The chimera states underlying many realistic dynamical processes have attracted ample attention in the area of dynamical systems.Here, we generalize the Kuramoto model with nonlocal coupling incorporating higher-order...The chimera states underlying many realistic dynamical processes have attracted ample attention in the area of dynamical systems.Here, we generalize the Kuramoto model with nonlocal coupling incorporating higher-order interactions encoded with simplicial complexes.Previous works have shown that higher-order interactions promote coherent states.However, we uncover the fact that the introduced higher-order couplings can significantly enhance the emergence of the incoherent state.Remarkably, we identify that the chimera states arise as a result of multi-attractors in dynamic states.Importantly, we review that the increasing higher-order interactions can significantly shape the emergent probability of chimera states.All the observed results can be well described in terms of the dimension reduction method.This study is a step forward in highlighting the importance of nonlocal higher-order couplings, which might provide control strategies for the occurrence of spatial-temporal patterns in networked systems.展开更多
Learning unlabeled data is a significant challenge that needs to han-dle complicated relationships between nominal values and attributes.Increas-ingly,recent research on learning value relations within and between att...Learning unlabeled data is a significant challenge that needs to han-dle complicated relationships between nominal values and attributes.Increas-ingly,recent research on learning value relations within and between attributes has shown significant improvement in clustering and outlier detection,etc.However,typical existing work relies on learning pairwise value relations but weakens or overlooks the direct couplings between multiple attributes.This paper thus proposes two novel and flexible multi-attribute couplings-based distance(MCD)metrics,which learn the multi-attribute couplings and their strengths in nominal data based on information theories:self-information,entropy,and mutual information,for measuring both numerical and nominal distances.MCD enables the application of numerical and nominal clustering methods on nominal data and quantifies the influence of involving and filtering multi-attribute couplings on distance learning and clustering perfor-mance.Substantial experiments evidence the above conclusions on 15 data sets against seven state-of-the-art distance measures with various feature selection methods for both numerical and nominal clustering.展开更多
基金Project supported by the National Natural Science Foundation of China (Grants Nos.12375031 and 11905068)the Natural Science Foundation of Fujian Province, China (Grant No.2023J01113)the Scientific Research Funds of Huaqiao University (Grant No.ZQN-810)。
文摘The chimera states underlying many realistic dynamical processes have attracted ample attention in the area of dynamical systems.Here, we generalize the Kuramoto model with nonlocal coupling incorporating higher-order interactions encoded with simplicial complexes.Previous works have shown that higher-order interactions promote coherent states.However, we uncover the fact that the introduced higher-order couplings can significantly enhance the emergence of the incoherent state.Remarkably, we identify that the chimera states arise as a result of multi-attractors in dynamic states.Importantly, we review that the increasing higher-order interactions can significantly shape the emergent probability of chimera states.All the observed results can be well described in terms of the dimension reduction method.This study is a step forward in highlighting the importance of nonlocal higher-order couplings, which might provide control strategies for the occurrence of spatial-temporal patterns in networked systems.
基金funded by the MOE(Ministry of Education in China)Project of Humanities and Social Sciences(Project Number:18YJC870006)from China.
文摘Learning unlabeled data is a significant challenge that needs to han-dle complicated relationships between nominal values and attributes.Increas-ingly,recent research on learning value relations within and between attributes has shown significant improvement in clustering and outlier detection,etc.However,typical existing work relies on learning pairwise value relations but weakens or overlooks the direct couplings between multiple attributes.This paper thus proposes two novel and flexible multi-attribute couplings-based distance(MCD)metrics,which learn the multi-attribute couplings and their strengths in nominal data based on information theories:self-information,entropy,and mutual information,for measuring both numerical and nominal distances.MCD enables the application of numerical and nominal clustering methods on nominal data and quantifies the influence of involving and filtering multi-attribute couplings on distance learning and clustering perfor-mance.Substantial experiments evidence the above conclusions on 15 data sets against seven state-of-the-art distance measures with various feature selection methods for both numerical and nominal clustering.
