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The problems of uniformly sampling and approximately counting contingency tables have been widely studied, but efficient solutions are only known in special cases. One appealing approach is the Diaconis and Gangolli Markov chain which updates the entries of a random 2 ×2 submatrix. This chain is known to be rapidly mixing for cell-bounded tables only when the cell bounds are all 1 and the row and...
This paper is concerned with finding a level ideal (LI) of a partially ordered set (poset): given a finite poset P, a level of each element p ∈ P is defined as the number of ideals which do not include p, then the problem is to find an ideal consisting of elements whose levels are less than a given integer i. We call the ideal as the i-th LI. The concept of the level ideal is naturally derived from...
We present a polynomial-time perfect sampler for the Q-Ising with a vertex-independent noise. The Q-Ising, one of the generalized models of the Ising, arose in the context of Bayesian image restoration in statistical mechanics. We study the distribution of Q-Ising on a two-dimensional square lattice over n vertices, that is, we deal with a discrete state space {1,...,Q}n for...
We study the task of deterministically extracting randomness from sources containing computational entropy. The sources we consider have the form of a conditional distribution $(f({\mathcal{X}})|{\mathcal{X}})$ , for some function f and some distribution , and we say that such a source has computational min-entropy k if any circuit of size 2k can only...
This paper explores the fundamental question of how many iterations the celebrated HITS algorithm requires on a general graph to converge in score and, perhaps more importantly, in rank (i.e. to “get right” the order of the nodes). We prove upper and almost matching lower bounds. We also extend our results to weighted graphs.
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