一种基于Bhattacharyya核的SVM

包括图像识别在内的很多应用领域里,把单个样本表示成向量的集合的形式是很自然的想法,利用一个合适的核函数我们可以把这些向量映射到一个更高维的Hilbert空间,在这个高维空间里用Kernel PCA方法找到样本的高斯分布族,这样就可以把样本上的核函数定义成它们所服从的高斯分布密度函数的Bhattacharrya仿射.这样得到的核函数具有比较好的性质,比如说在各种变换下有稳定性表现,从而也说明了即使还有别的表示样本的方法,用向量集合的形式来表示单个的样本也是具有合理性的.     

“快”带电离子通过固体时的“尾流”效应

简略介绍了“尾流”效应（ｗａｋｅｅｆｆｅｃｔ）的等离子体模型，并依之模拟计算了１．９１５ＭｅＶＨ、２．０６０ＭｅＶＨ在１００Ａ碳膜中分解后０°方向的能谱形式。给出了相同条件下的实验结果，将两者做了比较。     

一种寻找星图光斑质心的高精度算法及在成像畸变矫正中的应用

首先讨论星图识别中的质心寻找问题,提出了一种改进的匹配算法.使用高斯分布对光斑内像素点的强度分布进行近似模拟, 并采用最小二乘法中的法方程法对光斑图像质心坐标进行优化计算.算例表明该算法可以得到更为精确的结果, 在噪声小于最大像素值的$5\%$时,质心坐标计算精度高于0.04个像素, 优于以往的匹配算法的结果.最后讨论了算法在望远镜光学成像畸变矫正中的应用, 设计了矫正算法, 并通过算例验证了算法的合理性.     

GH分布族下资产收益率分布拟合优度比较——基于中国证券指数高频数据的实证研究

资产收益率分布假设对期权定价、对冲,风险度量和组合资产优化的结果有着重要影响.但由于资产收益率的"程式化性质",经典正态分布假设不能很好拟合实际收益率分布.广义双曲线分布,作为子分布及极限分布非常丰富的分布族,在资产收益率分布拟合中已取得良好效果.在讨论第三类修正贝塞尔函数和广义逆高斯分布性质基础上,借助于正态均值-方差混合理论,得到广义双曲线分布及其极限分布.在McNeil,Frey和Embrechts(2005)算法框架内,以及WenBo Hu(2005)算法改进基础上,对参数估计的算法做了实质性改进:用两个重要参数χ和ψ的线性关系,代替了一个包含第三类修正贝塞尔函数的方程,避免了对该方程数值求解.在实证部分,选择了3个主要指数,利用GH分布的两个子分布和两个极限分布对过滤后的指数收益率进行拟合,并对它们的拟合优度和收敛速度做了比较.     

非线性模型滞后相依的广义互信息检验

The general mutual information （GMI） and general conditional mutual information （GCMI） are considered to measure lag dependences in nonlinear time series. Both of the measures have the property of invariance with transform. The statistics based on GMI and GCMI are estimated using the correlation integral. Under the hypothesis of independent series, the estimators have Gaussian asymptotic distributions. Simulations applied to generated nonlinear series demonstrate that the methods appear to find frequently the correct lags.     

基于LED的标准太阳光谱灯拟合算法

在测量领域中需要使具有高稳定性及良好光谱匹配性的人工模拟太阳光谱标准灯.本文提出一种基于多种不同峰值波长LED光源的方法来准确模拟AM1.5的光谱分布.以最小二乘法和高斯分布数学模型为基础,在理论上实现了非均匀间隔峰值波长的光谱拟合,从而指导LED的种类选择及其所需的驱动电流值,并通过实验论证其可行性.结果表明:在300～1100 nm的范围内,使用较少LED种类的情况下,此方法光谱失配误差小于±2.76％.此算法可精确地分辨标准太阳光谱AM1.5的吸收谷,且应用于AM0的拟合时获得小于±1.67％的光谱失配度.在工程实践中,该算法对快速、准确获得标准太阳光谱灯具有良好的指导意义.     

The dynamics of one-dimensional random quantum XY system with Dzyaloshinskii-Moriya interaction

In this paper,the effects of random variables on the dynamics of the s = 1/2 XY model with the Dzyaloshinskii-Moriya interaction are studied.By means of the recurrence relation method in the high-temperature limit,we calculate the spin autocorrelation functions as well as the corresponding spectral densities for the cases that the exchange couplings between spins or external magnetic fields satisfy the double-Gaussian distribution.It is found that when the standard deviation of random exchange coupling δJ(or the standard deviation of random external field δB) is small,the dynamics of the system undergoes a crossover from a collective-mode behavior to a central-peak one.However,when δJ(or δB) is large,the crossover vanishes,and the system shows a central-peak behavior or the most disordered one.We also analyze the cases in which the exchange couplings or the external fields satisfy the bimodal and the Gaussian distributions.Our results show that for all the cases considered,the dynamics of the above system is similar to that of the one-dimensional random XY model.     

Extraction and verification of coherent structures in near-wall turbulence

According to the characteristics of coherent structures in near-wall turbulence, an accurate extraction and verification method is developed based on wavelet transform (WT) and correlation analysis in this paper. At first, the fluid field of a turbulent boundary layer is measured precisely in a gravitational low-speed water tunnel. On the basis of the distribution of the coherent structures, velocity data of three test points are selected and analyzed, whose dimensionless heights are 20.8, 33.5, and 42.6. According to the frequency range of power spectrum density (PSD), coherent and incoherent structures are both extracted from the original signals using continuous and orthogonal wavelet transforms. To confirm the validity of the extracted signals, the probability density function (PDF) of each extracted signal is calculated. The result demonstrates that the incoherent structures obey the Gaussian distribution, while the coherent structures deviate from the Gaussian distribution. The PDFs of the coherent structures and the original signals are similar, which shows that the coherent structures make most contributions to the turbulence. For further verification, a correlation parameter between coherent and incoherent structures is defined, which evidently proves the validity of the extraction method in this paper.     

关于最小不确定态的概率分布

本文借助于曲线坐标下动量算符的一种厄密形式,导出了广义坐标算符和广义动量算符的最小不确定态,并结合常见坐标分量取不同上、下限的情况讨论相应的概率分布,进而得到有关的结论.     

面向情感语音转换的韵律转换方法

面向情感语音转换,该文提出了一种韵律转换方法。该方法包含基频转换和时长转换两个部分,前者选择离散余弦变换(DCT)参数化基频,根据基频的层次结构特点,将基频分解为短语层和音节层两个层次,使用基于混合高斯模型(GMM)的转换方法对两个层次分别进行转换;后者使用基于分类回归树(CART)的方法以声韵母为基本单位对时长进行转换。一个包含三种基本情感的语料库用作训练和测试,客观评测以及主观评测实验结果显示该方法可有效进行情感韵律转换,其中悲伤情感在主观实验中达到了接近100%的正确率。