Collective Origin of the Coexistence of Apparent RMT Noise and Factors in Large Sample Correlation Matrices

Through simple analytical calculations and numerical simulations, we demonstrate the generic existence of a self-organized macroscopic state in any large multivariate system possessing non-vanishing average correlations between a finite fraction of all pairs of elements. The coexistence of an eigenvalue spectrum predicted by random matrix theory (RMT) and a few very large eigenvalues in large empirical correlation matrices is shown to result from a bottom-up collective effect of the underlying time series rather than a top-down impact of factors. Our results, in excellent agreement with previous results obtained on large financial correlation matrices, show that there is relevant information also in the bulk of the eigenvalue spectrum and rationalize the presence of market factors previously introduced in an ad hoc manner.Comment: 4 pages with 3 figur

Signatures of the disk-jet coupling in the Broad-line Radio Quasar 4C+74.26

Here we explore the disk-jet connection in the broad-line radio quasar 4C+74.26, utilizing the results of the multiwavelength monitoring of the source. The target is unique in that its radiative output at radio wavelengths is dominated by a moderately-beamed nuclear jet, at optical frequencies by the accretion disk, and in the hard X-ray range by the disk corona. Our analysis reveals a correlation (local and global significance of 96\% and 98\%, respectively) between the optical and radio bands, with the disk lagging behind the jet by $250 \pm 42$ days. We discuss the possible explanation for this, speculating that the observed disk and the jet flux changes are generated by magnetic fluctuations originating within the innermost parts of a truncated disk, and that the lag is related to a delayed radiative response of the disk when compared with the propagation timescale of magnetic perturbations along relativistic outflow. This scenario is supported by the re-analysis of the NuSTAR data, modelled in terms of a relativistic reflection from the disk illuminated by the coronal emission, which returns the inner disk radius $R_{\rm in}/R_{\rm ISCO} =35^{+40}_{-16}$. We discuss the global energetics in the system, arguing that while the accretion proceeds at the Eddington rate, with the accretion-related bolometric luminosity $L_{\rm bol} \sim 9 \times 10^{46}$ erg s$^{-1}$ $\sim 0.2 L_{\rm Edd}$, the jet total kinetic energy $L_\textrm{j} \sim 4 \times 10^{44}$ erg s$^{-1}$, inferred from the dynamical modelling of the giant radio lobes in the source, constitutes only a small fraction of the available accretion power.Comment: 9 pages and 6 figures, ApJ accepte

A Stable and Robust Calibration Scheme of the Log-Periodic Power Law Model

We present a simple transformation of the formulation of the log-periodic power law formula of the Johansen-Ledoit-Sornette model of financial bubbles that reduces it to a function of only three nonlinear parameters. The transformation significantly decreases the complexity of the fitting procedure and improves its stability tremendously because the modified cost function is now characterized by good smooth properties with in general a single minimum in the case where the model is appropriate to the empirical data. We complement the approach with an additional subordination procedure that slaves two of the nonlinear parameters to what can be considered to be the most crucial nonlinear parameter, the critical time $t_c$ defined as the end of the bubble and the most probably time for a crash to occur. This further decreases the complexity of the search and provides an intuitive representation of the results of the calibration. With our proposed methodology, metaheuristic searches are not longer necessary and one can resort solely to rigorous controlled local search algorithms, leading to dramatic increase in efficiency. Empirical tests on the Shanghai Composite index (SSE) from January 2007 to March 2008 illustrate our findings

Many-body Systems Interacting via a Two-body Random Ensemble (I): Angular Momentum distribution in the ground states

In this paper, we discuss the angular momentum distribution in the ground states of many-body systems interacting via a two-body random ensemble. Beginning with a few simple examples, a simple approach to predict P(I)'s, angular momenta I ground state (g.s.) probabilities, of a few solvable cases, such as fermions in a small single-j shell and d boson systems, is given. This method is generalized to predict P(I)'s of more complicated cases, such as even or odd number of fermions in a large single-j shell or a many-j shell, d-boson, sd-boson or sdg-boson systems, etc. By this method we are able to tell which interactions are essential to produce a sizable P(I) in a many-body system. The g.s. probability of maximum angular momentum $I_{max}$ is discussed. An argument on the microscopic foundation of our approach, and certain matrix elements which are useful to understand the observed regularities, are also given or addressed in detail. The low seniority chain of 0 g.s. by using the same set of two-body interactions is confirmed but it is noted that contribution to the total 0 g.s. probability beyond this chain may be more important for even fermions in a single-j shell. Preliminary results by taking a displaced two-body random ensemble are presented for the I g.s. probabilities.Comment: 39 pages and 8 figure

Density-matrix formalism with three-body ground-state correlations

A density-matrix formalism which includes the effects of three-body ground- state correlations is applied to the standard Lipkin model. The reason to consider the complicated three-body correlations is that the truncation scheme of reduced density matrices up to the two-body level does not give satisfactory results to the standard Lipkin model. It is shown that inclusion of the three-body correlations drastically improves the properties of the ground states and excited states. It is pointed out that lack of mean-field effects in the standard Lipkin model enhances the relative importance of the three-body ground-state correlations. Formal aspects of the density-matrix formalism such as a relation to the variational principle and the stability condition of the ground state are also discussed. It is pointed out that the three-body ground-state correlations are necessary to satisfy the stability condition

Precursor flares in OJ 287

We have studied three most recent precursor flares in the light curve of the blazar OJ 287 while invoking the presence of a precessing binary black hole in the system to explain the nature of these flares. Precursor flare timings from the historical light curves are compared with theoretical predictions from our model that incorporate effects of an accretion disk and post-Newtonian description for the binary black hole orbit. We find that the precursor flares coincide with the secondary black hole descending towards the accretion disk of the primary black hole from the observed side, with a mean z-component of approximately z_c = 4000 AU. We use this model of precursor flares to predict that precursor flare of similar nature should happen around 2020.96 before the next major outburst in 2022.Comment: to appear in the Astrophysical Journa

Convergence of the critical attractor of dissipative maps: Log-periodic oscillations, fractality and nonextensivity

For a family of logistic-like maps, we investigate the rate of convergence to the critical attractor when an ensemble of initial conditions is uniformly spread over the entire phase space. We found that the phase space volume occupied by the ensemble W(t) depicts a power-law decay with log-periodic oscillations reflecting the multifractal character of the critical attractor. We explore the parametric dependence of the power-law exponent and the amplitude of the log-periodic oscillations with the attractor's fractal dimension governed by the inflexion of the map near its extremal point. Further, we investigate the temporal evolution of W(t) for the circle map whose critical attractor is dense. In this case, we found W(t) to exhibit a rich pattern with a slow logarithmic decay of the lower bounds. These results are discussed in the context of nonextensive Tsallis entropies.Comment: 8 pages and 8 fig

Generic Rotation in a Collective SD Nucleon-Pair Subspace

Low-lying collective states involving many nucleons interacting by a random ensemble of two-body interactions (TBRE) are investigated in a collective SD-pair subspace, with the collective pairs defined dynamically from the two-nucleon system. It is found that in this truncated pair subspace collective vibrations arise naturally for a general TBRE hamiltonian whereas collective rotations do not. A hamiltonian restricted to include only a few randomly generated separable terms is able to produce collective rotational behavior, as long as it includes a reasonably strong quadrupole-quadrupole component. Similar results arise in the full shell model space. These results suggest that the structure of the hamiltonian is key to producing generic collective rotation.Comment: 11 pages, 5 figure

Universal Predictions for Statistical Nuclear Correlations

We explore the behavior of collective nuclear excitations under a multi-parameter deformation of the Hamiltonian. The Hamiltonian matrix elements have the form $P(|H_{ij}|)\propto 1/\sqrt{|H_{ij}|}\exp(-|H_{ij}|/V)$, with a parametric correlation of the type $\log \langle H(x)H(y)\rangle\propto -|x-y|$. The studies are done in both the regular and chaotic regimes of the Hamiltonian. Model independent predictions for a wide variety of correlation functions and distributions which depend on wavefunctions and energies are found from parametric random matrix theory and are compared to the nuclear excitations. We find that our universal predictions are observed in the nuclear states. Being a multi-parameter theory, we consider general paths in parameter space and find that universality can be effected by the topology of the parameter space. Specifically, Berry's phase can modify short distance correlations, breaking certain universal predictions.Comment: Latex file + 12 postscript figure