Consider the following growing network model in which each node i isassigned an attractiveness a¿ € N+ drawn from a distribution π(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 of the network chosen with probability II; given bywhereZ=Ili=aiZ'Σ aj.j=1,...,N(t−1) (B) Assume thatπ(a) = {and that Z ~āt.1,1 for a =0 for a 1,Derive the degree distribution P(k) of the network for large times, i.e.t>1, in the mean-field approximation.

In the mean-field approximation:(A) The expected degree of any node at any time is approximately…

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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3.1.1. (-) Find a maximum matching in each graph below. Prove that it is a maximum matching by exhibiting an optimal solution to the dual problem (minimum vertex cover). Explain why this proves that the matching is optimal.
prove the property
The table gives heavy - metal nuclear waste (in thousands of metric tons) from spent reactor fuel now stored temporarily at reactor sites, awaiting permanent storage. Waste y Year x 1995 32 2000 42 2010 61 2020 76 Let x = 0 represent 1995, x = 5 represent 2000 (since 2000 - 1995 = 5), and so on. a) For 1995, the ordered pair is (0, 32). Write the ordered pair for the data for the other years given in the table. b) Plot the ordered pairs (x,y). Do the points lie approximately in a straight line? c) Use the ordered pairs (0, 32) and (25, 76) to find the equation of a line that approximates the other ordered pairs. Write the equation in slope - intercept form and in standard form. d) Use the slope - intercept equation form from part (c) to estimate the amount of nuclear waste in 2005.
3. Of all customers purch asing automatic ga age-door openers, 60% purchase a chain-driven model. Let X - the number among the next 15 purch as ers who select the ch ain -driven model. Wh at is the probab il ity that more th an 12 of the 15 purch asers select a ch ain- (a) driven mo del? (b) purch ase a ch ain -driven model? Wh at is the probability that fewer th an 5 of the next 15 purchasers do not (c) Calculate P(9 < X < 13) Wh at is the probability that the nu mber of the next 15 purchasers who select (d) the chain driven model is wit hin one st and ard deviation of the expected value of X?
28. Show by short-cut method whether there is dissociation or positive or iegafive association in the following attributes A and B. (a) (b) (c). (A) = 470, (B) = 620, (AB) = 320, N= 1,000 (A) = 490, (AB) = 294, (a) = 570, (aß) = 380 (AB) = 256, (AB) = 48, (aB) = 144, aB) = 768 %3D
which of the following is true
Determine the optimal assignment that will maximize the total average production of shirt Enrichment Exercise 6.3 RSS garment manufacturer produces different kinds of shirts, which is supplies to various boutiques in the country. The production department records indicate that a different employee produces different number of items. The average number of outputs by each employee for each of six shirts is given in the following table. Shirts Employee В 1 98 123 97 118 122 66 110 2. 120 117 130 118 119 3. 125 105 96 116 115 110 4 90 96 122 110 95 126 110 120 115 108 132 118 6. 115 111 114 96 127 124 per week.
(a) Show that the number of paths from (0,0) to (n, m) taking steps of size (0,1) or (1,0) is ("m"). (b) Show that the number of integer partitions (of any size) with at most n parts and with largest part of size at most m equals ("+").
1. A company is contemplating the introduction of a new product with new packing to replace the existing product at much higher Price (P) or a moderate change in the composition of the existing product with a new packaging at a small increase in price (P2) or a small change in the composition of the existing product except the word "new" with a very small increase in price (P3). The three possible states of nature are : (i) high increase in sales (n), (ii) no change in sales (n), and (iii) decrease in sales (na). The marketing department of the company calculated the payoffs in terms of yearly net profits from each of the strategies (expected sales). This is represented in the following table : Strategies States of Nature 3000 1500 PI P2 P3 7000 5000 3000 4500 3000 3000 Which strategy should the concerned executive choose on the basis of: (i) Maximin criterion, (ii) Laplace criterion ?
The following table shows the stock market performance of 40 industries from five sectors of the U.S. economy in a certain year. (Take S to be the set of all 40 industries represented in the table.) Increased Decreased Unchanged (Z) Totals (X) (Y) Financials (F) 4 1 8. Manufacturing (M) 6. 4 4 14 Information 4 Technology (T) Health Care (H) 1 1 8. Utilities (U) 1 Totals 22 11 7 40 Use symbols to describe the event that an industry increased in value but was not in the manufacturing sector. OXn M' O X'U M' OX'n M OXUM X'n M' How many elements are in this event? 3.
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