At Eindhoven University of Technology, shared between the Electrical Engineering and Mathematics and Computer Science Departments, there is a vacancy for a PhD student. The intended supervisors are George Exarchakos (EE) and Remco van der Hofstad (MCS). The project will focus on distributed ways to measure centrality in networks, for example using the Game of Thieves protocol. In this protocol, several walkers run through the network looking for commodities, and, upon finding them, the commodities are moved to the starting point of the walks. The most central nodes are the ones that receive the least commodities. The aim of the project is to describe this centrality measure, possibly using local weak convergence techniques, as well as to study what happens when central nodes are being removed. We are also interested in the dynamical properties of this centrality measure, in particular what happens when the graph changes over time while the walkers run around on the network. 

We aim to approach these problems in a mathematically rigorous way, and we expect the candidate to have some experience in formally proving results. Some experience with simulations is welcome, though not required.

These questions are spurred by modern communication. Future communication networks are expected to be ultra dense in space and pervasive to our living spaces enabling far better coverage and higher bandwidth anywhere. Smart radio environments will play an important role to achieve this goal. Yet, their control has to become inherently distributed, autonomous and intelligent. The controllability of wireless mesh networks heavily depends on the properties of the graphs they form and their ability to coordinate in a local way. New intelligent methods are needed to achieve self-awareness of large-scale random wireless networks and to estimate the impact of a topology change. This project will study the fundamental models needed to achieve intelligence embedded at the nodes of the network. 

This PhD project is within the NETWORKS Gravitation program NETWORKS, and the student will be expected to actively participate in this program.

The project will be carried out at the Department of Mathematics and Computer Science and the Department of Electrical Engineering of the Eindhoven University of Technology. The departments offer a vibrant international environment, with a substantial part of the scientific staff being non-Dutch nationals and more than 100 PhD candidates. They have extensive experience in helping new (foreign) employees settle in.

Research  

The PhD candidate will be supported and supervised by an extensive research team of experienced faculty and industrial partners.

Preference will be given to candidates in any branch of applied mathematics and to candidates from a different background (e.g. engineering) but with strong mathematical foundation. Research experience will be highly valued. Strong knowledge of applied probability and analysis is highly desirable, as well as some programming experience.

The successful applicant will hold a Masters degree in Mathematics, applied Mathematics or related fields. All applications should include: a cover letter, curriculum vitae and transcript. Proficiency in English is also required.

We offer you:

• An exciting job in a dynamic work environment.
• A full time appointment for 4 years at Eindhoven University of Technology.
• The salary is in accordance with the Collective Labour Agreement of the Dutch Universities, increasing from € 2.325 per month initially, to € 2.972 in the fourth year.
• An attractive package of fringe benefits, including end-of-year bonus (8,3% in December), an extra holiday allowance (8% in May), moving expenses and excellent sports facilities.