Probability Theory is one of the most important tools for studying networks. Most things Probability Theory tries to explain are about average or typical observations.
When studying networks we use Probability Theory to answer questions like “what is an average degree in a network” or “what is the average time it takes to travel from A to B”. Sometimes, however, we want to know something about very rare events. For instance, we might ask “what is the probability that our electrical grid will be so overloaded that it breaks down?”
For such questions we can use Large Deviations Theory. The most important lesson that Large Deviations teaches us is that if something improbable must happen, then it will happen in the most probable of all improbable ways. I could go on to explain how Large Deviations Theory works, but fortunately I don’t have to because Nautilus has an article by David Steinsaltz, a Statistics professor at Oxford, that explains this amazing mathematical idea with improbable clarity.
In this article, we discuss several ways to quantify the importance of nodes in a network. We will discuss how a simple game can help study this special property, and how it can help us in cases like reducing fake news.
You have a job interview in 20 minutes and you are in a hurry to arrive at your application in time. To make matters even more stressful, there are many routes to your destination, but you have no idea which one to select. Luckily, you have access to a navigation system that can help you in your route selection process.
How can one hope to understand the precise structure of a virus if it is able to become unrecognizable within weeks? The mathematics behind this questions didn't let go of my mind for extensive periods of time during my PhD studies in Belgium.
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?
The scientific world would not be what it is today without normal distribution. It is the foundation of many statistical models for several good reasons. Most importantly, it appears commonly in nature. But this is only the tip of the iceberg.
