arXiv subjects
Publications and source records attributed to Jiawei Chen.
We introduce an abstract algorithm that aims to find the Bregman projection onto a closed convex set. As an application, the asymptotic behaviour of an iterative method for finding a fixed point of a quasi Bregman nonexpansive mapping with the fixed-point closedness property is analyzed. We also show that our result is applicable to Bregman subgradient projectors.
We introduce and analyze an abstract algorithm that aims to find the projection onto a closed convex subset of a Hilbert space. When specialized to the fixed point set of a quasi nonexpansive mapping, the required sufficient condition (termed "fixed-point closed") is less restrictive than the usual conditions based on the demiclosedness principle. A concrete example of a subgradient projector is presented which illustrates the applicability of this generalization.
In order to take the weight of connection into consideration and to find a natural measurement of weight, we have collected papers in Econophysics and constructed a network of scientific communication to integrate idea transportation among econophysicists by collaboration, citation and personal discussion. Some basic statistics such as weight per degree are discussed in \cite{fan}. In this paper, by including the papers published recently, further statistical results for the network are reported. Clustering coefficient of weighted network is introduced and empirically studied in this network. We also compare the typical statistics on this network under different weight measurements, including random and inverse weight. The conclusion from weight-randomized network is helpful to the investigation of the geometrical role of weight.
We construct a Markov process model to describe the evolution of labor division and its dynamical behavior is investigated by numerical simulations in detail. We have shown that under the mechanism of increasing returns, the division of labor will emerge from the initial homogenous distribution and with the change of parameters there are period-adding coarse-grained bifurcations in the model. The model gives an example of emergent property in the evolution of complex systems and reveals an interesting dynamical behavior of the Markov chain process. Key words: Evolution, Bifurcation, Pattern formation PACS number(s): 87.23.-n, 89.75.Fb, 05.45.-a
The evolution of specialization in a multi-agent system is studied both by computer simulation and Markov process model. Many individual agents search for and exploit resources to get global optimization in an environment without complete information. With the selection acting on agent specialization at the level of system and under the condition of increasing returns, the division of labor emerges as the results of long-term optimizing evolution. Mathematical analysis gives the optimum division of agents and a Markov chain model is proposed to describe the evolutionary dynamics. The results are in good agreement with that of simulation model.
The development of Econophysics is studied from the perspective of scientific communication networks. Papers in Econophysics published from 1992 to 2003 are collected. Then a weighted and directed network of scientific communication, including collaboration, citation and personal discussion, is constructed. Its static geometrical properties, including degree distribution, weight distribution, weight per degree, and betweenness centrality, give a nice overall description of the research works. The way we introduced here to measure the weight of connections can be used as a general one to construct weighted network.