Chapter Notes [2]

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Eco and Soc Networks Note on Chapter Notes [2], created by cheekymonky52 on 12/04/2013.

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 Created by cheekymonky52 almost 6 years ago
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Chapter Notes [1]
Chapter Notes[3]
Study Plan
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Ch 20 - Small World Phenomenon Watts-Strogatz Model - Assuming that all your friends are connected to new friends then the phenomenon that everyone is connected by a short path is quite understandable. However, assuming that triadic closure exists within a network this can be seen to limit the number of people you can reach by following short paths. Model shows how homophily creates a highly clustered network through triadic closure and how weak ties can create short paths. Two dimensional grid and each node can have two types of links; short links to neighbours within a distance of r and long range links to other random nodes. Clustering exponent can be used to determine whether two nodes v,w are connected by edge. If exponent is small then it is more likely to be a long range link i.e. more random but if exponent is small then it is more likely to be a short range link. The most optimal choice for exponent is 2 for decentralized search (how to find the short paths). Model can be adapted to not be placed in a grid i.e. using rank between two nodes which is the number of nodes closer to v then w, rank(w)-1 or social distance between two nodes which is the smallest size foci that both nodes share, s(v,w)-1.

Ch 21 - Epidemics 1. Branching Process - Disease spreads in waves. So the first person to enter into the network with the disease can pass on the disease to each person he meets with some probability, let’s say he meets k people. These k people then have a probability of infected a set of different people they meet, lets say they each meet k people so the maximum number of people infected become k2. The disease can die out after a finite number of steps if none of the k new people infected pass on the disease or it can continue infinitely. Basic Reproductive Number is the number of new cases of the disease caused by a single individual. If R &lt; 1 then disease will die out with probability of 1 i.e. it is certain but if R &gt; 1, the disease will permit with some probability greater than 0 i.e. it is not certain unless probability of infecting a new person is 1. 2. SIR Epidemic - Stages on the disease is susceptible, infected and removed. Progress of the epidemic is controlled by the probability of infection ‘p’ and the length of time an individual is infected ‘t’. 3. SIS Epidemic - There is no removed state meaning that there is not a bounded set of nodes. The epidemic can run for a very long time or if at any point all nodes are in the susceptible state then the disease will have died out. 4. SIRS Epidemic - Individuals can be temporarily immune but can become susceptible again after some time length. Transient Contacts - contact between two nodes can be between some time interval. Concurrency - a node is involved in two or more active partnerships that overlap in time. So disease can spread from both directions.