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. 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?
(6) Population Modeling with Discrete Dynamical Linear Systems. We now discuss populations with discrete breeding seasons, where reproduc- tion is limited to a particluar season of the year. For example, let's consider the number of female ruby-throated hummingbirds in a population with an annual breeding season of March to July. A female usually lays one clutch of two eggs; sometimes two clutches are laid. We will assume that the average life span of a female hummingbird is four years. We define the age of a bird at the END of a breeding season as follows: age zero (0) : any bird that is born during the current breeding season age one (1): any zero-year old bird which survives to the end of the next breeding season age two (2): any one-year old bird which survives to the end of the next breeding season age three (3): any two-year old bird which survives to the end of the next breeding season We make the following assumptions about the reproductive viability of female birds: age zero…
We are interested in studying cigarette demand by young adults. Lets consider thefollowing model:ncaj = β0 + β1price + β2age + β3income + uwhere ncaj is monthly cigarette consumption in packs, price is the price of a pack ofcigarettes in dollars, age is age in years, and income is annual income in thousandsof dollars. Consider now an extension of the model that allow the effect of theprice to differ by age. Holding all other factors fixed, is the effect of price onncaj constant? (This part is theoretical and you do not have to estimate themodel.)
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
s. Use the Greedy and Edge-Picking algorithms to find the Hamiltonian cycle with the least total weight in the complete graph shown below. 33 57 25 72 29 65 75 89 21 50 26 45 34 60 55
what are the steps that show schedule 2 is conflict serializable?
3. 3 jobs, with i.i.d. runtimes each U[0, 1], are to be run in parallel on 2 processors. By how much time does the expected flowtime decrease if the schedule is changed from a best fixed schedule to a best schedule with recourse?
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.
Draw and analyse the arrow network for the following activities by using PERT method assuming three estimated duration for each activity which are shown I the table below. Then, find: 1. The probability of completing the work of the whole project in 20 weeks 2. The completion time of the project at probability of 95% 3. The completion time of the project at probability of 100% Estimated duration (weeks) Activities Followed by to tm tp 8. A 4 6. B,G В 2 4 J C 2 8 D,E D 1 3 G E 7 9. F F 1/2 1 3/2 Н.К G 3 8. 7 I 1/2 1 3/2 I I 1 7 7 J J 3 4 11 K 1 3
A model of wages and prices is presented W =a, +a_P +a¸O̟ +u, P B,+ BW + B.Y+u, Where W is the wage rate, P is the price indicator, product, Y. the income -Establish what type of multiequational model it is -Indicate the endogenous and exogenous variables -Construct the synthetic version of the reduced form of the model. -Identify the system using the exclusion technique. Conclusion?
- Set up the structural equations
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