arXiv subjects

Koichi Sameshima

Publications and source records attributed to Koichi Sameshima.

4 recordsLinked to original sources

arXiv2026

Directed Q-Analysis and Directed Higher-Order Connectivity on Digraphs: A Quantitative Approach

Traditional graph analysis focuses on nodes and edges, that is, pairwise relationships. Yet many real-world networks, including biological, social, and communication networks, involve higher-order relationships in which multiple nodes interact simultaneously. This has led many to develop network topology analysis methods based on higher-order structures and higher-order connectivity, seeking to reveal complex interactions beyond node pairs. Many of the latter address only undirected networks. To overcome this, we lay out a mathematical formalism resting on directed clique complexes constructed from directed graphs (their "higher-order structures" or "simplicial structures''), stressing the interrelations between directed cliques (their "directed higher-order connectivities''), leading towards a more complete directed Q-analysis that allows quantifying, characterizing, and comparing similarities involving simplicial structures.

math.GM↗

arXiv2022

Partial Directed Coherence and the Vector Autoregressive Modelling Myth and a Caveat

Here we dispel the lingering myth that Partial Directed Coherence is a Vector Autoregressive (VAR) Modelling dependent concept. In fact, our examples show that it is spectral factorization that lies at its heart, for which VAR modelling is a mere, albeit very efficient and convenient, device. This applies to Granger Causality estimation procedures in general and also includes instantaneous Granger effects. Care, however, must be exercised for connectivity between multivariate data generated through nonminimum phase mechanisms as it may possibly be incorrectly captured.

stat.ME↗

arXiv2015

Consolidating a Link Centered Neural Connectivity Framework with Directed Transfer Function Asymptotics

We present a unified mathematical derivation of the asymptotic behaviour of three of the main forms of \textit{directed transfer function} (DTF) complementing recent partial directed coherence (PDC) results \cite{Baccala2013}. Based on these results and numerical examples we argue for a new directed `link' centered neural connectivity framework to replace the widespread correlation based effective/functional network concepts so that directed network influences between structures become classified as to whether links are \textit{active} in a \textit{direct} or in an \textit{indirect} way thereby leading to the new notions of \textit{Granger connectivity} and \textit{Granger influenciability} which are more descriptive than speaking of Granger causality alone.

q-bio.NC↗

arXiv2010

Information theoretic interpretation of frequency domain connectivity measures

To provide adequate multivariate measures of information flow between neural structures, modified expressions of Partial Directed Coherence (PDC) and Directed Transfer Function (DTF), two popular multivariate connectivity measures employed in neuroscience, are introduced and their formal relationship to mutual information rates are proved.

math.ST↗