The Queue-Number of Posets of Bounded Width or Height

Heath and Pemmaraju conjectured that the queue-number of a poset is bounded by its width and if the poset is planar then also by its height. We show that there are planar posets whose queue-number is larger than their height, refuting the second conjecture. On the other hand, we show that any poset of width $2$ has queue-number at most $2$, thus confirming the first conjecture in the first non-trivial case. Moreover, we improve the previously best known bounds and show that planar posets of width $w$ have queue-number at most $3w-2$ while any planar poset with $0$ and $1$ has queue-number at most its width.Comment: 14 pages, 10 figures, Appears in the Proceedings of the 26th International Symposium on Graph Drawing and Network Visualization (GD 2018

Upward Three-Dimensional Grid Drawings of Graphs

A \emph{three-dimensional grid drawing} of a graph is a placement of the vertices at distinct points with integer coordinates, such that the straight line segments representing the edges do not cross. Our aim is to produce three-dimensional grid drawings with small bounding box volume. We prove that every $n$-vertex graph with bounded degeneracy has a three-dimensional grid drawing with $O(n^{3/2})$ volume. This is the broadest class of graphs admiting such drawings. A three-dimensional grid drawing of a directed graph is \emph{upward} if every arc points up in the z-direction. We prove that every directed acyclic graph has an upward three-dimensional grid drawing with $(n^3)$ volume, which is tight for the complete dag. The previous best upper bound was $O(n^4)$. Our main result is that every $c$-colourable directed acyclic graph ($c$ constant) has an upward three-dimensional grid drawing with $O(n^2)$ volume. This result matches the bound in the undirected case, and improves the best known bound from $O(n^3)$ for many classes of directed acyclic graphs, including planar, series parallel, and outerplanar

Mixed Linear Layouts of Planar Graphs

A $k$-stack (respectively, $k$-queue) layout of a graph consists of a total order of the vertices, and a partition of the edges into $k$ sets of non-crossing (non-nested) edges with respect to the vertex ordering. In 1992, Heath and Rosenberg conjectured that every planar graph admits a mixed $1$-stack $1$-queue layout in which every edge is assigned to a stack or to a queue that use a common vertex ordering. We disprove this conjecture by providing a planar graph that does not have such a mixed layout. In addition, we study mixed layouts of graph subdivisions, and show that every planar graph has a mixed subdivision with one division vertex per edge.Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

Ethnic penalties and hiring discrimination: Comparing results from observational studies with field experiments in the UK.

Ethnic minorities fare less well on average in the labour market than their white British counterparts. Experimental research shows that employers discriminate against ethnic minority applicants while hiring, but it is impossible to say from these studies how much of minorities’ overall disadvantage – which reflects compositional differences and search behaviour as well as hiring – is due to discrimination. This paper connects results from two UK-based field experiments with ethnic penalties estimated from comparable samples of the UK Labour Force Survey and Understanding Society to show the relation between hiring discrimination and labour market penalties, for several ethnic minority groups. Higher hiring discrimination is indeed associated with worse ethnic employment penalties, but similarly discriminated against groups do not necessarily face the same ethnic penalties. We provide a discussion of possible reasons for this variation. Our research points to socio-economic resources and supply-side differences among ethnic groups as plausible explanations

Ordered Level Planarity, Geodesic Planarity and Bi-Monotonicity

We introduce and study the problem Ordered Level Planarity which asks for a planar drawing of a graph such that vertices are placed at prescribed positions in the plane and such that every edge is realized as a y-monotone curve. This can be interpreted as a variant of Level Planarity in which the vertices on each level appear in a prescribed total order. We establish a complexity dichotomy with respect to both the maximum degree and the level-width, that is, the maximum number of vertices that share a level. Our study of Ordered Level Planarity is motivated by connections to several other graph drawing problems. Geodesic Planarity asks for a planar drawing of a graph such that vertices are placed at prescribed positions in the plane and such that every edge is realized as a polygonal path composed of line segments with two adjacent directions from a given set $S$ of directions symmetric with respect to the origin. Our results on Ordered Level Planarity imply $NP$-hardness for any $S$ with $|S|\ge 4$ even if the given graph is a matching. Katz, Krug, Rutter and Wolff claimed that for matchings Manhattan Geodesic Planarity, the case where $S$ contains precisely the horizontal and vertical directions, can be solved in polynomial time [GD'09]. Our results imply that this is incorrect unless $P=NP$. Our reduction extends to settle the complexity of the Bi-Monotonicity problem, which was proposed by Fulek, Pelsmajer, Schaefer and \v{S}tefankovi\v{c}. Ordered Level Planarity turns out to be a special case of T-Level Planarity, Clustered Level Planarity and Constrained Level Planarity. Thus, our results strengthen previous hardness results. In particular, our reduction to Clustered Level Planarity generates instances with only two non-trivial clusters. This answers a question posed by Angelini, Da Lozzo, Di Battista, Frati and Roselli.Comment: Appears in the Proceedings of the 25th International Symposium on Graph Drawing and Network Visualization (GD 2017

Epoxide tannage : a way forward

An understanding of both the reactive functions of epoxide resins and collagen, suggests that some epoxides could be effectively used in organic tannage systems. As such epoxides may be regarded as alternatives to aldehydic tanning systems, having lower toxicity combined with specific polymerization ability. The commercial and technical potential of epoxides as tanning agents are assessed in this review paper. To this end, an introduction to epoxide chemistry is provided based on the tanning chemist’s viewpoint. The literature survey describes epoxide-protein/collagen addition reaction mechanisms and their kinetics, which in turn are discussed with respect to the potential for future work, where these resins will be utilised in novel tanning technology. The potential risks associated with epoxides and modifications to conventional techniques of tanning, are also discussed

The optimization of epoxide-based tannage systems: an initial study

Liquid epoxide resins have an obvious potential as collagen crosslinkers, in particular as alternatives to the aldehydic-types used. In the work reported here, some conditions for the effective use of epoxides in tanning systems have been studied and identified based on hide powder trials. Few commercial aromatic epoxides are found to be water-soluble, and also have relatively low reaction rates, proving another disadvantage. In a series of screening tests, it has been found that an epoxide with aromatic groups in its backbone, used to treat collagen, produces higher hydrothermal stability than that treated with aliphatic epoxide. However, of the commercial aliphatic epoxide resins examined in this research, the water-soluble, tetra-functional pentaerythritol polyglycidyl ether, (e.g. Denacol EX 411), has been shown to be suitable for the leather tannage applications. Different types of waterborne epoxide resins, including emulsion and emulsifiable resins based on BDEGA (bisphenol A diglycidyl ether), have been examined but gave disappointing results. It is thought that difficulties here lie in trying to achieve good penetration into the collagen’s fibrous structure, of the particles that make up such emulsions. Late stage tannage, giving a leather product with high shrinkage temperature (Ts = 85ºC) has been achieved; here the system required catalyst to produce acceptable conversion within 3 hr at 50ºC. The important factors influencing the effectiveness of a particular tannage, are discussed

Hsp70 and Hsp40 inhibit an inter-domain interaction necessary for transcriptional activity in the androgen receptor.

Molecular chaperones such as Hsp40 and Hsp70 hold the androgen receptor (AR) in an inactive conformation. They are released in the presence of androgens, enabling transactivation and causing the receptor to become aggregation-prone. Here we show that these molecular chaperones recognize a region of the AR N-terminal domain (NTD), including a FQNLF motif, that interacts with the AR ligand-binding domain (LBD) upon activation. This suggests that competition between molecular chaperones and the LBD for the FQNLF motif regulates AR activation. We also show that, while the free NTD oligomerizes, binding to Hsp70 increases its solubility. Stabilizing the NTD-Hsp70 interaction with small molecules reduces AR aggregation and promotes its degradation in cellular and mouse models of the neuromuscular disorder spinal bulbar muscular atrophy. These results help resolve the mechanisms by which molecular chaperones regulate the balance between AR aggregation, activation and quality control