Elaborazione teorico-informazionale dei segnali higher-order nei sistemi complessi

This thesis explores the application of higher-order information theory methods to analyze complex systems, focusing on real-world data derived from diverse domains, such as neuroscience and financial markets. The foundation of this research lies in the understanding that traditional analytical approaches, which often rely on pairwise interactions, may not sufficiently capture the intricate dynamics of complex systems. By extending concepts and tools from network science and information theory to encompass higher-order interactions, we aim to unveil the subtle nuances of systemic behavior and interactions. The study begins by establishing a theoretical framework that integrates basic network concepts with advanced information theory metrics. This framework is applied to synthetic data models to validate the methodological approach, followed by an in-depth analysis of real-world datasets including resting-state fMRI scans and financial time series. The research employs statistical methods and null models to rigorously test the hypotheses and ensure the reliability of the findings. A contribution of this work is the demonstration of how higher-order metrics, especially O-information, can discern complex patterns and dependencies that are not apparent through conventional analysis. For instance, in the analysis of financial markets, the application of higher-order information theory metrics enables the identification of group interactions directly from market trends, suggesting a nuanced layer of complexity within the data. The thesis underscores the potential of higher-order information theory metrics as insightful tools for exploring the multifaceted nature of complex systems. Through the discernment of higher-order interactions, this study contributes to a more nuanced comprehension of such systems, facilitating enhanced analytical perspectives.