Stability and convergence analysis of high-order numerical schemes with DtN-type absorbing boundary conditions for nonlocal wave equations

The stability and convergence analysis of high-order numerical approximations for the one- and two-dimensional nonlocal wave equations on unbounded spatial domains are considered. We first use the quadrature-based finite difference schemes to discretize the spatially nonlocal operator, and apply the explicit difference scheme to approximate the temporal derivative to achieve a fully discrete infinity system. After that, we construct the Dirichlet-to-Neumann (DtN)-type absorbing boundary conditions (ABCs) to reduce the infinite discrete system into a finite discrete system. To do so, we first adopt the idea in [Du, Zhang and Zheng, \emph{Commun. Comput. Phys.}, 24(4):1049--1072, 2018 and Du, Han, Zhang and Zheng, \emph{SIAM J. Sci. Comp.}, 40(3):A1430--A1445, 2018] to derive the Dirichlet-to-Dirichlet (DtD)-type mappings for one- and two-dimensional cases, respectively. We then use the discrete nonlocal Green's first identity to achieve the discrete DtN-type mappings from the DtD-type mappings. The resulting DtN-type mappings make it possible to perform the stability and convergence analysis of the reduced problem. Numerical experiments are provided to demonstrate the accuracy and effectiveness of the proposed approach.Comment: 26 pages, 4 figure

GAS: A Gaussian Mixture Distribution-Based Adaptive Sampling Method for PINNs

With recent study of the deep learning in scientific computation, the PINNs method has drawn widespread attention for solving PDEs. Compared with traditional methods, PINNs can efficiently handle high-dimensional problems, while the accuracy is relatively low, especially for highly irregular problems. Inspired by the idea of adaptive finite element methods and incremental learning, we propose GAS, a Gaussian mixture distribution-based adaptive sampling method for PINNs. During the training procedure, GAS uses the current residual information to generate a Gaussian mixture distribution for the sampling of additional points, which are then trained together with history data to speed up the convergence of loss and achieve a higher accuracy. Several numerical simulations on 2d to 10d problems show that GAS is a promising method which achieves the state-of-the-art accuracy among deep solvers, while being comparable with traditional numerical solvers

Multi-Platform Next-Generation Sequencing of the Domestic Turkey (Meleagris gallopavo): Genome Assembly and Analysis

The combined application of next-generation sequencing platforms has provided an economical approach to unlocking the potential of the turkey genome

Finishing the euchromatic sequence of the human genome

The sequence of the human genome encodes the genetic instructions for human physiology, as well as rich information about human evolution. In 2001, the International Human Genome Sequencing Consortium reported a draft sequence of the euchromatic portion of the human genome. Since then, the international collaboration has worked to convert this draft into a genome sequence with high accuracy and nearly complete coverage. Here, we report the result of this finishing process. The current genome sequence (Build 35) contains 2.85 billion nucleotides interrupted by only 341 gaps. It covers ∼99% of the euchromatic genome and is accurate to an error rate of ∼1 event per 100,000 bases. Many of the remaining euchromatic gaps are associated with segmental duplications and will require focused work with new methods. The near-complete sequence, the first for a vertebrate, greatly improves the precision of biological analyses of the human genome including studies of gene number, birth and death. Notably, the human enome seems to encode only 20,000-25,000 protein-coding genes. The genome sequence reported here should serve as a firm foundation for biomedical research in the decades ahead

Pivotal role for the ubiquitin Y59-E51 loop in lysine 48 polyubiquitination.

Lysine 48 (K48)-polyubiquitination is the predominant mechanism for mediating selective protein degradation, but the underlying molecular basis of selecting ubiquitin (Ub) K48 for linkage-specific chain synthesis remains elusive. Here, we present biochemical, structural, and cell-based evidence demonstrating a pivotal role for the Ub Y59-E51 loop in supporting K48-polyubiquitination. This loop is established by a hydrogen bond between Ub Y59s hydroxyl group and the backbone amide of Ub E51, as substantiated by NMR spectroscopic analysis. Loop residues Y59 and R54 are specifically required for the receptor activity enabling K48 to attack the donor Ub-E2 thiol ester in reconstituted ubiquitination catalyzed by Skp1-Cullin1-F-box (SCF)(βTrCP) E3 ligase and Cdc34 E2-conjugating enzyme. When introduced into mammalian cells, loop-disruptive mutant Ub(R54A/Y59A) diminished the production of K48-polyubiquitin chains. Importantly, conditional replacement of human endogenous Ub by Ub(R54A/Y59A) or Ub(K48R) yielded profound apoptosis at a similar extent, underscoring the global impact of the Ub Y59-E51 loop in cellular K48-polyubiquitination. Finally, disulfide cross-linking revealed interactions between the donor Ub-bound Cdc34 acidic loop and the Ub K48 site, as well as residues within the Y59-E51 loop, suggesting a mechanism in which the Ub Y59-E51 loop helps recruit the E2 acidic loop that aligns the receptor Ub K48 to the donor Ub for catalysis