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Integrative analysis of single-cell RNA sequencing, bulk RNA sequencing, and proteomic data identified NOTCH3 as a hub gene contributing to human intervertebral disc fibrosis. [PDF]

Sci Rep
Ding Q, Chen X, Zheng Q, Dou Q, Zuo C, Wang Q, Shen C.   +6 more
europepmc   +1 more source

Case Report: Novel <i>ADAMTSL2</i> compound heterozygous mutations in geleophysic dysplasia with bilateral glaucoma and keratoconus-like corneal ectasia. [PDF]

Front Genet
Lee CL, Chuang CK, Chiu HC, Chang YH, Tu YR, Lo YT, Wu JY, Lin HY, Lin SP.   +8 more
europepmc   +1 more source

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A novel Beta matrix function via Wiman matrix function and their applications

Analysis, 2023
Abstract Many authors defined and extended the beta function in various forms because the beta function has wide uses in different fields of science and applied science. In this article, we define a new more generalized form of the extended beta matrix function via the Wiman matrix function and describe their significant properties and ...
Nabiullah Khan, Saddam Husain
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On the singular gamma, Wishart, and beta matrix‐variate density functions

Canadian Journal of Statistics, 2022
AbstractWhen a real positive definite matrix follows a Wishart or, more generally, a matrix‐variate gamma distribution with shape parameter and positive definite scale parameter matrix , one can represent as for some matrix of dimension . When , has a singular distribution whose properties can be studied via the density function of .
Arak M. Mathai, Serge B. Provost
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Covariance matrix inequalities for functions of Beta random variables

Statistics & Probability Letters, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wei, Zhengyuan, Zhang, Xinsheng
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Some Properties of Extended Gamma and Beta Matrix Functions involving 3-Parameter Mittage-Leffler Matrix Function

Annals of Pure and Applied Mathematics, 2022
In this article, we involve three- parameter Mittage -Leffler matrix function for the study of the extended Gamma and Beta matrix functions. Mittage-Leffler matrix function requires for computing the context of Fractional Calculus theory. In this context, we also investigate symmetric relations, integral representations, summation relations, generating
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Generalized Euler's beta matrix and related functions

AIP Conference Proceedings, 2013
In this paper, we define generalizations of Euler's beta, gamma, hypergeometric and confluent hypergeometric matrix functions. Then, recurrence relations and integral representations are derived for generalizations of Euler's beta and gamma matrix functions.
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