Related papers: Order distances and split systems
Let R^d -> A be a query problem over R^d for which there exists a data structure S that can compute P(q) in O(log n) time for any query point q in R^d. Let D be a probability measure over R^d representing a distribution of queries. We…
We analyze the distribution of the distance between two nodes, sampled uniformly at random, in digraphs generated via the directed configuration model, in the supercritical regime. Under the assumption that the covariance between the…
We generalize the results from [X.-D. Zhang, X.-P. Lv, Y.-H. Chen, \textit{Ordering trees by the Laplacian coefficients}, Linear Algebra Appl. (2009), doi:10.1016/j.laa.2009.04.018] on the partial ordering of trees with given diameter. For…
Comparing the ranking of candidates by different voters is an important topic in social and information science with a high relevance from the point of view of practical applications. In general, ties and pairs of incomparable candidates…
Metrics for merge trees that are simultaneously stable, informative, and efficiently computable have so far eluded researchers. We show in this work that it is possible to devise such a metric when restricting merge trees to ordered domains…
We study questions inspired by Erd\H os' celebrated distance problems with dot products in lieu of distances, and for more than a single pair of points. In particular, we study point configurations present in large finite point sets in the…
An important problem in geometric computing is defining and computing similarity between two geometric shapes, e.g. point sets, curves and surfaces, etc. Important geometric and topological information of many shapes can be captured by…
The quartet distance is a measure of similarity used to compare two unrooted phylogenetic trees on the same set of $n$ leaves, defined as the number of subsets of four leaves related by a different topology in both trees. After a series of…
Many real objects are modeled as discrete sets of points, such as corners or other salient features. For our main applications in chemistry, points represent atomic centers in a molecule or a solid material. We study the problem of…
Different types of two- and three-dimensional representations of a finite metric space are studied that focus on the accurate representation of the linear order among the distances rather than their actual values. Lower and upper bounds for…
The order bound for the minimum distance of algebraic geometry codes was originally defined for the duals of one-point codes and later generalized for arbitrary algebraic geometry codes. Another bound of order type for the minimum distance…
This paper proposes to establish the distance between partial preference orderings based on two very different approaches. The first approach corresponds to the brute force method based on combinatorics. It generates all possible complete…
Learning about the relationship between distance to landmarks and events and phenomena of interest is a multi-faceted problem, as it may require taking into account multiple dimensions, including: spatial position of landmarks, timing of…
Tree comparison metrics have proven to be an invaluable aide in the reconstruction and analysis of phylogenetic (evolutionary) trees. The path-length distance between trees is a particularly attractive measure as it reflects differences in…
Optimal transport (\OT) theory defines a powerful set of tools to compare probability distributions. \OT~suffers however from a few drawbacks, computational and statistical, which have encouraged the proposal of several regularized variants…
Given two binary trees on $N$ labeled leaves, the quartet distance between the trees is the number of disagreeing quartets. By permuting the leaves at random, the expected quartets distance between the two trees is…
We develop a general framework for reasoning about distances between transition systems with quantitative information. Taking as starting point an arbitrary distance on system traces, we show how this leads to natural definitions of a…
Disordered systems like liquids, gels, glasses, or granular materials are not only ubiquitous in daily life and in industrial applications but they are also crucial for the mechanical stability of cells or the transport of chemical and…
It has been recently pointed out that dynamical systems depending on future values of the unknowns may be useful in different areas of knowledge. We explore in this context the extension of the concept of order reduction that has been…
A key problem in the study and design of complex systems is the apparent disconnection between the microscopic and the macroscopic. It is not straightforward to identify the local interactions that give rise to an observed global…