The new method of topological charge determination of optical vortices in the interference field of the optical vortex interferometer

In this paper, the new method of determination of the topological charge of vortex points in the interference field obtained by three plane waves interference is presented. Such optical fields are used in the optical vortex interferometer (OVI) and the determination of vortex points’ topological charge allows of unique determination of the relative phase between interfering waves (phase unwrapping problem). The new method uses additional plane wave, which produce a characteristic fork-like fringe structure in the neighbourhood of vortex points. By analysing the orientation of these fork-like patterns one can read the sign of the topological charge of the given vortex point. The method is simple and can be used for OVI calibration performed before the measurements.     

Method of fundamental solutions with optimal regularization techniques for the Cauchy problem of the Laplace equation with singular points

The purpose of this study is to propose a high-accuracy and fast numerical method for the Cauchy problem of the Laplace equation. Our problem is directly discretized by the method of fundamental solutions (MFS). The Tikhonov regularization method stabilizes a numerical solution of the problem for given Cauchy data with high noises. The accuracy of the numerical solution depends on a regularization parameter of the Tikhonov regularization technique and some parameters of the MFS. The L-curve determines a suitable regularization parameter for obtaining an accurate solution. Numerical experiments show that such a suitable regularization parameter coincides with the optimal one. Moreover, a better choice of the parameters of the MFS is numerically observed. It is noteworthy that a problem whose solution has singular points can successfully be solved. It is concluded that the numerical method proposed in this paper is effective for a problem with an irregular domain, singular points, and the Cauchy data with high noises.     

热应力边界元法中几乎超奇异积分的计算

通过分部积分变换将热弹性力学应力边界积分方程中的超奇异积分转化为强奇异积分,然后与另一个强奇异积分求和,得到仅含几乎强奇异的热应力自然边界积分方程.再对其中的几乎强奇异积分施以正则化,消除了热弹性力学边界元法中的几乎奇异积分,可以准确计算出热弹性力学问题中近边界内点的热应力.算例证明了方法的有效性.     

一种新的基于子线段的立体匹配算法

立体匹配是计算机视觉领域中最活跃的研究主题之一。为了精确并更快速的进行同名点匹配,提出了一种基于小波变换的子线段匹配方法。该方法利用样条二进小波变换系数在不同尺度下的模极大点,能提供在不同尺度下信号急速变化点的位置信息,采用由粗到细的匹配策略匹配这些特征点,并由这些特征点两两相邻的点构建子线段。采用加速方法,快速匹配子线段两端点之间的点。这种方法较好地解决了匹配精度和匹配速度之间的平衡问题。采用该方法对篦冷机内水泥熟料高度进行测量,实验表明,该方法能较精确地得出水泥熟料料层的分布状况。     

Simulating non-linear coupled oscillators by an iterative differential quadrature method

An iterative method based on differential quadrature rules is proposed as a new unified frame of resolution for non-linear two-degree-of-freedom systems. Dynamical systems with Duffing-type non-linearity have been considered. Differential quadrature rules have been applied with a careful distribution of sampling points to reduce the governing equation of motion to two second-order non-linear, non-autonomous ordinary differential equations and to solve the time-domain problem. The time domain of the problem is discretized by means of time intervals, with the same distribution of sampling points used to discretize the space domain (which can be seen as a single interval). It will be shown that accurate solutions depend not only on the choice of the distribution of sampling points, but also on the length of the time interval one refers to in the computations. The numerical results, utilized to draw Poincaré maps, are successfully compared with those obtained using the Runge-Kutta method.     

A novel infrared small moving target detection method based on tracking interest points under complicated background

Infrared moving target detection is an important part of infrared technology. We introduce a novel infrared small moving target detection method based on tracking interest points under complicated background. Firstly, Difference of Gaussians (DOG) filters are used to detect a group of interest points (including the moving targets). Secondly, a sort of small targets tracking method inspired by Human Visual System (HVS) is used to track these interest points for several frames, and then the correlations between interest points in the first frame and the last frame are obtained. Last, a new clustering method named as R-means is proposed to divide these interest points into two groups according to the correlations, one is target points and another is background points. In experimental results, the target-to-clutter ratio (TCR) and the receiver operating characteristics (ROC) curves are computed experimentally to compare the performances of the proposed method and other five sophisticated methods. From the results, the proposed method shows a better discrimination of targets and clutters and has a lower false alarm rate than the existing moving target detection methods.     

A new method for true and spurious eigensolutions of arbitrary cavities using the combined Helmholtz exterior integral equation formulation method

Integral equation methods have been widely used to solve interior eigenproblems and exterior acoustic problems (radiation and scattering). It was recently found that the real-part boundary element method (BEM) for the interior problem results in spurious eigensolutions if the singular (UT) or the hypersingular (LM) equation is used alone. The real-part BEM results in spurious solutions for interior problems in a similar way that the singular integral equation (UT method) results in fictitious solutions for the exterior problem. To solve this problem, a Combined Helmholtz Exterior integral Equation Formulation method (CHEEF) is proposed. Based on the CHEEF method, the spurious solutions can be filtered out if additional constraints from the exterior points are chosen carefully. Finally, two examples for the eigensolutions of circular and rectangular cavities are considered. The optimum numbers and proper positions for selecting the points in the exterior domain are analytically studied. Also, numerical experiments were designed to verify the analytical results. It is worth pointing out that the nodal line of radiation mode of a circle can be rotated due to symmetry, while the nodal line of the rectangular is on a fixed position.     

The construction of exact solutions of the model problem on rotating fluid in domains with angular points

A new method has been developed for the construction of a two-dimensional model problem on the oscillations of rotating ideal fluid in some domains containing angular points. It is proved that these solutions correspond to the absolutely continuous component of the spectrum of the linear operator connected with the problem.     

Calculation of bulkhead vibrations in a supported shell simulating a plane fuselage

Noise from external sources penetrates a plane cabin through the board construction in several ways. They include direct penetration through loose-fiber layers and indirect penetration through the attachment points of interior panels to transverse ribs (bulkheads). The analytical method of calculating vibrations of an orthogonally supported shell (developed by us earlier) makes it possible to correctly calculate bulkhead vibrations. As a result, noise penetration into the cabin through the attachment points of interior panels can be determined analytically. The first part of the solution to this problem is presented (i.e., the relations and examples of calculating bulkhead vibrations upon point excitation of the shell and excitation by pressure fluctuations of the turbulent boundary layer are given).     

A hierarchical feature graph matching method for recognition of complex human activities

Complex human activities in natural videos are often composed of several atomic-level actions organized hierarchically. We should not only consider the appearance variability of these action units, but also model the spatiotemporal relationships between them when recognizing such high-level complex activities. In this paper, we focus on the problem of recognition of complex human activities in an example-based video retrieval framework and propose a new method based on hierarchical feature-graph matching. A video depicting an activity is represented as a high-level feature graph (HLFG), and each node of the HLFG is a mid-level feature graph (MLFG) constructed on a local collection of spatiotemporal interest points. MLFG, the first level of our two-level graph structure, describes the local feature contents and spatiotemporal arrangements of interest points. HLFG, the second level, describes the appearance variability and spatiotemporal arrangements of atomic-level actions in a way. Final recognition is accomplished by matching the HLFGs of the query and test videos, and matching two HLFGs involves matching the MLFGs between them. We use an efficient spectral method to solve these two graph-matching problems. Our method does not require any preprocessing and gives reasonable results with even a small number of query examples. We evaluate our approach with one publicly available complex human activity dataset and achieve results comparable to other systems that have studied this problem.     

Use of local search in the metric traveling salesman problem

The traveling salesman problem (TSP) for points in the Euclidean plane is considered. For several approximation algorithms, such as the tree algorithm and algorithms based on matching, a local search method using permutation in groups of closely placed points in a route is applied. Some modifications of these algorithms are presented. The effect of applying the local search method for partially constructed routes is examined for the modifications. In this paper, experimental results from statistical modeling with randomly equidistributed points are discussed. It allows one to conclude on the advantage of one or the other algorithms. Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 129–134, March, 1999     

A method for solving stochastic equations by reduced order models and local approximations

A method is proposed for solving equations with random entries, referred to as stochastic equations (SEs). The method is based on two recent developments. The first approximates the response surface giving the solution of a stochastic equation as a function of its random parameters by a finite set of hyperplanes tangent to it at expansion points selected by geometrical arguments. The second approximates the vector of random parameters in the definition of a stochastic equation by a simple random vector, referred to as stochastic reduced order model (SROM), and uses it to construct a SROM for the solution of this equation.The proposed method is a direct extension of these two methods. It uses SROMs to select expansion points, rather than selecting these points by geometrical considerations, and represents the solution by linear and/or higher order local approximations. The implementation and the performance of the method are illustrated by numerical examples involving random eigenvalue problems and stochastic algebraic/differential equations. The method is conceptually simple, non-intrusive, efficient relative to classical Monte Carlo simulation, accurate, and guaranteed to converge to the exact solution.     

Adaptive multilayer method of fundamental solutions using a weighted greedy QR decomposition for the Laplace equation

The mixed boundary value problem of the Laplace equation is considered. The method of fundamental solutions (MFS) approximates the exact solution to the Laplace equation by a linear combination of independent fundamental solutions with different source points. The accuracy of the numerical solution depends on the distribution of source points. In this paper, a weighted greedy QR decomposition (GQRD) is proposed to choose significant source points by introducing a weighting parameter. An index called an average degree of approximation is defined to show the efficiency of the proposed method. From numerical experiments, it is concluded that the numerical solution tends to be more accurate when the average degree of approximation is larger, and that the proposed method can yield more accurate solutions with a less number of source points than the conventional GQRD.     

一类时变时滞混沌系统的参数辨识方法

时变的未知时滞参数普遍存在于混沌系统中,它使得混沌系统同步控制变得非常困难. 针对时滞混沌系统中参数时变且未知的问题, 提出了一种新颖的辨识方法. 该方法首先将未知时变参数用分段常数函数来近似, 把求解非线性函数的问题转化为参数向量选择问题, 其中分段常数函数的高度向量成为待求解参数向量; 然后推导了目标函数对分段常数高度向量的梯度信息, 结合序列二次规划法求解得最优分段函数; 随着分段数的增加, 最优分段函数将逼近原非线性时变函数. 数值实例结果验证了该方法的有效性.     

Transforming NMR data despite missing points.

Some NMR experiments produce data with several of the initial points missing. The inverse discrete Fourier transform (IDFT) assumes these points are present so the data cannot be so transformed without artifact-ridden results. This problem is often particularly severe when projection imaging with free-induction decays (FIDs). This paper compares recent methods for obtaining a projection from incomplete data and elaborates on their strengths and limitations. One method is to write the transform that would take the desired projection to the truncated data set, and then solve the matrix equation by singular value decomposition. A second replaces the missing data with zeros, so that an IDFT produces a projection with unwanted artifacts. Then one solves the matrix equation that takes the desired projection to the artifact-ridden projection. A third uses the same artifact-ridden projection, but fits the region outside the bandwidth of the sample with as many sinusoidal functions as there are missing data. The coefficients of these functions are estimates of the missing data, and the projection is obtained by transforming the completed FID or subtracting the extrapolation of the fitted curve from the region containing the object. We show that when all three methods are applicable, they theoretically produce the same result. They differ by ease of implementation and possibly by computational errors. They give a result similar to that of the previous method that iteratively corrects the FID and projection after repeated IDFTs and DFTs. We find that one can obtain a projection despite missing a substantial number of data.     

Augmented coupling interface method for solving eigenvalue problems with sign-changed coefficients

In this paper, we propose an augmented coupling interface method on a Cartesian grid for solving eigenvalue problems with sign-changed coefficients. The underlying idea of the method is the correct local construction near the interface which incorporates the jump conditions. The method, which is very easy to implement, is based on finite difference discretization. The main ingredients of the proposed method comprise (i) an adaptive-order strategy of using interpolating polynomials of different orders on different sides of interfaces, which avoids the singularity of the local linear system and enables us to handle complex interfaces; (ii) when the interface condition involves the eigenvalue, the original problem is reduced to a quadratic eigenvalue problem by introducing an auxiliary variable and an interfacial operator on the interface; (iii) the auxiliary variable is discretized uniformly on the interface, the rest of variables are discretized on an underlying rectangular grid, and a proper interpolation between these two grids are designed to reduce the number of stencil points. Several examples are tested to show the robustness and accuracy of the schemes.     

一种改进的无人机航空影像配准方法

针对目前无人机航空影像非同源、畸变大、处理量多的问题,提出一种改进的无人机航空影像配准方法。首先利用传统SIFT方法得到特征点,其次利用C均值聚类方法可实现准确的非监督分类的特点,对传统SIFT方法得到的特征点进行筛选,从而得出同名点。最后根据得到的同名点完成待匹配图像的投影变换完成配准。通过实验仿真证明该方法精度有较大提高,且可自适应处理不同图像,是一种有效的无人机航空影像匹配改良方法。     

Ising Model for Interpolation of Spatial Data on Regular Grids

We apply the Ising model with nearest-neighbor correlations (INNC) in the problem of interpolation of spatially correlated data on regular grids. The correlations are captured by short-range interactions between “Ising spins”. The INNC algorithm can be used with label data (classification) as well as discrete and continuous real-valued data (regression). In the regression problem, INNC approximates continuous variables by means of a user-specified number of classes. INNC predicts the class identity at unmeasured points by using the Monte Carlo simulation conditioned on the observed data (partial sample). The algorithm locally respects the sample values and globally aims to minimize the deviation between an energy measure of the partial sample and that of the entire grid. INNC is non-parametric and, thus, is suitable for non-Gaussian data. The method is found to be very competitive with respect to interpolation accuracy and computational efficiency compared to some standard methods. Thus, this method provides a useful tool for filling gaps in gridded data such as satellite images.     

Compact local integrated-RBF approximations for second-order elliptic differential problems

This paper presents a new compact approximation method for the discretisation of second-order elliptic equations in one and two dimensions. The problem domain, which can be rectangular or non-rectangular, is represented by a Cartesian grid. On stencils, which are three nodal points for one-dimensional problems and nine nodal points for two-dimensional problems, the approximations for the field variable and its derivatives are constructed using integrated radial basis functions (IRBFs). Several pieces of information about the governing differential equation on the stencil are incorporated into the IRBF approximations by means of the constants of integration. Numerical examples indicate that the proposed technique yields a very high rate of convergence with grid refinement.     

Improvement of least-squares finite difference method on simulating slider air bearings in head disk systems

Least-squares finite difference (LSFD) method, one of mesh-free methods, is used to solve slider air bearings problem through discritizing the generalized Reynolds equation into nonlinear systems of algebraic equations. Two approximation schemes for the linearization of these equations are presented and compared. And, some new techniques to search supporting points for the reference node in the mesh-free method were proposed and explored. Therefore, these improvements eliminate some potential limitation of the LSFD method previously published and further facilitate its employment in complex slider models. Advanced step slider as an example of negative pressure sliders is simulated and verified using the improved LSFD mesh-free method in head disk systems.