neuroimaging teams

Abstract: This article revisits entropy and related magnitudes (entropy density, effective measure complexity, and informational distance) for the analysis of sequential data. We present their mathematical foundations within information theory and ergodic theory, establishing connections between probabilistic Shannon entropy and algorithmic Kolmogorov complexity. A central result, Zivs theorem, demonstrates the asymptotic equivalence between the normalised number of distinct words and entropy density, providing the theoretical basis for estimation via Lempel-Ziv factorisation. We examine the convergence properties of these magnitudes and introduce estimation procedures for finite sequences, including a method for the effective measure complexity and the transfer entropy rate. An open-source software library implementing parallel algorithms for efficient Lempel-Ziv factorisation is presented. The practical utility of the framework is illustrated through three case studies: functional brain connectivity analysis from fMRI data, characterisation of spatiotemporal dynamics in coupled nonlinear oscillators, and electrocardiogram-based classification of atrial fibrillation, demonstrating how entropic measures capture meaningful structural and dynamical properties across diverse domains.

Abstract: Generating signals on graphs requires permutation-equivariant models that exhibit stability with respect to relative structural perturbations. While recent graph-aware Schrödinger bridge models incorporate topology information directly into their reference dynamics, it is unclear how perturbations of the graph propagate through these dynamics and affect the resulting generated distributions. In this paper, we analyze the structural stability of graph-aware continuous-time generative models whose drift combines a graph filter with a learned graph neural network. We derive explicit Wasserstein stability bounds that quantify the effect of relative graph perturbations on the generated distributions. Motivated by these bounds, we introduce a principled framework for designing stable graph filters that preserve the smoothing behavior of graph heat diffusion, while boosting structural stability. Experiments on synthetic and fMRI signals show our stable filters enhance structural robustness while matching or exceeding the generative quality of the heat equation baseline.