Problem : Consider the two maps provided by the MTA. On the left is the map of the Long Island Railroad network. On the
Posted: Wed May 11, 2022 12:39 pm
Problem : Consider the two maps provided by the MTA. On the left is the map of the Long Island Railroad network. On the right is the subway network in lower manhattan. Both networks contain about the same amount of nodes (stations). Which network has the higher entropy?
MANHATTAN 1.!! mm Long Island Roll Road .
• Problem 8: Given a random trip (two stations are selected), in which network will you visit fewer intermediate stops? • Problem 9: Suppose both networks are equally prone to station closures. Which network will be able to deliver you to your desired stop more consistently (Which network is more robust)? . Problem 10: Entropy on a node in a markov chain can be defined as (v.) = -log Pu where I, is the ith state/node, and Pu is the transition probability from state i to . Assume we have a node where each edge connected to it is equally weighted. For example, if co is connected to the two nodes 1 and 12, then each edge is weighted. With the described simplification, show that the more connections a node has the higher its entropy.
MANHATTAN 1.!! mm Long Island Roll Road .
• Problem 8: Given a random trip (two stations are selected), in which network will you visit fewer intermediate stops? • Problem 9: Suppose both networks are equally prone to station closures. Which network will be able to deliver you to your desired stop more consistently (Which network is more robust)? . Problem 10: Entropy on a node in a markov chain can be defined as (v.) = -log Pu where I, is the ith state/node, and Pu is the transition probability from state i to . Assume we have a node where each edge connected to it is equally weighted. For example, if co is connected to the two nodes 1 and 12, then each edge is weighted. With the described simplification, show that the more connections a node has the higher its entropy.