Pub Date : 2023-09-01DOI: 10.1007/s11464-021-0018-6
Bo Zheng, Yueqiang Shang
Based on finite element discretization, a new two-grid algorithm based on Newton iteration is proposed to solve the stationary Navier–Stokes equations with nonlinear damping term. The proposed new two-grid algorithm consists of three steps: in the first step, we solve one small nonlinear coarse grid problem, and then, in the second and third steps, we solve two linear fine grid problems based on Newton iteration which have the same stiffness matrices with only different right-hand sides. We analyze stability of the present algorithm and prove rate of convergence of the approximate solutions obtained from the algorithm. Numerical results are given to demonstrate the effectiveness of the present algorithm, showing that our algorithm greatly improves the accuracy of the approximate solutions comparable to that of the usual two-grid algorithm.
{"title":"A New Two-grid Algorithm Based on Newton Iteration for the Stationary Navier–Stokes Equations with Damping","authors":"Bo Zheng, Yueqiang Shang","doi":"10.1007/s11464-021-0018-6","DOIUrl":"https://doi.org/10.1007/s11464-021-0018-6","url":null,"abstract":"Based on finite element discretization, a new two-grid algorithm based on Newton iteration is proposed to solve the stationary Navier–Stokes equations with nonlinear damping term. The proposed new two-grid algorithm consists of three steps: in the first step, we solve one small nonlinear coarse grid problem, and then, in the second and third steps, we solve two linear fine grid problems based on Newton iteration which have the same stiffness matrices with only different right-hand sides. We analyze stability of the present algorithm and prove rate of convergence of the approximate solutions obtained from the algorithm. Numerical results are given to demonstrate the effectiveness of the present algorithm, showing that our algorithm greatly improves the accuracy of the approximate solutions comparable to that of the usual two-grid algorithm.","PeriodicalId":50429,"journal":{"name":"Frontiers of Mathematics in China","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134995423","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This study aimed to investigate the performance of 18F-DCFPyL positron emission tomography/computerized tomography (PET/CT) models for predicting benign-vs-malignancy, high pathological grade (Gleason score > 7), and clinical D'Amico classification with machine learning. The study included 138 patients with treatment-naïve prostate cancer presenting positive 18F-DCFPyL scans. The primary lesions were delineated on PET images, followed by the extraction of tumor-to-background-based general and higher-order textural features by applying five different binning approaches. Three layer-machine learning approaches were used to identify relevant in vivo features and patient characteristics and their relative weights for predicting high-risk malignant disease. The weighted features were integrated and implemented to establish individual predictive models for malignancy (Mm), high path-risk lesions (by Gleason score) (Mgs), and high clinical risk disease (by amico) (Mamico). The established models were validated in a Monte Carlo cross-validation scheme. In patients with all primary prostate cancer, the highest areas under the curve for our models were calculated. The performance of established models as revealed by the Monte Carlo cross-validation presenting as the area under the receiver operator characteristic curve (AUC): 0.97 for Mm, AUC: 0.73 for Mgs, AUC: 0.82 for Mamico. Our study demonstrated the clinical potential of 18F-DCFPyL PET/CT radiomics in distinguishing malignant from benign prostate tumors, and high-risk tumors, without biopsy sampling. And in vivo 18F-DCFPyL PET/CT can be considered a noninvasive tool for virtual biopsy for personalized treatment management.
Supplementary information: The online version contains supplementary material available at 10.1007/s43657-023-00108-y.
{"title":"Performance of <sup>18</sup>F-DCFPyL PET/CT in Primary Prostate Cancer Diagnosis, Gleason Grading and D'Amico Classification: A Radiomics-Based Study.","authors":"Yuekai Li, Fengcai Li, Shaoli Han, Jing Ning, Peng Su, Jianfeng Liu, Lili Qu, Shuai Huang, Shiwei Wang, Xin Li, Xiang Li","doi":"10.1007/s43657-023-00108-y","DOIUrl":"10.1007/s43657-023-00108-y","url":null,"abstract":"<p><p>This study aimed to investigate the performance of <sup>18</sup>F-DCFPyL positron emission tomography/computerized tomography (PET/CT) models for predicting benign-vs-malignancy, high pathological grade (Gleason score > 7), and clinical D'Amico classification with machine learning. The study included 138 patients with treatment-naïve prostate cancer presenting positive <sup>18</sup>F-DCFPyL scans. The primary lesions were delineated on PET images, followed by the extraction of tumor-to-background-based general and higher-order textural features by applying five different binning approaches. Three layer-machine learning approaches were used to identify relevant in vivo features and patient characteristics and their relative weights for predicting high-risk malignant disease. The weighted features were integrated and implemented to establish individual predictive models for malignancy (<i>M</i><sub>m</sub>), high path-risk lesions (by Gleason score) (<i>M</i><sub>gs</sub>), and high clinical risk disease (by amico) (<i>M</i><sub>amico</sub>). The established models were validated in a Monte Carlo cross-validation scheme. In patients with all primary prostate cancer, the highest areas under the curve for our models were calculated. The performance of established models as revealed by the Monte Carlo cross-validation presenting as the area under the receiver operator characteristic curve (AUC): 0.97 for <i>M</i><sub>m</sub>, AUC: 0.73 for <i>M</i><sub>gs</sub>, AUC: 0.82 for <i>M</i><sub>amico</sub>. Our study demonstrated the clinical potential of <sup>18</sup>F-DCFPyL PET/CT radiomics in distinguishing malignant from benign prostate tumors, and high-risk tumors, without biopsy sampling. And in vivo <sup>18</sup>F-DCFPyL PET/CT can be considered a noninvasive tool for virtual biopsy for personalized treatment management.</p><p><strong>Supplementary information: </strong>The online version contains supplementary material available at 10.1007/s43657-023-00108-y.</p>","PeriodicalId":50429,"journal":{"name":"Frontiers of Mathematics in China","volume":"13 1","pages":"576-585"},"PeriodicalIF":0.8,"publicationDate":"2023-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10781655/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81743175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-22DOI: 10.1007/s11464-020-0126-8
Zhen-Lin Wu, N. Yang
{"title":"CLTσ-group with σ-subnormal or Self-normalizing Subgroups","authors":"Zhen-Lin Wu, N. Yang","doi":"10.1007/s11464-020-0126-8","DOIUrl":"https://doi.org/10.1007/s11464-020-0126-8","url":null,"abstract":"","PeriodicalId":50429,"journal":{"name":"Frontiers of Mathematics in China","volume":"40 1","pages":"961 - 975"},"PeriodicalIF":0.0,"publicationDate":"2023-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87542044","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-22DOI: 10.1007/s11464-020-0051-x
Ji-zheng Huang, Huixia Mo
{"title":"A New Characterization of the Besov Spaces Associated with Hermite Operator","authors":"Ji-zheng Huang, Huixia Mo","doi":"10.1007/s11464-020-0051-x","DOIUrl":"https://doi.org/10.1007/s11464-020-0051-x","url":null,"abstract":"","PeriodicalId":50429,"journal":{"name":"Frontiers of Mathematics in China","volume":"33 1","pages":"863 - 882"},"PeriodicalIF":0.0,"publicationDate":"2023-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73364721","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-22DOI: 10.1007/s11464-020-0180-2
Qingzhi Yang, Yujin Paek, Wei Mei
{"title":"Further Investigation of Positive Semi-definiteness of Fourth-order Cauchy and Hilbert Tensors","authors":"Qingzhi Yang, Yujin Paek, Wei Mei","doi":"10.1007/s11464-020-0180-2","DOIUrl":"https://doi.org/10.1007/s11464-020-0180-2","url":null,"abstract":"","PeriodicalId":50429,"journal":{"name":"Frontiers of Mathematics in China","volume":"161 1","pages":"935 - 952"},"PeriodicalIF":0.0,"publicationDate":"2023-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75418438","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-22DOI: 10.1007/s11464-020-0011-5
An Wang, Chengchen Zhong
{"title":"Lu Qi-Keng Problem and Topological Properties of Zero Variety on the Thullen Domain","authors":"An Wang, Chengchen Zhong","doi":"10.1007/s11464-020-0011-5","DOIUrl":"https://doi.org/10.1007/s11464-020-0011-5","url":null,"abstract":"","PeriodicalId":50429,"journal":{"name":"Frontiers of Mathematics in China","volume":"18 1","pages":"817 - 836"},"PeriodicalIF":0.0,"publicationDate":"2023-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87174545","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-22DOI: 10.1007/s11464-020-0169-x
Yao Zhang
{"title":"The Finitistic Dimension and Global Dimension of an Artinian Ring with a Dualizing Complex","authors":"Yao Zhang","doi":"10.1007/s11464-020-0169-x","DOIUrl":"https://doi.org/10.1007/s11464-020-0169-x","url":null,"abstract":"","PeriodicalId":50429,"journal":{"name":"Frontiers of Mathematics in China","volume":"58 1","pages":"953 - 960"},"PeriodicalIF":0.0,"publicationDate":"2023-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85809839","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-22DOI: 10.1007/s11464-020-0142-8
Weiguo Lü
{"title":"The Batalin–Vilkovisky Structure over the Hochschild Cohomology Ring of Exterior Algebras","authors":"Weiguo Lü","doi":"10.1007/s11464-020-0142-8","DOIUrl":"https://doi.org/10.1007/s11464-020-0142-8","url":null,"abstract":"","PeriodicalId":50429,"journal":{"name":"Frontiers of Mathematics in China","volume":"105 1","pages":"903 - 934"},"PeriodicalIF":0.0,"publicationDate":"2023-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86263562","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-22DOI: 10.1007/s11464-021-0209-1
Bo Chen, Youde Wang
{"title":"Very Regular Solution to Landau–Lifshitz–Gilbert System with Spin-polarized Transport","authors":"Bo Chen, Youde Wang","doi":"10.1007/s11464-021-0209-1","DOIUrl":"https://doi.org/10.1007/s11464-021-0209-1","url":null,"abstract":"","PeriodicalId":50429,"journal":{"name":"Frontiers of Mathematics in China","volume":"55 1","pages":"751 - 795"},"PeriodicalIF":0.0,"publicationDate":"2023-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89943606","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-22DOI: 10.1007/s11464-020-0040-y
Tongxin Yan, Yifen Ke, Changfeng Ma
{"title":"Adaptive Parameter Alternating Direction Algorithm for Centrosymmetric Solutions of a Class of Generalized Coupled Sylvester-transpose Matrix Equations","authors":"Tongxin Yan, Yifen Ke, Changfeng Ma","doi":"10.1007/s11464-020-0040-y","DOIUrl":"https://doi.org/10.1007/s11464-020-0040-y","url":null,"abstract":"","PeriodicalId":50429,"journal":{"name":"Frontiers of Mathematics in China","volume":"38 1","pages":"977 - 998"},"PeriodicalIF":0.0,"publicationDate":"2023-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73456029","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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