Statistical Applications in Genetics and Molecular Biology最新文献

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False discovery control for penalized variable selections with high-dimensional covariates. 具有高维协变量的惩罚性变量选择的错误发现控制。
IF 0.9 4区 数学
Statistical Applications in Genetics and Molecular Biology Pub Date : 2018-12-15 DOI: 10.1515/sagmb-2018-0038
Kevin He, Xiang Zhou, Hui Jiang, Xiaoquan Wen, Yi Li
{"title":"False discovery control for penalized variable selections with high-dimensional covariates.","authors":"Kevin He, Xiang Zhou, Hui Jiang, Xiaoquan Wen, Yi Li","doi":"10.1515/sagmb-2018-0038","DOIUrl":"10.1515/sagmb-2018-0038","url":null,"abstract":"<p><p>Modern bio-technologies have produced a vast amount of high-throughput data with the number of predictors much exceeding the sample size. Penalized variable selection has emerged as a powerful and efficient dimension reduction tool. However, control of false discoveries (i.e. inclusion of irrelevant variables) for penalized high-dimensional variable selection presents serious challenges. To effectively control the fraction of false discoveries for penalized variable selections, we propose a false discovery controlling procedure. The proposed method is general and flexible, and can work with a broad class of variable selection algorithms, not only for linear regressions, but also for generalized linear models and survival analysis.</p>","PeriodicalId":49477,"journal":{"name":"Statistical Applications in Genetics and Molecular Biology","volume":"17 6","pages":""},"PeriodicalIF":0.9,"publicationDate":"2018-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6450074/pdf/nihms-1015624.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"37050068","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
A practical approach to adjusting for population stratification in genome-wide association studies: principal components and propensity scores (PCAPS). 在全基因组关联研究中调整人群分层的实用方法:主成分和倾向分数 (PCAPS)。
IF 0.9 4区 数学
Statistical Applications in Genetics and Molecular Biology Pub Date : 2018-12-04 DOI: 10.1515/sagmb-2017-0054
Huaqing Zhao, Nandita Mitra, Peter A Kanetsky, Katherine L Nathanson, Timothy R Rebbeck
{"title":"A practical approach to adjusting for population stratification in genome-wide association studies: principal components and propensity scores (PCAPS).","authors":"Huaqing Zhao, Nandita Mitra, Peter A Kanetsky, Katherine L Nathanson, Timothy R Rebbeck","doi":"10.1515/sagmb-2017-0054","DOIUrl":"10.1515/sagmb-2017-0054","url":null,"abstract":"<p><p>Genome-wide association studies (GWAS) are susceptible to bias due to population stratification (PS). The most widely used method to correct bias due to PS is principal components (PCs) analysis (PCA), but there is no objective method to guide which PCs to include as covariates. Often, the ten PCs with the highest eigenvalues are included to adjust for PS. This selection is arbitrary, and patterns of local linkage disequilibrium may affect PCA corrections. To address these limitations, we estimate genomic propensity scores based on all statistically significant PCs selected by the Tracy-Widom (TW) statistic. We compare a principal components and propensity scores (PCAPS) approach to PCA and EMMAX using simulated GWAS data under no, moderate, and severe PS. PCAPS reduced spurious genetic associations regardless of the degree of PS, resulting in odds ratio (OR) estimates closer to the true OR. We illustrate our PCAPS method using GWAS data from a study of testicular germ cell tumors. PCAPS provided a more conservative adjustment than PCA. Advantages of the PCAPS approach include reduction of bias compared to PCA, consistent selection of propensity scores to adjust for PS, the potential ability to handle outliers, and ease of implementation using existing software packages.</p>","PeriodicalId":49477,"journal":{"name":"Statistical Applications in Genetics and Molecular Biology","volume":"17 6","pages":""},"PeriodicalIF":0.9,"publicationDate":"2018-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6475581/pdf/nihms-1022442.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36745351","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
A novel method to accurately calculate statistical significance of local similarity analysis for high-throughput time series. 一种精确计算高通量时间序列局部相似度统计显著性的新方法。
IF 0.9 4区 数学
Statistical Applications in Genetics and Molecular Biology Pub Date : 2018-11-17 DOI: 10.1515/sagmb-2018-0019
Fang Zhang, Ang Shan, Yihui Luan
{"title":"A novel method to accurately calculate statistical significance of local similarity analysis for high-throughput time series.","authors":"Fang Zhang,&nbsp;Ang Shan,&nbsp;Yihui Luan","doi":"10.1515/sagmb-2018-0019","DOIUrl":"https://doi.org/10.1515/sagmb-2018-0019","url":null,"abstract":"<p><p>In recent years, a large number of time series microbial community data has been produced in molecular biological studies, especially in metagenomics. Among the statistical methods for time series, local similarity analysis is used in a wide range of environments to capture potential local and time-shifted associations that cannot be distinguished by traditional correlation analysis. Initially, the permutation test is popularly applied to obtain the statistical significance of local similarity analysis. More recently, a theoretical method has also been developed to achieve this aim. However, all these methods require the assumption that the time series are independent and identically distributed. In this paper, we propose a new approach based on moving block bootstrap to approximate the statistical significance of local similarity scores for dependent time series. Simulations show that our method can control the type I error rate reasonably, while theoretical approximation and the permutation test perform less well. Finally, our method is applied to human and marine microbial community datasets, indicating that it can identify potential relationship among operational taxonomic units (OTUs) and significantly decrease the rate of false positives.</p>","PeriodicalId":49477,"journal":{"name":"Statistical Applications in Genetics and Molecular Biology","volume":"17 6","pages":""},"PeriodicalIF":0.9,"publicationDate":"2018-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/sagmb-2018-0019","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36739757","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Determining the number of components in PLS regression on incomplete data set 不完全数据集PLS回归中分量数量的确定
IF 0.9 4区 数学
Statistical Applications in Genetics and Molecular Biology Pub Date : 2018-10-18 DOI: 10.1515/sagmb-2018-0059
T. Nengsih, F. Bertrand, M. Maumy-Bertrand, Nicolas Meyer
{"title":"Determining the number of components in PLS regression on incomplete data set","authors":"T. Nengsih, F. Bertrand, M. Maumy-Bertrand, Nicolas Meyer","doi":"10.1515/sagmb-2018-0059","DOIUrl":"https://doi.org/10.1515/sagmb-2018-0059","url":null,"abstract":"Abstract Partial least squares regression – or PLS regression – is a multivariate method in which the model parameters are estimated using either the SIMPLS or NIPALS algorithm. PLS regression has been extensively used in applied research because of its effectiveness in analyzing relationships between an outcome and one or several components. Note that the NIPALS algorithm can provide estimates parameters on incomplete data. The selection of the number of components used to build a representative model in PLS regression is a central issue. However, how to deal with missing data when using PLS regression remains a matter of debate. Several approaches have been proposed in the literature, including the Q2 criterion, and the AIC and BIC criteria. Here we study the behavior of the NIPALS algorithm when used to fit a PLS regression for various proportions of missing data and different types of missingness. We compare criteria to select the number of components for a PLS regression on incomplete data set and on imputed data set using three imputation methods: multiple imputation by chained equations, k-nearest neighbour imputation, and singular value decomposition imputation. We tested various criteria with different proportions of missing data (ranging from 5% to 50%) under different missingness assumptions. Q2-leave-one-out component selection methods gave more reliable results than AIC and BIC-based ones.","PeriodicalId":49477,"journal":{"name":"Statistical Applications in Genetics and Molecular Biology","volume":"18 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2018-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/sagmb-2018-0059","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46367347","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 24
EBADIMEX: an empirical Bayes approach to detect joint differential expression and methylation and to classify samples EBADIMEX:一种检测联合差异表达和甲基化并对样本进行分类的经验贝叶斯方法
IF 0.9 4区 数学
Statistical Applications in Genetics and Molecular Biology Pub Date : 2018-08-28 DOI: 10.1101/401232
Tobias Madsen, Michal P. Switnicki, Malene Juul, J. S. Pedersen
{"title":"EBADIMEX: an empirical Bayes approach to detect joint differential expression and methylation and to classify samples","authors":"Tobias Madsen, Michal P. Switnicki, Malene Juul, J. S. Pedersen","doi":"10.1101/401232","DOIUrl":"https://doi.org/10.1101/401232","url":null,"abstract":"Abstract DNA methylation and gene expression are interdependent and both implicated in cancer development and progression, with many individual biomarkers discovered. A joint analysis of the two data types can potentially lead to biological insights that are not discoverable with separate analyses. To optimally leverage the joint data for identifying perturbed genes and classifying clinical cancer samples, it is important to accurately model the interactions between the two data types. Here, we present EBADIMEX for jointly identifying differential expression and methylation and classifying samples. The moderated t-test widely used with empirical Bayes priors in current differential expression methods is generalised to a multivariate setting by developing: (1) a moderated Welch t-test for equality of means with unequal variances; (2) a moderated F-test for equality of variances; and (3) a multivariate test for equality of means with equal variances. This leads to parametric models with prior distributions for the parameters, which allow fast evaluation and robust analysis of small data sets. EBADIMEX is demonstrated on simulated data as well as a large breast cancer (BRCA) cohort from TCGA. We show that the use of empirical Bayes priors and moderated tests works particularly well on small data sets.","PeriodicalId":49477,"journal":{"name":"Statistical Applications in Genetics and Molecular Biology","volume":" ","pages":""},"PeriodicalIF":0.9,"publicationDate":"2018-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47425887","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Noise-robust assessment of SNP array based CNV calls through local noise estimation of log R ratios. 通过对数R比的局部噪声估计,对基于SNP阵列的CNV调用进行噪声鲁棒性评估。
IF 0.9 4区 数学
Statistical Applications in Genetics and Molecular Biology Pub Date : 2018-04-28 DOI: 10.1515/sagmb-2017-0026
Nele Cosemans, Peter Claes, Nathalie Brison, Joris Robert Vermeesch, Hilde Peeters
{"title":"Noise-robust assessment of SNP array based CNV calls through local noise estimation of log R ratios.","authors":"Nele Cosemans,&nbsp;Peter Claes,&nbsp;Nathalie Brison,&nbsp;Joris Robert Vermeesch,&nbsp;Hilde Peeters","doi":"10.1515/sagmb-2017-0026","DOIUrl":"https://doi.org/10.1515/sagmb-2017-0026","url":null,"abstract":"<p><p>Arrays based on single nucleotide polymorphisms (SNPs) have been successful for the large scale discovery of copy number variants (CNVs). However, current CNV calling algorithms still have limitations in detecting CNVs with high specificity and sensitivity, especially in case of small (<100 kb) CNVs. Therefore, this study presents a simple statistical analysis to evaluate CNV calls from SNP arrays in order to improve the noise-robustness of existing CNV calling algorithms. The proposed approach estimates local noise of log R ratios and returns the probability that a certain observation is different from this log R ratio noise level. This probability can be triggered at different thresholds to tailor specificity and/or sensitivity in a flexible way. Moreover, a comparison based on qPCR experiments showed that the proposed noise-robust CNV calls outperformed original ones for multiple threshold values.</p>","PeriodicalId":49477,"journal":{"name":"Statistical Applications in Genetics and Molecular Biology","volume":"17 2","pages":""},"PeriodicalIF":0.9,"publicationDate":"2018-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/sagmb-2017-0026","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"36054869","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On "A mutual information estimator with exponentially decaying bias" by Zhang and Zheng. 关于张和郑的“具有指数衰减偏差的互信息估计量”。
IF 0.9 4区 数学
Statistical Applications in Genetics and Molecular Biology Pub Date : 2018-03-30 DOI: 10.1515/sagmb-2018-0005
Jialin Zhang, Chen Chen
{"title":"On \"A mutual information estimator with exponentially decaying bias\" by Zhang and Zheng.","authors":"Jialin Zhang,&nbsp;Chen Chen","doi":"10.1515/sagmb-2018-0005","DOIUrl":"https://doi.org/10.1515/sagmb-2018-0005","url":null,"abstract":"<p><p>Zhang, Z. and Zheng, L. (2015): \"A mutual information estimator with exponentially decaying bias,\" Stat. Appl. Genet. Mol. Biol., 14, 243-252, proposed a nonparametric estimator of mutual information developed in entropic perspective, and demonstrated that it has much smaller bias than the plugin estimator yet with the same asymptotic normality under certain conditions. However it is incorrectly suggested in their article that the asymptotic normality could be used for testing independence between two random elements on a joint alphabet. When two random elements are independent, the asymptotic distribution of $sqrt{n}$n-normed estimator degenerates and therefore the claimed normality does not hold. This article complements Zhang and Zheng by establishing a new chi-square test using the same entropic statistics for mutual information being zero. The three examples in Zhang and Zheng are re-worked using the new test. The results turn out to be much more sensible and further illustrate the advantage of the entropic perspective in statistical inference on alphabets. More specifically in Example 2, when a positive mutual information is known to exist, the new test detects it but the log likelihood ratio test fails to do so.</p>","PeriodicalId":49477,"journal":{"name":"Statistical Applications in Genetics and Molecular Biology","volume":"17 2","pages":""},"PeriodicalIF":0.9,"publicationDate":"2018-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/sagmb-2018-0005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"35962346","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Ensemble survival tree models to reveal pairwise interactions of variables with time-to-events outcomes in low-dimensional setting. 集合生存树模型揭示了低维环境中变量与时间到事件结果的成对相互作用。
IF 0.9 4区 数学
Statistical Applications in Genetics and Molecular Biology Pub Date : 2018-02-17 DOI: 10.1515/sagmb-2017-0038
Jean-Eudes Dazard, Hemant Ishwaran, Rajeev Mehlotra, Aaron Weinberg, Peter Zimmerman
{"title":"Ensemble survival tree models to reveal pairwise interactions of variables with time-to-events outcomes in low-dimensional setting.","authors":"Jean-Eudes Dazard,&nbsp;Hemant Ishwaran,&nbsp;Rajeev Mehlotra,&nbsp;Aaron Weinberg,&nbsp;Peter Zimmerman","doi":"10.1515/sagmb-2017-0038","DOIUrl":"https://doi.org/10.1515/sagmb-2017-0038","url":null,"abstract":"<p><p>Unraveling interactions among variables such as genetic, clinical, demographic and environmental factors is essential to understand the development of common and complex diseases. To increase the power to detect such variables interactions associated with clinical time-to-events outcomes, we borrowed established concepts from random survival forest (RSF) models. We introduce a novel RSF-based pairwise interaction estimator and derive a randomization method with bootstrap confidence intervals for inferring interaction significance. Using various linear and nonlinear time-to-events survival models in simulation studies, we first show the efficiency of our approach: true pairwise interaction-effects between variables are uncovered, while they may not be accompanied with their corresponding main-effects, and may not be detected by standard semi-parametric regression modeling and test statistics used in survival analysis. Moreover, using a RSF-based cross-validation scheme for generating prediction estimators, we show that informative predictors may be inferred. We applied our approach to an HIV cohort study recording key host gene polymorphisms and their association with HIV change of tropism or AIDS progression. Altogether, this shows how linear or nonlinear pairwise statistical interactions of variables may be efficiently detected with a predictive value in observational studies with time-to-event outcomes.</p>","PeriodicalId":49477,"journal":{"name":"Statistical Applications in Genetics and Molecular Biology","volume":"17 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2018-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/sagmb-2017-0038","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"35840212","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: 2
Additive varying-coefficient model for nonlinear gene-environment interactions. 非线性基因-环境相互作用的加性变系数模型。
IF 0.9 4区 数学
Statistical Applications in Genetics and Molecular Biology Pub Date : 2018-02-08 DOI: 10.1515/sagmb-2017-0008
Cen Wu, Ping-Shou Zhong, Yuehua Cui
{"title":"Additive varying-coefficient model for nonlinear gene-environment interactions.","authors":"Cen Wu,&nbsp;Ping-Shou Zhong,&nbsp;Yuehua Cui","doi":"10.1515/sagmb-2017-0008","DOIUrl":"https://doi.org/10.1515/sagmb-2017-0008","url":null,"abstract":"<p><p>Gene-environment (G×E) interaction plays a pivotal role in understanding the genetic basis of complex disease. When environmental factors are measured continuously, one can assess the genetic sensitivity over different environmental conditions on a disease trait. Motivated by the increasing awareness of gene set based association analysis over single variant based approaches, we proposed an additive varying-coefficient model to jointly model variants in a genetic system. The model allows us to examine how variants in a gene set are moderated by an environment factor to affect a disease phenotype. We approached the problem from a variable selection perspective. In particular, we select variants with varying, constant and zero coefficients, which correspond to cases of G×E interaction, no G×E interaction and no genetic effect, respectively. The procedure was implemented through a two-stage iterative estimation algorithm via the smoothly clipped absolute deviation penalty function. Under certain regularity conditions, we established the consistency property in variable selection as well as effect separation of the two stage iterative estimators, and showed the optimal convergence rates of the estimates for varying effects. In addition, we showed that the estimate of non-zero constant coefficients enjoy the oracle property. The utility of our procedure was demonstrated through simulation studies and real data analysis.</p>","PeriodicalId":49477,"journal":{"name":"Statistical Applications in Genetics and Molecular Biology","volume":"17 2","pages":""},"PeriodicalIF":0.9,"publicationDate":"2018-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/sagmb-2017-0008","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"35810903","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 21
Distance-correlation based gene set analysis in longitudinal studies. 纵向研究中基于距离相关的基因集分析。
IF 0.9 4区 数学
Statistical Applications in Genetics and Molecular Biology Pub Date : 2018-02-05 DOI: 10.1515/sagmb-2017-0053
Jiehuan Sun, Jose D Herazo-Maya, Xiu Huang, Naftali Kaminski, Hongyu Zhao
{"title":"Distance-correlation based gene set analysis in longitudinal studies.","authors":"Jiehuan Sun,&nbsp;Jose D Herazo-Maya,&nbsp;Xiu Huang,&nbsp;Naftali Kaminski,&nbsp;Hongyu Zhao","doi":"10.1515/sagmb-2017-0053","DOIUrl":"https://doi.org/10.1515/sagmb-2017-0053","url":null,"abstract":"<p><p>Longitudinal gene expression profiles of subjects are collected in some clinical studies to monitor disease progression and understand disease etiology. The identification of gene sets that have coordinated changes with relevant clinical outcomes over time from these data could provide significant insights into the molecular basis of disease progression and lead to better treatments. In this article, we propose a Distance-Correlation based Gene Set Analysis (dcGSA) method for longitudinal gene expression data. dcGSA is a non-parametric approach, statistically robust, and can capture both linear and nonlinear relationships between gene sets and clinical outcomes. In addition, dcGSA is able to identify related gene sets in cases where the effects of gene sets on clinical outcomes differ across subjects due to the subject heterogeneity, remove the confounding effects of some unobserved time-invariant covariates, and allow the assessment of associations between gene sets and multiple related outcomes simultaneously. Through extensive simulation studies, we demonstrate that dcGSA is more powerful of detecting relevant genes than other commonly used gene set analysis methods. When dcGSA is applied to a real dataset on systemic lupus erythematosus, we are able to identify more disease related gene sets than other methods.</p>","PeriodicalId":49477,"journal":{"name":"Statistical Applications in Genetics and Molecular Biology","volume":"17 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2018-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/sagmb-2017-0053","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"35791378","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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