Degree distribution of random birth-and-death network with network size decline

In this paper,we provide a general method to obtain the exact solutions of the degree distributions for random birthand-death network（RBDN） with network size decline.First,by stochastic process rules,the steady state transformation equations and steady state degree distribution equations are given in the case of m ≥ 3 and 0 〈 p 〈 1/2,then the average degree of network with n nodes is introduced to calculate the degree distributions.Specifically,taking m = 3 for example,we explain the detailed solving process,in which computer simulation is used to verify our degree distribution solutions.In addition,the tail characteristics of the degree distribution are discussed.Our findings suggest that the degree distributions will exhibit Poisson tail property for the declining RBDN.

The Wartime Bridge Reliability Evaluation Model Based on Birth-and-Death Process

At first, the concept of bridge reliability is given, followed with its mathematic model. Then, based on the analysis about the mechanism of the damage and repair of bridges, and the state diversion of bridge network, the state diversion process is proved to be birth-and-death process. In the end, the state diversion balance equation of bridge network is built, and the evaluation model of wartime bridge reliability is got. The model is used in a certain example, and it is proved to be precise and credible.

Birth-and-Death Q-Matrix Problem With Instantaneous States

Let E be non-negative integer set Z+ or integer set Z. Q=（q : i, j∈E） is called a birth-and-death matrix if Q satisfies the following （ⅰ）—（ⅲ）: （ⅰ） q =0, |i-j|】1, 0【q 【+∞, |i-j|=1, （1） （ⅱ） sum from j≠i q ≤qi≡-qü≤+∞, （2） （ⅲ） if E=Z+, qi【+∞ and i≠0 or E=Z and qi【+∞ then qü-1+qü+1 =qi （3） Let Q be a birth-and-death matrix. We call Q a birth-and-death matrix with

PREFERENCE AND EVOLUTION IN THE ITERATED PRISONER'S DILEMMA

Game theory is extensively used to study strategy-making and actions of play- ers. The authors proposed an analysis method for study the evolutionary outcome and behaviors of players with preference in iterated prisoner＇s dilemma. In this article, a preference parameter k was introduced in the payoff matrix, wherein the value of k denotes the player＇s degree of egoism and altruism （preference）. Then, a game-theoretic dynamical model was formulated using Birth-and-Death process. The authors studied how preference influences the evolutionary equilibrium and behaviors of players. The authors get the general results： egoism leads to defection, and altruism can make players build trust and maintain cooperation, and so, the hope of the Pareto optimal solution. In the end, the simulation experiments proved the efficiency of the method.

MHC Class I Exon 4 in the Multiocellated Racerunners(Eremias multiocellata): Polymorphism, Duplication and Selection

The major histocompatibility complex （MHC） is a dynamic genetic region with an essential role in the adaptive immunity of jawed vertebrates. The MHC polymorphism is affected by many processes such as birth-and- death evolution, gene conversion, and concerted evolution. Studies investigating the evolution of MHC class I genes have been biased toward a few particular taxa and model species. However, the investigation of this region in nonavian reptiles is still in its infancy. We present the first characterization of MHC class I genes in a species from the family Lacertidae. We assessed genetic diversity and a role of selection in shaping the diversity of MHC class I exon 4 among 37 individuals of Eremias multiocellata from a population in Lanzhou, China. We generated 67 distinct DNA sequences using cloning and sequencing methods, and identified 36 putative functional variants as well as two putative pseudogene-variants. We found the number of variants within an individual varying between two and seven, indicating that there are at least four MHC class I loci in this species. Gene duplication plays a role in increasing copy numbers of MHC genes and allelic diversity in this species. The class I exon 4 sequences are characteristic of low nucleotide diversity. No signal of recombination is detected, but purifying selection is detected in β2-microglobulin interaction sites and some other silent sites outside of the function-constraint regions. Certain identical alleles are shared by Eremias multiocellata and E. przewalskii and E. brenchleyi, suggesting trans-species polymorphism. The data are compatible with a birth-and-death model of evolution.