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

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

Kondo regime in triangular arrangements of quantum dots: Molecular orbitals, interference and contact effects

Transport properties of an interacting triple quantum dot system coupled to three leads in a triangular geometry has been studied in the Kondo regime. Applying mean-field finite-U slave boson and embedded cluster approximations to the calculation of transport properties unveils a set of rich features associated to the high symmetry of this system. Results using both calculation techniques yield excellent overall agreement and provide additional insights into the physical behavior of this interesting geometry. In the case when just two current leads are connected to the three-dot system, interference effects between degenerate molecular orbitals are found to strongly affect the overall conductance. An S=1 Kondo effect is also shown to appear for the perfect equilateral triangle symmetry. The introduction of a third current lead results in an `amplitude leakage' phenomenon, akin to that appearing in beam splitters, which alters the interference effects and the overall conductance through the system.Comment: 14 pages, 9 figures, submitted to PR

Improving student support in professional placement learning: findings from the South west peninsula pilot of a new english national placement quality assurance and enhancement process.

English stakeholder collaboration has resulted in a new quality assurance process for non-medical health and social care placement providers and higher education institutions. This study aimed to discover the impact on student support that taking part in a pilot had on participating placement areas. Using a questionnaire survey with longitudinal follow-up one year later, we found that placement staff valued the opportunity to review and improve student support practices. This was still in evidence a year later where the pilot was described as giving the opportunity to provide evidence of aspects of student support practice; communicating and changing or developing aspects of that practice. Benefits accrued from interdisciplinary working in sharing and collaborating with other professions and organisations. Such activity could enhance clinical support staff activities and facilitate strategic partnerships between placement providers and higher education institutions

Crystallization of opals from polydisperse nanoparticles

We report the reversible formation of crystals of nanoparticles (opals) from solutions of polydisperse gold nanocrystals. The structures are identified by transmission electron microscopy, and are characterized by hexagonal domains of large particles at the center, surrounded radially by successively smaller particles. Simulated annealing Monte Carlo calculations are used to demonstrate that these configurations correspond to minimization of the mesoscopic van der Waals energy of polydisperse particles, and the driving force for ordering is the size dependence of dispersional attractions

C-terminal Truncations of the Yeast Nucleoporin Nup145p Produce a Rapid Temperature-conditional mRNA Export Defect and Alterations to Nuclear Structure.

A screen for temperature-sensitive mutants of Saccharomyces cerevisiae defective in nucleocytoplasmic trafficking of poly(A)+ RNA has identified an allele of the NUP145 gene, which encodes an essential nucleoporin. NUP145 was previously identified by using a genetic synthetic lethal screen (E. Fabre, W. C. Boelens, C. Wimmer, I. W. Mattaj, and E. C. Hurt, Cell 78:275-289, 1994) and by using a monoclonal antibody which recognizes the GLFG family of vertebrate and yeast nucleoporins (S. R. Wente and G. Blobel, J. Cell Biol. 125:955-969, 1994). Cells carrying the new allele, nup145-10, grew at 23 and 30 degrees C but were unable to grow at 37 degrees C. Many cells displayed a modest accumulation of poly(A)+ RNA under permissive growth conditions, and all cells showed dramatic and rapid nuclear accumulation of poly(A)+ RNA following a shift to 37 degrees C. The mutant allele contains a nonsense codon which truncates the 1,317-amino-acid protein to 698 amino acids. This prompted us to examine the role of the carboxyl half of Nup145p. Several additional alleles that encode C-terminally truncated proteins or proteins containing internal deletions of portions of the carboxyl half of Nup145p were constructed. Analysis of these mutants indicates that some sequences between amino acids 698 and 1095 are essential for RNA export and for growth at 37 degrees C. In these strains, nuclear accumulation of poly(A)+ RNA and fragmentation of the nucleolus occurred rapidly following a shift to 37 degrees C. Constitutive defects in nuclear pore complex distribution and nuclear structure were also seen in these strains. Although cells lacking Nup145p grew extremely slowly at 23 degrees C and did not grow at 30 degrees C, efficient growth at 23 or 30 degrees C occurred as long as cells produced either the amino 58% or the carboxyl 53% of Nup145p. Strains carrying alleles of NUP145 lacking up to 200 amino acids from the carboxy terminus were viable at 37 degrees C but displayed nucleolar fragmentation and some nuclear accumulation of poly(A)+ RNA following a shift to 37 degrees C. Surprisingly, these strains grew efficiently at 37 degrees C in spite of a reduction in the level of synthesis of rRNAs to approximately 25% of the wild-type level

Environmental influences predominate in remission from alcohol use disorder in young adult twins

Background. Familial influences on remission from alcohol use disorder (AUD) have been studied using family history of AUD rather than family history of remission. The current study used a remission phenotype in a twin sample to examine the relative contributions of genetic and environmental influences to remission

Nanostratification of optical excitation in self-interacting 1D arrays

The major assumption of the Lorentz-Lorenz theory about uniformity of local fields and atomic polarization in dense material does not hold in finite groups of atoms, as we reported earlier [A. E. Kaplan and S. N. Volkov, Phys. Rev. Lett., v. 101, 133902 (2008)]. The uniformity is broken at sub-wavelength scale, where the system may exhibit strong stratification of local field and dipole polarization, with the strata period being much shorter than the incident wavelength. In this paper, we further develop and advance that theory for the most fundamental case of one-dimensional arrays, and study nanoscale excitation of so called "locsitons" and their standing waves (strata) that result in size-related resonances and related large field enhancement in finite arrays of atoms. The locsitons may have a whole spectrum of spatial frequencies, ranging from long waves, to an extent reminiscent of ferromagnetic domains, -- to super-short waves, with neighboring atoms alternating their polarizations, which are reminiscent of antiferromagnetic spin patterns. Of great interest is the new kind of "hybrid" modes of excitation, greatly departing from any magnetic analogies. We also study differences between Ising-like near-neighbor approximation and the case where each atom interacts with all other atoms in the array. We find an infinite number of "exponential eigenmodes" in the lossless system in the latter case. At certain "magic" numbers of atoms in the array, the system may exhibit self-induced (but linear in the field) cancellation of resonant local-field suppression. We also studied nonlinear modes of locsitons and found optical bistability and hysteresis in an infinite array for the simplest modes.Comment: 39 pages, 5 figures; v2: Added the Conclusions section, corrected a typo in Eq. (5.3), corrected minor stylistic and grammatical imperfection