Random graph model with power-law distributed triangle subgraphs

Clustering is well-known to play a prominent role in the description and understanding of complex networks, and a large spectrum of tools and ideas have been introduced to this end. In particular, it has been recognized that the abundance of small subgraphs is important. Here, we study the arrangement of triangles in a model for scale-free random graphs and determine the asymptotic behavior of the clustering coefficient, the average number of triangles, as well as the number of triangles attached to the vertex of maximum degree. We prove that triangles are power-law distributed among vertices and characterized by both vertex and edge coagulation when the degree exponent satisfies $2<\beta<2.5$; furthermore, a finite density of triangles appears as $\beta=2+1/3$.Comment: 4 pages, 2 figure; v2: major conceptual change

Doping-Dependent Raman Resonance in the Model High-Temperature Superconductor HgBa2CuO4+d

We study the model high-temperature superconductor HgBa2CuO4+d with electronic Raman scattering and optical ellipsometry over a wide doping range. The resonant Raman condition which enhances the scattering cross section of "two-magnon" excitations is found to change strongly with doping, and it corresponds to a rearrangement of inter-band optical transitions in the 1-3 eV range seen by ellipsometry. This unexpected change of the resonance condition allows us to reconcile the apparent discrepancy between Raman and x-ray detection of magnetic fluctuations in superconducting cuprates. Intriguingly, the strongest variation occurs across the doping level where the antinodal superconducting gap reaches its maximum.Comment: 4 pages, 4 figures, contact authors for Supplemental Materia

Connection between charge-density-wave order and charge transport in the cuprate superconductors

Charge-density-wave (CDW) correlations within the quintessential CuO$_2$ planes have been argued to either cause [1] or compete with [2] the superconductivity in the cuprates, and they might furthermore drive the Fermi-surface reconstruction in high magnetic fields implied by quantum oscillation (QO) experiments for YBa$_2$Cu$_3$O$_{6+{\delta}}$ (YBCO) [3] and HgBa$_2$CuO$_{4+{\delta}}$ (Hg1201) [4]. Consequently, the observation of bulk CDW order in YBCO was a significant development [5,6,7]. Hg1201 features particularly high structural symmetry and recently has been demonstrated to exhibit Fermi-liquid charge transport in the relevant temperature-doping range of the phase diagram, whereas for YBCO and other cuprates this underlying property of the CuO$_2$ planes is partially or fully masked [8-10]. It therefore is imperative to establish if the pristine transport behavior of Hg1201 is compatible with CDW order. Here we investigate Hg1201 ($T_c$ = 72 K) via bulk Cu L-edge resonant X-ray scattering. We indeed observe CDW correlations in the absence of a magnetic field, although the correlations and competition with superconductivity are weaker than in YBCO. Interestingly, at the measured hole-doping level, both the short-range CDW and Fermi-liquid transport appear below the same temperature of about 200 K. Our result points to a unifying picture in which the CDW formation is preceded at the higher pseudogap temperature by $q$ = 0 magnetic order [11,12] and the build-up of significant dynamic antiferromagnetic correlations [13]. Furthermore, the smaller CDW modulation wave vector observed for Hg1201 is consistent with the larger electron pocket implied by both QO [4] and Hall-effect [14] measurements, which suggests that CDW correlations are indeed responsible for the low-temperature QO phenomenon

Universal quantum oscillations in the underdoped cuprate superconductors

The metallic state of the underdoped high-Tc cuprates has remained an enigma: How may seemingly disconnected Fermi surface segments, observed in zero magnetic field as a result of the opening of a partial gap (the pseudogap), possess conventional quasiparticle properties? How do the small Fermi-surface pockets evidenced by the observation of quantum oscillations (QO) emerge as superconductivity is suppressed in high magnetic fields? Such QO, discovered in underdoped YBa2Cu3O6.5 (Y123) and YBa2Cu4O8 (Y124), signify the existence of a conventional Fermi surface (FS). However, due to the complexity of the crystal structures of Y123 and Y124 (CuO2 double-layers, CuO chains, low structural symmetry), it has remained unclear if the QO are specific to this particular family of cuprates. Numerous theoretical proposals have been put forward to explain the route toward QO, including materials-specific scenarios involving CuO chains and scenarios involving the quintessential CuO2 planes. Here we report the observation of QO in underdoped HgBa2CuO4+{\delta} (Hg1201), a model cuprate superconductor with individual CuO2 layers, high tetragonal symmetry, and no CuO chains. This observation proves that QO are a universal property of the underdoped CuO2 planes, and it opens the door to quantitative future studies of the metallic state and of the Fermi-surface reconstruction phenomenon in this structurally simplest cuprate.Comment: 17 pages, 5 figure

Effect of fluoride toothpastes on enamel demineralization

BACKGROUND: It was the aim of this study to investigate the effect of four different toothpastes with differing fluoride compounds on enamel remineralization. METHODS: A 3 × 3 mm window on the enamel surface of 90 human premolars was demineralized in a hydroxyethylcellulose solution at pH 4.8. The teeth were divided into 6 groups and the lower half of the window was covered with varnish serving as control. The teeth were immersed in a toothpaste slurry containing: placebo tooth paste (group 1); remineralization solution (group 2); Elmex Anticaries (group 3); Elmex Sensitive (group 4); Blend-a-med Complete (group 5) and Colgate GRF (group 6). Ten teeth of each group were used for the determination of the F(- )content in the superficial enamel layer and acid solubility of enamel expressed in soluble phosphorus. Of 6 teeth of each group serial sections were cut and investigated with polarization light microscopy (PLM) and quantitative energy dispersive X-ray analysis (EDX). RESULTS: The PLM results showed an increased remineralization of the lesion body in the Elmex Anticaries, Elmex Sensitive and Colgate GRF group but not in the Blend-a-med group. A statistically significant higher Ca content was found in the Elmex Anticaries group. The fluoride content in the superficial enamel layer was significantly increased in both Elmex groups and the Blend-a-med group. Phosphorus solubility was significantly decreased in both Elmex groups and the Blend-a-med group. CONCLUSION: It can be concluded that amine fluoride compounds in toothpastes result in a clearly marked remineralization of caries like enamel lesions followed by sodium fluoride and sodium monofluorophosphate formulations

Socio-economic drivers of specialist anglers targeting the non-native European catfish (Silurus glanis) in the UK.

Information about the socioeconomic drivers of Silurus glanis anglers in the UK were collected using questionnaires from a cross section of mixed cyprinid fisheries to elucidate human dimensions in angling and non-native fisheries management. Respondents were predominantly male (95%), 30-40 years of age with £500 per annum. The proportion of time spent angling for S. glanis was significantly related to angler motivations; fish size, challenge in catch, tranquil natural surroundings, escape from daily stress and to be alone were considered important drivers of increased time spent angling. Overall, poor awareness of: the risks and adverse ecological impacts associated with introduced S. glanis, non-native fisheries legislation, problems in use of unlimited ground bait and high fish stocking rates in angling lakes were evident, possibly related to inadequate training and information provided by angling organisations to anglers, as many stated that they were insufficiently informed