设随机序列{X_n; n=0,±1…}可表示成为X_n=sum from j=-∞ to +∞(α_(j-n)ζ_j其中{α_j}是满足sum from j=-∞ to +∞(α_j^2)<∞的实数列,{ζ_j}是白噪声序列。通常用(?)_N(λ)=integral from 0 to λ(1/2πN)∣sum from k=1...设随机序列{X_n; n=0,±1…}可表示成为X_n=sum from j=-∞ to +∞(α_(j-n)ζ_j其中{α_j}是满足sum from j=-∞ to +∞(α_j^2)<∞的实数列,{ζ_j}是白噪声序列。通常用(?)_N(λ)=integral from 0 to λ(1/2πN)∣sum from k=1 to N(x_(?)e^(iμk)∣~2 dμ来估计{x_n}的未知的谱函数F(λ)。在一定的条件下,当{ζ_j}是独立同分布随机序列时,和[3]证明了:过程√(?)[(?)_N(λ)-F(λ)]的分布弱收敛到某个正态过程ζ(λ)在C[0,π]上产生的测度。本文在他们工作的基础上,运用鞅的极限定理和鞅不等式,改进了[3]中的两个关键引理,从而证明了当{ζ_j}是有控制分布的实四阶鞅差序列时,仍有相同的结果。展开更多
设{X_n,-∞<n<∞}为独立同分布平方可积正值随机变量序列,u=EX_1,σ~2=VarX_1>0.记S_n=sum from X_i,T_n=T-n(X_1,…,X_n)是一统计量(或随机函数),可被表示为T_n=a_nS_n+R_n,其中a_n>0为常数序列,R_n为余项.该文证明若R_n=o...设{X_n,-∞<n<∞}为独立同分布平方可积正值随机变量序列,u=EX_1,σ~2=VarX_1>0.记S_n=sum from X_i,T_n=T-n(X_1,…,X_n)是一统计量(或随机函数),可被表示为T_n=a_nS_n+R_n,其中a_n>0为常数序列,R_n为余项.该文证明若R_n=o(a_nn^(1/2))a.s.,则对统计量T_n的乘积的几乎处处中心极限定理成立,且给出了它的渐近分布和弱不变原理.并以U统计量,Von-Mises统计量,线性模型误差方差的估计等几个常见的统计量为例说明结果应用的广泛性.推广了以往文献中关于独立同分布随机变量和的乘积及U统计量乘积的相应结果.展开更多
Multiple morphological abnormalities of the sperm flagella(MMAF)are characterized by bent,irregular,short,coiled,and absent flagella.MMAF is caused by a variety of genes,some of which have been identified.However,the ...Multiple morphological abnormalities of the sperm flagella(MMAF)are characterized by bent,irregular,short,coiled,and absent flagella.MMAF is caused by a variety of genes,some of which have been identified.However,the underlying genetic factors responsible for the majority of MMAF cases are still largely unknown.The glutamine-rich 2(QRICH2)gene plays an essential role in the development of sperm flagella by regulating the expression of essential sperm flagellar biogenesis-associated proteins,and genetic variants of QRICH2 have been identified as the primary cause of MMAF in humans and mice.Here,we recruited a Pakistani consanguineous family to identify the genetic variant causing infertility in patients with MMAF.Whole-exome sequencing and Sanger sequencing were conducted to identify potentially pathogenic variants causing MMAF in infertile patients.Hematoxylin and eosin(HE)staining was performed to analyze sperm morphology.Quantitative polymerase chain reaction,western blot,and immunofluorescence staining analyses were conducted to observe the expression of QRICH2 in spermatozoa.A novel homozygous missense variant(c.4618C>T)in QRICH2 was identified in the affected patients.Morphological analysis of spermatozoa revealed the MMAF phenotype in infertile patients.qPCR revealed a significant reduction in the level of sperm QRICH2 mRNA,and immunofluorescence staining revealed a lack of sperm QRICH2 expression.Additionally,patients harboring a homozygous QRICH2 mutation presented reduced expression of outer dense fiber 2(ODF2)in sperm,whereas sperm expression of A-kinase anchor protein 4(AKAP4)was normal.These findings expand our understanding of the genetic causes of MMAF-associated male infertility and emphasize the importance of genetic counseling.展开更多
文摘设随机序列{X_n; n=0,±1…}可表示成为X_n=sum from j=-∞ to +∞(α_(j-n)ζ_j其中{α_j}是满足sum from j=-∞ to +∞(α_j^2)<∞的实数列,{ζ_j}是白噪声序列。通常用(?)_N(λ)=integral from 0 to λ(1/2πN)∣sum from k=1 to N(x_(?)e^(iμk)∣~2 dμ来估计{x_n}的未知的谱函数F(λ)。在一定的条件下,当{ζ_j}是独立同分布随机序列时,和[3]证明了:过程√(?)[(?)_N(λ)-F(λ)]的分布弱收敛到某个正态过程ζ(λ)在C[0,π]上产生的测度。本文在他们工作的基础上,运用鞅的极限定理和鞅不等式,改进了[3]中的两个关键引理,从而证明了当{ζ_j}是有控制分布的实四阶鞅差序列时,仍有相同的结果。
文摘设{X_n,-∞<n<∞}为独立同分布平方可积正值随机变量序列,u=EX_1,σ~2=VarX_1>0.记S_n=sum from X_i,T_n=T-n(X_1,…,X_n)是一统计量(或随机函数),可被表示为T_n=a_nS_n+R_n,其中a_n>0为常数序列,R_n为余项.该文证明若R_n=o(a_nn^(1/2))a.s.,则对统计量T_n的乘积的几乎处处中心极限定理成立,且给出了它的渐近分布和弱不变原理.并以U统计量,Von-Mises统计量,线性模型误差方差的估计等几个常见的统计量为例说明结果应用的广泛性.推广了以往文献中关于独立同分布随机变量和的乘积及U统计量乘积的相应结果.
基金supported by the National Key Research and Development Program of China(2021YFC2700202,2022YFA0806303 and 2022YFC2702601)the Global Select Project of the Institute of Health and Medicine,Hefei Comprehensive National Science Center(DJK-LX-2022010)+1 种基金USTC Research Funds of the Double First-Class Initiative(the Joint Fund for New Medicine of USTC)(YD9100002034)the Fundamental Research Funds for the Central Universities(WK9100000004).
文摘Multiple morphological abnormalities of the sperm flagella(MMAF)are characterized by bent,irregular,short,coiled,and absent flagella.MMAF is caused by a variety of genes,some of which have been identified.However,the underlying genetic factors responsible for the majority of MMAF cases are still largely unknown.The glutamine-rich 2(QRICH2)gene plays an essential role in the development of sperm flagella by regulating the expression of essential sperm flagellar biogenesis-associated proteins,and genetic variants of QRICH2 have been identified as the primary cause of MMAF in humans and mice.Here,we recruited a Pakistani consanguineous family to identify the genetic variant causing infertility in patients with MMAF.Whole-exome sequencing and Sanger sequencing were conducted to identify potentially pathogenic variants causing MMAF in infertile patients.Hematoxylin and eosin(HE)staining was performed to analyze sperm morphology.Quantitative polymerase chain reaction,western blot,and immunofluorescence staining analyses were conducted to observe the expression of QRICH2 in spermatozoa.A novel homozygous missense variant(c.4618C>T)in QRICH2 was identified in the affected patients.Morphological analysis of spermatozoa revealed the MMAF phenotype in infertile patients.qPCR revealed a significant reduction in the level of sperm QRICH2 mRNA,and immunofluorescence staining revealed a lack of sperm QRICH2 expression.Additionally,patients harboring a homozygous QRICH2 mutation presented reduced expression of outer dense fiber 2(ODF2)in sperm,whereas sperm expression of A-kinase anchor protein 4(AKAP4)was normal.These findings expand our understanding of the genetic causes of MMAF-associated male infertility and emphasize the importance of genetic counseling.
