Schizophrenia is a neuropsychiatric disease that affects the nonlinear dynamics of brain activity. The primary objective of this study was to explore the complexity of magnetoencephalograms (MEG) in patients with schizophrenia. We combined a multiscale method and weighted permutation entropy to characterize MEG signals from 19 schizophrenia patients and 16 healthy controls. When the scale was larger than 42, the MEG signals of schizophrenia patients were significantly more complex than those of healthy controls ($p<0.004$). The difference in complexity between patients with schizophrenia and the controls was strongest in the frontal and occipital areas ($p<0.001$), and there was almost no difference in the central area. In addition, the results showed that the dynamic range of MEG complexity is wider in healthy individuals than in people with schizophrenia. Overall, the multiscale weighted permutation entropy method reliably quantified the complexity of MEG from schizophrenia patients, contributing to the development of potential magnetoencephalographic biomarkers for schizophrenia.

Schizophrenia is a serious mental disorder. Network analysis of magnetoencephalogram signals may help to identify potential biomarkers of schizophrenia. The goal of this investigation was to identify potential biomarkers in the magnetoencephalogram signals of patients with schizophrenia, global brain connectivity measures was used for emotion recognition in discriminating the patients from controls. First, we employed a mutual information method to explore the topological characteristics of the brain network in patients with schizophrenia among different frequency bands in response to four different stimulus conditions. Second, multidimensional cross-recurrence quantification analysis was performed to investigate the differences in dynamic coupling among different frequencies of brain magnetic waves in patients with schizophrenia in response to four different stimulus conditions, as the major novel contribution of our study. We found that the differences in topological features of the brain network appear in different frequency bands under different stimulus conditions. The differences are evident in the alpha 1 (8-10 Hz) and beta (13-30 Hz) frequency bands in response to negative stimuli, in the alpha 1 (8-10 Hz) frequency band in response to positive stimuli, and in the theta (4-8 Hz) and alpha 1 (8-10 Hz) frequency bands in response to neutral and gray-cross stimuli. In addition, differences in dynamic coupling among pairs of frequency bands were the most prominent in response to positive stimuli. The characteristics identified by our methods may be potential markers of schizophrenia present in magnetoencephalogram data, which can facilitate the clinical identification of schizophrenia patients. Our method provides a comprehensive perspective of brain networks in patients with schizophrenia and has practical applications for the clinical diagnosis of this disease.

Network analysis is an important approach to explore complex brain structures under different pathological and physiological conditions. In this paper, we employ the multivariate inhomogeneous polynomial kernel Granger causality (MKGC) to construct directed weighted networks to characterize schizophrenia magnetoencephalography (MEG). We first generate data based on coupled autoregressive processes to test the effectiveness of MKGC in comparison with the bivariate linear Granger causality and bivariate inhomogeneous polynomial kernel Granger causality. The test results suggest that MKGC outperforms the other two methods. Based on these results, we apply MKGC to construct effective connectivity networks of MEG for patients with schizophrenia (SCZs). We measure three network features, i.e., strength, nonequilibrium, and complexity, to characterize schizophrenia MEG. Our results suggest that MEG of the healthy controls (HCs) has a denser effective connectivity network than that of SCZs. The most significant difference in the in-connectivity strength is observed in the right frontal network ($p=0.001$). The strongest out-connectivity strength for all subjects occurs in the temporal area, with the most significant between-group difference in the left occipital area ($p=0.0018$). The total connectivity strength of the frontal, temporal, and occipital areas of HCs exhibits higher values compared with SCZs. The nonequilibrium feature over the whole brain of SCZs is significantly higher than that of the HCs ($p=0.012$); however, the results of Shannon entropy suggest that healthy MEG networks have higher complexity than schizophrenia networks. Overall, MKGC provides a reliable approach to construct MEG brain networks and characterize the network characteristics.

The use of questionnaire survey results as a clinical diagnostic method for schizophrenia lacks a certain degree of objectivity; thus, markers of schizophrenia in different brain signals have been widely investigated. The objective of this investigation was to explore potential markers of schizophrenia by investigating nonequilibrium features in magnetoencephalography (MEG) signals. We propose a new method to quantify the nonequilibrium features of MEG signals: the multiscale permutation time irreversibility (MsPTIRR) index. The results revealed that the MsPTIRR indices of the MEG recordings of patients with schizophrenia were significantly lower than those of the healthy controls (HCs). Moreover, the MsPTIRR indices of the MEG recordings of patients with schizophrenia and HCs differed significantly in the frontal, occipital, and temporal lobe regions. Furthermore, the MsPTIRR indices of the MEG recordings differed significantly between patients with schizophrenia and HCs in the $\theta$, $\alpha$ and $\beta$ bands. Abnormal nonequilibrium features mined in MEG recordings using the MsPTIRR index may be used as potential markers for schizophrenia, assisting in the clinical diagnosis of this disorder.

Clarifying the mechanisms of altered brain network communication in Parkinson’s disease is crucial, yet conventional connectivity measures do not distinguish whether directed information flow is driven by phase synchrony or spectral amplitude modulation. To address this, we introduce Decomposed Transfer Entropy (DTE), which represents directed information flow as a mechanistic profile comprising phase, spectral, and interaction components. Simulations indicate that DTE identifies distinct coupling types and remains robust under noise; we further benchmark DTE against representative baseline measures and assess parameter sensitivity. Applied to θ band resting EEG, DTE reveals that the unmedicated (PD-OFF) state is characterized by a phase-dominant reweighting originating from the frontal midline hub Fz; medication shifts this mechanistic composition toward that of healthy reference. Hub-centric composition metrics derived from DTE discriminate PD-OFF from healthy controls, and the normalization of phase dominance relates to motor improvement (ΔUPDRS–III). Overall, DTE offers a mechanism-aware perspective on PD pathophysiology, suggesting that therapeutic benefit aligns with normalization of mechanistic composition rather than simple changes in connection strength, and provides a promising route toward mechanism-oriented biomarkers.