Related papers: Proximity Induced by Order Relations

In 1958, Sz\"{u}sz proved an inhomogeneous version of Khintchine's theorem on Diophantine approximation. Sz\"{u}sz's theorem states that for any non-increasing approximation function $\psi:\mathbb{N}\to (0,1/2)$ with $\sum_q \psi(q)=\infty$…

For an arbitrary self-adjoint operator $B$ in a Hilbert space $H$, we present direct and inverse theorems establishing the relationship between the degree of smoothness of a vector $x \in H$ with respect to the operator $B$, the rate of…

In this paper a first order analytical system of difference equations is considered. For an asymptotically stable fixed point x0 of the system a gradual approximation of the domain of attraction DA is presented in the case when the matrix…

In this paper we investigate phenomena of spontaneous emergence or purposeful formation of highly organized structures in networks of related agents. We show that the formation of large organized structures requires exponentially large, in…

The ternary relation $B(x,y,z)$ of betweenness states that an element $y$ is between the elements $x$ and $z$, in some sense depending on the considered structure. In a partially ordered set $(N,\leq)$, $B(x,y,z):\Longleftrightarrow…

Several researchers proposed using non-Euclidean metrics on point sets in Euclidean space for clustering noisy data. Almost always, a distance function is desired that recognizes the closeness of the points in the same cluster, even if the…

We study classes of graphs with bounded clique-width that are well-quasi-ordered by the induced subgraph relation, in the presence of labels on the vertices. We prove that, given a finite presentation of a class of graphs, one can decide…

The Prague dimension of a graph $G$ is defined as the minimum number of complete graphs whose direct product contains $G$ as an induced subgraph. Introduced in the 1970s by Ne\v{s}et\v{r}il, Pultr, and R\"odl -- and motivated by the work of…

This survey describes the method of approximation of operator semigroups, based on the Chernoff theorem. We outline recent results in this domain as well as clarify relations between constructed approximations, stochastic processes,…

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…

Vector similarity measures play a fundamental role in various fields, including machine learning, natural language processing, information retrieval, and data mining. These measures quantify the closeness between two vectors in a…

For a distributive join-semilattice S with zero, a S-valued poset measure on a poset P is a map m:PxP->S such that m(x,z) <= m(x,y)vm(y,z), and x <= y implies that m(x,y)=0, for all x,y,z in P. In relation with congruence lattice…

We derive analytically the asymptotic behavior of the Casimir interaction between a sphere and a plate when the distance between them, $d$, is much smaller than the radius of the sphere, $R$. The leading order and next-to-leading order…

Image ranking is to rank images based on some known ranked images. In this paper, we propose an improved linear ordinal distance metric learning approach based on the linear distance metric learning model. By decomposing the distance metric…

In previous articles, we showed that, based on large-order asymptotic behavior, one can approximate a divergent series via the parametrization of a specific hypergeometric approximant. The analytical continuation is then carried out through…

A semiorder is a model of preference relations where each element $x$ is associated with a utility value $\alpha(x)$, and there is a threshold $t$ such that $y$ is preferred to $x$ iff $\alpha(y) > \alpha(x)+t$. These are motivated by the…

Recent advances in the field of network embedding have shown that low-dimensional network representation is playing a critical role in network analysis. Most existing network embedding methods encode the local proximity of a node, such as…

A numbering of a countable family $S$ is a surjective map from the set of natural numbers $\omega$ onto $S$. The paper studies Rogers semilattices, i.e. upper semilattices induced by the reducibility between numberings, for families…

Recommendation systems for different Document Networks (DN) such as the World Wide Web (WWW) and Digital Libraries, often use distance functions extracted from relationships among documents and keywords. For instance, documents in the WWW…

In the regression framework, the empirical measure based on the responses resulting from the nearest neighbors, among the covariates, to a given point $x$ is introduced and studied as a central statistical quantity. First, the associated…