I was thinking about this problem a lot last week, and I only got as far as what you've just mentioned, i.e. you need a precise definition of how to measure "the effect [of] slight perturbations". I wouldn't hold my breath trying to find closed form solutions, or for that matter, any solution with fewer than n(n-1)/2 terms. The simplest solution might even be a matrix with n columns and n(n-1)/2 rows and some mess of O(n^n) symbols in each element, but that may be a bit pessimistic (-: On 6/18/12, James Propp <jamespropp@gmail.com> wrote:
Here's a (hopefully clearer) statement of the question. [...] suppose we have the additional goal of minimizing the effect that slight perturbations of the biases will have. Is there a unique best choice of biases, and if so, what is it? [...] What I actually want is not necessarily the most noise-insensitive way of biasing the junctions, but a reasonably noise-insensitive way of biasing the junctions that is also easy to compute and mathematically natural. (Yes, "natural" is even more vague than "noise-insensitive".) [...]
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