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Results 1 - 10
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475
THE RANDOM EDGE SIMPLEX ALGORITHM ON DUAL CYCLIC 4-POLYTOPES
, 2006
"... The simplex algorithm using the random edge pivot-rule on any realization of a dual cyclic 4-polytope with n facets does not take more than O(n) pivot-steps. 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 pivot-rule on any realization of a dual cyclic 4-polytope with n facets does not take more than O(n) pivot-steps. This even holds for general abstract objective functions (AOF) / acyclic unique sink orientations (AUSO). The methods can be used to show
A real-time algorithm for mobile robot mapping with applications to multi-robot 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 scan-matching for mapping, paired with a sample-based 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 multi-resolution 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 real-time. It is remarkably robust. Experimental results illustrate that accurate maps of large, cyclic environments can
Long Monotone Paths on Simple 4-Polytopes
, 2004
"... ... of vertices in a monotone path along edges of a d-dimensional 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 d-polytope 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 dual-to-cyclic polytopes. For each n ≥ 5, we exhibit a realization of a polar-to-neighborly 4-dimensional polytope with n facets and a Hamilton path through its vertices that is monotone with respect to a linear objective
Cyclic Self-Dual Codes
, 1983
"... It is shown that if the automorphism group of a binary self-dual code satisfies a certain condition then the code contains words of weight congruent to 2 modulo 4. In particular, no cyclic binary self-dual code can have all its weights divisible by 4. The number of cyclic binary self-dual codes of l ..."
Abstract
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Cited by 71 (5 self)
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It is shown that if the automorphism group of a binary self-dual code satisfies a certain condition then the code contains words of weight congruent to 2 modulo 4. In particular, no cyclic binary self-dual code can have all its weights divisible by 4. The number of cyclic binary self-dual codes
The Z_4-linearity 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 Nordstrom-Robinson, Kerdock, Preparata, Goethals, and Delsarte-Goethals. 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 4-Polytopes
, 2008
"... Previously we have investigated the medial layer graph G for a finite, self-dual, regular or chiral abstract 4-polytope 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, self-dual, regular or chiral abstract 4-polytope 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: Output-Sensitive Construction of 4-d Polytopes and 3-d Voronoi Diagrams
, 1997
"... In this paper, we give an algorithm for output-sensitive construction of an f-face 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 output-sensitive construction of an f-face 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,n-4)
, 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 Yang-Mills theory,” arXiv:0902.2987 [hep-th
"... Tree-level scattering amplitudes in N = 4 super Yang-Mills theory have recently been shown to transform covariantly with respect to a ‘dual ’ superconformal symmetry algebra, thus extending the conventional superconformal symmetry algebra psu(2,2|4) of the theory. In this paper we derive the action ..."
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Cited by 129 (15 self)
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Tree-level scattering amplitudes in N = 4 super Yang-Mills theory have recently been shown to transform covariantly with respect to a ‘dual ’ superconformal symmetry algebra, thus extending the conventional superconformal symmetry algebra psu(2,2|4) 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 Eckmann-Hilton duals. For instance, we classify the actions on an H-space that are compatible with the H-structure. 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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