Asymptotic solutions of a generalized eigenvalue problem

This paper provides a solution of a generalized eigenvalue problem for a fractional integrated processes. To this end two random matrices are constructed in order to take into account the stationarity properties of the differences of a fractional p-variate integrated process. The matrices are defined by some weight functions and the difference orders are assumed to vary in a continuous and discrete range. The asymptotic behavior of these matrices is obtained imposing some conditions on the weight functions. Using Bierens (1987) and Andersen et al. (1983) results, a generalized eigenvalues problem is solved

Some Nonparametric Asymptotic Results for a Class of Stochastic Processes

This paper provides a solution of a generalized eigenvalue problem for integrated processes of order 2 in a nonparametric framework. Our analysis focuses on a pair of random matrices related to such integrated process. The matrices are constructed considering some weight functions. Under asymptotic conditions on such weights, convergence results in distribution are obtained and the generalized eigenvalue problem is solved. Differential equations and stochastic calculus theory are used. This is an Accepted Manuscript of an article published by Taylor & Francis in Communications in Statistics - Theory and Methodson 13 July 2010 , available online: http://www.tandfonline.com/10.1080/0361092090306102

On the asymptotic behaviour of random matrices in a multivariate statistical model

This paper aims to provide a nonparametric analysis of the integrated processes of an integer order, via a theoretical solution of a generalized eigenvalue problem. To this end, we introduce a mean operator for the process, by using weights belonging to a Sobolev Space

New results on the convergence of random matrices

This paper extends the previous convergence results in Cerqueti and Costantini (2008) to a more general case using larger normed set of functions. In this regard, the weight-based convergence of the random matrices and their generalized eigenvalues is obtained under less restrictive requirements for the weights. This is an Accepted Manuscript of an article published by Taylor & Francis in Statistics on 10 January 2012, available online: http://www.tandfonline.com/10.1080/02331888.2011.64863

Abstraction and Refinement in Configuration Structures

An abstraction operator for configuration structures is defined and it is proven that it is left inverse to the traditional refinement operator. The abstraction operator describes how concrete behaviour looks when observed from a more abstract level, where the difference between concrete and abstract is given by a transformation mapping. This generates a notion of implementation: L is said to implement H iff L is mapped to H by the abstraction operator. The implementation relation generated by the abstraction operator is strictly more general than the implementation function defined by a refinement operator, thus allowing a more flexible design process for distributed systems

XMM-Newton observation of the ULIRG NGC 6240: The physical nature of the complex Fe K line emission

We report on an XMM-Newton observation of the ultraluminous infrared galaxy NGC 6240. The 0.3-10 keV spectrum can be successfully modelled with: (i) three collisionally ionized plasma components with temperatures of about 0.7, 1.4, and 5.5 keV; (ii) a highly absorbed direct power-law component; and (iii) a neutral Fe K_alpha and K_beta line. We detect a significant neutral column density gradient which is correlated with the temperature of the three plasma components. Combining the XMM-Newton spectral model with the high spatial resolution Chandra image we find that the temperatures and the column densities increase towards the center. With high significance, the Fe K line complex is resolved into three distinct narrow lines: (i) the neutral Fe K_alpha line at 6.4 keV; (ii) an ionized line at about 6.7 keV; and (iii) a higher ionized line at 7.0 keV (a blend of the Fe XXVI and the Fe K_beta line). While the neutral Fe K line is most probably due to reflection from optically thick material, the Fe XXV and Fe XXVI emission arises from the highest temperature ionized plasma component. We have compared the plasma parameters of the ultraluminous infrared galaxy NGC 6240 with those found in the local starburst galaxy NGC 253. We find a striking similarity in the plasma temperatures and column density gradients, suggesting a similar underlying physical process at work in both galaxies.Comment: 8 pages including 9 figures. Accepted for publication in A&

Effects of Chia Seed Supplementation on Biochemical Markers of Cardiometabolic Diseases in Spontaneously Hypertensive Rats

Some studies suggested a positive effect against cardiometabolic diseases of supplementation of alpha-linolenic acid (ALA, C18:3 n-3) rich foods in pathological subjects, even if the total literature is controversial. In order to clarify ALA-rich chia seed action in hypertensive model with the overt pathology and without drug interference, in the present study the biochemical markers of cardiometabolic diseases (endothelin-1, ET-1; nitric oxide, NO; and bradykinin, BK) in Spontaneously Hypertensive Rats (SHRs) were analysed after 5% chia seed dietary supplementation for five weeks, and compared with the staple raw material wheat and corn. At the end of the experimental period, also plasma antioxidant capacity and inflammatory condition were evaluated. Our results showed that the chia seed group was more oxidized. On the other hand, ET-1 significantly decreased in chia seed group, and there was no difference between groups for NO, BK, and the inflammatory C-reactive protein (CRP). In conclusion, some positive effects of chia seed consumption on cardiometabolic markers in SHRs were observed, despite this the association of chia seeds with antioxidants is suggested to avoid plasma oxidation increase

Revealing structure and evolution within the corona of the Seyfert galaxy I Zw 1

X-ray spectral timing analysis is presented of XMM-Newton observations of the narrow line Seyfert 1 galaxy I Zwicky 1 (I Zw 1) taken in 2015 January. After exploring the effect of background flaring on timing analyses, X-ray time lags between the reflection-dominated 0.3-1.0keV energy and continuum-dominated 1.0-4.0keV band are measured, indicative of reverberation off the inner accretion disc. The reverberation lag time is seen to vary as a step function in frequency; across lower frequency components of the variability, 3e-4 to 1.2e-3Hz a lag of 160s is measured, but the lag shortens to (59 +/- 4)s above 1.2e-3Hz. The lag-energy spectrum reveals differing profiles between these ranges with a change in the dip showing the earliest arriving photons. The low frequency signal indicates reverberation of X-rays emitted from a corona extended at low height over the disc while at high frequencies, variability is generated in a collimated core of the corona through which luminosity fluctuations propagate upwards. Principal component analysis of the variability supports this interpretation, showing uncorrelated variation in the spectral slope of two power law continuum components. The distinct evolution of the two components of the corona is seen as a flare passes inwards from the extended to the collimated portion. An increase in variability in the extended corona was found preceding the initial increase in X-ray flux. Variability from the extended corona was seen to die away as the flare passed into the collimated core leading to a second sharper increase in the X-ray count rate.Comment: 18 pages, 11 figures. Accepted for publication in MNRA

Behind the dust curtain: the spectacular case of GRB 160623A

We report on the X-ray dust-scattering features observed around the afterglow of the gamma ray burst GRB 160623A. With an XMM-Newton observation carried out ~2 days after the burst, we found evidence of at least six rings, with angular size expanding between ~2 and 9 arcmin, as expected for X-ray scattering of the prompt GRB emission by dust clouds in our Galaxy. From the expansion rate of the rings, we measured the distances of the dust layers with extraordinary precision: 528.1 +\- 1.2 pc, 679.2 +\- 1.9 pc, 789.0 +\- 2.8 pc, 952 +\- 5 pc, 1539 +\- 20 pc and 5079 +\- 64 pc. A spectral analysis of the ring spectra, based on an appropriate dust-scattering model (BARE-GR-B from Zubko et al. 2004}) and the estimated burst fluence, allowed us to derive the column density of the individual dust layers, which are in the range 7x10^20-1.5x10^22 cm^-2. The farthest dust-layer (i.e. the one responsible for the smallest ring) is also the one with the lowest column density and it is possibly very extended, indicating a diffuse dust region. The properties derived for the six dust-layers (distance, thickness, and optical depth) are generally in good agreement with independent information on the reddening along this line of sight and on the distribution of molecular and atomic gas.Comment: 9 pages, 10 figures, 1 table; accepted for publication in MNRA