Generalized metric spaces are a common generalization of preorders and ordinary metric spaces. Every generalized metric space can be isometrically embedded in a complete function space by means of a metric version of the categorical Yoneda embedding. This simple fact gives naturally rise to: 1. a topology for generalized metric spaces which for arbitrary preorders corresponds to the Alexandroo ...

A widely established set of unsupervised node embedding methods can be interpreted as consisting two distinctive steps: i) the definition a similarity matrix based on graph interest followed by ii) an explicit or implicit factorization such matrix. Inspired this viewpoint, we propose improvements in both steps framework. On one hand, to encode similarities free energy distance, which interpolat...

Information hiding techniques are become important in a number of application areas. In the field of Data Communication security of information is the major problem. The transmission of information via the Internet may expose it to detect and theft. So, data embedding technologies are developed to provide personal privacy, commercial and national security interests. In this work we consider the...

The existing Diffusion Maps method brings diffusion to data samples by Markov random walk. In this paper, to provide a general solution form of Diffusion Maps, first, we propose the generalized single-graph-diffusion embedding framework on the basis of graph embedding framework. Second, by designing the embedding graph of the framework, an algorithm, namely Locally Discriminant Diffusion Projec...

Let H be a subgroup of a group G. H is said to be S-embedded in G if G has a normal T such that HT is an S-permutable subgroup of G and H ∩ T ≤ H sG, where H denotes the subgroup generated by all those subgroups of H which are S-permutable in G. In this paper, we investigate the influence of minimal S-embedded subgroups on the structure of finite groups. We determine the structure the finite grou...

An efficient algorithm for isometry-invariant matching of surfaces is presented. The key idea is computing the minimum-distortion mapping between two surfaces. For this purpose, we introduce the generalized multidimensional scaling, a computationally efficient continuous optimization algorithm for finding the least distortion embedding of one surface into another. The generalized multidimension...

In this paper, we present a new approach to obtain the asymptotic expansion and superconvergence for the linear element on Union Jack mesh. First, we construct a generalized interpolation function and its discrete harmonic extension by using the energy embedding method and the method of separation of variables. Then, we present elaborate estimates for the generalized interpolation function and ...

It is often easier to study pseudo-Riemannian manifolds by presenting them as surfaces in some ambient space. We propose an algorithm for construction of explicit isometric embeddings with symmetries into space higher dimension. While most the existing methods are based on Gauss-Codazzi-Mainardi-Peterson equations, we do not use and instead concentrate a system equations which connects metric m...

Generalized metric spaces are a common generalization of preorders and ordinary metric spaces (Lawvere 1973). Combining Lawvere's (1973) enriched-categorical and Smyth' (1988, 1991) topological view on generalized metric spaces, it is shown how to construct 1. completion , 2. topology, and 3. powerdomains for generalized metric spaces. Restricted to the special cases of preorders and ordinary m...