Cubic Augmentation of Planar Graphs

In this paper we study the problem of augmenting a planar graph such that it becomes 3-regular and remains planar. We show that it is NP-hard to decide whether such an augmentation exists. On the other hand, we give an efficient algorithm for the variant of the problem where the input graph has a fixed planar (topological) embedding that has to be preserved by the augmentation. We further generalize this algorithm to test efficiently whether a 3-regular planar augmentation exists that additionally makes the input graph connected or biconnected. If the input graph should become even triconnected, we show that the existence of a 3-regular planar augmentation is again NP-hard to decide.Comment: accepted at ISAAC 201

Devil's staircase in kinetically limited growth of Ising model

The devil's staircase is a term used to describe surface or an equilibrium phase diagram in which various ordered facets or phases are infinitely closely packed as a function of some model parameter. A classic example is a 1-D Ising model [bak] wherein long-range and short range forces compete, and the periodicity of the gaps between minority species covers all rational values. In many physical cases, crystal growth proceeds by adding surface layers which have the lowest energy, but are then frozen in place. The emerging layered structure is not the thermodynamic ground state, but is uniquely defined by the growth kinetics. It is shown that for such a system, the grown structure tends to the equilibrium ground state via a devil's staircase traversing an infinity of intermediate phases. It would be extremely difficult to deduce the simple growth law based on measurement made on such an grown structure.Comment: 4 pages, PRL submitte

Changes in the expression of the type 2 diabetes-associated gene VPS13C in the β cell are associated with glucose intolerance in humans and mice

Single nucleotide polymorphisms (SNPs) close to the VPS13C, C2CD4A and C2CD4B genes on chromosome 15q are associated with impaired fasting glucose and increased risk of type 2 diabetes. eQTL analysis revealed an association between possession of risk (C) alleles at a previously implicated causal SNP, rs7163757, and lowered VPS13C and C2CD4A levels in islets from female (n = 40, P < 0.041) but not from male subjects. Explored using promoter-reporter assays in β-cells and other cell lines, the risk variant at rs7163757 lowered enhancer activity. Mice deleted for Vps13c selectively in the β-cell were generated by crossing animals bearing a floxed allele at exon 1 to mice expressing Cre recombinase under Ins1 promoter control (Ins1Cre). Whereas Vps13cfl/fl:Ins1Cre (βVps13cKO) mice displayed normal weight gain compared with control littermates, deletion of Vps13c had little effect on glucose tolerance. Pancreatic histology revealed no significant change in β-cell mass in KO mice vs. controls, and glucose-stimulated insulin secretion from isolated islets was not altered in vitro between control and βVps13cKO mice. However, a tendency was observed in female null mice for lower insulin levels and β-cell function (HOMA-B) in vivo. Furthermore, glucose-stimulated increases in intracellular free Ca2+ were significantly increased in islets from female KO mice, suggesting impaired Ca2+ sensitivity of the secretory machinery. The present data thus provide evidence for a limited role for changes in VPS13C expression in conferring altered disease risk at this locus, particularly in females, and suggest that C2CD4A may also be involved

Fourier Transform Scanning Tunneling Spectroscopy: the possibility to obtain constant energy maps and the band dispersion using a local measurement

We present here an overview of the Fourier Transform Scanning Tunneling spectroscopy technique (FT-STS). This technique allows one to probe the electronic properties of a two-dimensional system by analyzing the standing waves formed in the vicinity of defects. We review both the experimental and theoretical aspects of this approach, basing our analysis on some of our previous results, as well as on other results described in the literature. We explain how the topology of the constant energy maps can be deduced from the FT of dI/dV map images which exhibit standing waves patterns. We show that not only the position of the features observed in the FT maps, but also their shape can be explained using different theoretical models of different levels of approximation. Thus, starting with the classical and well known expression of the Lindhard susceptibility which describes the screening of electron in a free electron gas, we show that from the momentum dependence of the susceptibility we can deduce the topology of the constant energy maps in a joint density of states approximation (JDOS). We describe how some of the specific features predicted by the JDOS are (or are not) observed experimentally in the FT maps. The role of the phase factors which are neglected in the rough JDOS approximation is described using the stationary phase conditions. We present also the technique of the T-matrix approximation, which takes into account accurately these phase factors. This technique has been successfully applied to normal metals, as well as to systems with more complicated constant energy contours. We present results recently obtained on graphene systems which demonstrate the power of this technique, and the usefulness of local measurements for determining the band structure, the map of the Fermi energy and the constant-energy maps.Comment: 33 pages, 15 figures; invited review article, to appear in Journal of Physics D: Applied Physic

Water Availability and Deformation Processes in Smectite-Rich Gouges During Seismic Slip

Smectite clays occur in subduction zone fault cores at shallow depth (approximately 1 km; e.g., Japan Trench) and landslide d\ue9collements (e.g., Vajont, Italy, 1963). The availability of pore fluids affects the likelihood that seismic slip propagates from deeper to shallow fault depths or that a landslide accelerates to its final collapse. To investigate the deformation processes active during seismic faulting we performed friction experiments with a rotary machine on 2-mm-thick smectite-rich gouge layers (70/30 wt % Ca-montmorillonite/opal) sheared at 5-MPa normal stress, at slip rates of 0.001, 0.01, 0.1, and 1.3 m/s, and total displacement of 3 m. Experiments were performed on predried gouges under vacuum, under room humidity and under partly saturated conditions. The fault shear strength measured in the experiments was included in a one-dimensional numerical model incorporating frictional heating, thermal, and thermochemical pressurization. Quantitative X-ray powder diffraction and scanning electron microscopy investigations were performed on pristine and deformed smectite-rich gouges. Under dry conditions, cataclasis and amorphization dominated at slip rates of 0.001\u20130.1 m/s, whereas grain size sensitive flow and, under vacuum, frictional melting occurred at fast slip rates (1.3 m/s). Under partly saturated conditions, frictional slip in a smectite foliation occurred in combination with pressurization of water by shear-enhanced compaction and, for V = 0.01\u20131.3 m/s, with thermal pressurization. Pseudotachylytes, the only reliable microstructural markers for seismic slip, formed only with large frictional power (>2 MW/m2), which could be achieved at shallow depth with high slip rates, or, at depth, with high shear stress in dehydrated smectites

A new polymorphic material? Structural degeneracy of ZrMn_2

Based on density functional calculations, we propose that ZrMn_2 is a polymorphic material. We predict that at low temperatures the cubic C15, and the hexagonal C14 and C36 structures of the Laves phase compound ZrMn_2 are nearly equally stable within 0.3 kJmol^{-1} or 30 K. This degeneracy occurs when the Mn atoms magnetize spontaneously in a ferromagnetic arrangement forming the states of lowest energy. From the temperature dependent free energies at T approx 160K we predict a transition from the most stable C15 to the C14 structure, which is the experimentally observed structure at elevated temperatures.Comment: 4 pages, 3 figure

How should we measure psychological resilience in sport performers?

Psychological resilience is important in sport because athletes must constantly withstand a wide range of pressures to attain and sustain high performance. To advance psychologists’ understanding of this area, there exists an urgent need to develop a sport-specific measure of resilience. The purpose of this paper is to review psychometric issues in resilience research and to discuss the implications for sport psychology. Drawing on the wider general psychology literature to inform the discussion, the narrative is divided into three main sections relating to resilience and its assessment: adversity, positive adaptation, and protective factors. The first section reviews the different ways that adversity has been measured and considers the potential problems of using items with varying degrees of controllability and risk. The second section discusses the different approaches to assessing positive adaptation and examines the issue of circularity pervasive in resilience research. The final section explores the various issues related to the assessment of protective factors drawing directly from current measures of resilience in other psychology sub-disciplines. The commentary concludes with key recommendations for sport psychology researchers seeking to develop a measure of psychological resilience in athletes

Cultural basis of social ‘deficits’ in autism spectrum disorders

There is very little research that specifically looks at how autism spectrum disorders are perceived in various communities. This qualitative research was conducted with parents who had children on the autistic spectrum belonging to four different ethnic communities (White British, Somali, West African and South Asian- 63 in total) and living in the UK. The study found that the importance that the parents give to various social skills varied on the basis of their cultural background and the gender of the parent. This is an important aspect to consider while providing support and services to individuals on the autism spectrum and their family members if the services have to be appropriate for their needs. This consideration would also enable the individuals on the autism spectrum to develop appropriate social skills required within their cultural groups. This is a preliminary study and further research on the topic is required