On Fenchel-Nielsen coordinates on Teichm\"uller spaces of surfaces of infinite type

We introduce Fenchel-Nielsen coordinates on Teicm\"uller spaces of surfaces of infinite type. The definition is relative to a given pair of pants decomposition of the surface. We start by establishing conditions under which any pair of pants decomposition on a hyperbolic surface of infinite type can be turned into a geometric decomposition, that is, a decomposition into hyperbolic pairs of pants. This is expressed in terms of a condition we introduce and which we call Nielsen convexity. This condition is related to Nielsen cores of Fuchsian groups. We use this to define the Fenchel-Nielsen Teichm\"uller space associated to a geometric pair of pants decomposition. We study a metric on such a Teichm\"uller space, and we compare it to the quasiconformal Teichm\"uller space, equipped with the Teichm\"uller metric. We study conditions under which there is an equality between these Teichm\"uller spaces and we study topological and metric properties of the identity map when this map exists

Completing Single-Cell DNA Methylome Profiles via Transfer Learning Together With KL-Divergence

The high level of sparsity in methylome profiles obtained using whole-genome bisulfite sequencing in the case of low biological material amount limits its value in the study of systems in which large samples are difficult to assemble, such as mammalian preimplantation embryonic development. The recently developed computational methods for addressing the sparsity by imputing missing have their limits when the required minimum data coverage or profiles of the same tissue in other modalities are not available. In this study, we explored the use of transfer learning together with Kullback-Leibler (KL) divergence to train predictive models for completing methylome profiles with very low coverage (below 2%). Transfer learning was used to leverage less sparse profiles that are typically available for different tissues for the same species, while KL divergence was employed to maximize the usage of information carried in the input data. A deep neural network was adopted to extract both DNA sequence and local methylation patterns for imputation. Our study of training models for completing methylome profiles of bovine oocytes and early embryos demonstrates the effectiveness of transfer learning and KL divergence, with individual increase of 29.98 and 29.43%, respectively, in prediction performance and 38.70% increase when the two were used together. The drastically increased data coverage (43.80–73.6%) after imputation powers downstream analyses involving methylomes that cannot be effectively done using the very low coverage profiles (0.06–1.47%) before imputation

Multiresolution Time-Domain Scheme for Terminal Response of Two-Conductor Transmission Lines

This paper derives a multiresolution time-domain (MRTD) scheme for the two-conductor lossless transmission line equations based on Daubechies’ scaling functions. And a method is proposed to generate the scheme at the terminal and near the terminal of the lines. The stability and numerical dispersion of this scheme are studied, and the proposed scheme shows a better dispersion property than the conventional FDTD method. Then the MRTD scheme is extended to the two-conductor lossy transmission line equations. The MRTD scheme is implemented with different basis functions for both lossless and lossy transmission lines. Numerical results show that the MRTD schemes which use the scaling functions with high vanishing moment obtain more accurate results

Multiresolution Time-Domain Analysis of Multiconductor Transmission Lines Terminated in Linear Loads

This paper derives a multiresolution time-domain (MRTD) scheme for the multiconductor transmission line (MTL) equations based on Daubechies’ scaling functions. The terminations are characterized by a state-variable formulation which allows a general description of the termination networks. For the linear load terminations, a method incorporating the terminal constraints is proposed to work out the scheme at and close to the terminations. The MRTD scheme is implemented with different basis functions for linear components including resistances, inductances, and capacitances. Numerical results show that the MRTD schemes obtain a more stable result than the conventional finite difference time-domain (FDTD) method with a coarse space step.This work was supported by the National Natural Science Foundation of China (no. 11271370

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

Dynamics of Trophoblast Differentiation in Peri-Implantation–Stage Human Embryos

Single-cell RNA sequencing of cells from cultured human blastocysts has enabled us to define the transcriptomic landscape of placental trophoblast (TB) that surrounds the epiblast and associated embryonic tissues during the enigmatic day 8 (D8) to D12 peri-implantation period before the villous placenta forms. We analyzed the transcriptomes of 3 early placental cell types, cytoTB (CTB), syncytioTB (STB), and migratoryTB (MTB), picked manually from cultured embryos dissociated with trypsin and were able to follow sublineages that emerged from proliferating CTB at the periphery of the conceptus. A unique form of CTB with some features of STB was detectable at D8, while mature STB was at its zenith at D10. A form of MTB with a mixed MTB/CTB phenotype arose around D10. By D12, STB generation was in decline, CTB had entered a new phase of proliferation, and mature MTB cells had begun to move from the main body of the conceptus. Notably, the MTB transcriptome at D12 indicated enrichment of transcripts associated with IFN signaling, migration, and invasion and upregulation of HLA-C, HLA-E, and HLA-G. The STB, which is distinct from the STB of later villous STB, had a phenotype consistent with intense protein export and placental hormone production, as well as migration and invasion. The studies show that TB associated with human embryos is in rapid developmental flux during periimplantation period when it must invade, signal robustly to the mother to ensure that the pregnancy continues, and make first contact with the maternal immune system

On Quadratic Differential Metrics on a Closed Riemann Surface

We study properties of the space of quadratic differential metrics on a closed Riemann surface of genus g ≥ 2. First, we introduce a natural metric on this space defined via length distortions which is proper and compact. Second, we study topological properties of this space and show equivalence of various convergences. Besides, we relate the preceding metric to another metric which is obtained via global Lipschitz constants