The Alon-Roichman theorem states that for every ε > 0 there is a constant c(ε), such that the Cayley graph of a finite group G with respect to c(ε) log |G| elements of G, chosen independently and uniformly at random, has expected second largest eigenvalue less than ε. In particular, such a graph is an expander with high probability. Landau and Russell, and independently Loh and Schulman, improv...

We show that the measure on markings of Zn, d ≥ 3, with elements of {0,1} given by i.i.d. fair coin flips on the range R of a random walk X run until time T and 0 otherwise becomes indistinguishable from the uniform measure on such markings at the threshold T = 1 2 Tcov(Z d n). As a consequence of our methods, we show that the total variation mixing time of the random walk on the lamplighter gr...

We give a simple proof of the Alon–Roichman theorem, which asserts that the Cayley graph obtained by selecting cε log |G| elements, independently and uniformly at random, from a finite group G has expected second eigenvalue no more than ε; here cε is a constant that depends only on ε. In particular, such a graph is an expander with constant probability. Our new proof has three advantages over t...

Expander codes count among the numerous applications of expander graphs. The term was first coined by Sipser and Spielman when they showed how expander graphs can be used to devise error-correcting codes with large blocklengths that can correct efficiently a constant fraction of errors. This approach has since proved to be a fertile avenue of research that provides insight both into modern iter...

BACKGROUND Achieving symmetry is a key goal in breast reconstruction. Anatomically shaped tabbed expanders are a new tool in the armamentarium of the breast reconstruction surgeon. Suture tabs allow for full control over the expander position and thus inframammary fold position, and, in theory, tabbed expanders mitigate many factors responsible for poor symmetry. The impact of a tabbed expander...

Comparative energy and exergy investigations are reported for a transcritical N2O refrigeration cycle with a throttling valve or with an expander when the gas cooler exit temperature varies from 30 to 55 ◦C and the evaporating temperature varies from −40 to 10 ◦C. The system performance is also compared with that of similar cycles using CO2. Results show that the N2O expander cycle exhibits a l...

For every 1 > δ > 0 there exists a c = c(δ) > 0 such that for every group G of order n, and for a set S of c(δ) log n random elements in the group, the expected value of the second largest eigenvalue of the normalized adjacency matrix of the Cayley graph X(G,S) is at most (1−δ). This implies that almost every such a graph is an ε(δ)-expander. For Abelian groups this is essentially tight, and ex...

In this paper, we propose and study a new semi-random model for graph partitioning problems. We believe that it captures many properties of real–world instances. The model is more flexible than the semi-random model of Feige and Kilian and planted random model of Bui, Chaudhuri, Leighton and Sipser. We develop a general framework for solving semi-random instances and apply it to several problem...

One of the aims of this paper is to solve an open problem of Lovász about relations between graph spectra and cut-distance. The paper starts with several inequalities between two versions of the cut-norm and the two largest singular values of arbitrary complex matrices, extending, in particular, the well-known graph-theoretical Expander Mixing Lemma and giving a hitherto unknown converse of it....