The Experts below are selected from a list of 8859 Experts worldwide ranked by ideXlab platform
Dag Normann - One of the best experts on this subject based on the ideXlab platform.
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The Total Continuous Functionals
Higher-Order Computability, 2015Co-Authors: John Longley, Dag NormannAbstract:In this chapter and the next, we turn our attention again to type structures of total Functionals over N. From the point of view of computability theory, by far the most important such structure is the model Ct of total Continuous Functionals, which forms the subject of the present chapter.
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The Partial Continuous Functionals
Higher-Order Computability, 2015Co-Authors: John Longley, Dag NormannAbstract:In this chapter we will take a closer look at the type structure PC of partial Continuous Functionals and its effective analogue PCeff, as introduced in Subsection 3.2.2. These models have already played key roles in Chapters 8 and 9 in the construction of the total type structures Ct and HEO; they also featured in Chapter 7 as leading examples of models for Plotkin’s PCF. Our main purpose in this chapter is to survey a range of different characterizations of PC and PCeff, offering cumulative evidence that these are indeed natural mathematical objects. We also develop more systematically certain concepts that appeared in Chapter 8, such as the Scott topology.
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The extensional realizability model of Continuous Functionals and three weakly non-constructive classical theorems
Logical Methods in Computer Science, 2015Co-Authors: Dag NormannAbstract:We investigate wether three statements in analysis, that can be proved classically, are realizable in the realizability model of extensional Continuous Functionals induced by Kleene's second model $K_2$. We prove that a formulation of the Riemann Permutation Theorem as well as the statement that all partially Cauchy sequences are Cauchy cannot be realized in this model, while the statement that the product of two anti-Specker spaces is anti-Specker can be realized.
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internal density theorems for hierarchies of Continuous Functionals
Conference on Computability in Europe, 2008Co-Authors: Dag NormannAbstract:One standard way of constructing a hierarchy of total, Continuous Functionals over a fixed set of base types is to use a suitable cartesian closed category of domains where we may construct the corresponding hierarchy of partial Continuous Functionals, and then extract the hereditarily total ones. One important theorem, when available, is the Density Theorem: Each finitary domain object can be extended to a total one. We will see how we in the context of limit spaces, may formulate and prove versions of the density theorems and avoid domain theory.
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A Nonstandard Characterisation of the Type-structure of Continuous Functionals Over the Reals
Electronic Notes in Theoretical Computer Science, 2004Co-Authors: Dag NormannAbstract:We extend a hyperfinite discretisation of the real line to a typed structure of hyperfinite Functionals, and we show that the hereditarily near-standard Functionals correspond to the Continuous Functionals over the reals obtained from domain theory.
Andrew Delong - One of the best experts on this subject based on the ideXlab platform.
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an integral solution to surface evolution pdes via geo cuts
European Conference on Computer Vision, 2006Co-Authors: Yuri Boykov, Vladimir Kolmogorov, Daniel Cremers, Andrew DelongAbstract:We introduce a new approach to modelling gradient flows of contours and surfaces. While standard variational methods (e.g. level sets) compute local interface motion in a differential fashion by estimating local contour velocity via energy derivatives, we propose to solve surface evolution PDEs by explicitly estimating integral motion of the whole surface. We formulate an optimization problem directly based on an integral characterization of gradient flow as an infinitesimal move of the (whole) surface giving the largest energy decrease among all moves of equal size. We show that this problem can be efficiently solved using recent advances in algorithms for global hypersurface optimization [4,2,11]. In particular, we employ the geo-cuts method [4] that uses ideas from integral geometry to represent Continuous surfaces as cuts on discrete graphs. The resulting interface evolution algorithm is validated on some 2D and 3D examples similar to typical demonstrations of level-set methods. Our method can compute gradient flows of hypersurfaces with respect to a fairly general class of Continuous Functionals and it is flexible with respect to distance metrics on the space of contours/surfaces. Preliminary tests for standard L2 distance metric demonstrate numerical stability, topological changes and an absence of any oscillatory motion.
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ECCV (3) - An integral solution to surface evolution PDEs via geo-cuts
Computer Vision – ECCV 2006, 2006Co-Authors: Yuri Boykov, Vladimir Kolmogorov, Daniel Cremers, Andrew DelongAbstract:We introduce a new approach to modelling gradient flows of contours and surfaces. While standard variational methods (e.g. level sets) compute local interface motion in a differential fashion by estimating local contour velocity via energy derivatives, we propose to solve surface evolution PDEs by explicitly estimating integral motion of the whole surface. We formulate an optimization problem directly based on an integral characterization of gradient flow as an infinitesimal move of the (whole) surface giving the largest energy decrease among all moves of equal size. We show that this problem can be efficiently solved using recent advances in algorithms for global hypersurface optimization [4,2,11]. In particular, we employ the geo-cuts method [4] that uses ideas from integral geometry to represent Continuous surfaces as cuts on discrete graphs. The resulting interface evolution algorithm is validated on some 2D and 3D examples similar to typical demonstrations of level-set methods. Our method can compute gradient flows of hypersurfaces with respect to a fairly general class of Continuous Functionals and it is flexible with respect to distance metrics on the space of contours/surfaces. Preliminary tests for standard L2 distance metric demonstrate numerical stability, topological changes and an absence of any oscillatory motion.
Yuri Boykov - One of the best experts on this subject based on the ideXlab platform.
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an integral solution to surface evolution pdes via geo cuts
European Conference on Computer Vision, 2006Co-Authors: Yuri Boykov, Vladimir Kolmogorov, Daniel Cremers, Andrew DelongAbstract:We introduce a new approach to modelling gradient flows of contours and surfaces. While standard variational methods (e.g. level sets) compute local interface motion in a differential fashion by estimating local contour velocity via energy derivatives, we propose to solve surface evolution PDEs by explicitly estimating integral motion of the whole surface. We formulate an optimization problem directly based on an integral characterization of gradient flow as an infinitesimal move of the (whole) surface giving the largest energy decrease among all moves of equal size. We show that this problem can be efficiently solved using recent advances in algorithms for global hypersurface optimization [4,2,11]. In particular, we employ the geo-cuts method [4] that uses ideas from integral geometry to represent Continuous surfaces as cuts on discrete graphs. The resulting interface evolution algorithm is validated on some 2D and 3D examples similar to typical demonstrations of level-set methods. Our method can compute gradient flows of hypersurfaces with respect to a fairly general class of Continuous Functionals and it is flexible with respect to distance metrics on the space of contours/surfaces. Preliminary tests for standard L2 distance metric demonstrate numerical stability, topological changes and an absence of any oscillatory motion.
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ECCV (3) - An integral solution to surface evolution PDEs via geo-cuts
Computer Vision – ECCV 2006, 2006Co-Authors: Yuri Boykov, Vladimir Kolmogorov, Daniel Cremers, Andrew DelongAbstract:We introduce a new approach to modelling gradient flows of contours and surfaces. While standard variational methods (e.g. level sets) compute local interface motion in a differential fashion by estimating local contour velocity via energy derivatives, we propose to solve surface evolution PDEs by explicitly estimating integral motion of the whole surface. We formulate an optimization problem directly based on an integral characterization of gradient flow as an infinitesimal move of the (whole) surface giving the largest energy decrease among all moves of equal size. We show that this problem can be efficiently solved using recent advances in algorithms for global hypersurface optimization [4,2,11]. In particular, we employ the geo-cuts method [4] that uses ideas from integral geometry to represent Continuous surfaces as cuts on discrete graphs. The resulting interface evolution algorithm is validated on some 2D and 3D examples similar to typical demonstrations of level-set methods. Our method can compute gradient flows of hypersurfaces with respect to a fairly general class of Continuous Functionals and it is flexible with respect to distance metrics on the space of contours/surfaces. Preliminary tests for standard L2 distance metric demonstrate numerical stability, topological changes and an absence of any oscillatory motion.
Bruce M. Kapron - One of the best experts on this subject based on the ideXlab platform.
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Resource-bounded continuity and sequentiality for type-two Functionals
ACM Transactions on Computational Logic, 2002Co-Authors: Samuel R. Buss, Bruce M. KapronAbstract:We define notions of resource-bounded continuity and sequentiality for type-two Functionals with total inputs, and prove that in the resource-bounded model there are Continuous Functionals which cannot be efficiently simulated by sequential Functionals. We also show that for some naturally defined classes of Continuous Functionals an efficient simulation is possible.
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Resource-bounded Continuity and Sequentiality for Type-two Functionals (Extended Abstract)
2000Co-Authors: Samuel R. Buss, Bruce M. KapronAbstract:We define notions of resource-bounded continuity and sequentiality for type-two Functionals with total inputs, and prove that in the resource-bounded model there are Continuous Functionals which cannot be efficiently simulated by sequential Functionals. We also show that for some naturallydefined classes of Continuous Functionals, an efficient simulation is possible.
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LICS - Resource-bounded continuity and sequentiality for type-two Functionals
Proceedings Fifteenth Annual IEEE Symposium on Logic in Computer Science (Cat. No.99CB36332), 1Co-Authors: Samuel R. Buss, Bruce M. KapronAbstract:We define notions of resource-bounded continuity and sequentiality for type-two Functionals with total inputs, and prove that in the resource-bounded model there are Continuous Functionals which cannot be efficiently simulated by sequential Functionals. We also show that for some naturally defined classes of Continuous Functionals, an efficient simulation is possible.
H Chen - One of the best experts on this subject based on the ideXlab platform.
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approximations of Continuous Functionals by neural networks with application to dynamic systems
IEEE Transactions on Neural Networks, 1993Co-Authors: Tianping Chen, H ChenAbstract:The paper gives several strong results on neural network representation in an explicit form. Under very mild conditions a functional defined on a compact set in C(a, b) or L/sup p/(a, b), spaces of infinite dimensions, can be approximated arbitrarily well by a neural network with one hidden layer. The results are a significant development beyond earlier work, where theorems of approximating Continuous functions defined on a finite-dimensional real space by neural networks with one hidden layer were given. All the results are shown to be applicable to the approximation of the output of dynamic systems at any particular time. >