The results of numerical simulations of random-force-driven Navier-Stokes turbulence designed to test predictions of the renormalization group theory of turbulence are presented. By specially choosing the random force...
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Robertson and Seymour prove that a set of graphs of bounded tree-width is well-quasi-ordered by the graph minor relation. By extending their methods to matroids, Geelen, Gerards, and Whittle prove that a set of matroi...
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Single-particle cryo-electron microscopy (cryo-EM) has recently joined X-ray crystallography and NMR spectroscopy as a high-resolution structural method for biological macromolecules. Cryo-EM was selected by Nature Me...
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Classically, analysis on manifolds and graphs has been based on the study of the eigenfunctions of the Laplacian and its generalizations. These objects from differential geometry and analysis on manifolds have proven ...
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Classically, analysis on manifolds and graphs has been based on the study of the eigenfunctions of the Laplacian and its generalizations. These objects from differential geometry and analysis on manifolds have proven useful in applications to partial differential equations, and their discrete counterparts have been applied to optimization problems, learning, clustering, routing and many other algorithms.1-7 The eigenfunctions of the Laplacian are in general global: their support often coincides with the whole manifold, and they are affected by global properties of the manifold (for example certain global topological invariants). Recently a framework for building natural multiresolution structures on manifolds and graphs was introduced, that greatly generalizes, among other things, the construction of wavelets and wavelet packets in Euclidean spaces.8,9 This allows the study of the manifold and of functions on it at different scales, which are naturally induced by the geometry of the manifold. This construction proceeds bottom-up, from the finest scale to the coarsest scale, using powers of a diffusion operator as dilations and a numerical rank constraint to critically sample the multiresolution subspaces. In this paper we introduce a novel multiscale construction, based on a top-down recursive partitioning induced by the eigenfunctions of the Laplacian. This yields associated local cosine packets on manifolds, generalizing local cosines in Euclidean spaces.10 We discuss some of the connections with the construction of diffusion wavelets. These constructions have direct applications to the approximation, denoising, compression and learning of functions on a manifold and are promising in view of applications to problems in manifold approximation, learning, dimensionality reduction.
Recent work by some of the authors presented a novel construction of a multiresolution analysis on manifolds and graphs, acted upon by a given symmetric Markov semigroup {Tt}t≥o, for which T t has low rank for large ...
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Recent work by some of the authors presented a novel construction of a multiresolution analysis on manifolds and graphs, acted upon by a given symmetric Markov semigroup {Tt}t≥o, for which T t has low rank for large t.1 This includes important classes of diffusion-like operators, in any dimension, on manifolds, graphs, and in non-homogeneous media. The dyadic powers of an operator are used to induce a multiresolution analysis, analogous to classical Littlewood-Paley14 and wavelet theory, while associated wavelet packets can also be constructed.2 This extends multiscale function and operator analysis and signal processing to a large class of spaces, such as manifolds and graphs, with efficient algorithms. Powers and functions of T (notably its Green's function) are efficiently computed, represented and compressed. This construction is related and generalizes certain Fast Multipole Methods, 3 the wavelet representation of Calderón-Zygmund and pseudo-differential operators,4 and also relates to algebraic multigrid techniques.5 The original diffusion wavelet construction yields orthonormal bases for multiresolution spaces {Vj}. The orthogonality requirement has some advantages from the numerical perspective, but several drawbacks in terms of the space and frequency localization of the basis functions. Here we show how to relax this requirement in order to construct biorthogonal bases of diffusion scaling functions and wavelets. This yields more compact representations of the powers of the operator, better localized basis functions. This new construction also applies to non self-adjoint semigroups, arising in many applications.
We investigated the optimum hand-picking time of Nagano Purple, a rare Japanese table grape variety. The color sensitivity between pure red–purple–black and pure purple–black makes it difficult for farmers to harve...
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Presents two algorithms for LC unconstrained optimization problems which use the second order Dini upper directional derivative. Simplicity of the methods to use and perform; Discussion of related properties of the it...
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Presents two algorithms for LC unconstrained optimization problems which use the second order Dini upper directional derivative. Simplicity of the methods to use and perform; Discussion of related properties of the iteration function.
In recent years, Session Initiation Protocol (SIP) is more and more popular. However, there are many security problems in the Session Initiation Protocol. In 2005, Yang et al. [9] proposed a secure authentication sche...
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In recent years, Session Initiation Protocol (SIP) is more and more popular. However, there are many security problems in the Session Initiation Protocol. In 2005, Yang et al. [9] proposed a secure authentication scheme for Session Initiation Protocol. This authentication scheme is based on Diffie-Hellman [2] concept, so the computation cost of this authentication scheme is very high. In order to improve this shortcoming, Durlanik et al. [3] also proposed an authentication Scheme using ECDH in 2005. However, the computation cost of this authentication scheme is still very high. In this paper, we propose an efficient nonce-based authentication scheme. The computation cost of this authentication scheme is lower than Yang et al.s authentication scheme and Durlanik et al.s authentication scheme, and it is very suitable for low computation power equipment.
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