Optimized hash for network path encoding with minimized false positives

The Bloom filter is a space efficient randomized data structure for representing a set and supporting membership queries. Bloom filters intrinsically allow false positives. However, the space savings they offer outweigh the disadvantage if the false positive rates are kept sufficiently low. Inspired by the recent application of the Bloom filter in a novel multicast forwarding fabric, this paper proposes a variant of the Bloom filter, the optihash. The optihash introduces an optimization for the false positive rate at the stage of Bloom filter formation using the same amount of space at the cost of slightly more processing than the classic Bloom filter. Often Bloom filters are used in situations where a fixed amount of space is a primary constraint. We present the optihash as a good alternative to Bloom filters since the amount of space is the same and the improvements in false positives can justify the additional processing. Specifically, we show via simulations and numerical analysis that using the optihash the false positives occurrences can be reduced and controlled at a cost of small additional processing. The simulations are carried out for in-packet forwarding. In this framework, the Bloom filter is used as a compact link/route identifier and it is placed in the packet header to encode the route. At each node, the Bloom filter is queried for membership in order to make forwarding decisions. A false positive in the forwarding decision is translated into packets forwarded along an unintended outgoing link. By using the optihash, false positives can be reduced. The optimization processing is carried out in an entity termed the Topology Manger which is part of the control plane of the multicast forwarding fabric. This processing is only carried out on a per-session basis, not for every packet. The aim of this paper is to present the optihash and evaluate its false positive performances via simulations in order to measure the influence of different parameters on the false positive rate. The false positive rate for the optihash is then compared with the false positive probability of the classic Bloom filter.

Aluminium and the human breast

The human population is exposed to aluminium (Al) from diet, antacids and vaccine adjuvants, but frequent application of Al-based salts to the underarm as antiperspirant adds a high additional exposure directly to the local area of the human breast. Coincidentally the upper outer quadrant of the breast is where there is also a disproportionately high incidence of breast cysts and breast cancer. Al has been measured in human breast tissues/fluids at higher levels than in blood, and experimental evidence suggests that at physiologically relevant concentrations, Al can adversely impact on human breast epithelial cell biology. Gross cystic breast disease is the most common benign disorder of the breast and evidence is presented that Al may be a causative factor in formation of breast cysts. Evidence is also reviewed that Al can enable the development of multiple hallmarks associated with cancer in breast cells, in particular that it can cause genomic instability and inappropriate proliferation in human breast epithelial cells, and can increase migration and invasion of human breast cancer cells. In addition, Al is a metalloestrogen and oestrogen is a risk factor for breast cancer known to influence multiple hallmarks. The microenvironment is established as another determinant of breast cancer development and Al has been shown to cause adverse alterations to the breast microenvironment. If current useage patterns of Al-based antiperspirant salts contribute to causation of breast cysts and breast cancer, then reduction in exposure would offer a strategy for prevention, and regulatory review is now justified.