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

The rate of quasiparticle recombination probes the onset of coherence in cuprate superconductors

The condensation of an electron superfluid from a conventional metallic state at a critical temperature $T_c$ is described well by the BCS theory. In the underdoped copper-oxides, high-temperature superconductivity condenses instead from a nonconventional metallic "pseudogap" phase that exhibits a variety of non-Fermi liquid properties. Recently, it has become clear that a charge density wave (CDW) phase exists within the pseudogap regime, appearing at a temperature $T_{CDW}$ just above $T_c$. The near coincidence of $T_c$ and $T_{CDW}$, as well the coexistence and competition of CDW and superconducting order below $T_c$, suggests that they are intimately related. Here we show that the condensation of the superfluid from this unconventional precursor is reflected in deviations from the predictions of BSC theory regarding the recombination rate of quasiparticles. We report a detailed investigation of the quasiparticle (QP) recombination lifetime, $\tau_{qp}$, as a function of temperature and magnetic field in underdoped HgBa$_{2}$CuO$_{4+\delta}$ (Hg-1201) and YBa$_{2}$Cu$_{3}$O$_{6+x}$ (YBCO) single crystals by ultrafast time-resolved reflectivity. We find that $\tau_{qp}(T)$ exhibits a local maximum in a small temperature window near $T_c$ that is prominent in underdoped samples with coexisting charge order and vanishes with application of a small magnetic field. We explain this unusual, non-BCS behavior by positing that $T_c$ marks a transition from phase-fluctuating SC/CDW composite order above to a SC/CDW condensate below. Our results suggest that the superfluid in underdoped cuprates is a condensate of coherently-mixed particle-particle and particle-hole pairs

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

Transference of natural diversity from the apomictic germplasm of Paspalum notatum to a sexual synthetic population

Genetic improvement in apomictic forage species has been restricted because of the absence of genetic variability in sexual germplasm with the same ploidy level. Following a new breeding scheme, a sexual synthetic tetraploid population (SSTP) of Paspalum notatum has been generated. The objectives of this work were: (a) to evaluate the genetic variability in SSTP by means of molecular markers, morphologic and agronomic traits, and seed fertility and quality traits and (b) to assess the transference of genetic variability from the apomictic germplasm to the sexual one. Molecular markers revealed a twofold higher level of variability in the SSTP in comparison with the sexual germplasm utilised for its generation, and similar levels with the apomictic ones; moreover, markers showed that most of the variability was inherited from theapomictic germplasm. Morphologic and agronomic traits and seed fertility and quality traits showed high levels of variation in the three groups of genotypes indicating that the new breeding scheme was effective in transferring variability from the apomictic germplasm to the SSTP. This new population will be useful in breeding of P. notatum, and the breeding scheme used for its generation may be used in other apomictic species.Fil: Zilli, Alex Leonel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Nordeste. Instituto de Botánica del Nordeste. Universidad Nacional del Nordeste. Facultad de Ciencias Agrarias. Instituto de Botánica del Nordeste; ArgentinaFil: Acuña, Carlos Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Nordeste. Instituto de Botánica del Nordeste. Universidad Nacional del Nordeste. Facultad de Ciencias Agrarias. Instituto de Botánica del Nordeste; ArgentinaFil: Schulz, Roberto R.. Universidad Nacional del Nordeste; ArgentinaFil: Marcón, Florencia. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Nordeste. Instituto de Botánica del Nordeste. Universidad Nacional del Nordeste. Facultad de Ciencias Agrarias. Instituto de Botánica del Nordeste; ArgentinaFil: Brugnoli, Elsa Andrea. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Nordeste. Instituto de Botánica del Nordeste. Universidad Nacional del Nordeste. Facultad de Ciencias Agrarias. Instituto de Botánica del Nordeste; ArgentinaFil: Novo, Sabina F.. Universidad Nacional del Nordeste. Facultad de Ciencias Agrarias; ArgentinaFil: Quarin, Camilo Luis. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Nordeste. Instituto de Botánica del Nordeste. Universidad Nacional del Nordeste. Facultad de Ciencias Agrarias. Instituto de Botánica del Nordeste; ArgentinaFil: Martínez, Eric Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Nordeste. Instituto de Botánica del Nordeste. Universidad Nacional del Nordeste. Facultad de Ciencias Agrarias. Instituto de Botánica del Nordeste; Argentin