Raphael - MO412 A

Imagine a society where a new kind of virus is spreading, the Adamski Virus . Fear and caos are spreading faster than the virus it self because of the high spread rate (5). The media has also reported that each infected person, on average, infects 5 other people. If a researcher discover a vaccine that can make people immune to   Adamski , how many people (proportionally to the population total) should be immune in order to stop  Adamski outbreak? Consider a random immunization scenario and a SIS infection model on a Random networks. Tip: use <k²> = <k>² + <k> if necessary A) 0.82; B) 0.90; C) 0.10; D) 0.80; E) None of the above; Author: Raphael Adamski

Consider a one dimensional lattice with  N  nodes that form a circle, where each node connects to its two neighbors. Partition the line into  n c  consecutive clusters of size  N c =N/n c . According to the Maximum Modularity Hypothesis, the maximum of  M c  corresponds to the best partition. Obtain the community size  n c  corresponding to the best partition when N=15. A)  n c  = 5 B)  n c  = 3.87 C)  n c  = 0.97 D)  n c  = 5.47 E) None of the above Original idea from https://networksciencebook.com/chapter/9#homework9 Author: Raphael Adamski

Solve the Travel Salesperson Problem for the following undirected weighted graph and pick the best answer: A) Path ABCDEA and length 24 B) Path ABCEDA and length 20 C) Path ADEBCA and length 18 D) Path AEBCDA and length 19 E) None of the above Original question by: Raphael Adamski Original images from https://graphicmaths.com/computer-science/graph-theory/travelling-salesman-problem/