We show that r pseudo-random bits can be obtained by concatenating t blocks of r/t pseudo-random bits, where the blocks are generated in parallel. This can be considered as a parallel version of [a] recycling random bits by doing a random walk on an expander. The proof is based on the fact that t simultaneous independent random walks on an expander graph is equivalent to a random walk on a much...

Expander graphs are known to facilitate effective routing and most real-world networks have expansion properties. At the other extreme, it has been shown that in some special graphs, removing certain edges can lead to more efficient routing. This phenomenon is known as Braess’s paradox and is usually regarded as a rare event. In contrast to what one might expect, we show that Braess’s paradox i...

We compute the mixing rate of a non-backtracking random walk on a regular expander. Using some properties of Chebyshev polynomials of the second kind, we show that this rate may be up to twice as fast as the mixing rate of the simple random walk. The closer the expander is to a Ramanujan graph, the higher the ratio between the above two mixing rates is. As an application, we show that if G is a...

Informally, an expander is an undirected graph that has relatively sparse density, but whose vertices are nevertheless highly connected. Consequently, expanders have the property that any small subset of the vertices has a large set of neighbors outside of the set. This simple graph property has led to highly useful results in a number of branches of computer science. In addition, the study of ...

Primary skin closure after surgery for club foot in children can be difficult especially in revision operations. Between 1990 and 1996 a soft-tissue expander was implanted in 13 feet before such procedures. Two were primary operations and 11 were revisions. A standard technique was used for implantation of the expander. Skin augmentation was successful in 11 cases. There was failure of one expa...

We initiate the study of approximating the largest induced expander in a given graph G. Given a ∆-regular graph G with n vertices, the goal is to find the set with the largest induced expansion of size at least δ ·n. We design a bi-criteria approximation algorithm for this problem; if the optimum has induced spectral expansion λ our algorithm returns a λ log δ exp(∆/λ) -(spectral) expander of s...

RME was invented by Emerson Angell in 1860.1Angell EH. Treatment of irregularity the permanent or adult teeth.Dental Cosmos. 1860; 1 (599-600): 540-544Google Scholar His case report published Dental Cosmos, first national journal for dental profession. Angell's patient a 14-year-old girl fitted with transpalatal appliance that featured two counter-rotating screws. After weeks turning screws on ...