The Experts below are selected from a list of 51 Experts worldwide ranked by ideXlab platform
Tomoo Yokoyama - One of the best experts on this subject based on the ideXlab platform.
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recurrence pointwise almost periodicity and orbit closure relation for flows and foliations
Topology and its Applications, 2013Co-Authors: Tomoo YokoyamaAbstract:Abstract In this paper, we obtain a characterization of the recurrence of a Continuous Vector Field w of a closed connected surface M as follows. The following are equivalent: (1) w is pointwise recurrent. (2) w is pointwise almost periodic. (3) w is minimal or pointwise periodic. Moreover, if w is regular, then the following are equivalent: (1) w is pointwise recurrent. (2) w is minimal or the orbit space M / w is either [ 0 , 1 ] , or S 1 . (3) R is closed (where R : = { ( x , y ) ∈ M × M | y ∈ O ( x ) ¯ } is the orbit closure relation). On the other hand, we show that the following are equivalent for a codimension one foliation F on a compact connected manifold: (1) F is pointwise almost periodic. (2) F is minimal or compact. (3) F is R-closed. Also we show that if a foliated space on a compact metrizable space is either minimal or both compact and without infinite holonomy, then it is R-closed.
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recurrence pointwise almost periodicity and orbit closure relation for flows and foliations
arXiv: Dynamical Systems, 2012Co-Authors: Tomoo YokoyamaAbstract:In this paper, we obtain a characterizations of the recurrence of a Continuous Vector Field $w$ of a closed connected surface $M$ as follows. The following are equivalent: 1) $w$ is pointwise recurrent. 2)$w$ is pointwise almost periodic. 3) $w$ is minimal or pointwise periodic. Moreover, if $w$ is regular, then the following are equivalent: 1) $w$ is pointwise recurrent. 2)$w$ is minimal or the orbit space $M/w$ is either $[0,1]$, or $S^1$. 3) $R$ is closed (where $R := \{(x,y) \in M \times M \mid y \in \bar{O(x)} \}$ is the orbit closure relation). On the other hand, we show that the following are equivalent for a codimension one foliation $\mathcal{F}$ on a compact manifold: 1) $\mathcal{F}$ is pointwise almost periodic. 2) $\mathcal{F}$ is minimal or compact. 3) $\mathcal{F}$ is $R$-closed. Also we show that if a foliated space on a compact metrizable space is either minimal or is both compact and without infinite holonomy, then it is $R$-closed.
Hajimu Kawakami - One of the best experts on this subject based on the ideXlab platform.
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Vector Field approximation by model inclusive learning of neural networks
International Conference on Artificial Neural Networks, 2007Co-Authors: Yasuaki Kuroe, Hajimu KawakamiAbstract:The problem of Vector Field approximation arises in the wide range of Fields such as motion control, computer vision and so on. This paper proposes a method for reconstructing an entire Continuous Vector Field from a sparse set of sample data by training neural networks. In order to make approximation results possess inherent properties of Vector Fields and to attain reasonable approximation accuracy with computational efficiency, we include a priori knowledge on inherent properties of Vector Fields into the learning problem of neural networks, which we call model inclusive learning. An efficient learning algorithm of neural networks is derived. It is shown through numerical experiments that the proposed method makes it possible to reconstruct Vector Fields accurately and efficiently.
Yasuaki Kuroe - One of the best experts on this subject based on the ideXlab platform.
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Vector Field approximation by model inclusive learning of neural networks
International Conference on Artificial Neural Networks, 2007Co-Authors: Yasuaki Kuroe, Hajimu KawakamiAbstract:The problem of Vector Field approximation arises in the wide range of Fields such as motion control, computer vision and so on. This paper proposes a method for reconstructing an entire Continuous Vector Field from a sparse set of sample data by training neural networks. In order to make approximation results possess inherent properties of Vector Fields and to attain reasonable approximation accuracy with computational efficiency, we include a priori knowledge on inherent properties of Vector Fields into the learning problem of neural networks, which we call model inclusive learning. An efficient learning algorithm of neural networks is derived. It is shown through numerical experiments that the proposed method makes it possible to reconstruct Vector Fields accurately and efficiently.
Jiaojiao Ren - One of the best experts on this subject based on the ideXlab platform.
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the asymptotic stability of caputo fractional order switching systems with only Continuous Vector Field functions
IEEE Access, 2021Co-Authors: Jiaojiao RenAbstract:In this paper, a theorem with very weak conditions on Vector Field functions for asymptotic stability of Caputo fractional order switching systems is proposed. Based on Vainikko’s lemmas, the Caputo fractional derivative of a Continuously differentiable and convex Lyapunov function, along trajectories of any Caputo fractional order switching systems with Vector Field function being only Continuous, proves to be Continuous and have a very useful estimation. This weakens the smoothness requirement on the Vector Field functions for fractional stability analysis from differentiability as in existing results to only continuity. Finally, the numerical implementation of a Caputo fractional order switching system with only Continuous Vector Field function illustrates the effectiveness of the proposed theorem.
Gabriel Taubin - One of the best experts on this subject based on the ideXlab platform.
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VectorField isosurface based reconstruction from oriented points
International Conference on Computer Graphics and Interactive Techniques, 2005Co-Authors: Peter G Sibley, Gabriel TaubinAbstract:We present a new and much simpler formulation for the problem of reconstructing an implicit surface from an oriented point cloud acquired by a range scanner or a stereo vision system. Data Vectors are first extended to a Continuous Vector Field on a bounding volume, which is then integrated in the least squares sense yielding an implicit function whose zero level set approximates the data points. Function discretizations associated with regular grids automatically produce Iso-surface polygon meshes. Extrapolating missing and noisy data, integrating multiple scans, developing data structures and algorithms optimized for fast visualization and geometry processing, are challenging problems and active areas of research addressed by this work. We plan to use multi-resolution data structures to integrate streams of point clouds in real time. Implicit representations have the advantage of dealing with arbitrary topology. [Ohtake et al. 2003] introduces an adaptive hierarchal implicit representation composed of local quadric patches and weights associated with nodes in a oct-tree. Given that for rendering or post-processing we extract an isosurface over a regular grid (e.g., via Marching Cubes), it is worth exploring reconstruction algorithms that use implicit functions defined as a regular scalar Field. In the area of geometry processing, the notion of decoupling the filtering of normal Fields and geometry has emerged as a powerful method for denoising [Tasdizen et al. 2003]. We argue that a similar decoupling for the surface reconstruction problem is worth exploring. This preliminary work presents a volumetric method for surface reconstruction that directly incorporates both point and normal information. Instead of imposing constraints and regularization directly on the values of the potential (scalar) Field, we impose constraints and regularization on the gradient Field. We implement this using a combination of least-squares fitting and solving a Poisson problem over a uniform grid. The general problem of implicit surface reconstruction is as follows. Given an oriented point cloud i.e., m points and their normals, D = {(pi, ni)} sampled from a surface M, compute an implicit surface M ′ = {p| f (p) = 0} where f : R 3 → R and ∀(pi, ni) ∈ D ∇ f (pi) = ni and f (pi) = 0. (1) The least squares solution f using interpolatory constraints (1) will not, in general, produce satisfactory results without some regularization.