valdis laan in [5] introduced an extension of strong flatness which is called weak pullback flatness. in this paper we introduce a new property of acts over monoids, called u-wpf which is an extension of weak pullback flatness and give a classification of monoids by this property of their acts and also a classification of monoids when this property of acts implies others. we also show that regu...

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...

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...