Shape-based metrics measure how faithfully a drawing D represents the structure of graph G, using proximity S D. While some limited classes admit drawings (i.e., optimally shape-faithful drawings, where $$S = G$$ ), algorithms for general graphs have not been investigated. In this paper, we present first study graphs. First, conduct extensive comparison experiments popular layouts shape-based m...

A typical concept in quantum state analysis is based on the idea that states vicinity of some pure entangled share same properties, implying with a high fidelity must be entangled. States whose entanglement can detected this way are also called faithful. We prove structural result corresponding fidelity-based witnesses, resulting simple condition for faithfulness two-party state. For simplest c...

Let be a module over commutative ring with identity. Before studying the concept of Strongly Pseudo Nearly Semi-2-Absorbing submodule, we need to mention ideal and basics that you study submodule. Also, introduce several characteristics submodule in classes multiplication modules other types modules. We also had no luck because is not ideal. it noted under conditions, which this faithful module...

Squashed entanglement is a measure for the entanglement of bipartite quantum states. In this paper we present a lower bound for squashed entanglement in terms of a distance to the set of separable states. This implies that squashed entanglement is faithful, that is, it is strictly positive if and only if the state is entangled. We derive the lower bound on squashed entanglement from a lower bou...