Annals of Applied Statistics最新文献

Bayesian combinatorial MultiStudy factor analysis. 贝叶斯组合多因素分析。

IF 1.3 4区数学

Annals of Applied Statistics Pub Date : 2023-09-01 Epub Date: 2023-09-07 DOI: 10.1214/22-aoas1715

Isabella N Grabski, Roberta De Vito, Lorenzo Trippa, Giovanni Parmigiani

{"title":"Bayesian combinatorial MultiStudy factor analysis.","authors":"Isabella N Grabski, Roberta De Vito, Lorenzo Trippa, Giovanni Parmigiani","doi":"10.1214/22-aoas1715","DOIUrl":"10.1214/22-aoas1715","url":null,"abstract":"Mutations in the BRCA1 and BRCA2 genes are known to be highly associated with breast cancer. Identifying both shared and unique transcript expression patterns in blood samples from these groups can shed insight into if and how the disease mechanisms differ among individuals by mutation status, but this is challenging in the high-dimensional setting. A recent method, Bayesian Multi-Study Factor Analysis (BMSFA), identifies latent factors common to all studies (or equivalently, groups) and latent factors specific to individual studies. However, BMSFA does not allow for factors shared by more than one but less than all studies. This is critical in our context, as we may expect some but not all signals to be shared by BRCA1-and BRCA2-mutation carriers but not necessarily other high-risk groups. We extend BMSFA by introducing a new method, Tetris, for Bayesian combinatorial multi-study factor analysis, which identifies latent factors that any combination of studies or groups can share. We model the subsets of studies that share latent factors with an Indian Buffet Process, and offer a way to summarize uncertainty in the sharing patterns using credible balls. We test our method with an extensive range of simulations, and showcase its utility not only in dimension reduction but also in covariance estimation. When applied to transcript expression data from high-risk families grouped by mutation status, Tetris reveals the features and pathways characterizing each group and the sharing patterns among them. Finally, we further extend Tetris to discover groupings of samples when group labels are not provided, which can elucidate additional structure in these data.","PeriodicalId":50772,"journal":{"name":"Annals of Applied Statistics","volume":"17 3","pages":"2212-2235"},"PeriodicalIF":1.3,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10543692/pdf/nihms-1926927.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41156472","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

THE SCALABLE BIRTH-DEATH MCMC ALGORITHM FOR MIXED GRAPHICAL MODEL LEARNING WITH APPLICATION TO GENOMIC DATA INTEGRATION. 用于混合图形模型学习的可扩展出生路径MCMC算法及其在基因组数据集成中的应用。

IF 1.8 4区数学

Annals of Applied Statistics Pub Date : 2023-09-01 Epub Date: 2023-10-07 DOI: 10.1214/22-aoas1701

Nanwei Wang, Hélène Massam, Xin Gao, Laurent Briollais

{"title":"THE SCALABLE BIRTH-DEATH MCMC ALGORITHM FOR MIXED GRAPHICAL MODEL LEARNING WITH APPLICATION TO GENOMIC DATA INTEGRATION.","authors":"Nanwei Wang, Hélène Massam, Xin Gao, Laurent Briollais","doi":"10.1214/22-aoas1701","DOIUrl":"10.1214/22-aoas1701","url":null,"abstract":"Recent advances in biological research have seen the emergence of high-throughput technologies with numerous applications that allow the study of biological mechanisms at an unprecedented depth and scale. A large amount of genomic data is now distributed through consortia like The Cancer Genome Atlas (TCGA), where specific types of biological information on specific type of tissue or cell are available. In cancer research, the challenge is now to perform integrative analyses of high-dimensional multi-omic data with the goal to better understand genomic processes that correlate with cancer outcomes, e.g. elucidate gene networks that discriminate a specific cancer subgroups (cancer sub-typing) or discovering gene networks that overlap across different cancer types (pan-cancer studies). In this paper, we propose a novel mixed graphical model approach to analyze multi-omic data of different types (continuous, discrete and count) and perform model selection by extending the Birth-Death MCMC (BDMCMC) algorithm initially proposed by Stephens (2000) and later developed by Mohammadi and Wit (2015). We compare the performance of our method to the LASSO method and the standard BDMCMC method using simulations and find that our method is superior in terms of both computational efficiency and the accuracy of the model selection results. Finally, an application to the TCGA breast cancer data shows that integrating genomic information at different levels (mutation and expression data) leads to better subtyping of breast cancers.","PeriodicalId":50772,"journal":{"name":"Annals of Applied Statistics","volume":"17 3","pages":"1958-1983"},"PeriodicalIF":1.8,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10569451/pdf/nihms-1886934.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41219379","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

BAYESIAN INFERENCE AND DYNAMIC PREDICTION FOR MULTIVARIATE LONGITUDINAL AND SURVIVAL DATA. 多变量纵向和生存数据的贝叶斯推理和动态预测。

IF 1.3 4区数学

Annals of Applied Statistics Pub Date : 2023-09-01 Epub Date: 2023-09-07 DOI: 10.1214/23-aoas1733

Haotian Zou, Donglin Zeng, Luo Xiao, Sheng Luo

{"title":"BAYESIAN INFERENCE AND DYNAMIC PREDICTION FOR MULTIVARIATE LONGITUDINAL AND SURVIVAL DATA.","authors":"Haotian Zou, Donglin Zeng, Luo Xiao, Sheng Luo","doi":"10.1214/23-aoas1733","DOIUrl":"10.1214/23-aoas1733","url":null,"abstract":"Alzheimer's disease (AD) is a complex neurological disorder impairing multiple domains such as cognition and daily functions. To better understand the disease and its progression, many AD research studies collect multiple longitudinal outcomes that are strongly predictive of the onset of AD dementia. We propose a joint model based on a multivariate functional mixed model framework (referred to as MFMM-JM) that simultaneously models the multiple longitudinal outcomes and the time to dementia onset. We develop six functional forms to fully investigate the complex association between longitudinal outcomes and dementia onset. Moreover, we use the Bayesian methods for statistical inference and develop a dynamic prediction framework that provides accurate personalized predictions of disease progressions based on new subject-specific data. We apply the proposed MFMM-JM to two large ongoing AD studies: the Alzheimer's Disease Neuroimaging Initiative (ADNI) and National Alzheimer's Coordinating Center (NACC), and identify the functional forms with the best predictive performance. our method is also validated by extensive simulation studies with five settings.","PeriodicalId":50772,"journal":{"name":"Annals of Applied Statistics","volume":"17 3","pages":"2574-2595"},"PeriodicalIF":1.3,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10500582/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"10339586","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

PROBABILISTIC LEARNING OF TREATMENT TREES IN CANCER. 癌症治疗树的概率学习。

IF 1.8 4区数学

Annals of Applied Statistics Pub Date : 2023-09-01 Epub Date: 2023-09-07 DOI: 10.1214/22-aoas1696

Tsung-Hung Yao, Zhenke Wu, Karthik Bharath, Jinju Li, Veerabhadran Baladandayuthapani

{"title":"PROBABILISTIC LEARNING OF TREATMENT TREES IN CANCER.","authors":"Tsung-Hung Yao, Zhenke Wu, Karthik Bharath, Jinju Li, Veerabhadran Baladandayuthapani","doi":"10.1214/22-aoas1696","DOIUrl":"10.1214/22-aoas1696","url":null,"abstract":"Accurate identification of synergistic treatment combinations and their underlying biological mechanisms is critical across many disease domains, especially cancer. In translational oncology research, preclinical systems such as patient-derived xenografts (PDX) have emerged as a unique study design evaluating multiple treatments administered to samples from the same human tumor implanted into genetically identical mice. In this paper, we propose a novel Bayesian probabilistic tree-based framework for PDX data to investigate the hierarchical relationships between treatments by inferring treatment cluster trees, referred to as treatment trees (Rx-tree). The framework motivates a new metric of mechanistic similarity between two or more treatments accounting for inherent uncertainty in tree estimation; treatments with a high estimated similarity have potentially high mechanistic synergy. Building upon Dirichlet Diffusion Trees, we derive a closed-form marginal likelihood encoding the tree structure, which facilitates computationally efficient posterior inference via a new two-stage algorithm. Simulation studies demonstrate superior performance of the proposed method in recovering the tree structure and treatment similarities. Our analyses of a recently collated PDX dataset produce treatment similarity estimates that show a high degree of concordance with known biological mechanisms across treatments in five different cancers. More importantly, we uncover new and potentially effective combination therapies that confer synergistic regulation of specific downstream biological pathways for future clinical investigations. Our accompanying code, data, and shiny application for visualization of results are available at: https://github.com/bayesrx/RxTree.","PeriodicalId":50772,"journal":{"name":"Annals of Applied Statistics","volume":"17 3","pages":"1884-1908"},"PeriodicalIF":1.8,"publicationDate":"2023-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10501503/pdf/nihms-1857187.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"10308161","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

IDENTIFICATION OF IMMUNE RESPONSE COMBINATIONS ASSOCIATED WITH HETEROGENEOUS INFECTION RISK IN THE IMMUNE CORRELATES ANALYSIS OF HIV VACCINE STUDIES. 在艾滋病毒疫苗研究的免疫相关性分析中确定与异质性感染风险相关的免疫反应组合。

IF 1.8 4区数学

Annals of Applied Statistics Pub Date : 2023-06-01 Epub Date: 2023-05-01 DOI: 10.1214/22-aoas1665

Chaeryon Kang, Ying Huang

{"title":"IDENTIFICATION OF IMMUNE RESPONSE COMBINATIONS ASSOCIATED WITH HETEROGENEOUS INFECTION RISK IN THE IMMUNE CORRELATES ANALYSIS OF HIV VACCINE STUDIES.","authors":"Chaeryon Kang, Ying Huang","doi":"10.1214/22-aoas1665","DOIUrl":"10.1214/22-aoas1665","url":null,"abstract":"In HIV vaccine/prevention research, probing into the vaccine-induced immune responses that can help predict the risk of HIV infection provides valuable information for the development of vaccine regimens. Previous correlate analysis of the Thai vaccine trial aided the discovery of interesting immune correlates related to the risk of developing an HIV infection. The present study aimed to identify the combinations of immune responses associated with the heterogeneous infection risk. We explored a \"change-plane\" via combination of a subset of immune responses that could help separate vaccine recipients into two heterogeneous subgroups in terms of the association between immune responses and the risk of developing infection. Additionally, we developed a new variable selection algorithm through a penalized likelihood approach to investigate a parsimonious marker combination for the change-plane. The resulting marker combinations can serve as candidate correlates of protection and can be used for predicting the protective effect of the vaccine against HIV infection. The application of the proposed statistical approach to the Thai trial has been presented, wherein the marker combinations were explored among several immune responses and antigens.","PeriodicalId":50772,"journal":{"name":"Annals of Applied Statistics","volume":"17 2","pages":"1199-1219"},"PeriodicalIF":1.8,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10312353/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9755428","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

CO-CLUSTERING OF SPATIALLY RESOLVED TRANSCRIPTOMIC DATA. 空间分辨转录组数据的联合聚类。

IF 1.8 4区数学

Annals of Applied Statistics Pub Date : 2023-06-01 Epub Date: 2023-05-01 DOI: 10.1214/22-aoas1677

Andrea Sottosanti, Davide Risso

{"title":"CO-CLUSTERING OF SPATIALLY RESOLVED TRANSCRIPTOMIC DATA.","authors":"Andrea Sottosanti, Davide Risso","doi":"10.1214/22-aoas1677","DOIUrl":"10.1214/22-aoas1677","url":null,"abstract":"Spatial transcriptomics is a groundbreaking technology that allows the measurement of the activity of thousands of genes in a tissue sample and maps where the activity occurs. This technology has enabled the study of the spatial variation of the genes across the tissue. Comprehending gene functions and interactions in different areas of the tissue is of great scientific interest, as it might lead to a deeper understanding of several key biological mechanisms, such as cell-cell communication or tumor-microenvironment interaction. To do so, one can group cells of the same type and genes that exhibit similar expression patterns. However, adequate statistical tools that exploit the previously unavailable spatial information to more coherently group cells and genes are still lacking. In this work, we introduce SpaRTaCo, a new statistical model that clusters the spatial expression profiles of the genes according to a partition of the tissue. This is accomplished by performing a co-clustering, i.e., inferring the latent block structure of the data and inducing two types of clustering: of the genes, using their expression across the tissue, and of the image areas, using the gene expression in the spots where the RNA is collected. Our proposed methodology is validated with a series of simulation experiments and its usefulness in responding to specific biological questions is illustrated with an application to a human brain tissue sample processed with the 10X-Visium protocol.","PeriodicalId":50772,"journal":{"name":"Annals of Applied Statistics","volume":"17 2","pages":"1444-1468"},"PeriodicalIF":1.8,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10552783/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41163012","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

BAYESIAN ANALYSIS FOR IMBALANCED POSITIVE-UNLABELLED DIAGNOSIS CODES IN ELECTRONIC HEALTH RECORDS. 电子病历中不平衡阳性未标记诊断码的贝叶斯分析。

IF 1.8 4区数学

Annals of Applied Statistics Pub Date : 2023-06-01 DOI: 10.1214/22-AOAS1666

Ru Wang, Ye Liang, Zhuqi Miao, Tieming Liu

{"title":"BAYESIAN ANALYSIS FOR IMBALANCED POSITIVE-UNLABELLED DIAGNOSIS CODES IN ELECTRONIC HEALTH RECORDS.","authors":"Ru Wang, Ye Liang, Zhuqi Miao, Tieming Liu","doi":"10.1214/22-AOAS1666","DOIUrl":"https://doi.org/10.1214/22-AOAS1666","url":null,"abstract":"With the increasing availability of electronic health records (EHR), significant progress has been made on developing predictive inference and algorithms by health data analysts and researchers. However, the EHR data are notoriously noisy due to missing and inaccurate inputs despite the information is abundant. One serious problem is that only a small portion of patients in the database has confirmatory diagnoses while many other patients remain undiagnosed because they did not comply with the recommended examinations. The phenomenon leads to a so-called positive-unlabelled situation and the labels are extremely imbalanced. In this paper, we propose a model-based approach to classify the unlabelled patients by using a Bayesian finite mixture model. We also discuss the label switching issue for the imbalanced data and propose a consensus Monte Carlo approach to address the imbalance issue and improve computational efficiency simultaneously. Simulation studies show that our proposed model-based approach outperforms existing positive-unlabelled learning algorithms. The proposed method is applied on the Cerner EHR for detecting diabetic retinopathy (DR) patients using laboratory measurements. With only 3% confirmatory diagnoses in the EHR database, we estimate the actual DR prevalence to be 25% which coincides with reported findings in the medical literature.","PeriodicalId":50772,"journal":{"name":"Annals of Applied Statistics","volume":"17 2","pages":"1220-1238"},"PeriodicalIF":1.8,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10156089/pdf/nihms-1852796.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9563428","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Robust joint modelling of left-censored longitudinal data and survival data with application to HIV vaccine studies. 左删失纵向数据和生存数据的稳健联合建模，并将其应用于艾滋病疫苗研究。

IF 1.8 4区数学

Annals of Applied Statistics Pub Date : 2023-06-01 Epub Date: 2023-05-01 DOI: 10.1214/22-aoas1656

Tingting Yu, Lang Wu, Jin Qiu, Peter B Gilbert

引用次数: 0

DYNAMIC RISK PREDICTION TRIGGERED BY INTERMEDIATE EVENTS USING SURVIVAL TREE ENSEMBLES. 利用存活树集合对中间事件引发的动态风险进行预测。

IF 1.8 4区数学

Annals of Applied Statistics Pub Date : 2023-06-01 Epub Date: 2023-05-01 DOI: 10.1214/22-aoas1674

Yifei Sun, Sy Han Chiou, Colin O Wu, Meghan McGarry, Chiung-Yu Huang

{"title":"DYNAMIC RISK PREDICTION TRIGGERED BY INTERMEDIATE EVENTS USING SURVIVAL TREE ENSEMBLES.","authors":"Yifei Sun, Sy Han Chiou, Colin O Wu, Meghan McGarry, Chiung-Yu Huang","doi":"10.1214/22-aoas1674","DOIUrl":"10.1214/22-aoas1674","url":null,"abstract":"With the availability of massive amounts of data from electronic health records and registry databases, incorporating time-varying patient information to improve risk prediction has attracted great attention. To exploit the growing amount of predictor information over time, we develop a unified framework for landmark prediction using survival tree ensembles, where an updated prediction can be performed when new information becomes available. Compared to conventional landmark prediction with fixed landmark times, our methods allow the landmark times to be subject-specific and triggered by an intermediate clinical event. Moreover, the nonparametric approach circumvents the thorny issue of model incompatibility at different landmark times. In our framework, both the longitudinal predictors and the event time outcome are subject to right censoring, and thus existing tree-based approaches cannot be directly applied. To tackle the analytical challenges, we propose a risk-set-based ensemble procedure by averaging martingale estimating equations from individual trees. Extensive simulation studies are conducted to evaluate the performance of our methods. The methods are applied to the Cystic Fibrosis Foundation Patient Registry (CFFPR) data to perform dynamic prediction of lung disease in cystic fibrosis patients and to identify important prognosis factors.","PeriodicalId":50772,"journal":{"name":"Annals of Applied Statistics","volume":"17 2","pages":"1375-1397"},"PeriodicalIF":1.8,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10241448/pdf/nihms-1846847.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9974256","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

INDIVIDUALIZED RISK ASSESSMENT OF PREOPERATIVE OPIOID USE BY INTERPRETABLE NEURAL NETWORK REGRESSION. 可解释神经网络回归对术前阿片类药物使用的个体化风险评估。

IF 1.8 4区数学

Annals of Applied Statistics Pub Date : 2023-03-01 DOI: 10.1214/22-aoas1634

Yuming Sun, Jian Kang, Chad Brummett, Yi Li

{"title":"INDIVIDUALIZED RISK ASSESSMENT OF PREOPERATIVE OPIOID USE BY INTERPRETABLE NEURAL NETWORK REGRESSION.","authors":"Yuming Sun, Jian Kang, Chad Brummett, Yi Li","doi":"10.1214/22-aoas1634","DOIUrl":"https://doi.org/10.1214/22-aoas1634","url":null,"abstract":"Preoperative opioid use has been reported to be associated with higher preoperative opioid demand, worse postoperative outcomes, and increased postoperative healthcare utilization and expenditures. Understanding the risk of preoperative opioid use helps establish patient-centered pain management. In the field of machine learning, deep neural network (DNN) has emerged as a powerful means for risk assessment because of its superb prediction power; however, the blackbox algorithms may make the results less interpretable than statistical models. Bridging the gap between the statistical and machine learning fields, we propose a novel Interpretable Neural Network Regression (INNER), which combines the strengths of statistical and DNN models. We use the proposed INNER to conduct individualized risk assessment of preoperative opioid use. Intensive simulations and an analysis of 34,186 patients expecting surgery in the Analgesic Outcomes Study (AOS) show that the proposed INNER not only can accurately predict the preoperative opioid use using preoperative characteristics as DNN, but also can estimate the patient-specific odds of opioid use without pain and the odds ratio of opioid use for a unit increase in the reported overall body pain, leading to more straight-forward interpretations of the tendency to use opioids than DNN. Our results identify the patient characteristics that are strongly associated with opioid use and is largely consistent with the previous findings, providing evidence that INNER is a useful tool for individualized risk assessment of preoperative opioid use.","PeriodicalId":50772,"journal":{"name":"Annals of Applied Statistics","volume":"17 1","pages":"434-453"},"PeriodicalIF":1.8,"publicationDate":"2023-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10065608/pdf/nihms-1836641.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9282926","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0