Conformal triangles and zig-zag diagrams

The zig-zag product

The expander constructions based on algebraic methods can give expanders that are both explicit (i.e. we can quickly construct the graph, or even obtain neighborhood information without constructing the entire graph, and Ramanujan, meaning that the spectral gap is essentially as large as possible. It also follows from this spectral bound that the edge expansion of Ramanujan graphs is essentiall...

Zig-zag Path to Understanding

OUT understanding of the fundamental physical limits of information handling has developed along a very convoluted path. Most of the initially plausible physical conjectures have turned out to be wrong. A participant’s personal view of these events is not a disciplined contribution to the history of science. I do, however, last my own mistakes along with those of others.

Reverse mathematics and Isbell's zig-zag theorem

ZIG-ZAG PVD – A Nontraditional Approach

Communication has to be secure in order to be kept private. The latest developments in the field of digital communication have made secret communication possible. Image hiding is a method in which a secret image is hidden in a cover image thereby forming a hybrid or stego image. In this paper, data hiding is performed by taking difference value of three and two neighbouring pixels by adapting Z...

Expander Constructions ( Zig - Zag Expanders ) Lecturer : Cynthia

Construction 7.1 (Margulis [Mar]) Fix a positive integerM and let [M ] = {1, 2, . . . ,M}. Define the bipartite graph G = (V,E) as follows. Let V = [M ]2∪ [M ]2, where vertices in the first partite set are denoted (x, y)1 and vertices in the second partite set are denoted (x, y)2. From each vertex (x, y)1, put in edges to (x, y)2, (x, x+ y)2, (x, x+ y+1)2, (x+ y, y)2, and (x+ y+ 1, y)2, where a...