Long memory in volatility, modelling and forecasting in the wavelet domain

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La “Nouvelle administration politique” de Rhigas. Dimension sociale et politique de la citoyenneté de ses membres

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Temporal analysis of the least energetic events in pulsar data from observations with the high energy stereoscopic system

It has been more than 60 years since astronomers turned their attention towards the 7֊ray window (> 100 TeV). Nowadays, 7֊ray astronomy has won its place as a separate branch of astronomy in its own right. The present thesis introduces the reader to 7-ray observations in the 〜 100 GeV-100 TeV energy window, but focuses, in particular, on the efforts to describe and detect the pulsed, Very High-Energy (VHE) 7-ray emission from pulsars. Pulsars are highly magnetised {B 〜 101շ G) ， rapidly rotating (P ~ 10—2 s) neutron stars. Periodic radio emission from pulsars has been detected in more than 1,500 cases, in contrast to their 7-ray signature which has been confirmed for only six of them and only up to a few GeV. There are many models in existence which attempt to reproduce the observed pulsed profiles and energy spectra in high energies (optical, X and ๆ rays). Nevertheless, two classes of models are the most popular: the Polar Cap and the Outer Gap models. Both predict spectral cut-offs at tens of GeV, which are consistent with previous upper limits in the VHE range. The six most energetic pulsars have been detected with the EGRET (Energetic Gamma Ray Experiment Telescope) instrument on-board the с GRO (Compton Gamma Ray Observatory) satellite. Probing the universe at higher energies requires a different detection technique. The Imaging Atmospheric Technique (lACT) exploits the Earth's atmosphere with the use of large, ground-based reflectors that are very sensitive to Cherenkov light (300-600 nm). The latter is produced during electromagnetic particle cascades, triggered by the interaction of VHE 7 rays with the top atmospheric layers. So far there has not been a confirmed pulsar detection using Cherenkov astronomy. The High Energy Stereoscopic System (H.E.S.S.) in Namibia is an array of four telescopes, which is sensitive above 100 GeV. H.E.S.S. uses the lACT to reject the lO3 times more abundant cosmic-ray events that suppress the 7-ray signal. The system is capable of stereoscopic observations of the same source with all four telescopes, which further eliminates background events. Despite the fact that imaging with H.E.S.S. is not effective below 100 GeV, lower energy events can still be recorded, along with a large portion of the background. The present thesis deals with the least energetic events (< 100 ĢeV) detectable with H.E.ร.ร., where pulsar 7-ray emission is likely to be present. A very sensitive temporal analysis has been performed in order to identify the potentially periodic events in the large background. The necessary procedures and parameters of the analysis are described in detail, prior to the results. The author has analysed data from two 7-ray pulsars, the Crab and PSR B1706-44, which were seen with EGRET up to ~ 20 GeV, as well as the binary radio pulsar PSR B1259-63, which has not been detected at high energies (> 1 eV). The data were optimised for the lowest energies, and the lowest energy threshold achieved was 75 GeV (in the case of PSR B1706-44). In all cases studied, the author coded and applied a number of periodicity tests that check for significant deviations from random noise. The resulting probabilities were not significantly low to support signal presence. Based on the background levels in the data sets, the author derived upper limits on the integral and differential flux. These upper limits were consistent with the Polar Cap and Outer Gap scenarios, within statistical errors, but constrain the alternative model of a spectrum with a simple exponential cut-off in the case of PSR B1706—44. Despite the lack of detection, these results represent the lowest energies explored with H.E.S.S.， yet

Pulsar Spin--Velocity Alignment: Further Results and Discussion

The reported alignment between the projected spin-axes and proper motion directions of pulsars is revisited in the light of new data from Jodrell Bank and Effelsberg. The present investigation uses 54 pulsars, the largest to date sample of pulsars with proper-motion and absolute polarisation, to study this effect. Our study has found strong evidence for pulsar spin-velocity alignment, excluding that those two vectors are completely uncorrelated, with >99% confidence. Although we cannot exclude the possibility of orthogonal spin-velocity configurations, comparison of the data with simulations shows that the scenario of aligned vectors is more likely than that of the orthogonal case. Moreover, we have determined the spread of velocities that a spin-aligned and spin-orthogonal distribution of kicks must have to produce the observed distribution of spin-velocity angle offsets. If the observed distribution of spin-velocity offset angles is the result of spin-aligned kicks, then we find that the distribution of kick-velocity directions must be broad with {\sigma}_v~30\degree if the orthogonal-kick scenario is assumed, then the velocity distribution is much narrower with {\sigma}_v<10\degree. Finally, in contrast to previous studies, we have performed robustness tests on our data, in order to determine whether our conclusions are the result of a statistical and/or systematic bias. The conclusion of a correlation between the spin and velocity vectors is independent of a bias introduced by subsets in the total sample. Moreover, we estimate that the observed alignment is robust to within 10% systematic uncertainties on the determination of the spin-axis direction from polarisation data.Comment: 20 pages, 7 figures, 1 Table, accepted in MNRA

Pulsar Spin-Velocity Alignment: Kinematic Ages, Birth Periods and Braking Indices

This paper presents a detailed investigation of the dependence of pulsar spin-velocity alignment, which has been observed for a sample of 58 pulsars, on pulsar age. At first, our study considers only pulsar characteristic ages, resulting in no change in the degree of correlation as a function of age, up to at least 100 Myr. Subsequently, we consider a more reliable estimate of pulsar age, the kinematic age, assuming that pulsars are born near the Galactic plane. We derive kinematic ages for 52 pulsars, based on the measured pulsar proper motions and positions, by modelling the trajectory of the pulsars in a Galactic potential. The sample of 52 pulsar kinematic ages constitutes the largest number of independently estimated pulsar ages to date. Using only the 33 most reliable kinematic ages from our simulations, we revisit the evolution of spin- velocity alignment, this time as a function of kinematic age. We find that the strong correlation seen in young pulsars is completely smeared out for pulsars with kinematic ages above 10 Myr, a length of time beyond which we expect the gravitational pull of the Galaxy to have a significant effect on the directions of pulsar velocities. In the discussion, we investigate the impact of large distance uncertainties on the reliability of the calculated kinematic ages. Furthermore, we present a detailed investigation of the implications of our revised pulsar ages for the braking-index and birth-period distributions. Finally, we discuss the predictions of various SN-kick mechanisms and their compatibility with our results.Comment: 24 pages, 19 figures, MNRAS accepte

On Perron–Frobenius property of matrices having some negative entries

AbstractWe extend the theory of nonnegative matrices to the matrices that have some negative entries. We present and prove some properties which give us information, when a matrix possesses a Perron–Frobenius eigenpair. We apply also this theory by proposing the Perron–Frobenius splitting for the solution of the linear system Ax=b by classical iterative methods. Perron–Frobenius splittings constitute an extension of the well known regular splittings, weak regular splittings and nonnegative splittings. Convergence and comparison properties are given and proved

Superlinear convergence for PCG using band plus algebra preconditioners for Toeplitz systems

AbstractThe paper studies fast and efficient solution algorithms for n×n symmetric ill conditioned Toeplitz systems Tn(f)x=b where the generating function f is known a priori, real valued, nonnegative, and has isolated roots of even order. The preconditioner that we propose is a product of a band Toeplitz matrix and matrices that belong to a certain trigonometric algebra. The basic idea behind the proposed scheme is to combine the advantages of all components of the product that are well known when every component is used as a stand-alone preconditioner. As a result we obtain a flexible preconditioner which can be applied to the system Tn(f)x=b infusing superlinear convergence to the PCG method. The important feature of the proposed technique is that it can be extended to cover the 2D case, i.e. ill-conditioned block Toeplitz matrices with Toeplitz blocks. We perform many numerical experiments, whose results confirm the theoretical analysis and effectiveness of the proposed strategy