Inverse monoids and immersions of 2-complexes

It is well known that under mild conditions on a connected topological space $\mathcal X$, connected covers of $\mathcal X$ may be classified via conjugacy classes of subgroups of the fundamental group of $\mathcal X$. In this paper, we extend these results to the study of immersions into 2-dimensional CW-complexes. An immersion $f : {\mathcal D} \rightarrow \mathcal C$ between CW-complexes is a cellular map such that each point $y \in {\mathcal D}$ has a neighborhood $U$ that is mapped homeomorphically onto $f(U)$ by $f$. In order to classify immersions into a 2-dimensional CW-complex $\mathcal C$, we need to replace the fundamental group of $\mathcal C$ by an appropriate inverse monoid. We show how conjugacy classes of the closed inverse submonoids of this inverse monoid may be used to classify connected immersions into the complex

P16-52. HIV-activated human plasmacytoid DCs induce Tregs through an indoleamine 2,3-dioxygenase-dependent mechanism

International audiencen.

Regular obstructed categories and TQFT

A proposal of the concept of $n$-regular obstructed categories is given. The corresponding regularity conditions for mappings, morphisms and related structures in categories are considered. An n-regular TQFT is introduced. It is shown the connection of time reversibility with the regularity.Comment: 22 pages in Latex. To be published in J. Math. Phy

Light and Motion in SDSS Stripe 82: The Catalogues

We present a new public archive of light-motion curves in Sloan Digital Sky Survey (SDSS) Stripe 82, covering 99 deg in right ascension from RA = 20.7 h to 3.3 h and spanning 2.52 deg in declination from Dec = -1.26 to 1.26 deg, for a total sky area of ~249 sq deg. Stripe 82 has been repeatedly monitored in the u, g, r, i and z bands over a seven-year baseline. Objects are cross-matched between runs, taking into account the effects of any proper motion. The resulting catalogue contains almost 4 million light-motion curves of stellar objects and galaxies. The photometry are recalibrated to correct for varying photometric zeropoints, achieving ~20 mmag and ~30 mmag root-mean-square (RMS) accuracy down to 18 mag in the g, r, i and z bands for point sources and extended sources, respectively. The astrometry are recalibrated to correct for inherent systematic errors in the SDSS astrometric solutions, achieving ~32 mas and ~35 mas RMS accuracy down to 18 mag for point sources and extended sources, respectively. For each light-motion curve, 229 photometric and astrometric quantities are derived and stored in a higher-level catalogue. On the photometric side, these include mean exponential and PSF magnitudes along with uncertainties, RMS scatter, chi^2 per degree of freedom, various magnitude distribution percentiles, object type (stellar or galaxy), and eclipse, Stetson and Vidrih variability indices. On the astrometric side, these quantities include mean positions, proper motions as well as their uncertainties and chi^2 per degree of freedom. The here presented light-motion curve catalogue is complete down to r~21.5 and is at present the deepest large-area photometric and astrometric variability catalogue available.Comment: MNRAS accepte

Preliminary Parallaxes of 40 L and T Dwarfs from the U.S. Naval Observatory Infrared Astrometry Program

We present preliminary trigonometric parallaxes and proper motions for 22 L dwarfs and 18 T dwarfs measured using the ASTROCAM infrared imager. Relative to absolute parallax corrections are made by employing 2MASS and/or SDSS photometry for reference frame stars. We combine USNO infrared and optical parallaxes with the best available CIT system photometry to determine M_J, M_H, and M_K values for 37 L dwarfs between spectral types L0 to L8 and 19 T dwarfs between spectral types T0.5 and T8 and present selected absolute magnitude versus spectral type and color diagrams, based on these results. Luminosities and temperatures are estimated for these objects. Of special interest are the distances of several objects which are at or near the L-T dwarf boundary so that this important transition can be better understood. The previously reported early-mid T dwarf luminosity excess is clearly confirmed and found to be present at J, H, and K. The large number of objects that populate this luminosity excess region indicates that it cannot be due entirely to selection effects. The T dwarf sequence is extended to M_J~16.9 by 2MASS J041519-0935 which, at d = 5.74 pc, is found to be the least luminous [log(L/L_sun)=-5.58] and coldest (T_eff~760 K) brown dwarf known. Combining results from this paper with earlier USNO CCD results we find that, in contrast to the L dwarfs, there are no examples of low velocity (V_tan < 20 km/s) T dwarfs. We briefly discuss future directions for the USNO infrared astrometry program.Comment: 73 pages, 9 figures, 9 tables, accepted for publication in The Astronomical Journa

Equations over free inverse monoids with idempotent variables

We introduce the notion of idempotent variables for studying equations in inverse monoids. It is proved that it is decidable in singly exponential time (DEXPTIME) whether a system of equations in idempotent variables over a free inverse monoid has a solution. The result is proved by a direct reduction to solve language equations with one-sided concatenation and a known complexity result by Baader and Narendran: Unification of concept terms in description logics, 2001. We also show that the problem becomes DEXPTIME hard , as soon as the quotient group of the free inverse monoid has rank at least two. Decidability for systems of typed equations over a free inverse monoid with one irreducible variable and at least one unbalanced equation is proved with the same complexity for the upper bound. Our results improve known complexity bounds by Deis, Meakin, and Senizergues: Equations in free inverse monoids, 2007. Our results also apply to larger families of equations where no decidability has been previously known.Comment: 28 pages. The conference version of this paper appeared in the proceedings of 10th International Computer Science Symposium in Russia, CSR 2015, Listvyanka, Russia, July 13-17, 2015. Springer LNCS 9139, pp. 173-188 (2015