Sensitive observations at 1.4 and 250 GHz of z > 5 QSOs

We present 1.4 and 5 GHz observations taken with the Very Large Array (VLA), and observations at 250 GHz obtained with the Max-Planck millimeter bolometer (MAMBO) at the IRAM 30~m telescope, of ten optically selected Quasi-stellar Objects (QSOs) at 5.0 < z < 6.28. Four sources are detected at 1.4 GHz two of which are radio loud and are also detected at 5 GHz. These results are roughly consistent with there being no evolution of the radio-loud QSO fraction out to z~6. Three sources have been detected at 250 GHz or 350 GHz at much higher levels than their 1.4 GHz flux densities suggesting that the observed mm emission is likely thermal emission from warm dust, although more exotic possibilities cannot be precluded. The highest redshift source in our sample (J1030+0524 at z=6.28) is not detected at 1.4 or 250 GHz, but four fairly bright radio sources (flux density at 1.4GHz > 0.2 mJy) are detected in a 2' field centered on the QSO, including an edge-brightened ('FRII') double radio source with an extent of about 1'. A similar over-density of radio sources is seen in the field of the highest redshift QSO J1148+5251. We speculate that these over-densities of radio sources may indicate clusters along the lines-of-sight, in which case gravitational lensing by the cluster could magnify the QSO emission by a factor 2 or so without giving rise to arcsecond-scale distortions in the optical images of the QSOs.Comment: 25 pages, 12 figures. accepted by A

Finding community structure in networks using the eigenvectors of matrices

We consider the problem of detecting communities or modules in networks, groups of vertices with a higher-than-average density of edges connecting them. Previous work indicates that a robust approach to this problem is the maximization of the benefit function known as "modularity" over possible divisions of a network. Here we show that this maximization process can be written in terms of the eigenspectrum of a matrix we call the modularity matrix, which plays a role in community detection similar to that played by the graph Laplacian in graph partitioning calculations. This result leads us to a number of possible algorithms for detecting community structure, as well as several other results, including a spectral measure of bipartite structure in networks and a new centrality measure that identifies those vertices that occupy central positions within the communities to which they belong. The algorithms and measures proposed are illustrated with applications to a variety of real-world complex networks.Comment: 22 pages, 8 figures, minor corrections in this versio

Higher-order Mechanics: Variational Principles and other topics

After reviewing the Lagrangian-Hamiltonian unified formalism (i.e, the Skinner-Rusk formalism) for higher-order (non-autonomous) dynamical systems, we state a unified geometrical version of the Variational Principles which allows us to derive the Lagrangian and Hamiltonian equations for these kinds of systems. Then, the standard Lagrangian and Hamiltonian formulations of these principles and the corresponding dynamical equations are recovered from this unified framework.Comment: New version of the paper "Variational principles for higher-order dynamical systems", which was presented in the "III Iberoamerican Meeting on Geometry, Mechanics and Control" (Salamanca, 2012). The title is changed. A detailed review is added. Sections containing results about variational principles are enlarged with additional comments, diagrams and summarizing results. Bibliography is update

Band-structure trend in hole-doped cuprates and correlation with Tcmax

By calculation and analysis of the bare conduction bands in a large number of hole-doped high-temperature superconductors, we have identified the energy of the so-called axial-orbital as the essential, material-dependent parameter. It is uniquely related to the range of the intra-layer hopping. It controls the Cu 4s-character, influences the perpendicular hopping, and correlates with the observed Tc at optimal doping. We explain its dependence on chemical composition and structure, and present a generic tight-binding model.Comment: 5 pages, Latex, 5 eps figure

Cutting edges at random in large recursive trees

We comment on old and new results related to the destruction of a random recursive tree (RRT), in which its edges are cut one after the other in a uniform random order. In particular, we study the number of steps needed to isolate or disconnect certain distinguished vertices when the size of the tree tends to infinity. New probabilistic explanations are given in terms of the so-called cut-tree and the tree of component sizes, which both encode different aspects of the destruction process. Finally, we establish the connection to Bernoulli bond percolation on large RRT's and present recent results on the cluster sizes in the supercritical regime.Comment: 29 pages, 3 figure

Certainty Closure: Reliable Constraint Reasoning with Incomplete or Erroneous Data

Constraint Programming (CP) has proved an effective paradigm to model and solve difficult combinatorial satisfaction and optimisation problems from disparate domains. Many such problems arising from the commercial world are permeated by data uncertainty. Existing CP approaches that accommodate uncertainty are less suited to uncertainty arising due to incomplete and erroneous data, because they do not build reliable models and solutions guaranteed to address the user's genuine problem as she perceives it. Other fields such as reliable computation offer combinations of models and associated methods to handle these types of uncertain data, but lack an expressive framework characterising the resolution methodology independently of the model. We present a unifying framework that extends the CP formalism in both model and solutions, to tackle ill-defined combinatorial problems with incomplete or erroneous data. The certainty closure framework brings together modelling and solving methodologies from different fields into the CP paradigm to provide reliable and efficient approches for uncertain constraint problems. We demonstrate the applicability of the framework on a case study in network diagnosis. We define resolution forms that give generic templates, and their associated operational semantics, to derive practical solution methods for reliable solutions.Comment: Revised versio

The Unusual Infrared Object HDF-N J123656.3+621322

We describe an object in the Hubble Deep Field North with very unusual near-infrared properties. It is readily visible in Hubble Space Telescope NICMOS images at 1.6um and from the ground at 2.2um, but is undetected (with signal-to-noise <~ 2) in very deep WFPC2 and NICMOS data from 0.3 to 1.1um. The f_nu flux density drops by a factor >~ 8.3 (97.7% confidence) from 1.6 to 1.1um. The object is compact but may be slightly resolved in the NICMOS 1.6um image. In a low-resolution, near-infrared spectrogram, we find a possible emission line at 1.643um, but a reobservation at higher spectral resolution failed to confirm the line, leaving its reality in doubt. We consider various hypotheses for the nature of this object. Its colors are unlike those of known galactic stars, except perhaps the most extreme carbon stars or Mira variables with thick circumstellar dust shells. It does not appear to be possible to explain its spectral energy distribution as that of a normal galaxy at any redshift without additional opacity from either dust or intergalactic neutral hydrogen. The colors can be matched by those of a dusty galaxy at z >~ 2, by a maximally old elliptical galaxy at z >~ 3 (perhaps with some additional reddening), or by an object at z >~ 10 whose optical and 1.1um light have been suppressed by the intergalactic medium. Under the latter hypothesis, if the luminosity results from stars and not an AGN, the object would resemble a classical, unobscured protogalaxy, with a star formation rate >~ 100 M_sun/yr. Such UV-bright objects are evidently rare at 2 < z < 12.5, however, with a space density several hundred times lower than that of present-day L* galaxies.Comment: Accepted for publication in the Astrophysical Journal. 27 pages, LaTeX, with 7 figures (8 files); citations & references updated + minor format change

Dissipative effects on quantum glassy systems

We discuss the behavior of a quantum glassy system coupled to a bath of quantum oscillators. We show that the system localizes in the absence of interactions when coupled to a subOhmic bath. When interactions are switched on localization disappears and the system undergoes a phase transition towards a glassy phase. We show that the position of the critical line separating the disordered and the ordered phases strongly depends on the coupling to the bath. For a given type of bath, the ordered glassy phase is favored by a stronger coupling. Ohmic, subOhmic and superOhmic baths lead to different transition lines. We draw our conclusions from the analysis of the partition function using the replicated imaginary-time formalism and from the study of the real-time dynamics of the coupled system using the Schwinger-Keldysh closed time-path formalism.Comment: 39 pages, 13 figures, RevTe

Large times off-equilibrium dynamics of a particle in a random potential

We study the off-equilibrium dynamics of a particle in a general $N$-dimensional random potential when $N \to \infty$. We demonstrate the existence of two asymptotic time regimes: {\it i.} stationary dynamics, {\it ii.} slow aging dynamics with violation of equilibrium theorems. We derive the equations obeyed by the slowly varying part of the two-times correlation and response functions and obtain an analytical solution of these equations. For short-range correlated potentials we find that: {\it i.} the scaling function is non analytic at similar times and this behaviour crosses over to ultrametricity when the correlations become long range, {\it ii.} aging dynamics persists in the limit of zero confining mass with universal features for widely separated times. We compare with the numerical solution to the dynamical equations and generalize the dynamical equations to finite $N$ by extending the variational method to the dynamics.Comment: 70 pages, 7 figures included, uuencoded Z-compressed .tar fil

Real-time non-equilibrium dynamics of quantum glassy systems

We develop a systematic analytic approach to aging effects in quantum disordered systems in contact with an environment. Within the closed-time path-integral formalism we include dissipation by coupling the system to a set of independent harmonic oscillators that mimic a quantum thermal bath. After integrating over the bath variables and averaging over disorder we obtain an effective action that determines the real-time dynamics of the system. The classical limit yields the Martin-Siggia-Rose generating functional associated to a colored noise. We apply this general formalism to a prototype model related to the $p$ spin-glass. We show that the model has a dynamic phase transition separating the paramagnetic from the spin-glass phase and that quantum fluctuations depress the transition temperature until a quantum critical point is reached. We show that the dynamics in the paramagnetic phase is stationary but presents an interesting crossover from a region controlled by the classical critical point to another one controlled by the quantum critical point. The most characteristic property of the dynamics in a glassy phase, namely aging, survives the quantum fluctuations. In the sub-critical region the quantum fluctuation-dissipation theorem is modified in a way that is consistent with the notion of effective temperatures introduced for the classical case. We discuss these results in connection with recent experiments in dipolar quantum spin-glasses and the relevance of the effective temperatures with respect to the understanding of the low temperature dynamics.Comment: 56 pages, Revtex, 17 figures include