Unambiguous Turn Position and Rational Trace Languages

We show the existence of rational trace languages defined over direct products of free monoids that have inherent ambiguity of the order of log n and n 1/2 . This result is obtained by studying the relationship between trace languages and linear context-free grammars that satisfy a special unambiguity condition on the position of the last step of derivation

Pattern statistics and Vandermonde matrices

In this paper we determine some limit distributions of pattern statistics in rational stochastic models. We present a general approach to analyze these statistics in rational models having an arbitrary number of strongly connected components. We explicitly establish the limit distributions in most significant cases; they are characterized by a family of unimodal density functions defined by means of confluent Vandermonde matrices

Probabilistic models for pattern statistics

In this work we study some probabilistic models for the random generation of words over a given alphabet used in the literature in connection with pattern statistics. Our goal is to compare models based on Markovian processes (where the occurrence of a symbol in a given position only depends on a finite number of previous occurrences) and the stochastic models that can generate a word of given length from a regular language under uniform distribution. We present some results that show the differences between these two stochastic models and their relationship with the rational probabilistic measures

Imaging extended sources with coded mask telescopes: Application to the INTEGRAL IBIS/ISGRI instrument

Context. In coded mask techniques, reconstructed sky images are pseudo-images: they are maps of the correlation between the image recorded on a detector and an array derived from the coded mask pattern. Aims. The INTEGRAL/IBIS telescope provides images where the flux of each detected source is given by the height of the local peak in the correlation map. As such, it cannot provide an estimate of the flux of an extended source. What is needed is intensity sky images giving the flux per solide angle as typically done at other wavelengths. Methods. In this paper, we present the response of the INTEGRAL IBIS/ISGRI coded mask instrument to extended sources. We develop a general method based on analytical calculations in order to measure the intensity and the associated error of any celestial source and validated with Monte-Carlo simulations. Results. We find that the sensitivity degrades almost linearly with the source extent. Analytical formulae are given as well as an easy-to-use recipe for the INTEGRAL user. We check this method on IBIS/ISGRI data but these results are general and applicable to any coded mask telescope.Comment: 9 pages, 6 figures, Accepted for publication in A&

First observations of the X-ray transient EXO 2030+375 with IBIS/ISGRI

We present a first INTEGRAL observation of the 42s transient X-ray pulsar EXO 2030+375 with IBIS/ISGRI. The source was detected during Cyg X-1 observations in December 2002. We analyzed observations during the outburst period from 9 to 21 December 2002 with a total exposure time of ~770 kiloseconds. EXO 2030+375 was almost always detected during single ~30 minute exposures in the 18-45 energy bands. The source light curve shows the characteristic outburst shape observed in this source.Comment: 4 pages, 3 figures (1 in CMYK color), accepted by Astronomy and Astrophysics, INTEGRAL special issue, 200

Echoes of multiple outbursts of Sagittarius A* revealed by Chandra

The relatively rapid spatial and temporal variability of the X-ray radiation from some molecular clouds near the Galactic center shows that this emission component is due to the reflection of X-rays generated by a source that was luminous in the past, most likely the central supermassive black hole, Sagittarius A*. Studying the evolution of the molecular cloud reflection features is therefore a key element to reconstruct Sgr A*'s past activity. The aim of the present work is to study this emission on small angular scales in order to characterize the source outburst on short time scales. We use Chandra high-resolution data collected from 1999 to 2011 to study the most rapid variations detected so far, those of clouds between 5' and 20' from Sgr A* towards positive longitudes. Our systematic spectral-imaging analysis of the reflection emission, notably of the Fe Kalpha line at 6.4 keV and its associated 4-8 keV continuum, allows us to characterize the variations down to 15" angular scale and 1-year time scale. We reveal for the first time abrupt variations of few years only and in particular a short peaked emission, with a factor of 10 increase followed by a comparable decrease, that propagates along the dense filaments of the Bridge cloud. This 2-year peaked feature contrasts with the slower 10-year linear variations we reveal in all the other molecular structures of the region. Based on column density constraints, we argue that these two different behaviors are unlikely to be due to the same illuminating event. The variations are likely due to a highly variable active phase of Sgr A* sometime within the past few hundred years, characterized by at least two luminous outbursts of a few-year time scale and during which the Sgr A* luminosity went up to at least 10^39 erg/s.Comment: 17 pages, 16 figures, Accepted for publication in Astronomy & Astrophysic

Frequency of symbol occurrences in simple non-primitive stochastic models

We study the random variable Y-n representing the number of occurrences of a given symbol in a word of length n generated at random. The stochastic model we assume is a simple non-ergodic model defined by the product of two primitive rational formal series, which form two distinct ergodic components. We obtain asymptotic evaluations for the mean and the variance of Y-n and its limit distribution. It turns out that there are two main cases: if one component is dominant and non-degenerate we get a Gaussian limit distribution; if the two components are equipotent and have different leading terms of the mean, we get a uniform limit distribution. Other particular limit distributions are obtained in the case of a degenerate dominant component and in the equipotent case when the leading terms of the expectation values are equal

Frequency of symbol occurrences in bicomponent stochastic models

We give asymptotic estimates of the frequency of occurrences of a symbol in a random word Generated by any bicomponent stochastic model. More precisely, we consider the random variable Y-n representing the number of occurrences of a given symbol in a word of length n generated at random; the stochastic model is defined by a rational formal series r having a linear representation with two primitive components. This model includes the case when r is the product or the sum of two primitive rational formal series. We obtain asymptotic evaluations for the mean value and the variance of Yn and its limit distribution

The INTEGRAL IBIS/ISGRI System Point Spread Function and Source Location Accuracy

The imager on board INTEGRAL (IBIS) presently provides the most detailed sky images ever obtained at energies above 30 keV. The telescope is based on a coded aperture imaging system which allows to obtain sky images in a large field of view 29deg x 29deg with an angular resolution of 12'. The System Point Spread Function of the telescope and its detailed characteristics are here described along with the specific analysis algorithms used to derive the accurate point-like source locations. The derived location accuracy is studied using the first in-flight calibration data on strong sources for the IBIS/ISGRI system. The dependence of the calibrated location accuracy with the signal to noise ratio of the sources is presented. These preliminary studies demonstrate that the IBIS/ISGRI telescope and the standard scientific analysis software allow source localizations with accuracy at 90% confidence level better than 1' for sources with signal to noise ratios > 30 over the whole field of view, in agreement with the expected performances of the instrument.Comment: 5 pages, 5 figures, accepted for publication in A&A Lett (INTEGRAL special issue