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

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

Modeling transport through single-molecule junctions

Non-equilibrium Green's functions (NEGF) formalism combined with extended Huckel (EHT) and charging model are used to study electrical conduction through single-molecule junctions. Analyzed molecular complex is composed of asymmetric 1,4-Bis((2'-para-mercaptophenyl)-ethinyl)-2-acetyl-amino-5-nitro-benzene molecule symmetrically coupled to two gold electrodes [Reichert et al., Phys. Rev. Lett. Vol.88 (2002), pp. 176804]. Owing to this model, the accurate values of the current flowing through such junction can be obtained by utilizing basic fundamentals and coherently deriving model parameters. Furthermore, the influence of the charging effect on the transport characteristics is emphasized. In particular, charging-induced reduction of conductance gap, charging-induced rectification effect and charging-generated negative value of the second derivative of the current with respect to voltage are observed and examined for molecular complex.Comment: 8 pages, 3 figure

Current Profiles of Molecular Nanowires; DFT Green Function Representation

The Liouville-space Green function formalism is used to compute the current density profile across a single molecule attached to electrodes. Time ordering is maintained in real, physical, time, avoiding the use of artificial time loops and backward propagations. Closed expressions for molecular currents, which only require DFT calculations for the isolated molecule, are derived to fourth order in the molecule/electrode coupling.Comment: 21 page

Promotion of access to essential medicines for Non-Communicable Diseases: Practical implications of the UN Political Declaration

Access to medicines and vaccines to prevent and treat non-communicable diseases (NCDs) is unacceptably low worldwide. In the 2011 UN political declaration on the prevention and control of NCDs, heads of government made several commitments related to access to essential medicines, technologies, and vaccines for such diseases. 30 years of experience with policies for essential medicines and 10 years of scaling up of HIV treatment have provided the knowledge needed to address barriers to long-term effective treatment and prevention of NCDs. More medicines can be acquired within existing budgets with efficient selection, procurement, and use of generic medicines. Furthermore, low-income and middle-income countries need to increase mobilisation of domestic resources to cater for the many patients with NCDs who do not have access to treatment. Existing initiatives for HIV treatment offer useful lessons that can enhance access to pharmaceutical management of NCDs and improve adherence to long-term treatment of chronic illness; policy makers should also address unacceptable inequities in access to controlled opioid analgesics. In addition to off-patent medicines, governments can promote access to new and future on-patent medicinal products through coherent and equitable health and trade policies, particularly those for intellectual property. Frequent conflicts of interest need to be identified and managed, and indicators and targets for access to NCD medicines should be used to monitor progress. Only with these approaches can a difference be made to the lives of hundreds of millions of current and future patients with NCDs

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

Similarities in drinking behavior of twin's friends: moderation of heritability of alcohol use

Previous research has indicated that friends' drinking may influence alcohol use in adolescents and young adults. We explored whether similarities in the drinking behavior of friends of twins influence the genetic architecture of alcohol use in adolescence and young adulthood. Survey data from The Netherlands Twin Register were available for 1,526 twin pairs aged 16-25 years. We categorized the twin pairs as concordant (both report similar alcohol use in their friends) or discordant for the alcohol use of their friends. Genetic moderator models were tested by carrying out multi-group analyzes in Mplus. Findings showed a significant moderation effect. Genetic factors were more and common environment less important in the explanation of variation in alcohol use in twins discordant for alcohol use of friends than in twins concordant for alcohol use of friend

Apraxia and motor dysfunction in corticobasal syndrome

Background: Corticobasal syndrome (CBS) is characterized by multifaceted motor system dysfunction and cognitive disturbance; distinctive clinical features include limb apraxia and visuospatial dysfunction. Transcranial magnetic stimulation (TMS) has been used to study motor system dysfunction in CBS, but the relationship of TMS parameters to clinical features has not been studied. The present study explored several hypotheses; firstly, that limb apraxia may be partly due to visuospatial impairment in CBS. Secondly, that motor system dysfunction can be demonstrated in CBS, using threshold-tracking TMS, and is linked to limb apraxia. Finally, that atrophy of the primary motor cortex, studied using voxel-based morphometry analysis (VBM), is associated with motor system dysfunction and limb apraxia in CBS.   Methods: Imitation of meaningful and meaningless hand gestures was graded to assess limb apraxia, while cognitive performance was assessed using the Addenbrooke's Cognitive Examination - Revised (ACE-R), with particular emphasis placed on the visuospatial subtask. Patients underwent TMS, to assess cortical function, and VBM.   Results: In total, 17 patients with CBS (7 male, 10 female; mean age 64.4+/2 6.6 years) were studied and compared to 17 matched control subjects. Of the CBS patients, 23.5% had a relatively inexcitable motor cortex, with evidence of cortical dysfunction in the remaining 76.5% patients. Reduced resting motor threshold, and visuospatial performance, correlated with limb apraxia. Patients with a resting motor threshold <50% performed significantly worse on the visuospatial sub-task of the ACE-R than other CBS patients. Cortical function correlated with atrophy of the primary and pre-motor cortices, and the thalamus, while apraxia correlated with atrophy of the pre-motor and parietal cortices.   Conclusions: Cortical dysfunction appears to underlie the core clinical features of CBS, and is associated with atrophy of the primary motor and pre-motor cortices, as well as the thalamus, while apraxia correlates with pre-motor and parietal atrophy