Convex Independence in Permutation Graphs

A set C of vertices of a graph is P_3-convex if every vertex outside C has at most one neighbor in C. The convex hull \sigma(A) of a set A is the smallest P_3-convex set that contains A. A set M is convexly independent if for every vertex x \in M, x \notin \sigma(M-x). We show that the maximal number of vertices that a convexly independent set in a permutation graph can have, can be computed in polynomial time

A Counterexample Regarding Labelled Well-Quasi-Ordering

Korpelainen, Lozin, and Razgon conjectured that a hereditary property of graphs which is well-quasi-ordered by the induced subgraph order and defined by only finitely many minimal forbidden induced subgraphs is labelled well-quasi-ordered, a notion stronger than that of n-well-quasi-order introduced by Pouzet in the 1970s. We present a counterexample to this conjecture. In fact, we exhibit a hereditary property of graphs which is well-quasi-ordered by the induced subgraph order and defined by finitely many minimal forbidden induced subgraphs yet is not 2-well-quasi-ordered. This counterexample is based on the widdershins spiral, which has received some study in the area of permutation patterns

New Approaches in the Differentiation of Human Embryonic Stem Cells and Induced Pluripotent Stem Cells toward Hepatocytes

Orthotropic liver transplantation is the only established treatment for end-stage liver diseases. Utilization of hepatocyte transplantation and bio-artificial liver devices as alternative therapeutic approaches requires an unlimited source of hepatocytes. Stem cells, especially embryonic stem cells, possessing the ability to produce functional hepatocytes for clinical applications and drug development, may provide the answer to this problem. New discoveries in the mechanisms of liver development and the emergence of induced pluripotent stem cells in 2006 have provided novel insights into hepatocyte differentiation and the use of stem cells for therapeutic applications. This review is aimed towards providing scientists and physicians with the latest advancements in this rapidly progressing field

Geometric Realization of Simplicial Complexes

We show that an abstract simplicial complex \Delta may be realized on a grid of \mathbb{R}^{d-1}, where d = dim P(\Delta) is the order dimension (Dushnik-Miller dimension) of the face poset of \Delta

Trade-Offs in Cryptographic Implementations of Temporal Access Control

Abstract. In recent years, we have seen the development of key assignment schemes that use cryptography to enforce time-based authorization policies. One of the most important aspects of these schemes is the balance between the time required to derive keys and the amount of storage required for the public information from which keys are derived. The derivation time and storage are dependent on the number of time periods used in the authorization policy. In this paper, we discuss novel schemes that achieve good trade-offs between these competing parameters and for which explicit bounds can be given in terms of the number of time periods.