Let{Xn;n≥1}be a sequence of i.i.d, random variables with finite variance,Q（n）be the related R/S statistics. It is proved that lim ε↓0 ε^2 ∑n=1 ^8 n log n/1 P{Q（n）≥ε√2n log log n}=2/1 EY^2,where Y=sup0≤t...Let{Xn;n≥1}be a sequence of i.i.d, random variables with finite variance,Q（n）be the related R/S statistics. It is proved that lim ε↓0 ε^2 ∑n=1 ^8 n log n/1 P{Q（n）≥ε√2n log log n}=2/1 EY^2,where Y=sup0≤t≤1B（t）-inf0≤t≤sB（t）,and B（t） is a Brownian bridge.展开更多
In basketball, each player’s skill level is the key to a team’s success or failure, the skill level is affected by many personal and environmental factors. A physics-informed AI statistics has become extremely impor...In basketball, each player’s skill level is the key to a team’s success or failure, the skill level is affected by many personal and environmental factors. A physics-informed AI statistics has become extremely important. In this article, a complex non-linear process is considered by taking into account the average points per game of each player, playing time, shooting percentage, and others. This physics-informed statistics is to construct a multiple linear regression model with physics-informed neural networks. Based on the official data provided by the American Basketball League, and combined with specific methods of R program analysis, the regression model affecting the player’s average points per game is verified, and the key factors affecting the player’s average points per game are finally elucidated. The paper provides a novel window for coaches to make meaningful in-game adjustments to team members.展开更多
In 2023,a multivariate normality test based on a chi-square approximation was developed.This method assumes independence among Gaussian random variables,and defines the test statistic,denoted by Q,as the sum of square...In 2023,a multivariate normality test based on a chi-square approximation was developed.This method assumes independence among Gaussian random variables,and defines the test statistic,denoted by Q,as the sum of squared values.This study aims to develop R scripts that implement the Q-test for mul-tivariate normality using either the Shapiro-Wilk W statistic(QSWa)or the Shapiro-Francia W’statistic(QSFa).A bootstrap version of the Q-test(QSWb and QSFb),which does not assume independence,is also included.Addition-ally,it incorporates Royston’s H-test.The use of the scripts is illustrated with a sample of 50 participants assessed on a variable across four yearly admin-istrations.The sampling distribution generated by the bootstrap method dif-fers from the chi-square distribution and corresponds to a generalized chisquare distribution-namely,the distribution of a sum of squares of correlated variables.This distribution is less peaked and has a heavier right tail than the chi-square distribution.It is concluded that the bootstrap approach is con-servative under the null hypothesis of multivariate normality;however,it is theoretically more appropriate than the chi-square approximation.To ap-proximate the distributions of the two versions of the Q-test,it is recom-mended that the z or z’values set to zero in the calculation of the Q statistic not be subtracted when determining the degrees of freedom in the chi-square approximation.Moreover,a significance level of 10%is suggested for the bootstrap approach,rather than the conventional 5%.展开更多
Background:Intratumoral flora and its metabolites play an important role in the occurrence,development and treatment of cancer,and are correlated with the genotype expression of breast cancer;However,the internal rela...Background:Intratumoral flora and its metabolites play an important role in the occurrence,development and treatment of cancer,and are correlated with the genotype expression of breast cancer;However,the internal relationship between intratumoral flora and triple negative breast cancer(TNBC)has not been elucidated.Methods:Fourteen patients with TNBC who met the criteria were included.The tumor tissues and adjacent tissues were respectively taken as the patient group and the control group.The 5R 16S sequencing technique was used to detect the abundance and distribution of the intratumoral flora between the two groups,and the differences between the groups were analyzed to find the bacteria with significant differences between groups(P<0.05).Results:The abundance of intratumoral microbiota in TNBC patients was significantly lower than that in adjacent tissues(P<0.05).The differential bacteria in TNBC tumors(P<0.05)included Acinetobacter,Renibacterium,Flavobacterium,Dechloromonas and others.The differential bacteria genera(P<0.05)in the adjacent tissues included Comamonas,Bacillus,Caulobacter,Afipia,Aerococcus,Roseomonas and so on.Conclusion:There is a significant difference in the flora structure between the tumor and normal tissues in TNBC patients.Proteobacteria plays an important role in the occurrence,development and treatment of TNBC.Among them,Acinetobacter may be the key reason for the metastasis of TNBC.展开更多
基金Project Supported by NSFC (10131040)SRFDP (2002335090)
文摘A law of iterated logarithm for R/S statistics with the help of the strong approximations of R/S statistics by functions of a Wiener process is shown.
文摘Let{Xn;n≥1}be a sequence of i.i.d, random variables with finite variance,Q（n）be the related R/S statistics. It is proved that lim ε↓0 ε^2 ∑n=1 ^8 n log n/1 P{Q（n）≥ε√2n log log n}=2/1 EY^2,where Y=sup0≤t≤1B（t）-inf0≤t≤sB（t）,and B（t） is a Brownian bridge.
文摘In basketball, each player’s skill level is the key to a team’s success or failure, the skill level is affected by many personal and environmental factors. A physics-informed AI statistics has become extremely important. In this article, a complex non-linear process is considered by taking into account the average points per game of each player, playing time, shooting percentage, and others. This physics-informed statistics is to construct a multiple linear regression model with physics-informed neural networks. Based on the official data provided by the American Basketball League, and combined with specific methods of R program analysis, the regression model affecting the player’s average points per game is verified, and the key factors affecting the player’s average points per game are finally elucidated. The paper provides a novel window for coaches to make meaningful in-game adjustments to team members.
文摘In 2023,a multivariate normality test based on a chi-square approximation was developed.This method assumes independence among Gaussian random variables,and defines the test statistic,denoted by Q,as the sum of squared values.This study aims to develop R scripts that implement the Q-test for mul-tivariate normality using either the Shapiro-Wilk W statistic(QSWa)or the Shapiro-Francia W’statistic(QSFa).A bootstrap version of the Q-test(QSWb and QSFb),which does not assume independence,is also included.Addition-ally,it incorporates Royston’s H-test.The use of the scripts is illustrated with a sample of 50 participants assessed on a variable across four yearly admin-istrations.The sampling distribution generated by the bootstrap method dif-fers from the chi-square distribution and corresponds to a generalized chisquare distribution-namely,the distribution of a sum of squares of correlated variables.This distribution is less peaked and has a heavier right tail than the chi-square distribution.It is concluded that the bootstrap approach is con-servative under the null hypothesis of multivariate normality;however,it is theoretically more appropriate than the chi-square approximation.To ap-proximate the distributions of the two versions of the Q-test,it is recom-mended that the z or z’values set to zero in the calculation of the Q statistic not be subtracted when determining the degrees of freedom in the chi-square approximation.Moreover,a significance level of 10%is suggested for the bootstrap approach,rather than the conventional 5%.
基金Administration of Traditional Chinese Medicine of Zhejiang Province and Young Talents Fund Project of Zhejiang Province Traditional Chinese Medicine Scienese and Technology Project(2022ZQ015).
文摘Background:Intratumoral flora and its metabolites play an important role in the occurrence,development and treatment of cancer,and are correlated with the genotype expression of breast cancer;However,the internal relationship between intratumoral flora and triple negative breast cancer(TNBC)has not been elucidated.Methods:Fourteen patients with TNBC who met the criteria were included.The tumor tissues and adjacent tissues were respectively taken as the patient group and the control group.The 5R 16S sequencing technique was used to detect the abundance and distribution of the intratumoral flora between the two groups,and the differences between the groups were analyzed to find the bacteria with significant differences between groups(P<0.05).Results:The abundance of intratumoral microbiota in TNBC patients was significantly lower than that in adjacent tissues(P<0.05).The differential bacteria in TNBC tumors(P<0.05)included Acinetobacter,Renibacterium,Flavobacterium,Dechloromonas and others.The differential bacteria genera(P<0.05)in the adjacent tissues included Comamonas,Bacillus,Caulobacter,Afipia,Aerococcus,Roseomonas and so on.Conclusion:There is a significant difference in the flora structure between the tumor and normal tissues in TNBC patients.Proteobacteria plays an important role in the occurrence,development and treatment of TNBC.Among them,Acinetobacter may be the key reason for the metastasis of TNBC.
