This year, the Department of Mathematics at the University of Malta lost one of its longest-standing members, Professor Anton Buhagiar, who passed away very recently. Anton will be remembered by many students both in the Mathematics Department and outside it, since he was one of the automatic go-to persons for many who needed statistical help to analyse their research data. He faced problems, whether mathematical or those thrown at him by life, with a cheerful disposition which he maintained right through to the end when he would still come regularly to the Department to lecture, advise students and be with colleagues.
Few might know that Anton was as much a theoretical physicist as a mathematician. His speciality was statistical mechanics and he wrote his thesis under the supervision of Oliver Penrose, the brother of the famous Roger Penrose. When one is studying the behaviour of, for example, a gas inside a sealed container, one can measure its macroscopic properties, such as its temperature and pressure. But in statistical mechanics one takes a microscopic point of view by trying to analyse the gas as a system of a massive number N of particles moving at various velocities, hitting each other and the sides of the container. But, in such a system, N is so large that it is impossible to analyse the movement of so many individual particles and their interactions individually.
So, in statistical mechanics, one tries to work out the average value of, for example, the velocity of the particles, and how these values vary across their averages. Then, the heat content of the gas becomes the average kinetic energy of the particles, and pressure is the average of the impacts of these particles on the sides of the container.
The remarkable success of statistical mechanics is that it predicts correctly the relationship between macroscopic parameters such as pressure, temperature and volume, as well as phenomena of phase transitions, such as the temperature at which a liquid freezes into a solid.
In the last 20 years, physicists and mathematicians have applied the techniques of statistical mechanics to the study of large complex networks, such as the World Wide Web or networks of social interactions. Very topically for these times, this work has included the study of the spread of epidemics on complex networks and a great deal of effort has gone into a very important phase transition in this context: at what point does the spread of a disease turn into an epidemic or die off, and is there a parameter (analogous to the R-factor) which can mark this changeover?
Prof. Josef Lauri, Dr. James Borg and Prof. Peter Borg are members of the Department of Mathematics within the Faculty of Science of the University of Malta.
Sound bites
Anton Buhagiar and the Mathematics of Elections: In 1994, the parliamentary commission known as the Gonzi Commission was set up in order to study both the electoral system and the Maltese electoral process. It asked Prof. Buhagiar to write a report with proposals to address the problem of disproportional results in our elections. The Buhagiar report, Can One Achieve Nationwide Proportional Representation in Malta Without Major Changes to the Present Method of Elections?, proposed the novel idea of combining the STV system with the d’Hondt divisor method, and it can be found in https://www.um.edu.mt/__data/assets/pdf_file/0004/207787/buhag.pdf. Two later papers on this proposal, one by Buhagiar and Lauri, STV in Malta: A Crisis?, and another by Bezzina and Buhagiar, STV 4+: A Proportional System for Malta’s Electoral Process, appeared in the journal Voting Matters and can be found at http://www.votingmatters.org.uk/ISSUE26/I26P1.pdf and http://www.votingmatters.org.uk/ISSUE28/I28P1.pdf, respectively.
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