Let G and H be graphs. A substitution of H in G instead of a vertex v 2 V (G) is the graph G(v ! H), which consists of disjoint union of H and G ? v with the additional edge-set fxy : x 2 V (H); y 2 N G (v)g. For a hereditary class of graphs P, the substitutional closure of P is deened as the class P consisting of all graphs which can be obtained from graphs in P by repeated substitutions. Let ...

It is argued that the prevailing definition of quasicrystals, requiring them to contain an axis of symmetry that is forbidden in periodic crystals, is inadequate. This definition is too restrictive in that it excludes an important and interesting collection of structures that exhibit all the well-known properties of quasicrystals without possessing any forbidden symmetries.

This paper proposes a framework for establishing quantitative measures and mathematically reproducible definitions of structural resiliency as it pertains to a structure's ability to minimize the potential for undesirable response to low-probability-high-consequence events. The resiliency assessment and design process follow a logical progression of steps starting with the characterization of h...

Abstract Background and Aims Acute kidney injury (AKI) is a very common condition in inpatients. Severe AKI frequently associated with by neurological disorders such as confusion, the mechanisms of which are poorly understood. We have shown several animal models that chronic disease impaired cognitive performance memory increased permeability blood-brain barrier (BBB), related to accumulation u...