Musical Actions of Dihedral Groups

The sequence of pitches which form a musical melody can be transposed or inverted. Since the 1970s, music theorists have modeled musical transposition and inversion in terms of an action of the dihedral group of order 24. More recently music theorists have found an intriguing second way that the dihedral group of order 24 acts on the set of major and minor chords. We illustrate both geometrically and algebraically how these two actions are {\it dual}. Both actions and their duality have been used to analyze works of music as diverse as Hindemith and the Beatles.Comment: 27 pages, 11 figures. To appear in the American Mathematical Monthly

q-Deformed quaternions and su(2) instantons

We have recently introduced the notion of a q-quaternion bialgebra and shown its strict link with the SO_q(4)-covariant quantum Euclidean space R_q^4. Adopting the available differential geometric tools on the latter and the quaternion language we have formulated and found solutions of the (anti)selfduality equation [instantons and multi-instantons] of a would-be deformed su(2) Yang-Mills theory on this quantum space. The solutions depend on some noncommuting parameters, indicating that the moduli space of a complete theory should be a noncommutative manifold. We summarize these results and add an explicit comparison between the two SO_q(4)-covariant differential calculi on R_q^4 and the two 4-dimensional bicovariant differential calculi on the bi- (resp. Hopf) algebras M_q(2),GL_q(2),SU_q(2), showing that they essentially coincide.Comment: Latex file, 18 page

The spectrum of screening masses near T_c: predictions from universality

We discuss the spectrum of screening masses in a pure gauge theory near the deconfinement temperature from the point of view of the dimensionally reduced model describing the spontaneous breaking of the center symmetry. Universality arguments can be used to predict the values of the mass ratios in the scaling region of the deconfined phase when the transition is of second order. One such prediction is that the scalar sector of the screening spectrum in SU(2) pure gauge theory contains a bound state of the fundamental excitation, corresponding through universality to the bound state found in the 3D Ising model and phi^4 theory in the broken symmetry phase. A Monte Carlo evaluation of the screening masses in the gauge theory confirms the validity of the prediction. We briefly discuss the possibility of using similar arguments for first order deconfinement transitions, and in particular for the physically relevant case of SU(3).Comment: 12 pages, 3 figures. Some changes in the discussion, added references, results unchanged. Version to appear in Phys. Rev.

Quark-antiquark contribution to the BFKL kernel

The quark-antiquark contribution to the BFKL kernel is calculated. Using the effective vertex for the $q\bar q$ pair production in the Reggeon-Reggeon collision we find this contribution by integrating the square of this vertex over relative transverse momenta and fractions of longitudinal momenta of produced particles.Comment: 12 pages, Late

q-Quaternions and q-deformed su(2) instantons

We construct (anti)instanton solutions of a would-be q-deformed su(2) Yang-Mills theory on the quantum Euclidean space R_q^4 [the SO_q(4)-covariant noncommutative space] by reinterpreting the function algebra on the latter as a q-quaternion bialgebra. Since the (anti)selfduality equations are covariant under the quantum group of deformed rotations, translations and scale change, by applying the latter we can generate new solutions from the one centered at the origin and with unit size. We also construct multi-instanton solutions. As they depend on noncommuting parameters playing the roles of `sizes' and `coordinates of the centers' of the instantons, this indicates that the moduli space of a complete theory will be a noncommutative manifold. Similarly, gauge transformations should be allowed to depend on additional noncommutative parameters.Comment: Latex file, 39 pages. Final version appeared in JM

An X-ray Survey in SA 57 with XMM-Newton

The maximum number density of Active Galactic Nuclei (AGNs), as deduced from X-ray studies, occurs at z<~1, with lower luminosity objects peaking at smaller redshifts. Optical studies lead to a different evolutionary behaviour, with a number density peaking at z~2 independently of the intrinsic luminosity, but this result is limited to active nuclei brighter than the host galaxy. A selection based on optical variability can detect low luminosity AGNs (LLAGNs), where the host galaxy light prevents the identification by non-stellar colours. We want to collect X-ray data in a field where it exists an optically-selected sample of "variable galaxies'', i.e. variable objects with diffuse appearance, to investigate the X-ray and optical properties of the population of AGNs, particularly of low luminosity ones, where the host galaxy is visible. We observed a field of 0.2 deg^2 in the Selected Area 57, for 67ks with XMM-Newton. We detected X-ray sources, and we correlated the list with a photographic survey of SA 57, complete to B_J~23 and with available spectroscopic data. We obtained a catalogue of 140 X-ray sources to limiting fluxes 5x10^-16, 2x10^-15 erg/cm^2/s in the 0.5-2 keV and 2-10 keV respectively, 98 of which are identified in the optical bands. The X-ray detection of part of the variability-selected candidates confirms their AGN nature. Diffuse variable objects populate the low luminosity side of the sample. Only 25/44 optically-selected QSOs are detected in X-rays. 15% of all QSOs in the field have X/O<0.1.Comment: 13 pages, 6 figures, 4 tables, A&A in pres

Personalization framework for adaptive robotic feeding assistance

The final publication is available at link.springer.comThe deployment of robots at home must involve robots with pre-defined skills and the capability of personalizing their behavior by non-expert users. A framework to tackle this personalization is presented and applied to an automatic feeding task. The personalization involves the caregiver providing several examples of feeding using Learning-by- Demostration, and a ProMP formalism to compute an overall trajectory and the variance along the path. Experiments show the validity of the approach in generating different feeding motions to adapt to user’s preferences, automatically extracting the relevant task parameters. The importance of the nature of the demonstrations is also assessed, and two training strategies are compared. © Springer International Publishing AG 2016.Peer ReviewedPostprint (author's final draft

A search for changing-look AGN in the Grossan catalog

We observed with XMM-Newton 4 objects selected from the Grossan catalog, with the aim to search for new 'changing-look' AGN. The sample includes all the sources which showed in subsequent observations a flux much lower than the one measured with HEAO A-1: NGC 7674, NGC 4968, IRAS 13218+0552 and NGC 1667. None of the sources was caught in a high flux state during the XMM-Newton observations, whose analysis reveal they are all likely Compton-thick objects. We suggest that, for all the sources, potential problems with the HEAO A-1 source identification and flux measurement prevent us from being certain that the HEAO A-1 data represent a putative 'high' state for these objects. Nonetheless, based on the high flux state and Compton-thin spectrum of its GINGA observation, NGC 7674 represents probably the sixth known case of a 'changing-look' Seyfert 2 galaxy. From the X-ray variability pattern, we can estimate a likely lower limit of a few parsec to the distance of the inner walls of the torus in this object. Remarkably, IRAS 13218+0552 was not detected by XMM-Newton, despite being currently classified as a Seyfert 1 with a large [OIII] flux. However, the original classification was likely to be affected by an extreme velocity outflow component in the emission lines. The object likely harbors an highly obscured AGN and should be re-classified as a Type 2 source.Comment: 11 pages, 12 figures, accepted for publication in A&