Social networks are remarkably small, in the sense that you can hop between any two individuals in them using only a few hops. This video explains what such small-world networks are, why social networks are so small.
Phenomena like social cohesion and polarisation emerge from individual interactions on the social network of relationships between people. So, what does this network look like?
If, after reading the title, your immediate response is to shout "1/6-th", then you have correctly answered the question. Well done! However, in this article we will focus on the meaning of this question. What exactly is this "chance" of which you've just exclaimed it equals 1/6-th?
One of the main building blocks of modern AI-tools are artificial neural networks, abstract models inspired by the structure and functions of biological neural networks which enable machines to "learn". In this article, I will discuss some thoughts on this topic.
Common sense tells us that objects of comparable size should be equally hard to find. Yet, when searching inside a random network, surprises are awaiting . . .
In a seminar talk in Cambridge this week, Julian Sahasrabudhe announced that he, together with his colleagues Marcelo Campos, Simon Griffiths and Rob Morris, had obtained an exponential improvement to the upper bound for Ramsey's theorem.