Key Laboratory of Mathematics

Beijing, China

Key Laboratory of Mathematics

Beijing, China

Time filter

Source Type

Zhang Z.,Peking University | Zhang Z.,Key Laboratory of Mathematics | Jiang X.,Key Laboratory of Mathematics | Ma L.,Key Laboratory of Mathematics | And 3 more authors.
Acta Physica Polonica B | Year: 2010

Dynamical properties of diffusion process on complex networks with arbitrary degree distribution are investigated. The rule of the diffusion process encompasses both the structural characteristics and the information processing dynamics. Considering the influence of a node on the global dynamical behavior, the dynamical generating function of the process, which is deeply reflecting the basic characteristic of the process and mutually decided with the dynamical process, is proposed. Based on the analysis of the dynamical generating function we introduce dynamical centrality for each node, which determines the relative importance of nodes and the capability of the given node to collect and communicate information with its neighbouring environment in the network via the diffusion process. Furthermore, a new parameter, dynamical entropy, is proposed to measure the interplay between dynamical centrality and diffusion dynamics. The experimental results on large-scale complex networks with Poisson distribution confirm our analytical prediction.


Li W.,Beihang University | Jia Y.,Beihang University | Jia Y.,Key Laboratory of Mathematics
IET Control Theory and Applications | Year: 2013

The paper proposed an adaptive filter for jump Markov systems with unknown measurement noise covariance. The filter is derived by treating covariance as a random matrix and an inverse-Wishart distribution is adopted as the conjugate prior. The variational Bayesian approximation method is employed to derive mode-conditioned estimates and mode-likelihood functions in the framework of interacting multiple model. A numerical example is provided to illustrate the performance of the proposed filter.© The Institution of Engineering and Technology 2013.


Yang X.,Key Laboratory of Mathematics | Yang X.,Beihang University | Shi Y.,Key Laboratory of Mathematics | Shi Y.,Beihang University | And 4 more authors.
IEEE Transactions on Image Processing | Year: 2010

In this paper, we present the lifting scheme of wavelet bi-frames along with theory analysis, structure, and algorithm. We show how any wavelet bi-frame can be decomposed into a finite sequence of simple filtering steps. This decomposition corresponds to a factorization of a polyphase matrix of a wavelet bi-frame. Based on this concept, we present a new idea for constructing wavelet bi-frames. For the construction of symmetric bi-frames, we use generalized Bernstein basis functions, which enable us to design symmetric prediction and update filters. The construction allows more efficient implementation and provides tools for custom design of wavelet bi-frames. By combining the different designed filters for the prediction and update steps, we can devise practically unlimited forms of wavelet bi-frames. Moreover, we present an algorithm of increasing the number of vanishing moments of bi-framelets to arbitrary order via the presented lifting scheme, which adopts an iterative algorithm and ensures the shortest lifting scheme. Several construction examples are given to illustrate the results. © 2010 IEEE.


Zhao C.,Beihang University | Zhao C.,Key Laboratory of Mathematics | Zheng Z.,Beihang University | Zheng Z.,Key Laboratory of Mathematics
Information Processing Letters | Year: 2011

We consider a random constraint satisfaction problem named model RB, which exhibits a sharp satisfiability phase-transition phenomenon when the control parameters pass through the critical values denoted by rcr and pcr. Using finite-size scaling analysis, we bound the width of the transition region for finite problem size n, which might be the first rigorous study on the threshold behaviors of NP-complete problems. © 2011 Elsevier B.V. All rights reserved.


Zhang Z.,Central University of Finance and Economics | Zhang Z.,Key Laboratory of Mathematics
Modern Physics Letters B | Year: 2014

Diffusion processes have been widely investigated to understand some essential features of complex networks, and have attracted much attention from physicists, statisticians and computer scientists. In order to understand the evolution of the diffusion process and design the optimal routing strategy according to the maximal entropic diffusion on networks, we propose the information entropy comprehending the structural characteristics and information propagation on the network. Based on the analysis of the diffusion process, we analyze the coupling impact of the structural factor and information propagating factor on the information entropy, where the analytical results fit well with the numerical ones on scale-free complex networks. The information entropy can better characterize the complex behaviors on networks and provides a new way to deepen the understanding of the diffusion process. © 2014 World Scientific Publishing Company.


Zhang Z.,Central University of Finance and Economics | Zhang Z.,Key Laboratory of Mathematics | Li H.,Central University of Finance and Economics
Modern Physics Letters B | Year: 2016

Coupling centrality and authority of co-processing model on complex networks are investigated in this paper. As one crucial factor to determine the processing ability of nodes, the information flow with potential time lag is modeled by co-processing diffusion which couples the continuous time processing and the discrete diffusing dynamics. Exact results on master equation and stationary state are obtained to disclose the formation. Considering the influence of a node to the global dynamical behavior, coupling centrality and authority are introduced for each node, which determine the relative importance and authority of nodes in the diffusion process. Furthermore, the experimental results on large-scale complex networks confirm our analytical prediction. © World Scientific Publishing Company.


Zhang Z.,Central University of Finance and Economics | Zhang Z.,Key Laboratory of Mathematics
Acta Physica Polonica B | Year: 2015

Information properties of co-processing model on communication networks are investigated in this paper. As one crucial factor to determine the processing ability of nodes, the information flow with potential time lag is modeled by co-processing diffusion which couples the continuous time processing and the discrete diffusing dynamics. Exact results on master equation and stationary state are achieved to disclose the formation. Considering the influence of a node to the global dynamical behavior, co-processing centrality is introduced for each node, which determines the relative importance of nodes and exhibits the capability that a node communicates information with its neighbor environment over the network in the diffusion process. Furthermore, a new parameter, co-processing entropy, is proposed to measure the interplay between co-processing centrality and diffusion dynamics. At last, the information function of the co-processing model is investigated to deeply detect the properties of the diffusion process. The experimental results on large-scale complex networks with Poisson distribution confirm our analytical prediction.


Zhang Z.,Central University of Finance and Economics | Zhang Z.,Key Laboratory of Mathematics
Modern Physics Letters B | Year: 2015

Coupling entropy of co-processing model on social networks is investigated in this paper. As one crucial factor to determine the processing ability of nodes, the information flow with potential time lag is modeled by co-processing diffusion which couples the continuous time processing and the discrete diffusing dynamics. Exact results on master equation and stationary state are achieved to disclose the formation. In order to understand the evolution of the co-processing and design the optimal routing strategy according to the maximal entropic diffusion on networks, we propose the coupling entropy comprehending the structural characteristics and information propagation on social network. Based on the analysis of the co-processing model, we analyze the coupling impact of the structural factor and information propagating factor on the coupling entropy, where the analytical results fit well with the numerical ones on scale-free social networks. © 2015 World Scientific Publishing Company.


Ma L.,Capital University of Economics and Business | Zhang Z.,Central University of Finance and Economics | Li M.,Key Laboratory of Mathematics
International Journal of Modern Physics C | Year: 2016

In this paper, taking the traffic of Beijing city as an instance, we study city traffic states, especially traffic congestion, based on the concept of network community structure. Concretely, using the floating car data (FCD) information of vehicles gained from the intelligent transport system (ITS) of the city, we construct a new traffic network model which is with floating cars as network nodes and time-varying. It shows that this traffic network has Gaussian degree distributions at different time points. Furthermore, compared with free traffic situations, our simulations show that the traffic network generally has more obvious community structures with larger values of network fitness for congested traffic situations, and through the GPSspg web page, we show that all of our results are consistent with the reality. Then, it indicates that network community structure should be an available way for investigating city traffic congestion problems. © 2016 World Scientific Publishing Company


PubMed | Key Laboratory of Mathematics, Educational Equipment Research & Development Center and AVIC Economics & Technology Research Establishment
Type: Journal Article | Journal: PloS one | Year: 2016

Algorithms using 4-pixel Feistel structure and chaotic systems have been shown to resolve security problems caused by large data capacity and high correlation among pixels for color image encryption. In this paper, a fast color image encryption algorithm based on the modified 4-pixel Feistel structure and multiple chaotic maps is proposed to improve the efficiency of this type of algorithm. Two methods are used. First, a simple round function based on a piecewise linear function and tent map are used to reduce computational cost during each iteration. Second, the 4-pixel Feistel structure reduces round number by changing twist direction securely to help the algorithm proceed efficiently. While a large number of simulation experiments prove its security performance, additional special analysis and a corresponding speed simulation show that these two methods increase the speed of the proposed algorithm (0.15s for a 256*256 color image) to twice that of an algorithm with a similar structure (0.37s for the same size image). Additionally, the method is also faster than other recently proposed algorithms.

Loading Key Laboratory of Mathematics collaborators
Loading Key Laboratory of Mathematics collaborators