COBE Constraints on a Local group X-ray Halo

We investigate the effect of a putative X-ray emitting halo surrounding the Local Group of galaxies, and specifically the possible temperature anisotropies induced in the COBE-DMR four-year sky maps by an associated Sunyaev-Zel'dovich effect. By fitting the isothermal spherical halo model proposed by Suto et.al. (1996) to the coadded four-year COBE-DMR 53 and 90 GHz sky maps in Galactic coordinates, we find no significant evidence of a contribution. We therefore reject the claim that such a halo can affect the estimation of the primordial spectral index and amplitude of density perturbations as inferred from the DMR data. We find that correlation with the DMR data imposes constraints on the plausible contribution of such an X-ray emitting halo to a distortion in the CMB spectrum (as specified by the Compton-y parameter), up to a value for R -- the ratio of the core radius of the isothermal halo gas distribution to the distance to the Local Group centroid -- of 0.68. For larger values of R, the recent cosmological upper limit derived by COBE-FIRAS provides stronger constraints on the model parameters. Over the entire parameter space for R, we find an upper limit to the inferred sky-RMS anisotropy signal of 14 microKelvin (95% c.l.), a negligible amount relative to the 35 microKelvin signal observed in the COBE-DMR data.Comment: 4 pages, 3 figures; accepted for publication in MNRAS pink page

Scale free effects in world currency exchange network

A large collection of daily time series for 60 world currencies' exchange rates is considered. The correlation matrices are calculated and the corresponding Minimal Spanning Tree (MST) graphs are constructed for each of those currencies used as reference for the remaining ones. It is shown that multiplicity of the MST graphs' nodes to a good approximation develops a power like, scale free distribution with the scaling exponent similar as for several other complex systems studied so far. Furthermore, quantitative arguments in favor of the hierarchical organization of the world currency exchange network are provided by relating the structure of the above MST graphs and their scaling exponents to those that are derived from an exactly solvable hierarchical network model. A special status of the USD during the period considered can be attributed to some departures of the MST features, when this currency (or some other tied to it) is used as reference, from characteristics typical to such a hierarchical clustering of nodes towards those that correspond to the random graphs. Even though in general the basic structure of the MST is robust with respect to changing the reference currency some trace of a systematic transition from somewhat dispersed -- like the USD case -- towards more compact MST topology can be observed when correlations increase.Comment: Eur. Phys. J. B (2008) in pres

World currency exchange rate cross-correlations

World currency network constitutes one of the most complex structures that is associated with the contemporary civilization. On a way towards quantifying its characteristics we study the cross correlations in changes of the daily foreign exchange rates within the basket of 60 currencies in the period December 1998 -- May 2005. Such a dynamics turns out to predominantly involve one outstanding eigenvalue of the correlation matrix. The magnitude of this eigenvalue depends however crucially on which currency is used as a base currency for the remaining ones. Most prominent it looks from the perspective of a peripheral currency. This largest eigenvalue is seen to systematically decrease and thus the structure of correlations becomes more heterogeneous, when more significant currencies are used as reference. An extreme case in this later respect is the USD in the period considered. Besides providing further insight into subtle nature of complexity, these observations point to a formal procedure that in general can be used for practical purposes of measuring the relative currencies significance on various time horizons.Comment: 4 pages, 3 figures, LaTe

Accuracy analysis of the box-counting algorithm

Accuracy of the box-counting algorithm for numerical computation of the fractal exponents is investigated. To this end several sample mathematical fractal sets are analyzed. It is shown that the standard deviation obtained for the fit of the fractal scaling in the log-log plot strongly underestimates the actual error. The real computational error was found to have power scaling with respect to the number of data points in the sample ($n_{tot}$). For fractals embedded in two-dimensional space the error is larger than for those embedded in one-dimensional space. For fractal functions the error is even larger. Obtained formula can give more realistic estimates for the computed generalized fractal exponents' accuracy.Comment: 3 figure

Coevolution of Information Processing and Topology in Hierarchical Adaptive Random Boolean Networks

Random Boolean networks (RBNs) are frequently employed for modelling complex systems driven by information processing, e.g. for gene regulatory networks (GRNs). Here we propose a hierarchical adaptive RBN (HARBN) as a system consisting of distinct adaptive RBNs - subnetworks - connected by a set of permanent interlinks. Information measures and internal subnetworks topology of HARBN coevolve and reach steady-states that are specific for a given network structure. We investigate mean node information, mean edge information as well as a mean node degree as functions of model parameters and demonstrate HARBN's ability to describe complex hierarchical systems.Comment: 9 pages, 6 figure