Discriminative Analysis of Schizophrenia Patients Using Topological Properties of Structural and Functional Brain Networks: A Multimodal Magnetic Resonance Imaging Study

Interest in the application of machine learning (ML) techniques to multimodal magnetic resonance imaging (MRI) data for the diagnosis of schizophrenia (SZ) at the individual level is growing. However, a few studies have applied the features of structural and functional brain networks derived from multimodal MRI data to the discriminative analysis of SZ patients at different clinical stages. In this study, 205 normal controls (NCs), 61 first-episode drug-naive SZ (FESZ) patients, and 79 chronic SZ (CSZ) patients were recruited. We acquired their structural MRI, diffusion tensor imaging, and resting-state functional MRI data and constructed brain networks for each participant, including the gray matter network (GMN), white matter network (WMN), and functional brain network (FBN). We then calculated 3 nodal properties for each brain network, including degree centrality, nodal efficiency, and betweenness centrality. Two classifications (SZ vs. NC and FESZ vs. CSZ) were performed using five ML algorithms. We found that the SVM classifier with the input features of the combination of nodal properties of both the GMN and FBN achieved the best performance to discriminate SZ patients from NCs [accuracy, 81.2%; area under the receiver operating characteristic curve (AUC), 85.2%; p < 0.05]. Moreover, the SVM classifier with the input features of the combination of the nodal properties of both the GMN and WMN achieved the best performance to discriminate FESZ from CSZ patients (accuracy, 86.2%; AUC, 92.3%; p < 0.05). Furthermore, the brain areas in the subcortical/cerebellum network and the frontoparietal network showed significant importance in both classifications. Together, our findings provide new insights to understand the neuropathology of SZ and further highlight the potential advantages of multimodal network properties for identifying SZ patients at different clinical stages.

Effects of polygenic risk score of type 2 diabetes on the hippocampal topological property and episodic memory

Purpose Type 2 diabetes is associated with a higher risk of dementia. The pathogenesis is complex, partly influenced by genetic factors. The hippocampus is the most vulnerable brain region in individuals with type 2 diabetes. However, whether the genetic risk of type 2 diabetes is associated with the hippocampus and episodic memory remains unclear. This study explored the influence of polygenic risk score (PRS) of type 2 diabetes on the white matter topological properties of the hippocampus among individuals with and without type 2 diabetes and its associations with episodic memory. Methods This study included 103 individuals with type 2 diabetes and 114 well-matched individuals without type 2 diabetes. All the participants were genotyped, and a diffusion tensor imaging-based structural network was constructed. PRS was calculated based on a genome-wide association study of type 2 diabetes. The PRS-by-disease interactions on the bilateral hippocampal topological network properties were evaluated by analysis of variance (ANOVA). Results There were significant PRS-by-disease interaction effects on the nodal topological properties of the right hippocampus node. In the individuals with type 2 diabetes, the PRS was correlated with the right hippocampal nodal properties, and the nodal properties were correlated with the episodic memory. In addition, the right hippocampal nodal properties mediated the effect of PRS on the episodic memory in individuals with type 2 diabetes. Conclusion Our results suggested a gene-brain-cognition biological pathway, which might help understand the neural mechanism of the genetic risk of type 2 diabetes affects episodic memory in type 2 diabetes.

Global Bifurcation of Fourth-Order Nonlinear Eigenvalue Problems’ Solution

In this paper, we study the global bifurcation of infinity of a class of nonlinear eigenvalue problems for fourth-order ordinary differential equations with nondifferentiable nonlinearity. We prove the existence of two families of unbounded continuance of solutions bifurcating at infinity and corresponding to the usual nodal properties near bifurcation intervals.

Unilateral Global Bifurcation from Infinity in Nonlinearizable One-Dimensional Dirac Problems

In this paper, we study the unilateral global bifurcation from infinity in nonlinearizable eigenvalue problems for the one-dimensional Dirac equation. We show the existence of two families of unbounded continua of the set of nontrivial solutions emanating from asymptotically bifurcation intervals and having the usual nodal properties near these intervals.

Time-varying nodal measures with temporal community structure: a cautionary note to avoid misinterpretation

In network neuroscience, temporal network models have gained popularity. In these models, network properties have been related to cognition and behaviour. Here we demonstrate that calculating nodal properties that are dependent on temporal community structure (such as the participation coefficient) in time-varying contexts can potentially lead to misleading results. Specifically, with regards to the participation coefficient, increases in integration can be inferred when the opposite is occuring. Further, we present a temporal extension to the participation coefficient measure (temporal participation coefficient) that circumnavigates this problem by jointly considering all community partitions assigned to a node through time. The proposed method allows us to track a node’s integration through time while adjusting for the possible changes in the community structure of the overall network.

Nodal solutions for the fractional Yamabe problem on Heisenberg groups

We prove that the fractional Yamabe equation ${\rm {\cal L}}_\gamma u = \vert u \vert ^{((4\gamma )/(Q-2\gamma ))}u$ on the Heisenberg group ℍn has [n + 1/2] sequences of nodal (sign-changing) weak solutions whose elements have mutually different nodal properties, where ${\rm {\cal L}}_\gamma $ denotes the CR fractional sub-Laplacian operator on ℍn, Q = 2n + 2 is the homogeneous dimension of ℍn, and $\gamma \in \bigcup\nolimits_{k = 1}^n [k,((kQ)/Q-1)))$. Our argument is variational, based on a Ding-type conformal pulling-back transformation of the original problem into a problem on the CR sphere S2n + 1 combined with a suitable Hebey-Vaugon-type compactness result and group-theoretical constructions for special subgroups of the unitary group U(n + 1).