Henrik Wiechers, Benjamin Eltzner, Kanti V Mardia, Stephan F Huckemann
Abstract Three-dimensional RNA structures frequently contain atomic clashes. Usually, corrections approximate the biophysical chemistry, which is computationally intensive and often does not correct all clashes. We propose fast, data-driven reconstructions from clash-free benchmark data with two-scale shape analysis: microscopic (suites) dihedral backbone angles, mesoscopic sugar ring centre landmarks. Our analysis relates concentrated mesoscopic scale neighbourhoods to microscopic scale clusters, correcting within-suite-backbone-to-backbone clashes exploiting angular shape and size-and-shape Fréchet means. Validation shows that learned classes highly correspond with literature clusters and reconstructions are well within physical resolution. We illustrate the power of our method using cutting-edge SARS-CoV-2 RNA.
{"title":"Learning torus PCA-based classification for multiscale RNA correction with application to SARS-CoV-2","authors":"Henrik Wiechers, Benjamin Eltzner, Kanti V Mardia, Stephan F Huckemann","doi":"10.1093/jrsssc/qlad004","DOIUrl":"https://doi.org/10.1093/jrsssc/qlad004","url":null,"abstract":"Abstract Three-dimensional RNA structures frequently contain atomic clashes. Usually, corrections approximate the biophysical chemistry, which is computationally intensive and often does not correct all clashes. We propose fast, data-driven reconstructions from clash-free benchmark data with two-scale shape analysis: microscopic (suites) dihedral backbone angles, mesoscopic sugar ring centre landmarks. Our analysis relates concentrated mesoscopic scale neighbourhoods to microscopic scale clusters, correcting within-suite-backbone-to-backbone clashes exploiting angular shape and size-and-shape Fréchet means. Validation shows that learned classes highly correspond with literature clusters and reconstructions are well within physical resolution. We illustrate the power of our method using cutting-edge SARS-CoV-2 RNA.","PeriodicalId":49981,"journal":{"name":"Journal of the Royal Statistical Society Series C-Applied Statistics","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136091430","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}
Stochastic models are appealing for mortality forecasting in their ability to generate intervals that quantify uncertainties underlying the forecasts. We present a fully Bayesian implementation of the age-period-cohort-improvement (APCI) model with overdispersion, which is compared with the Lee–Carter model with cohorts. We show that naive prior specification can yield misleading inferences, where we propose Laplace prior as an elegant solution. We also perform model averaging to incorporate model uncertainty. Our findings indicate that the APCI model offers better fit and forecast for England and Wales data spanning 1961–2002. Our approach also allows coherent inclusion of multiple sources of uncertainty, producing well-calibrated probabilistic intervals.
{"title":"Bayesian model comparison for mortality forecasting","authors":"Jackie S. T. Wong, J. Forster, Peter W. F. Smith","doi":"10.1093/jrsssc/qlad021","DOIUrl":"https://doi.org/10.1093/jrsssc/qlad021","url":null,"abstract":"\u0000 Stochastic models are appealing for mortality forecasting in their ability to generate intervals that quantify uncertainties underlying the forecasts. We present a fully Bayesian implementation of the age-period-cohort-improvement (APCI) model with overdispersion, which is compared with the Lee–Carter model with cohorts. We show that naive prior specification can yield misleading inferences, where we propose Laplace prior as an elegant solution. We also perform model averaging to incorporate model uncertainty. Our findings indicate that the APCI model offers better fit and forecast for England and Wales data spanning 1961–2002. Our approach also allows coherent inclusion of multiple sources of uncertainty, producing well-calibrated probabilistic intervals.","PeriodicalId":49981,"journal":{"name":"Journal of the Royal Statistical Society Series C-Applied Statistics","volume":"46 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88234572","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}
High-resolution circumference dendrometers measure the irreversible growth and the reversible shrinking and swelling due to the water content of a tree stem. We propose a novel statistical method to decompose these measurements into a permanent and a temporary component, while explaining differences between the trees and years by covariates. Our model embeds Gaussian processes with parametric mean and covariance functions as response structures in a distributional regression framework with structured additive predictors. We discuss different mean and covariance functions, connections with other model classes, Markov chain Monte Carlo inference, and the efficiency of our sampling scheme.
{"title":"Modelling intra-annual tree stem growth with a distributional regression approach for Gaussian process responses","authors":"Hannes Riebl, N. Klein, T. Kneib","doi":"10.1093/jrsssc/qlad015","DOIUrl":"https://doi.org/10.1093/jrsssc/qlad015","url":null,"abstract":"\u0000 High-resolution circumference dendrometers measure the irreversible growth and the reversible shrinking and swelling due to the water content of a tree stem. We propose a novel statistical method to decompose these measurements into a permanent and a temporary component, while explaining differences between the trees and years by covariates. Our model embeds Gaussian processes with parametric mean and covariance functions as response structures in a distributional regression framework with structured additive predictors. We discuss different mean and covariance functions, connections with other model classes, Markov chain Monte Carlo inference, and the efficiency of our sampling scheme.","PeriodicalId":49981,"journal":{"name":"Journal of the Royal Statistical Society Series C-Applied Statistics","volume":"26 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84823517","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}
Existing integer-valued generalised autoregressive conditional heteroskedasticity (INGARCH) models for spatio-temporal counts do not allow for negative parameter and autocorrelation values. Using approximately linear INGARCH models, the unified and flexible spatio-temporal (B)INGARCH framework for modelling unbounded (bounded) counts is proposed. These models combine negative dependencies with kinds of a long memory. They are easily adapted to special marginal features or cross-dependencies: When modelling precipitation data (counts of rainy hours), we account for zero-inflation, while for cloud-coverage data (counts of okta), we deal with missing data and additional cross-correlation. A copula related to the spatial error model shows an appealing performance.
{"title":"Approximately linear INGARCH models for spatio-temporal counts","authors":"Malte Jahn, C. Weiß, Hee-Young Kim","doi":"10.1093/jrsssc/qlad018","DOIUrl":"https://doi.org/10.1093/jrsssc/qlad018","url":null,"abstract":"\u0000 Existing integer-valued generalised autoregressive conditional heteroskedasticity (INGARCH) models for spatio-temporal counts do not allow for negative parameter and autocorrelation values. Using approximately linear INGARCH models, the unified and flexible spatio-temporal (B)INGARCH framework for modelling unbounded (bounded) counts is proposed. These models combine negative dependencies with kinds of a long memory. They are easily adapted to special marginal features or cross-dependencies: When modelling precipitation data (counts of rainy hours), we account for zero-inflation, while for cloud-coverage data (counts of okta), we deal with missing data and additional cross-correlation. A copula related to the spatial error model shows an appealing performance.","PeriodicalId":49981,"journal":{"name":"Journal of the Royal Statistical Society Series C-Applied Statistics","volume":"126 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80040119","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}
Pub Date : 2023-03-15eCollection Date: 2023-05-01DOI: 10.1093/jrsssc/qlac005
Bora Jin, David B Dunson, Julia E Rager, David M Reif, Stephanie M Engel, Amy H Herring
We aim to infer bioactivity of each chemical by assay endpoint combination, addressing sparsity of toxicology data. We propose a Bayesian hierarchical framework which borrows information across different chemicals and assay endpoints, facilitates out-of-sample prediction of activity for chemicals not yet assayed, quantifies uncertainty of predicted activity, and adjusts for multiplicity in hypothesis testing. Furthermore, this paper makes a novel attempt in toxicology to simultaneously model heteroscedastic errors and a nonparametric mean function, leading to a broader definition of activity whose need has been suggested by toxicologists. Real application identifies chemicals most likely active for neurodevelopmental disorders and obesity.
{"title":"Bayesian matrix completion for hypothesis testing.","authors":"Bora Jin, David B Dunson, Julia E Rager, David M Reif, Stephanie M Engel, Amy H Herring","doi":"10.1093/jrsssc/qlac005","DOIUrl":"10.1093/jrsssc/qlac005","url":null,"abstract":"<p><p>We aim to infer bioactivity of each chemical by assay endpoint combination, addressing sparsity of toxicology data. We propose a Bayesian hierarchical framework which borrows information across different chemicals and assay endpoints, facilitates out-of-sample prediction of activity for chemicals not yet assayed, quantifies uncertainty of predicted activity, and adjusts for multiplicity in hypothesis testing. Furthermore, this paper makes a novel attempt in toxicology to simultaneously model heteroscedastic errors and a nonparametric mean function, leading to a broader definition of activity whose need has been suggested by toxicologists. Real application identifies chemicals most likely active for neurodevelopmental disorders and obesity.</p>","PeriodicalId":49981,"journal":{"name":"Journal of the Royal Statistical Society Series C-Applied Statistics","volume":"72 2","pages":"254-270"},"PeriodicalIF":1.0,"publicationDate":"2023-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10184491/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9480094","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}
Designs for screening experiments usually include factors with two levels only. Adding a few four-level factors allows for the inclusion of multi-level categorical factors or quantitative factors with possible quadratic or third-order effects. Three examples motivated us to generate a large catalogue of designs with two-level factors as well as four-level factors. To create the catalogue, we considered three methods. In the first method, we select designs using a search table, and in the second method, we use a procedure that selects candidate designs based on the properties of their projections into fewer factors. The third method is actually a benchmark method, in which we use a general orthogonal array enumeration algorithm. We compare the efficiencies of the new methods for generating complete sets of nonisomorphic designs. Finally, we use the most efficient method to generate a catalogue of designs with up to three four-level factors and up to 20 two-level factors for run sizes 16, 32, 64, and 128. In some cases, a complete enumeration was infeasible. For these cases, we used a bounded enumeration strategy instead. We demonstrate the usefulness of the catalogue by revisiting the motivating examples.
{"title":"Enumeration of regular fractional factorial designs with four-level and two-level factors","authors":"Alexandre Bohyn, E. Schoen, P. Goos","doi":"10.1093/jrsssc/qlad031","DOIUrl":"https://doi.org/10.1093/jrsssc/qlad031","url":null,"abstract":"\u0000 Designs for screening experiments usually include factors with two levels only. Adding a few four-level factors allows for the inclusion of multi-level categorical factors or quantitative factors with possible quadratic or third-order effects. Three examples motivated us to generate a large catalogue of designs with two-level factors as well as four-level factors. To create the catalogue, we considered three methods. In the first method, we select designs using a search table, and in the second method, we use a procedure that selects candidate designs based on the properties of their projections into fewer factors. The third method is actually a benchmark method, in which we use a general orthogonal array enumeration algorithm. We compare the efficiencies of the new methods for generating complete sets of nonisomorphic designs. Finally, we use the most efficient method to generate a catalogue of designs with up to three four-level factors and up to 20 two-level factors for run sizes 16, 32, 64, and 128. In some cases, a complete enumeration was infeasible. For these cases, we used a bounded enumeration strategy instead. We demonstrate the usefulness of the catalogue by revisiting the motivating examples.","PeriodicalId":49981,"journal":{"name":"Journal of the Royal Statistical Society Series C-Applied Statistics","volume":"45 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90815208","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}
This paper develops a spatial Durbin stochastic frontier model for panel data introducing spillover effects in the determinants of technical efficiency (SDF-STE). The model nests several existing spatial and non-spatial stochastic frontier specifications and is estimated using maximum-likelihood techniques. Estimates are shown to be unbiased even for small sample sizes and for alternative specifications of the spatial weight matrix implementing different Monte Carlo simulations. Finally, an application to the Italian accommodation sector is provided. Empirical findings suggest the relevance of the SDF-STE model in capturing labour productivity and knowledge spillover effects.
{"title":"A spatial stochastic frontier model introducing inefficiency spillovers","authors":"Federica Galli","doi":"10.1093/jrsssc/qlad012","DOIUrl":"https://doi.org/10.1093/jrsssc/qlad012","url":null,"abstract":"\u0000 This paper develops a spatial Durbin stochastic frontier model for panel data introducing spillover effects in the determinants of technical efficiency (SDF-STE). The model nests several existing spatial and non-spatial stochastic frontier specifications and is estimated using maximum-likelihood techniques. Estimates are shown to be unbiased even for small sample sizes and for alternative specifications of the spatial weight matrix implementing different Monte Carlo simulations. Finally, an application to the Italian accommodation sector is provided. Empirical findings suggest the relevance of the SDF-STE model in capturing labour productivity and knowledge spillover effects.","PeriodicalId":49981,"journal":{"name":"Journal of the Royal Statistical Society Series C-Applied Statistics","volume":"18 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81544168","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}
K. Brumberg, Darcy E. Ellis, D. Small, S. Hennessy, P. Rosenbaum
Fluoroquinolones are widely prescribed antibiotics that carry a US Food and Drug Administration warning about possible side-effects on the central and peripheral nervous system. We compare 436,891 patients with sinusitis treated with fluoroquinolones to two control groups treated with azithromycin or amoxicillin. In addition to looking for nervous system complications, we look for evidence of bias using outcomes for which an effect was not anticipated. The comparison uses ‘natural strata’ that form control groups proportional in size to the treated group and balance many covariates beyond those that define the strata. The main technical contribution is a new method for near-optimal construction of natural strata with multiple groups. The online supplement material contains proofs, details, and information about the R package natstrat and replication.
{"title":"Using natural strata when examining unmeasured biases in an observational study of neurological side effects of antibiotics","authors":"K. Brumberg, Darcy E. Ellis, D. Small, S. Hennessy, P. Rosenbaum","doi":"10.1093/jrsssc/qlad010","DOIUrl":"https://doi.org/10.1093/jrsssc/qlad010","url":null,"abstract":"\u0000 Fluoroquinolones are widely prescribed antibiotics that carry a US Food and Drug Administration warning about possible side-effects on the central and peripheral nervous system. We compare 436,891 patients with sinusitis treated with fluoroquinolones to two control groups treated with azithromycin or amoxicillin. In addition to looking for nervous system complications, we look for evidence of bias using outcomes for which an effect was not anticipated. The comparison uses ‘natural strata’ that form control groups proportional in size to the treated group and balance many covariates beyond those that define the strata. The main technical contribution is a new method for near-optimal construction of natural strata with multiple groups. The online supplement material contains proofs, details, and information about the R package natstrat and replication.","PeriodicalId":49981,"journal":{"name":"Journal of the Royal Statistical Society Series C-Applied Statistics","volume":"1 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84822538","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}
Statistical extreme value models allow estimation of the frequency, magnitude and spatio-temporal extent of extreme temperature events in the presence of climate change. Unfortunately, the assumptions of many standard methods are not valid for complex environmental data sets, with a realistic statistical model requiring appropriate incorporation of scientific context. We examine two case studies in which the application of routine extreme value methods result in inappropriate models and inaccurate predictions. In the first scenario, record-breaking temperatures experienced in the US in the summer of 2021 are found to exceed the maximum feasible temperature predicted from a standard extreme value analysis of pre-2021 data. Incorporating random effects into the standard methods accounts for additional variability in the model parameters, reflecting shifts in unobserved climatic drivers and permitting greater accuracy in return period prediction. The second scenario examines ice surface temperatures in Greenland. The temperature distribution is found to have a poorly-defined upper tail, with a spike in observations just below 0◦C and an unexpectedly large number of measurements above this value. A Gaussian mixture model fit to the full range of measurements improves fit and predictive abilities in the upper tail when compared to traditional extreme value methods.
{"title":"The importance of context in extreme value analysis with application to extreme temperatures in the USA and Greenland","authors":"D. Clarkson, E. Eastoe, A. Leeson","doi":"10.1093/jrsssc/qlad020","DOIUrl":"https://doi.org/10.1093/jrsssc/qlad020","url":null,"abstract":"\u0000 Statistical extreme value models allow estimation of the frequency, magnitude and spatio-temporal extent of extreme temperature events in the presence of climate change. Unfortunately, the assumptions of many standard methods are not valid for complex environmental data sets, with a realistic statistical model requiring appropriate incorporation of scientific context. We examine two case studies in which the application of routine extreme value methods result in inappropriate models and inaccurate predictions. In the first scenario, record-breaking temperatures experienced in the US in the summer of 2021 are found to exceed the maximum feasible temperature predicted from a standard extreme value analysis of pre-2021 data. Incorporating random effects into the standard methods accounts for additional variability in the model parameters, reflecting shifts in unobserved climatic drivers and permitting greater accuracy in return period prediction. The second scenario examines ice surface temperatures in Greenland. The temperature distribution is found to have a poorly-defined upper tail, with a spike in observations just below 0◦C and an unexpectedly large number of measurements above this value. A Gaussian mixture model fit to the full range of measurements improves fit and predictive abilities in the upper tail when compared to traditional extreme value methods.","PeriodicalId":49981,"journal":{"name":"Journal of the Royal Statistical Society Series C-Applied Statistics","volume":"32 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87796961","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}
Yang Han, Yujia Sun, Lingjiao Wang, Wei Liu, F. Bretz
Statistical calibration using regression is a useful statistical tool with many applications. For confidence sets for x-values associated with infinitely many future y-values, there is a consensus in the statistical literature that the confidence sets constructed should guarantee a key property. While it is well known that the confidence sets based on the simultaneous tolerance intervals (STIs) guarantee this key property conservatively, it is desirable to construct confidence sets that satisfy this property exactly. Also, there is a misconception that the confidence sets based on the pointwise tolerance intervals (PTIs) also guarantee this property. This paper constructs the weighted simultaneous tolerance intervals (WSTIs) so that the confidence sets based on the WSTIs satisfy this property exactly if the future observations have the x-values distributed according to a known specific distribution F(⋅). Through the lens of the WSTIs, convincing counter examples are also provided to demonstrate that the confidence sets based on the PTIs do not guarantee the key property in general and so should not be used. The WSTIs have been applied to real data examples to show that the WSTIs can produce more accurate calibration intervals than STIs and PTIs.
{"title":"Statistical calibration for infinite many future values in linear regression: simultaneous or pointwise tolerance intervals or what else?","authors":"Yang Han, Yujia Sun, Lingjiao Wang, Wei Liu, F. Bretz","doi":"10.1093/jrsssc/qlac004","DOIUrl":"https://doi.org/10.1093/jrsssc/qlac004","url":null,"abstract":"\u0000 Statistical calibration using regression is a useful statistical tool with many applications. For confidence sets for x-values associated with infinitely many future y-values, there is a consensus in the statistical literature that the confidence sets constructed should guarantee a key property. While it is well known that the confidence sets based on the simultaneous tolerance intervals (STIs) guarantee this key property conservatively, it is desirable to construct confidence sets that satisfy this property exactly. Also, there is a misconception that the confidence sets based on the pointwise tolerance intervals (PTIs) also guarantee this property. This paper constructs the weighted simultaneous tolerance intervals (WSTIs) so that the confidence sets based on the WSTIs satisfy this property exactly if the future observations have the x-values distributed according to a known specific distribution F(⋅). Through the lens of the WSTIs, convincing counter examples are also provided to demonstrate that the confidence sets based on the PTIs do not guarantee the key property in general and so should not be used. The WSTIs have been applied to real data examples to show that the WSTIs can produce more accurate calibration intervals than STIs and PTIs.","PeriodicalId":49981,"journal":{"name":"Journal of the Royal Statistical Society Series C-Applied Statistics","volume":"85 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2023-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83880930","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}
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