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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.

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### Predicting optimal routes in unpredictable networks•

How does your navigation system find the fastest route in a road network, if it does not know where traffic jams occur and how long they last?
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### Why you may need to reconsider your route selection criterium•

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.
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### Centrality measures: who is the most important in a network?••

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.
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### Is a rapidly mutating virus unstoppable?•••

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.
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### How Aho and Ullman slayed the Dragon•••

Alfred Aho and Jeffrey Ullman received the 2020 A.M Turing Award for their contributions to computer science. Let’s explore how their contributions have shaped the principles, techniques and tools for writing compilers.
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