Some Useful Integral Representations for Information-Theoretic Analyses

This work is an extension of our earlier article, where a well-known integral representation of the logarithmic function was explored and was accompanied with demonstrations of its usefulness in obtaining compact, easily-calculable, exact formulas for quantities that involve expectations of the logarithm of a positive random variable. Here, in the same spirit, we derive an exact integral representation (in one or two dimensions) of the moment of a nonnegative random variable, or the sum of such independent random variables, where the moment order is a general positive non-integer real (also known as fractional moments). The proposed formula is applied to a variety of examples with an information-theoretic motivation, and it is shown how it facilitates their numerical evaluations. In particular, when applied to the calculation of a moment of the sum of a large number, n, of nonnegative random variables, it is clear that integration over one or two dimensions, as suggested by our proposed integral representation, is significantly easier than the alternative of integrating over n dimensions, as needed in the direct calculation of the desired moment.     

弱湍流大气激光通信中的光强闪烁研究

大气激光通信中，湍流引起的光强闪烁严重影响通信系统的性能指标（误码率）。通过对湍流条件下光强分布的数值仿真，得出弱湍流时接收光强服从对数正态分布，与Rytov理论一致。用随机过程分析的方法给出了系统误码率与光强闪烁的关系，并进行MATLAB数值模拟。研究表明误码率随对数振幅方差（湍流强度）的增加而上升，且当对数振幅方差在0～0．02时，误码率随对数振幅方差的变化较快，近似呈线性递增。在工程中，可采用自适应光学或多发射机等技术抑制湍流对大气激光通信的影响。     

Optimal estimation of the diffusion coefficient from non-averaged and averaged noisy magnitude data

The magnitude operation changes the signal distribution in MRI images from Gaussian to Rician. This introduces a bias that must be taken into account when estimating the apparent diffusion coefficient. Several estimators are known in the literature. In the present paper, two novel schemes are proposed. Both are based on simple least squares fitting of the measured signal, either to the median (MD) or to the maximum probability (MP) value of the Probability Density Function (PDF). Fitting to the mean (MN) or a high signal-to-noise ratio approximation to the mean (HS) is also possible. Special attention is paid to the case of averaged magnitude images. The PDF, which cannot be expressed in closed form, is analyzed numerically. A scheme for performing maximum likelihood (ML) estimation from averaged magnitude images is proposed. The performance of several estimators is evaluated by Monte Carlo (MC) simulations. We focus on typical clinical situations, where the number of acquisitions is limited. For non-averaged data the optimal choice is found to be MP or HS, whereas uncorrected schemes and the power image (PI) method should be avoided. For averaged data MD and ML perform equally well, whereas uncorrected schemes and HS are inadequate. MD provides easier implementation and higher computational efficiency than ML. Unbiased estimation of the diffusion coefficient allows high resolution diffusion tensor imaging (DTI) and may therefore help solving the problem of crossing fibers encountered in white matter tractography.     

Spherical harmonics MUSIC versus conventional MUSIC

With the three-dimensional symmetry and wide potential application, spherical array signal processing has been a hot research area for years. This paper devotes to the direction-of-arrival (DOA) estimation of the spherical arrays. Based on the orthogonality of the sensors’ location, MUSIC algorithm in spherical space is proposed, named as SH-MUSIC. Similar to beamspace MUSIC, spherical harmonics transformation is operated before MUSIC algorithm and a better performance is gotten because SH-MUSIC utilizes the array configuration’s orthogonality. On account of the transformation matrix’s orthogonality, spherical harmonics transformation is suggested to be operated firstly in other improved MUSIC algorithms without rejection, and it is demonstrated in beamspace MUSIC. In addition, owing to the tiny error between the steering vectors and the spherical harmonics with high order, sphere array data models including open sphere and rigid sphere are constructed. Simulation proves SH-MUSIC to be effective. Moreover, experimental data from a rigid sphere microphone array is dealt with by SH-MUSIC and the DOAs are estimated accurately.     

Optimization of magnetic field sweep and field modulation amplitude for continuous-wave EPR oximetry

For continuous-wave electron paramagnetic resonance spectroscopy, what settings of magnetic field sweep width and field modulation amplitude yield the best accuracy in estimated linewidth? Statistical bounds on estimation error presented in this work provide practical guidance: set the sweep width and modulation amplitude to 8 and 4 times the half-width half-maximum linewidth, Γ, respectively. For unknown linewidths in the range [Γ(min),Γ(max)] the worst-case estimation error is minimized by using settings designed for Γ(max). The analysis assumes a Lorentzian lineshape and a constant modulation amplitude across the extent of the irradiated paramagnetic probe. The analytical guidelines are validated using L-band spectroscopy with a particulate LiNc-BuO probe.     

Gaussian pre-filtering for uncertainty minimization in digital image correlation using numerically-designed speckle patterns

This paper discusses the effect of pre-processing image blurring on the uncertainty of two-dimensional digital image correlation (DIC) measurements for the specific case of numerically-designed speckle patterns having particles with well-defined and consistent shape, size and spacing. Such patterns are more suitable for large measurement surfaces on large-scale specimens than traditional spray-painted random patterns without well-defined particles. The methodology consists of numerical simulations where Gaussian digital filters with varying standard deviation are applied to a reference speckle pattern. To simplify the pattern application process for large areas and increase contrast to reduce measurement uncertainty, the speckle shape, mean size and on-center spacing were selected to be representative of numerically-designed patterns that can be applied on large surfaces through different techniques (e.g., spray-painting through stencils). Such “designer patterns” are characterized by well-defined regions of non-zero frequency content and non-zero peaks, and are fundamentally different from typical spray-painted patterns whose frequency content exhibits near-zero peaks. The effect of blurring filters is examined for constant, linear, quadratic and cubic displacement fields. Maximum strains between ±250 and ±20,000 µε are simulated, thus covering a relevant range for structural materials subjected to service and ultimate stresses. The robustness of the simulation procedure is verified experimentally using a physical speckle pattern subjected to constant displacements. The stability of the relation between standard deviation of the Gaussian filter and measurement uncertainty is assessed for linear displacement fields at varying image noise levels, subset size, and frequency content of the speckle pattern. It is shown that bias error as well as measurement uncertainty are minimized through Gaussian pre-filtering. This finding does not apply to typical spray-painted patterns without well-defined particles, for which image blurring is only beneficial in reducing bias errors.     

Hartmann势加新环型势的相对论束缚态解(英文)

在矢势与标势相等的情况下,对Hartmann势加新环型势的Klein-Gordon方程精确求解.给出了归一化的角向和径向波函数,同时获得了能谱方程.     

新颖的高温流场红外辐射物性参数计算方法

为解决高速飞行器红外辐射特性研究中高温气体辐射参数计算问题,在转动平滑谱带（smeared rotational band, SRB）模型的假设下,首次提出基于贝叶斯估计的跳转马尔科夫链蒙特卡罗（reversible jump Markov chain monte carlo, RJMCMC）方法来计算高温流场中气体组分红外光谱物性参数。仿真计算和实验测量表明,仅需很少的先验知识,且不需要相关跃迁系数,该方法可以很好的估计主要振动跃迁带的位置,所提取的SRB模型参数的变化规律与SRB理论模型结果一致,利用拟合参数计算得到不同温度下谱带积分发射和吸收系数与逐线计算的结果非常近似。     

流体PVT的对应关系

本文依据对应态原理,提出新定义的对比压缩因子Zr=(1-Z)/(1-ZC)的无量纲交换式和对饱和温度的对比温度Tsr=T/Ts式,并根据两种流体工质对比压力Pr1=Pr2,对比温度Tsr1=Tsr2相等时,Zr1=Zr2相等的原则,导出了从一种已知PVT关系的物质推算它种物质的PVT值的通用方法。用本方法以水为标准物质推算了R12、R131、R134a、C2H4等几种物质在过热气体区、超临界区和液体区比容,计算值与文献实验值的平均偏差小于2,最大偏差小于4%。