On Upward Drawings of Trees on a Given Grid

Computing a minimum-area planar straight-line drawing of a graph is known to be NP-hard for planar graphs, even when restricted to outerplanar graphs. However, the complexity question is open for trees. Only a few hardness results are known for straight-line drawings of trees under various restrictions such as edge length or slope constraints. On the other hand, there exist polynomial-time algorithms for computing minimum-width (resp., minimum-height) upward drawings of trees, where the height (resp., width) is unbounded. In this paper we take a major step in understanding the complexity of the area minimization problem for strictly-upward drawings of trees, which is one of the most common styles for drawing rooted trees. We prove that given a rooted tree $T$ and a $W\times H$ grid, it is NP-hard to decide whether $T$ admits a strictly-upward (unordered) drawing in the given grid.Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

RELATIVIZING RELATIVIZED COMPUTATIONS

AbstractThis paper introduces a technique of relativizing already relativized computations and gives two interesting applications. The techniques developed here are simpler than the usual methods for constructing oracles that satisfy several requirements simultaneously. The first application shows that a result of Karp and Lipton (if sets in NP are decidable with polynomial-size circuits, then ΣP2 = ΠP2) cannot be strengthened in the presence of certain oracles. This means that relativizable proof techniques cannot strengthen the conclusion to, say, P=NP. Such a stronger conclusion would be desirable as it would establish the equivalence of polynomial-time programs and polynomial-size circuits for solving NP-complete problems and would extend the known equivalence of polynomial-time programs and programs that are allowed a single query to a polynomial-size table. The second application gives an oracle C for which PC ≠ (NPC ∩ coNPC) ≠ NPC and NPC ∩ coNPC has complete sets under polynomial-time many-one reductions. This complements a result of Sipser in which an oracle B is constructed for which NPB ∩ coNPB has no complete sets. These results suggest that current proof methods will not settle whether NP ∩ coNP has complete sets

Pubertal development and its influences on bone mineral density in Australian children and adolescents with cystic fibrosis

Background: Pubertal delay is thought to contribute to suboptimal peak bone mass acquisition in young people with cystic fibrosis (CF), leading to an increased fracture incidence. This study aims to compare pubertal development in young people with CF with that of a local healthy population and assess the influence it has on areal bone mineral density (aBMD)

A major advance of tropical Andean glaciers during the Antarctic cold reversal

International audienc

Identification of DNA-dependent protein kinase catalytic subunit (DNA-PKcs) as a novel target of bisphenol A.

Bisphenol A (BPA) forms the backbone of plastics and epoxy resins used to produce packaging for various foods and beverages. BPA is also an estrogenic disruptor, interacting with human estrogen receptors (ER) and other related nuclear receptors. Nevertheless, the effects of BPA on human health remain unclear. The present study identified DNA-dependent protein kinase catalytic subunit (DNA-PKcs) as a novel BPA-binding protein. DNA-PKcs, in association with the Ku heterodimer (Ku70/80), is a critical enzyme involved in the repair of DNA double-strand breaks. Low levels of DNA-PK activity are previously reported to be associated with an increased risk of certain types of cancer. Although the Kd for the interaction between BPA and a drug-binding mutant of DNA-PKcs was comparatively low (137 nM), high doses of BPA were required before cellular effects were observed (100-300 μM). The results of an in vitro kinase assay showed that BPA inhibited DNA-PK kinase activity in a concentration-dependent manner. In M059K cells, BPA inhibited the phosphorylation of DNA-PKcs at Ser2056 and H2AX at Ser139 in response to ionizing radiation (IR)-irradiation. BPA also disrupted DNA-PKcs binding to Ku70/80 and increased the radiosensitivity of M059K cells, but not M059J cells (which are DNA-PKcs-deficient). Taken together, these results provide new evidence of the effects of BPA on DNA repair in mammalian cells, which are mediated via inhibition of DNA-PK activity. This study may warrant the consideration of the possible carcinogenic effects of high doses of BPA, which are mediated through its action on DNA-PK