The Experts below are selected from a list of 303 Experts worldwide ranked by ideXlab platform
Abbas Edalat - One of the best experts on this subject based on the ideXlab platform.
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domain theory and differential calculus functions of one variable
Mathematical Structures in Computer Science, 2004Co-Authors: Abbas Edalat, Andre LieutierAbstract:We introduce a domain-theoretic framework for differential calculus. We define the set of primitive maps as well as the derivative of an interval-valued Scott continuous function on the domain of intervals, and show that they are dually related, providing an extension of the classical duality of differentiation and integration as in the fundamental theorem of calculus. It is shown that, for locally Lipschitz functions of a real variable, the domain-theoretic derivative coincides with the Clarke's derivative. We then construct a domain for differentiable real-valued functions of a real variable by pairing consistent information about the function and information about its derivative. The set of classical $C^1$ functions, equipped with its $C^1$ norm, is embedded into the set of maximal elements of this countably based, bounded complete continuous domain. This domain also provides a model for the differential properties of piecewise $C^1$ functions, locally Lipschitz functions and more generally of all continuous functions. We prove that consistency of function information and derivative information is decidable on rational step functions, which shows that our domain can be given an Effective Structure. We thus obtain a data type for differential calculus. As an immediate application, we present a domain-theoretic formulation of Picard's theorem, which provides a data type for solving differential equations.
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dynamical systems measures and fractals via domain theory
Information & Computation, 1995Co-Authors: Abbas EdalatAbstract:Abstract We introduce domain theory in dynamical systems, iterated function systems (fractals), and measure theory. For a discrete dynamical system given by the action of a continuous map f : X → X on a metric space X , we study the extended dynamical systems ( VX , Vf ), ( UX , Uf ), and ( LX , Lf ), where V , U , and L are respectively the Vietoris hyperspace, the upper hyperspace, and the lower hyperspace functors. We show that if ( X , f ) is chaotic, then so is ( UX , Uf ). When X is locally compact UX , is a continuous bounded complete dcpo. If X is second countable as well, then UX will be ω-continuous and can be given an Effective Structure. We show how strange attractors, attractors of iterated function systems (fractals) and Julia sets are obtained Effectively as fixed points of deterministic functions on UX or fixed points of non-deterministic functions on CUX where C is the convex (Plotkin) power domain. We also show that the set, M ( X ), of finite Borel measures on X can be embedded in PUX , where P is the probabilistic power domain. This provides an Effective framework for measure theory. We then prove that the invariant measure of an hyperbolic iterated function system with probabilities can he obtained as the unique fixed point of an associated continuous function on PUX .
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dynamical systems measures and fractals via domain theory
Formal Methods, 1993Co-Authors: Abbas EdalatAbstract:We introduce domain theory in the computation of dynamical systems, iterated function systems (fractals) and measures. For a discrete dynamical system (X, f), given by the action of a continuous map f: X → X on a metric space X, we study the extended dynamical systems (VX, Vf) and (UX, Uf) where V is the Vietoris functor and U is the upper space functor. In fact, from the point of view of computing the attractors of (X, f), it is natural to study the other two systems: A compact attractor of (X, f) is a fixed point of (VX, Vf) and a fixed point of (UX, Uf). We show that if (X, f) is chaotic, then so is (UX, Uf). When X is locally compact UX is a continuous bounded complete dcpo. If X is second countable as well, then UX will be ω-continuous and can be given an Effective Structure. We show how strange attractors, attractors of iterated function systems (fractals) and Julia sets are obtained Effectively as fixed points of deterministic functions on UX or fixed points of non-deterministic functions on CUX where C is the convex (Plotkin) power domain. We also establish an interesting link between measure theory and domain theory. We show that the set, M(X), of Borel measures on X can be embedded in PUX, where P is the probabilistic power domain. This provides an Effective way of obtaining measures on X. We then prove that the invariant measure of an hyperbolic iterated function system with probabilities can be obtained as the unique fixed point of an associated continuous function on PUX.
Chen Change Loy - One of the best experts on this subject based on the ideXlab platform.
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liteflownet a lightweight convolutional neural network for optical flow estimation
Computer Vision and Pattern Recognition, 2018Co-Authors: Takwai Hui, Xiaoou Tang, Chen Change LoyAbstract:FlowNet2 [14], the state-of-the-art convolutional neural network (CNN) for optical flow estimation, requires over 160M parameters to achieve accurate flow estimation. In this paper we present an alternative network that attains performance on par with FlowNet2 on the challenging Sintel final pass and KITTI benchmarks, while being 30 times smaller in the model size and 1.36 times faster in the running speed. This is made possible by drilling down to architectural details that might have been missed in the current frameworks: (1) We present a more Effective flow inference approach at each pyramid level through a lightweight cascaded network. It not only improves flow estimation accuracy through early correction, but also permits seamless incorporation of descriptor matching in our network. (2) We present a novel flow regularization layer to ameliorate the issue of outliers and vague flow boundaries by using a feature-driven local convolution. (3) Our network owns an Effective Structure for pyramidal feature extraction and embraces feature warping rather than image warping as practiced in FlowNet2. Our code and trained models are available at github.com/twhui/LiteFlowNet.
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liteflownet a lightweight convolutional neural network for optical flow estimation
arXiv: Computer Vision and Pattern Recognition, 2018Co-Authors: Takwai Hui, Xiaoou Tang, Chen Change LoyAbstract:FlowNet2, the state-of-the-art convolutional neural network (CNN) for optical flow estimation, requires over 160M parameters to achieve accurate flow estimation. In this paper we present an alternative network that outperforms FlowNet2 on the challenging Sintel final pass and KITTI benchmarks, while being 30 times smaller in the model size and 1.36 times faster in the running speed. This is made possible by drilling down to architectural details that might have been missed in the current frameworks: (1) We present a more Effective flow inference approach at each pyramid level through a lightweight cascaded network. It not only improves flow estimation accuracy through early correction, but also permits seamless incorporation of descriptor matching in our network. (2) We present a novel flow regularization layer to ameliorate the issue of outliers and vague flow boundaries by using a feature-driven local convolution. (3) Our network owns an Effective Structure for pyramidal feature extraction and embraces feature warping rather than image warping as practiced in FlowNet2. Our code and trained models are available at this https URL .
Yuliang Chen - One of the best experts on this subject based on the ideXlab platform.
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electric field control of li doping induced phase transition in vo2 film with crystal facet dependence
Nano Energy, 2018Co-Authors: Yuliang Chen, Zhaowu Wang, Shi Chen, Hui Ren, Wensheng Yan, Guobin Zhang, Jun Jiang, Chongwen ZouAbstract:Abstract The use of electric-field to manipulate the transport properties of correlated oxides is promising for achieving nano-functional electronic devices. As a typical correlated oxide material, vanadium dioxide (VO2) displays a special metal-insulator transition (MIT) at about 340 K. In this work, we select a water-free electrolyte gel, Li+/propylene carbonate, to achieve a non-volatile and reversible Li-doping and phase modulation in nano-VO2 crystal film under gating voltages. Synchrotron characterizations indicate the originally insulating VO2 undergoes an Effective Structure change and an increased V 3d-O 2p hybrid t2g-orbital occupancy, which is responsible for the metallic state formation as proved by first-principle calculation. The field-driving Li-doping shows pronounced facet dependence, indicating the existence of energetically favored channels for Li-ions diffusion along V-V chains as proved by dynamic stimulation. Our current findings will supply opportunities for the electric-field control of atomic sieve, correlated ionitronics and synaptic transistor.
Chongwen Zou - One of the best experts on this subject based on the ideXlab platform.
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electric field control of li doping induced phase transition in vo2 film with crystal facet dependence
Nano Energy, 2018Co-Authors: Yuliang Chen, Zhaowu Wang, Shi Chen, Hui Ren, Wensheng Yan, Guobin Zhang, Jun Jiang, Chongwen ZouAbstract:Abstract The use of electric-field to manipulate the transport properties of correlated oxides is promising for achieving nano-functional electronic devices. As a typical correlated oxide material, vanadium dioxide (VO2) displays a special metal-insulator transition (MIT) at about 340 K. In this work, we select a water-free electrolyte gel, Li+/propylene carbonate, to achieve a non-volatile and reversible Li-doping and phase modulation in nano-VO2 crystal film under gating voltages. Synchrotron characterizations indicate the originally insulating VO2 undergoes an Effective Structure change and an increased V 3d-O 2p hybrid t2g-orbital occupancy, which is responsible for the metallic state formation as proved by first-principle calculation. The field-driving Li-doping shows pronounced facet dependence, indicating the existence of energetically favored channels for Li-ions diffusion along V-V chains as proved by dynamic stimulation. Our current findings will supply opportunities for the electric-field control of atomic sieve, correlated ionitronics and synaptic transistor.
Zhaowu Wang - One of the best experts on this subject based on the ideXlab platform.
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electric field control of li doping induced phase transition in vo2 film with crystal facet dependence
Nano Energy, 2018Co-Authors: Yuliang Chen, Zhaowu Wang, Shi Chen, Hui Ren, Wensheng Yan, Guobin Zhang, Jun Jiang, Chongwen ZouAbstract:Abstract The use of electric-field to manipulate the transport properties of correlated oxides is promising for achieving nano-functional electronic devices. As a typical correlated oxide material, vanadium dioxide (VO2) displays a special metal-insulator transition (MIT) at about 340 K. In this work, we select a water-free electrolyte gel, Li+/propylene carbonate, to achieve a non-volatile and reversible Li-doping and phase modulation in nano-VO2 crystal film under gating voltages. Synchrotron characterizations indicate the originally insulating VO2 undergoes an Effective Structure change and an increased V 3d-O 2p hybrid t2g-orbital occupancy, which is responsible for the metallic state formation as proved by first-principle calculation. The field-driving Li-doping shows pronounced facet dependence, indicating the existence of energetically favored channels for Li-ions diffusion along V-V chains as proved by dynamic stimulation. Our current findings will supply opportunities for the electric-field control of atomic sieve, correlated ionitronics and synaptic transistor.
