Galois representations, embedding problems and modular forms

To an odd irreducible 2-dimensional complex linear representation of the absolute Galois group of the field Q of rational numbers, a modular form of weight 1 is associated (modulo Artin's conjecture on the L-series of the representation in the icosahedral case). In addition, linear liftings of 2-dimensional projective Galois representations are related to solutions of certain Galois embedding problems. In this paper we present some recent results on the existence of liftings of projective representations and on the explicit resolution of embedding problems associated to orthogonal Galois representations, and explain how these results can be used to construct modular forms.

Three-dimensional magnetic resonance myocardial motion tracking from a single image plane.

Three-dimensional imaging for the quantification of myocardial motion is a key step in the evaluation of cardiac disease. A tagged magnetic resonance imaging method that automatically tracks myocardial displacement in three dimensions is presented. Unlike other techniques, this method tracks both in-plane and through-plane motion from a single image plane without affecting the duration of image acquisition. A small z-encoding gradient is subsequently added to the refocusing lobe of the slice-selection gradient pulse in a slice following CSPAMM acquisition. An opposite polarity z-encoding gradient is added to the orthogonal tag direction. The additional z-gradients encode the instantaneous through plane position of the slice. The vertical and horizontal tags are used to resolve in-plane motion, while the added z-gradients is used to resolve through-plane motion. Postprocessing automatically decodes the acquired data and tracks the three-dimensional displacement of every material point within the image plane for each cine frame. Experiments include both a phantom and in vivo human validation. These studies demonstrate that the simultaneous extraction of both in-plane and through-plane displacements and pathlines from tagged images is achievable. This capability should open up new avenues for the automatic quantification of cardiac motion and strain for scientific and clinical purposes.

Das römische Theater von Avenches/Aventicum : Architektur, Baugeschichte, kulturhistorische Aspekte

Résumée Le théâtre romain d'Aventicum s'inscrit entre la petite ville moderne d'Avenches et le village de Donatyre, au pied d'une colline en pente douce délimitant au sud-est la plaine de la Broye. Il se situe à l'ouest des quartiers urbains antiques, construits selon un plan orthogonal, et s'intègre à une zone comptant divers temples et édifices publics. Dès l'hiver 1889/1890, l'Association Pro Aventico nouvellement fondée lança les premières fouilles archéologiques. Jusqu'en 1914, on dégagea les parties originales de la maçonnerie tout en assurant la restauration de l'édifice. En 1926/1927 et de 1939 à 1942 auront lieu d'autres fouilles de grande envergure, accompagnées de mesures de conservation. En 2001, la Fondation Pro Aventico lança un projet visant à étudier l'histoire de la construction ainsi que l'architecture du monument, alors connues en partie seulement. Sur la base de vestiges attestant la présence d'édifices antérieurs au théâtre, on définira pour la construction de ce dernier un terminus post quem entre 100 et 120 ap. J.-C. Comme l'indique l'étude du plan au sol, ce projet nécessita une importante planification. L'édifice lui-même se constitue d'une zone en demi-cercle réservée au public, dont les substructions indiquent qu'elle était partiellement isolée des autres. La cavea, subdivisée en trois secteurs concentriques, se termine par le bâtiment des halles et par les aditus; on relèvera que les rangées supérieures réservées aux spectateurs s'étendaient sans doute au-delà des halles et jusqu'à la façade. Les aditus permettaient d'accéder à la zone de l'orchestra et de la scène, dominée par une plate-forme de plan rectangulaire et bordée d'une proédrie. On disposait de deux voies d'accès différentes: l'une à l'avant, par les arcades des halles, et l'une à l'arrière, pratiquée dans le mur en demi-cercle; apparemment, on ne pouvait pénétrer que dans la partie centrale de ce dernier. On ne parvient à restituer que partiellement les voies de circulation dans les substructions de la cavea, en raison de leur piètre état de conservation. On a par contre pu repérer le deambulatorium, à la périphérie, ainsi que cinq vomitoria sur la première praecinctio et six vomitoria sur la seconde praecinctio. On peut admettre, sans toutefois disposer d'arguments à toute épreuve, que la troisième rangée, en haut, était accessible par des cages d'escaliers conduisant à la summa cavea. Ces hypothèses, fondées essentiellement sur le plan au sol de l'édifice et touchant aux voies de circulation, sont corroborées par une restitution des gradins des parties en élévation, aujourd'hui disparus. Quelques éléments architecturaux fournissent des arguments décisifs pour cette restitution, comme par exemple un bloc de gradin qui permet de conclure à un pendage de la cavea de 26.5°. On peut par ailleurs démontrer que le module architectural défini sur la base du plan au sol fut également appliqué lors de la planification de l'élévation. Grâce à des fragments de corniche, à deux chapiteaux de pilastre ornés de feuilles d'acanthe, à une base de pilastre engagée in situ dans la maçonnerie restaurée, et en tenant compte du module architectural, on peut proposer une reconstitution approximative de la composition de la façade de l'enceinte en demi-cercle. Si les structures architecturales révèlent que le théâtre fut planifié et édifié selon un seul et unique concept, on observe cependant quelques transformations et modifications au cours du temps. D'une part, on décèle en divers endroits des traces de réparation et de consolidation, visant sans doute à stabiliser un bâtiment ayant visiblement subi des dégâts. Par ailleurs, on a également entrepris des modifications structurelles ou fonctionnelles, comme l'édification ultérieure du postscaenium le long du mur de scène extérieur. Dans un contexte identique, on relèvera également deux murs flanquant les basiliques, qu'on suppose être en relation avec l'agrandissement du complexe architectural du temple du Cigognier et du théâtre, augmenté des deux temples édifiés au milieu du 2e s. ap. J.-C. au lieu-dit Au Lavoëx. L'excavation, au cours du dernier tiers du IIIe siècle ap. J.-C., d'un fossé de près de 6 m de large pour 1.5 m de profondeur tout autour de l'édifice fit du théâtre un véritable lieu fortifié. Au-dessus du fossé, on a pu relever une séquence stratigraphique témoignant d'une activité d'habitation à proximité du théâtre pour la période allant du IVe au VIIe siècle ap. J.-C. Il s'agit de l'un des rares cas où l'on peut, à Avenches, évoquer la présence d'un habitat de la période du Haut Moyen Age.

One-sided jet at milliarcsecond scales in LSI+61·303

We present Very Long Baseline Interferometry (VLBI) observations of the high mass X-ray binary LSI+61303, carried out with the European VLBI Network (EVN). Over the 11 hour observing run, performed 10 days after a radio outburst, the radio source showed a constant flux density, which allowed sensitive imaging of the emission distribution. The structure in the map shows a clear extension to the southeast. Comparing our data with previous VLBI observations we interpret the extension as a collimated radio jet as found in several other X-ray binaries. Assuming that the structure is the result of an expansion that started at the onset of the outburst, we derive an apparent expansion velocity of 0.003 c, which, in the context of Doppler boosting, corresponds to an intrinsic velocity of at least 0.4 c for an ejection close to the line of sight. From the apparent velocity in all available epochs we are able to establish variations in the ejection angle which imply a precessing accretion disk. Finally we point out that LSI+61303, like SS433 and Cygnus X-1, shows evidence for an emission region almost orthogonal to the relativistic jet.

Testing Spatial Autocorrelation in Weighted Networks : the Modes Permutation Test

In a weighted spatial network, as specified by an exchange matrix, the variances of the spatial values are inversely proportional to the size of the regions. Spatial values are no more exchangeable under independence, thus weakening the rationale for ordinary permutation and bootstrap tests of spatial autocorrelation. We propose an alternative permutation test for spatial autocorrelation, based upon exchangeable spatial modes, constructed as linear orthogonal combinations of spatial values. The coefficients obtain as eigenvectors of the standardised exchange matrix appearing in spectral clustering, and generalise to the weighted case the concept of spatial filtering for connectivity matrices. Also, two proposals aimed at transforming an acessibility matrix into a exchange matrix with with a priori fixed margins are presented. Two examples (inter-regional migratory flows and binary adjacency networks) illustrate the formalism, rooted in the theory of spectral decomposition for reversible Markov chains.

Generalized Schmidt decomposition and classification of three-quantum-bit states

We prove for any pure three-quantum-bit state the existence of local bases which allow one to build a set of five orthogonal product states in terms of which the state can be written in a unique form. This leads to a canonical form which generalizes the two-quantum-bit Schmidt decomposition. It is uniquely characterized by the five entanglement parameters. It leads to a complete classification of the three-quantum-bit states. It shows that the right outcome of an adequate local measurement always erases all entanglement between the other two parties.

Numerical investigation of iso-spectral cavities built from trinagles

We present computational approaches as alternatives to a recent microwave cavity experiment by S. Sridhar and A. Kudrolli [Phys. Rev. Lett. 72, 2175 (1994)] on isospectral cavities built from triangles. A straightforward proof of isospectrality is given, based on the mode-matching method. Our results show that the experiment is accurate to 0.3% for the first 25 states. The level statistics resemble those of a Gaussian orthogonal ensemble when the integrable part of the spectrum is removed.

Epiphysenfugenverletzungen der distalen Tibia. Sinnvolle Mehrinformation durch die MRT? [Epiphyseal injuries of the distal tibia. Does MRI provide useful additional information?]

Plain film radiography often underestimates the extent of injury in children with epiphyseal fracture. Especially Salter-Harris V fractures (crush fracture of the epiphyseal plate) are often primarily not detected. MRI of the ankle was performed in 10 children aged 9-17 (mean 14) years with suspected epiphyseal injury using 1.0-T Magnetom Expert. The fractures were classified according to the Salter-Harris-Rang-Odgen classification and compared with the results of plain radiography. In one case MRI could exclude epiphyseal injury; in four cases the MRI findings changed the therapeutic management. The visualisation of the fracture in three orthogonal planes and the possibility of detection of cartilage and ligamentous injury in MR imaging makes this method superior to conventional radiography and CT. With respect to radiation exposure MRI instead of CT should be used for the diagnosis of epiphyseal injuries in children.

A steroidomic approach for biomarkers discovery in doping control.

Anti-doping authorities have high expectations of the athlete steroidal passport (ASP) for anabolic-androgenic steroids misuse detection. However, it is still limited to the monitoring of known well-established compounds and might greatly benefit from the discovery of new relevant biomarkers candidates. In this context, steroidomics opens the way to the untargeted simultaneous evaluation of a high number of compounds. Analytical platforms associating the performance of ultra-high pressure liquid chromatography (UHPLC) and the high mass-resolving power of quadrupole time-of-flight (QTOF) mass spectrometers are particularly adapted for such purpose. An untargeted steroidomic approach was proposed to analyse urine samples from a clinical trial for the discovery of relevant biomarkers of testosterone undecanoate oral intake. Automatic peak detection was performed and a filter of reference steroid metabolites mass-to-charge ratio (m/z) values was applied to the raw data to ensure the selection of a subset of steroid-related features. Chemometric tools were applied for the filtering and the analysis of UHPLC-QTOF-MS(E) data. Time kinetics could be assessed with N-way projections to latent structures discriminant analysis (N-PLS-DA) and a detection window was confirmed. Orthogonal projections to latent structures discriminant analysis (O-PLS-DA) classification models were evaluated in a second step to assess the predictive power of both known metabolites and unknown compounds. A shared and unique structure plot (SUS-plot) analysis was performed to select the most promising unknown candidates and receiver operating characteristic (ROC) curves were computed to assess specificity criteria applied in routine doping control. This approach underlined the pertinence to monitor both glucuronide and sulphate steroid conjugates and include them in the athletes passport, while promising biomarkers were also highlighted.

Bi-planar 2D-to-3D registration in Fourier domain for stereoscopic X-ray motion tracking

In this paper we present a new method to track bonemovements in stereoscopic X-ray image series of the kneejoint. The method is based on two different X-ray imagesets: a rotational series of acquisitions of the stillsubject knee that will allow the tomographicreconstruction of the three-dimensional volume (model),and a stereoscopic image series of orthogonal projectionsas the subject performs movements. Tracking the movementsof bones throughout the stereoscopic image series meansto determine, for each frame, the best pose of everymoving element (bone) previously identified in the 3Dreconstructed model. The quality of a pose is reflectedin the similarity between its simulated projections andthe actual radiographs. We use direct Fourierreconstruction to approximate the three-dimensionalvolume of the knee joint. Then, to avoid the expensivecomputation of digitally rendered radiographs (DRR) forpose recovery, we reformulate the tracking problem in theFourier domain. Under the hypothesis of parallel X-raybeams, we use the central-slice-projection theorem toreplace the heavy 2D-to-3D registration of projections inthe signal domain by efficient slice-to-volumeregistration in the Fourier domain. Focusing onrotational movements, the translation-relevant phaseinformation can be discarded and we only consider scalarFourier amplitudes. The core of our motion trackingalgorithm can be implemented as a classical frame-wiseslice-to-volume registration task. Preliminary results onboth synthetic and real images confirm the validity ofour approach.

Generalized Weyl solutions

It was shown by Weyl that the general static axisymmetric solution of the vacuum Einstein equations in four dimensions is given in terms of a single axisymmetric solution of the Laplace equation in three-dimensional flat space. Weyls construction is generalized here to arbitrary dimension D>~4. The general solution of the D-dimensional vacuum Einstein equations that admits D-2 orthogonal commuting non-null Killing vector fields is given either in terms of D-3 independent axisymmetric solutions of Laplaces equation in three-dimensional flat space or by D-4 independent solutions of Laplaces equation in two-dimensional flat space. Explicit examples of new solutions are given. These include a five-dimensional asymptotically flat black ring with an event horizon of topology S1S2 held in equilibrium by a conical singularity in the form of a disk.

eVOC: a controlled vocabulary for unifying gene expression data.

Expression data contribute significantly to the biological value of the sequenced human genome, providing extensive information about gene structure and the pattern of gene expression. ESTs, together with SAGE libraries and microarray experiment information, provide a broad and rich view of the transcriptome. However, it is difficult to perform large-scale expression mining of the data generated by these diverse experimental approaches. Not only is the data stored in disparate locations, but there is frequent ambiguity in the meaning of terms used to describe the source of the material used in the experiment. Untangling semantic differences between the data provided by different resources is therefore largely reliant on the domain knowledge of a human expert. We present here eVOC, a system which associates labelled target cDNAs for microarray experiments, or cDNA libraries and their associated transcripts with controlled terms in a set of hierarchical vocabularies. eVOC consists of four orthogonal controlled vocabularies suitable for describing the domains of human gene expression data including Anatomical System, Cell Type, Pathology and Developmental Stage. We have curated and annotated 7016 cDNA libraries represented in dbEST, as well as 104 SAGE libraries,with expression information,and provide this as an integrated, public resource that allows the linking of transcripts and libraries with expression terms. Both the vocabularies and the vocabulary-annotated libraries can be retrieved from http://www.sanbi.ac.za/evoc/. Several groups are involved in developing this resource with the aim of unifying transcript expression information.

Particle orientation distribution in Y-Fe2O3magnetic tapes by Mössbauer and hysteresis loop measurements

The particle orientation in several Y-Fe2O3magnetic tapes has been quantitatively evaluated by using the data of both Mössbauer and hysteresis loop measurements performed in the three orthogonal directions. A texture function has been obtained as a development of real harmonics. The profile of the texture function gives the quality of the different magnetic tapes. A different degree of particle orientation at the surface of the tape is evidenced by means of conversion electron Mössbauer spectra.

Quantum critical effects in mean-field glassy systems

We consider the effects of quantum fluctuations in mean-field quantum spin-glass models with pairwise interactions. We examine the nature of the quantum glass transition at zero temperature in a transverse field. In models (such as the random orthogonal model) where the classical phase transition is discontinuous an analysis using the static approximation reveals that the transition becomes continuous at zero temperature.