In the small world experiment, it was observed that anyone in the world could reach any other person in the world in about 5.2 intermediates (thus 6-degree of separation). This observation was made more than 50 years ago. The Internet should have shortened this average path distance. Suppose with the use of Internet and online social networks, every person in the world increases their number of friends by doubling it (2x). Please estimate the new degree of separation. Explain your estimation.

In the small world experiment, it was observed that anyone in the world could reach any other person in the world in about 5.2 intermediates (thus 6-degree of separation). This observation was made more than 50 years ago. The Internet should have shortened this average path distance. Suppose with the use of Internet and online social networks, every person in the world increases their number of friends by doubling it (2x). Please estimate the new degree of separation. Explain your estimation.

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter20: Queuing Theory

Section: Chapter Questions

Problem 7RP

See similar textbooks

Similar questions

A Bayesian network has four variables: C,S,R,W, where -- C is independent, with P(C)=0.5 -- S is conditional on C, with P(S|C)=0.1, and P(S|~C)=0.5 -- R is conditional on C, with P(R|C)=0.8, and P(R|~C)=0.2 -- W is conditional on S and R, with P(W|S,R)=0.99, P(W|S,~R)=0.9, P(W|~S,R)=0.9,P(W|~S,~R)=0. a) List possible states of this world.b) Calculate the probability P(R|S).
Find the total number Q of tunable parameters in a general L-hidden-layer neural network, in terms of variables expressed in the layer sizes below 1 layer_sizes= [N, U_1, ., U_L, C] (b) Based on your answer in part (a), explain how the input dimension N and number of data points P each contributes to Q. How is this different from kernel methods
This paper deals with Extended Huffman Codes. For instance, for a source emitting two symbols A and B, the second order extension involves coding messages AA, AB, BA and BB (2^2 in number). The third order extension involves messages such as AAA, AAB, etc. (2^3 in number). The probabilities of such strings are computed by multiplying the individual probabilities. Calculate third, fourth and fifth order extensions of a source message. 1. Choose an alphabet a set of at least six (6) symbols with assigned probabilities. It can be assigned as [ A=0.3; B= 0.7; C=0.1;D=0.2;E=0.5;F=0.15]. Compute the third, fourth and fifth order extension probabilities. Using the built-in algorithm, derive the Huffman Code for each extension. Compute the following quantities: (i) Average length of the codeword; (ii) The code efficiency; (iii) The Compression Ratio. Note: I am assuming but needs to be verified that if we need are using 6 symbols A to F. 6^3=216, the 6 to the third power comes…
1. We consider a Bayesian network with 20 random variables. We only know that 10 of the variables are isolated from the other 10. What are the number of parameters required to represent the joint distribution? a. 2^10-1 b. 2(2^10-1) c. 2*10 d. 2^20-1
Q-2 Suppose that you pick a bit string from the set of all bit strings of length ten. What is the probability that the bit string has more 0s than 1s?
Draw a recurrent network with ‘4’ neurons, but with no feedback from the same neuron by including the unit delay in output? (please the solution, enter it written on the keyboard)
Consider the Cartesian (x-y) grid. If you can only move right and up, how many paths are there: a.From A(0, 0) to B(6, 3)? b. b. From A(0, 0) to C(9, 10) if you must pass through D(5, 4) and E(7, 8)?
For n=5 , In base there are more than 5 stars, however it should be equal to 5 like I shared picture in Question. For 10, In base there are more than 10 stars, however it should be equal to 10 like I shared picture in Question. Please solve.
Model a common roadway occurrence, where a lane is closed and a flag person is directing traffic. There is a two-lane road with one lane closed, and vehicles are approaching from the North and South directions. Due to the traffic lights, the cars arrive in bursts. When a car reaches the construction area, there is an 80% chance that another car will follow it. However, if no car comes, there will be a 20-second gap (utilizing the provided pthread_sleep function) before any new car arrives. During the intervals where no cars are at either end, the flag person will rest. However, when a car arrives at either end, the flag person will wake up and manage the traffic flow from that side, until there are no more cars from that side or until there are 10 or more cars waiting in the opposite direction. If there are 10 or more cars on the opposite side, the flag person must allow those cars to pass first. Each car takes one second to travel through the construction area. Your task…
a. Write down the factorization of P(D, I, G, S, L) based on the Bayesian network.
Consider a lengthy rural road (which can be considered to be a line segment with an eastern endpoint and a western endpoint). Along the road, residences are thinly spaced. Your challenge is to decide where to locate mobile phone base stations along the road in such a way that the total number of base stations is minimised and each residence is within four miles of a base station. Now, provide an efficient solution to this issue. Nota bene: you must demonstrate that your algorithm is valid.
Show how a neural network with any number of hidden layers (>=0) can be made equivalent to logistic regression. You can draw the network and write equations to explain and justify your answer.