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 II₁ ai = Z where Z = Σ aj. j=1,...,N(t−1) 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 II₁ ai = Z where Z = Σ aj. j=1,...,N(t−1)

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 II₁ ai = Z where Z = Σ aj. j=1,...,N(t−1) 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 II₁ ai = Z where Z = Σ aj. j=1,...,N(t−1)

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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23. Consider a simple economy with just two industries: farming and manufacturing. Farming consumes 1/2 of the food and 1/3 of the manufactured goods. Manufacturing consumes 1/2 of the food and 2/3 of the manufactured goods. Assuming the economy is closed and in equilibrium, find the relative outputs of the farming and manufacturing industries.
2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.7. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.7 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 3 Food C 1 1 1
Redo Exercise 5, assuming that the house blend contains 300 grams of Colombian beans, 50 grams of Kenyan beans, and 150 grams of French roast beans and the gourmet blend contains 100 grams of Colombian beans, 350 grams of Kenyan beans, and 50 grams of French roast beans. This time the merchant has on hand 30 kilograms of Colombian beans, 15 kilograms of Kenyan beans, and 15 kilograms of French roast beans. Suppose one bag of the house blend produces a profit of $0.50, one bag of the special blend produces a profit of $1.50, and one bag of the gourmet blend produces a profit of $2.00. How many bags of each type should the merchant prepare if he wants to use up all of the beans and maximize his profit? What is the maximum profit?
Suppose the coal and steel industries form a closed economy. Every $1 produced by the coal industry requires $0.30 of coal and $0.70 of steel. Every $1 produced by steel requires $0.80 of coal and $0.20 of steel. Find the annual production (output) of coal and steel if the total annual production is $20 million.
A farmer wants to decide which of the three crops he should plant on his 100-acre farm. The profit from each is dependent on the rainfall during the growing seasons. The farmer has categorized the amount of rainfall as high, medium, low. His estimated profit for each is shown in the table. If the farmer wishes to plant only one crop, decide which will be his choice using the EMV rule, prove your judgement by comparing the EMV of each crop. (Indicate the EMV in each crop, comparison and the right choice).
2. Consider a connected network of two individuals. At each period t, each individual forms beliefs as a weighted average of his own beliefs with weight p = [0, 1] and the other agent's beliefs with weight 1 - p. (d) If p = 0, what happens to beliefs of each player as t→∞? (e) Express b2, beliefs in period 2, as a function of initial beliefs bo and p. Comment on the relationship between p and the difference in beliefs. (f) (Harder) What value of p will cause beliefs to converge fastest? Relate this to the second eigenvalue of the updating matrix A (Hint: your answer to (e) is helpful here.)
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, 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 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 Π II₁ = z = Σ αγ j=1,...,N(t-1) Provide the mean-field solution of the model by considering the following two points. (A) Assume that Zat, 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 node i in the mean-field approximation.
The value y (in 1982–1984 dollars) of each dollar paid by consumers in each of the years from 1994 through 2008 in a country is represented by the ordered pairs. (1994, 0.675) (1995, 0.654) (1996, 0.643) (1997, 0.618) (1998, 0.611) (1999, 0.599) (2000, 0.585) (2001, 0.562) (2002, 0.559) (2003, 0.539) (2004, 0.529) (2005, 0.513) (2006, 0.493) (2007, 0.482) (2008, 0.462) (b) Use the regression feature of the spreadsheet software program to find a linear model for the data. (Let trepresent time. Round your numerical values to four decimal places.) y = (c) Use the model to predict the value (in 1982–1984 dollars) of 1 dollar paid by consumers in 2010 and in 2011. (Round your answers to two decimal places.)
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.
A company manufacture two different types of call phone F and E, each unit of call phone S costs (OR .7)and each unit of call phone E costs (OR. 6). The company insists that total costs for the two types call phone be (OR .400). Assuming that company manufactures in total 88 products. How many products are of type Fand E? (solve the problem using Crammer's Rule)
Draw a network showing the quantities obtained in the final iteration and the optimal value of z.