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.
Read more ยป
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.
Read more ยป
Labels: Como Category Seminar