Sobolev H1 geometry of the symplectomorphism group

For a closed symplectic manifold $(M,\omega )$ with compatible Riemannian metric g we study the Sobolev $H^1$ geometry of the group of all $H^s$ diffeomorphisms on M which preserve the symplectic structure. We show that, for sufficiently large s, the $H^1$ metric admits globally defined geodesics and the corresponding exponential map is a non-linear Fredholm map of index zero. Finally, we show that the $H^1$ metric carries conjugate points via some simple examples.     

一类压缩型映射的不动点定理

在完备的度量空间中,讨论了一类新型的非线性压缩映射ρ(Tx,Ty)≤a(ρ(x,y))ρ(x,Tx)+b(ρ(x,y))ρ(y,Ty)+c(ρ(x,y))ρ(x,y)通过构造迭代序列,指出该映射的不动点的存在性和唯一性,并给出相应的误差估计式,拓展和改进了有关文献的范围.     

Hyperplane sections of determinantal varieties over finite fields and linear codes

We determine the number of ${\mathbb{F}}_q$-rational points of hyperplane sections of classical determinantal varieties defined by the vanishing of minors of a fixed size of a generic matrix, and identify the hyperplane sections giving the maximum number of ${\mathbb{F}}_q$-rational points. Further we consider similar questions for sections by linear subvarieties of a fixed codimension in the ambient projective space. This is closely related to the study of linear codes associated to determinantal varieties, and the determination of their weight distribution, minimum distance, and generalized Hamming weights. The previously known results about these are generalized and expanded significantly. Connections to eigenvalues of certain association schemes, distance regular graphs, and rank metric codes are also indicated.     

The Szegö kernel on a class of non-compact CR manifolds of high codimension

We generalize Nagel’s formula for the Szegö kernel and use it to compute the Szegö kernel on a class of non-compact CR manifolds whose tangent space decomposes into one complex direction and several totally real directions. We also discuss the control metric on these manifolds and relate it to the size of the Szegö kernel.     

Setting local rank constraints by orthogonal projections for image resolution analysis: Application to the determination of a low dose pharmaceutical compound

Raman chemical imaging provides chemical and spatial information about pharmaceutical drug product. By using resolution methods on acquired spectra, the objective is to calculate pure spectra and distribution maps of image compounds. With multivariate curve resolution-alternating least squares, constraints are used to improve the performance of the resolution and to decrease the ambiguity linked to the final solution. Non negativity and spatial local rank constraints have been identified as the most powerful constraints to be used.     

非齐度量测度空间上Morrey-Herz空间上的广义分数次积分算子及其交换子

设(χ,d,μ)是一个同时满足上双倍条件和几何双倍条件的非齐度量测度空间,对于引进的一类非齐度量测度空间上的Morrey-Herz空间,利用非齐度量测度空间的特征,证明了广义分数次积分算子及其交换子在非齐度量测度空间上MorreyHerz空间的有界性.     

Similar,or dissimilar,that is the question. How different are methods for comparison of compounds similarity?

Comparison of compounds similarity is one of the main strategies of virtual screening protocols. Both similarity and dissimilarity concepts are of great importance during the search for new active compounds. Similarity is important due to the assumption that underlies the process of searching for new drug candidates: structurally similar compounds should induce similar biological response. On the other hand, we are also interested in dissimilarity, as we usually aim to find structurally novel ligands. In the study, we compared several approaches of evaluating compound similarity. Various representations and metrics were applied and we indicated the rate of variation of the results that can occur when shifting from one strategy to another. We compared both general similarity of datasets using different approaches, as well as examined the changes in the set of nearest neighbors when changing one compound representation into another, and the influence of representation/metric settings on the clustering outcome. We hope that the study will be of great help during the preparation of virtual screening experiments, stressing the need for careful selection of the way, the compound similarity is assessed. The differences in the results that can be obtained via the application of particular strategy can significantly influence the outcome of comparison studies; therefore, its settings should be carefully selected beforerunning the comparison.     

卷积神经网络用于近红外光谱古筝面板木材分级

目前,我国乐器制作行业在古筝面板用木材等级的筛选上主要依赖于技师主观评判,但此法缺少科学理论的依据,效率低,客观性及出材率的提高等方面受到限制,无法满足乐器市场的大量需求。实现古筝面板用木材快速、智能化的分级工作是一个急需解决的课题。近红外光谱非常适用于测量含氢的有机物质。古筝面板木材主要化学成分的化学键均由含氢基团组成,不同等级板材的化学成分存在差异,这些差异反映在近红外光谱中,为判断木材等级提供了可能。同时卷积神经网络对非线性数据具有较强的特征提取能力,所以提出一种应用卷积神经网络模型对光谱数据进行分析的方法,进而判别木材的等级。应用了Savitzky Golay一阶、二阶微分两种预处理方法和核主成分分析、连续投影算法两种数据压缩方法,通过所设计的卷积神经网络模型以样本识别准确率和模型构建过程中的损失值作为判定指标选出最佳预处理和数据压缩方法。为了提高模型提取分析光谱数据的能力和避免过拟合现象,应用了多通道卷积核、批量归一化和early stopping策略,将通过两层卷积层提取的特征信息送入全连接层,从而充分提取剩余信息,通过Softmax函数获得板材的最终预测等级,从而确定了最终模型。最终Savitzky Golay一阶微分和核主成分分析为最佳数据处理方法,同时得出用于区分不同等级的古筝面板用木材的主要关键谱带,分别为1 163~1 243, 1 346~1 375和1 525~1 584 nm。将该模型应用于测试集样本,古筝面板用木材的等级识别准确率为95.5%。实验结果表明所提出的方法可以高效地处理光谱数据,有效识别区分不同等级的古筝面板用木材的关键特征,从而为广阔的乐器市场提供一定的技术支持。     

A Unified Approach to Local Quantum Uncertainty and Interferometric Power by Metric Adjusted Skew Information

Local quantum uncertainty and interferometric power were introduced by Girolami et al. as geometric quantifiers of quantum correlations. The aim of the present paper is to discuss their properties in a unified manner by means of the metric adjusted skew information defined by Hansen.