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Litonly sigmagame and its dual game
, 2009
"... Let Γ be a simple connected graph. The vertices of Γ can have one of two states, on or off. A configuration of the litonly sigmagame on Γ is an assignment of states to all vertices of Γ. We move by selecting a vertex i of on state and then change the states of all neighbors of i. We find the dual ..."
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connection between litonly sigmagame on Γ and another game, which every time we select a vertex i of Γ having an odd number of on neighbors and change the state of i. A consequence is that if Γ is a tree with a perfect matching, the orbits of the litonly sigmagame on Γ are determined, and we show
Litonly sigma game on a line graph
"... V (Γ) Let Γ be a connected graph. For any x ∈ F2, a move of the litonly sigma game consists of choosing some v ∈ V (Γ) with x(v) = 1 and changing the values of x at all those neighbors of v. An orbit is a maximal V (Γ) subset of F2 any two of which can reach each other by a series of moves. The min ..."
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Cited by 3 (2 self)
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to max{ρ(σ 1 (Γ)), b(Γ)}, with equality holding when #V (Γ) is odd. We also show that the minimum light number of the line graph of Γ is b(Γ) when Γ is a tree. If the tree Γ has n ≥ 3 vertices, we prove that the group formed by the moves of the litonly sigma game on the line graph of Γ is the symmetric
Planning Algorithms
, 2004
"... This book presents a unified treatment of many different kinds of planning algorithms. The subject lies at the crossroads between robotics, control theory, artificial intelligence, algorithms, and computer graphics. The particular subjects covered include motion planning, discrete planning, planning ..."
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Cited by 1108 (51 self)
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, planning under uncertainty, sensorbased planning, visibility, decisiontheoretic planning, game theory, information spaces, reinforcement learning, nonlinear systems, trajectory planning, nonholonomic planning, and kinodynamic planning.
Iterative point matching for registration of freeform curves and surfaces
, 1994
"... A heuristic method has been developed for registering two sets of 3D curves obtained by using an edgebased stereo system, or two dense 3D maps obtained by using a correlationbased stereo system. Geometric matching in general is a difficult unsolved problem in computer vision. Fortunately, in ma ..."
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Cited by 659 (7 self)
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A heuristic method has been developed for registering two sets of 3D curves obtained by using an edgebased stereo system, or two dense 3D maps obtained by using a correlationbased stereo system. Geometric matching in general is a difficult unsolved problem in computer vision. Fortunately, in many practical applications, some a priori knowledge exists which considerably simplifies the problem. In visual navigation, for example, the motion between successive positions is usually approximately known. From this initial estimate, our algorithm computes observer motion with very good precision, which is required for environment modeling (e.g., building a Digital Elevation Map). Objects are represented by a set of 3D points, which are considered as the samples of a surface. No constraint is imposed on the form of the objects. The proposed algorithm is based on iteratively matching points in one set to the closest points in the other. A statistical method based on the distance distribution is used to deal with outliers, occlusion, appearance and disappearance, which allows us to do subsetsubset matching. A leastsquares technique is used to estimate 3D motion from the point correspondences, which reduces the average distance between points in the two sets. Both synthetic and real data have been used to test the algorithm, and the results show that it is efficient and robust, and yields an accurate motion estimate.
The English noun phrase in its sentential aspect
, 1987
"... This dissertation is a defense of the hypothesis that the noun phrase is headed by afunctional element (i.e., \nonlexical " category) D, identi ed with the determiner. In this way, the structure of the noun phrase parallels that of the sentence, which is headed by In (ection), under assump ..."
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Cited by 509 (4 self)
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This dissertation is a defense of the hypothesis that the noun phrase is headed by afunctional element (i.e., \nonlexical " category) D, identi ed with the determiner. In this way, the structure of the noun phrase parallels that of the sentence, which is headed by In (ection), under assumptions now standard within the GovernmentBinding (GB) framework. The central empirical problem addressed is the question of the proper analysis of the socalled \Possing " gerund in English. This construction possesses simultaneously many properties of sentences, and many properties of noun phrases. The problem of capturing this dual aspect of the Possing construction is heightened by current restrictive views of Xbar theory, which, in particular, rule out the obvious structure for Possing, [NP NP VPing], by virtue of its exocentricity. Consideration of languages in which nouns, even the most basic concrete nouns, show agreement (AGR) with their possessors, points to an analysis
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