7,522 research outputs found
Total Representations
Almost all representations considered in computable analysis are partial. We
provide arguments in favor of total representations (by elements of the Baire
space). Total representations make the well known analogy between numberings
and representations closer, unify some terminology, simplify some technical
details, suggest interesting open questions and new invariants of topological
spaces relevant to computable analysis.Comment: 30 page
Efficient Schemes for Computing α-tree Representations
International audienceHierarchical image representations have been addressed by various models by the past, the max-tree being probably its best representative within the scope of Mathematical Morphology. However, the max-tree model requires to impose an ordering relation between pixels, from the lowest values (root) to the highest (leaves). Recently, the α-tree model has been introduced to avoid such an ordering. Indeed, it relies on image quasi-flat zones, and as such focuses on local dissimilarities. It has led to successful attempts in remote sensing and video segmentation. In this paper, we deal with the problem of α-tree computation, and propose several efficient schemes which help to ensure real-time (or near-real time) morphological image processing
New D=4 gauged supergravities from N=4 orientifolds with fluxes
We consider classes of T_6 orientifolds, where the orientifold projection
contains an inversion I_{9-p} on 9-p coordinates, transverse to a Dp-brane. In
absence of fluxes, the massless sector of these models corresponds to diverse
forms of N=4 supergravity, with six bulk vector multiplets coupled to N=4
Yang--Mills theory on the branes. They all differ in the choice of the duality
symmetry corresponding to different embeddings of SU(1,1)\times SO(6,6+n) in
Sp(24+2n,R), the latter being the full group of duality rotations. Hence, these
Lagrangians are not related by local field redefinitions. When fluxes are
turned on one can construct new gaugings of N=4 supergravity, where the twelve
bulk vectors gauge some nilpotent algebra which, in turn, depends on the choice
of fluxes.Comment: 51 pages, 1 figure. Latex. Reference added. Typos corrected.
Discussion on gaugings expande
Regularization of Toda lattices by Hamiltonian reduction
The Toda lattice defined by the Hamiltonian with , which
exhibits singular (blowing up) solutions if some of the , can be
viewed as the reduced system following from a symmetry reduction of a subsystem
of the free particle moving on the group G=SL(n,\Real ). The subsystem is
, where consists of the determinant one matrices with
positive principal minors, and the reduction is based on the maximal nilpotent
group . Using the Bruhat decomposition we show that the full
reduced system obtained from , which is perfectly regular, contains
Toda lattices. More precisely, if is odd the reduced system
contains all the possible Toda lattices having different signs for the .
If is even, there exist two non-isomorphic reduced systems with different
constituent Toda lattices. The Toda lattices occupy non-intersecting open
submanifolds in the reduced phase space, wherein they are regularized by being
glued together. We find a model of the reduced phase space as a hypersurface in
{\Real}^{2n-1}. If for all , we prove for that the
Toda phase space associated with is a connected component of this
hypersurface. The generalization of the construction for the other simple Lie
groups is also presented.Comment: 42 pages, plain TeX, one reference added, to appear in J. Geom. Phy
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