Consider the following growing network model in which each node i isassigned an attractiveness a, EN+ 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 hasinitially 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 existingnode i of the network chosen with probability II, given bywhereΠ II₁ =z =Σ αγj=1,...,N(t-1)Provide the mean-field solution of the model by considering thefollowing two points.(A) Assume thatZat,where a indicates the average of a over the distribution (a).Derive the time evolution k = k(t) of the expected degree k; of a nodei in the mean-field approximation.

I can help you understand the mean-field solution of the growing network model.*Model…

Answered: Consider the following growing network…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Use the Massey Method with a 10 max point differential for the following system: During the Early Part of the Season: Team B beats C by 8 points. Team D beats E by 5 points. During the Middle Part of the Season: Team A beats D by 10 points. Team E beats C by 5 points. During the Later Part of the Season: Team A beats E by 4. Team E beats B by 20 points. a. Draw a directed graph of this the season. Note that this question asks you to cap the point differential. b. Write the system of equations for this season using the Massey method. c. Solve the system (using least squares) to find the ratings for each team, and use those ratings to rank them.
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Consider the following model to grow simple networks. At time t = 1 we start with a complete network with no = 6 nodes. At each time step t> 1 a new node is added to the network. The node arrives together with m = = 2 new links, which are connected to 2 different nodes already present in the network. The probability II; that a new link is connected to node i is: m = N(t-1) Π ki - 1 Z with Z = Σ (ky - 1) j=1 I where ki is the degree of node i, and N(t - 1) is the number of nodes in the network at time t-1.
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National income from manufacturing industries is to be estimated for 1989 from a sample of 6 of the 19 industry categories that reported figures early for that year. Incomes from all 19 industries are known for 1980 and the total is $674 billion. From the data provided, estimate the total national income from manufacturing in 1989, with a bound on the error. All figures are in billions of constant (1982) dollars. Industry 1980 1989 Lumber and wood products Electrie and electronie 21 63 26 91 equipment Motor vehicles and 91 47 equipment Food and kindred products Textile mill products 70 70 60 70 Chemicals and allied 50 50 products a. Find a ratio estimator of the 1989 total income, and place a bound on the error of estimation. Interpret the results. b. Find a regression estimator of the 1989 total income, and place a bound on the error of estimation. Interpret the results. c. Find a difference estimator of the 1989 total income, and place a bound on the error of estimation. d. Which of…

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