In this paper, we discuss complete convergence and complete moment convergence results for extended negatively dependent random variables. The obtained theorems not only extend the Baum-Katz type theorem to the case of END random variables, but also improve them.

With the development of artificial intelligence, deep learning as an important branch has been paid attention to for its important achievements in machine learning, which has been developed rapidly and widely used in different fields. The complexity and uncertainty of meteorological environment, as well as the exponential and incremental index of meteorological data and the introduction of deep learning, can help to improve the accuracy of weather forecasting and related work. This paper summarizes the current situation and problems of the application of deep learning in the field of meteorology, and provides reference for scholars who further improve the accuracy of deep learning and weather forecasting.

Atmospheric temperature forecast plays an important role in weather forecast and has a significant impact on human daily and economic life. However, due to the complexity and uncertainty of the atmospheric system, exploring advanced forecasting methods to improve the accuracy of meteorological prediction has always been a research topic for scientists. With the continuous improvement of computer performance and data acquisition technology, meteorological data has gained explosive growth, which creates the necessary hardware support conditions for more accurate weather forecast. The more accurate forecast results need advanced weather forecast methods suitable for hardware. Therefore, this paper proposes a deep learning model called BL-FC based on Bidirectional Long Short-Term Memory (Bi-LSTM) Network for temperature modeling and forecasting, which is suitable for big data processing. BL-FC consists of four layers: the first layer is a Bi-LSTM layer, which is used to learn features from continuous temperature data in forward and backward directions; the other three layers are fully connected layers, the second and third layers are used to further extract data features, and the last layer is used to map the final output of temperature prediction. Based on the meteorological data of 19822 consecutive hours provided by Belmalit Mayo Weather Station in Mayo County, Ireland, the data set is established by using the sliding window method. Compared with other three different deep learning models, including Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), and Recurrent Neural Network (RNN), the BL-FC model has higher short-term temperature prediction accuracy, especially in the case of abnormal temperature.

With the continuous improvement of observation technology, the complexity of meteorological data elements has increased sharply, and the volume of the model has expanded, which brings inconvenience to conventional weather forecasting and conventional weather forecasting methods based on traditional statistical forecasting. This paper proposes a LSTM weather forecast method based on Bayesian optimization. Through the constructed sample data, the Bayesian optimization method is used to select the optimal parameters of the LSTM, and then the sample is reconstructed through the optimal LSTM, which has achieved better results in terms of accuracy. This study can explore more reasonable sample construction methods for weather attribute characteristics, and LSTM optimal parameter selection methods, and provide a simple, easy-to-use, high-precision weather prediction method for meteorological experts.

As a kind of clean energy, wind energy is widely disseminated and has been widely researched. Compared with other methods, the support vector machine algorithm is more logical. Least squares support vector machine can improve training efficiency. Therefore, the method of multi-output least squares support vector regression is used to forecast the wind speed and wind direction in this paper. The bat algorithm is simple in structure and easy to understand. It has been applied to solve optimisation problems with MSVR. Compared with single output support vector machines, multi-output support vector machine readily solves problems of complex structure. The simulation model is established to predict the value of wind speed and wind direction by using different algorithms. The simulation results show that the multi-output least squares support vector machines prediction model based on bat optimisation algorithm has better feasibility and effectiveness.

核四元数主成分分析（KQPCA）被成功应用于处理非线性四元数信号,然而,核矩阵维数太高使其对角化非常耗时,目前二维形式的KQPCA（2DKQPCA）并没有成功实现.对此,采用基于块处理和并行计算的思想,提出基于块的2DKQPCA（B2DKQPCA）,实现真正意义上的2DKQPCA.基于时间复杂度、应用性能和分块矩阵应为四元数Hermitian矩阵的综合考虑,B2DKQPCA重点处理主对角线、反对角线和主对角线旁3个方向的小块.然后,结合B2DKQPCA与RGB-D图像四元数表示方法,将B2DKQPCA应用于RGB-D目标识别领域.在2个公开库上的实验结果表明,提出的基于列向B2DKQPCA的RGB-D识别算法优于现有基于主成分分析算法和基于卷积神经网络的一些算法.

支持向量机回归是一种重要的机器学习算法,虽然已成功应用于多个领域,但针对复杂系统,单输出支持向量回归算法的训练时间过长并且缺乏实用性.多输出直觉模糊最小二乘支持向量回归(Intuitionistic Fuzzy Least Squares Support Vector Regression,IFLS-SVR)在多输出支持向量机的基础上引入了直觉模糊,解决了不确定多输出复杂系统问题,减少了训练时间.生活中复杂的多输出模型更为常见,文中在传统支持向量回归的基础上对其进行改进,提出多输出IFLS-SVR模型.多输出IFLS-SVR采用直觉模糊算法将实际数据转化为模糊数据,将二次规划优化问题转化为求解一系列线性方程组.与现有的模糊支持向量回归相比,多输出IFLS-SVR采用直觉模糊方法来计算隶属度函数,采用最小二乘法提高了算法的训练效率,减少了训练时间,获得了更精确的解.仿真结果表明,与其他方法相比,多输出IFLS-SVR取得了较好的效果.最后将多输出IFLS-SVR模型应用于复杂的风速风向预测,也取得了较好的效果.

针对高校信息类工科学生培养的特点,从对其实施课外创新能力培养的必要性、方案以及益处等方面进行探讨研究.

In this study, by using the quaternion algebra, multiple-parameter fractional quaternion Fourier transform (MPFrQFT) is proposed to generalise the conventional multiple-parameter fractional Fourier transform (MPFrFT) to quaternion signal processing in a holistic manner. First, the new transform MPFrQFT and its inverse transform are defined. An efficient discrete implementation method of MPFrQFT is then proposed, in which the relationship between MPFrQFT and MPFrFT of four components is utilised for a quaternion signal. Finally, a new colour image encryption algorithm based on the proposed MPFrQFT and the double random phase encoding technique is proposed to evaluate the performance of the proposed MPFrQFT. Experimental results demonstrate that: (i) the computational time of the proposed implementation method is almost a half of the direct method's time; (ii) the proposed MPFrQFT-based encryption algorithm has an overall better performance than eight compared algorithms in security test and robustness test: it is more secure than the compared frequency-based algorithms due to the larger key space and the more sensitive key ‘transform orders’; it is also more robust than the compared spatial-domain algorithms.

Support vector regression (SVR) is an important machine learning algorithm, although some successful applications have been achieved. The algorithm for complex system is still worth studying. Multiple output intuitionistic fuzzy least squares support vector regression (IFLS-SVR) is improved by using the intuitionistic fuzzy to solve the problem of the uncertain multiple output complex system. Compared with the traditional fuzzy support vector regression, the model with the fuzzy membership and non-fuzzy membership is more close to the practical system. Multiple output IFLS-SVR transforms the actual data into fuzzy data and transforms the quadratic programming optimization problem into a series of linear equations. Compared with the current fuzzy support vector regression, multiple output IFLS-SVR in this paper adopted the intuitionistic fuzzy method to calculate membership functions, improving the training efficiency of the algorithm and reducing the training time by using the least square method. Through the simulation model, multiple output IFLS-SVR has achieved good results compared with other methods. The application of multiple output IFLS-SVR to the prediction of complex wind weather has also achieved good results.

In this paper, we further study some sufficient conditions for complete convergence for weighted sums of arrays of rowwise negatively dependent random variables with non-identical distribution under some weaker moment conditions. Our result generalize and improve the corresponding result of Wang et al. [7].

Consider a non-standard renewal risk model with dependence structures, where claim sizes follow a one-sided linear process with independent and identically distributed step sizes, the step sizes and inter-arrival times respectively form a sequence of independent and identically distributed random pairs, with each pair obeying a dependence structure. An insurance company is allowed to make risk-free and risky investments, where the price process of the investment portfolio follows an exponential Levy process. When the step-size distribution is dominatedly-varying-tailed, some asymptotic estimates for the finite-and infinite-time ruin probabilities are obtained.

For the Multi-output Support Vector Regression (MSVR) algorithm based on gradient descent method in the process of model parameter fitting,the convergence rate is slow and the prediction accuracy is low.A modified version of the Quasi-Newton algorithm (BFGS) with second-order convergence rate based on the rank-2 correction rule was used to fit the model parameters of MSVR algorithm.At the same time,to ensure the decrease of the iterative process and the global convergence,the step size factor was determined by the non-exact linear search technique.Based on the analysis of the geometry structure of kernel function in Support Vector Machine (SVM),a data-dependent kernel function was substituted for the traditional kernel function,and the multi-output data-dependent kernel support vector regression model was generated.The model was compared with the multi-output support vector regression model based on gradient descent method and modified Newton method.The experimental results show that in the case of 200 samples,the iterative time of the proposed algorithm is 72.98 s,the iterative time of modified Newton's algorithm is 116.34 s and the iterative time of gradient descent method is 2 065.22 s.The proposed algorithm can reduce the model iteration time and has faster convergence speed.

In this article, we establish a complete convergence theorem for arrays of rowwise mnegatively dependent (m-ND) random variables. Our results generalize those on complete convergence theorem previously obtained by Hu et al. (1998) and Sung et al. (2005) from independent distributed case to m-ND arrays.

气温预报是天气预报的重要因素之一,但大气系统是一个复杂的非线性系统,要提高预报精度,需要探索新的预报方法.研究一种多元时/间序列局部支特向量回归的日气温预测方法,以日最高、最低气温为例,使用C-C方法和最小预测误差法构造日最高、最低气温的多元对间序列,将分段提取最近邻点的方法应用于局部支持向量回归,建立提前1天的每日最高、最低气温局部预测模型.以中国753站资料包中的数据进行仿真实验,与欧氏距离提取最近邻点相比,分段提取最近邻点的方法能有效提高日气温的预测精度.多元时间序列局部预测模型在日气温的短期预测(10天以内)上比单元时间序列有着更好的应用价值.

The development of wind power has a higher requirement for the accurate prediction of wind. In this paper, a trustworthy and practical approach, Multidimensional Support Vector Regression (MSVR) with Data-Dependent Kernel(DDK), is proposed. In the prediction model, we applied the longitudinal component and lateral component of the wind speed, changed from original wind speed and direction, as the input of this model. Then the Data-Dependent kernel is instead of classic kernels. In order to prove this model, actual wind data from NCEP/NCAR is used to test. MSVR with DDK model has higher accuracy comparing with MSVR without DDK, single SVR, Neural Networks.

This article investigates the ruin probabilities of a discrete time risk model with dependent claim sizes and dependent relation between insurance risks and financial risks. The risk-free and risky investments of an insurer lead to stochastic discount factors {(n)}(n 1). The claim sizes are assumed to follow a one-sided linear process with independent and identically distributed (i.i.d.) innovations {E-n}(n 1). The i.i.d. random pairs {(E-n, (n))}(n 1) follow a common bivariate Sarmanov-dependent distribution. When the common distribution of the innovations is heavy tailed, we establish some asymptotic estimates for the ruin probabilities of this discrete time risk model.

In this paper, an almost sure central limit theorem is obtained for self-normalized weighted sums of the phi mixing random variables. Our results extend and give substantial improvement for the result obtained by Zhang [12] and our results also extend the earlier work on almost sure central limit theorem such as Wu [13].

The Gaussian Mixture Model (GMM) with the spatial constraint, e.g. Hidden Markov Random Field (HMRF), has been proven effective for image segmentation. The parameter β in the HMRF model is used to balance between robustness to noise and effectiveness of preserving the detail of the image. In other words, the determination of parameter β is, in fact, noise dependent to some degree. In this paper, we propose a simple and effective algorithm to make the traditional Gaussian Mixture Model more robust to noise, with consideration of the relationship between the local spatial information and the pixel intensity value information. The conditional probability of an image pixel is influenced by the probabilities of pixels in its immediate neighborhood to incorporate the spatial and the intensity information. In this case, the parameter β can be assigned to a small value to preserve image sharpness and detail in non-noise images. Meanwhile, the neighborhood window is used to tolerate the noise for heavy-noised images. Thus, the parameter β is independent of image noise degree in our model. Furthermore, we propose another algorithm for our modified GMM (MGMM) with the simplification of conditional probability computation (MGMM_S). Finally, our algorithm is not limited to GMM – it is general enough so that it can be applied to other distributions based on the construction of the Finite Mixture Model (FMM) technique. Experimental results of synthetic and real images demonstrate the improved robustness and effectiveness of our approach.