Related papers: Optimal homeomorphisms between closed curves

The phenomenon, known as "supersmoothness" was first observed for bivariate splines and attributed to the polynomial nature of splines. Using only standard tools from multivatiate calculus, we show that if we continuously glue two smooth…

As graphical summaries for topological spaces and maps, Reeb graphs are common objects in the computer graphics or topological data analysis literature. Defining good metrics between these objects has become an important question for…

It is shown that the existence of a biseparating map between a large class of spaces of vector-valued continuous functions A(X,E) and A(Y,F) implies that some compactifications of X and Y are homeomorphic. In some cases, conditions are…

We characterize maps between $n$-dimensional N\"obeling manifolds that can be approximated by homeomorphisms.

We introduce and study isomorphic distances between ordinal elections (with the same numbers of candidates and voters). The main feature of these distances is that they are invariant to renaming the candidates and voters, and two elections…

Describing shapes by suitable measures in object segmentation, as proposed in [24], allows to combine the advantages of the representations as parametrized contours and indicator functions. The pseudo-Riemannian structure of optimal…

In this paper we study the common distance between points and the behavior of a constant length step discrete random walk on finite area hyperbolic surfaces. We show that if the second smallest eigenvalue of the Laplacian is at least 1/4,…

Data consisting of a graph with a function mapping into $\mathbb{R}^d$ arise in many data applications, encompassing structures such as Reeb graphs, geometric graphs, and knot embeddings. As such, the ability to compare and cluster such…

We study the stable translation length of homeomorphisms of a surface acting on the fine nonseparating curve graph and compare it to the stable translation lengths of its finite approximations - mapping classes relative to a finite…

We describe an explicit method for constructing pseudo-automorphisms of a space $X$ which is obtained by blowing up points of $P^k$ (or a product $P^k \times \cdots \times P^k$). The centers of blowup are chosen to lie on an elliptic normal…

Behaviour distances to measure the resemblance of two states in a (nondeterministic) fuzzy transition system have been proposed recently in the literature. Such a distance, defined as a pseudo-ultrametric over the state space of the model,…

The problem of quantifying the difference between evolutions of an open quantum system (in particular, between the actual evolution of an open system and the ideal target operation on the corresponding closed system) is important in quantum…

Any $n$-tuple of points in the plane can be moved to any other $n$-tuple by a continuous motion with at most $\binom{n}{3}$ intermediate changes of the order type. Even for tuples with the same order type, the cubic bound is sharp: there…

This work considers the problem of estimating the distance between two covariance matrices directly from the data. Particularly, we are interested in the family of distances that can be expressed as sums of traces of functions that are…

Many statistical and machine learning approaches rely on pairwise distances between data points. The choice of distance metric has a fundamental impact on performance of these procedures, raising questions about how to appropriately…

This paper is devoted to the study of isometrically homogeneous spaces from the view point of metric geometry. Mainly we focus on those spaces that are homeomorphic to lines. One can reduce the study to those distances on $\R$ that are…

Lipman et al. [ACM Transactions on Graphics 29 (3) (2010), 1--11] introduced the concept of biharmonic distance to measure the distances between pairs of points on a 3D surface. Biharmonic distance has some advantages over resistance…

We prove two theorems on the removal of singularities on the boundary of a pseudo-holomorphic curve. In one theorem, we need no apriori assumption on the area of the curve. The proof uses a doubling argument with the goal of converting…

The total variation distance is proposed as a privacy measure in an information disclosure scenario when the goal is to reveal some information about available data in return of utility, while retaining the privacy of certain sensitive…

This paper introduces the use of unbalanced optimal transport methods as a similarity measure for diffeomorphic matching of imaging data. The similarity measure is a key object in diffeomorphic registration methods that, together with the…