So far, we discussed clustering algorithms that involve a hard assignment of each datapoint to a cluster, typically based on its proximity to other points in that cluster. However, simply assigning points to the nearest cluster is not always adequate to capture more complex structure. For example, the lecture slides show an example where one cluster is much larger and less dense than another. W...

In this paper, we construct a weighted industrial cluster complex network model according to preferential attachment and local world mechanism, in which the logistics amount of business contact between one enterprise and others is defined as edge weight. We simulate and analyze statistic characteristics of the industrial cluster model such as degree distribution, point strength, point strengthp...

We present a novel, generally applicable Monte Carlo algorithm for the simulation of fluid systems. Geometric transformations are used to identify clusters of particles in such a manner that every cluster move is accepted, irrespective of the nature of the pair interactions. The rejection-free and nonlocal nature of the algorithm make it particularly suitable for the efficient simulation of com...

This paper investigates a new cluster antisynchronization scheme in the time-varying delays coupled complex dynamical networks with nonidentical nodes. Based on the community structure of the networks, the controllers are designed differently between the nodes in one community that have direct connections to the nodes in other communities and the nodes without direct connections with the nodes ...

Based on the ordering and competition of length scales in complex multi-scale systems, it is shown how clustering of active quantities into concentrated sets, like bubbles in a Swiss cheese, is a generic property that dominates the intermittent structure. The halo-like surfaces of these clusters have scaling exponents lower than that of their kernels, which can be as high as the domain dimensio...

Non-standard database applications require adequate modeling facilities for their application objects which in general have an internal structure to be maintained by the database system. For this purpose, the database system has to provide fast access to such an object as a whole as well as to its components. In systems which support complex objects with a statically established structure, clus...

The “algorithm driven by the density estimate for the identification of clusters” (DEDICA, Pisani 1993, 1996) is applied to the A3558 cluster complex in order to find substructures. This complex, located at the center of the Shapley Concentration supercluster, is a chain formed by the ACO clusters A3556, A3558 and A3562 and the two poor clusters SC 1327-312 and SC 1329-313. We find a large numb...

a r t i c l e i n f o a b s t r a c t Cluster synchronization of complex dynamical networks with fractional-order dynamical nodes is discussed in the Letter. By using the stability theory of fractional-order differential system and linear pinning control, a sufficient condition for the stability of the synchronization behavior in complex networks with fractional order dynamics is derived. Only ...

Abstract—In this paper, the fixed-time cluster synchronization problem for complex networks via pinning control is discussed. Fixed-time synchronization has been a hot topic in recent years, which means that the network can achieve synchronization in finite-time and the settling time is bounded by a constant for any initial values. To realize the fixed-time cluster synchronization, a simple dis...

Synchronization is of central importance in power distribution, telecommunication, neuronal and biological networks. Many networks are observed to produce patterns of synchronized clusters, but it has been difficult to predict these clusters or understand the conditions under which they form. Here we present a new framework and develop techniques for the analysis of network dynamics that shows ...