Temporal Evolution of Financial Market Correlations

We investigate financial market correlations using random matrix theory and principal component analysis. We use random matrix theory to demonstrate that correlation matrices of asset price changes contain structure that is incompatible with uncorrelated random price changes. We then identify the principal components of these correlation matrices and demonstrate that a small number of components accounts for a large proportion of the variability of the markets that we consider. We then characterize the time-evolving relationships between the different assets by investigating the correlations between the asset price time series and principal components. Using this approach, we uncover notable changes that occurred in financial markets and identify the assets that were significantly affected by these changes. We show in particular that there was an increase in the strength of the relationships between several different markets following the 2007--2008 credit and liquidity crisis.Comment: 15 pages, 10 figures, 1 table. Accepted for publication in Phys. Rev. E. v2 includes additional section

Temporal evolution of oscillating coronal loops

Context. Transverse oscillations of coronal structures are currently intensively studied to explore the associated magnetohydrodynamic wave physics and perform seismology of the local medium. Aims. We make a first attempt to measure the thermodynamic evolution of a sample of coronal loops that undergo decaying kink oscillations in response to an eruption in the corresponding active region. Methods. Using data from the six coronal wavelengths of SDO/AIA, we performed a differential emission measure (DEM) analysis of 15 coronal loops before, during, and after the eruption and oscillation. Results. We find that the emission measure, temperature, and width of the DEM distribution undergo significant variations on time scales relevant for the study of transverse oscillations. There are no clear collective trends of increases or decreases for the parameters we analysed. The strongest variations of the parameters occur during the initial perturbation of the loops, and the influence of background structures may also account for much of this variation. Conclusions. The DEM analysis of oscillating coronal loops in erupting active regions shows evidence of evolution on time scales important for the study of the oscillations. Further work is needed to separate the various observational and physical mechanisms that may be responsible for the variations in temperature, DEM distribution width, and total emission measure.Comment: Accepted in A&

Evolution of network structure by temporal learning

We study the effect of learning dynamics on network topology. A network of discrete dynamical systems is considered for this purpose and the coupling strengths are made to evolve according to a temporal learning rule that is based on the paradigm of spike-time-dependent plasticity. This incorporates necessary competition between different edges. The final network we obtain is robust and has a broad degree distribution.Comment: revised manuscript in communicatio

Propagation of hydrodynamic interactions between particles in a compressible fluid

Hydrodynamic interactions are transmitted by viscous diffusion and sound propagation: the temporal evolution of hydrodynamic interactions by both mechanisms is studied by direct numerical simulation in this paper. The hydrodynamic interactions for a system of two particles in a fluid are estimated by the velocity correlation of the particles. In an incompressible fluid, hydrodynamic interactions propagate instantaneously at the infinite speed of sound, followed by the temporal evolution of viscous diffusion. On the other hand, in a compressible fluid, sound propagates at a finite speed, which affects the temporal evolution of the hydrodynamic interactions by the order of magnitude relation between the time scales of viscous diffusion and sound propagation. The hydrodynamic interactions are characterized by introducing the ratio of these time scales as an interactive compressibility factor.Comment: 12 pages, 8 figure

The very fast evolution of Sakurai's object

V4334 Sgr (a.k.a. Sakurai's object) is the central star of an old planetary nebula that underwent a very late thermal pulse a few years before its discovery in 1996. We have been monitoring the evolution of the optical emission line spectrum since 2001. The goal is to improve the evolutionary models by constraining them with the temporal evolution of the central star temperature. In addition the high resolution spectral observations obtained by X-shooter and ALMA show the temporal evolution of the different morphological components.Comment: 2 pages, 2 figures to appear in the Proceedings of the IAU Symp. 323: "Planetary nebulae: Multi-wavelength probes of stellar and galactic evolution". Eds. X.-W. Liu, L. Stanghellini and A. Karaka