Measuring clock jumps using pulsar timing

In this paper,we investigate the statistical signal-processing algorithm to measure the instant local clock jump from the timing data of multiple pulsars.Our algorithm is based on the framework of Bayesian statistics.In order to make the Bayesian algorithm applicable with limited computational resources,we dedicated our efforts to the analytic marginalization of irrelevant parameters.We found that the widely used parameter for pulsar timing systematics,the"Efac"parameter,can be analytically marginalized.This reduces the Gaussian likelihood to a function very similar to the Student’s t-distribution.Our iterative method to solve the maximum likelihood estimator is also explained in the paper.Using pulsar timing data from the Yunnan Kunming 40-m radio telescope,we demonstrate the application of the method,where 80-ns level precision for the clock jump can be achieved.Such a precision is comparable to that of current commercial time transferring service using satellites.We expect that the current method could help developing the autonomous pulsar time scale.     

Skeleton and fractal scaling in complex networks

We find that the fractal scaling in a class of scale-free networks originates from the underlying tree structure called a skeleton, a special type of spanning tree based on the edge betweenness centrality. The fractal skeleton has the property of the critical branching tree. The original fractal networks are viewed as a fractal skeleton dressed with local shortcuts. An in silico model with both the fractal scaling and the scale-invariance properties is also constructed. The framework of fractal networks is useful in understanding the utility and the redundancy in networked systems.     

Bayesian estimation of Karplus parameters and torsion angles from three-bond scalar couplings constants

We apply Bayesian inference to analyze three-bond scalar coupling constants in an objective and consistent way. The Karplus curve and a Gaussian error law are used to model scalar coupling measurements. By applying Bayes' theorem, we obtain a probability distribution for all unknowns, i.e., the torsion angles, the Karplus parameters, and the standard deviation of the Gaussian. We infer all these unknowns from scalar coupling data using Markov chain Monte Carlo sampling and analytically derive a probability distribution that only involves the torsion angles.     

Graceful exit from inflation using quantum cosmology

A massless scalar field without self-interaction and string coupled to gravity is quantized in the framework of quantum cosmology using the Bohm–de Broglie interpretation. Gaussian superpositions of the quantum solutions of the corresponding Wheeler–DeWitt equation in minisuperspace are constructed. The Bohmian trajectories obtained exhibit a graceful exit from the inflationary pre-big bang epoch to the decelerated expansion phase.     

Multiple small objects tracking based on dynamic Bayesian networks with spatial prior

This paper proposes an end-to-end algorithm for multiple small objects tracking in noisy video using a combination of Gaussian mixture based background segmentation along with a Dynamic Bayesian Networks (DBNs) based tracking. Background segmentation is based on an adaptive backgrounding method that models each pixel as a mixture of Gaussians with spatial prior and uses an online approximation to update the model, the spatial prior is constructed for small objects. Furthermore, we create observation model with hidden variable based on multi-cue statistical object model and employ Kalman filter as inference algorithm. Finally, we use linear assignment problem (LAP) algorithm to perform the models matching. The experimental results show the proposed method outperforms competing method, and demonstrate the effectiveness of the proposed method.     

水声信号稀疏重构的高阶累积量波达方向估计

高阶累积量具有高斯噪声抑制和阵元扩展特性,将高阶累积量引入水声信号的方位估计中,提出了离格稀疏贝叶斯学习重构的高阶累积量测向算法。该方法利用高阶累积量对高斯噪声的自然盲性,计算阵列信号四阶累积量来滤除高斯噪声,使阵元在原来的结构上扩展了一倍;并构造出选择矩阵剔除了四阶累积量中的冗余项,能再一次的扩展阵元,得到的新观测模型具有更好的统计性能;最后利用空域稀疏性,推导出四阶累积量下的离格稀疏表示模型,采用贝叶斯学习解算出源信号的最大后验概率,实现了目标方位估计。数值仿真和海试实验数据表明,该方法在相邻声源方位间隔为4°的情况下分辨概率可达到95%以上,在信噪比大于-5 dB时目标方位估计的均方根误差在1°以内,可显著抑制背景噪声干扰,在多声源密集分布条件下也能准确、稳健的对水声目标方位进行估计。      

Mixture-Based Probabilistic Graphical Models for the Label Ranking Problem

The goal of the Label Ranking (LR) problem is to learn preference models that predict the preferred ranking of class labels for a given unlabeled instance. Different well-known machine learning algorithms have been adapted to deal with the LR problem. In particular, fine-tuned instance-based algorithms (e.g., k-nearest neighbors) and model-based algorithms (e.g., decision trees) have performed remarkably well in tackling the LR problem. Probabilistic Graphical Models (PGMs, e.g., Bayesian networks) have not been considered to deal with this problem because of the difficulty of modeling permutations in that framework. In this paper, we propose a Hidden Naive Bayes classifier (HNB) to cope with the LR problem. By introducing a hidden variable, we can design a hybrid Bayesian network in which several types of distributions can be combined: multinomial for discrete variables, Gaussian for numerical variables, and Mallows for permutations. We consider two kinds of probabilistic models: one based on a Naive Bayes graphical structure (where only univariate probability distributions are estimated for each state of the hidden variable) and another where we allow interactions among the predictive attributes (using a multivariate Gaussian distribution for the parameter estimation). The experimental evaluation shows that our proposals are competitive with the start-of-the-art algorithms in both accuracy and in CPU time requirements.     

基于Contourlet变换的遥感图像去噪新算法

提出了一个新的有效的基于Contourlet变换的遥感图像去噪方法。对有噪图像进行Contourlet分解;对Contourlet变换系数引入一个几何先验模型,结合噪声和有用信号的条件分布进行贝叶斯估计,得到每一系数作为有用信号的后验概率,以之作为修正因子修正小波萎缩因子;对重构图像进行递归循环运算处理。仿真实验结果表明,去噪后图像去除了常见的伪吉布斯现象,峰值信噪比提高了1~2 dB。     

Optimal Reception of a Stochastic Signal with Unknown Duration Against the Background of White Noise

We obtain algorithms for optimal (Bayesian) detection and measurement of the duration of a random pulse observed against a background of white Gaussian noise. Potential reception characteristics are determined as a result of computer simulation of the synthesized algorithms.     

A Bayesian tutorial for data assimilation

Data assimilation is the process by which observational data are fused with scientific information. The Bayesian paradigm provides a coherent probabilistic approach for combining information, and thus is an appropriate framework for data assimilation. Viewing data assimilation as a problem in Bayesian statistics is not new. However, the field of Bayesian statistics is rapidly evolving and new approaches for model construction and sampling have been utilized recently in a wide variety of disciplines to combine information. This article includes a brief introduction to Bayesian methods. Paying particular attention to data assimilation, we review linkages to optimal interpolation, kriging, Kalman filtering, smoothing, and variational analysis. Discussion is provided concerning Monte Carlo methods for implementing Bayesian analysis, including importance sampling, particle filtering, ensemble Kalman filtering, and Markov chain Monte Carlo sampling. Finally, hierarchical Bayesian modeling is reviewed. We indicate how this approach can be used to incorporate significant physically based prior information into statistical models, thereby accounting for uncertainty. The approach is illustrated in a simplified advection–diffusion model.     

Uncertainty analysis in matched-field geoacoustic inversions

Quantifying uncertainty for parameter estimates obtained from matched-field geoacoustic inversions using a Bayesian approach requires estimation of the uncertainties in the data due to ambient noise as well as modeling errors. In this study, the variance parameter of the Gaussian error model, hereafter called error variance, is assumed to describe the data uncertainty. In practice, this parameter is not known a priori, and choosing a particular value is often difficult. Hence, to account for the uncertainty in error variance, several methods are introduced for implementing both the full and empirical Bayesian approaches. A full Bayesian approach that permits uncertainty of the error variance to propagate through the parameter estimation processes is a natural way of incorporating the uncertainty of error variance. Due to the large number of unknown parameters in the full Bayesian uncertainty analysis, an alternative, the empirical Bayesian approach, is developed, in which the posterior distributions of model parameters are conditioned on a point estimate of the error variance. Comparisons between the full and empirical Bayesian inferences of model parameters are presented using both synthetic and experimental data.     

Scaled unscented transform Gaussian sum filter: Theory and application

In this work we consider the state estimation problem in nonlinear/non-Gaussian systems. We introduce a framework, called the scaled unscented transform Gaussian sum filter (SUT-GSF), which combines two ideas: the scaled unscented Kalman filter (SUKF) based on the concept of scaled unscented transform (SUT) (Julier and Uhlmann (2004) [16]), and the Gaussian mixture model (GMM). The SUT is used to approximate the mean and covariance of a Gaussian random variable which is transformed by a nonlinear function, while the GMM is adopted to approximate the probability density function (pdf) of a random variable through a set of Gaussian distributions. With these two tools, a framework can be set up to assimilate nonlinear systems in a recursive way. Within this framework, one can treat a nonlinear stochastic system as a mixture model of a set of sub-systems, each of which takes the form of a nonlinear system driven by a known Gaussian random process. Then, for each sub-system, one applies the SUKF to estimate the mean and covariance of the underlying Gaussian random variable transformed by the nonlinear governing equations of the sub-system. Incorporating the estimations of the sub-systems into the GMM gives an explicit (approximate) form of the pdf, which can be regarded as a “complete” solution to the state estimation problem, as all of the statistical information of interest can be obtained from the explicit form of the pdf (Arulampalam et al. (2002) [7]).In applications, a potential problem of a Gaussian sum filter is that the number of Gaussian distributions may increase very rapidly. To this end, we also propose an auxiliary algorithm to conduct pdf re-approximation so that the number of Gaussian distributions can be reduced. With the auxiliary algorithm, in principle the SUT-GSF can achieve almost the same computational speed as the SUKF if the SUT-GSF is implemented in parallel.As an example, we will use the SUT-GSF to assimilate a 40-dimensional system due to Lorenz and Emanuel (1998) [27]. We will present the details of implementing the SUT-GSF and examine the effects of filter parameters on the performance of the SUT-GSF.     

Reception of a Signal with Unknown Duration

The maximum likely and optimal (Bayesian) algorithms for detecting an arbitrary-shaped signal observed against the background of Gaussian white noise and for measuring the duration are synthesized. Exact expressions for the characteristics of the maximum likely algorithms are found. The characteristics of the Bayesian algorithms are obtained using computer simulations.     

Gaussian beam scattering by a chiral sphere

Based on the generalized Lorenz–Mie theory that provides the general framework, an analytic solution to Gaussian beam scattering by a chiral sphere is constructed, by expanding the incident Gaussian beam, scattered fields and internal fields in terms of spherical vector wave functions. The unknown expansion coefficients are determined by a system of equations derived from the boundary conditions. For a localized beam model, numerical results of the normalized differential scattering cross section are presented.     

场共轭数值模拟研究

给出了一种考虑光源的强度分布后用两个变形镜头实现场共轭的算法,并对高斯光束进行了数值模拟,结果表明这种算法是有效的。变形镜平滑的表面可以剔除相位局部跳变,明显改善光强分布。对高斯光束,发射面相位面形状十分简单,易于用变形镜构造。本文还讨论了两变形镜之间距离的影响,最后指出如何改进现有算法。     

Exciton States in a Gaussian Confining Potential Well

We consider the problem of an electron-hole pair in a Gaussian confining potential well. This problem is treated within the effective-mass approximation framework using the method of numerical matrix diagonalization. The energy levels of the low-lying states are calculated as a function of the electron-hole effective mass ratio and the size of the confining potential.     

Exciton States in a Gaussian Confining Potential Well

We consider the problem of an electron-hole pair in a Gaussian confining potential well. This problem is treated within the effective-mass approximation framework using the method of numerical matrix diagonalization. The energy levels of the low-lying states are calculated as a function of the electron-hole effective mass ratio and the size of the confining potential.     

一种快速稀疏贝叶斯学习的水声目标方位估计方法研究

针对以具有时序结构的稀疏贝叶斯学习(Temporally multiple sparse Bayesian learning,TMSBL)为重构算法的水声目标DOA (Direction-of-arrival)估计方法存在运算速度慢的问题,结合块稀疏贝叶斯学习(Block-spare Bayesian learning,BSBL)理论框架下DOA估计模型与特点,采用MacKay提出的定点方法(Fixed-point method)对TMSBL算法中的核心超参量进行求解,提出一种快速的水声目标方位估计稀疏贝叶斯学习的方法,该方法具有运算速度快,重构概率高的特点,并通过实验仿真从运算时间、失败率和均方根误差等方面与TMSBL算法进行比较,验证了该方法的可行性与有效性。      

Fidelity criterion for quantum-domain transmission and storage of coherent states beyond the unit-gain constraint

We generalize the experimental success criterion for quantum teleportation (memory) in continuous-variable quantum systems to be suitable for a non-unit-gain condition by considering attenuation (amplification) of the coherent-state amplitude. The new criterion can be used for a nonideal quantum memory and long distance quantum communication as well as quantum devices with amplification process. It is also shown that the framework to measure the average fidelity is capable of detecting all Gaussian channels in the quantum domain.     

Bayesian wavelet-based analysis of functional magnetic resonance time series

Wavelet methods for image regularization offer a data-driven alternative to Gaussian smoothing in functional magnetic resonance (fMRI) analysis. Their impact has been limited by the difficulties in integrating regularization in the wavelet domain and inference in the image domain, precluding the probabilistic decision on which areas are activated by a task. Here we present an integrated framework for Bayesian estimation and regularization in wavelet space that allows the usual voxelwise hypothesis testing. This framework is flexible, being an adaptation to fMRI time series of a more general wavelet-based functional mixed-effect model. Through testing on a combination of simulated and real fMRI data, we show evidence of improved signal recovery, without compromising test accuracy in image space.