Consider the following growing network model in which each node i isassigned 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 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 bywhereaiII¿Zz =Σaj.j=1,...,N(t-1)Provide the mean-field solution of the model by considering thefollowing two points.(A) Assume thatZāt,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 nodei in the mean-field approximation.

This Is The Expression For The Expected Degree ki(t) of a node in the mean-field…

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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Let A and B represent two variants (alleles) of the DNA at a certain locus on the genome. Assume that 40% of all the alleles in a certain population are type A and 30% are type B. The locus is said to be in Hardy-Weinberg equilibrium if the proportion of organisms that are of type AB is (0.40)(0.30) = 0.12. In a sample of 300 organisms, 43 are of type AB. Can you conclude that this locus is not in Hardy- Weinberg equilibrium? Find the P-value and state a conclusion. Round the answer to four decimal places. The P-value is We (Click to select) conclude that the locus is not in Hardy-Weinberg equilibrium.
Let A and B represent two variants (alleles) of the DNA at a certain locus on the genome. Let p represent the proportion of alleles in a population that are of type A, and let q represent the proportion of alleles that are of type B. The Hardy–Weinberg equilibrium principle states that the proportion PAB of organisms that are of type AB is equal to pq. In a population survey of a particular species, the proportion of alleles of type A is estimated to be 0.360 ± 0.048 and the proportion of alleles of type B is independently estimated to be 0.250 ± 0.043. a) Estimate the proportion of organisms that are of type AB, and find the uncertainty in the estimate. b) Find the relative uncertainty in the estimated proportion. c) Which would provide a greater reduction in the uncertainty in the proportion: reducing the uncertainty in the type A proportion to 0.02 or reducing the uncertainty in the type B proportion to 0.02?
Consider the directed bipartite graph Km,n where all edges go from the m side to the n side. Introduce a new vertex s and edges from it to the m side. Similarly, introduce t and edges to it from the n side. Give all the edges capacity 1, making this a flow network G with vertex set V and edges set E. m (a) Naively, what is the maximum flow on this network? (b) Assuming m≤n, describe a (simple) min cut. (c) Assuming m≥n, describe a min cut. n C
SO what would be the L, Lq, and Wq of this problem? Assuming we are trying to develop and sovle a waiting line system that can accomodate this increased leel of passenger traffic.
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Maximize = 3x +2x, +x, 2.x, +x, +x, s150 Subject to 2x, +2x, +8x, s 200 2x, +3x, +x, 5320 with x 20,x, 20,x, 20 4 B Beta -3 -2 -1 x3 1 3 4 5 6 Beta 1 2 3 4 5 6 B Beta 0,5 1 2 3 -3 8 1,5 -0,5 -14 250 50 -2 75 85 100 160 225 150 70 -1 200 320 170 70 x1 x2 x3 x4 x5 x6 Find the initial solution using the Method of the Minimal Element.
Consider a Qunat vars X and Y and suppose we have collected data on both of them from an underlying population: PowerPoint Slide Show-LinearReg.pptx]-PowerPoint Bivariate Analysis: Modelling a Linear Relation XY After checking their scatter graph and correlation, if the amount of linear relation between the two was high enough, we can model the relation using a linear function: Y=f(X)=a+bX b= x1,x2,...,xn У1. Уг...... Уп To that end, we need to estimate a and b. a= nΣ(xy) - ΣxΣy nΣx²-(x)² Σy-bΣx n Ex: Linear of Model of Whr and Salary. Oba 1 2 3 4 E 5 6 7 8 9 10 Whrs Salary Y X 6 8 9 9 10 9 8 7 6 7 8 20 30 35 50 38 25 23 15 26 48 160 270 315 500 342 200 161 90 182 X^2 36 64 81 81 100 81 64 49 36 49 = MULTIPLE CHOICE QUESTION The Cor(X,Y)=0.9, hence b in Y=a+bX is negative negative positive Rewatch Submit
The degree distribution of a network has the following functional form: Pk = Cak, Where a < 1 is a constant, and k ≥ 1 is the degree. a. Find out the value of C. b. Find out its probability generating function go(z) in compact form. C. Find out the corresponding generating function g₁(z) for its excess degree distribution in compact form. d. Find out the probability that a node in this network has zero 2nd neighbors. condition for a such that a giant component is present. e. Find out the f. When 1 - fraction of nodes are randomly removed, find out the critical value of when giant cluster emerges. g. What is the size of the giant cluster if it exists?
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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…
Let A and B represent two variants (alleles) of the DNA at a certain locus on the genome. Assume that 40% of all the alleles in a certain population are type A and 30% are type B. The locus is said to be in Hardy- Weinberg equilibrium if the proportion of organisms that are of type AB is (0.40) (0.30) = 0.12. In a sample of 300 organisms, 42 are of type AB. Can you conclude that this locus is not in Hardy-Weinberg equilibrium?

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