31,283 research outputs found
Two-dimensional patterns with distinct differences; constructions, bounds, and maximal anticodes
A two-dimensional (2-D) grid with dots is called a configuration with distinct differences if any two lines which connect two dots are distinct either in their length or in their slope. These configurations are known to have many applications such as radar, sonar, physical alignment, and time-position synchronization. Rather than restricting dots to lie in a square or rectangle, as previously studied, we restrict the maximum distance between dots of the configuration; the motivation for this is a new application of such configurations to key distribution in wireless sensor networks. We consider configurations in the hexagonal grid as well as in the traditional square grid, with distances measured both in the Euclidean metric, and in the Manhattan or hexagonal metrics. We note that these configurations are confined inside maximal anticodes in the corresponding grid. We classify maximal anticodes for each diameter in each grid. We present upper bounds on the number of dots in a pattern with distinct differences contained in these maximal anticodes. Our bounds settle (in the negative) a question of Golomb and Taylor on the existence of honeycomb arrays of arbitrarily large size. We present constructions and lower bounds on the number of dots in configurations with distinct differences contained in various 2-D shapes (such as anticodes) by considering periodic configurations with distinct differences in the square grid
Experimental Constraints on the Neutralino-Nucleon Cross Section
In the light of recent experimental results for the direct detection of dark
matter, we analyze in the framework of SUGRA the value of the
neutralino-nucleon cross section. We study how this value is modified when the
usual assumptions of universal soft terms and GUT scale are relaxed. In
particular we consider scenarios with non-universal scalar and gaugino masses
and scenarios with intermediate unification scale. We also study superstring
constructions with D-branes, where a combination of the above two scenarios
arises naturally. In the analysis we take into account the most recent
experimental constraints, such as the lower bound on the Higgs mass, the branching ratio, and the muon .Comment: References added, bsgamma upper bound improved, results unchanged,
Talk given at Corfu Summer Institute on Elementary Particle Physics, August
31-September 20, 200
Folding, Tiling, and Multidimensional Coding
Folding a sequence into a multidimensional box is a method that is used
to construct multidimensional codes. The well known operation of folding is
generalized in a way that the sequence can be folded into various shapes.
The new definition of folding is based on lattice tiling and a direction in the
-dimensional grid. There are potentially different folding
operations. Necessary and sufficient conditions that a lattice combined with a
direction define a folding are given. The immediate and most impressive
application is some new lower bounds on the number of dots in two-dimensional
synchronization patterns. This can be also generalized for multidimensional
synchronization patterns. We show how folding can be used to construct
multidimensional error-correcting codes and to generate multidimensional
pseudo-random arrays
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