Discrete network dynamics stirs
After the setback where my DND1 paper Discrete network dynamics. Part 1: Operator theory (which can be found in arXiv at cs.NE/0511027) was rejected (see here for some remarks about this problem, and in the comments here for some less diplomatic remarks), I have finally started the ball rolling again by actually sitting down to prepare the draft of the second paper in the series (i.e. DND2).
I have published a lot of material on vector quantisers of various types, but unfortunately the common underlying thread behind all of this work is not at all clear from my papers on the subject. Historically, I started working on VQs in the mid-1980's, and I was a refugee from Markov random field models which were too computationally costly for the rather slow computers that we used back then. I have always had an MRF style of thinking (i.e. joint probabilities, Bayesian inference, etc), and VQs offered me a computationally cheap and cheerful way of using some of the properties of MRF models.
One of the many reasons why I introduced (in DND1) the operator framework for formulating MCMC algorithms was to unify all of my past work on VQs. Therefore the provisional title of DND2 will be "Discrete network dynamics. Part 2: Vector quantisers". I don't know how long DND2 will be in gestation, because I usually get side-tracked by some new angle that occurs to me whilst I am writing, which then explodes into a whole new line of research that diverts me entirely away from the original task. I will try to avoid that pitfall, but I can't promise that it won't happen.
Anyway, I thought that you should know that DND is alive and well (even if the reviewers of DND1 didn't think so!).
Update: In my spare time I have been busy "evolving" my DND2 paper. I can't just write down a paper in its final form, rather I have to evolve it from nothing until it reaches a fixed point. As predicted, during this process I have been side-tracked, but it has been onto fertile ground which directly relates to DND2, and which pulls together all of my vector quantiser work even more nicely than I had originally anticipated. As long as 20 years ago I knew all of the operator techniques that I am using in DND2, so you can imagine how annoyed I feel about the circuitous path my research has taken during the intervening years. My evolution of DND2 continues apace, and I will keep you updated as this process converges towards a fixed point.
Update: I have just returned from a long Summer holiday during which I thought about my DND2 paper for precisely 0% of the time. Now I have to try to remember where I was in the process of writing DND2, so its gestation will be fairly long as I hinted at in my original posting.