Night Ride - April 18, 1775 Paul Revere and William Dawes.
Revere alerted influential militia leaders on his ride to Lexington.
Led to American forces winning the first battle of the Revolutionary War.
Malcolm Gladwel describes Paul Revere as a “Connector” in The Tipping Point Medici Family in Renaissance Florence 15 prominent families
Medici had 50% higher degree than Strozzi and Guadagni.
But the Medicis influential power was much greater than explained by the 50%....
For any node to possibly flip, there must be some nodes that have the disease at \(t = 0\). These nodes are called seeders.
Brings topology into the picture: flip iff \(p\) of your neighbors have flipped.
Assumes that each node has the same flipping threshold \(p\) Will the Whole Network Flip? For a cluster of nodes, let \(d_i\) be the fraction of the neighbors of \(i\) that are in the cluster....
Models state transitions through differential equations over continuous time \(t\). Commonly used to model the spread of diseases.
Possible states that proportions of the population could be in at time \(t\) are: susceptible \(S(t)\), infected \(I(t)\), and recovered \(R(t)\)
The SI Model Assumes that one can only move from state \(S\) to state \(I\), with probability \(\beta\).
$$ S'(t) = - \beta S(t) I(t);\ \ \ \ I'(t) = \beta S(t) I(t) $$...