Non-Oscillatory Hierarchical Reconstruction for Central and Finite Volume Schemes

This is the continuation of the paper "central discontinuous Galerkin methods on overlapping cells with a non-oscillatory hierarchical reconstruction" by the same authors. The hierarchical reconstruction introduced therein is applied to central schemes on overlapping cells and to nite volume schemes on non-staggered grids. This takes a new nite volume approach for approximating non-smooth solutions. A critical step for high order nite volume schemes is to reconstruct a nonoscillatory high degree polynomial approximation in each cell out of nearby cell averages. In the paper this procedure is accomplished in two steps: first to reconstruct a high degree polynomial in each cell by using e.g., a central reconstruction, which is easy to do despite the fact that the reconstructed polynomial could be oscillatory; then to apply the hierarchical reconstruction to remove the spurious oscillations while maintaining the high resolution. All numerical computations for systems of conservation laws are performed without characteristic decomposition. In particular, we demonstrate that this new approach can generate essentially non-oscillatory solutions even for 5th order schemes without characteristic decomposition.The research of Y. Liu was supported in part by NSF grant DMS-0511815. The research of C.-W. Shu was supported in part by the Chinese Academy of Sciences while this author was visiting the University of Science and Technology of China (grant 2004-1-8) and the Institute of Computational Mathematics and Scienti c/Engineering Computing. Additional support was provided by ARO grant W911NF-04-1-0291 and NSF grant DMS-0510345. The research of E. Tadmor was supported in part by NSF grant 04-07704 and ONR grant N00014-91-J-1076. The research of M. Zhang was supported in part by the Chinese Academy of Sciences grant 2004-1-8

Image Synthesis under Limited Data: A Survey and Taxonomy

Deep generative models, which target reproducing the given data distribution to produce novel samples, have made unprecedented advancements in recent years. Their technical breakthroughs have enabled unparalleled quality in the synthesis of visual content. However, one critical prerequisite for their tremendous success is the availability of a sufficient number of training samples, which requires massive computation resources. When trained on limited data, generative models tend to suffer from severe performance deterioration due to overfitting and memorization. Accordingly, researchers have devoted considerable attention to develop novel models that are capable of generating plausible and diverse images from limited training data recently. Despite numerous efforts to enhance training stability and synthesis quality in the limited data scenarios, there is a lack of a systematic survey that provides 1) a clear problem definition, critical challenges, and taxonomy of various tasks; 2) an in-depth analysis on the pros, cons, and remain limitations of existing literature; as well as 3) a thorough discussion on the potential applications and future directions in the field of image synthesis under limited data. In order to fill this gap and provide a informative introduction to researchers who are new to this topic, this survey offers a comprehensive review and a novel taxonomy on the development of image synthesis under limited data. In particular, it covers the problem definition, requirements, main solutions, popular benchmarks, and remain challenges in a comprehensive and all-around manner.Comment: 230 references, 25 pages. GitHub: https://github.com/kobeshegu/awesome-few-shot-generatio

Bifurcations and Turing patterns in a diffusive Gierer-Meinhardt model

In this paper, the Hopf bifurcations and Turing bifurcations of the Gierer– Meinhardt activator-inhibitor model are studied. The very interesting and complex spatially periodic solutions and patterns induced by bifurcations are analyzed from both theoretical and numerical aspects respectively. Firstly, the conditions for the existence of Hopf bifurcation and Turing bifurcation are established in turn. Then, the Turing instability region caused by diffusion is obtained. In addition, to uncover the diffusion mechanics of Turing patterns, the dynamic behaviors are studied near the Turing bifurcation by using weakly nonlinear analysis techniques, and the type of spatial pattern was predicted by the amplitude equation. And our results show that the spatial patterns in the Turing instability region change from the spot, spot-stripe to stripe in order. Finally, the results of the analysis are verified by numerical simulations

Therapeutic Effect of Targeting Branched-Chain Amino Acid Catabolic Flux in Pressure-Overload Induced Heart Failure.

Background Branched-chain amino acid (BCAA) catabolic defect is an emerging metabolic hallmark in failing hearts in human and animal models. The therapeutic impact of targeting BCAA catabolic flux under pathological conditions remains understudied. Methods and Results BT2 (3,6-dichlorobenzo[b]thiophene-2-carboxylic acid), a small-molecule inhibitor of branched-chain ketoacid dehydrogenase kinase, was used to enhance BCAA catabolism. After 2 weeks of transaortic constriction, mice with significant cardiac dysfunctions were treated with vehicle or BT2. Serial echocardiograms showed continuing pathological deterioration in left ventricle of the vehicle-treated mice, whereas the BT2-treated mice showed significantly preserved cardiac function and structure. Moreover, BT2 treatment improved systolic contractility and diastolic mechanics. These therapeutic benefits appeared to be independent of impacts on left ventricle hypertrophy but associated with increased gene expression involved in fatty acid utilization. The BT2 administration showed no signs of apparent toxicity. Conclusions Our data provide the first proof-of-concept evidence for the therapeutic efficacy of restoring BCAA catabolic flux in hearts with preexisting dysfunctions. The BCAA catabolic pathway represents a novel and potentially efficacious target for treatment of heart failure

Unusual pressure-induced electronic structure evolution in organometal halide perovskite predicted from first-principles

Pressure has been demonstrated to be an effective parameter to alter the atomic and electronic structures of materials. By using the first-principles calculations based on density functional theory (DFT), we systematically investigated the changes in the atomic and electronic structures of the cubic MAPbI(3) phase under pressures. It is found that the band gap of the compressed cubic MAPbI(3) structure exhibits a remarkable redshift to 1.114/1.380 eV in DFT/HSE-SOC calculation under a mild pressure of 2.772 GPa, and subsequently shows a widening at higher pressures until similar to 20 GPa. As the pressure further increases, the band gap closes at similar to 80 GPa. Detailed structural and electronic characteristic analyses indicate that the band gap of the cubic MAPbI(3) structure is determined by two competing effects: the lattice contraction decreases its band gap while the PbI6 octahedral filling increases it. Given that, pressure can be a powerful tool to help understanding the optoelectronic properties of perovskite materials

A new type of simplified inverse Lax-Wendroff boundary treatment I: hyperbolic conservation laws

In this paper, we design a new kind of high order inverse Lax-Wendroff (ILW) boundary treatment for solving hyperbolic conservation laws with finite difference method on a Cartesian mesh. This new ILW method decomposes the construction of ghost point values near inflow boundary into two steps: interpolation and extrapolation. At first, we impose values of some artificial auxiliary points through a polynomial interpolating the interior points near the boundary. Then, we will construct a Hermite extrapolation based on those auxiliary point values and the spatial derivatives at boundary obtained via the ILW procedure. This polynomial will give us the approximation to the ghost point value. By an appropriate selection of those artificial auxiliary points, high-order accuracy and stable results can be achieved. Moreover, theoretical analysis indicates that comparing with the original ILW method, especially for higher order accuracy, the new proposed one would require fewer terms using the relatively complicated ILW procedure and thus improve computational efficiency on the premise of maintaining accuracy and stability. We perform numerical experiments on several benchmarks, including one- and two-dimensional scalar equations and systems. The robustness and efficiency of the proposed scheme is numerically verified

Integrative transcriptome and proteome revealed high-yielding mechanisms of epsilon-poly-L-lysine by Streptomyces albulus

Introductionε-poly-L-lysine (ε-PL) is a high value, widely used natural antimicrobial peptide additive for foods and cosmetic products that is mainly produced by Streptomyces albulus. In previous work, we developed the high-yield industrial strain S. albulus WG-608 through successive rounds of engineering.MethodsHere, we use integrated physiological, transcriptomic, and proteomics association analysis to resolve the complex mechanisms underlying high ε-PL production by comparing WG-608 with the progenitor strain M-Z18.ResultsOur results show that key genes in the glycolysis, pentose phosphate pathway, glyoxylate pathway, oxidative phosphorylation, and L-lysine biosynthesis pathways are differentially upregulated in WG-608, while genes in the biosynthetic pathways for fatty acids, various branched amino acids, and secondary metabolite by-products are downregulated. This regulatory pattern results in the introduction of more carbon atoms into L-lysine biosynthesis and ε-PL production. In addition, significant changes in the regulation of DNA replication, transcription, and translation, two component systems, and quorum sensing may facilitate the adaptability to environmental pressure and the biosynthesis of ε-PL. Overexpression of ppk gene and addition of polyP6 further enhanced the ε-PL production.DiscussionThis study enables comprehensive understanding of the biosynthetic mechanisms of ε-PL in S. albulus WG-608, while providing some genetic modification and fermentation strategies to further improve the ε-PL production