Raffaelli, G. T. | bioRxiv Science

bioRxiv2026

HORDCOIN: A Software Library for Higher Order Connected Information and Entropic Constraints Approximation

Background and objectiveQuantifying higher-order statistical dependencies in multivariate biomedical data is essential for understanding collective dynamics in complex systems such as neuronal populations. The connected information framework provides a principled decomposition of the total information content into contributions from interactions of increasing order. However, its application has been limited by the computational complexity of conventional maximum entropy formulations. In this work, we present a generalised formulation of connected information based on maximum entropy problems constrained by entropic quantities. MethodsThe entropic-constraint approach, contrasting with the original constraints based on marginals or moments, transforms the original nonconvex optimisation into a tractable linear program defined over polymatroid cones. This simplification enables efficient, robust estimation even under undersampling conditions. ResultsWe present theoretical foundations, algorithmic implementation, and validation through numerical experiments and real-world data. Applications to symbolic sequences, large-scale neuronal recordings, and DNA sequences demonstrate that the proposed method accurately detects higher-order interactions and remains stable even with limited data. ConclusionsThe accompanying open-source software library, HORDCOIN (Higher ORDer COnnected INformation), provides user-friendly tools for computing connected information using both marginal- and entropy-based formulations. Overall, this work bridges the gap between abstract information-theoretic measures and practical biomedical data analysis, enabling scalable investigation of higher-order dependencies in neurophysiological and other complex biological systems such as the genome.

bioinformatics↗

bioRxiv2024

Nonlinear brain connectivity from neurons to networks: quantification, sources and localization.

Connectivity is a widespread tool for the study of complex systems dynamics. Since the first studies in functional connectivity, Pearsons correlation has been the primary tool to determine interdependencies in the activity at different brain locations. Over the years, concern over the information neglected by correlation has pushed toward using different measures accounting for non-linearity. However, one may pragmatically argue that, at the most common clinical observation scales, a linear description of the brain captures a vast majority of the information. Therefore, we measured the fraction of information disregarded using a linear description and which regions would be most affected. To assess how the spatial and temporal observation scale impacts the amount of non-linearity across multiple orders of magnitude, we considered fMRI, EEG, iEEG, and single-unit spikes. We observe that by treating the system as linear, the information loss is relatively mild for modalities with large temporal or spatial averaging (fMRI and EEG) and gains relevance on more fine descriptions of the activity (iEEG and single unit spikes). We conclude that Pearsons correlation coefficient adequately describes pairwise interactions in time series from current recording techniques for most non-invasive human applications. At the same time, microscale (typically invasive) measurements might be a more suitable field for mining information on nonlinear interactions. Significance StatementIn complex systems research, including neuroscience, the ubiquitous interest in network characterization by statistical dependencies (functional connectivity) invites increasingly sophisticated approaches. Various nonlinear measures, ultimately Mutual Information, emerge as alternatives to the conventional linear Pearsons correlation coefficient. To fundamentally inform such decisions, we systematically assess the amount and reliability of non-linearity of brain functional connectivity across imaging modalities and spatial and temporal scales. We demonstrate more pronounced non-linearity in microscale recordings, while it is limited and unreliable in more accessible, non-invasive, large-scale modalities: functional magnetic resonance imaging and scalp electrophysiology. This result fundamentally supports the use of robust and easily interpretable linear tools in large-scale neuroimaging and brings essential insights concerning the non-linearity of microscale connectivity, including the link to brain state dynamics.

neuroscience↗