The Identity Correspondence Problem and its Applications

In this paper we study several closely related fundamental problems for words and matrices. First, we introduce the Identity Correspondence Problem (ICP): whether a finite set of pairs of words (over a group alphabet) can generate an identity pair by a sequence of concatenations. We prove that ICP is undecidable by a reduction of Post's Correspondence Problem via several new encoding techniques. In the second part of the paper we use ICP to answer a long standing open problem concerning matrix semigroups: "Is it decidable for a finitely generated semigroup S of square integral matrices whether or not the identity matrix belongs to S?". We show that the problem is undecidable starting from dimension four even when the number of matrices in the generator is 48. From this fact, we can immediately derive that the fundamental problem of whether a finite set of matrices generates a group is also undecidable. We also answer several question for matrices over different number fields. Apart from the application to matrix problems, we believe that the Identity Correspondence Problem will also be useful in identifying new areas of undecidable problems in abstract algebra, computational questions in logic and combinatorics on words.Comment: We have made some proofs clearer and fixed an important typo from the published journal version of this article, see footnote 3 on page 1

Coupling the actuator line method to the high order meteorological les model Meso-NH to study wind farm wakes impacts on local meteorology

Offshore wind energy is now reaching the technological maturity, its capacity is increasing all over the world and this trend is projected to continue for several more years. Given this expectation, a better understanding of the relationship between the presence of wind farms and the atmospheric boundary layer is needed. Turbulent wakes produced by wind turbines can significantly impact the flow dynamics within wind farms and downstream of them. Operating offshore parks have already shown losses on energy production and effects on the local climate. In order to analyse the interactions occurring during these impacts, a new tool has been developed. This numerical tool is a coupling between the Actuator Line Method (ALM) and the open-source, non-hydrostatic mesoscale atmospheric model Meso-NH, based on the Large Eddy Simulation (LES) framework. The coupled Meso-NH + ALM system is first validated by using the experimental data obtained during the New MEXICO experiments. In particular, simulated and experimental loadings along the blades are compared. Then, a simulation of an idealized Horns Rev wind farm is performed using met mast measurements and reanalysis data for the “Horns Rev 1 photo case” as initial conditions. This new coupled system allows the exploration of the impact of wind farms on the lower levels of the atmosphere.Fil: Joulin, P. A.. French Institute of Petroleum Énergies nouvelles; Francia. Centre National de Recherches Météorologiques; FranciaFil: Mayol, María Laura. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Centro de Simulación Computacional para Aplicaciones Tecnológicas; ArgentinaFil: Blondel, F.. French Institute of Petroleum Énergies nouvelles; FranciaFil: Masson, Viviana Patricia. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Centre National de Recherches Météorologiques; FranciaFil: Rodier, Q.. Centre National de Recherches Météorologiques; FranciaFil: Lac, C.. Centre National de Recherches Météorologiques; Franci

The supercuspidal representations of p-adic classical groups

Let G be a unitary, symplectic or special orthogonal group over a locally compact non-archimedean local field of odd residual characteristic. We construct many new supercuspidal representations of G, and Bushnell-Kutzko types for these representations. Moreover, we prove that every irreducible supercuspidal representation of G arises from our constructions.Comment: 55 pages -- minor changes from 1st version (mostly in sections 2.2, 4.2 and 6.2). To appear in Inventiones mathematicae, 2008 (DOI is not yet active as at 12 Nov 2007

Top quark production at future lepton colliders in the asymptotic regime

The production of a tt(bar) pair from lepton-antilepton annihilation is considered for values of the center of mass energy much larger than the top mass, typically of the few TeV size. In this regime a number of simplifications occurs that allows to derive the leading asymptotic terms of various observables using the same theoretical description that was used for light quark production. Explicit examples are shown for the Standard Model and the Minimal Supersymmetric Standard Model cases.Comment: 20 pages and 13 figures. e-mail: [email protected]

Magnetism, rotation and accretion in Herbig Ae-Be stars

Studies of stellar magnetism at the pre-main sequence phase can provide important new insights into the detailed physics of the late stages of star formation, and into the observed properties of main sequence stars. This is especially true at intermediate stellar masses, where magnetic fields are strong and globally organised, and therefore most amenable to direct study. This talk reviews recent high-precision ESPaDOnS observations of pre-main sequence Herbig Ae-Be stars, which are yielding qualitatively new information about intermediate-mass stars: the origin and evolution of their magnetic fields, the role of magnetic fields in generating their spectroscopic activity and in mediating accretion in their late formative stages, and the factors influencing their rotational angular momentum.Comment: 8 page

Observations of T-Tauri Stars using HST-GHRS: I. Far Ultraviolet Emission Lines

We have analyzed GHRS data of eight CTTS and one WTTS. The GHRS data consists of spectral ranges 40 A wide centered on 1345, 1400, 1497, 1550, and 1900 A. These UV spectra show strong SiIV, and CIV emission, and large quantities of sharp (~40 km/s) H2 lines. All the H2 lines belong to the Lyman band and all the observed lines are single peaked and optically thin. The averages of all the H2 lines centroids for each star are negative which may indicate that they come from an outflow. We interpret the emission in H2 as being due to fluorescence, mostly by Ly_alpha, and identify seven excitation routes within 4 A of that line. We obtain column densities (10^12 to 10^15 cm^-2) and optical depths (~1 or less) for each exciting transition. We conclude that the populations are far from being in thermal equilibrium. We do not observe any lines excited from the far blue wing of Ly_alpha, which implies that the molecular features are excited by an absorbed profile. SiIV and CIV (corrected for H2 emission) have widths of ~200 km/s, and an array of centroids (blueshifted lines, centered, redshifted). These characteristics are difficult to understand in the context of current models of the accretion shock. For DR Tau we observe transient strong blueshifted emission, perhaps the a result of reconnection events in the magnetosphere. We also see evidence of multiple emission regions for the hot lines. While CIV is optically thin in most stars in our sample, SiIV is not. However, CIV is a good predictor of SiIV and H2 emission. We conclude that most of the flux in the hot lines may be due to accretion processes, but the line profiles can have multiple and variable components.Comment: 67 pages, 19 figures, Accepted in Ap

Fast-neutron induced background in LaBr3:Ce detectors

The response of a scintillation detector with a cylindrical 1.5-inch LaBr3:Ce crystal to incident neutrons has been measured in the energy range En = 2-12 MeV. Neutrons were produced by proton irradiation of a Li target at Ep = 5-14.6 MeV with pulsed proton beams. Using the time-of-flight information between target and detector, energy spectra of the LaBr3:Ce detector resulting from fast neutron interactions have been obtained at 4 different neutron energies. Neutron-induced gamma rays emitted by the LaBr3:Ce crystal were also measured in a nearby Ge detector at the lowest proton beam energy. In addition, we obtained data for neutron irradiation of a large-volume high-purity Ge detector and of a NE-213 liquid scintillator detector, both serving as monitor detectors in the experiment. Monte-Carlo type simulations for neutron interactions in the liquid scintillator, the Ge and LaBr3:Ce crystals have been performed and compared with measured data. Good agreement being obtained with the data, we present the results of simulations to predict the response of LaBr3:Ce detectors for a range of crystal sizes to neutron irradiation in the energy range En = 0.5-10 MeVComment: 28 pages, 10 figures, 4 Table

Information and Discrimination from b Quark Production on Z Resonance

We introduce and define operatively in a model independent way a new ``heavy" b-vertexparameter, $\eta_b$, that can be derived from the measurement of a special polarization asymmetry for production of b-quarks on Z resonance. We show that the combination of the measurement of $\eta_b$ with that of a second and previously defined ``heavy" b-vertex parameter $\delta_{bV}$ can discriminate a number of models of New Physics that remain associated to different ``trajectories" in the plane of the variations of the two parameters. This is shown in particular for some popular SUSY and technicolor-type models. In general, this discrimination is possible if a measurement of \underline{both} parameters is performed.Comment: 22 pages, 6 figures available by air mail upon request, (e-mail [email protected] PM/94-04, UTS-DFT-94-02 .( revised version with corrected references

ISGRI: the INTEGRAL Soft Gamma-Ray Imager

For the first time in the history of high energy astronomy, a large CdTe gamma-ray camera is operating in space. ISGRI is the low-energy camera of the IBIS telescope on board the INTEGRAL satellite. This paper details its design and its in-flight behavior and performances. Having a sensitive area of 2621 cm$^2$ with a spatial resolution of 4.6 mm, a low threshold around 12 keV and an energy resolution of $\sim$ 8% at 60 keV, ISGRI shows absolutely no signs of degradation after 9 months in orbit. All aspects of its in-flight behavior and scientific performance are fully nominal, and in particular the observed background level confirms the expected sensitivity of 1 milliCrab for a 10$^6$s observation.Comment: INTEGRAL A&A special issu

Interplay between telecommunications and face-to-face interactions - a study using mobile phone data

In this study we analyze one year of anonymized telecommunications data for over one million customers from a large European cellphone operator, and we investigate the relationship between people's calls and their physical location. We discover that more than 90% of users who have called each other have also shared the same space (cell tower), even if they live far apart. Moreover, we find that close to 70% of users who call each other frequently (at least once per month on average) have shared the same space at the same time - an instance that we call co-location. Co-locations appear indicative of coordination calls, which occur just before face-to-face meetings. Their number is highly predictable based on the amount of calls between two users and the distance between their home locations - suggesting a new way to quantify the interplay between telecommunications and face-to-face interactions