Stochastic Optimization Theory of Backward Stochastic Differential Equations Driven by G-Brownian Motion

In this paper, we consider the stochastic optimal control problems under G-expectation. Based on the theory of backward stochastic differential equations driven by G-Brownian motion, which was introduced in [10.11], we can investigate the more general stochastic optimal control problems under G-expectation than that were constructed in [28]. Then we obtain a generalized dynamic programming principle and the value function is proved to be a viscosity solution of a fully nonlinear second-order partial differential equation.Comment: 25 page

Transcriptional profiles of bovine in vivo pre-implantation development

© 2014 Jiang et al.; licensee BioMed Central Ltd. Background: During mammalian pre-implantation embryonic development dramatic and orchestrated changes occur in gene transcription. The identification of the complete changes has not been possible until the development of the Next Generation Sequencing Technology.Results: Here we report comprehensive transcriptome dynamics of single matured bovine oocytes and pre-implantation embryos developed in vivo. Surprisingly, more than half of the estimated 22,000 bovine genes, 11,488 to 12,729 involved in more than 100 pathways, is expressed in oocytes and early embryos. Despite the similarity in the total numbers of genes expressed across stages, the nature of the expressed genes is dramatically different. A total of 2,845 genes were differentially expressed among different stages, of which the largest change was observed between the 4- and 8-cell stages, demonstrating that the bovine embryonic genome is activated at this transition. Additionally, 774 genes were identified as only expressed/highly enriched in particular stages of development, suggesting their stage-specific roles in embryogenesis. Using weighted gene co-expression network analysis, we found 12 stage-specific modules of co-expressed genes that can be used to represent the corresponding stage of development. Furthermore, we identified conserved key members (or hub genes) of the bovine expressed gene networks. Their vast association with other embryonic genes suggests that they may have important regulatory roles in embryo development; yet, the majority of the hub genes are relatively unknown/under-studied in embryos. We also conducted the first comparison of embryonic expression profiles across three mammalian species, human, mouse and bovine, for which RNA-seq data are available. We found that the three species share more maternally deposited genes than embryonic genome activated genes. More importantly, there are more similarities in embryonic transcriptomes between bovine and humans than between humans and mice, demonstrating that bovine embryos are better models for human embryonic development.Conclusions: This study provides a comprehensive examination of gene activities in bovine embryos and identified little-known potential master regulators of pre-implantation development

Optimal control for controllable stochastic linear systems

This paper is concerned with a constrained stochastic linear-quadratic optimal control problem, in which the terminal state is fixed and the initial state is constrained to lie in a stochastic linear manifold. The controllability of stochastic linear systems is studied. Then the optimal control is explicitly obtained by considering a parameterized unconstrained backward LQ problem and an optimal parameter selection problem. A notable feature of our results is that, instead of solving an equation involving derivatives with respect to the parameter, the optimal parameter is characterized by a matrix equation

A cross-species bi-clustering approach to identifying conserved co-regulated genes

© 2016 The Author 2016. Published by Oxford University Press. Motivation: A growing number of studies have explored the process of pre-implantation embryonic development of multiple mammalian species. However, the conservation and variation among different species in their developmental programming are poorly defined due to the lack of effective computational methods for detecting co-regularized genes that are conserved across species. The most sophisticated method to date for identifying conserved co-regulated genes is a two-step approach. This approach first identifies gene clusters for each species by a cluster analysis of gene expression data, and subsequently computes the overlaps of clusters identified from different species to reveal common subgroups. This approach is ineffective to deal with the noise in the expression data introduced by the complicated procedures in quantifying gene expression. Furthermore, due to the sequential nature of the approach, the gene clusters identified in the first step may have little overlap among different species in the second step, thus difficult to detect conserved co-regulated genes. Results: We propose a cross-species bi-clustering approach which first denoises the gene expression data of each species into a data matrix. The rows of the data matrices of different species represent the same set of genes that are characterized by their expression patterns over the developmental stages of each species as columns. A novel bi-clustering method is then developed to cluster genes into subgroups by a joint sparse rank-one factorization of all the data matrices. This method decomposes a data matrix into a product of a column vector and a row vector where the column vector is a consistent indicator across the matrices (species) to identify the same gene cluster and the row vector specifies for each species the developmental stages that the clustered genes co-regulate. Efficient optimization algorithm has been developed with convergence analysis. This approach was first validated on synthetic data and compared to the two-step method and several recent joint clustering methods. We then applied this approach to two real world datasets of gene expression during the pre-implantation embryonic development of the human and mouse. Co-regulated genes consistent between the human and mouse were identified, offering insights into conserved functions, as well as similarities and differences in genome activation timing between the human and mouse embryos

Stochastic Optimization Theory of Backward Stochastic Differential Equations Driven by G-Brownian Motion

National Basic Research Program of China [973-2007CB814901]We consider the stochastic optimal control problems under G-expectation. Based on the theory of backward stochastic differential equations driven by G-Brownian motion, which was introduced in Hu et al. (2012), we can investigate the more general stochastic optimal control problems under G-expectation than that were constructed in Zhang (2011). Then we obtain a generalized dynamic programming principle, and the value function is proved to be a viscosity solution of a fully nonlinear second-order partial differential equation

Analyzing predictors of customer satisfaction and assessment of retail banking problems in Pakistan

The current study has tried to explore the types of services provided by Pakistan. A total of 1,089 bank customers affiliated with eight major banks across four major cities were interviewed through specified questionnaire. The gender wise distribution is 87% males and 13% female of the interviewed, individuals; while account type-based distribution is 24% business account, 37% salary account, and 39% general account holders. Regression analysis showed that customer satisfaction was governed by multiple significant predictors which include bank staff behavior (β = 0.18, p < 0.001), guidance inside bank (β = 0.04, p < 0.01), variety in service products (β = 0.03, p < 0.05), access to account statements (β = 0.11, p < 0.001), availability of cash (β = 0.11, p < 0.001) in ATM, and knowledge of bank staff (β = 0.40, p < 0.001). It is concluded that the retail banking in Pakistan has enormous room to capture more customers provided that private and public sector banks should invest more in infrastructure development along with the provision of swift banking services to their customers