The main purposes of this paper are (1) To survey the area of coarse embeddability of metric spaces into Banach spaces, and, in particular, coarse embeddability of different Banach spaces into each other; (2) To present new results on the problems: (a) Whether coarse non-embeddability into l2 implies presence of expander-like structures? (b) To what extent l2 is the most difficult space to embe...

Let G V E be an r regular expander graph Certain algorithms for nding edge disjoint paths require the edges of G to be partitioned into E E E Ek so that the graphs Gi V Ei are each expanders In this paper we give a non constructive proof of a very good split plus an algorithm which improves on that given in Broder Frieze and Upfal Existence and construction of edge disjoint paths on expander gr...

I have three goals for this lecture. The first is to introduce one of the most important familes of graphs: expander graphs. They are the source of much combinatorial power, and the counterexample to numerous conjectures. We will become acquainted with these graphs by examining random walks on them. To facilitate the analysis of random walks, we will examine these graphs through their adjacency...

Tesla bladeless expanders are promising in energy harvesting and small-scale power generation applications due to their lower cost simplicity design. Although such exhibit very high rotor efficiency (analytical total static ~ 90%), it shows poor performance when coupled with a stator (experimental ~30%) losses present the stator-rotor interaction. This paper presents design experiment of novel,...

In this lecture, we shall look at Expander Codes, Tanner Codes which are a generalization of Expander Codes and Distance amplification codes. These codes visualize the code as a graph where the value of the ith bit of a codeword corresponds to, for example, the value associated with the ith vertex or the ith edge of the graph. The properties of the graph determine the properties such as distanc...