Meifeng Dai

Random walks on non-homogenous weighted Koch networks.

In this paper, we introduce new models of non-homogenous weighted Koch networks on real traffic systems depending on the three scaling factors r1,r2,r3∈(0,1). Inspired by the definition of the average weighted shortest path (AWSP), we define the average weighted receiving time (AWRT). Assuming that the walker, at each step, starting from its current node, moves uniformly to any of its neighbors, we show that in large network, the AWRT grows as power-law function of the network order with the exponent, represented by θ(r1,r2,r3)=log4(1+r1+r2+r3). Moreover, the AWSP, in the infinite network order limit, only depends on the sum of scaling factors r1,r2,r3.

SCALING OF THE AVERAGE RECEIVING TIME ON A FAMILY OF WEIGHTED HIERARCHICAL NETWORKS

In this paper, based on the un-weight hierarchical networks, a family of weighted hierarchical networks are introduced, the weight factor is denoted by r. The weighted hierarchical networks depend on the number of nodes in complete bipartite graph, denoted by n1, n2 and n = n1 + n2. Assume that the walker, at each step, starting from its current node, moves to any of its neighbors with probability proportional to the weight of edge linking them. We deduce the analytical expression of the average receiving time (ART). The obtained remarkable results display two conditions. In the large network, when nr > n1n2, the ART grows as a power-law function of the network size |V (Gk)| with the exponent, represented by θ =logn( nr n1n2 ), 0 < θ < 1. This means that the smaller the value of θ, the more efficient the process of receiving information. When nr ≤ n1n2, the ART grows with increasing order |V (Gk)| as logn|V (Gk)| or (logn|V (Gk)|)2.

FIRST-ORDER NETWORK COHERENCE AND EIGENTIME IDENTITY ON THE WEIGHTED CAYLEY NETWORKS

In this paper, we first study the first-order network coherence, characterized by the entire mean first-passage time (EMFPT) for weight-dependent walk, on the weighted Cayley networks with the weight factor. The analytical formula of the EMFPT is obtained by the definition of the EMFPT. The obtained results show that the scalings of first-order coherence with network size obey four laws along with the range of the weight factor. Then, we study eigentime identity quantifying as the sum of reciprocals of all nonzero normalized Laplacian eigenvalues on the weighted Cayley networks with the weight factor. We show that all their eigenvalues can be obtained by calculating the roots of several small-degree polynomials defined recursively. The obtained results show that the scalings of the eigentime identity on the weighted Cayley networks obey two laws along with the range of the weight factor.

The entire mean weighted first-passage time on infinite families of weighted tree networks

We propose the entire mean weighted first-passage time (EMWFPT) for the first time in the literature. The EMWFPT is obtained by the sum of the reciprocals of all nonzero Laplacian eigenvalues on weighted networks. Simplified calculation of EMWFPT is the key quantity in the study of infinite families of weighted tree networks, since the weighted complex systems have become a fundamental mechanism for diverse dynamic processes. We base on the relationships between characteristic polynomials at different generations of their Laplacian matrix and Laplacian eigenvalues to compute EMWFPT. This technique of simplified calculation of EMWFPT is significant both in theory and practice. In this paper, firstly, we introduce infinite families of weighted tree networks with recursive properties. Then, we use the sum of the reciprocals of all nonzero Laplacian eigenvalues to calculate EMWFPT, which is equal to the average of MWFPTs over all pairs of nodes on infinite families of weighted networks. In order to compute EMWFPT, we try to obtain the analytical expressions for the sum of the reciprocals of all nonzero Laplacian eigenvalues. The key step here is to calculate the constant terms and the coefficients of first-order terms of characteristic polynomials. Finally, we obtain analytically the closed-form solutions to EMWFPT on the weighted tree networks and show that the leading term of EMWFPT grows superlinearly with the network size.

SPECTRAL ANALYSIS FOR WEIGHTED ITERATED TRIANGULATIONS OF GRAPHS

Much information about the structural properties and dynamical aspects of a network is measured by the eigenvalues of its normalized Laplacian matrix. In this paper, we aim to present a first study on the spectra of the normalized Laplacian of weighted iterated triangulations of graphs. We analytically obtain all the eigenvalues, as well as their multiplicities from two successive generations. As an example of application of these results, we then derive closed-form expressions for their multiplicative Kirchhoff index, Kemeny’s constant and number of weighted spanning trees.

MIXED MULTIFRACTAL ANALYSIS OF CRUDE OIL, GOLD AND EXCHANGE RATE SERIES

The multifractal analysis of one time series, e.g. crude oil, gold and exchange rate series, is often referred. In this paper, we apply the classical multifractal and mixed multifractal spectrum to study multifractal properties of crude oil, gold and exchange rate series and their inner relationships. The obtained results show that in general, the fractal dimension of gold and crude oil is larger than that of exchange rate (RMB against the US dollar), reflecting a fact that the price series in gold and crude oil are more heterogeneous. Their mixed multifractal spectra have a drift and the plot is not symmetric, so there is a low level of mixed multifractal between each pair of crude oil, gold and exchange rate series.

Coherence analysis of a class of weighted networks

This paper investigates consensus dynamics in a dynamical system with additive stochastic disturbances that is characterized as network coherence by using the Laplacian spectrum. We introduce a class of weighted networks based on a complete graph and investigate the first- and second-order network coherence quantifying as the sum and square sum of reciprocals of all nonzero Laplacian eigenvalues. First, the recursive relationship of its eigenvalues at two successive generations of Laplacian matrix is deduced. Then, we compute the sum and square sum of reciprocal of all nonzero Laplacian eigenvalues. The obtained results show that the scalings of first- and second-order coherence with network size obey four and five laws, respectively, along with the range of the weight factor. Finally, it indicates that the scalings of our studied networks are smaller than other studied networks when 1d

EFFECTS OF FRACTAL INTERPOLATION FILTER ON MULTIFRACTAL ANALYSIS

Fractal interpolation filter is proposed for the first time in the literatures to transform original signals. Using the multifractal detrended fluctuation analysis (MFDFA), the authors investigate how the filter affects the multifractal scaling properties for both artificial and traffic signals. Specifically, the authors compare the multifractal scaling properties of signals before and after the transforms. It is shown that the fractal interpolation filter changes slightly the maximum value of the multifractal spectrum, while the values of spectrum width and maximum point of spectrum are much more affected by vertical scaling factor. The multifractal spectrum shrinks dramatically after the fractal interpolation filter. The fractal exponents in the signal change dramatically for the negative values of vertical scaling factor while remain stable otherwise. Thus, an appropriate vertical scaling factor can be found in order to minimize the effects of filter when one uses the fractal interpolation filter.

Eigentime identities for on weighted polymer networks

In this paper, we first analytically calculate the eigenvalues of the transition matrix of a structure with very complex architecture and their multiplicities. We call this structure polymer network. Based on the eigenvalues obtained in the iterative manner, we then calculate the eigentime identity. We highlight two scaling behaviors (logarithmic and linear) for this quantity, strongly depending on the value of the weight factor. Finally, by making use of the obtained eigenvalues, we determine the weighted counting of spanning trees.

Coherence analysis of a class of weighted tree-like polymer networks

Complex networks have elicited considerable attention from scientific communities. This paper investigates consensus dynamics in a linear dynamical system with additive stochastic disturbances, which is characterized as network coherence by the Laplacian spectrum. Firstly, we introduce a class of weighted tree-like polymer networks with the weight factor. Then, we deduce the recursive relationship of the eigenvalues of Laplacian matrix at two successive generations. Finally, we calculate the first- and second-order network coherence quantifying as the sum and square sum of reciprocals of all nonzero Laplacian eigenvalues. The obtained results show that the scalings of first-order coherence with network size obey four laws along with the range of the weight factor and the scalings of second-order coherence with network size obey five laws along with the range of the weight factor.