Using a tunable clustering coeffcient model withoutchanging the degree distribution, we investigate the effect of clustering coefficient on synchronization of networks with both unweighted and weighted couplings. For ...Using a tunable clustering coeffcient model withoutchanging the degree distribution, we investigate the effect of clustering coefficient on synchronization of networks with both unweighted and weighted couplings. For several typical categories of complex networks, the more triangles are in the networks, the worse the synchronizability of the networks is.展开更多
With the purpose of providing a categorical treatment of weak multiplier bialgebras （introduced by BShm, Gomez-Torrecillas and Ldpez-Centella in 2015）, an ap- propriate notion of morphism for these algebraic objects...With the purpose of providing a categorical treatment of weak multiplier bialgebras （introduced by BShm, Gomez-Torrecillas and Ldpez-Centella in 2015）, an ap- propriate notion of morphism for these algebraic objects is proposed. This allows us to define a category wmb of （regular） weak multiplier bialgebras （with a right full comultipli- cation）, containing as a full subcategory the category wba of weak bialgebras defined by BShm, Gomez-Torrecillas and Lopez-Centella in 2014. We present a great source of ex- amples of these morphisms proving that, under some assumption, a functor between small categories induces a morphism of this kind between the natural weak multiplier bialgebra structures carried by the linear spans of the arrow sets of the categories. We explore the notion of elements of group-like type in a weak multiplier bialgebra, proposing a definition in the line of the one by the aforementioned authors for weak bialgebras. We show a big number of its properties and provide more general versions of many results known in the context of weak bialgebras. In particular, in analogy with the classical bialgebra setting （where the set of group-like elements is a monoid）, we prove that the set of these elements possesses a structure of category.展开更多
基金The project partly supported by National Natural Science Foundation for Distinguished Young Scholars of China under Grant No. 60225013, National Natural Science Foundation of China under Grants Nos. 70271072, 70431002, and 90412004, and Shanghai RisingStar Program under Grant No.05QMX1436Author （X. Li） also acknowledges the support from the Alexander von Humboldt Foundation.
文摘Using a tunable clustering coeffcient model withoutchanging the degree distribution, we investigate the effect of clustering coefficient on synchronization of networks with both unweighted and weighted couplings. For several typical categories of complex networks, the more triangles are in the networks, the worse the synchronizability of the networks is.
文摘With the purpose of providing a categorical treatment of weak multiplier bialgebras （introduced by BShm, Gomez-Torrecillas and Ldpez-Centella in 2015）, an ap- propriate notion of morphism for these algebraic objects is proposed. This allows us to define a category wmb of （regular） weak multiplier bialgebras （with a right full comultipli- cation）, containing as a full subcategory the category wba of weak bialgebras defined by BShm, Gomez-Torrecillas and Lopez-Centella in 2014. We present a great source of ex- amples of these morphisms proving that, under some assumption, a functor between small categories induces a morphism of this kind between the natural weak multiplier bialgebra structures carried by the linear spans of the arrow sets of the categories. We explore the notion of elements of group-like type in a weak multiplier bialgebra, proposing a definition in the line of the one by the aforementioned authors for weak bialgebras. We show a big number of its properties and provide more general versions of many results known in the context of weak bialgebras. In particular, in analogy with the classical bialgebra setting （where the set of group-like elements is a monoid）, we prove that the set of these elements possesses a structure of category.
