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475
THE RANDOM EDGE SIMPLEX ALGORITHM ON DUAL CYCLIC 4POLYTOPES
, 2006
"... The simplex algorithm using the random edge pivotrule on any realization of a dual cyclic 4polytope with n facets does not take more than O(n) pivotsteps. This even holds for general abstract objective functions (AOF) / acyclic unique sink orientations (AUSO). The methods can be used to show a ..."
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The simplex algorithm using the random edge pivotrule on any realization of a dual cyclic 4polytope with n facets does not take more than O(n) pivotsteps. This even holds for general abstract objective functions (AOF) / acyclic unique sink orientations (AUSO). The methods can be used to show
A realtime algorithm for mobile robot mapping with applications to multirobot and 3D mapping
 In IEEE International Conference on Robotics and Automation
, 2000
"... We present an incremental method for concurrent mapping and localization for mobile robots equipped with 2D laser range finders. The approach uses a fast implementation of scanmatching for mapping, paired with a samplebased probabilistic method for localization. Compact 3D maps are generated using ..."
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Cited by 318 (36 self)
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using a multiresolution approach adopted from the computer graphics literature, fed by data from a dual laser system. Our approach builds 3D maps of large, cyclic environments in realtime. It is remarkably robust. Experimental results illustrate that accurate maps of large, cyclic environments can
Long Monotone Paths on Simple 4Polytopes
, 2004
"... ... of vertices in a monotone path along edges of a ddimensional polytope with n facets can be as large as conceivably possible: Is M(d, n) = Mubt(d, n), the maximal number of vertices that a dpolytope with n facets can have according to the Upper Bound Theorem? We show that in dimension d = 4, t ..."
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Cited by 2 (1 self)
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, the answer is “yes”, despite the fact that it is “no” if we restrict ourselves to the dualtocyclic polytopes. For each n ≥ 5, we exhibit a realization of a polartoneighborly 4dimensional polytope with n facets and a Hamilton path through its vertices that is monotone with respect to a linear objective
Cyclic SelfDual Codes
, 1983
"... It is shown that if the automorphism group of a binary selfdual code satisfies a certain condition then the code contains words of weight congruent to 2 modulo 4. In particular, no cyclic binary selfdual code can have all its weights divisible by 4. The number of cyclic binary selfdual codes of l ..."
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Cited by 71 (5 self)
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It is shown that if the automorphism group of a binary selfdual code satisfies a certain condition then the code contains words of weight congruent to 2 modulo 4. In particular, no cyclic binary selfdual code can have all its weights divisible by 4. The number of cyclic binary selfdual codes
The Z_4linearity of Kerdock, Preparata, Goethals, and related codes
, 2001
"... Certain notorious nonlinear binary codes contain more codewords than any known linear code. These include the codes constructed by NordstromRobinson, Kerdock, Preparata, Goethals, and DelsarteGoethals. It is shown here that all these codes can be very simply constructed as binary images under the ..."
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Cited by 178 (15 self)
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the Gray map of linear codes over ¡ 4, the integers mod 4 (although this requires a slight modification of the Preparata and Goethals codes). The construction implies that all these binary codes are distance invariant. Duality in the ¡ 4 domain implies that the binary images have dual weight distributions
Cayley Graphs and Symmetric 4Polytopes
, 2008
"... Previously we have investigated the medial layer graph G for a finite, selfdual, regular or chiral abstract 4polytope P. Here we study the Cayley graph C on a natural group generated by polarities of P, show that C covers G in a readily computable way and construct C as a voltage graph over G. We ..."
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Cited by 2 (0 self)
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Previously we have investigated the medial layer graph G for a finite, selfdual, regular or chiral abstract 4polytope P. Here we study the Cayley graph C on a natural group generated by polarities of P, show that C covers G in a readily computable way and construct C as a voltage graph over G. We
Primal Dividing and Dual Pruning: OutputSensitive Construction of 4d Polytopes and 3d Voronoi Diagrams
, 1997
"... In this paper, we give an algorithm for outputsensitive construction of an fface convex hull of a set of n points in general position in E 4 . Our algorithm runs in O((n + f)log 2 f) time and uses O(n + f) space. This is the first algorithm within a polylogarithmic factor of optimal O(n log f ..."
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Cited by 38 (3 self)
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In this paper, we give an algorithm for outputsensitive construction of an fface convex hull of a set of n points in general position in E 4 . Our algorithm runs in O((n + f)log 2 f) time and uses O(n + f) space. This is the first algorithm within a polylogarithmic factor of optimal O(n log
The number of triangulations of the cyclic polytope C(n,n4)
, 2000
"... We show that the exact number of triangulations of the cyclic polytope C(n; n \Gamma 4) is (n + 4)2 n\Gamma4 2 \Gamma n if n is even and i 3n+11 2 p 2 j 2 n\Gamma4 2 \Gamma n if n is odd. These formulas were previously conjectured by the second author. Our techniques are based on Gal ..."
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We show that the exact number of triangulations of the cyclic polytope C(n; n \Gamma 4) is (n + 4)2 n\Gamma4 2 \Gamma n if n is even and i 3n+11 2 p 2 j 2 n\Gamma4 2 \Gamma n if n is odd. These formulas were previously conjectured by the second author. Our techniques are based
Yangian symmetry of scattering amplitudes
 in N = 4 super YangMills theory,” arXiv:0902.2987 [hepth
"... Treelevel scattering amplitudes in N = 4 super YangMills theory have recently been shown to transform covariantly with respect to a ‘dual ’ superconformal symmetry algebra, thus extending the conventional superconformal symmetry algebra psu(2,24) of the theory. In this paper we derive the action ..."
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Cited by 129 (15 self)
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Treelevel scattering amplitudes in N = 4 super YangMills theory have recently been shown to transform covariantly with respect to a ‘dual ’ superconformal symmetry algebra, thus extending the conventional superconformal symmetry algebra psu(2,24) of the theory. In this paper we derive the action
HOMOTOPY ACTIONS, CYCLIC MAPS AND THEIR DUALS
, 2005
"... Abstract. An action of A on X is a map F: A × X → X such that F X = id: X → X. The restriction F A: A → X of an action is called a cyclic map. Special cases of these notions include group actions and the Gottlieb groups of a space, each of which has been studied extensively. We prove some general ..."
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results about actions and their EckmannHilton duals. For instance, we classify the actions on an Hspace that are compatible with the Hstructure. As a corollary, we prove that if any two actions F and F ′ of A on X have cyclic maps f and f ′ with Ωf = Ωf ′ , then ΩF and ΩF ′ give the same action of ΩA
Results 1  10
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475