scholarly journals Small data solutions for the Euler-Poisson-Darboux equation with a power nonlinearity

2021 ◽  
Vol 286 ◽  
pp. 531-556
Author(s):  
Marcello D'Abbicco
2009 ◽  
Vol 29 (2) ◽  
pp. 421-423 ◽  
Author(s):  
Dong LIU ◽  
Li-fang WANG ◽  
Ze-jun JIAGN ◽  
Zhi-qiang LIU
Keyword(s):  

2015 ◽  
Vol 2015 (4) ◽  
pp. 1-15
Author(s):  
Henrietta Locklear ◽  
Jennifer Fitts ◽  
Chris McPhee
Keyword(s):  

Sensors ◽  
2020 ◽  
Vol 20 (20) ◽  
pp. 5966
Author(s):  
Ke Wang ◽  
Gong Zhang

The challenge of small data has emerged in synthetic aperture radar automatic target recognition (SAR-ATR) problems. Most SAR-ATR methods are data-driven and require a lot of training data that are expensive to collect. To address this challenge, we propose a recognition model that incorporates meta-learning and amortized variational inference (AVI). Specifically, the model consists of global parameters and task-specific parameters. The global parameters, trained by meta-learning, construct a common feature extractor shared between all recognition tasks. The task-specific parameters, modeled by probability distributions, can adapt to new tasks with a small amount of training data. To reduce the computation and storage cost, the task-specific parameters are inferred by AVI implemented with set-to-set functions. Extensive experiments were conducted on a real SAR dataset to evaluate the effectiveness of the model. The results of the proposed approach compared with those of the latest SAR-ATR methods show the superior performance of our model, especially on recognition tasks with limited data.


2012 ◽  
Vol 197 ◽  
pp. 271-277
Author(s):  
Zhu Ping Gong

Small data set approach is used for the estimation of Largest Lyapunov Exponent (LLE). Primarily, the mean period drawback of Small data set was corrected. On this base, the LLEs of daily qualified rate time series of HZ, an electronic manufacturing enterprise, were estimated and all positive LLEs were taken which indicate that this time series is a chaotic time series and the corresponding produce process is a chaotic process. The variance of the LLEs revealed the struggle between the divergence nature of quality system and quality control effort. LLEs showed sharp increase in getting worse quality level coincide with the company shutdown. HZ’s daily qualified rate, a chaotic time series, shows us the predictable nature of quality system in a short-run.


Author(s):  
Jianping Ju ◽  
Hong Zheng ◽  
Xiaohang Xu ◽  
Zhongyuan Guo ◽  
Zhaohui Zheng ◽  
...  

AbstractAlthough convolutional neural networks have achieved success in the field of image classification, there are still challenges in the field of agricultural product quality sorting such as machine vision-based jujube defects detection. The performance of jujube defect detection mainly depends on the feature extraction and the classifier used. Due to the diversity of the jujube materials and the variability of the testing environment, the traditional method of manually extracting the features often fails to meet the requirements of practical application. In this paper, a jujube sorting model in small data sets based on convolutional neural network and transfer learning is proposed to meet the actual demand of jujube defects detection. Firstly, the original images collected from the actual jujube sorting production line were pre-processed, and the data were augmented to establish a data set of five categories of jujube defects. The original CNN model is then improved by embedding the SE module and using the triplet loss function and the center loss function to replace the softmax loss function. Finally, the depth pre-training model on the ImageNet image data set was used to conduct training on the jujube defects data set, so that the parameters of the pre-training model could fit the parameter distribution of the jujube defects image, and the parameter distribution was transferred to the jujube defects data set to complete the transfer of the model and realize the detection and classification of the jujube defects. The classification results are visualized by heatmap through the analysis of classification accuracy and confusion matrix compared with the comparison models. The experimental results show that the SE-ResNet50-CL model optimizes the fine-grained classification problem of jujube defect recognition, and the test accuracy reaches 94.15%. The model has good stability and high recognition accuracy in complex environments.


2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Ryoya Shiode ◽  
Mototaka Kabashima ◽  
Yuta Hiasa ◽  
Kunihiro Oka ◽  
Tsuyoshi Murase ◽  
...  

AbstractThe purpose of the study was to develop a deep learning network for estimating and constructing highly accurate 3D bone models directly from actual X-ray images and to verify its accuracy. The data used were 173 computed tomography (CT) images and 105 actual X-ray images of a healthy wrist joint. To compensate for the small size of the dataset, digitally reconstructed radiography (DRR) images generated from CT were used as training data instead of actual X-ray images. The DRR-like images were generated from actual X-ray images in the test and adapted to the network, and high-accuracy estimation of a 3D bone model from a small data set was possible. The 3D shape of the radius and ulna were estimated from actual X-ray images with accuracies of 1.05 ± 0.36 and 1.45 ± 0.41 mm, respectively.


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