Objective. Several data-driven approaches based on information theory have been proposed for analyzing high-order interactions (HOIs) involving three or more components of a network system. The existing methods do not account for temporal correlations in the data, or are defined only in the time domain and rely on the assumption of stationarity in the underlying dynamics, making them inherently unable to detect frequency-specific behaviors and track transient functional links in physiological networks.Approach. This study introduces a new framework which enables the time-varying and time-frequency analysis of HOIs in networks of random processes through the spectral representation of vector autoregressive models. The time- and frequency-resolved analysis of synergistic and redundant interactions among groups of processes is ensured by a robust identification procedure based on a recursive least squares estimator with a forgetting factor.Main results. Validation on simulated networks illustrates how the time-frequency analysis is able to highlight transient synergistic behaviors emerging in specific frequency bands which cannot be detected by time-domain stationary analyzes. The application on brain evoked potentials in rats elicits the presence of redundant information timed with whisker stimulation and mostly occurring in the contralateral hemisphere. The application to cardiovascular oscillations reveals a reduction in redundant information following head-up tilt, reflecting a functional disconnection within the physiological network of heart period, respiratory, and arterial pressure signals.Significance. The proposed framework enables a comprehensive time-varying and time-frequency analysis of the hierarchical organization of dynamic networks. As our approach goes beyond pairwise interactions, it is well suited for the study of transient high-order behaviors arising during state transitions in many network systems commonly studied in physiology, neuroscience and other fields.

BackgroundPapillary thyroid carcinoma (PTC) has an excellent prognosis, yet recurrence remains a clinical concern. Patients at intermediate risk may benefit from additional prognostic markers. We aimed to evaluate whether tumor desmoplasia predicts recurrence in intermediate-risk PTC patients and to assess its prognostic clinical utility.MethodsWe conducted a retrospective study with follow-up of at least 36 months at a high-volume tertiary endocrine center. We included 121 patients with intermediate-risk PTC who achieved an excellent or indeterminate response to initial therapy at 12 months. Tumor desmoplasia was assessed on hematoxylin–eosin-stained thyroid sections by two pathologists. Desmoplasia was graded on a semi-quantitative 4-point scale based on the proportion of tumor area occupied by fibrotic stromal tissue. Patients were followed for the occurrence of biochemical or structural recurrence, which was defined as the primary study endpoint.ResultsDesmoplasia was significantly associated with recurrence (odds ratio = 2.99; 95% CI: 1.51–6.34; P < 0.01). Receiver operating characteristic analysis identified grade 2 as the optimal cut-off for predicting recurrence. Notably, the negative predictive value reached 95% in patients with absent or mild desmoplasia. Kaplan–Meier analysis confirmed a significant difference in recurrence-free survival between patients with mild versus severe desmoplasia (hazard ratio = 3.00; 95% CI: 1.45–6.24; P = 0.003).ConclusionDesmoplasia is an independent predictor of recurrence in intermediate-risk PTC. Patients with minimal or no desmoplasia have an extremely low risk of recurrence. These findings support the potential role of desmoplasia as a prognostic feature in risk stratification and personalized management of intermediate-risk PTC.