The Painlevé property for a(2+1)-dimensional Korteweg–de Vries(KdV) extension, the combined KP3(Kadomtsev–Petviashvili) and KP4(cKP3-4), is proved by using Kruskal’s simplification. The truncated Painlevé...The Painlevé property for a(2+1)-dimensional Korteweg–de Vries(KdV) extension, the combined KP3(Kadomtsev–Petviashvili) and KP4(cKP3-4), is proved by using Kruskal’s simplification. The truncated Painlevé expansion is used to find the Schwartz form, the Bäcklund/Levi transformations, and the residual nonlocal symmetry. The residual symmetry is localized to find its finite Bäcklund transformation. The local point symmetries of the model constitute a centerless Kac–Moody–Virasoro algebra. The local point symmetries are used to find the related group-invariant reductions including a new Lax integrable model with a fourth-order spectral problem. The finite transformation theorem or the Lie point symmetry group is obtained by using a direct method.展开更多
To overcome the computational burden of processing three-dimensional(3 D)medical scans and the lack of spatial information in two-dimensional(2 D)medical scans,a novel segmentation method was proposed that integrates ...To overcome the computational burden of processing three-dimensional(3 D)medical scans and the lack of spatial information in two-dimensional(2 D)medical scans,a novel segmentation method was proposed that integrates the segmentation results of three densely connected 2 D convolutional neural networks(2 D-CNNs).In order to combine the lowlevel features and high-level features,we added densely connected blocks in the network structure design so that the low-level features will not be missed as the network layer increases during the learning process.Further,in order to resolve the problems of the blurred boundary of the glioma edema area,we superimposed and fused the T2-weighted fluid-attenuated inversion recovery(FLAIR)modal image and the T2-weighted(T2)modal image to enhance the edema section.For the loss function of network training,we improved the cross-entropy loss function to effectively avoid network over-fitting.On the Multimodal Brain Tumor Image Segmentation Challenge(BraTS)datasets,our method achieves dice similarity coefficient values of 0.84,0.82,and 0.83 on the BraTS2018 training;0.82,0.85,and 0.83 on the BraTS2018 validation;and 0.81,0.78,and 0.83 on the BraTS2013 testing in terms of whole tumors,tumor cores,and enhancing cores,respectively.Experimental results showed that the proposed method achieved promising accuracy and fast processing,demonstrating good potential for clinical medicine.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11975131 and 11435005)the K C Wong Magna Fund in Ningbo University。
文摘The Painlevé property for a(2+1)-dimensional Korteweg–de Vries(KdV) extension, the combined KP3(Kadomtsev–Petviashvili) and KP4(cKP3-4), is proved by using Kruskal’s simplification. The truncated Painlevé expansion is used to find the Schwartz form, the Bäcklund/Levi transformations, and the residual nonlocal symmetry. The residual symmetry is localized to find its finite Bäcklund transformation. The local point symmetries of the model constitute a centerless Kac–Moody–Virasoro algebra. The local point symmetries are used to find the related group-invariant reductions including a new Lax integrable model with a fourth-order spectral problem. The finite transformation theorem or the Lie point symmetry group is obtained by using a direct method.
基金the National Natural Science Foundation of China(No.81830052)the Shanghai Natural Science Foundation of China(No.20ZR1438300)the Shanghai Science and Technology Support Project(No.18441900500),China。
文摘To overcome the computational burden of processing three-dimensional(3 D)medical scans and the lack of spatial information in two-dimensional(2 D)medical scans,a novel segmentation method was proposed that integrates the segmentation results of three densely connected 2 D convolutional neural networks(2 D-CNNs).In order to combine the lowlevel features and high-level features,we added densely connected blocks in the network structure design so that the low-level features will not be missed as the network layer increases during the learning process.Further,in order to resolve the problems of the blurred boundary of the glioma edema area,we superimposed and fused the T2-weighted fluid-attenuated inversion recovery(FLAIR)modal image and the T2-weighted(T2)modal image to enhance the edema section.For the loss function of network training,we improved the cross-entropy loss function to effectively avoid network over-fitting.On the Multimodal Brain Tumor Image Segmentation Challenge(BraTS)datasets,our method achieves dice similarity coefficient values of 0.84,0.82,and 0.83 on the BraTS2018 training;0.82,0.85,and 0.83 on the BraTS2018 validation;and 0.81,0.78,and 0.83 on the BraTS2013 testing in terms of whole tumors,tumor cores,and enhancing cores,respectively.Experimental results showed that the proposed method achieved promising accuracy and fast processing,demonstrating good potential for clinical medicine.
