In this paper, 30-slot/24-pole five-phase PMSM with hybrid single/double layer (HL) fractional-slot concentrated winding (FSCW) is designed for wheel-driving application in electric vehicles (EVs). Third harmonic current injection in different operating stages of the machine is investigated, including normal operation and fault-tolerant operation. HL FSCW machine is validated to be suitable for injecting third harmonic current to enhance torque by both theoretical analysis and finite-element analysis (FEA), and compared with 20-slot/24-pole single-layer (SL) and double-layer (DL) FSCW machine under constant rms and peak harmonic injection. Besides, a novel flux weakening control method with third harmonic current injection is proposed, which improves torque and efficiency of HL FSCW machine. The influence of nonlinearity caused by stator core saturation and higher order harmonics contained in back electromotive force (EMF) is included in flux weakening operation with harmonic injection. Finally, fault-tolerant control of HL FSCW machine with one-phase open-circuit fault is investigated, and two compensatory strategies with and without third harmonic current injection are proposed. Torque ripple caused by one-phase opencircuit fault is suppressed effectively by the proposed strategies.INDEX TERMS Permanent-magnet synchronous machine (PMSM), five-phase, fractional-slot concentrated winding (FSCW), third harmonic injection, flux weakening, fault-tolerant control, open-circuit.

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The dynamics of competing opinions on networks has attracted multi-disciplinary research. Most modelling approaches assume uniform or heterogeneous behaviour among all individuals, while the role of distinctive group behaviour is rarely addressed. Here, we consider competition occurring between two opinion groups with bound rewiring rules, i.e., opinion-preferred rewiring, degree-preferred rewiring and random rewiring. When two opinions share a balanced initial proportion, opinion-preferred rewiring is superior to the other rules under low rewiring rates, and coexistence occurs under high rewiring rates. For unbalanced proportions, the best response rule for the minority/majority is unfixed, and this depends on the initial proportion and rewiring frequency. Furthermore, we find evolution processes for all competing cases belong to two categories. Evolution Category I shows an obvious correlation between opinion proportions and the density of discordant edges (connecting nodes with different opinions), and these trends can be effectively described by numerical approximations. However, for Evolution Category II, no such correlation exists for individuals or linking pairs, and an analysis of local structures reveals the emergence of large numbers of open triads with the same opinions, denoting group prevalence. This work broadens the understanding of opinion competition and inspires exploring group strategies employed in social dynamic systems.

Attention mechanisms have made significant strides in graph learning, yet they still exhibit notable limitations: local attention faces challenges in capturing long-range information due to the inherent problems of the message-passing scheme, while global attention cannot reflect the hierarchical neighborhood structure and fails to capture fine-grained local information. In this paper, we propose a novel multihop graph attention mechanism, named Subtree Attention (STA), to address the aforementioned issues. STA seamlessly bridges the fully-attentional structure and the rooted subtree, with theoretical proof that STA approximates the global attention under extreme settings. By allowing direct computation of attention weights among multi-hop neighbors, STA mitigates the inherent problems in existing graph attention mechanisms. Further we devise an efficient form for STA by employing kernelized softmax, which yields a linear time complexity. Our resulting GNN architecture, the STAGNN, presents a simple yet performant STA-based graph neural network leveraging a hop-aware attention strategy. Comprehensive evaluations on ten node classification datasets demonstrate that STA-based models outperform existing graph transformers and mainstream GNNs. The code is available at https://github.com/LUMIA-Group/SubTree-Attention.