Related papers: Parametric set-wise injective maps

We characterize locally injective semialgebraic maps between two semialgebraic sets in terms of the induced homomorphism between their rings of (continuous) semialgebraic functions.

We consider the maximal number of arbitrary points in a special fibre that can be simultaneously approached by points in one sequence of general fibres. Several results about this topological invariant and their applications describe the…

We introduce and study embeddings of graphs in finite projective planes, and present related results for some families of graphs including complete graphs and complete bipartite graphs. We also make connections between embeddings of graphs…

In this paper, we introduce the neutrosophic contractive and neutrosophic mapping. We establish some results on fixed points of a neutrosophic mapping.

This letter introduces an abstract learning problem called the "set embedding": The objective is to map sets into probability distributions so as to lose less information. We relate set union and intersection operations with corresponding…

The book is devoted to constructing embedding finite-dimensional maps into trivial bundles and investigating the corresponding general position properties.

We introduce a new intrinsic metric in subdomains of a metric space and give upper and lower bounds for it in terms of well-known metrics. We also prove distortion results for this metric under quasiregular maps.

This work presents an innovative method for point set self-embedding, that encodes the structural information of a dense point set into its sparser version in a visual but imperceptible form. The self-embedded point set can function as the…

In this paper, we study some new fixed point results for self maps defined on partial metric type spaces. In particular, we give common fixed point theorems in the same setting. Some examples are given which illustrate the results.

We generalize to vector bundles the techniques introduced for line bundles in prior work of the author with Liu, Osserman and Zhang. We then use this method to prove the injectivity of the Petri map for vector bundles and the surjectivity…

Graph embeddings deal with injective maps from a given simple, undirected graph $G=(V,E)$ into a metric space, such as $\mathbb{R}^n$ with the Euclidean metric. This concept is widely studied in computer science, see \cite{ge1}, but also…

Spectral embedding finds vector representations of the nodes of a network, based on the eigenvectors of a properly constructed matrix, and has found applications throughout science and technology. Many networks are multipartite, meaning…

We review the recent advances reported in the field of integrated photonic waveguide meshes, both from the theoretical as well as from the experimental point of view. We show how these devices can be programmed to implement both traditional…

In this paper we introduce the notion of Hurewicz fibrations in the class of embedding maps of orbifold charts by giving the concept of E-fibration embedding. We study the fundamental properties of this concept such as the restriction,…

Graph embedding is a transformation of nodes of a network into a set of vectors. A good embedding should capture the underlying graph topology and structure, node-to-node relationship, and other relevant information about the graph, its…

Stable topological invariants are a cornerstone of persistence theory and applied topology, but their discriminative properties are often poorly-understood. In this paper we study a rich homology-based invariant first defined by Dey, Shi,…

Fixed point results with respect to generalized rational contractive mappings in semi-metric spaces endowed with a directed graph are proved. Some examples are provided to illustrate the results. The obtained results extend, improve and…

The concept of quasi-isometric embedding maps between $*$-algebras is introduced. We have obtained some basic results related to this notion and similar to quasi-isometric embedding maps on metric spaces, under some conditions, we give a…

In this note, we discuss some fixed point theorems for contractive self mappings defined on a $G$-metric spaces. More precisely, we give fised point theorems for mappings with a contractive iterate at a point.

Majority of the current dimensionality reduction or retrieval techniques rely on embedding the learned feature representations onto a computable metric space. Once the learned features are mapped, a distance metric aids the bridging of gaps…