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We introduce and study the bounded word problem and the precise word problem for groups given by means of generators and defining relations. For example, for every finitely presented group, the bounded word problem is in

Credit rating is an important part of bank credit risk management. Since the traditional radial basis function network model is more susceptible to outliers and cannot effectively process the classification data, it is very sensitive in terms of the initial center and class width of the selected model. This paper mainly studies the application of the radial basis function neural network model combined with the optimal segmentation algorithm in the personal loan credit rating model of banks or other financial institutions. The optimal segmentation algorithm is improved and applied to the training of RBF neural network parameters in this paper to increase the center and width of the class, and the center and width of the RBF network model are further improved. Finally, the adaptive selection of the number of hidden nodes is realized by using the differential objective function of the class to adjust dynamically the structure of the radial basis function network model, which is used to establish the credit rating model. The experimental results show that the improved model has higher precision when dealing with non-numeric data, and the robustness of the improved model has been improved.

A software defect report is a bug in the software system that developers and users submit to the software defect library during software development and maintenance. Managing a software defect report that is overwhelming is a challenging task. The traditional method is manual identification, which is time-consuming and laborious and delays the repair of important software defects. Based on the above background, the purpose of this paper is to study the software defect prediction (SDP) model based on LASSO–SVM. In this paper, the problem of poor prediction accuracy of most SDP models is proposed. A SDP model combining minimum absolute value compression and selection method and support vector machine algorithm is proposed. Firstly, the feature selection ability of the minimum absolute value compression and selection method is used to reduce the dimension of the original data set, and the data set not related to SDP is removed. Then, the optimal value of SVM is obtained by using the parameter optimization ability of cross-validation algorithm. Finally, the SDP is completed by the nonlinear computing ability of SVM. The accuracy of simulation results is 93.25% and 66.67%, recall rate is 78.04%, and f-metric is 72.72%. The results show that the proposed defect prediction model has higher prediction accuracy than the traditional defect prediction model, and the prediction speed is faster.

This is the first comprehensive teaching resource and textbook for the teaching of Matlab in the Neurosciences and in Psychology. Matlab is unique in that it can be used to learn the entire empirical and experimental process, including stimulus generation, experimental control, data collection, data analysis and modeling. Thus a wide variety of computational problems can be addressed in a single programming environment. The idea is to empower advanced undergraduates and beginning graduate students by allowing them to design and implement their own analytical tools. As students advance in their research careers, they will have achieved the fluency required to understand and adapt more specialized tools as opposed to treating them as \"black boxes\".

Due to the characteristics of time-varying traffic and nonlinearity, the short-term traffic flow data are difficult to predict accurately. The purpose of this paper is to improve the short-term traffic flow prediction accuracy through the proposed improved wavelet neural network prediction model and provide basic data and decision support for the intelligent traffic management system. In view of the extremely strong nonlinear processing power, self-organization, self-adaptation and learning ability of wavelet neural network (WNN), this paper uses it as the basic prediction model and uses the particle swarm optimization algorithm for the slow convergence rate and local optimal problem of WNN prediction algorithm. With the advantages of fast convergence, high robustness and strong global search ability, an improved particle swarm optimization algorithm is proposed to optimize the wavelet neural network prediction model. The improved wavelet neural network is used to predict short-term traffic flow. The experimental results show that the proposed algorithm is more efficient than the WNN and PSO–WNN algorithms alone. The prediction results are more stable and more accurate. Compared with the traditional wavelet neural network, the error is reduced by 14.994%.

With the rapid development of the Internet, image information is explosively growing. Traditional image classification methods are difficult to deal with huge image data and cannot meet people’s requirements on the accuracy and speed of image classification. In recent years, the convolutional neural network (CNN) has been developing rapidly, and it has performed extremely well. The image classification method based on CNN breaks through the bottleneck of traditional image classification methods and becomes the mainstream image classification algorithm at present. CT image classification algorithm is one of the research hot spots in the field of medical image. The purpose of this paper is to apply convolutional neural network to CT image classification, so as to speed up CT image classification and improve the accuracy of CT image classification and so as to reduce the workload of doctors and improve work efficiency. In this paper, CT images are classified by CDBN model. Vector machine SVM is used as the feature classifier of CDBN model to enhance feature transfer and reuse so as to enrich the features. It also suppresses features that are not very useful for current tasks and improves the performance of the model. Using CDBN to classify CT images, several commonly used gray images are compared. Comparing the results of the ordinary gradient algorithm with Adam algorithm, we can get the CDBN model using Adam optimization algorithm. In CT image classification, both accuracy and speed have a good effect. The experimental results show that the training speed of CDBN model of Adam optimization algorithm in CT image classification is 3% faster than that of general gradient algorithm.

With the leaps and bounds of computer performance and the advent of the era of big data, deep learning has drawn more and more attention from all walks of life. It can combine low-level features to form more abstract high-level features and describe the data more essentially. Therefore, it is widely used in various fields such as computer vision. Image segmentation is one of the most basic research topics in the field of computer vision. The main purpose is to extract regions of interest from images for later image processing research. In 3D reconstruction based on sequence images, the segmentation accuracy and speed of sequence images determine the quality and efficiency of target reconstruction. Therefore, when facing large-scale sequence images, the biggest problem is how to improve the segmentation speed while ensuring accuracy. Based on the above background, the research content of this article is an indoor scene segmentation algorithm based on full convolutional neural network. According to the characteristics of indoor application scenes, this paper proposes a fast convolutional neural network image segmentation method to segment the indoor scene image and construct the fast fully convolutional networks (FFCN) for indoor scene image segmentation uses inter-layer fusion to reduce the amount of network calculation parameters and avoid the loss of picture feature information by continuous convolution. In order to verify the effectiveness of the network, in this paper, a basic living object data set (XAUT data set) in an indoor environment is created. The XAUT data set is used to train the FFCN network under the Caffe framework to obtain an indoor scene segmentation model. In order to compare the effectiveness of the model, the structure of the worn FCN8s, FCN16s, and FCN32s models was fine-tuned, and the corresponding algorithm model for indoor scene segmentation was obtained by training with the XAUT data set. The experimental results show that the pixel recognition accuracy of all types of networks has reached 86%, and the mean IU ratio has reached more than 63%. The mean IU of the FCN8s network is the highest at 70.38%, but its segmentation speed is only 1/5 of FFCN. On the premise that other types of indicators are not much different, the average segmentation speed on FFCN fast segmentation convolutional neural network reaches 40 fps. It can be seen that the scale fusion technology can well avoid the loss of image feature information in the network convolution and reddening process. Compared with other FCN networks, it has a faster speed and is conducive to real-time image preprocessing.