Path-Fault-Tolerant Approximate Shortest-Path Trees

Let $G=(V,E)$ be an $n$-nodes non-negatively real-weighted undirected graph. In this paper we show how to enrich a {\em single-source shortest-path tree} (SPT) of $G$ with a \emph{sparse} set of \emph{auxiliary} edges selected from $E$, in order to create a structure which tolerates effectively a \emph{path failure} in the SPT. This consists of a simultaneous fault of a set $F$ of at most $f$ adjacent edges along a shortest path emanating from the source, and it is recognized as one of the most frequent disruption in an SPT. We show that, for any integer parameter $k \geq 1$, it is possible to provide a very sparse (i.e., of size $O(kn\cdot f^{1+1/k})$) auxiliary structure that carefully approximates (i.e., within a stretch factor of $(2k-1)(2|F|+1)$) the true shortest paths from the source during the lifetime of the failure. Moreover, we show that our construction can be further refined to get a stretch factor of $3$ and a size of $O(n \log n)$ for the special case $f=2$, and that it can be converted into a very efficient \emph{approximate-distance sensitivity oracle}, that allows to quickly (even in optimal time, if $k=1$) reconstruct the shortest paths (w.r.t. our structure) from the source after a path failure, thus permitting to perform promptly the needed rerouting operations. Our structure compares favorably with previous known solutions, as we discuss in the paper, and moreover it is also very effective in practice, as we assess through a large set of experiments.Comment: 21 pages, 3 figures, SIROCCO 201

Open and / or laparoscopic surgical treatment of liver hydatic cysts

Hydatid disease is a severe parasitic disease with a widely ranging distribution. In the human being the liver is the most frequent organ affected. 1 The treatment should be individualized to the morphology, size, number and location of the cysts, that is why a variety of surgical operations have been advocated from complete resection like total pericystectomy or partial hepatectomy to laparoscopy to a minimally invasive procedures like percutaneous aspiration of cysts to conservative drug therapy. 3-4 This study compares laparoscopic versus open management of the hydatid cyst of liver the surgical approach to liver echinococcosis is still a controversial issue and shows our results of surgical treatment of liver hydatid cysts during a 3-years period

Fully-dynamic Approximation of Betweenness Centrality

Betweenness is a well-known centrality measure that ranks the nodes of a network according to their participation in shortest paths. Since an exact computation is prohibitive in large networks, several approximation algorithms have been proposed. Besides that, recent years have seen the publication of dynamic algorithms for efficient recomputation of betweenness in evolving networks. In previous work we proposed the first semi-dynamic algorithms that recompute an approximation of betweenness in connected graphs after batches of edge insertions. In this paper we propose the first fully-dynamic approximation algorithms (for weighted and unweighted undirected graphs that need not to be connected) with a provable guarantee on the maximum approximation error. The transfer to fully-dynamic and disconnected graphs implies additional algorithmic problems that could be of independent interest. In particular, we propose a new upper bound on the vertex diameter for weighted undirected graphs. For both weighted and unweighted graphs, we also propose the first fully-dynamic algorithms that keep track of such upper bound. In addition, we extend our former algorithm for semi-dynamic BFS to batches of both edge insertions and deletions. Using approximation, our algorithms are the first to make in-memory computation of betweenness in fully-dynamic networks with millions of edges feasible. Our experiments show that they can achieve substantial speedups compared to recomputation, up to several orders of magnitude

Quantum teardrops

Algebras of functions on quantum weighted projective spaces are introduced, and the structure of quantum weighted projective lines or quantum teardrops are described in detail. In particular the presentation of the coordinate algebra of the quantum teardrop in terms of generators and relations and classification of irreducible *-representations are derived. The algebras are then analysed from the point of view of Hopf-Galois theory or the theory of quantum principal bundles. Fredholm modules and associated traces are constructed. C*-algebras of continuous functions on quantum weighted projective lines are described and their K-groups computed.Comment: 18 page

Quantum Isometries of the finite noncommutative geometry of the Standard Model

We compute the quantum isometry group of the finite noncommutative geometry F describing the internal degrees of freedom in the Standard Model of particle physics. We show that this provides genuine quantum symmetries of the spectral triple corresponding to M x F where M is a compact spin manifold. We also prove that the bosonic and fermionic part of the spectral action are preserved by these symmetries.Comment: 29 pages, no figures v3: minor change

Chemical Abundance Analysis of Tucana III, the Second rr-process Enhanced Ultra-Faint Dwarf Galaxy

We present a chemical abundance analysis of four additional confirmed member stars of Tucana III, a Milky Way satellite galaxy candidate in the process of being tidally disrupted as it is accreted by the Galaxy. Two of these stars are centrally located in the core of the galaxy while the other two stars are located in the eastern and western tidal tails. The four stars have chemical abundance patterns consistent with the one previously studied star in Tucana III: they are moderately enhanced in $r$-process elements, i.e. they have $\approx +$0.4 dex. The non-neutron-capture elements generally follow trends seen in other dwarf galaxies, including a metallicity range of 0.44 dex and the expected trend in $\alpha$-elements, i.e., the lower metallicity stars have higher Ca and Ti abundance. Overall, the chemical abundance patterns of these stars suggest that Tucana III was an ultra-faint dwarf galaxy, and not a globular cluster, before being tidally disturbed. As is the case for the one other galaxy dominated by $r$-process enhanced stars, Reticulum II, Tucana III's stellar chemical abundances are consistent with pollution from ejecta produced by a binary neutron star merger, although a different $r$-process element or dilution gas mass is required to explain the abundances in these two galaxies if a neutron star merger is the sole source of $r$-process enhancement.Comment: 18 pages, 10 figures; accepted by Ap

Forward Global Photometric Calibration of the Dark Energy Survey

Many scientific goals for the Dark Energy Survey (DES) require calibration of optical/NIR broadband $b = grizY$ photometry that is stable in time and uniform over the celestial sky to one percent or better. It is also necessary to limit to similar accuracy systematic uncertainty in the calibrated broadband magnitudes due to uncertainty in the spectrum of the source. Here we present a "Forward Global Calibration Method (FGCM)" for photometric calibration of the DES, and we present results of its application to the first three years of the survey (Y3A1). The FGCM combines data taken with auxiliary instrumentation at the observatory with data from the broad-band survey imaging itself and models of the instrument and atmosphere to estimate the spatial- and time-dependence of the passbands of individual DES survey exposures. "Standard" passbands are chosen that are typical of the passbands encountered during the survey. The passband of any individual observation is combined with an estimate of the source spectral shape to yield a magnitude $m_b^{\mathrm{std}}$ in the standard system. This "chromatic correction" to the standard system is necessary to achieve sub-percent calibrations. The FGCM achieves reproducible and stable photometric calibration of standard magnitudes $m_b^{\mathrm{std}}$ of stellar sources over the multi-year Y3A1 data sample with residual random calibration errors of $\sigma=5-6\,\mathrm{mmag}$ per exposure. The accuracy of the calibration is uniform across the $5000\,\mathrm{deg}^2$ DES footprint to within $\sigma=7\,\mathrm{mmag}$. The systematic uncertainties of magnitudes in the standard system due to the spectra of sources are less than $5\,\mathrm{mmag}$ for main sequence stars with $0.5<g-i<3.0$.Comment: 25 pages, submitted to A

Polariton propagation in weak confinement quantum wells

Exciton-polariton propagation in a quantum well, under centre-of-mass quantization, is computed by a variational self-consistent microscopic theory. The Wannier exciton envelope functions basis set is given by the simple analytical model of ref. [1], based on pure states of the centre-of-mass wave vector, free from fitting parameters and "ad hoc" (the so called additional boundary conditions-ABCs) assumptions. In the present paper, the former analytical model is implemented in order to reproduce the centre-of-mass quantization in a large range of quantum well thicknesses (5a_B < L < inf.). The role of the dynamical transition layer at the well/barrier interfaces is discussed at variance of the classical Pekar's dead-layer and ABCs. The Wannier exciton eigenstates are computed, and compared with various theoretical models with different degrees of accuracy. Exciton-polariton transmission spectra in large quantum wells (L>> a_B) are computed and compared with experimental results of Schneider et al.\cite{Schneider} in high quality GaAs samples. The sound agreement between theory and experiment allows to unambiguously assign the exciton-polariton dips of the transmission spectrum to the pure states of the Wannier exciton center-of-mass quantization.Comment: 15 pages, 15 figures; will appear in Phys.Rev.

Prospects in Constraining the Dark Energy Potential

We generalize to non-flat geometries the formalism of Simon et al. (2005) to reconstruct the dark energy potential. This formalism makes use of quantities similar to the Horizon-flow parameters in inflation, can, in principle, be made non-parametric and is general enough to be applied outside the simple, single scalar field quintessence. Since presently available and forthcoming data do not allow a non-parametric and exact reconstruction of the potential, we consider a general parametric description in term of Chebyshev polynomials. We then consider present and future measurements of H(z), Baryon Acoustic Oscillations surveys and Supernovae type 1A surveys, and investigate their constraints on the dark energy potential. We find that, relaxing the flatness assumption increases the errors on the reconstructed dark energy evolution but does not open up significant degeneracies, provided that a modest prior on geometry is imposed. Direct measurements of H(z), such as those provided by BAO surveys, are crucially important to constrain the evolution of the dark energy potential and the dark energy equation of state, especially for non-trivial deviations from the standard LambdaCDM model.Comment: 22 pages, 7 figures. 2 references correcte

Properties of Type Ia supernovae inside rich galaxy clusters

We used the Gaussian Mixture Brightest Cluster Galaxy catalogue and Sloan Digital Sky Survey-II supernovae data with redshifts measured by the Baryon Oscillation Spectroscopic Survey to identify 48 Type Ia supernovae (SNe Ia) residing in rich galaxy clusters and compare their properties with 1015 SNe Ia in the field. Their light curves were parametrized by the SALT2 model and the significance of the observed differences was assessed by a resampling technique. To test our samples and methods, we first looked for known differences between SNe Ia residing in active and passive galaxies. We confirm that passive galaxies host SNe Ia with smaller stretch, weaker colour–luminosity relation [β of 2.54(22) against 3.35(14)], and that are ∼0.1 mag more luminous after stretch and colour corrections. We show that only 0.02 per cent of random samples drawn from our set of SNe Ia in active galaxies can reach these values. Reported differences in the Hubble residuals scatter could not be detected, possibly due to the exclusion of outliers. We then show that, while most field and cluster SNe Ia properties are compatible at the current level, their stretch distributions are different (∼3σ): besides having a higher concentration of passive galaxies than the field, the cluster’s passive galaxies host SNe Ia with an average stretch even smaller than those in field passive galaxies (at 95 per cent confidence).We argue that the older age of passive galaxies in clusters is responsible for this effect since, as we show, old passive galaxies host SNe Ia with smaller stretch than young passive galaxies (∼4σ).Web of Scienc