Cancelation norm and the geometry of biinvariant word metrics

We study biinvariant word metrics on groups. We provide an efficient algorithm for computing the biinvariant word norm on a finitely generated free group and we construct an isometric embedding of a locally compact tree into the biinvariant Cayley graph of a nonabelian free group. We investigate the geometry of cyclic subgroups. We observe that in many classes of groups cyclic subgroups are either bounded or detected by homogeneous quasimorphisms. We call this property the bq-dichotomy and we prove it for many classes of groups of geometric origin.Comment: 32 pages, to appear in Glasgow Journal of Mathematic

On the k-Boundedness for Existential Rules

The chase is a fundamental tool for existential rules. Several chase variants are known, which differ on how they handle redundancies possibly caused by the introduction of nulls. Given a chase variant, the halting problem takes as input a set of existential rules and asks if this set of rules ensures the termination of the chase for any factbase. It is well-known that this problem is undecidable for all known chase variants. The related problem of boundedness asks if a given set of existential rules is bounded, i.e., whether there is a predefined upper bound on the number of (breadth-first) steps of the chase, independently from any factbase. This problem is already undecidable in the specific case of datalog rules. However, knowing that a set of rules is bounded for some chase variant does not help much in practice if the bound is unknown. Hence, in this paper, we investigate the decidability of the k-boundedness problem, which asks whether a given set of rules is bounded by an integer k. We prove that k-boundedness is decidable for three chase variants, namely the oblivious, semi-oblivious and restricted chase.Comment: 20 pages, revised version of the paper published at RuleML+RR 201

A method to localize gamma-ray bursts using POLAR

The hard X-ray polarimeter POLAR aims to measure the linear polarization of the 50-500 keV photons arriving from the prompt emission of gamma-ray bursts (GRBs). The position in the sky of the detected GRBs is needed to determine their level of polarization. We present here a method by which, despite of the polarimeter incapability of taking images, GRBs can be roughly localized using POLAR alone. For this purpose scalers are attached to the output of the 25 multi-anode photomultipliers (MAPMs) that collect the light from the POLAR scintillator target. Each scaler measures how many GRB photons produce at least one energy deposition above 50 keV in the corresponding MAPM. Simulations show that the relative outputs of the 25 scalers depend on the GRB position. A database of very strong GRBs simulated at 10201 positions has been produced. When a GRB is detected, its location is calculated searching the minimum of the chi2 obtained in the comparison between the measured scaler pattern and the database. This GRB localization technique brings enough accuracy so that the error transmitted to the 100% modulation factor is kept below 10% for GRBs with fluence Ftot \geq 10^(-5) erg cm^(-2) . The POLAR localization capability will be useful for those cases where no other instruments are simultaneously observing the same field of view.Comment: 13 pages, 10 figure

GRB030406 an extremely hard burst outside of the INTEGRAL field of view

Using the IBIS Compton mode, the INTEGRAL satellite is able to detect and localize bright and hard GRBs, which happen outside of the nominal INTEGRAL telescopes field of view. We have developed a method of analyzing such INTEGRAL data to obtain the burst location and spectra. We present the results for the case of GRB030406. The burst is localized with the Compton events, and the location is consistent with the previous Interplanetary Network position. A spectral analysis is possible with the detailed modeling of the detector response for such a far off-axis source with the offset of 36.9 $^\circ$. The average spectrum of the burst is extremely hard: the photon index above 400 \kev is -1.7, with no evidence of a break up to 1.1 \mev at 90% confidence level.Comment: Astronomy and Astrophysics in pres

Disclination vortices in elastic media

The vortex-like solutions are studied in the framework of the gauge model of disclinations in elastic continuum. A complete set of model equations with disclination driven dislocations taken into account is considered. Within the linear approximation an exact solution for a low-angle wedge disclination is found to be independent from the coupling constants of the theory. As a result, no additional dimensional characteristics (like the core radius of the defect) are involved. The situation changes drastically for 2\pi vortices where two characteristic lengths, l_\phi and l_W, become of importance. The asymptotical behaviour of the solutions for both singular and nonsingular 2\pi vortices is studied. Forces between pairs of vortices are calculated.Comment: 13 pages, published versio

Exceptional flaring activity of the anomalous X-ray pulsar 1E 1547.0-5408

(Abridged) We studied an exceptional period of activity of the anomalous X-ray pulsar 1E 1547.0-5408 in January 2009, during which about 200 bursts were detected by INTEGRAL. The major activity episode happened when the source was outside the field of view of all the INTEGRAL instruments. But we were still able to study the properties of 84 bursts detected simultaneously by the anti-coincidence shield of the spectrometer SPI and by the detector of the imager ISGRI. We find that the luminosity of the 22 January 2009 bursts of 1E 1547.0-5408 was > 1e42 erg/s. This luminosity is comparable to that of the bursts of soft gamma repeaters (SGR) and is at least two orders of magnitude larger than the luminosity of the previously reported bursts from AXPs. Similarly to the SGR bursts, the brightest bursts of 1E 1547.0-5408 consist of a short spike of ~100 ms duration with a hard spectrum, followed by a softer extended tail of 1-10 s duration, which occasionally exhibits pulsations with the source spin period of ~2 s. The observation of AXP bursts with luminosities comparable to the one of SGR bursts strengthens the conjecture that AXPs and SGRs are different representatives of one and the same source type.Comment: 9 pages, 10 figures, accepted to Astronomy & Astrophysic

Physical Electronics

Contains reports on three research projects

Catchment-Scale Analysis Reveals High Cost-Effectiveness of Wetland Buffer Zones as a Remedy to Non-Point Nutrient Pollution in North-Eastern Poland

Large-scale re-establishment of wetland buffer zones (WBZ) along rivers is regarded as an effective measure in order to reduce non-point source nitrogen (N) and phosphorus (P) pollution in agricultural catchments. We estimated efficiency and costs of a hypothetical establishment of WBZs along all watercourses in an agricultural landscape of the lower Narew River catchment (north-eastern Poland, 16,444 km2, amounting to 5% of Poland) by upscaling results obtained in five sub-catchments (1087 km2). Two scenarios were analysed, with either rewetting selected wetland polygons that collect water from larger areas (polygonal WBZs) or reshaping and rewetting banks of rivers (linear WBZs), both considered in all ecologically suitable locations along rivers. Cost calculation included engineering works necessary in order to establish WBZs, costs of land purchase where relevant, and compensation costs of income forgone to farmers (needed only for polygonal WBZs). Polygonal WBZs were estimated in order to remove 11%–30% N and 14%–42% P load from the catchment, whereas linear WBZs were even higher with 33%–82% N and 41%–87% P. Upscaled costs of WBZ establishment for the study area were found to be 8.9 M EUR plus 26.4 M EUR per year (polygonal WBZ scenario) or 170.8 M EUR (linear WBZ scenario). The latter value compares to costs of building about 20 km of an express road. Implementation of buffer zones on a larger scale is thus a question of setting policy priorities rather than financial impossibility

POLAR, an instrument to measure GRB polarization. Design and laboratory tests.

International audienceReliable polarization measurements of photons from Gamma Ray Bursts (GRB) would make the understanding of the GRB phenomenon progress enormously. POLAR is a concept for an instrument that would enable such a measurement. We report about performances predicted by of Monte-Carlo and on laboratory tests to validate some critical aspects of the desig