A Second-Order Statistics Based Algorithm for Blind Separation of Signals

We propose an information theory based objective function for measuring the statistics independent of source signals. Then, we develop a learlling algorithm for blind separation of nonstationary signals by minimizing the objective function, in which the property of nonstationary and direct architecture neural network is applied. The analysis demonstrates the equiralence of two neural architectures in some special cases. The computer simulation shows the validity of the proposed algorithm. We give the performance surface of the object function at the last of the paper.

Bi-iterative least squares algorithms for blind channel identification and equalization with second-order statistics

We present an adaptive algorithm for blind identification and equalization of single-input multiple-output （SIMO） FIR channels with second-order statistics. We first reformulate the blind channel identification problem into a low-rank matrix approximation solution based on the QR decomposition of the received data matrix. Then, a fast recursive algorithm is developed based on the bi-iterative least squares （Bi-LS） subspace tracking method. The new algorithm requires only a computational complexity of O（md2） at each iteration, or even as low as O（md） if only equalization is necessary, where m is the dimension of the received data vector （or the row rank of channel matrix） and d is the dimension of the signal subspace （or the column rank of channel matrix）. To overcome the shortcoming of the back substitution, an inverse QR iteration algorithm for subspace tracking and channel equalization is also developed. The inverse QR iteration algorithm is well suited for the parallel implementation in the systolic array. Simulation results are presented to illustrate the effectiveness of the proposed algorithms for the channel identification and equalization.

Source enumeration method by combining diagonal loading and constructing second-order statistics

A source enumeration method based on diagonal loading of eigenvalues and constructing second-order statistics is proposed,for the case that the antenna array observed signals are overlapped with spatial colored noise,and the number of antennas compared with the number of snapshots meet the requirement of general asymptotic regime.Firstly,the sample covariance matrix of the observed signals is obtained,the eigenvalues of the sample covariance matrix can be acquired by eigenvalue decomposition,and the eigenvalues are diagonally loaded,and a new formula for calculating the diagonal loading is presented.Based on the diagonal loaded eigenvalues,the difference values are calculated for the adjacent eigenvalues after diagonal loading,and the statistical variance of the difference values is calculated.On this basis,the second-order statistics of the difference values are constructed,and when the second-order statistics are minimized,the corresponding number of sources is estimated.The proposed method has wide applicability,which is suitable for both general asymptotic regime and classical asymptotic system,and is suitable for both white Gaussian noise environment and colored noise environment.The method makes up for the lack of source enumeration methods in the case of general asymptotic system and colored noise.

Lottery Numbers and Ordered Statistics

The lottery has long captivated the imagination of players worldwide, offering the tantalizing possibility of life-changing wins. While winning the lottery is largely a matter of chance, as lottery drawings are typically random and unpredictable. Some people use the lottery terminal randomly generates numbers for them, some players choose numbers that hold personal significance to them, such as birthdays, anniversaries, or other important dates, some enthusiasts have turned to statistical analysis as a means to analyze past winning numbers identify patterns or frequencies. In this paper, we use order statistics to estimate the probability of specific order of numbers or number combinations being drawn in future drawings.

A multi-scale second-order autoregressive recursive filter approach for the sea ice concentration analysis

To effectively extract multi-scale information from observation data and improve computational efficiency,a multi-scale second-order autoregressive recursive filter(MSRF)method is designed.The second-order autoregressive filter used in this study has been attempted to replace the traditional first-order recursive filter used in spatial multi-scale recursive filter(SMRF)method.The experimental results indicate that the MSRF scheme successfully extracts various scale information resolved by observations.Moreover,compared with the SMRF scheme,the MSRF scheme improves computational accuracy and efficiency to some extent.The MSRF scheme can not only propagate to a longer distance without the attenuation of innovation,but also reduce the mean absolute deviation between the reconstructed sea ice concentration results and observations reduced by about 3.2%compared to the SMRF scheme.On the other hand,compared with traditional first-order recursive filters using in the SMRF scheme that multiple filters are executed,the MSRF scheme only needs to perform two filter processes in one iteration,greatly improving filtering efficiency.In the two-dimensional experiment of sea ice concentration,the calculation time of the MSRF scheme is only 1/7 of that of SMRF scheme.This means that the MSRF scheme can achieve better performance with less computational cost,which is of great significance for further application in real-time ocean or sea ice data assimilation systems in the future.

Effect Evaluation of CBL Combined with Rain Classroom Teaching Method in Medical Statistics

Objective: To explore the application effect of CBL combined with rain classroom teaching method in medical statistics courses. Methods: The undergraduate students of medical imaging technology in 2019 and 2020 in a university were selected as the research objects. A cluster sampling method was used to select 79 undergraduate students from 2019 in the control group and 75 undergraduate students from 2020 in the experimental group. Traditional teaching method and CBL combined with rain classroom teaching method was used in the control group and experimental group respectively. The final examination scores of the two groups were compared. In experimental group, the correlation between the average score in the rain classroom and the final examination score was tested, and the teaching effect was evaluated. Results: The average score of final examination in experimental group and control group was 79.13 ± 10.32 points and 71.54 ± 14.752 points, respectively, which had a statistically significant difference (Z = 2.586, P = 0.012);the final examination scores of the students in the experimental group were positively correlated with the average scores of the rain classroom (r = 0.372, P = 0.001), and the proportion of satisfaction in the experimental group was 94.7%. Conclusion: The CBL combined with rain classroom teaching method can improve the teaching effectiveness of medical statistics courses.

Statistical second-order two-scale analysis and computation for heat conduction problem with radiation boundary condition in porous materials

This paper discusses a statistical second-order two-scale（SSOTS） analysis and computation for a heat conduction problem with a radiation boundary condition in random porous materials.Firstly,the microscopic configuration for the structure with random distribution is briefly characterized.Secondly,the SSOTS formulae for computing the heat transfer problem are derived successively by means of the construction way for each cell.Then,the statistical prediction algorithm based on the proposed two-scale model is described in detail.Finally,some numerical experiments are proposed,which show that the SSOTS method developed in this paper is effective for predicting the heat transfer performance of porous materials and demonstrating its significant applications in actual engineering computation.

Statistical Distribution of Depth-Integrated Local Horizontal Momentum for Second-Order Random Ocean Waves in Finite Water Depth

Based on the second order random wave solutions of water wave equations in finite water depth, statistical distributions of the depth integrated local horizontal momentum components are derived by use of the characteristic function expansion method. The parameters involved in the distributions can be all determined by the water depth and the wave number spectrum of ocean waves. As an illustrative example, a fully developed wind generated sea is considered and the parameters are calculated for typical wind speeds and water depths by means of the Donelan and Pierson spectrum. The effects of nonlinearity and water depth on the distributions are also investigated.

Innovations and Challenges in Economic Census Methodology:A Study by the Bureau of Statistics

The Bureau of Statistics has demonstrated a forward-looking strategic approach in its economic census.By leveraging dual innovations in technology and management,and incorporating modern technologies such as big data,cloud computing,and the Internet of Things,it has deepened the reform of the census methodology.Additionally,the Bureau has built a multi-dimensional collaborative network that enhances international cooperation,departmental coordination,and public participation.This approach not only addresses the limitations of traditional statistical methods in a complex economic environment but also improves data quality and census efficiency,providing an accurate and reliable foundation for national economic decision-making.

An Approach to Fault Diagnosis of Rotating Machinery Using the Second-Order Statistical Features of Thermal Images and Simplified Fuzzy ARTMAP

Thermal image, or thermogram, becomes a new type of signal for machine condition monitoring and fault diagnosis due to the capability to display real-time temperature distribution and possibility to indicate the machine’s operating condition through its temperature. In this paper, an investigation of using the second-order statistical features of thermogram in association with minimum redundancy maximum relevance (mRMR) feature selection and simplified fuzzy ARTMAP (SFAM) classification is conducted for rotating machinery fault diagnosis. The thermograms of different machine conditions are firstly preprocessed for improving the image contrast, removing noise, and cropping to obtain the regions of interest (ROIs). Then, an enhanced algorithm based on bi-dimensional empirical mode decomposition is implemented to further increase the quality of ROIs before the second-order statistical features are extracted from their gray-level co-occurrence matrix (GLCM). The highly relevant features to the machine condition are selected from the total feature set by mRMR and are fed into SFAM to accomplish the fault diagnosis. In order to verify this investigation, the thermograms acquired from different conditions of a fault simulator including normal, misalignment, faulty bearing, and mass unbalance are used. This investigation also provides a comparative study of SFAM and other traditional methods such as back-propagation and probabilistic neural networks. The results show that the second-order statistical features used in this framework can provide a plausible accuracy in fault diagnosis of rotating machinery.

The Convergence Rate of Fréchet Distribution under the Second-Order Regular Variation Condition

In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order regular variation condition.

Research on the Application of PBL+SPOC Blended Teaching Model in Probability and Statistics Course

To cultivate talents with an exploratory spirit and practical skills in the era of information technology,it is imperative to reform teaching methods and approaches.In the teaching process of the Probability and Statistics course,an application-oriented blended teaching model combining problem-based learning and small private online course was explored.By organizing and implementing online and offline teaching activities based on problem-based learning,a multidimensional process-oriented learning assessment system was established.Practice has shown that this model can effectively enhance classroom teaching effectiveness,benefiting the improvement of students’overall skills and mathematical literacy.

Integration of Ideological and Political Education into the Probability Theory and Mathematical Statistics Course:A Teaching Design Based on Estimation and Hypothesis Testing

With the rapid development of higher education in China,colleges and universities are facing new challenges and impacts in talent training.Probability Theory and Mathematical Statistics is one of the important courses in higher education for science and engineering majors and economics and management majors.Its critical role in cultivating students’thinking skills and improving their problem-solving skills is self-evident.Course ideological and political education construction is an important link in college talent training work.Combining ideological and political education with course teaching can help students establish correct value concepts and play a certain role in improving their comprehensive ability and quality.At present,the construction of ideological and political education in the Probability Theory and Mathematical Statistics course still faces some problems,mainly manifested in the lack of attention paid by teachers to course ideological and political education,insufficient exploitation of ideological and political elements,and the simplification of ideological and political education implementation methods.In order to comprehensively deepen the construction of course ideological and political education in line with the actual needs of Probability Theory and Mathematical Statistics course teaching,we should strengthen the construction of teacher teams,improve teachers’ability to carry out course ideological and political education,integrate educational resources,develop educational resources for ideological and political education,and innovate teaching methods to improve the overall effect of ideological and political education integration.

Dynamic thermo-mechanical coupled simulation of statistically inhomogeneous materials by statistical second-order two-scale method

In this paper,a statistical second-order twoscale（SSOTS） method is developed to simulate the dynamic thcrmo-mechanical performances of the statistically inhomogeneous materials.For this kind of composite material,the random distribution characteristics of particles,including the shape,size,orientation,spatial location,and volume fractions,are all considered.Firstly,the repre.sentation for the microscopic configuration of the statistically inhomogeneous materials is described.Secondly,the SSOTS formulation for the dynamic thermo-mechanical coupled problem is proposed in a constructive way,including the cell problems,effective thermal and mechanical parameters,homogenized problems,and the SSOTS formulas of the temperatures,displacements,heat flux densities and stresses.And then the algorithm procedure corresponding to the SSOTS method is brought forward.The numerical results obtained by using the SSOTS algorithm are compared with those by classical methods.In addition,the thermo-mechanical coupling effect is studied by comparing the results of coupled case with those of uncoupled case.It demonstrates that the coupling effect on the temperatures,heat flux densities,displacements,and stresses is very distinct.The results show that the SSOTS method is valid to predict the dynamic thermo-mechanical coupled performances of statistically inhomogeneous materials.

Reservoir parameter inversion based on weighted statistics

Variation of reservoir physical properties can cause changes in its elastic parameters. However, this is not a simple linear relation. Furthermore, the lack of observations, data overlap, noise interference, and idealized models increases the uncertainties of the inversion result. Thus, we propose an inversion method that is different from traditional statistical rock physics modeling. First, we use deterministic and stochastic rock physics models considering the uncertainties of elastic parameters obtained by prestack seismic inversion and introduce weighting coefficients to establish a weighted statistical relation between reservoir and elastic parameters. Second, based on the weighted statistical relation, we use Markov chain Monte Carlo simulations to generate the random joint distribution space of reservoir and elastic parameters that serves as a sample solution space of an objective function. Finally, we propose a fast solution criterion to maximize the posterior probability density and obtain reservoir parameters. The method has high efficiency and application potential.

Wave statistics for ship seakeeping in China offshore

Ocean waves are the core environmental elements affecting the movements and structure design of ships. Statistical analysis of wave parameters is the basis for the establishment of long-term ship environmental adaptability prediction model. The observations from coastal stations, buoys, altimeters and volunteer ships that cover from 1993 to 2011 were interpolated into miller Ion-lat grids by using bilinear method and the analytical fields of ocean waves were given. By using optimal interpolation, the analysis wave fields were assimilated into the WAVEWATCH III （WW3） simulation results. From the assimilated results, the wave rose statistics, the wave height of muitiyear return period and the extreme 2-D wave spectrum are related to the ship seakeeping were calculated. Finally, the wave statistics in China offshore were analyzed in detail.

基于statistics的316L不锈钢柠檬酸钝化工艺正交实验数据分析

从statistics的数据处理能力出发,运用统计学知识对316L不锈钢柠檬酸钝化工艺参数正交实验数据进行分析,找出钝化速率的主要影响因素;柠檬酸含量5wt%、双氧水含量5wt%、钝化时间60 min为最佳的实验方案;双氧水含量为钝化速率的主要影响因素。

Second-Order Raman Scattering from n- and p-Type 4H-SiC

The results of second-order Raman-scattering experiments on n- and p-type 4H-SiC are presented,covering the acoustic and the optical overtone spectral regions.Some of the observed structures in the spectra are assigned to particular phonon branches and the points in the Brillouin zone from which the scattering originates.There exists a doublet at 626/636cm -1 with energy difference about 10cm -1 in both n- and p-type 4H-SiC,which is similar to the doublet structure with the same energy difference founded in hexagonal GaN,ZnO, and AlN.The cutoff frequency at 1926cm -1 of the second-order Raman is not the overtone of the A 1(LO) peak of the n-type doping 4H-SiC,but that of the undoping one.The second-order Raman spectrum of 4H-SiC can hardly be affected by doping species or doping density.

Identification of Sewage Monitoring Data Based on Mathematical Statistics

In order to reduce the enormous pressure to environmental monitoring work brought by the false sewage monitoring data, Grubbs method, box plot, t test and other methods are used to make depth analysis to the data, providing a set of technological process to identify the sewage monitoring data, which is convenient and simple.

Anti-periodic solutions to a class of second-order evolution equations

In this paper we discuss the anti-periodic problem for a class of abstractnonlinear second-order evolution equations associated with maximal monotone operators in Hilbertspaces and give some new assumptions on operators. We establish the existence and uniqueness ofanti-periodic solutions, which improve andgeneralize the results that have been obtained. Finally weillustrate the abstract theory by discussing a simple example of an anti-periodic problem fornonlinear partial differential equations.