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Some methods for differential games with highdimensional state space1
"... The Dynamic Programming approach and the Isaacs partial differential equation play a fundamental role in the study of twoperson, zerosum differential games. This method, however, suffers the wellknown “curse of dimensionality”, that is, the complexity of its numerical algorithms increases rapidl ..."
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rapidly with the dimension of the statespace of the system. Therefore, reducing this dimension is an important issue, and often one tries to do it by separating the state variables that evolve on different timescales. A rigorous way to decouple fast and slow variables is by means of Singular
Visual tracking in highdimensional state space by appearanceguided particle filtering,” Trans
 Img. Proc
, 2008
"... Abstract—In this paper, we propose a new approach, appearanceguided particle filtering (AGPF), for high degreeoffreedom visual tracking from an image sequence. This method adopts some known attractors in the state space and integrates both appearance and motiontransition information for visual t ..."
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Cited by 8 (0 self)
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Abstract—In this paper, we propose a new approach, appearanceguided particle filtering (AGPF), for high degreeoffreedom visual tracking from an image sequence. This method adopts some known attractors in the state space and integrates both appearance and motiontransition information for visual
PARTICLE ALGORITHMS FOR FILTERING IN HIGH DIMENSIONAL STATE SPACES: A CASE STUDY IN GROUP OBJECT TRACKING
"... We briefly present the current stateoftheart approaches for group and extended object tracking with an emphasis on particle methods which have high potential to handle complex structured scenarios. The big dimensionality attributed to the group tracking problem poses a major difficulty to particl ..."
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Cited by 5 (0 self)
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We briefly present the current stateoftheart approaches for group and extended object tracking with an emphasis on particle methods which have high potential to handle complex structured scenarios. The big dimensionality attributed to the group tracking problem poses a major difficulty
Quantum Key Distribution in a HighDimensional State Space: Exploiting the Transverse Degree of Freedom of the Photon
"... We describe a procedure to construct a freespace quantum key distribution system that can carry many bits of information per photon. We also describe the current status of our laboratory implementation of these plans. ..."
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Cited by 1 (1 self)
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We describe a procedure to construct a freespace quantum key distribution system that can carry many bits of information per photon. We also describe the current status of our laboratory implementation of these plans.
Estimating the Support of a HighDimensional Distribution
, 1999
"... Suppose you are given some dataset drawn from an underlying probability distribution P and you want to estimate a "simple" subset S of input space such that the probability that a test point drawn from P lies outside of S is bounded by some a priori specified between 0 and 1. We propo ..."
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Cited by 766 (29 self)
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Suppose you are given some dataset drawn from an underlying probability distribution P and you want to estimate a "simple" subset S of input space such that the probability that a test point drawn from P lies outside of S is bounded by some a priori specified between 0 and 1. We
The particel swarm: Explosion, stability, and convergence in a multidimensional complex space
 IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTION
"... The particle swarm is an algorithm for finding optimal regions of complex search spaces through interaction of individuals in a population of particles. Though the algorithm, which is based on a metaphor of social interaction, has been shown to perform well, researchers have not adequately explained ..."
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Cited by 822 (10 self)
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The particle swarm is an algorithm for finding optimal regions of complex search spaces through interaction of individuals in a population of particles. Though the algorithm, which is based on a metaphor of social interaction, has been shown to perform well, researchers have not adequately
Probabilistic Roadmaps for Path Planning in HighDimensional Configuration Spaces
 IEEE INTERNATIONAL CONFERENCE ON ROBOTICS AND AUTOMATION
, 1996
"... A new motion planning method for robots in static workspaces is presented. This method proceeds in two phases: a learning phase and a query phase. In the learning phase, a probabilistic roadmap is constructed and stored as a graph whose nodes correspond to collisionfree configurations and whose edg ..."
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Cited by 1276 (124 self)
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A new motion planning method for robots in static workspaces is presented. This method proceeds in two phases: a learning phase and a query phase. In the learning phase, a probabilistic roadmap is constructed and stored as a graph whose nodes correspond to collisionfree configurations and whose edges correspond to feasible paths between these configurations. These paths are computed using a simple and fast local planner. In the query phase, any given start and goal configurations of the robot are connected to two nodes of the roadmap; the roadmap is then searched for a path joining these two nodes. The method is general and easy to implement. It can be applied to virtually any type of holonomic robot. It requires selecting certain parameters (e.g., the duration of the learning phase) whose values depend on the scene, that is the robot and its workspace. But these values turn out to be relatively easy to choose, Increased efficiency can also be achieved by tailoring some components of the method (e.g., the local planner) to the considered robots. In this paper the method is applied to planar articulated robots with many degrees of freedom. Experimental results show that path planning can be done in a fraction of a second on a contemporary workstation (=150 MIPS), after learning for relatively short periods of time (a few dozen seconds)
The Xtree: An index structure for highdimensional data
 In Proceedings of the Int’l Conference on Very Large Data Bases
, 1996
"... In this paper, we propose a new method for indexing large amounts of point and spatial data in highdimensional space. An analysis shows that index structures such as the R*tree are not adequate for indexing highdimensional data sets. The major problem of Rtreebased index structures is the over ..."
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Cited by 592 (15 self)
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In this paper, we propose a new method for indexing large amounts of point and spatial data in highdimensional space. An analysis shows that index structures such as the R*tree are not adequate for indexing highdimensional data sets. The major problem of Rtreebased index structures
Actions as spacetime shapes
 In ICCV
, 2005
"... Human action in video sequences can be seen as silhouettes of a moving torso and protruding limbs undergoing articulated motion. We regard human actions as threedimensional shapes induced by the silhouettes in the spacetime volume. We adopt a recent approach [14] for analyzing 2D shapes and genera ..."
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Cited by 642 (4 self)
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Human action in video sequences can be seen as silhouettes of a moving torso and protruding limbs undergoing articulated motion. We regard human actions as threedimensional shapes induced by the silhouettes in the spacetime volume. We adopt a recent approach [14] for analyzing 2D shapes
N Degrees of Separation: MultiDimensional Separation of Concerns
 IN PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON SOFTWARE ENGINEERING
, 1999
"... Done well, separation of concerns can provide many software engineering benefits, including reduced complexity, improved reusability, and simpler evolution. The choice of boundaries for separate concerns depends on both requirements on the system and on the kind(s) of decompositionand composition a ..."
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Cited by 514 (8 self)
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Done well, separation of concerns can provide many software engineering benefits, including reduced complexity, improved reusability, and simpler evolution. The choice of boundaries for separate concerns depends on both requirements on the system and on the kind(s) of decompositionand composition a given formalism supports. The predominant methodologies and formalisms available, however, support only orthogonal separations of concerns, along single dimensions of composition and decomposition. These characteristics lead to a number of wellknown and difficult problems. This paper describes a new paradigm for modeling and implementing software artifacts, one that permits separation of overlapping concerns along multiple dimensions of composition and decomposition. This approach addresses numerous problems throughout the software lifecycle in achieving wellengineered, evolvable, flexible software artifacts and traceability across artifacts.
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