基于支持向量描述的自适应高光谱异常检测算法

提出了一种应用于高光谱异常检测的自适应支持向量数据描述方法.根据高光谱数据和局部异常检测模型的特点,通过局部背景分波段二阶分布统计,分析了核参量与局部背景总体标准差的变化关系,构造了随检测背景变化的局部检测核参量,使得检测算法针对不同背景分布自适应地调整检测核参量.克服了传统支持向量描述算法由于采用固定核参量带来的复杂背景下检测性能下降的问题.通过模拟数据和真实高光谱数据的测试检验,接收机特性曲线表明该算法相对于传统固定核参量支持向量数据描述方法,在相同虚警概率下检测概率提高了10%.     

Comparison of the generalized Riemann solver and the gas-kinetic scheme for inviscid compressible flow simulations

The generalized Riemann problem (GRP) scheme for the Euler equations and gas-kinetic scheme (GKS) for the Boltzmann equation are two high resolution shock capturing schemes for fluid simulations. The difference is that one is based on the characteristics of the inviscid Euler equations and their wave interactions, and the other is based on the particle transport and collisions. The similarity between them is that both methods can use identical MUSCL-type initial reconstructions around a cell interface, and the spatial slopes on both sides of a cell interface involve in the gas evolution process and the construction of a time-dependent flux function. Although both methods have been applied successfully to the inviscid compressible flow computations, their performances have never been compared. Since both methods use the same initial reconstruction, any difference is solely coming from different underlying mechanism in their flux evaluation. Therefore, such a comparison is important to help us to understand the correspondence between physical modeling and numerical performances. Since GRP is so faithfully solving the inviscid Euler equations, the comparison can be also used to show the validity of solving the Euler equations itself. The numerical comparison shows that the GRP exhibits a slightly better computational efficiency, and has comparable accuracy with GKS for the Euler solutions in 1D case, but the GKS is more robust than GRP. For the 2D high Mach number flow simulations, the GKS is absent from the shock instability and converges to the steady state solutions faster than the GRP. The GRP has carbuncle phenomena, likes a cloud hanging over exact Riemann solvers. The GRP and GKS use different physical processes to describe the flow motion starting from a discontinuity. One is based on the assumption of equilibrium state with infinite number of particle collisions, and the other starts from the non-equilibrium free transport process to evolve into an equilibrium one through particle collisions. The different mechanism in the flux evaluation deviates their numerical performance. Through this study, we may conclude scientifically that it may NOT be valid to use the Euler equations as governing equations to construct numerical fluxes in a discretized space with limited cell resolution. To adapt the Navier–Stokes (NS) equations is NOT valid either because the NS equations describe the flow behavior on the hydrodynamic scale and have no any corresponding physics starting from a discontinuity. This fact alludes to the consistency of the Euler and Navier–Stokes equations with the continuum assumption and the necessity of a direct modeling of the physical process in the discretized space in the construction of numerical scheme when modeling very high Mach number flows. The development of numerical algorithm is similar to the modeling process in deriving the governing equations, but the control volume here cannot be shrunk to zero.     

二维阵列光场衍射自成像效应的倒格矢分析

基于衍射的角谱理论,分析了一般二维周期阵列光场的衍射特性.提出了一种用阵列光场的倒格矢来研究和描述衍射自成像（或泰伯效应）的方法.给出了用倒格矢表示的一般衍射自成像条件.在此基础上,对典型的非正交六方型二维周期阵列光场的泰伯效应和分数泰伯效应进行了定量分析和计算机模拟.     

Note on Generalized Quantum Gates and Quantum Operations

Recently, Gudder proved that the set of all generalized quantum gates coincides the set of all contractions in a finite-dimensional Hilbert space (S. Gudder, Int. J. Theor. Phys. 47:268–279, 2008). In this note, we proved that the set of all generalized quantum gates is a proper subset of the set of all contractions on an infinite dimensional separable Hilbert space ℋ. Meanwhile, we proved that the quantum operation deduced by an isometry is an extreme point of the set of all quantum operations on ℋ. This subject is supported by NSF of China (10571113).     

基于支持向量机的模型传递方法研究

模型传递是以数学方法通过在2台不同仪器之间寻求一种变换关系来增强光谱仪数据通用性、可比性的一种基本途径。由于实际测量数据具有非线性特征,加上校正样本集合的有限性,使得解决小样本条件下非线性关系的模型传递问题显得尤为重要。文章在概述支持向量机基本原理的基础上,探讨了支持向量机方法在光谱仪的模型传递问题中的应用,提出了基于支持向量机的分段直接校正方法,最后采用计算机模拟的方式对该方法进行了举例说明,并和人工神经网络方法进行了相应的比较。     

混合气体红外光谱支持向量机分析的新方法

介绍了一种基于支持向量机的混合气体红外光谱组分浓度和种类分析的新方法。利用核函数将组分气体特征吸收谱线重叠严重的混合气体光谱在高维空间变换后,建立SVM回归校正模型,进行混合气体浓度分析。在利用支持向量机回归校正模型进行混合气体组分浓度分析的同时,证明支持向量机回归校正模型也可用于混合气体组分种类分析。对不同组分和不同组分浓度的混合气体红外光谱数据进行了实验,研究了谱仪扫描间隔、分析特征波长范围、核函数和惩罚因子等因素对分析结果的影响。混合气体组分浓度实验结果的最大平均绝对误差Mean AE为0.132%;混合气体组分种类识别的准确率大于94%。解决了传统的光谱分析方法中光谱特征谱线重叠、光谱数据的维数大、定性和定量分析无法使用同一方法等问题,可用于其他混合气体的红外光谱分析,具有实际应用价值。     

激光陀螺中背向散射的研究

为了研究谐振腔形状变化对激光陀螺中背向散射的影响,基于矢量叠加理论,分析了激光陀螺背向散射源及其对总的背向散射的影响.根据背向散射对顺逆时针光的耦合作用,推导出了总的背向散射系数与顺逆时针旋转光光强的关系式.基于这一关系,设计实验,通过施加电压使谐振腔反射镜到不同位置来改变光腔形状变化,同时测量光强交流量的振幅,得到了总的背向散射系数的变化曲线.通过与仿真结果对比,验证了背向散射的矢量叠加理论.     

Optimising time-varying gradient orientation for microstructure sensitivity in diffusion-weighted MR

Here we investigate whether varying the diffusion-gradient orientation during a general waveform single pulsed-field gradient sequence improves sensitivity to the size of coherently oriented pores over having a fixed orientation. The experiment optimises the shape and the orientation of the gradient waveform in each of a set of measurements to minimise the expected variance of estimates of the parameters of a simple model. A key application motivating the work is measuring the size of axons in white matter. Thus, we use a two compartment white matter model with impermeable, single-radius cylinders, and search for waveforms that maximise the sensitivity to axon radius, intra-cellular volume fraction and diffusion constants. Output of the optimisation suggests the only benefit of allowing the gradient orientation to vary in the plane perpendicular to the cylinders is that we can gain perpendicular gradient strength by maximising two orthogonal gradients simultaneously. This suggests that varying orientation in itself does not increase the sensitivity to model parameters. On the other hand, the variation in a plane containing the parallel direction increases the sensitivity significantly because parallel sensitivity improves the diffusion constant estimates. However, we also find that similar improvement in the estimates can be achieved without optimising the orientation, but by having one measurement in the parallel and the rest in the perpendicular direction. The optimisation searches a very large space where it cannot hope to find the global minimum so we cannot make a categorical conclusion. However, given the consistency of the results in multiple reruns and variations of the experiments reported here, we can suggest that for probing coherently oriented systems, pulse sequences with variable orientation, such as double-wave vector sequences, do not offer more advantage than fixed orientation sequences with optimised shape. The advantage of varying orientation is however likely to emerge for more complex systems with dispersed pore orientation.     

94 GHz回旋管准光模式变换器设计

基于几何光学理论和矢量绕射理论,研究了将回旋管及其他高功率微波器件的振荡输出模式转换成准光高斯波束的模式变换器,采用伏拉索夫(Vlasov)辐射器和三级准光反射面实现了准高斯模TEM₀₀的横向输出.研究了Vlasov辐射器的工作机理,运用矢量绕射理论计算出波导辐射场,口面电流分布的方法计算反射面辐射场.通过编写程序设计了将94 GHz,模式为TE₆₂的毫米波转化为准光高斯波束的内置式准光模式变换器. 关键词： 94 GHz回旋管 内置式准光模式变换器 Vlasov辐射器 矢量绕射理论     

具连续偏差变元的向量抛物型方程的H-振动性

考虑一类具连续偏差变元的向量抛物型偏微分方程的振动性,利用Domslak引进的H-振动的概念及内积降维的方法,将多维振动问题化为一维泛函微分不等式不存在最终正解的问题,给出了该类方程在Robin边值条件下所有解H-振动的若干充分条件,这里H是R^M中的单位向量．