Monday, March 21, 2011

Como category seminar: Open Markov chains

Today (16th March 2011) was the defence of the doctoral thesis of our student Luisa de Francesco Albasini. I will describe one aspect of her work. Traditional markov chains are an extremely useful tool in diverse applications. Just to give one example Google uses a markov chain to rank web pages creating some order in the internet.
A markov chain is a system whose dynamics is encoded in a square matrix of non-negative reals whose row sums are all 1. The rows (and columns) may be thought of as states of a system and the i,j th element of the matrix as the probability of a transition from state i to state j. The k th power of the matrix gives the probabilities of paths of length k.
A markov chain is easily represented also as a labelled graph or automaton:
Systems modelled in this way are closed systems. An essential aspect of compositionality of systems
is that one needs to consider open systems.



Tuesday, March 15, 2011

Como Category Seminar

I have said that the original motivation for this blog was to rant about problems with university reform in Italy. However I realize now that another reason for the blog is that I miss having a scientific seminar in Como. My scientific life in Sydney was always bound up with the Sydney Category Seminar. Here in Como, despite some attempts, I have never been able to create a regular seminar, so I am going to use part of this blog to take the place of a seminar. If I can get others to contribute all the better, but in any case I will record here the kind of lectures I used to give in Sydney;  that is, work in progress, comments on other research etc.


Thursday, March 10, 2011

The purpose of a university

From Peter Cameron's blog:
"The purpose of a university used to be teaching and research; now it is making money and scoring well in league tables".