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Combinatorial duality and intersection product  [PDF]
Karl-Heinz Fieseler
Mathematics , 2003,
Abstract: In two articles by Barthel, Brasselet, Fieseler and Kaup, and, Bressler and Lunts, a combinatorial theory of intersection cohomology and perverse sheaves has been developed on fans. In the first one, one tried to present everything on an elementary level,using only some commutative algebra and no derived categories. There remained two major gaps: First of all the Hard Lefschetz Theorem was only conjectured and secondly the intersection product seemed to depend on some non-canonical choices. Meanwhile the Hard Lefschetz theorem has been proved by Karu. The proof relies heavily on the intersection product, since what finally has to be shown are the Hodge-Riemann relations. In fact here again choices enter: The intersection product is induced from the intersection product on some simplicial subdivision via a direct embedding of the corresponding intersection cohomology sheaves, a fact, which makes the argumentation quite involved. In a recent paper by Bressler and Lunts, one shows by a detailed analysis that eventually all possible choices do not affect the definition of the pairing. Our goal here is the same, but we shall try to follow the spirit of the first cited paper avoiding the formalism of derived categories. For perverse sheaves we define their dual sheaf and check that the intersection cohomology sheaf is self- dual in a natural way.
Combinatorial Intersection Cohomology for Fans  [PDF]
Gottfried Barthel,Jean-Paul Brasselet,Karl-Heinz Fieseler,Ludger Kaup
Mathematics , 2000,
Abstract: We continue the approach toward a purely combinatorial "virtual" intersection cohomology for possibly non-rational fans, based on our investigation of equivariant intersection cohomology for toric varieties (see math.AG/9904159). Fundamental objects of study are "minimal extension sheaves" on "fan spaces". These are flabby sheaves of graded modules over a sheaf of polynomial rings, satisfying three relatively simple axioms that characterize the properties of the equivariant intersection cohomology sheaf on a toric variety, endowed with the finite topology given by open invariant subsets. These sheaves are models for the "pure" objects of a "perverse category"; a "Decomposition Theorem" is shown to hold. -- Formalizing those fans that define "equivariantly formal" toric varieties (where equivariant and non-equivariant intersection cohomology determine each other by Kunneth type formulae), we study "quasi-convex" fans (including fans with convex or with "co-convex" support). For these, there is a meaningful "virtual intersection cohomology". We characterize quasi-convex fans by a topological condition on the support of their boundary fan and prove a generalization of Stanley's "Local-Global" formula realizing the intersection Poincare polynomial of a complete toric variety in terms of local data. Virtual intersection cohomology of quasi-convex fans is shown to satify Poincare duality. To describe the local data in terms of virtual intersection cohomology of lower-dimensional complete polytopal fans, one needs a "Hard Lefschetz" type theorem. It requires a vanishing condition that is known to hold for rational cones, but yet remains to be proven in the general case.
Remarks on the combinatorial intersection cohomology of fans  [PDF]
Tom Braden
Mathematics , 2005,
Abstract: We review the theory of combinatorial intersection cohomology of fans developed by Barthel-Brasselet-Fieseler-Kaup, Bressler-Lunts, and Karu. This theory gives a substitute for the intersection cohomology of toric varieties which has all the expected formal properties but makes sense even for non-rational fans, which do not define a toric variety. As a result, a number of interesting results on the toric $g$ and $h$ polynomials have been extended from rational polytopes to general polytopes. We present explicit complexes computing the combinatorial IH in degrees one and two; the degree two complex gives the rigidity complex previously used by Kalai to study $g_2$. We present several new results which follow from these methods, as well as previously unpublished proofs of Kalai that $g_k(P) = 0$ implies $g_k(P^*) = 0$ and $g_{k+1}(P) = 0$.
Combinatorial Duality and Intersection Product: A Direct Approach  [PDF]
Gottfried Barthel,Jean-Paul Brasselet,Karl-Heinz Fieseler,Ludger Kaup
Mathematics , 2003,
Abstract: The proof of the combinatorial Hard Lefschetz Theorem for the ``virtual'' intersection cohomology of a not necessarily rational polytopal fan that has been presented by K. Karu completely establishes Stanley's conjectures for the generalized $h$-vector of an arbitrary polytope. The main ingredients, namely, Poincare Duality and the Hard Lefschetz Theorem, both rely on the intersection product. In the constructions of Barthel, Brasselet, Fieseler and Kaup and Bressler and Lunts, there remained an apparent ambiguity. The recent solution of this problem by Bressler and Lunts uses the formalism of derived categories. The present article gives a straightforward approach to combinatorial duality and a natural intersection product, completely within the framework of elementary sheaf theory and commutative algebra, thus avoiding derived categories.
Vehicle Speed Detection Based on Video at Urban Intersection
Zhenqian Shen,Shifu Zhou,Changyun Miao,Yan Zhang
Research Journal of Applied Sciences, Engineering and Technology , 2013,
Abstract: In order to obtain the average speed of vehicle at plane intersection on urban traffic, an algorithm of average speed measurement based on the video is proposed in this study. Video is captured against the motion of the vehicle by the camera which is mounted on the cross bar at the intersection. The detection zone is set between the stop line and the pedestrian road. These methods of background difference, shadow removal and region filling of morphology are applied to detection zone. Then, method of vertical projection is employed to the obtained binary image, judging whether the vehicles exist in the detection region by vertical projection diagram and calculating the total frames that the vehicle drive into and depart out the detection region. The instantaneous velocity is obtained by using the frame rate of the camera and the width of the detection region and then to calculate the mean velocity.
Research on Intelligent Vehicle Development

HU Hai-feng,SHI Zhong-ke,XU De-wen,

计算机应用研究 , 2004,
Abstract: The importance of improving transportation safety by research on intelligent vehicle is discussed;the history,development and research trend are summarized.In addition,this paper presents a new intelligent vehicle model based on information fusion,describes the modules in this model,and suggests some approaches to introduce fusion method to intelligent vehicle research.Prospects of intelligent vehicle are proposed.
Research on Intelligent Vehicle platoon Driving Simulation Experiment System under the Coordination between Vehicle and Highway  [cached]
Yulin Ma,Xinping Yan,Qing Wu,Rui Zhang
Journal of Computers , 2010, DOI: 10.4304/jcp.5.11.1767-1774
Abstract: Intelligent vehicle platoon driving is a process of the flexible formation based on the coordination between vehicle and highway in the intelligent vehicle-highway system, which can increase the controllability of traffic, simplify the complexity of traffic control, and ease the traffic pressure. It has been constructed that the intelligent vehicle platoon driving simulation experiment system under the coordination between vehicle and highway by means of the one-tenth of model cars, simulated road and the technology about intelligent control and wireless communication. On the basis of the experimental platform and analysis, it has been studied that the autonomous driving technology for intelligent vehicle, and that the information interaction between vehicle and highway as well as that with the main console by the wireless communication networks built, providing the technical and experimental basis for further research on intelligent vehicle platoon driving control under the coordination between vehicle and highway.
The Intelligent Vehicle Coordination of the Cybernetic Transportation System
Fenghui Wang,Ming Yang,Ruqing Yang
International Journal of Advanced Robotic Systems , 2009,
Abstract: Cybernetic Transportation System (CTS) is a new branch of Intelligent Transportation Systems (ITS), which is a solution to the urban transportation problem. The coordination of intelligent vehicles is critical for the operation of the Cybernetic Transportation System. We present a distributed coordination approach for the intelligent vehicles of the Cybernetic Transportation System, which is based on an agent-based framework. Each vehicle agent generates intention independently by considering its and other agents' shared status and intentions in the coordination. Typical coordination scenes, including platoon and overtaking, have been demonstrated in the two-lane, two-way traffic situation and the effectiveness of the proposed coordination approach has been validated.
Discussion on the Intelligent Vehicle Technologies

WANG Guo-yin,CHEN Qiao-song,WANG Jin,

计算机科学 , 2012,
Abstract: Nowadays,the pollution of the environment,traffic safety and congestion are truly severe problems affectingthe entire world. hhe intelligent vehicle(IV) is an attempt to move towards a new traffic paradigm, where drive becomes enjoyable experience, and cars don't crash anymore, and traffic congestion is drastically reduced. Therefore, the development of intelligent vehicle in new generation becomes one of the most important strategic objectives in main developed countries. In this paper, intelligent vehicle was creatively defined as a car with power-driven and intelligent control. Five basic functional features should be realized in intelligent vehicle,which consists of the vehicle-to-vehicle(V2V) interaction, vehiclcto-pcople( V2P) interaction, vchiclcto-road ( V2R) interaction, vehiclcto-network(V2N) interaction and energy-saving. These four interactions prescribe a cooperative system between the intelligent vehicles and surroundings,while the energy-saving focuses on the clean and economical energy management system. Meanwhile, the novel theories and technologies for the development of intelligent vehicle were discussed in this paper. Finally, the autonomous driving simulation experiment was performed by miniature intelligent vehicles, and the future of intelligent vehicle industry was prospected.
Towards a combinatorial Intersection Cohomology for Fans  [PDF]
Karl-Heinz Fieseler
Mathematics , 2000, DOI: 10.1016/S0764-4442(00)00149-X
Abstract: The real intersection cohomology of a toric variety is described in a purely combinatorial way using methods of elementary commutative algebra only. We define, for arbitrary fans, the notion of a ``minimal extension sheaf'' on the fan as an axiomatic characterization of the equivariant intersection cohomology sheaf. This provides a purely algebraic interpretation of Stanley's generalized f- and g-vector of an arbitrary polytope or complete fan under a natural vanishing condition. -- The results presented in this note originate from joint work with G.Barthel, J.-P.Brasselet and L.Kaup, continuing earlier research (see math.AG/9904159). A detailed exposition will appear elsewhere (see math.AG/0002181).

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