Protocols. The analysis of the experimental locomotion data is currently under review at Bioinspiration & Biomimetics.
The project contributes to human resource development through the training of one Master’s student, PhD students, and postdoctoral researchers, enhancing advanced skills in theoretical modeling, data analysis, and interdisciplinary research.
Alongside theoretical advances in State-Transition Networks (STNs), the project develops computational methods applicable to biological and other complex time series data.
Preliminary tests on biological datasets demonstrate the applicability and relevance of the proposed methods to real-world systems.
An open-source software package is developed (see the Software menu), enabling broad access, reproducibility, and reuse of the methodologies by the scientific community.
Through science popularization activities, the project promotes scientific careers among students and younger generations and highlights the interdisciplinary applicability of physics-based approaches.