Solid immersion lens at the aplanatic condition for enhancing the spectral bandwidth of a waveguide grating coupler

We report a technique to substantially boost the spectral bandwidth of a conventional waveguide grating coupler by using a solid immersion cylindrical lens at the aplanatic condition to create a highly anamorphic beam and reach a much larger numerical aperture, thus enhancing the spectral bandwidth of a free-space propagating optical beam coupled into a single-mode planar integrated optical waveguide (IOW). Our experimental results show that the broadband IOW spectrometer thus created almost doubles (94% enhancement) the coupled spectral bandwidth of a conventional configuration. To exemplify the benefits made possible by the developed approach, we applied the technique to the broadband spectroscopic characterization of a protein submonolayer; our experimental data confirm the enhanced spectral bandwidth (around 380–nm) and illustrate the potentials of the developed technology. Besides the enhanced bandwidth, the broadband coupler of the single-mode IOW spectrometer described here is more robust and user-friendly than those previously reported in the literature and is expected to have an important impact on spectroscopic studies of surface-adsorbed molecular layers and surface phenomena

k-core organization of complex networks

We analytically describe the architecture of randomly damaged uncorrelated networks as a set of successively enclosed substructures -- k-cores. The k-core is the largest subgraph where vertices have at least k interconnections. We find the structure of k-cores, their sizes, and their birth points -- the bootstrap percolation thresholds. We show that in networks with a finite mean number z_2 of the second-nearest neighbors, the emergence of a k-core is a hybrid phase transition. In contrast, if z_2 diverges, the networks contain an infinite sequence of k-cores which are ultra-robust against random damage.Comment: 5 pages, 3 figure

GHASP: an H{\alpha} kinematic survey of spiral and irregular galaxies -- IX. The NIR, stellar and baryonic Tully-Fisher relations

We studied, for the first time, the near infrared, stellar and baryonic Tully-Fisher relations for a sample of field galaxies taken from an homogeneous Fabry-Perot sample of galaxies (the GHASP survey). The main advantage of GHASP over other samples is that maximum rotational velocities were estimated from 2D velocity fields, avoiding assumptions about the inclination and position angle of the galaxies. By combining these data with 2MASS photometry, optical colors, HI masses and different mass-to-light ratio estimators, we found a slope of 4.48\pm0.38 and 3.64\pm0.28 for the stellar and baryonic Tully-Fisher relation, respectively. We found that these values do not change significantly when different mass-to-light ratios recipes were used. We also point out, for the first time, that rising rotation curves as well as asymmetric rotation curves show a larger dispersion in the Tully-Fisher relation than flat ones or than symmetric ones. Using the baryonic mass and the optical radius of galaxies, we found that the surface baryonic mass density is almost constant for all the galaxies of this sample. In this study we also emphasize the presence of a break in the NIR Tully-Fisher relation at M(H,K)\sim-20 and we confirm that late-type galaxies present higher total-to-baryonic mass ratios than early-type spirals, suggesting that supernova feedback is actually an important issue in late-type spirals. Due to the well defined sample selection criteria and the homogeneity of the data analysis, the Tully-Fisher relation for GHASP galaxies can be used as a reference for the study of this relation in other environments and at higher redshifts.Comment: 16 pages, 6 figures. Accepted for publication in MNRA

Multifractal properties of growing networks

We introduce a new family of models for growing networks. In these networks new edges are attached preferentially to vertices with higher number of connections, and new vertices are created by already existing ones, inheriting part of their parent's connections. We show that combination of these two features produces multifractal degree distributions, where degree is the number of connections of a vertex. An exact multifractal distribution is found for a nontrivial model of this class. The distribution tends to a power-law one, $\Pi (q) \sim q^{-\gamma}$, $\gamma =\sqrt{2}$ in the infinite network limit. Nevertheless, for finite networks's sizes, because of multifractality, attempts to interpret the distribution as a scale-free would result in an ambiguous value of the exponent $\gamma$.Comment: 7 pages epltex, 1 figur

k-core (bootstrap) percolation on complex networks: Critical phenomena and nonlocal effects

We develop the theory of the k-core (bootstrap) percolation on uncorrelated random networks with arbitrary degree distributions. We show that the k-core percolation is an unusual, hybrid phase transition with a jump emergence of the k-core as at a first order phase transition but also with a critical singularity as at a continuous transition. We describe the properties of the k-core, explain the meaning of the order parameter for the k-core percolation, and reveal the origin of the specific critical phenomena. We demonstrate that a so-called ``corona'' of the k-core plays a crucial role (corona is a subset of vertices in the k-core which have exactly k neighbors in the k-core). It turns out that the k-core percolation threshold is at the same time the percolation threshold of finite corona clusters. The mean separation of vertices in corona clusters plays the role of the correlation length and diverges at the critical point. We show that a random removal of even one vertex from the k-core may result in the collapse of a vast region of the k-core around the removed vertex. The mean size of this region diverges at the critical point. We find an exact mapping of the k-core percolation to a model of cooperative relaxation. This model undergoes critical relaxation with a divergent rate at some critical moment.Comment: 11 pages, 8 figure

O efeito de factores climáticos no consumo de energia eléctrica

Neste trabalho identificam-se as causas responsáveis por variações no consumo horário de energia com base na identificação de padrões e relações entre os dados de consumo e várias variáveis climatéricas. Para tal utilizam-se técnicas de data mining, nomeadamente a metodologia CRISP-DM e software de data warehouse MS SQL Server. Assim, foi possível verificar que as variáveis climatéricas têm influência muito significativa na produção de energia eléctrica, tendo sido possível prever os consumos de 2007 com um erro absoluto médio de 1,4 MW. Identificam-se ainda vários padrões no comportamento do consumo ou produção de energia eléctrica, nem todos espectáveis face ao conhecimento actual de domínio.info:eu-repo/semantics/publishedVersio

Laplacian spectra of complex networks and random walks on them: Are scale-free architectures really important?

We study the Laplacian operator of an uncorrelated random network and, as an application, consider hopping processes (diffusion, random walks, signal propagation, etc.) on networks. We develop a strict approach to these problems. We derive an exact closed set of integral equations, which provide the averages of the Laplacian operator's resolvent. This enables us to describe the propagation of a signal and random walks on the network. We show that the determining parameter in this problem is the minimum degree $q_m$ of vertices in the network and that the high-degree part of the degree distribution is not that essential. The position of the lower edge of the Laplacian spectrum $\lambda_c$ appears to be the same as in the regular Bethe lattice with the coordination number $q_m$. Namely, $\lambda_c>0$ if $q_m>2$, and $\lambda_c=0$ if $q_m\leq2$. In both these cases the density of eigenvalues $\rho(\lambda)\to0$ as $\lambda\to\lambda_c+0$, but the limiting behaviors near $\lambda_c$ are very different. In terms of a distance from a starting vertex, the hopping propagator is a steady moving Gaussian, broadening with time. This picture qualitatively coincides with that for a regular Bethe lattice. Our analytical results include the spectral density $\rho(\lambda)$ near $\lambda_c$ and the long-time asymptotics of the autocorrelator and the propagator.Comment: 25 pages, 4 figure