arXiv subjects

Luiz A. Baccalá

Publications and source records attributed to Luiz A. Baccalá.

3 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↗

arXiv2018

Kernel Methods for Nonlinear Connectivity Detection

In this paper, we show that the presence of nonlinear coupling between time series may be detected employing kernel feature space representations alone dispensing with the need to go back to solve the pre-image problem to gauge model adequacy. As a consequence, the canonical methodology for model construction, diagnostics, and Granger connectivity inference applies with no change other than computation using kernels in lieu of second-order moments.

eess.SP↗

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↗