一种基于高斯混合模型的改进EM算法研究

针对传统EM算法存在估计参数不具有最优性,以及在参数估计中需要人工参与等问题,提出一种基于高斯混合模型的改进EM算法。采用无人工参与的无监督思想,获取高斯混合模型对直方图拟合的最优参数组合。实验表明,该算法不仅能够快速地估计模型参量,而且能够给出最优参数,并在图像增强中使细节更明显,对比度更适中。     

二维映射神经元模型中的相干双共振

在具有稳定次阈值振荡特性的二维映射神经元模型中,研究了在没有外界输入信号时噪声对体系动力学的影响.通过数值计算发现了当体系的确定性动力学处于静息状态时,噪声可以诱导出神经元膜电位的随机振荡,而且随着噪声强度的变化,这种振荡的相干性具有两个极大值.另外我们还研究了当体系的确定性动力学处于稳定次阈值振荡及神经脉冲状态时的噪声效应,结果表明噪声对体系动力学的影响与其确定性动力学的分岔特性密切相关.     

The Weierstrass–Mandelbrot Process Revisited

We derive a functional central limit theorem for quasi-Gaussian processes. In particular, we prove that the limit of the Mandelbrot–Weierstrass process is a complex fractional Brownian motion.     

平面上方二维介质目标对高斯波束的电磁散射研究

基于矩量法、互易性定理及镜像理论,提出了一种新的混合方法用于研究水平分界面上方二维介质目标对垂直入射高斯波束的差值散射场.应用镜像理论,介质水平分界面可被原始目标相对于该分界面的镜像目标所替代,从而给出散射问题的等效模型.在等效模型中,应用矩量法求解了原始目标及镜像目标对高斯波束的散射场,同时结合互易性定理得到了原目标与其镜像目标之间的耦合散射场.数值计算结果与相关文献方法及MoM所得结果进行了比较,验证了该混合方法的有效性. 关键词： 互易性定理 电磁散射 高斯波束 二维目标     

色散介质中啁啾高斯脉冲的时间和光谱特性

对啁啾高斯脉冲光束在色散介质中的时间和光谱特性作了研究.给出了远场光谱蓝移和脉冲展宽的解析式.结果表明：通过选择适当的啁啾参量,啁啾高斯脉冲光束沿轴上传输色散长度时,脉冲可恢复到初始值.随啁啾参量增加,谱线宽度展宽,轴上光谱蓝移增加,在远场蓝移趋于一渐近值.随啁啾参量增加,离轴光谱红移增加.     

Gradient force evolution of Gaussian beam induced by a phase plate

The evolution of gradient force pattern induced by an annular phase distribution plate is numerically investigated in this paper. The phase plate, which may alter the wavefront phase of incident Gaussian beam with tunable topological charge, consists of two concentric portions, one center circle portion and one annular portion. Numerical simulations show that the proposed plate can induce the tunable gradient force on the particles in the focal region. By adjusting the geometrical parameters or changing the topological charge of the phase-shifting plate, some novel trap patterns may occur, such as triangle shape trap, quadrangle shape trap, pentagon shape trap, hexagon shape trap, and the shapes of optical traps change very considerably. Therefore, the phase plate may be very advantageous for constructing tunable optical traps. The method is more versatile in that it allows precise control of the parameters and has the possibility of generating specific patterns of optical vortices. The gradient force pattern focal of intensity distribution depends on both the annular width and the topological charge.     

Systematics on fission fragment mass distribution of neutron induced 235U fission

Based on the neutron induced fission fragment mass distribution data up to neutron energy 20 MeV measured with the double kinetic energy method (KEM) and the radio active method (RAM), the systematics of fission fragment mass distribution was investigated by using 5 Gaussian model and the systematics parameters were obtained by fitting the experimental data. With the systematics, the yields of any mass A and at any energy in the region from 0 to 20 MeV of neutron energy can be calculated. The calculated results could well reproduce the experimental data measured with KEM, but show some systematical deviation from the data measured by RAM, which reflects some systematical deviations between the two kinds of measured data.The error of systematics yield was calculated in an exact error transformation way, including from the error of the experimental yield data to the error of the discrete parameters, then to the systematics parameters,and at last to the yield calculated with systematics.     

高斯拟合算法在光谱建模中的应用研究

采用高斯拟合算法对光谱进行特征提取,利用拟合得到的特征参量表征光谱信息,并结合多元校正方法对光谱模型进行优化和解释,建立了样品快速准确的测定方法。实验以玉米活体叶片为研究对象,建立叶片光谱与叶绿素含量之间的关系模型,采用三个高斯峰对原始光谱的1 551个数据拟合后,光谱数据转换为9个高斯特征量(约为整个波段的0.58%),进而利用该高斯特征量来预测叶绿素含量。实验结果显示,采用高斯拟合分别与偏最小二乘法和主成分回归结合建模,其预测集相关系数分别为0.960和0.962;不采用高斯拟合算法而直接采用偏最小二乘法和主成分回归对全光谱建模,其预测集相关系数分别为0.957和0.919。可见,将高斯拟合算法运用到定量分析模型中是可行的,该方法不仅简化了模型参数,而且提高了模型的可解释性。     

Complex geometrical optics of Kerr type nonlinear media

The paper generalizes paraxial complex geometrical optics (PCGO) for Gaussian beam (GB) propagation in nonlinear media of Kerr type. Ordinary differential equations for the beam amplitude and for complex curvature of the wave front are derived, which describe the evolution of axially symmetric GB in a Kerr type nonlinear medium. It is shown that PCGO readily provides the solutions of NLS equation obtained earlier from diffraction theory on the basis of the aberration-free approach. Besides reproducing classical results of self-focusing PCGO readily describes an influence of the initial curvature of the wave front on the beam evolution in a medium of Kerr type including a nonlinear graded-index fiber. The range of applicability of the PCGO theory is discussed as well which is helpful for avoiding nonphysical solutions.     

基于相依成分分析-红外光谱法的黄芩炮制过程分析

将相依成分分析(DCA)算法用于模拟混合组分红外光谱(IR)分析及黄芩炮制过程分析与终点确定。研究结果表明,DCA法能从黄芩炮制过程测定的IR信号中提取相依组分(DC)信息,而且这些DC对应的光谱特征信息与对应的黄芩活性组分光谱特征相一致;通过观测DC相对强度变化趋势,确定黄芩炮制过程终点为55 min。该研究为黄芩炮制过程分析与终点确定提供了新途径。