Related papers: Proximity Induced by Order Relations

We study the proximity effect in good contacts between normal metals and high Tc (d-wave) superconductors. We present theoretical results for the spatially dependent order parameter and local density of states, including effects of impurity…

Order of magnitude reasoning - reasoning by rough comparisons of the sizes of quantities - is often called 'back of the envelope calculation', with the implication that the calculations are quick though approximate. This paper exhibits an…

Assortativity was first introduced by Newman and has been extensively studied and applied to many real world networked systems since then. Assortativity is a graph metrics and describes the tendency of high degree nodes to be directly…

We show that attractors are semicontinuous for closed relations on compact Hausdorff spaces. Semicontinuity is what guarantees that small changes to a system do not result in massive growth of certain features, notably attractors. That is,…

While relation extraction is an essential task in knowledge acquisition and representation, and new-generated relations are common in the real world, less effort is made to predict unseen relations that cannot be observed at the training…

S. B. Rao conjectured that graphic sequences are well-quasi-ordered under an inclusion based on induced subgraphs. This conjecture has now been proved by Chudnovsky and Seymour. We give an independent short proof of the labelled version of…

A partial order on the set of metric measure spaces is defined; it generalizes the Lipschitz order of Gromov. We show that our partial order is closed when metric measure spaces are equipped with the Gromov-weak topology and give a new…

Correlation measure of order $k$ is an important measure of randomness in binary sequences. This measure tries to look for dependence between several shifted version of a sequence. We study the relation between the correlation measure of…

The problem of measuring similarity of graphs and their nodes is important in a range of practical problems. There is a number of proposed measures, some of them being based on iterative calculation of similarity between two graphs and the…

We introduce sparse polynomial zonotopes, a new set representation for formal verification of hybrid systems. Sparse polynomial zonotopes can represent non-convex sets and are generalizations of zonotopes, polytopes, and Taylor models.…

The emerging theory of graph limits exhibits an analytic perspective on graphs, showing that many important concepts and tools in graph theory and its applications can be described more naturally (and sometimes proved more easily) in…

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 $(X,h_X)$…

In this paper we prove two new abstract compactness criteria in normed spaces. To this end we first introduce the notion of an equinormed set using a suitable family of semi-norms on the given normed space satisfying some natural…

The z-measures on partitions originated from the problem of harmonic analysis of linear representations of the infinite symmetric group in the works of Kerov, Olshanski and Vershik (1993, 2004). A similar family corresponding to projective…

There are two methods to study families of conformal theories in the operator formalism. In the first method we begin with a theory and a family of deformed theories is defined in the state space of the original theory. In the other there…

For an ordered point set in a Euclidean space or, more generally, in an abstract metric space, the ordered Nearest Neighbor Graph is obtained by connecting each of the points to its closest predecessor by a directed edge. We show that for…

In this paper, we generalize Dranishnikov's asymptotic inductive dimension to the setting of coarse proximity spaces. We show that in this more general context, the asymptotic inductive dimension of a coarse proximity space is bigger or…

The statistical convergence is defined for sequences with the asymptotic density on the natural numbers, in general. In this paper, we introduce the statistical convergence for nets in Riesz spaces by using the finite additive measures on…

For a given partially ordered set (poset) and a given family of mappings of the poset into itself, we study the problem of the description of joint fixed points of this family. Well-known Tarski's theorem gives the structure of the set of…

In this paper we are using the poset representation to describe the complex answers given by IR systems after a clustering and ranking processes. The answers considered may be given by cartographical representations or by thematic sub-lists…