Thomas F. Varley, Pedro A. M. Mediano, Alice Patania, Josh Bongard The study of irreducible higher-order interactions has become a core topic of study in complex systems. Two of the most well-developed frameworks, topological data analysis and multivariate information theory, aim to provide formal tools for identifying higher-order interactions in empirical data. Despite similar aims, however, these two approaches are built on markedly different mathematical foundations and have been developed largely in parallel. In this study, we present a head-to-head comparison of topological data analysis and information-theoretic approaches to describing higher-order interactions in multivariate data; with the aim of assessing the similarities and differences between how the frameworks define ``higher-order structures." We begin with toy examples with known topologies, before turning to naturalistic data: fMRI signals collected from the human brain. We find that intrinsic, higher-order synergistic information is associated with three-dimensional cavities in a point cloud: shapes such as spheres are synergy-dominated. In fMRI data, we find strong correlations between synergistic information and both the number and size of three-dimensional cavities. Furthermore, we find that dimensionality reduction techniques such as PCA preferentially represent higher-order redundancies, and largely fail to preserve both higher-order information and topological structure, suggesting that common manifold-based approaches to studying high-dimensional data are systematically failing to identify important features of the data. These results point towards the possibility of developing a rich theory of higher-order interactions that spans topological and information-theoretic approaches while simultaneously highlighting the profound limitations of more conventional methods. Read the full article at: arxiv.org

Former church volunteer and foster youth mentor Ryan Patania, 35, from Star, Idaho, has been sentenced to 40 years in prison for possession of child exploitative material. The case highlights the impo...

Fabbriche abbandonate, residui di amianto, polveri pericolose che si disperdono del vento e olio lubrificante che penetra nel terreno. Questi i segreti svelati da un cittadino legnanese, Marco Patania...

Fabbriche abbandonate, residui di amianto, polveri pericolose che si disperdono del vento e olio lubrificante che penetra nel terreno. Questi i segreti svelati da un cittadino legnanese, Marco Patania...

MultiSearch Tag Explorer - Explore tags and search results by aéPiot - aéPiot: Independent SEMANTIC Web 4.0 Infrastructure (Est. 2009). High-density Functional Semantic Connectivity with 100/100 Trust...