分类: 物理学 >> 基本粒子与场物理学 提交时间: 2016-05-08
摘要: Aiming to understand real-world hierarchical networks whose degree distributions are neither power law nor exponential, we construct a hybrid clique network that includes both homogeneous and inhomogeneous parts, and introduce an inhomogeneity parameter to tune the ratio between the homogeneous part and the inhomogeneous one. We perform Monte-Carlo simulations to study various properties of such a network, including the degree distribution, the average shortest-path-length, the clustering coefficient, the clustering spectrum, and the communicability.
分类: 物理学 >> 基本粒子与场物理学 提交时间: 2016-05-08
摘要: We design an irreversible Markov chain Monte Carlo algorithm for the self-avoiding walk (SAW). It outperforms the Berretti-Sokal algorithm. The gained efficiency increases with the spatial dimension, from about 10 times in two dimensions to around 40 times in five dimensions. The algorithm violates the widely used detailed balance condition and satisfies the weaker balance condition. We employ the irreversible method to study the finite-size scaling of SAW above the upper critical dimension.
分类: 物理学 提交时间: 2016-05-08
摘要: There are more than eight hundred interest rates published in China bond market every day.Which are the benchmark interest rates that have broad influences on most interest rates is a major concern for economists. In this paper, multi-variable Granger causality test is developed and applied to construct a directed network of interest rates, whose important nodes, regarded as key interest rates, are evaluated with inverse Page Rank scores. The results indicate that some short-term interest rates have larger influences on the most key interest rates, while repo rates are the benchmark of short-term rates. It is also found that central bank bills rates are in the core position of mid-term interest rates network, and treasury bond rates are leading the long-term bonds rates.The evolution of benchmark interest rates is also studied from 2008 to 2014, and it’s found that SHIBOR has generally become the benchmark interest rate in China. In the frequency domain we detect the properties of information flows between interest rates and the result confirms the existence of market segmentation in China bond market.
分类: 物理学 提交时间: 2016-05-08
摘要: Using finite-size scaling, we have investigated the percolation phase transitions of evolving random networks under a generalized Achlioptas process (GAP). During this GAP, the edge with a minimum product of two connecting cluster sizes is taken with a probability p from two randomly chosen edges. This model becomes the Erdos-Renyi network at p = 0.5 and the random network under the Achlioptas process at p = 1. Using both the fixed point of the size ratio s(2)/s(1) and the straight line of ln s(1), where s(1) and s(2) are the reduced sizes of the largest and the second-largest cluster, we demonstrate that the phase transitions of this model are continuous for 0.5 = 0.9, beta, upsilon, and s(2)/s(1) at critical point vary with p and the universality class of phase transitions depends on p.
分类: 物理学 提交时间: 2016-05-08
摘要: The percolation phase transitions of two-dimensional lattice networks under a generalized Achlioptas process (GAP) are investigated. During the GAP, two edges are chosen randomly from the lattice and the edge with minimum product of the two connecting cluster sizes is taken as the next occupied bond with a probability p. At p = 0.5, the GAP becomes the random growth model and leads to the minority product rule at p = 1. Using the finite-size scaling analysis, we find that the percolation phase transitions of these systems with 0.5 <= p <= 1 are always continuous and their critical exponents depend on p. Therefore, the universality class of the critical phenomena in two-dimensional lattice networks under the GAP is related to the probability parameter p in addition.
分类: 物理学 提交时间: 2016-05-08
摘要: We have investigated both site and bond percolation on two-dimensional lattice under the random rule and the product rule respectively. With the random rule, sites or bonds are added randomly into the lattice. From two candidates picked randomly, the site or bond with the smaller size product of two connected clusters is added when the product rule is taken. Not only the size of the largest cluster but also its size jump are studied to characterize the universality class of percolation. The finite-size scaling forms of giant cluster size and size jump are proposed and used to determine the critical exponents of percolation from Monte Carlo data. It is found that the critical exponents of both size and size jump in random site percolation are equal to that in random bond percolation. With the random rule, site and bond percolation belong to the same universality class. We obtain the critical exponents of the site percolation under the product rule, which are different from that of both random percolation and the bond percolation under the product rule. The universality class of site percolation differs different from that of bond percolation when the product rule is used.