Approximate solutions to large nonsymmetric differential Riccati problems with applications to transport theory

In the present paper, we consider large scale nonsymmetric differential matrix Riccati equations with low rank right hand sides. These matrix equations appear in many applications such as control theory, transport theory, applied probability and others. We show how to apply Krylov-type methods such as the extended block Arnoldi algorithm to get low rank approximate solutions. The initial problem is projected onto small subspaces to get low dimensional nonsymmetric differential equations that are solved using the exponential approximation or via other integration schemes such as Backward Differentiation Formula (BDF) or Rosenbrok method. We also show how these technique could be easily used to solve some problems from the well known transport equation. Some numerical experiments are given to illustrate the application of the proposed methods to large-scale problem

Recovery of an embedded obstacle and the surrounding medium for Maxwell's system

In this paper, we are concerned with the inverse electromagnetic scattering problem of recovering a complex scatterer by the corresponding electric far-field data. The complex scatterer consists of an inhomogeneous medium and a possibly embedded perfectly electric conducting (PEC) obstacle. The far-field data are collected corresponding to incident plane waves with a fixed incident direction and a fixed polarisation, but frequencies from an open interval. It is shown that the embedded obstacle can be uniquely recovered by the aforementioned far-field data, independent of the surrounding medium. Furthermore, if the surrounding medium is piecewise homogeneous, then the medium can be recovered as well. Those unique recovery results are new to the literature. Our argument is based on low-frequency expansions of the electromagnetic fields and certain harmonic analysis techniques.Comment: 15 page

Additional file 1: Table S1. of Genetic effects of PDGFRB and MARCH1 identified in GWAS revealing strong associations with semen production traits in Chinese Holstein bulls

Genotype frequencies, allele frequencies, results of the chi-squared tests of identified SNPs in 730 Chinese Holstein bulls and their corresponding primers for the SNP detection of PDE3A, MARCH1 and PDGFRB genes. (DOCX 30 kb

Table_1_Genome Wide Identification of Novel Long Non-coding RNAs and Their Potential Associations With Milk Proteins in Chinese Holstein Cows.XLSX

<p>Long non-coding RNAs (lncRNAs) have emerged as a novel class of regulatory molecules involved in various biological processes. However, their role in milk performance is unknown. Here, whole transcriptome RNA sequencing was used to generate the lncRNA transcriptome profiles in mammary tissue samples from 6 Chinese Holstein cows with 3 extremely high and 3 low milk protein percentage phenotypes. In this study, 6,450 lncRNA transcripts were identified through 5 stringent steps and filtration by coding potential. In total, 31 lncRNAs and 18 novel genes were identified to be differentially expressed in high milk protein samples (HP) relative to low milk protein samples (LP), respectively. Differentially expressed lncRNAs were selected to predict target genes through bioinformatics analysis, followed by the integration of differentially expressed mRNA data, gene function, gene ontology (GO) and pathway, genome wide association study (GWAS) and quantitative trait locus (QTL) information, as well as network analysis to further characterize potential interactions. Several lncRNAs were found (such as XLOC_059976) that could be used as candidate markers for milk protein content prediction. This is the first study to perform global expression profiling of lncRNAs and mRNAs related to milk protein traits in dairy cows. These results provide important information and insights into the synthesis of milk proteins, and potential targets for the future improvement of milk quality.</p

Table_10_Genome Wide Identification of Novel Long Non-coding RNAs and Their Potential Associations With Milk Proteins in Chinese Holstein Cows.XLSX

<p>Long non-coding RNAs (lncRNAs) have emerged as a novel class of regulatory molecules involved in various biological processes. However, their role in milk performance is unknown. Here, whole transcriptome RNA sequencing was used to generate the lncRNA transcriptome profiles in mammary tissue samples from 6 Chinese Holstein cows with 3 extremely high and 3 low milk protein percentage phenotypes. In this study, 6,450 lncRNA transcripts were identified through 5 stringent steps and filtration by coding potential. In total, 31 lncRNAs and 18 novel genes were identified to be differentially expressed in high milk protein samples (HP) relative to low milk protein samples (LP), respectively. Differentially expressed lncRNAs were selected to predict target genes through bioinformatics analysis, followed by the integration of differentially expressed mRNA data, gene function, gene ontology (GO) and pathway, genome wide association study (GWAS) and quantitative trait locus (QTL) information, as well as network analysis to further characterize potential interactions. Several lncRNAs were found (such as XLOC_059976) that could be used as candidate markers for milk protein content prediction. This is the first study to perform global expression profiling of lncRNAs and mRNAs related to milk protein traits in dairy cows. These results provide important information and insights into the synthesis of milk proteins, and potential targets for the future improvement of milk quality.</p

Table_3_Genome Wide Identification of Novel Long Non-coding RNAs and Their Potential Associations With Milk Proteins in Chinese Holstein Cows.XLSX

<p>Long non-coding RNAs (lncRNAs) have emerged as a novel class of regulatory molecules involved in various biological processes. However, their role in milk performance is unknown. Here, whole transcriptome RNA sequencing was used to generate the lncRNA transcriptome profiles in mammary tissue samples from 6 Chinese Holstein cows with 3 extremely high and 3 low milk protein percentage phenotypes. In this study, 6,450 lncRNA transcripts were identified through 5 stringent steps and filtration by coding potential. In total, 31 lncRNAs and 18 novel genes were identified to be differentially expressed in high milk protein samples (HP) relative to low milk protein samples (LP), respectively. Differentially expressed lncRNAs were selected to predict target genes through bioinformatics analysis, followed by the integration of differentially expressed mRNA data, gene function, gene ontology (GO) and pathway, genome wide association study (GWAS) and quantitative trait locus (QTL) information, as well as network analysis to further characterize potential interactions. Several lncRNAs were found (such as XLOC_059976) that could be used as candidate markers for milk protein content prediction. This is the first study to perform global expression profiling of lncRNAs and mRNAs related to milk protein traits in dairy cows. These results provide important information and insights into the synthesis of milk proteins, and potential targets for the future improvement of milk quality.</p

Image_6_Genome Wide Identification of Novel Long Non-coding RNAs and Their Potential Associations With Milk Proteins in Chinese Holstein Cows.PDF

<p>Long non-coding RNAs (lncRNAs) have emerged as a novel class of regulatory molecules involved in various biological processes. However, their role in milk performance is unknown. Here, whole transcriptome RNA sequencing was used to generate the lncRNA transcriptome profiles in mammary tissue samples from 6 Chinese Holstein cows with 3 extremely high and 3 low milk protein percentage phenotypes. In this study, 6,450 lncRNA transcripts were identified through 5 stringent steps and filtration by coding potential. In total, 31 lncRNAs and 18 novel genes were identified to be differentially expressed in high milk protein samples (HP) relative to low milk protein samples (LP), respectively. Differentially expressed lncRNAs were selected to predict target genes through bioinformatics analysis, followed by the integration of differentially expressed mRNA data, gene function, gene ontology (GO) and pathway, genome wide association study (GWAS) and quantitative trait locus (QTL) information, as well as network analysis to further characterize potential interactions. Several lncRNAs were found (such as XLOC_059976) that could be used as candidate markers for milk protein content prediction. This is the first study to perform global expression profiling of lncRNAs and mRNAs related to milk protein traits in dairy cows. These results provide important information and insights into the synthesis of milk proteins, and potential targets for the future improvement of milk quality.</p

Table_13_Genome Wide Identification of Novel Long Non-coding RNAs and Their Potential Associations With Milk Proteins in Chinese Holstein Cows.XLSX

<p>Long non-coding RNAs (lncRNAs) have emerged as a novel class of regulatory molecules involved in various biological processes. However, their role in milk performance is unknown. Here, whole transcriptome RNA sequencing was used to generate the lncRNA transcriptome profiles in mammary tissue samples from 6 Chinese Holstein cows with 3 extremely high and 3 low milk protein percentage phenotypes. In this study, 6,450 lncRNA transcripts were identified through 5 stringent steps and filtration by coding potential. In total, 31 lncRNAs and 18 novel genes were identified to be differentially expressed in high milk protein samples (HP) relative to low milk protein samples (LP), respectively. Differentially expressed lncRNAs were selected to predict target genes through bioinformatics analysis, followed by the integration of differentially expressed mRNA data, gene function, gene ontology (GO) and pathway, genome wide association study (GWAS) and quantitative trait locus (QTL) information, as well as network analysis to further characterize potential interactions. Several lncRNAs were found (such as XLOC_059976) that could be used as candidate markers for milk protein content prediction. This is the first study to perform global expression profiling of lncRNAs and mRNAs related to milk protein traits in dairy cows. These results provide important information and insights into the synthesis of milk proteins, and potential targets for the future improvement of milk quality.</p

Table_8_Genome Wide Identification of Novel Long Non-coding RNAs and Their Potential Associations With Milk Proteins in Chinese Holstein Cows.xlsx

<p>Long non-coding RNAs (lncRNAs) have emerged as a novel class of regulatory molecules involved in various biological processes. However, their role in milk performance is unknown. Here, whole transcriptome RNA sequencing was used to generate the lncRNA transcriptome profiles in mammary tissue samples from 6 Chinese Holstein cows with 3 extremely high and 3 low milk protein percentage phenotypes. In this study, 6,450 lncRNA transcripts were identified through 5 stringent steps and filtration by coding potential. In total, 31 lncRNAs and 18 novel genes were identified to be differentially expressed in high milk protein samples (HP) relative to low milk protein samples (LP), respectively. Differentially expressed lncRNAs were selected to predict target genes through bioinformatics analysis, followed by the integration of differentially expressed mRNA data, gene function, gene ontology (GO) and pathway, genome wide association study (GWAS) and quantitative trait locus (QTL) information, as well as network analysis to further characterize potential interactions. Several lncRNAs were found (such as XLOC_059976) that could be used as candidate markers for milk protein content prediction. This is the first study to perform global expression profiling of lncRNAs and mRNAs related to milk protein traits in dairy cows. These results provide important information and insights into the synthesis of milk proteins, and potential targets for the future improvement of milk quality.</p

Image_2_Genome Wide Identification of Novel Long Non-coding RNAs and Their Potential Associations With Milk Proteins in Chinese Holstein Cows.PDF

<p>Long non-coding RNAs (lncRNAs) have emerged as a novel class of regulatory molecules involved in various biological processes. However, their role in milk performance is unknown. Here, whole transcriptome RNA sequencing was used to generate the lncRNA transcriptome profiles in mammary tissue samples from 6 Chinese Holstein cows with 3 extremely high and 3 low milk protein percentage phenotypes. In this study, 6,450 lncRNA transcripts were identified through 5 stringent steps and filtration by coding potential. In total, 31 lncRNAs and 18 novel genes were identified to be differentially expressed in high milk protein samples (HP) relative to low milk protein samples (LP), respectively. Differentially expressed lncRNAs were selected to predict target genes through bioinformatics analysis, followed by the integration of differentially expressed mRNA data, gene function, gene ontology (GO) and pathway, genome wide association study (GWAS) and quantitative trait locus (QTL) information, as well as network analysis to further characterize potential interactions. Several lncRNAs were found (such as XLOC_059976) that could be used as candidate markers for milk protein content prediction. This is the first study to perform global expression profiling of lncRNAs and mRNAs related to milk protein traits in dairy cows. These results provide important information and insights into the synthesis of milk proteins, and potential targets for the future improvement of milk quality.</p