Stochastic simulation of fluid flow in porous media by the complex variable expression method

A stochastic simulation of fluid flow in porous media using a complex variable expression method （SFCM） is presented in this paper. Hydraulic conductivity is considered as a random variable and is then expressed in complex variable form, the real part of which is a deterministic value and the imaginary part is a variable value. The stochastic seepage flow is simulated with the SFCM and is compared with the results calculated with the Monte Carlo stochastic finite element method. In using the Monte Carlo method to simulate the stochastic seepage flow field, the hydraulic conductivity is assumed in three different probability distributions using random sampling method. The obtained seepage flow field is examined through skewness analysis, and the skewed distribution probability density function is given. The head mode value and the head comprehensive standard deviation are used to represent the statistics of calculation results obtained by the Monte Carlo method. The stochastic seepage flow field simulated by the SFCM is confirmed to be similar to that given by the Monte Carlo method from numerical aspects. The range of coefficient of variation of hydraulic conductivity in SFCM is larger than used previously in stochastic seepage flow field simulations, and the computation time is short. The results proved that the SFCM is a convenient calculating method for solving the complex problems.

Comprehensive Analysis of Ubiquitously Expressed Genes in Humans from A Data-driven Perspective

Comprehensive characterization of spatial and temporal gene expression patterns in humans is critical for uncovering the regulatory codes of the human genome and understanding the molecular mechanisms of human diseases.Ubiquitously expressed genes(UEGs)refer to the genes expressed across a majority of,if not all,phenotypic and physiological conditions of an organism.It is known that many human genes are broadly expressed across tissues.However,most previous UEG studies have only focused on providing a list of UEGs without capturing their global expression patterns,thus limiting the potential use of UEG information.In this study,we proposed a novel data-driven framework to leverage the extensive collection of40,000 human transcriptomes to derive a list of UEGs and their corresponding global expression patterns,which offers a valuable resource to further characterize human transcriptome.Our results suggest that about half(12,234;49.01%)of the human genes are expressed in at least 80%of human transcriptomes,and the median size of the human transcriptome is 16,342 genes(65.44%).Through gene clustering,we identified a set of UEGs,named LoVarUEGs,which have stable expression across human transcriptomes and can be used as internal reference genes for expression measurement.To further demonstrate the usefulness of this resource,we evaluated the global expression patterns for 16 previously predicted disallowed genes in islet beta cells and found that seven of these genes showed relatively more varied expression patterns,suggesting that the repression of these genes may not be unique to islet beta cells.