82 research outputs found
Classes of Symmetric Cayley Graphs over Finite Abelian Groups of Degrees 4 and 6
The present work is devoted to characterize the family of symmetric
undirected Cayley graphs over finite Abelian groups for degrees 4 and 6.Comment: 12 pages. A previous version of some of the results in this paper
where first announced at 2010 International Workshop on Optimal
Interconnection Networks (IWONT 2010). It is accessible at
http://upcommons.upc.edu/revistes/handle/2099/1037
Perfect Mannheim, Lipschitz and Hurwitz weight codes
In this paper, upper bounds on codes over Gaussian integers, Lipschitz
integers and Hurwitz integers with respect to Mannheim metric, Lipschitz and
Hurwitz metric are given.Comment: 21 page
Perfect 1-error-correcting Lipschitz weight codes
Let be a Lipschitz prime and . Perfect 1-error-correcting codes in are constructed for every prime number . This completes a result of the authors in an earlier work, emph{Perfect Mannheim, Lipschitz and Hurwitz weight codes}, (Mathematical Communications, Vol 19, No 2, pp. 253 -- 276 (2014)), where a construction is given in the case
Symmetric Interconnection Networks from Cubic Crystal Lattices
Torus networks of moderate degree have been widely used in the supercomputer
industry. Tori are superb when used for executing applications that require
near-neighbor communications. Nevertheless, they are not so good when dealing
with global communications. Hence, typical 3D implementations have evolved to
5D networks, among other reasons, to reduce network distances. Most of these
big systems are mixed-radix tori which are not the best option for minimizing
distances and efficiently using network resources. This paper is focused on
improving the topological properties of these networks.
By using integral matrices to deal with Cayley graphs over Abelian groups, we
have been able to propose and analyze a family of high-dimensional grid-based
interconnection networks. As they are built over -dimensional grids that
induce a regular tiling of the space, these topologies have been denoted
\textsl{lattice graphs}. We will focus on cubic crystal lattices for modeling
symmetric 3D networks. Other higher dimensional networks can be composed over
these graphs, as illustrated in this research. Easy network partitioning can
also take advantage of this network composition operation. Minimal routing
algorithms are also provided for these new topologies. Finally, some practical
issues such as implementability and preliminary performance evaluations have
been addressed
Codes over Hurwitz integers
In this study, we obtain new classes of linear codes over Hurwitz integers
equipped with a new metric. We refer to the metric as Hurwitz metric. The codes
with respect to Hurwitz metric use in coded modu- lation schemes based on
quadrature amplitude modulation (QAM)-type constellations, for which neither
Hamming metric nor Lee metric. Also, we define decoding algorithms for these
codes when up to two coordinates of a transmitted code vector are effected by
error of arbitrary Hurwitz weight.Comment: 11 page
Structural stability of meandering-hyperbolic group actions
In his 1985 paper Sullivan sketched a proof of his structural stability
theorem for group actions satisfying certain expansion-hyperbolicity axioms. In
this paper we relax Sullivan's axioms and introduce a notion of meandering
hyperbolicity for group actions on general metric spaces. This generalization
is substantial enough to encompass actions of certain non-hyperbolic groups,
such as actions of uniform lattices in semisimple Lie groups on flag manifolds.
At the same time, our notion is sufficiently robust and we prove that
meandering-hyperbolic actions are still structurally stable. We also prove some
basic results on meandering-hyperbolic actions and give other examples of such
actions.Comment: 58 pages, 5 figures; [v2] Corollary 3.19 is wrong and thus removed;
[v3] Introduced a new notion of meandering hyperbolicity, generalized the
main structural stability theorem even further, and added a new Section 5 on
uniform lattices and their structural stabilit
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