ترغب بنشر مسار تعليمي؟ اضغط هنا

Degree-distribution Stability of Growing Networks

360   0   0.0 ( 0 )
 نشر من قبل Xiangxing Kong
 تاريخ النشر 2009
  مجال البحث فيزياء
والبحث باللغة English




اسأل ChatGPT حول البحث

In this paper, we abstract a kind of stochastic processes from evolving processes of growing networks, this process is called growing network Markov chains. Thus the existence and the formulas of degree distribution are transformed to the corresponding problems of growing network Markov chains. First we investigate the growing network Markov chains, and obtain the condition in which the steady degree distribution exists and get its exact formulas. Then we apply it to various growing networks. With this method, we get a rigorous, exact and unified solution of the steady degree distribution for growing networks.

قيم البحث

اقرأ أيضاً

From the perspective of probability, the stability of growing network is studied in the present paper. Using the DMS model as an example, we establish a relation between the growing network and Markov process. Based on the concept and technique of fi rst-passage probability in Markov theory, we provide a rigorous proof for existence of the steady-state degree distribution, mathematically re-deriving the exact formula of the distribution. The approach based on Markov chain theory is universal and performs well in a large class of growing networks.
Based on the concept and techniques of first-passage probability in Markov chain theory, this letter provides a rigorous proof for the existence of the steady-state degree distribution of the scale-free network generated by the Barabasi-Albert (BA) m odel, and mathematically re-derives the exact analytic formulas of the distribution. The approach developed here is quite general, applicable to many other scale-free types of complex networks.
We study the stability of quantum pure states and, more generally, subspaces for stochastic dynamics that describe continuously--monitored systems. We show that the target subspace is almost surely invariant if and only if it is invariant for the ave rage evolution, and that the same equivalence holds for the global asymptotic stability. Moreover, we prove that a strict linear Lyapunov function for the average evolution always exists, and latter can be used to derive sharp bounds on the Lyapunov exponents of the associated semigroup. Nonetheless, we also show that taking into account the measurements can lead to an improved bound on stability rate for the stochastic, non-averaged dynamics. We discuss explicit examples where the almost sure stability rate can be made arbitrary large while the average one stays constant.
121 - P.L. Ferrari 2017
We consider the totally asymmetric simple exclusion process with initial conditions generating a shock. The fluctuations of particle positions are asymptotically governed by the randomness around the two characteristic lines joining at the shock. Unl ike in previous papers, we describe the correlation in space-time emph{without} employing the mapping to the last passage percolation, which fails to exists already for the partially asymmetric model. We then consider a special case, where the asymptotic distribution is a cut-off of the distribution of the largest eigenvalue of a finite GUE matrix. Finally we discuss the strength of the probabilistic and physically motivated approach and compare it with the mathematical difficulties of a direct computation.
A preferential attachment model for a growing network incorporating deletion of edges is studied and the expected asymptotic degree distribution is analyzed. At each time step $t=1,2,ldots$, with probability $pi_1>0$ a new vertex with one edge attach ed to it is added to the network and the edge is connected to an existing vertex chosen proportionally to its degree, with probability $pi_2$ a vertex is chosen proportionally to its degree and an edge is added between this vertex and a randomly chosen other vertex, and with probability $pi_3=1-pi_1-pi_2<1/2$ a vertex is chosen proportionally to its degree and a random edge of this vertex is deleted. The model is intended to capture a situation where high-degree vertices are more dynamic than low-degree vertices in the sense that their connections tend to be changing. A recursion formula is derived for the expected asymptotic fraction $p_k$ of vertices with degree $k$, and solving this recursion reveals that, for $pi_3<1/3$, we have $p_ksim k^{-(3-7pi_3)/(1-3pi_3)}$, while, for $pi_3>1/3$, the fraction $p_k$ decays exponentially at rate $(pi_1+pi_2)/2pi_3$. There is hence a non-trivial upper bound for how much deletion the network can incorporate without loosing the power-law behavior of the degree distribution. The analytical results are supported by simulations.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا