Hyperkähler structures and infinite-dimensional Grassmannians

In this paper, we describe an example of a hyperkähler quotient of a Banach manifold by a Banach Lie group. Although the initial manifold is not diffeomorphic to a Hilbert manifold (not even to a manifold modelled on a reflexive Banach space), the quotient space obtained is a Hilbert manifold, which can be furthermore identified either with the cotangent space of a connected component (j∈Z), of the restricted Grassmannian or with a natural complexification of this connected component, thus proving that these two manifolds are isomorphic hyperkähler manifolds. Moreover, Kähler potentials associated with the natural complex structure of the cotangent space of and with the natural complex structure of the complexification of are computed using Kostant-Souriau's theory of prequantization.     

Low-temperature helium in bulk and in restricted geometries

Experiments with helium in thin films and small pores show that the bulk properties are greatly modified. With ⁴He, the onset of superfluidity is depressed and the specific heat anomaly is rounded and also depressed to lower temperatures. With ³He new features are found such as surface magnetism and free path effects. Bulk superfluid ⁴He is shown to have a sharp transition to turbulence, and bulk ³He the characteristics of a Fermi fluid.     

连续音素的改进深信度网络的识别算法*

为提高连续语音识别中的音素识别率,提出一种基于改进并行回火训练的受限波尔兹曼机的音素识别算法。首先,利用经过等能量划分后的改进并行回火算法来训练受限玻尔兹曼机,接着将受限玻尔兹曼机堆叠组成一个深信度网络,从而作为深度神经网络预训练的基础模型,然后通过softmax层输出,得到用于音素状态后验概率检测的深度神经网络。接着,利用少量的标签数据,根据反向传播算法对网络权重进行微调。最后,将所得后验概率作为隐马尔科夫的发射概率,然后利用Viterbi解码器实现音素识别。在TIMIT语料库上的实验表明,识别率相比于传统的对比散度类算法提高了约4.5%,在不增加计算量的情况下比原始并行回火算法提高约1%。     

Spectral characterization of diffusion with chemical shift resolution: Highly concentrated water-in-oil emulsion

We present a modulated gradient spin-echo method, which uses a train of sinusoidally shaped gradient pulses separated by 180° radio-frequency (RF) pulses. The RF pulses efficiently refocus chemical shifts and de-phasing due to susceptibility differences, resulting in undistorted, high-resolution diffusion weighted spectra. This allows for the simultaneous spectral characterization of the diffusion of several molecular species with different chemical shifts. The technique is robust against susceptibility artifacts, field inhomogeneity and imperfections in the gradient generating equipment. The feasibility of the technique is demonstrated by measuring the diffusion of water, oil, and water-soluble salt in a highly concentrated water-in-oil emulsion. The diffusion of water and salt reveal precise information about the droplet size distribution below the μm-range. Common droplet size distribution explains both the data for water with finite long-range diffusion and the data for salt with negligible long-range diffusion. The results of water diffusion show that the technique is efficient in deconvolving the effects of molecular exchange between droplets and restricted diffusion within droplets. The effects of water exchange suggest that droplets of different sizes are uniformly distributed within the sample.     

限进介质固相萃取及其应用

系统地介绍了限进介质固相萃取的原理、特点、发展现状及其发展趋势,并对该技术在生物和环境样品前处理中的应用作了较详细的综述。引用文献58篇。     

Selective on-line serum peptide extraction and multidimensional separation by coupling a restricted-access material-based capillary trap column with nanoliquid chromatography–tandem mass spectrometry

As the serum peptidome gets increasing attention for biomarker discovery, one of the important issues is how to efficiently extract the peptides from highly complex human serum for peptidome analysis. Here we developed a fully automated platform for direct injection, on-line extraction, multidimensional separation and MS detection of peptides present in human serum. A capillary SPE column packed with a novel mix mode restricted access material (RAM) exhibiting strong cation exchange and size exclusion chromatography (SCX/SEC) properties were coupled with a nanoliquid chromatography–mass spectrometry (nanoLC-MS) system. The capillary SPE column excludes the high abundant serum proteins such as HSA by size exclusion chromatography and simultaneously extracts the low molecular weight peptides by binding to sulfonic acid residues. Subsequently, the trapped peptides are eluted to a capillary LC column packed with a RP-C18 stationary phase. After injection of only 2 μL human serum to the one-dimensional nanoLC-MS system around 400 peptides could be identified. When conducting a multidimensional separation, the described SCX/SEC/RP-MS platform allows the separation and identification of 1286 peptides present in human serum by the injection and on-line processing of 20 μL human serum sample.     

Manifold Reconstruction in Arbitrary Dimensions Using Witness Complexes

It is a well-established fact that the witness complex is closely related to the restricted Delaunay triangulation in low dimensions. Specifically, it has been proved that the witness complex coincides with the restricted Delaunay triangulation on curves, and is still a subset of it on surfaces, under mild sampling conditions. In this paper, we prove that these results do not extend to higher-dimensional manifolds, even under strong sampling conditions such as uniform point density. On the positive side, we show how the sets of witnesses and landmarks can be enriched, so that the nice relations that exist between restricted Delaunay triangulation and witness complex hold on higher-dimensional manifolds as well. We derive from our structural results an algorithm that reconstructs manifolds of any arbitrary dimension or co-dimension at different scales. The algorithm combines a farthest-point refinement scheme with a vertex pumping strategy. It is very simple conceptually, and it does not require the input point sample to be sparse. Its running time is bounded by c(d)n ², where n is the size of the input point cloud, and c(d) is a constant depending solely (yet exponentially) on the dimension d of the ambient space. Although this running time makes our reconstruction algorithm rather theoretical, recent work has shown that a variant of our approach can be made tractable in arbitrary dimensions, by building upon the results of this paper. This work was done while S.Y. Oudot was a post-doctoral fellow at Stanford University. His email there is no longer valid.     

A restricted nonlinear large eddy simulation model for high Reynolds number flows

Recent numerical studies of the restricted nonlinear (RNL) model have demonstrated its ability to reproduce important features of wall turbulence despite a severe reduction in the number of degrees of freedom. In these prior studies, the RNL model included full resolution of the viscous term. In this work, we extend the RNL model to arbitrarily high Reynolds numbers by developing a RNL large eddy simulation (LES) framework along with a method to systematically identify an appropriate streamwise wavenumber support based on spectral properties of wall turbulence. This method leads to a band-limited RNL–LES system which is successful in reproducing some of the most important statistical features captured in previous low to moderate Reynolds number simulations, e.g. the mean velocity and second-order moment profiles. The RNL–LES framework offers a new approach to understanding the connection between coherent structures and the momentum transfer mechanisms of wall turbulence at arbitrarily high Reynolds numbers, where resolution of the viscous terms can become computationally expensive even with the relatively low computational complexity afforded through the dynamical restriction of the RNL model.     

Metrically Regular Mapping and Its Utilization to Convergence Analysis of a Restricted Inexact Newton-Type Method

In the present paper,we study the restricted inexact Newton-type method for solving the generalized equation 0∈f(x)+F(x),where X and Y are Banach spaces,f:X→Y is a Frechet differentiable function and F:X■Y is a set-valued mapping with closed graph.We establish the convergence criteria of the restricted inexact Newton-type method,which guarantees the existence of any sequence generated by this method and show this generated sequence is convergent linearly and quadratically according to the particular assumptions on the Frechet derivative of f.Indeed,we obtain semilocal and local convergence results of restricted inexact Newton-type method for solving the above generalized equation when the Frechet derivative of f is continuous and Lipschitz continuous as well as f+F is metrically regular.An application of this method to variational inequality is given.In addition,a numerical experiment is given which illustrates the theoretical result.     

极小Cayley图的限制性边连通度

一个连通图X的边集的一个子集C称为一个限制性边割,如果它是一个边割,且X／C不含孤立点。X的限制性边连通度λ′（X）定义为所有限制性边割的最小基数。本文完全决定了极小Cayley图的限制性边连通度。