Abstract The discovery of hyperbolic lattices has provided an unprecedented platform to extend topological phases of matter from Euclidean to non-Euclidean spaces. However, to date, most studies on hyperbolic topological states have been limited to type-I hyperbolic lattices, with few reports on type-II hyperbolic lattices. Inspired by the recent experimental realization of topological Anderson insulators and the study of non-Euclidean lattices, we investigate the impact of disorder on type-II hyperbolic quantum spin Hall insulator (QSHI). Our study demonstrates that the helical edge states of the QSHI phase are robust against weak disorder. Most notably, we find that disorder can induce a phase transition from a trivial phase to a QSHI phase, as confirmed by numerical results based on the real-space spin Bott index. Finally, by calculating the quantized conductance and real-space density distributions, we identify this disorder-induced phase as a type-II hyperbolic topological Anderson insulator (HTAI).

Abstract Alzheimer’s Disease (AD) is a neurodegenerative disorder that poses a serious threat to the quality of life of the elderly population, and its early diagnosis is crucial for slowing disease progression. This study proposes a novel multimodal classification framework that integrates structural magnetic resonance imaging (sMRI) and APOE genotype data with deep learning techniques to improve AD classification performance. Specifically, three core modules are designed: 1) the Spatial Enhancement Weighting Module (SEWM), which enhances local anatomical feature extraction from sMRI data using channel and spatial attention mechanisms; 2) the Parallel Multi-Scale Feature Fusion Module (PMSFM), which fuses multi-scale features through pixel-level attention mechanisms to capture subtle pathological changes; and 3) the Abstract Patch (AP) module, which compresses high-dimensional data using depthwise separable convolutions and multi-head self-attention mechanisms to reduce computational complexity. Experiments were conducted using data from the ADNI database, with ADNI1, ADNI GO, and ADNI2 as the training set and ADNI3 as the independent validation set. Results show that the proposed method achieves an accuracy of 86.2% in the three-class classification task (CN versus MCI versus AD) and up to 96.2% in the binary classification task (CN versus AD), surpassing existing multimodal models. Further analysis demonstrates that the synergistic effects among the modules effectively enhance the model’s ability to distinguish MCI heterogeneity and AD pathological features. This study provides an efficient technical approach for the early diagnosis of AD. Future work will focus on model lightweighting and cross-center data validation.

Abstract Color multiplets of the gauge fields and fermions on mass shell in SU (N ) Yang-Mills theory are classified according to representations of the Weyl group W (SU (N )). The multiplet structure of quark and gluon multiplets has been studied in the framework of a non-perturbative approach by considering complete exact equations of motion of the SU (N ) Yang-Mills theory with matter fields. An important case of singlet non-Abelian gluon solutions corresponding to one-dimensional singlet representations of the Weyl group is revised on a rigorous mathematical basis. We demonstrate that Weyl group as a finite color subgroup of SU (N ) reveals an inherent color symmetry of quarks and gluons on mass shell which determines a universal color multiplet structure of quark-gluon solutions in a pure SU (N ) Yang-Mills theory and in Abelian projected Yang-Mills theories with quarks. The obtained results allow to introduce strict concepts of fundamental particles, quarks and gluons, which differ drastically from the particle definitions in the conventional perturbative Yang-Mills theory. Possible applications of our results in non-perturbative quantum chromodynamics and hadron physics are discussed.