Improving referencing and chronotherapy with the same tool?
Olivier Fercoq was awarded one of the two thesis prizes from the Programme Gaspard Monge pour l'optimisation et la recherche opérationnelle (PGMO - Gaspard Monge Program for optimisation and operational research) for a topic that combines two very different applications: web referencing and chronotherapy. He will receive his prize on 3 October 2013 at the PGMO Days.
How did you define the topic for your thesis?
For my thesis, I started with a problem raised by Orange : we consider a webmaster who has a website and who would like to know what to do with hyperlinks to be highly ranked by search engines . In fact, we know the general mathematical principle for the Google search engine, even though some details are a technological trade secret. I had to use a mathematical tool called Perron eigenvectors of positive matrices . To explain, one can think of a positive matrix as a table of numbers, where all the numbers are positive. The table can thus help classify information. The concept of an eigenvector evokes an idea of movement over time: in our example, an internet user moving within the pages. But as often happens in maths, when one is interested in one area, one discovers that the tool applies to others.
How did your thesis expand to chronotherapy?
Optimal link strategy for the Website in grey: the PageRank (the eigenvector calculated by Google and used to classify pages) is maximised if all pages on the site point to page c - ©Olivier Fercoq - ©Olivier Fercoq
I searched the scientific literature for areas where Perron eigenvectors might apply. For example, there was a topic on mobile telephone networks, to know how much power to give the various telephones to avoid interference. But I was more interested in chronotherapy and the cell population dynamic , which is to say, how they change over time. This involved a very concrete optimisation of the process: to determine how much of which medication to give at what time . This gave me the opportunity to find an algorithm that would work to resolve this problem, with the idea of helping to fight cancer! This work was not done in direct collaboration with hospitals, but I was in a cross-disciplinary group with Paris 6.
To conclude, could you tell us about your background, and where you are today?
I am from Bordeaux, where I earned my Baccalaureate S (sciences), and I completed a preparatory year at the lycée Montaigne. Then I joined the ENSTA in the mathematics and optimisation section, while completing a research masters program at Paris 6. I worked on my thesis "Optimisation of Perron eigenvectors and applications: from web page referencing to chronotherapy" as part of the Maxplus project team, with a thesis topic developed by Stéphane Gaubert and Mustapha Bouhtou. Today I am in a post-doc in Edinburgh . I still work in the area of optimisation, but now, instead of moving from applications to an algorithm, I start by studying algorithms and seek to apply them. Next, I plan to continue with my research in France or abroad.
PGMO Thesis Prize
The Gaspard Monge Program for optimisation and operational research (PGMO), created through EDF patronage at the Fondation Mathématique Jacques Hadamard (FMJH - Jacques Hadamard Mathematics Foundation), awards two thesis prizes with the participation and scientific sponsorship of ROADEF and the SMAI (MODE subject group). They are intended as awards for two doctoral theses defended in France during the 2012 calendar year that make significant contributions to optimisation and operational research, both from a theoretical and application point of view, in mathematics and/or computer science. The award ceremony will be on 3 October 2013 during the PGMO evaluation day at the ENSTA, during which they will present their work.