Large Scale Cross-Correlations in Internet Traffic

The Internet is a complex network of interconnected routers and the existence of collective behavior such as congestion suggests that the correlations between different connections play a crucial role. It is thus critical to measure and quantify these correlations. We use methods of random matrix theory (RMT) to analyze the cross-correlation matrix C of information flow changes of 650 connections between 26 routers of the French scientific network `Renater'. We find that C has the universal properties of the Gaussian orthogonal ensemble of random matrices: The distribution of eigenvalues--up to a rescaling which exhibits a typical correlation time of the order 10 minutes--and the spacing distribution follow the predictions of RMT. There are some deviations for large eigenvalues which contain network-specific information and which identify genuine correlations between connections. The study of the most correlated connections reveals the existence of `active centers' which are exchanging information with a large number of routers thereby inducing correlations between the corresponding connections. These strong correlations could be a reason for the observed self-similarity in the WWW traffic.Comment: 7 pages, 6 figures, final versio

Freezing of dynamical exponents in low dimensional random media

A particle in a random potential with logarithmic correlations in dimensions $d=1,2$ is shown to undergo a dynamical transition at $T_{dyn}>0$. In $d=1$ exact results demonstrate that $T_{dyn}=T_c$, the static glass transition temperature, and that the dynamical exponent changes from $z(T)=2 + 2 (T_c/T)^2$ at high temperature to $z(T)= 4 T_c/T$ in the glass phase. The same formulae are argued to hold in $d=2$. Dynamical freezing is also predicted in the 2D random gauge XY model and related systems. In $d=1$ a mapping between dynamics and statics is unveiled and freezing involves barriers as well as valleys. Anomalous scaling occurs in the creep dynamics.Comment: 5 pages, 2 figures, RevTe

Surface metal-insulator transition in the Hubbard model

The correlation-driven metal-insulator (Mott) transition at a solid surface is studied within the Hubbard model for a semi-infinite lattice by means of the dynamical mean-field theory. The transition takes place at a unique critical strength of the interaction. Depending on the surface geometry, the interaction strength and the wave vector, we find one-electron excitations in the coherent part of the surface-projected metallic spectrum which are confined to two dimensions.Comment: LaTeX, 9 pages, 5 eps figures included, Phys. Rev. B (in press

Scaling of the distribution of price fluctuations of individual companies

We present a phenomenological study of stock price fluctuations of individual companies. We systematically analyze two different databases covering securities from the three major US stock markets: (a) the New York Stock Exchange, (b) the American Stock Exchange, and (c) the National Association of Securities Dealers Automated Quotation stock market. Specifically, we consider (i) the trades and quotes database, for which we analyze 40 million records for 1000 US companies for the 2-year period 1994--95, and (ii) the Center for Research and Security Prices database, for which we analyze 35 million daily records for approximately 16,000 companies in the 35-year period 1962--96. We study the probability distribution of returns over varying time scales $\Delta t$, where $\Delta t$ varies by a factor of $\approx 10^5$---from 5 min up to $\approx$ 4 years. For time scales from 5~min up to approximately 16~days, we find that the tails of the distributions can be well described by a power-law decay, characterized by an exponent $\alpha \approx 3$ ---well outside the stable L\'evy regime $0 < \alpha < 2$. For time scales $\Delta t \gg (\Delta t)_{\times} \approx 16$days, we observe results consistent with a slow convergence to Gaussian behavior. We also analyze the role of cross correlations between the returns of different companies and relate these correlations to the distribution of returns for market indices.Comment: 10pages 2 column format with 11 eps figures. LaTeX file requiring epsf, multicol,revtex. Submitted to PR

Active galactic nucleus X-ray luminosity function and absorption function in the Early Universe (3 ≤ z ≤ 6)

The X-ray luminosity function (XLF) of active galactic nuclei (AGN) offers a robust tool to study the evolution and the growth of the supermassive black-hole population over cosmic time. Owing to the limited area probed by X-ray surveys, optical surveys are routinely used to probe the accretion in the high-redshift Universe z ≥ 3. However, optical surveys may be incomplete because they are strongly affected by dust redenning. In this work we derive the XLF and its evolution at high redshifts (z ≥ 3) using a large sample of AGN selected in different fields with various areas and depths covering a wide range of luminosities. Additionally, we put the tightest yet constraints on the absorption function in this redshift regime. In particular, we used more than 600 soft X-ray selected (0.5 − 2 keV) high-z sources in the Chandra deep fields, the Chandra COSMOS Legacy survey, and the XMM-XXL northern field. We derived the X-ray spectral properties for all sources via spectral fitting, using a consistent technique and model. To model the parametric form of the XLF and the absorption function, we used a Bayesian methodology, allowing us to correctly propagate the uncertainties for the observed X-ray properties of our sources and also the absorption effects. The evolution of XLF is in agreement with a pure density evolution model similar to what is witnessed at optical wavelengths, although a luminosity-dependent density evolution model cannot be securely ruled out. A large fraction (∼60%) of our sources are absorbed by column densities of NH ≥ 1023 cm−2, while ∼17% of the sources are Compton-Thick. Our results favour a scenario where both the interstellar medium of the host and the AGN torus contribute to the obscuration. The derived black hole accretion rate density is roughly in agreement with the large-scale cosmological hydrodynamical simulations, if one takes into account the results that the X-ray AGN are hosted by massive galaxies, while it differs from that derived using JWST data. The latter could be due to the differences in the AGN and host-galaxy properties

Anomalous Diffusion in Aperiodic Environments

We study the Brownian motion of a classical particle in one-dimensional inhomogeneous environments where the transition probabilities follow quasiperiodic or aperiodic distributions. Exploiting an exact correspondence with the transverse-field Ising model with inhomogeneous couplings we obtain many new analytical results for the random walk problem. In the absence of global bias the qualitative behavior of the diffusive motion of the particle and the corresponding persistence probability strongly depend on the fluctuation properties of the environment. In environments with bounded fluctuations the particle shows normal diffusive motion and the diffusion constant is simply related to the persistence probability. On the other hand in a medium with unbounded fluctuations the diffusion is ultra-slow, the displacement of the particle grows on logarithmic time scales. For the borderline situation with marginal fluctuations both the diffusion exponent and the persistence exponent are continuously varying functions of the aperiodicity. Extensions of the results to disordered media and to higher dimensions are also discussed.Comment: 11 pages, RevTe

Statistical properties of power-law random banded unitary matrices in the delocalization-localization transition regime

Power-law random banded unitary matrices (PRBUM), whose matrix elements decay in a power-law fashion, were recently proposed to model the critical statistics of the Floquet eigenstates of periodically driven quantum systems. In this work, we numerically study in detail the statistical properties of PRBUM ensembles in the delocalization-localization transition regime. In particular, implications of the delocalization-localization transition for the fractal dimension of the eigenvectors, for the distribution function of the eigenvector components, and for the nearest neighbor spacing statistics of the eigenphases are examined. On the one hand, our results further indicate that a PRBUM ensemble can serve as a unitary analog of the power-law random Hermitian matrix model for Anderson transition. On the other hand, some statistical features unseen before are found from PRBUM. For example, the dependence of the fractal dimension of the eigenvectors of PRBUM upon one ensemble parameter displays features that are quite different from that for the power-law random Hermitian matrix model. Furthermore, in the time-reversal symmetric case the nearest neighbor spacing distribution of PRBUM eigenphases is found to obey a semi-Poisson distribution for a broad range, but display an anomalous level repulsion in the absence of time-reversal symmetry.Comment: 10 pages + 13 fig

Probing the roles of orientation and multi-scale gas distributions in shaping the obscuration of Active Galactic Nuclei through cosmic time

The origin of obscuration in Active Galactic Nuclei (AGN) is still an open debate. In particular, it is unclear what drives the relative contributions to the line-of-sight column densities from galaxy-scale and torus-linked obscuration. The latter source is expected to play a significant role in Unification Models, while the former is thought to be relevant in both Unification and Evolutionary Models. In this work, we make use of a combination of cosmological semi-analytic models and semi-empirical prescriptions for the properties of galaxies and AGN, to study AGN obscuration. We consider a detailed object-by-object modelling of AGN evolution, including different AGN light curves (LCs), gas density profiles, and also AGN feedback-induced gas cavities. Irrespective of our assumptions on specific AGN LC or galaxy gas fractions, we find that, on the strict assumption of an exponential profile for the gas component, galaxy-scale obscuration alone can hardly reproduce the fraction of $\log (N_{\rm H}/$cm$^{-2}) \geq 24$ sources at least at $z\lesssim3$. This requires an additional torus component with a thickness that decreases with luminosity to match the data. The torus should be present in all evolutionary stages of a visible AGN to be effective, although galaxy-scale gas obscuration may be sufficient to reproduce the obscured fraction with $22<\log (N_{\rm H}/$cm$^{-2})<24$ (Compton-thin, CTN) if we assume extremely compact gas disc components. The claimed drop of CTN fractions with increasing luminosity does not appear to be a consequence of AGN feedback, but rather of gas reservoirs becoming more compact with decreasing stellar mass.Comment: MNRAS, accepted, 19 pages, 15 figures, 3 appendice

Will the US Economy Recover in 2010? A Minimal Spanning Tree Study

We calculated the cross correlations between the half-hourly times series of the ten Dow Jones US economic sectors over the period February 2000 to August 2008, the two-year intervals 2002--2003, 2004--2005, 2008--2009, and also over 11 segments within the present financial crisis, to construct minimal spanning trees (MSTs) of the US economy at the sector level. In all MSTs, a core-fringe structure is found, with consumer goods, consumer services, and the industrials consistently making up the core, and basic materials, oil and gas, healthcare, telecommunications, and utilities residing predominantly on the fringe. More importantly, we find that the MSTs can be classified into two distinct, statistically robust, topologies: (i) star-like, with the industrials at the center, associated with low-volatility economic growth; and (ii) chain-like, associated with high-volatility economic crisis. Finally, we present statistical evidence, based on the emergence of a star-like MST in Sep 2009, and the MST staying robustly star-like throughout the Greek Debt Crisis, that the US economy is on track to a recovery.Comment: elsarticle class, includes amsmath.sty, graphicx.sty and url.sty. 68 pages, 16 figures, 8 tables. Abridged version of the manuscript presented at the Econophysics Colloquim 2010, incorporating reviewer comment

Reaction Diffusion Models in One Dimension with Disorder

We study a large class of 1D reaction diffusion models with quenched disorder using a real space renormalization group method (RSRG) which yields exact results at large time. Particles (e.g. of several species) undergo diffusion with random local bias (Sinai model) and react upon meeting. We obtain the large time decay of the density of each specie, their associated universal amplitudes, and the spatial distribution of particles. We also derive the spectrum of exponents which characterize the convergence towards the asymptotic states. For reactions with several asymptotic states, we analyze the dynamical phase diagram and obtain the critical exponents at the transitions. We also study persistence properties for single particles and for patterns. We compute the decay exponents for the probability of no crossing of a given point by, respectively, the single particle trajectories ($\theta$) or the thermally averaged packets ($\bar{\theta}$). The generalized persistence exponents associated to n crossings are also obtained. Specifying to the process $A+A \to \emptyset$ or A with probabilities $(r,1-r)$, we compute exactly the exponents $\delta(r)$ and $\psi(r)$ characterizing the survival up to time t of a domain without any merging or with mergings respectively, and $\delta_A(r)$ and $\psi_A(r)$ characterizing the survival up to time t of a particle A without any coalescence or with coalescences respectively. $\bar{\theta}, \psi, \delta$ obey hypergeometric equations and are numerically surprisingly close to pure system exponents (though associated to a completely different diffusion length). Additional disorder in the reaction rates, as well as some open questions, are also discussed.Comment: 54 pages, Late