效应代数中的模糊滤子

在效应代数中引入模糊滤子和模糊理想的概念,讨论了它们的性质;引入并研究了强模糊滤子;在全序效应代数中提出了一个模糊同余关系并证明了这样生成的同余类是一个全序格效应代数.     

一类效应代数的态表示定理

1994年, Foulis和Bennett在表示不可精确测量的量子逻辑结构时引入了效应代数. 该文用直接构造的方法, 给出一类效应代数上的态表示定理. 即, 若Ω是紧的 Hausdorff 拓扑空间, 令E(Ω)={f: f∈C(Ω), 0≤f≤1}, 则φ 是(E(Ω),Ο, 0, 1) 上的态当且仅当Ω 上存在唯一的正则Borel 概率测度μ使得对每个f (E(Ω),Ο, 0, 1),φ (f)=∫_Ω f dμ.     

Deformation Techniques for Sparse Systems

We exhibit a probabilistic symbolic algorithm for solving zero-dimensional sparse systems. Our algorithm combines a symbolic homotopy procedure, based on a flat deformation of a certain morphism of affine varieties, with the polyhedral deformation of Huber and Sturmfels. The complexity of our algorithm is cubic in the size of the combinatorial structure of the input system. This size is mainly represented by the cardinality and mixed volume of Newton polytopes of the input polynomials and an arithmetic analogue of the mixed volume associated to the deformations under consideration. Research was partially supported by the following grants: UBACyT X112 (2004–2007), UBACyT X847 (2006–2009), PIP CONICET 2461, PIP CONICET 5852/05, ANPCyT PICT 2005 17-33018, UNGS 30/3005, MTM2004-01167 (2004–2007), MTM2007-62799 and CIC 2007–2008.     

土壤水分对近红外光谱实时检测土壤全氮的影响研究

利用近红外光谱技术实时预测土壤全氮含量是精细农业的研究热点之一,但是由于土壤水分在近红外波段的吸收系数较高,影响了土壤全氮含量的实时预测精度。使用布鲁克MATRIX_I傅里叶近红外光谱分析仪对不同土壤水分的土壤样本进行了近红外光谱扫描,定性和定量的分析了土壤水分对近红外光谱的影响,并提出了一种消除土壤水分对土壤全氮含量预测影响的方法。近红外光谱扫描结果显示在同一全氮含量水平下,随着土壤水分含量的增加,光谱吸光度呈逐渐上升的趋势,且变化趋势为非线性。通过对1 450和1 940 nm两个水分吸收波段的差分处理,设计了水分吸收指数MAI（moisture absorbance index）,再对土壤按照水分含量梯度进行分类,提出了相应的修正系数。修正后的6个土壤全氮特征波段处(940,1 050,1 100,1 200,1 300和1 550 nm)的土壤吸光度值作为建模自变量,使用BP神经网络建立了土壤全氮预测模型,模型的R_C,R_V,RMSEC,RMSEP和RPD分别达到了0.86,0.81,0.06,0.05和2.75;与原始吸光度所建模型相比较模型精度得到了显著提高。实验结果表明本方法可以有效地消除土壤水分对近红外光谱检测土壤全氮含量预测的影响,为土壤全氮含量实时预测提供了理论和技术支持。     

基于FTIR技术和稀疏线性判别分析的秦艽种类鉴别

傅里叶变换红外光谱通常包含有大量的波长变量点,对其进行定性分析需要建立稳健的、可解释性的分类模型。稀疏线性判别分析(SLDA)是一种较为新颖和有效的机器学习算法,常用于高维度、小样本数据的变量筛选和判别分析,SLDA通过在线性判别分析中引入正则项,使分类器训练过程和变量选择过程同时完成,不同判别方向上载荷系数的稀疏性则增强了模型的可解释性。采集甘肃不同产地的秦艽样本94个,其中麻花秦艽(Gentiana straminea Maxim)30个,黄管秦艽(Gentiana officinalis)28个,大叶秦艽(Gentiana macrophylla Pall)36个,利用傅里叶变换红外光谱法获得所有样本的光谱图。取其中70个样本构成训练集,剩余24个为测试集。使用训练集建立SLDA模型,对2个判别方向上不为0的载荷系数个数进行网格化寻优,得到了最优的参数空间。利用建立的SLDA模型对测试样本进行预测,其分类准确率达到100%,实现了对三种秦艽的快速、准确鉴别。实验结果表明,与PLS-DA方法相比,SLDA模型在分类准确率、稀疏性及可解释性方面均具有一定优势,是一种新颖、有效的光谱定性分析方法。     

Stochastic phenomena in a fiber Raman amplifier

The interplay of such cornerstones of modern nonlinear fiber optics as a nonlinearity, stochasticity and polarization leads to variety of the noise induced instabilities including polarization attraction and escape phenomena harnessing of which is a key to unlocking the fiber optic systems specifications required in high resolution spectroscopy, metrology, biomedicine and telecommunications. Here, by using direct stochastic modeling, the mapping of interplay of the Raman scattering‐based nonlinearity, the random birefringence of a fiber, and the pump‐to‐signal intensity noise transfer has been done in terms of the fiber Raman amplifier parameters, namely polarization mode dispersion, the relative intensity noise of the pump laser, fiber length, and the signal power. The obtained results reveal conditions for emergence of the random birefringence‐induced resonance‐like enhancement of the gain fluctuations (stochastic anti‐resonance) accompanied by pulse broadening and rare events in the form of low power output signals having probability heavily deviated from the Gaussian distribution.

     

基于改进基追踪去噪的水声单载波频域均衡信道估计

针对低信噪比下单载波频域均衡信道估计精度低导致均衡效果差的问题,利用基追踪去噪方法估计稀疏信道有效抽头具有的稳定特性,提出了一种在平稳水声信道条件下单载波频域均衡系统中应用的改进基追踪去噪稀疏信道估计方法。方法利用延拓循环前缀作为导频进行多次信道估计,将估计结果累积平均,再采用门限判决提取有效抽头得到信道估计值,从而提高了稀疏信道的估计精度。通过合理选择循环前缀延拓次数,尽可能地降低导频长度对频带利用率的影响。仿真对比分析了改进基追踪去噪算法与匹配滤波、最小平方以及传统基追踪去噪信道估计算法的性能以及对单载波频域均衡系统误码率的影响。仿真实验结果表明,改进基追踪去噪信道估计算法具有更优的估计精度,在单载波频域均衡系统中可以提高约3 dB的接收信噪比增益。     

Sparse representation-based classification algorithm for optical Tibetan character recognition

A sparse representation-based two-phase classification algorithm is proposed for off-line handwritten Tibetan character recognition. The first phase realizes coarse classification with the K-NN classifier by finding the K nearest neighbours of a test sample in the dictionary constructed by K-SVD with samples of all classes, and the classes of these neighbours are regarded as the candidate classes of the test sample. The second phase performs fine classification with the sparse representation classifier by sparsely representing the test sample with all elements of the dictionary constructed by K-SVD with samples of all candidate classes, and the test sample is finally classified into the candidate class with the maximal contribution in sparse representation. Experiments on the Tibetan off-line handwritten character database show that an optimal recognition rate of 97.17% has been reached and it is 2.12% higher than that of K-NN.