Related papers: Distance statistics in large toroidal maps
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The curse of dimensionality is a common phenomenon which affects analysis of datasets characterized by large numbers of variables associated with each point. Problematic scenarios of this type frequently arise in classification algorithms…
Tree rotations (left and right) are basic local deformations allowing to transform between two unlabeled binary trees of the same size. Hence, there is a natural problem of practically finding such transformation path with low number of…
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Multi-marginal optimal transport enables one to compare multiple probability measures, which increasingly finds application in multi-task learning problems. One practical limitation of multi-marginal transport is computational scalability…
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Wasserstein distance, which measures the discrepancy between distributions, shows efficacy in various types of natural language processing (NLP) and computer vision (CV) applications. One of the challenges in estimating Wasserstein distance…
A distance labeling scheme is an assignments of labels, that is binary strings, to all nodes of a graph, so that the distance between any two nodes can be computed from their labels and the labels are as short as possible. A major open…
We consider a random walk of $n$ steps starting at $x_0=0$ with a double exponential (Laplace) jump distribution. We compute exactly the distribution $p_{k,n}(\Delta)$ of the gap $d_{k,n}$ between the $k^{\rm th}$ and $(k+1)^{\rm th}$…
We consider random walks indexed by arbitrary finite random or deterministic trees. We derive a simple sufficient criterion which ensures that the maximal displacement of the tree-indexed random walk is determined by a single large jump.…
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Recent years have witnessed a tremendous growth using topological summaries, especially the persistence diagrams (encoding the so-called persistent homology) for analyzing complex shapes. Intuitively, persistent homology maps a potentially…