a) Imagine that you have a startup idea that needs some funding to succeed. You decide...

   

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a) Imagine that you have a startup idea that needs some funding to succeed. You decide to open an account in one of the crowdfunding websites, such as gofundme.com and hope that people will fund your idea. Assume that 10 of your friends have agreed to financially support you and provide their donations via this website. Based on the rich-get-richer model, explain whether it is better for your friends to provide their donations as soon as you advertise your idea on the platform or wait until some other people provide their donations and gradually donate over time. (5 points) b) Assume that node a is initially infected with COVID-19 in Network 1. Assume that the probability of becoming infected is p = 1, and let t₁ = 1. Using the SIR epidemic model, determine the state of the network (which nodes are infected, susceptible, and removed) at each time step until it reaches its final state. (10 points) c) Is there a single node in Network 1, that if it is infected initially, all other nodes will become infected eventually? If yes, indicate it; otherwise, explain why. (5 points) d) Remove the arrows in Network 1 so that all edges are undirected. We are going to examine the spread of some behaviour A in this network. Assume that initially node a has adopted behaviour A and the threshold of all the nodes is q = 1/2. Does a complete cascade happen? If yes, show the state of the network at each time step. If no, find a cluster density of a threshold greater than 1-q. (10 points) e) [Bonus] Please fill in the questionnaire for the course and write "done" here once you have done so. (10 points) + (e) a d Figure 1: Network 1 a) Imagine that you have a startup idea that needs some funding to succeed. You decide to open an account in one of the crowdfunding websites, such as gofundme.com and hope that people will fund your idea. Assume that 10 of your friends have agreed to financially support you and provide their donations via this website. Based on the rich-get-richer model, explain whether it is better for your friends to provide their donations as soon as you advertise your idea on the platform or wait until some other people provide their donations and gradually donate over time. (5 points) b) Assume that node a is initially infected with COVID-19 in Network 1. Assume that the probability of becoming infected is p = 1, and let t₁ = 1. Using the SIR epidemic model, determine the state of the network (which nodes are infected, susceptible, and removed) at each time step until it reaches its final state. (10 points) c) Is there a single node in Network 1, that if it is infected initially, all other nodes will become infected eventually? If yes, indicate it; otherwise, explain why. (5 points) d) Remove the arrows in Network 1 so that all edges are undirected. We are going to examine the spread of some behaviour A in this network. Assume that initially node a has adopted behaviour A and the threshold of all the nodes is q = 1/2. Does a complete cascade happen? If yes, show the state of the network at each time step. If no, find a cluster density of a threshold greater than 1-q. (10 points) e) [Bonus] Please fill in the questionnaire for the course and write "done" here once you have done so. (10 points) + (e) a d Figure 1: Network 1

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a It is better for your friends to provide their donations gradually over time This is because the richgetricher model suggests that if a few people d... View the full answer