SUMMARY Recently, Mooij et al. proposed new sufficient conditions for convergence of the sum-product algorithm, and it was also shown that if the factor graph is a tree, Mooij's sufficient condition for convergence is always activated. In this letter, we show that the converse of the above statement is also true under some assumption, and that the assumption holds for the sum-product decoding. ...

Term graph rewriting provides a formalism for implementing term rewriting in an efficient manner by avoiding duplication. Infinitary term rewriting has been introduced to study infinite term reduction sequences. Such infinite reductions can be used to model non-strict evaluation. In this paper, we unify term graph rewriting and infinitary term rewriting thereby addressing both components of laz...

Discussions about different graph Laplacians, mainly normalized and unnormalized versions of the graph Laplacians, have been ardent with respect to various methods in clustering and graph based semi-supervised learning. Previous research on the graph Laplacians investigated their convergence properties to Laplacian operators on continuous manifolds. There is still no strong proof on convergence...

An explicit representation of the Gamma limit a single-well Modica--Mortola functional is given for one-dimensional space under graph convergence which finer than conventional $L^1$-convergence or in measure. As an application, singular Kobayashi-Warren-Carter energy, popular materials science, given. Some compactness also established. Such formulas, as well compactness, useful to characterize ...

Term graph rewriting provides a simple mechanism to finitely represent restricted forms of infinitary term rewriting. The correspondence between infinitary term rewriting and term graph rewriting has been studied to some extent. However, this endeavour is impaired by the lack of an appropriate counterpart of infinitary rewriting on the side of term graphs. We aim to fill this gap by devising tw...

The regularization functional induced by the graph Laplacian of a random neighborhood graph based on the data is adaptive in two ways. First it adapts to an underlying manifold structure and second to the density of the data-generating probability measure. We identify in this paper the limit of the regularizer and show uniform convergence over the space of Hölder functions. As an intermediate s...