14,711 research outputs found
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 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
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