Existing tree decoder is only suitable for solving single variable problems， but has no good effect of solving multivariate problems. At the same time， most mathematical solvers select truth expression wrongly， which leads to learning deviation occurred in training. Aiming at the above problems， a Graph to Equation Tree （GET） model based on expression level-by-level aggregation and dynamic selection was proposed. Firstly， text semantics was learned through the graph encoder. Then， subexpressions were obtained by aggregating quantities and unknown variables iteratively from bottom of the equation tree layer by layer. Finally， combined with the longest prefix of output expression， truth expression was selected dynamically to minimize the deviation. Experimental results show that the precision of proposed model reaches 83.10% on Math23K dataset， which is 5.70 percentage points higher than that of Graph to Tree （Graph2Tree） model. Therefore， the proposed model can be applied to solution of complex multivariate mathematical problems， and can reduce influence of learning deviation on experimental results.

Aiming at the problem that the deraining methods based on tensor product wavelet cannot capture high-frequency rain streaks in all directions， a Dual U-Former Network （DUFN） based on non-separable lifting wavelet was proposed. Firstly， the isotropic non-separable lifting wavelet was used to capture high-frequency rain streaks in all directions. In this way， compared with tensor product wavelets such as Haar wavelet， which can only capture high-frequency rain streaks in three directions， DUFN was able to obtain more comprehensive rain streak information. Secondly， two U-Nets composed of Transformer Blocks （TBs） were connected in series at various scales， so that the semantic features of the shallow decoder were transferred to the deep stage， and the rain streaks were removed more thoroughly. At the same time， the scale-guide encoder was used to guide the coding stage by using the information of various scales in the shallow layer， and Gated Fusion Module （GFM） based on CBAM （Convolutional Block Attention Module） was used to make the fusion process put more focus on the rain area. Experimental results on Rain200H， Rain200L， Rain1200 and Rain12 synthetic datasets show that the Structure SIMilarity （SSIM） of DUFN is improved by 0.009 7 on average compared to that of the advanced method SPDNet （Structure-Preserving Deraining Network）. And on Rain200H， Rain200L and Rain12 synthetic datasets， the Peak Signal-to-Noise Ratio （PSNR） of DUFN is improved by 0.657 dB averagely. On real-world dataset SPA-Data， PSNR and SSIM of DUFN are improved by 0.976 dB and 0.003 1 respectively compared with those of the advanced method ECNetLL （Embedding Consistency Network+Layered Long short-term memory）. The above verifies that DUFN can improve the rain removal performance by enhancing the ability to capture high-frequency information.

Due to the introduction of MonoDepth2， unsupervised monocular ranging has made great progress in the field of visible light. However， visible light is not applicable in some scenes， such as at night and in some low-visibility environments. Infrared thermal imaging can obtain clear target images at night and under low-visibility conditions， so it is necessary to estimate the depth of infrared image. However， due to the different characteristics of visible and infrared images， it is unreasonable to migrate existing monocular depth estimation algorithms directly to infrared images. An infrared monocular ranging algorithm based on multiscale feature fusion after improving the MonoDepth2 algorithm can solve this problem. A new loss function， edge loss function， was designed for the low texture characteristic of infrared image to reduce pixel mismatch during image reprojection. The previous unsupervised monocular ranging simply upsamples the four-scale depth maps to the original image resolution to calculate projection errors， ignoring the correlation between scales and the contribution differences between different scales. A weighted Bi-directional Feature Pyramid Network （BiFPN） was applied to feature fusion of multiscale depth maps so that the blurring of depth map edge was solved. In addition， Residual Network （ResNet） structure was replaced by Cross Stage Partial Network （CSPNet） to reduce network complexity and increase operation speed. The experimental results show that edge loss is more suitable for infrared image ranging， resulting in better depth map quality. After adding BiFPN structure， the edge of depth image is clearer. After replacing ResNet with CSPNet， the inference speed is improved by about 20 percentage points. The proposed algorithm can accurately estimate the depth of the infrared image， solving the problem of depth estimation in night low-light scenes and some low-visibility scenes， and the application of this algorithm can also reduce the cost of assisted driving to a certain extent.

Concerning the issue that the traditional price prediction model for agricultural product cannot predict the market price of apple quickly and accurately under the big data scenario， an apple price prediction method based on distributed neural network was proposed. Firstly， the relative factors that affect the market price of apple were studied， and the historical price of apple， historical price of alternatives， household consumption level and oil price were selected as the input of the neural network. Secondly， a distributed neural network prediction model containing price fluctuation law was constructed to implement the short-term prediction for the market price of apple. Experimental results show that the proposed model has a high prediction accuracy， and the average relative error is only 0.50%， which satisfies the requirements of apple market price prediction. It indicates that the distributed neural network model can reveal the price fluctuation law and development trend of apple market price through the characteristic of self-learning. The proposed method not only can provide scientific basis for stabilizing apple market order and macroeconomic regulation of market price， but also can reduce the harms brought by price fluctuations， helping farmers to avoid the market risks.

Multiple feature fusion based tracking is one of the most active research topic in tracking field, but the tracking accuracy needs improving in complex environment and most of them use single fusion rule. In this paper, a new adaptive fusion strategy was proposed for multi-feature fusion. First, the local background information was introduced to strengthen the description of the target, and then the feature weight was calculated by a variety of criteria in the fusion process. In addition, the framework of mean shift was considered to realize target tracking. An extensive number of comparative experimental results show that the proposed algorithm is more stable and robust than the single fusion rule.

The Artificial Fish Swarm Algorithm (AFSA) has low search speed and it is difficult to obtain accurate value. To solve the problems, an improved algorithm based on social learning mechanism was proposed. In the latter optimization period, the authors used convergence and divergence behaviors to improve the algorithm. The two acts had fast search speed and high optimization accuracy, meanwhile, the divergence behavior enhanced the population diversity and the ability of skipping over the local extremum. To a certain extent, the improved algorithm enhanced the search performance. The experimental results show that the proposed algorithm is feasible and efficacious.

In response to the issue that GPS is unable to carry out Location-Based Service (LBS) in indoor environment, a LBS indoor channel allocation model, credibility evaluation and control method was presented in this paper, which integrated GPS, Wi-Fi, ZigBee and Bluetooth technologies. It solved the problem arising from combination channel allocation, including the evaluation of the traffic load, the available Radio Frequency (RF), and non-overlapping RF channels number of each node. Each Access Point(AP)'s signal strength built the prediction model with reference point. The optimization algorithm was designed to determine and select the credibility of combination channel based on the energy evaluation. It adaptively selected neighbors with highest comprehensive effects to participate in iterative optimization. The simulation result indicates this method can effectively inhibit the proliferation of communication interference error in the network, reduce the positioning complexity, and improve the positioning accuracy in addition to improving scalability and robustness of the entire network.

Password-based authentication and key exchange protocol have been widely used in various network services due to easy memory of password. Unfortunately, password-based authentication scheme also suffers from attacks because of the low entropy of password. In the year 2011, Islam et al.（ISLAM SK H, BISWAS G P. Improved remote login scheme based on ECC. IEEE-International Conference on Recent Trends in Information Technology. Washington, DC: IEEE Computer Society, 2011： 1221-1226）proposed an improved remote login scheme based on Elliptic Curve Cryptography (ECC).Whereas, the scheme was vulnerable to stolen-verifier and impersonation attacks and failed to provide mutual authentication. Therefore, the authors proposed a password-based Remote Authentication with Key Agreement (RAKA) protocol using ECC to tackle the problems in Islam et al.'s scheme. RAKA was based on Elliptic Curve Discrete Logarithm Problem (ECDLP) and needed to compute six elliptic curve scale multiplications and seven hash function operations during a protocol run. The efficiency improves by about 15%〖BP(〗 percent〖BP)〗. It is more secure and efficient than Islam et al.'s scheme.

Session Initiation Protocol (SIP) provides authentication and session key agreement to ensure the security of the successive session. In 2010, Yoon et al. (YOON E-J, YOO K-Y. A three-factor authenticated key agreement scheme for SIP on elliptic curves. NSS '10: 4th International Conference on Network and System Security. Piscataway: IEEE, 2010: 334-339.) proposed a three-factor authenticated key agreement scheme named TAKASIP for SIP. However, the scheme is vulnerable to insider attack, server-spoofing attack, off-line password attack, and losing token attack. Moreover, it does not provide mutual authentication. To overcome these flaws of TAKASIP, a new three-factor authentication scheme named ETAKASIP based on Elliptic Curve Cryptosystem (ECC) was proposed. ETAKASIP, on the basis of elliptic curve discrete logarithm problem, provides higher security than TAKASIP. It needs 7 elliptic curve scalar multiplication operations, 1 additional operation and up to 6 Hash operations, and of high efficiency.

Collaborative filtering is the most popular personalized recommendation technology at present. However, the existing algorithms are limited to the user-item rating matrix, which suffers from sparsity and cold-start problems. Neighbours' similarity only considers the items which users evaluate together, but ignores the correlation of item attribute and user characteristic. In addition, the traditional ones have taken users' interests in different time into equal consideration. As a result, they lack real-time nature. Concerning the above problems, this paper proposed a nonlinear combinatorial collaborative filtering algorithm consequently. In order to obtain more accurate nearest neighbour sets, it improved neighbours' similarity calculated approach based on item attribute and user characteristic respectively. Furthermore, the initial prediction rating fills in the rating matrix, so makes it much denser. Lastly, it added time weight to the final prediction rating, so then let users' latest interests take the biggest weight. The experimental results show that the optimized algorithm can increase prediction precision, by way of reducing sparsity and cold-start problems, and realizing real-time recommendation effectively.

The major disadvantages of the current software reliability models were discussed. And then based on analyzing classic PSO-SVM model and the characteristics of software reliability prediction, some measures of the improved PSO-SVM model were proposed and an improved model was established. Lastly, the simulation results show that compared with classic models，the improved model has better prediction precision，better generalization ability and lower dependence on the number of sample, which is more applicable for software reliability prediction.