Synchronization Stability in Weighted Complex Networks with Coupling Delays

Realistic networks display not only a complex topological structure, but also a heterogeneous distribution of weights in connection strengths. In addition, the information spreading through a complex network is often associated with time delays due to the finite speed of signal transmission over a distance. Hence, the weighted complex network with coupling delays have meaningful implications in real world, and resultantly gains increasing attention in various fields of science and engineering. Based on the theory of asymptotic stability of linear time-delay systems, synchronization stability of the weighted complex dynamical network with coupling delays is investigated, and simple criteria are obtained for both delay-independent and delay-dependent stabilities of synchronization states. The obtained criteria in this paper encompass the established results in the literature as special cases. Some examples are given to illustrate the theoretical results.

Hash function construction using weighted complex dynamical networks

A novel scheme to construct a hash function based on a weighted complex dynamical network （WCDN） generated from an original message is proposed in this paper. First, the original message is divided into blocks. Then, each block is divided into components, and the nodes and weighted edges are well defined from these components and their relations. Namely, the WCDN closely related to the original message is established. Furthermore, the node dynamics of the WCDN are chosen as a chaotic map. After chaotic iterations, quantization and exclusive-or operations, the fixed-length hash value is obtained. This scheme has the property that any tiny change in message can be diffused rapidly through the WCDN, leading to very different hash values. Analysis and simulation show that the scheme possesses good statistical properties, excellent confusion and diffusion, strong collision resistance and high efficiency.

有向图的加权解析挠率

In 2020,Alexander Grigor'yan,Yong Lin and Shing-Tung Yau[6]introduced the Reidemeister torsion and the analytic torsion for digraphs by means of the path complex and the path homology theory.Based on the analytic torsion for digraphs introduced in[6],we consider the notion of weighted analytic torsion for vertex-weighted digraphs.For any non-vanishing real functions f and g on the vertex set,we consider the vertex-weighted digraphs with the weights(f;g).We calculate the(f;g)-weighted analytic torsion by examples and prove that the(f;g)-weighted analytic torsion only depend on the ratio f=g.In particular,if the weight is of the diagonal form(f;f),then the weighted analytic torsion equals to the usual(un-weighted)torsion.

Modeling of Malicious Code Propagations in Internet of Things

Nowadays, the main communication object of Internet is human-human. But it is foreseeable that in the near future any object will have a unique identification and can be addressed and con- nected. The Internet will expand to the Internet of Things. IPv6 is the cornerstone of the Internet of Things. In this paper, we investigate a fast active worm, referred to as topological worm, which can propagate twice to more than three times faster tl^an a traditional scan-based worm. Topological worm spreads over AS-level network topology, making traditional epidemic models invalid for modeling the propagation of it. For this reason, we study topological worm propagation relying on simulations. First, we propose a new complex weighted network mod- el, which represents the real IPv6 AS-level network topology. And then, a new worm propagation model based on the weighted network model is constructed, which descries the topological worm propagation over AS-level network topology. The simulation results verify the topological worm model and demonstrate the effect of parameters on the propagation.

The Fine Continuity for Complex Generalized Weights

In this paper the notions of fine complex weights and the Choquet type for complex weights are introduced. And we discuss the relations between quasi continuity and fine continuity quasi everywhere.

A New Evaluation Method of Node Importance in Directed Weighted Complex Networks

Current researches on node importance evaluation mainly focus on undirected and unweighted networks, which fail to reflect the real world in a comprehensive and objective way. Based on directed weighted complex network models, the paper introduces the concept of in-weight intensity of nodes and thereby presents a new method to identify key nodes by using an importance evaluation matrix. The method not only considers the direction and weight of edges, but also takes into account the position importance of nodes and the importance contributions of adjacent nodes. Finally, the paper applies the algorithm to a microblog-forwarding network composed of 34 users, then compares the evaluation results with traditional methods. The experiment shows that the method proposed can effectively evaluate the node importance in directed weighted networks.

Trichlorozirconium η~2-Hydrazonides： Synthesis, Characterization and Their Catalytic Behavior toward Ethylene Polymerization

The trichlorozirconium η~2-hydrazonides（R=H, A; R=CH_3, B） were synthesized through the finely controlled stoichiometrical reactions of anhydrous zirconium tetrachloride with the lithium salt of either 1-（furan-2-ylmethylene）-2-phenylhydrazonide or 1-（furan-2-ylethylidene）-2-phenyl hydrazonide in the solvent tetrahydrofuran（THF）, respectively. These complexes were highly sensitive to air and moisture due to solely using less bulky ligand of hydrazonides. The molecular structures of the title complexes, determined by means of single crystal X-ray diffraction, were found to be the distorted pentagonal bipyramid geometry around zirconium atom, with three chlorides and the hydrazonato ligand acting as the η~2-coordination mode as well as two incorporated THF molecules. Upon activation with either methylaluminoxane（MAO） or modified methylaluminoxane（MMAO）, both complexes A and B exhibited catalytic activities toward ethylene polymerization, producing polyethylenes with ultra-high molecular weights.