... signal theory, theory of random processes, coding theory, numerical transmission, optical communications, mobile communications, deep space communications, digital television, multicarrier modulation systems and the digital cinema.

I must also thank Carlo Bertoluzza, my Tesi di Laurea supervisor, for having acted many times and in different occasions in my support, and for having equipped me with the foundations of the Theory of Uncertainty, which has been most helpful to me ever since I learned it.

I would like to thank Fire Chief Fabio Dattilo, Fire Chief Robert Triozzi, Fire Officer Vincenzo Valeri and all the Fire-Fighters of Padova Fire Station, who gave me an everlasting lesson during 365 unforgettable days of military service.

I first wish to express my gratitude to Giorgio Balconi, who introduced me to the beauty and elegance of graph theory, and who made me decide that I wanted to be a graph theorist.

I am most grateful to Lars Dovling Andersen for providing me, in 1998-99, with the nicest graph-theoretic environment of all my life at Aalborg University, Denmark, where I arrived after a very difficult time of my life, and for his personal care and support.

... for having given back to me a sense of safety that I had lost, acting, very professionally, as the best consultant I ever met.

Mathematically speaking I am the son of David Daykin, the grandson of Richard Rado and the great-grandson of both Issai Schur and G H Hardy.

I am indebted for life to my supervisor, A J W Hilton, for having granted me the privilege of being one of his students at the University of Reading. Among the innumerable things that I learnt from Professor Hilton during these four years, one of the most valuable is, I believe, not to refrain from undertaking the study of a difficult mathematical problem, and to maintain the same enthusiasm and perseverance even when the signs of any progress are not immediately visible.

I must greatly thank David Daykin, my academic grandfather, for having provided me with the strongest moral support since my arrival in Reading, and for having constantly been in touch with me.

His studies [at the University of Reading] were funded at different times by his adoring brother Dimitri, and by his father Professor Gianfranco Cariolaro. His supervisor, Professor Anthony Hilton, reports that David was a diligent, hard-working student, who found it quite difficult to get to grips with his research topic, but eventually showed considerable insight and imagination. Together with Matthew Johnson, he organised a conference in Reading for graduate students studying Combinatorics. On occasions he would entertain others by performances on the clarinet. After obtaining a Ph.D.. but before leaving Reading, he married his wife, Shu Ning.

If one looks at the most common mathematical structures, e.g. groups, rings, fields, vector spaces, Hilbert Spaces, etc. it is difficult to escape the impression that they are all objects of a very specialized kind. Sometimes five, ten or even fifteen axioms are needed to define these objects. Of course one may easily feel that the choice of these axioms is somehow arbitrary. Therefore it seems that pursuing the study of these structures would result in putting a strong bias to one's mathematical activity in the long term. I was attracted by graphs because they express a concept that may be described by a single axiom: friendship. We are either friends or not, there is no alternative, no third excluded. This is in some sense what the structure of a graph conveys: when you see two points connected by a line that is the geometrical expression of this relation, whereby the two points can be considered "friends", or as we say: "neighbours". Of course what one immediately learns is that, if A is a friend of B and B is a friend of C, that does not mean that A should be a friend of C: that is, the relation of friendship is not transitive (as we know very well). Now the word friendship may be changed, if you wish, with any symmetric relation that you like, or even asymmetric, provided we are ready to switch to the world of digraphs, or directed graphs. The relation may not be limited to two people only, it may involve any number of people, provided we pass from the world of graphs to the world of hypergraphs.

Professor Cariolaro needs our HELP

David Cariolaro is an Associate Professor in the Department of Mathematical Sciences at Xi'an Jiaotong-Liverpool University, China. On 20 September David had a serious accident and is currently struggling for his life in the hospital in Sozhu, assisted by his wife and father, Prof Gianfranco Cariolaro of the University of Padua.

David's condition is very critical and requires complex medical care whose cost, unfortunately not covered by any insurance, is so high that it has consumed our life savings in a few weeks. Unfortunately his condition does not allow transfer to an Italian hospital.

The Italian Consulate in Shanghai is taking an interest in the problem and is trying to make the Italian community in China aware of the situation but at the moment Gianfranco is not receiving any concrete financial support.

The purpose of this site is to present this dramatic story to as many people as possible, friends and acquaintances of David and Gianfranco, and to facilitate individual contributions giving everyone the possibility offering help and support.

David's condition is not sufficiently stable to enable a transfer to an Italian hospital where he could receive the delicate lifesaving neurological surgery that China cannot provide. Family members seeking funds to bring him back to Italy with the only possible alternative for now being a private medically equipped flight but that would cost around 150 thousand euro. Complicating Cariolaro's case is the fact that the Veneto Region has no legal requirement for pay for the flight. The problem of transport is that no airline accepts such seriously ill people unless accompanied by a medical team and supported by suitable equipment.

David Cariolaro's return to Italy occurred late on Friday with a flight from Shanghai made available by the government. During the trip, the professor from Padua was accompanied by a team consisting of neurosurgeons, anesthetists and resuscitation experts from the Hospital of Padua authorized by the Venetian governor Luca Zaia. On Saturday morning the hospital in Padua issued a first medical report, in which it noted that the condition of the professor, who was admitted around midnight, "was substantially stable despite the challenging transportation, but his condition was serious."