We study the initial ideal of binomial edge ideal in degree 2 ([in<(JG)]2), associated to a graph G. We computed dimension, depth, Castelnuovo-Mumford regularity, Hilbert function and Betti numbers of [in<(JG)]2 for some classes of graphs. AMS Mathematics Subject Classification (2010): 05E40, 16E30

The twisted plywood architecture, known as the Bouligand structure, is a ubiquitous biological and synthetic fibrous composite structure, analogous to that of cholesteric liquid crystals. Twisted plywoods can show ideal or non-ideal structures and are formed via equilibrium or non-equilibrium liquid crystal self-assembly processes. A key to the structure characterisation of plywood films is the...

We introduce the notion of a weak ideal compression function, which is vulnerable to strong forms of attack, but is otherwise random. We show that such weak ideal compression functions can be used to create secure hash functions, thereby giving a design that can be used to eliminate attacks caused by undesirable properties of compression functions. We prove that the construction we give, which ...