Paolo Sarti | Searcharxiv

arXiv2026

Conditional preservation of chimera states under equitable network coarse-graining

Chimera states, characterized by the coexistence of coherent and incoherent dynamics in networks of coupled oscillators, are among the most intriguing collective phenomena in nonlinear systems and are strongly shaped by the underlying topology and initial conditions. Their analysis in large-scale networks remains computationally demanding and motivates the development of coarse-graining strategies that reduce network size while retaining the essential dynamical features of chimera behavior. In this Letter, we investigate whether equitable-partition-based quotient graphs can preserve chimera patterns under substantial reductions of network size. Using nonlocally coupled FitzHugh-Nagumo (FHN) oscillators, we exploit the fact that, for an equitable partition, the full-network dynamics restricted to the associated cluster-synchronous subspace coincide exactly with the quotient dynamics. We ask whether this structural exactness is sufficient to preserve chimera signatures after the network size reduction. Our results show that this is not necessarily the case: agreement between quotient and full-network chimera dynamics depends on the equitable partition, and exact quotient dynamics do not necessarily guarantee the transverse stability of the corresponding full-network trajectory. Importantly, when the cluster-synchronous solution becomes transversely unstable, the full network may depart from the exact quotient trajectory while remaining in a macroscopic chimera regime. Therefore, structural exactness and dynamical preservation are distinct requirements, and transverse stability provides a complementary criterion for assessing quotient-based coarse-graining of chimera states.

physics.comp-ph↗

arXiv2026

Inverse generalised spin models of answers to questionnaires

Network psychometrics conceptualises psychological constructs as emergent properties of systems of interacting items. Energy-based probabilistic models have gained popularity as models of these interactions, but their psychometric application has so far been limited to binary responses, bilinear interactions, and approximated inference methods. To fill these gaps, we here infer and analyse three generalized-spin models of ordinal questionnaire data: the Ising, Blume-Capel (BC), and Blume-Emery-Griffiths (BEG) models. These are maximum-entropy models that accommodate ordinal responses on Likert-type scales with an arbitrary number of options, allowing for single-site anisotropy (BC, BEG) and bi-quadratic item interactions (BEG). We prove the concavity of the maximum likelihood estimation of their parameters, as well as the gauge invariance of the Ising and BC models. We introduce a stochastic gradient ascent algorithm for maximum likelihood inference, and apply this procedure to eleven psychometric and sociological questionnaire datasets. Evaluating the predictive ability of the inferred models reveals that the BEG model systematically outperforms Factor Analysis and the other spin models in capturing the distributions of factors and distances of subject answers to the mean, across all datasets. By leveraging a competitive interplay between the quadratic and bi-quadratic energy terms, the BEG model uniquely captures individual average-extremist response styles, alongside standard latent factor positioning. Moreover, only the spin models can account for the non-concavity and multi-modality of factor histograms in the most polarizing questionnaires. Finally, the analysis reveals other highly non-linear traits of ordinal data---such as the fat-tailed distribution of Mahalanobis distances to the mean---that escape satisfactory description by both factor and spin models.

physics.data-an↗