Quantum synchronization in complex networks
As many phenomena in the classical world have quantum counter part, it raises the question if this is also true for synchronization. As synchronization is a collective phenomenon, it may help gaining a better understanding of how collective phenomena in the classical and quantum world are connected.
Complex networks
Have you ever wondered what mathematicians mean when they talk about mathematical models of real-life phenomena? And what can such a model tell us about the network-phenomenon we are studying?
Vaccination and the friendship paradox!
On social media it seems like everyone around me is more popular than what I am. It is a mathematical statement: the friendship paradox!
Degrees in graphs III: Which degrees sequences are possible?
Paul Erdős and Tibor Gallai developed a beautiful criterion to decide precisely when a degree sequence is graphical.
A network made of math
Alexander Grothendieck (1928—2014) is viewed by many as one of the greatest mathematicians of all time. He made contributions to many different fields, but the work he is mainly celebrated for is his shaping of some of the most abstract, fundamental branches of mathematics.
Large Deviations Theory: understanding the incredibly rare
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.
Degrees in graphs II: Degree sequences
The degree sequence of a graph is the sequence of degrees of all its elements.
Statistical physics
Interacting particle systems Statistical physics aims at describing collective behaviour in systems consisting of a very large number of interacting particles (= atoms or molecules). This is a daunting task: a glass of water or a piece of iron can easily contain 100.000.000.000.000.000.000.000 particles. Still, the hope is that the macroscopic properties of these particles […]
Stochastic models for random-access networks
Wireless communication networks play a crucial role in connecting laptops, smartphones, sensors and countless physical devices, and in exchanging data among persons, computer brains and other parts of our information society.
A Santa Claus network
Poor Santa has to travel all across the country to deliver all his presents. How does he do this?