# Week Seven

This week I worked on setting up Python and NumPy onto my computer. I also worked on studying a Python code by Diogojc called PageRank. The way the code should work is I will be given a matrix of ones and zeros representing relationships between different news stories. Then, my code should be able to calculate how much relation there is between each story using PageRank. My code should then produce a graph to show how likely it is for a news story to be true.

I spent the rest of the time reading a paper called ”Collective influence Maximization in Threshold Models of Information Cascading with First-Order Transitions” by Sen Pei, Xian Teng, Jeffrey Shaman, Flaviano Morone, and Hernan A. Makse. The paper talked about Collective Influence in Threshold Models, optimal percolation, the CI-TM algorithm, message passing, and linearization. Here is one example the paper gives: “Subcritical paths and collective influence of spreaders. (a), Three combinations of neighbors P1, P2, and P3 corresponding to V(i->j) in message passing equation. Node i has a threshold mi = 2. The full activation of at least one combination will lead to V(i->j) = 1. (b) For link i->j with an active neighbor k1 and inactive ones k2 and k3, I(k1->i,i->j) = 0 since i has 0 ( < mi – 1) active neighbor excluding k1 and j, while I(k2->i,i->j) = 1 because i has 1 ( = mi -1) active neighbors k1 excluding k2 and j. (c), Illustrations of subcritical paths ending with link i->j for L=0,1,2. Red dots stand for seeds, while squares represent m – 1 active neighbors attached to subcritical nodes. Subcritical paths are highlighted by thick links. (d), The contribution of seed i to ||v(->)|| exerted through subcritical paths of length L=0,1,2. (e), Calculation  method of CI-TM(L) (i).  Subcritical paths starting from i with length l =< L are displayed by different colors. (f), An example of a subcritical cluster. Assuming a uniform threshold m = 3, nodes inside the circle are subcritical since they all have 2 active neighbors, represented by blue nodes. Activation of the red node will trigger a cascade covering all subcritical nodes.”

Next week I plan on getting Python to work on my computer, running the PageRank code, and maybe modifying the code so it works with our project.