The criteria on separation cutoff for birth and death chains were obtained by Diaconis and Saloff-Coste in 2006. These criteria are involving all eigenvalues. In this paper, we obtain the explicit criterion, which dep...The criteria on separation cutoff for birth and death chains were obtained by Diaconis and Saloff-Coste in 2006. These criteria are involving all eigenvalues. In this paper, we obtain the explicit criterion, which depends only on the birth and death rates. Furthermore, we present two ways to estimate moments of the fastest strong stationary time and then give another but equivalent criterion explicitly.展开更多
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 stat...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.展开更多
A new stochastic epidemic model, that is, a general continuous time birth and death chain model, is formulated based on a deterministic model including vaccination. We use continuous time Markov chain to construct the...A new stochastic epidemic model, that is, a general continuous time birth and death chain model, is formulated based on a deterministic model including vaccination. We use continuous time Markov chain to construct the birth and death process. Through the Kolmogorov forward equation and the theory of moment generating function, the corresponding population expectations are studied. The theoretical result of the stochastic model and deterministic version is also given. Finally, numerical simulations are carried out to substantiate the theoretical results of random walk.展开更多
Subsequent to a peripheral nerve injury, there are changes in gene expression within the dorsal root ganglia in response to the damage. This review selects factors which are well-known to be vital for inflammation, ce...Subsequent to a peripheral nerve injury, there are changes in gene expression within the dorsal root ganglia in response to the damage. This review selects factors which are well-known to be vital for inflammation, cell death and nociception, and highlights how alterations in their gene expression within the dorsal root ganglia can affect functional recovery. The majority of studies used polymerase chain reaction within animal models to analyse the dynamic changes following peripheral nerve injuries. This review aims to highlight the factors at the gene expression level that impede functional recovery and are hence are potential targets for therapeutic approaches. Where possible the experimental model, specific time-points and cellular location of expression levels are reported.展开更多
基金Acknowledgements This work was supported in part by 985 Project, 973 Project （No. 2011CB808000）, the National Natural Science Foundation of China （Grant No. 11131003）, the Specialized Research Fund for the Doctoral Program of Higher Education （No. 20100003110005）, and the Fundamental Research Funds for the Central Universities.
文摘The criteria on separation cutoff for birth and death chains were obtained by Diaconis and Saloff-Coste in 2006. These criteria are involving all eigenvalues. In this paper, we obtain the explicit criterion, which depends only on the birth and death rates. Furthermore, we present two ways to estimate moments of the fastest strong stationary time and then give another but equivalent criterion explicitly.
基金Project supported by the National Natural Science Foundation of China(Grant No.61273015)the Chinese Scholarship Council
文摘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.
文摘A new stochastic epidemic model, that is, a general continuous time birth and death chain model, is formulated based on a deterministic model including vaccination. We use continuous time Markov chain to construct the birth and death process. Through the Kolmogorov forward equation and the theory of moment generating function, the corresponding population expectations are studied. The theoretical result of the stochastic model and deterministic version is also given. Finally, numerical simulations are carried out to substantiate the theoretical results of random walk.
基金supported by the Hargreaves and Ball Trust,the National Institute for Health Research(II-LA-0313-20003)(to AJR)the Rosetrees Trust,the Academy of Medical Sciences,and the Manchester Regenerative Medicine Network(MaRMN)(to AF and AJR)Progetto Eccellenza from the Italian Ministry of Research(to VM)
文摘Subsequent to a peripheral nerve injury, there are changes in gene expression within the dorsal root ganglia in response to the damage. This review selects factors which are well-known to be vital for inflammation, cell death and nociception, and highlights how alterations in their gene expression within the dorsal root ganglia can affect functional recovery. The majority of studies used polymerase chain reaction within animal models to analyse the dynamic changes following peripheral nerve injuries. This review aims to highlight the factors at the gene expression level that impede functional recovery and are hence are potential targets for therapeutic approaches. Where possible the experimental model, specific time-points and cellular location of expression levels are reported.
