Consider the following growing network model in which each node i is assigned an attractiveness a € N+ drawn from a distribution (a). Let N(t) denote the total number of nodes at time t. At time t = 1 the network is formed by two nodes joined by a link. - At every time step a new node joins the network. Every new node has initially a single link that connects it to the rest of the network. - At every time step t the link of the new node is attached to an existing node i of the network chosen with probability II, given by where ai II¿ Z z = Σ aj. j=1,...,N(t-1) Provide the mean-field solution of the model by considering the following two points. (A) Assume that Zāt, where a indicates the average of a over the distribution (a). Derive the time evolution ki = ki(t) of the expected degree k; of a node i in the mean-field approximation.
Consider the following growing network model in which each node i is assigned an attractiveness a € N+ drawn from a distribution (a). Let N(t) denote the total number of nodes at time t. At time t = 1 the network is formed by two nodes joined by a link. - At every time step a new node joins the network. Every new node has initially a single link that connects it to the rest of the network. - At every time step t the link of the new node is attached to an existing node i of the network chosen with probability II, given by where ai II¿ Z z = Σ aj. j=1,...,N(t-1) Provide the mean-field solution of the model by considering the following two points. (A) Assume that Zāt, where a indicates the average of a over the distribution (a). Derive the time evolution ki = ki(t) of the expected degree k; of a node i in the mean-field approximation.
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 23EQ:
23. Consider a simple economy with just two industries: farming and manufacturing. Farming consumes...
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