On the maximal connected component of hypercube with faulty vertices

In evaluating an interconnection network, it is indispensable to estimate the size of the maximal connected components of the underlying graph when the network begins to lose processors. Hypercube is one of the most popular interconnection networks. This article addresses the maximal connected components of an n -dimensional cube with faulty processors. We first prove that an n -cube with a set F of at most 2n - 3 failing processors has a component of size greater than or equal to2(n) - \F\ - 1. We then prove that an n -cube with a set F of at most 3n - 6 missing processors has a component of size greater than or equal to2(n) - \F\ - 2.

On the maximal connected component of hypercube with faulty vertices (II)

evaluating the fault tolerance of an interconnection network, it is essential to estimate the size of a maximal connected component of the network at the presence of faulty processors. Hypercube is one of the most popular interconnection networks. In this paper, we prove that for ngreater than or equal to6, an n-dimensional cube with a set F of at most (4n-10) failing processors has a component of size greater than or equal to2"-\F-3. This result demonstrates the superiority of hypercube in terms of the fault tolerance.

On the maximal connected component of a hypercube with faulty vertices III

Hypercube is one of the most popular topologies for connecting processors in multicomputer systems. In this paper we address the maximum order of a connected component in a faulty cube. The results established include several known conclusions as special cases. We conclude that the hypercube structure is resilient as it includes a large connected component in the presence of large number of faulty vertices.

Exposure to parabens at the concentration of maximal proliferative response increases migratory and invasive activity of human breast cancer cells in vitro

Alkyl esters of p–hydroxybenzoic acid (parabens) are widely used as preservatives in personal care products, foods and pharmaceuticals. Their oestrogenic activity, their measurement in human breast tissue and their ability to drive proliferation of oestrogen-responsive human breast cancer cells has opened a debate on their potential to influence breast cancer development. Since proliferation is not the only hallmark of cancer cells, we have investigated the effects of exposure to parabens at concentrations of maximal proliferative response on migratory and invasive properties using three oestrogen-responsive human breast cancer cell lines (MCF-7, T-47-D, ZR-75-1). Cells were maintained short-term (1 week) or long-term (20±2 weeks) in phenol-red-free medium containing 5% charcoal-stripped serum with no addition, 10-8M 17-oestradiol, 1-5x10-4M methylparaben, 10-5M n-propylparaben or 10-5M n-butylparaben. Long-term exposure (20±2 weeks) of MCF-7 cells to methylparaben, n-propylparaben or n-butylparaben increased migration as measured using a scratch assay, time-lapse microscopy and xCELLigence technology: invasive properties were found to increase in matrix degradation assays and migration through matrigel on xCELLigence. Western immunoblotting showed an associated downregulation of E-cadherin and -catenin in the long-term paraben-exposed cells which could be consistent with a mechanism involving epithelial to mesenchymal transition. Increased migratory activity was demonstrated also in long-term paraben-exposed T-47-D and ZR-75-1 cells using a scratch assay and time-lapse microscopy. This is the first report that in vitro, parabens can influence not only proliferation but also migratory and invasive properties of human breast cancer cells.