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

On graphs associated to sets of rankings

In this paper we analyze families of rankings by studying structural properties of graphs. Given a finite number of elements and a set of rankings of those elements, two elements compete when they exchange their relative positions in at least two rankings, and we can associate an undirected graph to a set of rankings by connecting elements that compete. We call this graph a competitivity graph. Competitivity graphs have already appeared in the literature as co-comparability graphs, f-graphs or intersection graphs associated to a concatenation of permutation diagrams. We introduce certain important sets of nodes in a competitivity graph. For example, nodes that compete among them form a competitivity set and nodes connected by chains of competitors form a set of eventual competitors. These sets are analyzed and a method to obtain sets of eventual competitors directly from a set of rankings is shown. © 2015 Elsevier B.V.This paper was partially supported by Spanish MICINN Funds and FEDER Funds MTM2009-13848, MTM2010-16153 and MTM2010-18674, and Junta de Andalucia Funds FQM-264. The authors would like to thank an anonymous referee for the valuable comments and remarks.Criado Herrero, R.; García, E.; Pedroche Sánchez, F.; Romance, M. (2016). On graphs associated to sets of rankings. Journal of Computational and Applied Mathematics. 291:497-508. doi:10.1016/j.cam.2015.03.009S49750829

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

Specific Knockdown of OCT4 in Human Embryonic Stem Cells by Inducible Short Hairpin RNA Interference

Manipulation of gene function in embryonic stem cells by either over expression or downregulation is critical for understanding their subsequent cell fate. We have developed a tetracycline-inducible short hairpin RNA interference (shRNAi) for human embryonic stem cells (hESCs) and demonstrated doxycycline dose-dependent knockdown of the transcription factor OCT4 and the cell surface antigen β2-microglobulin. The induced knockdown of OCT4 resulted in rapid differentiation of hESCs with a significant increase in transcription of genes associated with trophoblast and endoderm lineages, the extent of which was controlled by the degree of induction. Transgene toxicity, which may occur in conditional over-expression strategies with hESCs, was not observed with wild-type Tet repressor protein. The system allows efficient, reversible, and long-term downregulation of target genes in hESCs and enables the generation of stable transfectants for the knockdown of genes essential for cell survival and self-renewal, not necessarily possible by nonconditional shRNAi methods

Efficient and Directive Generation of Two Distinct Endoderm Lineages from Human ESCs and iPSCs by Differentiation Stage-Specific SOX17 Transduction

The establishment of methods for directive differentiation from human embryonic stem cells (ESCs) and induced pluripotent stem cells (iPSCs) is important for regenerative medicine. Although Sry-related HMG box 17 (SOX17) overexpression in ESCs leads to differentiation of either extraembryonic or definitive endoderm cells, respectively, the mechanism of these distinct results remains unknown. Therefore, we utilized a transient adenovirus vector-mediated overexpression system to mimic the SOX17 expression pattern of embryogenesis. The number of alpha-fetoprotein-positive extraembryonic endoderm (ExEn) cells was increased by transient SOX17 transduction in human ESC- and iPSC-derived primitive endoderm cells. In contrast, the number of hematopoietically expressed homeobox (HEX)-positive definitive endoderm (DE) cells, which correspond to the anterior DE in vivo, was increased by transient adenovirus vector-mediated SOX17 expression in human ESC- and iPSC-derived mesendoderm cells. Moreover, hepatocyte-like cells were efficiently generated by sequential transduction of SOX17 and HEX. Our findings show that a stage-specific transduction of SOX17 in the primitive endoderm or mesendoderm promotes directive ExEn or DE differentiation by SOX17 transduction, respectively

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