产品定级中挑选专家的数学模型

在工农业产品评定级别中，专家组的水平是至关重要的。文中给出一个挑选专家组成员的数学模型，可以检验专家对参评产品的决策水平，为评价所评结论的可信度提供参考依据。     

基于神经网络的VQ图象编码

文章给出将神经网络与矢量量化相结合的两种编码方法，介绍了其原理和实现的算法。经计算机模拟表明，在比特率低于０．３ｂｐｐ时仍可得到高质量的编码图象。     

Quantitative theory of living free‐radical polymerization. III. Calculation of copolymerization products' spinodal

The problem of finding conditions of the loss of thermodynamic stability by the reaction system was solved on the basis of the developed theory of living free‐radical copolymerization. The spinodal's calculations were carried out for a significant number of systems differing in the values of kinetic, stoichiometric, and thermodynamic parameters. Analysis of the results of such calculations revealed some regularities in the spinodal curves' behavior and permitted us to classify their possible topological types. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 892–902, 2003     

Some geometrical aspects of semidefinite linear complementarity problems

This article studies some geometrical aspects of the semidefinite linear complementarity problem (SDLCP), which can be viewed as a generalization of the well-known linear complementarity problem (LCP). SDLCP is a special case of a complementarity problem over a closed convex cone, where the cone considered is the closed convex cone of positive semidefinite matrices. It arises naturally in the unified formulation of a pair of primal-dual semidefinite programming problems. In this article, we introduce the notion of complementary cones in the semidefinite setting using the faces of the cone of positive semidefinite matrices and show that unlike complementary cones induced by an LCP, semidefinite complementary cones need not be closed. However, under R₀-property of the linear transformation, closedness of all the semidefinite complementary cones induced by L is ensured. We also introduce the notion of a principal subtransformation with respect to a face of the cone of positive semidefinite matrices and show that for a self-adjoint linear transformation, strict copositivity is equivalent to strict semimonotonicity of each principal subtransformation. Besides the above, various other solution properties of SDLCP will be interpreted and studied geometrically.     

Some identities for products and degree raising of splines

In this paper it is shown how the algebraic product of two spline functions, each represented in terms of B-splines, can again be represented as a linear combination of suitable B-splines. As a corollary to this result we obtain an explicit representation of a given B-spline function in terms of B-splines of some arbitrary higher degree. This generalizes some known results for raising the degree by one. Recurrence relations for both products and degree raising are established that may be useful for computation.Communicated by Larry L. Schumaker.     

Analysis on Optimal Error Exponents of Binary Classification for Source with Multiple Subclasses

We consider a binary classification problem for a test sequence to determine from which source the sequence is generated. The system classifies the test sequence based on empirically observed (training) sequences obtained from unknown sources P1 and P2. We analyze the asymptotic fundamental limits of statistical classification for sources with multiple subclasses. We investigate the first- and second-order maximum error exponents under the constraint that the type-I error probability for all pairs of distributions decays exponentially fast and the type-II error probability is upper bounded by a small constant. In this paper, we first give a classifier which achieves the asymptotically maximum error exponent in the class of deterministic classifiers for sources with multiple subclasses, and then provide a characterization of the first-order error exponent. We next provide a characterization of the second-order error exponent in the case where only P2 has multiple subclasses but P1 does not. We generalize our results to classification in the case that P1 and P2 are a stationary and memoryless source and a mixed memoryless source with general mixture, respectively.     

基于知识蒸馏与改进ViT网络的花卉图像细粒度分类

由于自然条件下拍摄的花卉图像背景复杂,而且其存在类内差异性大和类间相似性高的问题,现有主流方法仅依靠卷积模块提取花卉的局部特征难以实现准确的细粒度分类。针对上述问题,本文提出了1种高精度、轻量化的花卉分类方法(ConvTrans-ResMLP),通过结合Transformer模块和残差MLP(multi-layer perceptron)模块实现对花卉图像的全局特征提取,并在Transformer模块中加入卷积计算使得模型仍保留提取局部特征的能力;同时,为了进一步将花卉分类模型部署到边缘设备中,本研究基于知识蒸馏技术实现对模型的压缩与优化。实验结果表明,本文所提出的方法在Oxford 17、Oxford 102和自制的Flowers 32数据集上的准确率分别达98.62%、97.61%和98.40%;知识蒸馏后本文的轻量化模型的大小约为原来的1/18,而准确率仅下降2%左右。因此,本研究能较好地提升边缘设备下花卉细粒度分类的效率,对促进花卉培育的自动化发展具有切实意义。     

Differential Expression Analysis of Single-Cell RNA-Seq Data: Current Statistical Approaches and Outstanding Challenges

With the advent of single-cell RNA-sequencing (scRNA-seq), it is possible to measure the expression dynamics of genes at the single-cell level. Through scRNA-seq, a huge amount of expression data for several thousand(s) of genes over million(s) of cells are generated in a single experiment. Differential expression analysis is the primary downstream analysis of such data to identify gene markers for cell type detection and also provide inputs to other secondary analyses. Many statistical approaches for differential expression analysis have been reported in the literature. Therefore, we critically discuss the underlying statistical principles of the approaches and distinctly divide them into six major classes, i.e., generalized linear, generalized additive, Hurdle, mixture models, two-class parametric, and non-parametric approaches. We also succinctly discuss the limitations that are specific to each class of approaches, and how they are addressed by other subsequent classes of approach. A number of challenges are identified in this study that must be addressed to develop the next class of innovative approaches. Furthermore, we also emphasize the methodological challenges involved in differential expression analysis of scRNA-seq data that researchers must address to draw maximum benefit from this recent single-cell technology. This study will serve as a guide to genome researchers and experimental biologists to objectively select options for their analysis.     

空间谱估计无线电测向系统

空间谱估计测向方法以其超分辨力、高灵敏度和高准确度的测向性能被广泛应用,并在无线电管理领域扮演主要角色.在对空间谱估计测向理论研究的基础上,给出了具体算法,并对算法进行了仿真,最后通过对比测试论证了空间谱估计测向系统的实用性和优越性.     

数据挖掘中的数据分类算法综述

在数据挖掘的过程中,使用到很多分类算法,可见分类算法在数据挖掘中占有非常重要的地位。数据分类算法有很多种,各有不同的优缺点,因此,通过对不同算法特性的研究,有助于后期对算法进行相应的改进,确保新的分类算法能够具备更好的实用性能。数据分类算法的性能优良,不仅可以提高数据挖掘的功能性和实用性,还可以确保使用者对算法具备更多的选择性,基于此,对数据挖掘中不同的数据分类算法进行了研究和分析。