An efficient parallel algorithm for the tree-decomposition problem for fixed width w is presented. The algorithm runs in time O(log/sup 3/ n) and uses O(n) processors on a concurrent-read, concurrent-write parallel ra...
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An efficient parallel algorithm for the tree-decomposition problem for fixed width w is presented. The algorithm runs in time O(log/sup 3/ n) and uses O(n) processors on a concurrent-read, concurrent-write parallel random access machine (CRCW PRAM). This result can be used to construct efficient parallel algorithms for three important classes of problems: MS (monadic second-order) properties, linear EMS (extended monadic second-order) extremum problems, and enumeration problems for MS properties, for graphs of tree width at most w. The sequential time complexity of the tree-composition problem for fixed w is improved, and some implications for this improvement are stated.< >
A probabilistic artificial neural network is presented. It is of a one-layer, feedback-coupled type with graded units. The learning rule is derived from Bayes's rule. Learning is regarded as collecting statistics ...
A probabilistic artificial neural network is presented. It is of a one-layer, feedback-coupled type with graded units. The learning rule is derived from Bayes's rule. Learning is regarded as collecting statistics and recall as a statistical inference process. Units correspond to events and connections come out as compatibility coefficients in a logarithmic combination rule. The input to a unit via connections from other active units affects the a posteriori belief in the event in question. The new model is compared to an earlier binary model with respect to storage capacity, noise tolerance, etc. in a content addressable memory (CAM) task. The new model is a real time network and some results on the reaction time for associative recall are given. The scaling of learning and relaxation operations is considered together with issues related to representation of information in one-layer artificial neural networks. An extension with complex units is discussed.
The cylindrical algebraic decomposition method decomposes E r into regions over which a given polynomial has constant sign by extension of one complicated decomposition of E r-1 . We investigate a method which decompo...
The cylindrical algebraic decomposition method decomposes E r into regions over which a given polynomial has constant sign by extension of one complicated decomposition of E r-1 . We investigate a method which decomposes E r into sign-invariant region by combining several but simpler decompositions of E r-1 . We can obtain a sign-invariaat decomposition of E 2 defined by a bivariate polynomial of total degree n and coefficient size d in time O(n 12 (d + log n) 2 log n) . Preliminary experiments suggest that the method is useful in practice.
The edge focusing method produces a series of edge images ranging from coarser to finer scale resolution. The displacements of these extracted edges in this series are discussed. A three-step method of labelling the e...
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The edge focusing method produces a series of edge images ranging from coarser to finer scale resolution. The displacements of these extracted edges in this series are discussed. A three-step method of labelling the extracted edges as coming from objects or as coming from shadows and other illumination phenomena using this series is tried. More precisely, we show that it seems possible to label edges into the categories ‘diffuse’ and ‘non-diffuse’ from a binary multi-scale representation, i.e. without using the image intensities directly.
A method is developed for the measurement of short-range visual motion in image sequences, making use of the motion of image features such as edges and points. Each feature generates a Gaussian activation profile in a...
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A method is developed for the measurement of short-range visual motion in image sequences, making use of the motion of image features such as edges and points. Each feature generates a Gaussian activation profile in a spatiotemporal neighborhood of specified scale around the feature itself; this profile is then convected with motion of the feature. The authors show that image velocity estimates can be obtained from such dynamic activation profiles using a modification of familiar gradient techniques. The resulting estimators can be formulated in terms of simple ratios of spatiotemporal filters (i.e. receptive fields) convolved with image feature maps. A family of activation profiles of varying scale must be utilized to cover a range of possible image velocities. They suggest a characteristic speed normalization of the estimate obtained from each filter in order to decide which estimate is to be accepted. They formulate the velocity estimators for dynamic edges in 1-D and 2-D image sequences, as well as that for dynamic feature points in 2-D image sequences.< >
We consider Lipschitz-continuous nonlinear maps in finite-dimensional Banach and Hilbert spaces. Boundedness and monotonicity of the operator are characterized quantitatively in terms of certain functionals. These fun...
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We consider Lipschitz-continuous nonlinear maps in finite-dimensional Banach and Hilbert spaces. Boundedness and monotonicity of the operator are characterized quantitatively in terms of certain functionals. These functionals are used to assess qualitative properties such as invertibility, and also enable a generalization of some well-known matrix results directly to nonlinear operators. Closely related to the numerical range of a matrix, the Gerschgorin domain is introduced for nonlinear operators. This point set in the complex plane is always convex and contains the spectrum of the operator's Jacobian matrices. Finally, we focus on nonlinear operators in Hilbert space and hint at some generalizations of the von Neumann spectral theory.
In this paper the relations between semi-infinite programs and optimisation problems with finitely many variables and constraints are reviewed. Two classes of convex semi-infinite programs are defined, one based on th...
In this paper the relations between semi-infinite programs and optimisation problems with finitely many variables and constraints are reviewed. Two classes of convex semi-infinite programs are defined, one based on the fact that a convex set may be represented as the intersection of closed halfspaces, while the other class is defined using the representation of the elements of a convex set as convex combinations of points and directions. Extension to nonconvex problems is given. A common technique of solving a semi-infinite program computationally is to derive necessary conditions for optimality in the form of a nonlinear system of equations with finitely many equations and unknowns. In the three-phase algorithm, this system is constructed from the optimal solution of a discretised version of the given semi-infinite program. i.e. a problem with finitely many variables and constraints. The system is solved numerically, often by means of some linearisation method. One option is to use a direct analog of the familiar SOLVER method.
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