单峰高斯分布适应面上的误差阈

在Eigen的单峰适应面模型基础上,提出了生物体的适应值为高斯分布的随机适应面模型。 利用系综平均的方法, 计算了在单峰高斯分布适应面上准物种的浓度分布和误差阈。 结果表明, 对于小的适应面涨落, 准物种分布和误差阈与确定情形相比变化极小,误差阈对于小的涨落是稳定的。 然而, 当适应值涨落较大时,从准物种到误差灾变的转变不再明显。 误差阈变宽, 并且在涨落增加时向大的突变率方向移动。 Based on the Eigen model with a single peak fitness landscape, the fitness values of all sequence types are assumed to be random with Gaussian distribution. By ensemble average method, the concentration distribution and error threshold of quasispecies on single peak Gaussian distributed fitness landscapes were evaluated. It is shown that the concentration distribution and error threshold change little in comparing with deterministic case for small fluctuations, which implies that the error threshold is stable against small perturbation. However, as the fluctuation increases, the situation is quite different. The transition from quasi species to error catastrophe is no longer sharp. The error threshold becomes a narrow band which broadens and shifts toward large values of error rate with increasing fluctuation.     

Measurement Error Correction for Distributed Properties – Filter Cake Thickness Measurements

The measurement of a distributed property is frequently encountered in engineering applications. The impact of a possible measurement error on the measured distribution is described and two methods to account for such an error are detailed: A Fourier transform based deconvolution procedure and a moment based deconvolution approach via kernel estimators are presented. The deconvolution methods can be used in many particle characterization and process applications where particle features or properties are commonly presented in a distributed form. In the current instance, these methods are carefully explored by using artificially generated data and applied to experimental data obtained from filter cake thickness measurements.     

随机化的Eigen模型研究

为了使Eigen模型能够更真实地描述物种的演化过程,将确定性Eigen模型改造成随机模型.以Eigen模型为理论框架,把基因序列中每一个位点的突变率看作一个高斯随机变量,从而导出随机性Eigen模型.对于此随机性Eigen模型,当突变率的涨落强度较小时,准物种的误差阈位置几乎没有改变,仍是个相变点;而当突变率的涨落强度变大时,误差阈由一个相变点变为一个转变区域.在真实的物种演化过程中,误差阈应是一个转变区域,而且在解决实际问题时应考虑该转变区域的上限.     

A Family of Fitness Landscapes Modeled through Gene Regulatory Networks

Fitness landscapes are a powerful metaphor for understanding the evolution of biological systems. These landscapes describe how genotypes are connected to each other through mutation and related through fitness. Empirical studies of fitness landscapes have increasingly revealed conserved topographical features across diverse taxa, e.g., the accessibility of genotypes and “ruggedness”. As a result, theoretical studies are needed to investigate how evolution proceeds on fitness landscapes with such conserved features. Here, we develop and study a model of evolution on fitness landscapes using the lens of Gene Regulatory Networks (GRNs), where the regulatory products are computed from multiple genes and collectively treated as phenotypes. With the assumption that regulation is a binary process, we prove the existence of empirically observed, topographical features such as accessibility and connectivity. We further show that these results hold across arbitrary fitness functions and that a trade-off between accessibility and ruggedness need not exist. Then, using graph theory and a coarse-graining approach, we deduce a mesoscopic structure underlying GRN fitness landscapes where the information necessary to predict a population’s evolutionary trajectory is retained with minimal complexity. Using this coarse-graining, we develop a bottom-up algorithm to construct such mesoscopic backbones, which does not require computing the genotype network and is therefore far more efficient than brute-force approaches. Altogether, this work provides mathematical results of high-dimensional fitness landscapes and a path toward connecting theory to empirical studies.     

数字波面恢复中的高斯门限法

在工程干涉度量中获得的干涉图往往信噪比低且不为常值,这给采用条纹细化和拟合方法恢复波面带来困难,并导致较大的测量误差.本文提出的高斯门限法不仅克服了常用技术的不足,简便易行,而且经计算机模拟分析和测试实例分析表明,本法具有很高的精度和可靠性.文中详述了高斯门限的原理、算法,提供了实例分析结果.     

Comparison of SRS thresholds under pumping by Gaussian and Bessel beams

In the paraxial approximation, it has been shown that the quasi-stationary SRS amplification coefficient in the near-threshold region is determined by the product of the pump intensity in the beam center and the overlap integral of the transverse structure of the pump and the Stokes component. Expressions for the overlap integral and the scattering powers have been obtained and analyzed for the following cases: the pump and the Stokes field are Gaussian beams; the pump and the Stokes field are Bessel beams; the pump is a Bessel beam and the Stokes field is an axial Gaussian beam. Relations between the SRS excitation thresholds in different cases have been found.Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 71, No. 6, pp. 778–787, November–December, 2004.This revised version was published online in April 2005 with a corrected cover date.     

简易高斯灰度扩散模型的误差分析及适用性研究

为了验证简易高斯灰度扩散模型的适用性,与传统高斯灰度扩散模型进行了对比分析。将两种高斯模型做归一化处理,设定检验像素,分析检验像元灰度的归一化值的相对误差;进行星图模拟,得到4个不同高斯半径(σ)下灰度赋值相对误差与像点映射位置偏离值的关系曲线,整体上误差随σ的增大而减小;对星图模拟得到的系列星像点采用灰度重心法提取质心,质心误差随σ增大而减小,传统模型模拟像点的质心提取精度比简易模型高约2个数量级。无噪声条件下σ=0.671时,简易模型模拟像点最大质心误差仅为0.033pixel。仿真结果表明:单就像点外形仿真而言,当σ较小时,简易模型不再适用;但针对像点的质心定位及后续算法,简易模型带来质心误差量级可以忽略,运算量更小,适于应用。     

物理学中常用的高斯与类高斯型积分

本文展示了基于大学数学基础对不同积分限的高斯与类高斯型积分的求解方法,并列举了高斯与类高斯型积分在“热力学与统计物理”、“光学”、“量子力学”、“量子光学”等物理学科中的若干应用实例.     

Utility–Privacy Trade-Off in Distributed Machine Learning Systems

In distributed machine learning (DML), though clients’ data are not directly transmitted to the server for model training, attackers can obtain the sensitive information of clients by analyzing the local gradient parameters uploaded by clients. For this case, we use the differential privacy (DP) mechanism to protect the clients’ local parameters. In this paper, from an information-theoretic point of view, we study the utility–privacy trade-off in DML with the help of the DP mechanism. Specifically, three cases including independent clients’ local parameters with independent DP noise, dependent clients’ local parameters with independent/dependent DP noise are considered. Mutual information and conditional mutual information are used to characterize utility and privacy, respectively. First, we show the relationship between utility and privacy for the three cases. Then, we show the optimal noise variance that achieves the maximal utility under a certain level of privacy. Finally, the results of this paper are further illustrated by numerical results.     

Variational Sparse Bayesian Learning for Estimation of Gaussian Mixture Distributed Wireless Channels

In this paper, variational sparse Bayesian learning is utilized to estimate the multipath parameters for wireless channels. Due to its flexibility to fit any probability density function (PDF), the Gaussian mixture model (GMM) is introduced to represent the complicated fading phenomena in various communication scenarios. First, the expectation-maximization (EM) algorithm is applied to the parameter initialization. Then, the variational update scheme is proposed and implemented for the channel parameters’ posterior PDF approximation. Finally, in order to prevent the derived channel model from overfitting, an effective pruning criterion is designed to eliminate the virtual multipath components. The numerical results show that the proposed method outperforms the variational Bayesian scheme with Gaussian prior in terms of root mean squared error (RMSE) and selection accuracy of model order.     

曲率波前传感器探测高斯光束时的信号误差

曲率波前传感器已被用于天文自适应光学和光学度量等领域。在这些领域使用时都假设入射波前光强均匀,但这种假设与曲率传感技术的基本原理不一致。利用傅里叶光学理论,给出了光强不均匀情况下曲率波前传感器的曲率信号解析式,并利用光强均匀和不均匀情况下的信号表达式对探测高斯光束时的信号误差进行了数值分析。结果表明：曲率波前传感器探测高斯光束时存在一定误差,相位分布为4阶Zernike多项式时,误差最大,且阶数越高,误差越小;分区平均曲率信号误差较小,一般在10％以下。     

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.     

聚丙烯酸酯泡沫密度均匀性的射线检测技术

低密度泡沫材料大多存在一定程度的密度不均匀性，这对其后续使用性能将带来不良影响。文中简述了ICF靶用聚丙烯酸酯泡沫的制备方法，并利用β射线和X射线检测技术，对直径为mm量级的低密度聚丙烯酸酯泡沫柱进行密度分布表征。研究结果表明:泡沫柱沿轴向的密度分布比较均匀，而沿径向呈内低外高分布，形成了明显的密度梯度。实验表明:射线检测技术测量靶用低密度泡沫的方法可基本满足目前的实验要求，但密度分辨率和空间分辨率还有待进一步提高。     

Effect of structural parameters of Gaussian repaired pit on light intensity distribution inside KH_2PO_4 crystal

KH2PO4 （KDP） crystal with excellent optical properties is a very important element of inertial confinement fusion （ICF） device. However, KDP crystal surface micro-defects severely reduce the crystal laser damage threshold, affecting the crystal service life. In this paper, Gaussian repaired pit is used to replace the crystal surface micro-defects, in order to improve the laser damage resistance of the KDP crystal with surface micro-defects. At first, the physical model of Gaussian repaired pit is built by Fourier model method, and the accuracy of the method is analyzed. It is found that the calculation error can be reduced by increasing the product of the width-period ratio and the truncation constant of the repaired pit. The calculation results about the physical model of Gaussian repaired pit show that the light intensity distribution within the crystal is symmetrical, and there are evidently enhanced light intensity regions in the crystal. Meanwhile, the maximum relative intensity inside the KDP crystal decreases gradually with the increase of the width of the Gaussian repaired pit. Secondly, the Gaussian repaired pits with different widths and the same depth of 20 μm are processed by micro-milling. Their surfaces are very smooth and present the ductile cutting state under the microscope. Finally, the laser damage threshold of the Gaussian repaired pits on the surface of the KDP crystal sample is measured by a 3 ω, 6-ns laser. The results showthat the maximum threshold of the Gaussian repaired pits is 3.12 J/cm2, which is 60% higher than the threshold of initial damage point, and the laser damage threshold increases with the increase of the width of the Gaussian repaired pit.     

Stochastic Symmetry-Breaking in a Gaussian Hopfield Model

We study a two-pattern Hopfield model with Gaussian disorder. We find that there are infinitely many pure states at low temperatures in this model, and that the metastate is supported on an infinity of symmetric pairs of pure states. The origin of this phenomenon is the random breaking of a rotation symmetry of the distribution of the disorder variables.     

MEMS惯性传感器随机误差分析与去噪研究

针对MEMS传感器中存在的误差,采用Allan方差法分析法分析其存在的误差类型,并通过改进小波阈值函数、调整分解尺度观察存在的误差项在去噪前后的变化,探究各误差项与阈值函数、分解尺度之间存在的关系,从而有针对性地对MEMS惯性传感器中存在的特定随机误差进行降噪。结果表明：几类改进阈值函数对角(速)度随机游走的抑制效果与软、硬阈值函数无明显差异,效果并不理想;不同的尺度分解可以去除不同的误差项,从而提高MEMS传感器精度。     

Collapse arrest in a two-dimensional Airy Gaussian beam and Airy Gaussian vortex beam in nonlocal nonlinear media

Propagation dynamics of a two-dimensional Airy Gaussian beam and Airy Gaussian vortex beam are investigated numerically in local and nonlocal nonlinear media. The self-healing and collapse of the beam crucially depend on the distribution factor b and the topological charge m. With the aid of nonlocality, a stable Airy Gaussian beam and an Airy Gaussian vortex beam with larger amplitude can be obtained, which always collapse in local nonlinear media. When the distribution factor b is large enough, the Airy Gaussian vortex beam will transfer into quasi-vortex solitons in nonlocal nonlinear media.     

非傍轴矢量高斯光束的光强表示

 基于瑞利-索末菲衍射积分,未使用任何近似,对非傍轴矢量光束的两种光强表示式,即传统光强公式和时间平均坡印廷矢量的z分量进行了研究。对非傍轴矢量高斯光束详细数值计算结果的比较表明,两种表示式之间的差异,即两者的相对误差与束腰宽度及传输距离和波长的比值有关。对非傍轴矢量高斯光束,若传输距离与波长的比值为10,束腰宽度与波长的比值大于等于0.8,则最大相对误差不到1.5%。因此,传统光强公式是可用的。