摘要：
The construction of quantum maximum distance separable (MDS for short) codes is one of the hot issues in quantum information theory. As far as we know, researchers have done a lot of constructive work in the construction of quantum MDS codes. However, the known results do not cover all parameters. In this paper, we propose an efficient construction implemented by concatenating two existing quantum MDS codes. Compared to a previous work (Fang and Luo in Quantum Inf Process 19(1):16, 2020), we relax the restrictions of the construction and propose some new quantum MDS codes.
作者机构：
[Feng, Yun] Wuhan Polytech Univ, Sch Math & Comp Sci, Wuhan 430023, Peoples R China.;[Lin, Wensong] Southeast Univ, Sch Math, Nanjing 210096, Peoples R China.
通讯机构：
[Yun Feng] S;School of Mathematics and Computer Science, Wuhan Polytechnic University, Wuhan 430023, China<&wdkj&>Author to whom correspondence should be addressed.
作者机构：
[Wang, Zemin; An, Jiachun; Ma, Yuanyuan; Li, Fei; Liu, Shunlun; Li, Bing] Wuhan Univ, Chinese Antarctic Ctr Surveying & Mapping, Wuhan 430079, Peoples R China.;[Ma, Yuanyuan; Li, Fei] Wuhan Univ, Elect Informat Sch, Wuhan 430072, Peoples R China.;[Wang, Zemin; An, Jiachun; Ma, Yuanyuan; Li, Fei; Liu, Shunlun] MNR, Key Lab Polar Surveying & Mapping, Wuhan 430079, Peoples R China.;[Li, Bing] Wuhan Polytech Univ, Sch Math & Comp Sci, Wuhan 430048, Peoples R China.;[Ma, Weifeng] Yunnan Normal Univ, Fac Geog, Kunming 650050, Yunnan, Peoples R China.
通讯机构：
[Wang, ZM ] W;Wuhan Univ, Chinese Antarctic Ctr Surveying & Mapping, Wuhan 430079, Peoples R China.;MNR, Key Lab Polar Surveying & Mapping, Wuhan 430079, Peoples R China.
关键词：
glacier mass balance;SAR interferometry;ice motion;ionospheric effects;reformulation of the split-spectrum method;ionospheric correction
摘要：
Ice motion is an essential element for accurately evaluating glacier mass balance. Interferometric synthetic aperture radar (InSAR) has been widely applied for monitoring ice motion with high precision and wide coverage in the Antarctic. However, the ionospheric effects can significantly impact InSAR-based ice-motion measurements. At low radar frequencies in particular, the ionospheric effects have been regarded as a serious source of noise in L-band SAR data. The split-spectrum method (SSM) is commonly used for correcting the ionospheric effects of the InSAR technique. However, it requires spatial filtering with the relatively large factors used to scale the sub-bands' interferograms, which often results in an unwrapped phase error. In this paper, a reformulation of the split-spectrum method (RSSM) is introduced to correct the ionospheric effects in the Grove Mountains of East Antarctica, which have slow ice flow and frequent ionosphere changes. The results show that RSSM can effectively correct the ionospheric effects of InSAR-based ice-motion measurements. To evaluate the ability of ionospheric correction using RSSM, the result of ionospheric correction derived from SSM is compared with the results of RSSM. In addition, ionosphere-corrected ice motion is also compared with GPS and MEaSUREs. The results show that the ionosphere-corrected ice velocities are in good agreement with GPS observations and MEaSUREs. The average ice velocity from the InSAR time series is compared to that from MEaSUREs, and the average ionosphere-corrected ice velocity error reduces 43.9% in SSM and 51.1% in RSSM, respectively. The ionosphere-corrected ice velocity error is the most significant, reducing 86.9% in SSM and 90.4% in RSSM from 1 November 2007 to 19 December 2007. The results show that the ability of RSSM to correct ionospheric effects is slightly better than that of SSM. Therefore, we deduce that the RSSM offers a feasible way to correct ionospheric effects in InSAR-based ice-motion measurements in Antarctica.
摘要：
Clustering noisy, high-dimensional, and structurally complex data has always been a challenging task. As most existing clustering methods are not able to deal with both the adverse impact of noisy samples and the complex structures of data, in this paper, we propose a novel Robust and Sparse Possibilistic K-Subspace Clustering algorithm (RSPKS) to integrate subspace recovery and possibilistic clustering algorithms under a unified sparse framework. First, the proposed method sparsifies the membership matrix and the subspace projection vector under a dual-sparse framework to handle high-dimensional noisy data. This unifies dimensionality reduction and clustering using one objective function, for which the optimization can be realized through synchronous iteration. Second, the reconstruction error of each sample in the local subspace is used as the distance metric for classification. That is, each sample itself is treated as a clustering prototype so as not to be affected by the structure of the overall data distribution. Therefore, the clustering prototype construction problem of data with complex structures can be better addressed. Finally, to deal with non-linear regions, our RSPKS method is further extended into a kernelized version, namely the Kernelized Robust and Sparse Possibilistic K-Subspace Clustering (KRSPKS) algorithm. Experimental results on both synthetic and real-world datasets demonstrate that our proposed method outperforms state-of-the-art algorithms in terms of clustering accuracy. IEEE
通讯机构：
[Shan Zeng] S;School of Mathematics and Computer Science, Wuhan Polytechnic University, Wuhan 430023, China<&wdkj&>Author to whom correspondence should be addressed.
关键词：
deep learning;hyperspectral image classification;attention mechanism;feature fusion;3D CNN
摘要：
With the continuous development of hyperspectral image technology and deep learning methods in recent years, an increasing number of hyperspectral image classification models have been proposed. However, due to the numerous spectral dimensions of hyperspectral images, most classification models suffer from issues such as breaking spectral continuity and poor learning of spectral information. In this paper, we propose a new classification model called the enhanced spectral fusion network (ESFNet), which contains two parts: an optimized multi-scale fused spectral attention module (FsSE) and a 3D convolutional neural network (3D CNN) based on the fusion of different spectral strides (SSFCNN). Specifically, after sampling the hyperspectral images, our model first implements the weighting of the spectral information through the FsSE module to obtain spectral data with a higher degree of information richness. Then, the weighted spectral data are fed into the SSFCNN to realize the effective learning of spectral features. The new model can maximize the retention of spectral continuity and enhance the spectral information while being able to better utilize the enhanced information to improve the model’s ability to learn hyperspectral image features, thus improving the classification accuracy of the model. Experiment results on the Indian Pines and Pavia University datasets demonstrated that our method outperforms other relevant baselines in terms of classification accuracy and generalization performance.
通讯机构：
[Cao Yuan] S;School of Mathematics and Computer Science, Wuhan Polytechnic University, Wuhan 430024, China<&wdkj&>Author to whom correspondence should be addressed.
关键词：
end to end;deep learning;point cloud completion;squeeze and excitation;trilinear interpolation
摘要：
We propose a conceptually simple, general framework and end-to-end approach to point cloud completion, entitled PCA-Net. This approach differs from the existing methods in that it does not require a “simple” network, such as multilayer perceptrons (MLPs), to generate a coarse point cloud and then a “complex” network, such as auto-encoders or transformers, to enhance local details. It can directly learn the mapping between missing and complete points, ensuring that the structure of the input missing point cloud remains unchanged while accurately predicting the complete points. This approach follows the minimalist design of U-Net. In the encoder, we encode the point clouds into point cloud blocks by iterative farthest point sampling (IFPS) and k-nearest neighbors and then extract the depth interaction features between the missing point cloud blocks by the attention mechanism. In the decoder, we introduce a new trilinear interpolation method to recover point cloud details, with the help of the coordinate space and feature space of low-resolution point clouds, and missing point cloud information. This paper also proposes a method to generate multi-view missing point cloud data using a 3D point cloud hidden point removal algorithm, so that each 3D point cloud model generates a missing point cloud through eight uniformly distributed camera poses. Experiments validate the effectiveness and superiority of PCA-Net in several challenging point cloud completion tasks, and PCA-Net also shows great versatility and robustness in real-world missing point cloud completion.
摘要：
Hyperspectral imaging can simultaneously acquire spectral and spatial information of the samples and is, therefore, widely applied in the non-destructive detection of grain quality. Supervised learning is the mainstream method of hyperspectral imaging for pixel-level detection of mildew in corn kernels, which requires a large number of training samples to establish the prediction or classification models. This paper presents an unsupervised redundant co-clustering algorithm (FCM-SC) based on multi-center fuzzy c-means (FCM) clustering and spectral clustering (SC), which can effectively detect non-uniformly distributed mildew in corn kernels. This algorithm first carries out fuzzy c-means clustering of sample features, extracts redundant cluster centers, merges the cluster centers by spectral clustering, and finally finds the category of corresponding cluster centers for each sample. It effectively solves the problems of the poor ability of the traditional fuzzy c-means clustering algorithm to classify the data with complex structure distribution and the complex calculation of the traditional spectral clustering algorithm. The experimental results demonstrated that the proposed algorithm could describe the complex structure of mildew distribution in corn kernels and exhibits higher stability, better anti-interference ability, generalization ability, and accuracy than the supervised classification model.
期刊：
Advances in Mathematics,2022年410:108716 ISSN：0001-8708
通讯作者：
Chuntai Liu<&wdkj&>Sze-Man Ngai
作者机构：
[Deng, Guotai] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Deng, Guotai] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.;[Liu, Chuntai] Wuhan Polytech Univ, Sch Math & Comp Sci, Wuhan 430023, Peoples R China.;[Ngai, Sze -Man] Hunan Normal Univ, Coll Math & Stat, Key Lab High Performance Comp & Stochast Informat, HPCSIP,Minist Educ China, Changsha 410081, Hunan, Peoples R China.;[Ngai, Sze -Man] Georgia Southern Univ, Dept Math Sci, Statesboro, GA 30460 USA.
通讯机构：
[Chuntai Liu] S;[Sze-Man Ngai] K;School of Mathematics and Computer Science, Wuhan Polytechnic University, Wuhan 430023, PR China<&wdkj&>Key Laboratory of High Performance Computing and Stochastic Information Processing (HPCSIP) (Ministry of Education of China), College of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan 410081, PR China<&wdkj&>Department of Mathematical Sciences, Georgia Southern University, Statesboro, GA 30460-8093, USA
关键词：
Ball-like tile;Brouwer's invariance of domain theorem;Horizontal distance;Self-affine tile;Tame ball
摘要：
We study a family of self-affine tiles in Rd (d >= 2) with noncollinear digit sets, which naturally generalizes a two-dimensional class studied originally by Deng and Lau and its extension to R3 by the authors. By using Brouwer's invariance of domain theorem, along with a tool which we call horizontal distance, we obtain necessary and sufficient conditions for the tiles to be d-dimensional tame balls. This answers positively the conjecture in an earlier paper by the authors stating that a member in a certain class of self-affine tiles is homeomorphic to a d-dimensional ball if and only if its interior is connected. (c) 2022 Elsevier Inc. All rights reserved.
期刊：
Nonlinear Analysis: Real World Applications,2022年63:103411 ISSN：1468-1218
通讯作者：
Hou, Meichen
作者机构：
[Hou, Meichen] Northwest Univ, Sch Math, Xian 710069, Peoples R China.;[Hou, Meichen] Northwest Univ, CNS, Xian 710069, Peoples R China.;[Fan, Lili] Wuhan Polytech Univ, Sch Math & Comp Sci, Wuhan 430023, Peoples R China.
通讯机构：
[Hou, Meichen] N;Northwest Univ, Sch Math, Xian 710069, Peoples R China.;Northwest Univ, CNS, Xian 710069, Peoples R China.
关键词：
Inflow problem;Non-viscous;Contact wave
摘要：
This paper is devoted to studying the inflow problem governed by the non-viscous and heat-conductive gas dynamic system in the one-dimensional half space. We establish the unique global-in-time existence and the asymptotic stability of the viscous contact wave. The contact discontinuity in the linearly degenerate field is less stable, and the dissipative mechanism for non-viscous systems is also weaker than that of viscous systems, these all make the problem more challenging. We used the weighted energy estimates to overcome those difficulties. Some technical discussions were created carefully by taking good advantage of properties of the supersonic region and the viscous contact wave. (C) 2021 Elsevier Ltd. All rights reserved.
作者机构：
[Wang, Li; Huang, Wentao] East China Jiaotong Univ, Sch Basic Sci, Nanchang, Jiangxi, Peoples R China.;[Wang, Qingfang] Wuhan Polytech Univ, Sch Math & Comp Sci, Wuhan, Peoples R China.
通讯机构：
[Wang, Qingfang] W;Wuhan Polytech Univ, Sch Math & Comp Sci, Wuhan, Peoples R China.
关键词：
35J20;35J62;58E05;invariant sets of descending flow;Quasilinear Schrödinger equation;sign-changing solutions
摘要：
This paper is motivated by the study of the following quasilinear Schrodinger equation - Delta u + V(x)u - [ Delta(1 + u(2))(1/2)] u/2(1 + u(2))(1/2) = lambda h(u), x is an element of R-N, where N >= 3, lambda > 0 is a parameter and V(x) is a given positive potential. As an example, the nonlinearity includes the pure power type of h(u) = vertical bar u vertical bar(p-2)u for the well-studied case 12 - 4 root 6 < p < 2*, and the case 2 < p < 12 - 4 root 6 in which few existence results are known. Distinguishing from the existing results in the literature, we are more interested in the existence and multiplicity of sign-changing solutions for the above problem.
通讯机构：
[Zhang, C.] W;Wuhan Polytechnic University, China
关键词：
adaptive dynamic genetic optimization algorithm;Dynamic neural network optimization model;radial basis function neural network;soil heavy metal content prediction
摘要：
To improve the accuracy of soil heavy metal content prediction, this study proposes a dynamic neural network optimization model (DNNOM). The model is based on a radial basis function neural network (RBFNN). The weights and bias of the output layer of the RBFNN were generated using an adaptive dynamic genetic optimization algorithm (ADGOA), and the center point of the hidden layer of the RBFNN was determined using an efficient density peak clustering algorithm (EDPC). An adaptive variance measure (AVM) was then used to generate the width vector of RBFNN hidden layer. The model was applied to the predict soil heavy metal content in six new urban areas in Wuhan. Through comparison with support vector machine(SVM), light gradient boosting machine(LightGBM), RBFNN, and genetic algorithm optimizes the radial basis function neural network(GA-RBFNN), the experimental results demonstrate that the DNNOM is closer to the real value than the other four models, and the four error indicator values are also significantly lower than those of the other comparison models, which have higher prediction accuracy. Especially when compared with RBFNN, the MAPE and SMAPE of DNNOM decreased by 3.98% and 3.9%, respectively.
通讯机构：
[Shengyong Xu] C;College of Engineering, Huazhong Agricultural University, Wuhan 430070, China<&wdkj&>Key Laboratory of Agricultural Equipment for the Middle and Lower Reaches of the Yangtze River, Ministry of Agriculture, Wuhan 430070, China<&wdkj&>Shenzhen Branch, Guangdong Laboratory for Lingnan Modern Agriculture, Genome Analysis Laboratory of the Ministry of Agriculture, Agricultural Genomics Institute at Shenzhen, Chinese Academy of Agricultural Sciences, Shenzhen 518000, China<&wdkj&>Shenzhen Institute of Nutrition and Health, Huazhong Agricultural University, Shenzhen 518000, China<&wdkj&>Author to whom correspondence should be addressed.
关键词：
point cloud segmentation;point cloud completion;leaf area measurement;MIX-Net;seedlings;deep learning
摘要：
In this paper, a novel point cloud segmentation and completion framework is proposed to achieve high-quality leaf area measurement of melon seedlings. In particular, the input of our algorithm is the point cloud data collected by an Azure Kinect camera from the top view of the seedlings, and our method can enhance measurement accuracy from two aspects based on the acquired data. On the one hand, we propose a neighborhood space-constrained method to effectively filter out the hover points and outlier noise of the point cloud, which can enhance the quality of the point cloud data significantly. On the other hand, by leveraging the purely linear mixer mechanism, a new network named MIX-Net is developed to achieve segmentation and completion of the point cloud simultaneously. Different from previous methods that separate these two tasks, the proposed network can better balance these two tasks in a more definite and effective way, leading to satisfactory performance on these two tasks. The experimental results prove that our methods can outperform other competitors and provide more accurate measurement results. Specifically, for the seedling segmentation task, our method can obtain a 3.1% and 1.7% performance gain compared with PointNet++ and DGCNN, respectively. Meanwhile, the R-2 of leaf area measurement improved from 0.87 to 0.93 and MSE decreased from 2.64 to 2.26 after leaf shading completion.
通讯机构：
[Yaqin Li] S;School of Mathematics and Computer Science, Wuhan Polytechnic University, Wuhan 430024, China<&wdkj&>Author to whom correspondence should be addressed.
关键词：
deep learning;generative adversarial network;deep generative model;super-resolution;feature transform;multiscale feature extraction
期刊：
JOURNAL OF GEOMETRIC ANALYSIS,2022年32(11):1-42 ISSN：1050-6926
通讯作者：
Chunhua Wang
作者机构：
[He, Qihan] Guangxi Univ, Coll Math & Informat Sci, Nanning 530003, Guangxi, Peoples R China.;[Wang, Chunhua] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Wang, Chunhua] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.;[Wang, Qingfang] Wuhan Polytech Univ, Sch Math & Comp Sci, Wuhan 430023, Peoples R China.
通讯机构：
[Chunhua Wang] S;School of Mathematics and Statistics & Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan, People’s Republic of China
摘要：
In this paper, we investigate the following critical elliptic equation
$$-\Delta u+V(y)u=u^{\frac{N+2}{N-2}},\;u>0,\;\text {in}\,{\mathbb {R}}^{N},\;u\in H^{1}({\mathbb {R}}^{N}),$$
where V(y) is a bounded non-negative function in
$${\mathbb {R}}^{N}.$$
Assuming that
$$V(y)=V(|\hat{y}|,y^{*}),y=(\hat{y},y^{*})\in {\mathbb {R}}^{4}\times {\mathbb {R}}^{N-4}$$
and gluing together bubbles with different concentration rates, we obtain new solutions provided that
$$N\ge 7,$$
whose concentrating points are close to the point
$$(r_{0},y^{*}_{0})$$
which is a stable critical point of the function
$$r^{2}V(r,y^{*})$$
satisfying
$$r_{0}>0$$
and
$$V(r_{0},y^{*}_{0})>0.$$
In order to construct such new bubble solutions for the above problem, we first prove a non-degenerate result for the positive multi-bubbling solutions constructed in Peng et al. (J Funct Anal 274:2606–2633, 2018) by some local Pohozaev identities, which is of great interest independently. Moreover, we give an example which satisfies the assumptions we impose.
