Hopf algebra of multi-decorated rooted forests, free matching Rota-Baxter algebras and Gr\"obner-Shirshov bases

Recent advances in stochastic PDEs, Hopf algebras of typed trees and integral equations have inspired the study of algebraic structures with replicating operations. To understand their algebraic and combinatorial nature, we first use rooted forests with multiple decoration sets to construct free Hopf algebras with multiple Hochschild 1-cocycle conditions. Applying the universal property of the underlying operated algebras and the method of Gr\"obner-Shirshov bases, we then construct free objects in the category of matching Rota-Baxter algebras which is a generalization of Rota-Baxter algebras to allow multiple Rota-Baxter operators. Finally the free matching Rota-Baxter algebras are equipped with a cocycle Hopf algebra structure.Comment: 27 page

Population and allelic variation of A-to-I RNA editing in human transcriptomes.

BackgroundA-to-I RNA editing is an important step in RNA processing in which specific adenosines in some RNA molecules are post-transcriptionally modified to inosines. RNA editing has emerged as a widespread mechanism for generating transcriptome diversity. However, there remain significant knowledge gaps about the variation and function of RNA editing.ResultsIn order to determine the influence of genetic variation on A-to-I RNA editing, we integrate genomic and transcriptomic data from 445 human lymphoblastoid cell lines by combining an RNA editing QTL (edQTL) analysis with an allele-specific RNA editing (ASED) analysis. We identify 1054 RNA editing events associated with cis genetic polymorphisms. Additionally, we find that a subset of these polymorphisms is linked to genome-wide association study signals of complex traits or diseases. Finally, compared to random cis polymorphisms, polymorphisms associated with RNA editing variation are located closer spatially to their respective editing sites and have a more pronounced impact on RNA secondary structure.ConclusionsOur study reveals widespread cis variation in RNA editing among genetically distinct individuals and sheds light on possible phenotypic consequences of such variation on complex traits and diseases

Application of different colorants in the surgery of idiopathic macular hole

Internal limiting membrane(ILM)peeling is commonly used in the operation of idiopathic macular hole(IMH)surgery. The success of ILM peeling has been greatly improved with the assistance of vital dyes. Currently, several kinds of vital dyes such as indocyanine green(ICG), brilliant blue G(BBG)are applied in the ILM staining. However, all of the vital dyes have potential toxicity and side effects on the retina. In recent years, many kinds of dyes and staining improved emerge in endlessly. This paper reports the progress in the application of different colorants in the operation of IMH

Dynamic Simulation of Deposition Processes of Spacecraft Molecular Contamination

Accurate simulation and calculation of the deposition of outgassing molecule can shorten the cycle and reduce the cost of vacuum tests on satellites. It also provides a reference for contamination protection design by systems engineers. In this study, the molecular outgassing, transport and deposition processes were simulated by diffusion theory, the angle coefficient method, and the first-order desorption equation, respectively. The simulation results were consistent with the test data trends, but deviated from the test values. Given the effect of initial molecular outgassing rate, diffusion coefficient and residence time on the deposition mass, it was surmised that considering the molecular species and the weight mass rate would improve the calculation result. These considerations indeed improved the numerical simulations of high-vacuum contamination

Study on Strength and Ultrasonic Velocity of Air-Entrained Concrete and Plain Concrete in Cold Environment

Nondestructive testing technology is essential in the quality inspection of repair, alteration, and renovation of the existing engineering, especially for concrete structure in severe environment. The objective of this work is to deal with the behavior of ultrasonic velocity and mechanical properties of plain concrete and air-entrained concrete subjected to freeze-thaw cycles (F-T-C). The ultrasonic velocity and mechanical properties (tensile strength, compressive strength, cubic compressive strength, and splitting strength) of C30 air-entrained concrete and plain concrete with different water-cement ratio (water-cement ratio was 0.55, 0.45, and 0.50, resp.) after F-T cycles were measured. The influences of F-T cycles on ultrasonic velocity and mechanical properties of C30 air-entrained concrete and plain concrete were analyzed. And the relationship between mechanical properties and ultrasonic velocity was established. The experimental results can be useful for the design of new concrete structure, maintenance and life prediction of existing concrete structure such as offshore platform and concrete dock wall

Search for heavy Majorana neutrinos at future lepton colliders

The nonzero neutrino mass can be a signal for new physics beyond the standard model. To explain the tiny neutrino mass, we can extend the standard model with right-handed Majorana neutrinos in a low-scale seesaw mechanism, while the CP violation effect can be induced due to the CP phase in the interference of heavy Majorana neutrinos. The existence of heavy Majorana neutrinos may lead to lepton number violation processes, which can be used as a probe to search for the signal of heavy Majorana neutrinos. In this paper, we focus on the CP violation effect related to two generations of heavy Majorana neutrinos for $15$ GeV $<m_N<$ $70$ GeV in the pair production of W bosons and rare decays. It is valuable to investigate the Majorana neutrino production signals and the related CP violation effects in the W boson rare decays at future lepton colliders.Comment: 12 pages, 8 figure