Related papers: On distances and metrics in discrete ordered sets

We discuss a general method by which a higher order difference equation on a group is transformed into an equivalent triangular system of two difference equations of lower orders. This breakdown into lower order equations is based on the…

Symmetries are known to dictate important physical properties and can be used as a design principle in particular in wave physics, including wave structures and the resulting propagation dynamics. Local symmetries, in the sense of a…

For a fixed set $X$, an arbitrary \textit{weight structure} $d \in [0,\infty]^{X \times X}$ can be interpreted as a distance assignment between pairs of points on $X$. Restrictions (i.e. \textit{metric axioms}) on the behaviour of any such…

In this article, we propose tree edit distance with variables, which is an extension of the tree edit distance to handle trees with variables and has a potential application to measuring the similarity between mathematical formulas,…

The quantale of distance distributions is of fundamental importance for understanding probabilistic metric spaces as enriched categories. Motivated by the categorical interpretation of partial metric spaces, we are led to investigate the…

By using the random interchanging algorithm, we investigate the relations between average distance, standard deviation of degree distribution and synchronizability of complex networks. We find that both increasing the average distance and…

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…

Motivated by a concept studied in [1], we consider a property of matrices over finite fields that generalizes triangular totally nonsingular matrices to block matrices. We show that (1) matrices with this property suffice to construct good…

This is a survey article on trees, with a modest number of proofs to give a flavor of the way these topologies can be efficiently handled. Trees are defined in set-theorist fashion as partially ordered sets in which the elements below each…

We study a family of distance functions on rankings that allow for asymmetric treatments of alternatives and consider the distinct relevance of the top and bottom positions for ordered lists. We provide a full axiomatic characterization of…

The Mitsch order is already known as a natural partial order for semigroups and rings. The purpose of this paper is to further study of the Mitsch order on modules by investigating basic properties via endomorphism rings. And so this study…

For non-empty sets X we define notions of distance and pseudo metric with values in a partially ordered set that has a smallest element $\theta $. If $h_X$ is a distance in $X$ (respectively, a pseudo metric in $X$), then the pair $(X,h_X)$…

We investigate the size of the distance set determined by two subsets of finite dimensional vector spaces over finite fields. A lower bound of the size is given explicitly in terms of cardinalities of the two subsets. As a result, we…

We apply the techniques of computable model theory to the distance function of a graph. This task leads us to adapt the definitions of several truth-table reducibilities so that they apply to functions as well as to sets, and we prove…

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…

The surrounding of a vertex in a network can be more or less symmetric. We derive measures of a specific kind of symmetry of a vertex which we call degree symmetry -- the property that many paths going out from a vertex have overlapping…

Distance metric learning algorithms aim to appropriately measure similarities and distances between data points. In the context of clustering, metric learning is typically applied with the assist of side-information provided by experts,…

We give a general construction of triangulations starting from a walk in the quarter plane with small steps, which is a discrete version of the mating of trees. We use a special instance of this construction to give a bijection between maps…

We characterize factor congruences in semilattices by using generalized notions of order ideal and of direct sum of ideals. When the semilattice has a minimum (maximum) element, these generalized ideals turn into ordinary (dual) ideals.

There is a basic paradigm, called here the radius of well-posedness, which quantifies the "distance" from a given well-posed problem to the set of ill-posed problems of the same kind. In variational analysis, well-posedness is often…