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Register a new userDecay of Scale-Free Property in Birth-and-Death Network
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In this paper, a baseline model termed as random birth-and-death network model (RBDN) is considered, in which at each time step, a new node is added into the network with probability p (0<p <1) connect it with m old nodes uniformly, or an existing node is deleted from the network with probability q=1-p. This model allows for fluctuations in size, which may reach many different disciplines in physics, ecology and economics. The purpose of this study is to develop the RBDN model and explore its basic statistical properties. For different p, we first discuss the network size of RBDN. And then combining the stochastic process rules (SPR) based Markov chain method and the probability generating function method, we provide the exact solutions of the degree distributions. Finally, the characteristics of the tail of the degree distributions are explored after simulation verification. Our results show that the tail of the degree distribution for RBDN exhibits a Poisson tail in the case of 0<p<=1/2 and an exponential tail as p approaches to 1.
Simulations of physicists for the competition between adult languages since 2003 are reviewed. How many languages are spoken by how many people? How many languages are contained in various language families? How do language similarities decay with geographical distance, and what effects do natural boundaries have? New simulations of bilinguality are given in an appendix.
We model information traffic on scale-free networks by introducing the bandwidth as the delivering ability of links. We focus on the effects of bandwidth on the packet delivering ability of the traffic system to better understand traffic dynamic in real network systems. Such ability can be measured by a phase transition from free flow to congestion. Two cases of node capacity C are considered, i.e., C=constant and C is proportional to the nodes degree. We figured out the decrease of the handling ability of the system together with the movement of the optimal local routing coefficient $alpha_c$, induced by the restriction of bandwidth. Interestingly, for low bandwidth, the same optimal value of $alpha_c$ emerges for both cases of node capacity. We investigate the number of packets of each node in the free flow state and provide analytical explanations for the optimal value of $alpha_c$. Average packets traveling time is also studied. Our study may be useful for evaluating the overall efficiency of networked traffic systems, and for allevating traffic jam in such systems.
We use methods from combinatorics and algebraic statistics to study analogues of birth-and-death processes that have as their state space a finite subset of the $m$-dimensional lattice and for which the $m$ matrices that record the transition probabilities in each of the lattice directions commute pairwise. One reason such processes are of interest is that the transition matrix is straightforward to diagonalize, and hence it is easy to compute $n$ step transition probabilities. The set of commuting birth-and-death processes decomposes as a union of toric varieties, with the main component being the closure of all processes whose nearest neighbor transition probabilities are positive. We exhibit an explicit monomial parametrization for this main component, and we explore the boundary components using primary decomposition.
This letter propose a new model for characterizing traffic dynamics in scale-free networks. With a replotted road map of cities with roads mapped to vertices and intersections to edges, and introducing the road capacity L and its handling ability at intersections C, the model can be applied to urban traffic system. Simulations give the overall capacity of the traffic system which is quantified by a phase transition from free flow to congestion. Moreover, we report the fundamental diagram of flow against density, in which hysteresis is found, indicating that the system is bistable in a certain range of vehicle density. In addition, the fundamental diagram is significantly different from single-lane traffic model and 2-D BML model with four states: free flow, saturated flow, bistable and jammed.
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