Numerical integration rules with improved accuracy close to singularities

Sometimes it is necessary to obtain a numerical integration using only discretised data. In some cases, the data contains singularities which position is known but does not coincide with a discretisation point, and the jumps in the function and its derivatives are available at these positions. The motivation of this paper is to use the previous information to obtain numerical quadrature formulas that allow approximating the integral of the discrete data over certain intervals accurately. This work is devoted to the construction and analysis of a new nonlinear technique that allows to obtain accurate numerical integrations of any order using data that contains singularities, and when the integrand is only known at grid points. The novelty of the technique consists in the inclusion of correction terms with a closed expression that depends on the size of the jumps of the function and its derivatives at the singularities, that are supposed to be known. The addition of these terms allows recovering the accuracy of classical numerical integration formulas even close to the singularities, as these correction terms account for the error that the classical integration formulas commit up to their accuracy at smooth zones. Thus, the correction terms can be added during the integration or as post-processing, which is useful if the main calculation of the integral has been already done using classical formulas. The numerical experiments performed allow us to confirm the theoretical conclusions reached in this paper.Comment: 23 pages, 5 Figures, 3 Table

Complete Genomes of Symbiotic Cyanobacteria Clarify the Evolution of Vanadium-Nitrogenase.

Plant endosymbiosis with nitrogen-fixing cyanobacteria has independently evolved in diverse plant lineages, offering a unique window to study the evolution and genetics of plant-microbe interaction. However, very few complete genomes exist for plant cyanobionts, and therefore little is known about their genomic and functional diversity. Here, we present four complete genomes of cyanobacteria isolated from bryophytes. Nanopore long-read sequencing allowed us to obtain circular contigs for all the main chromosomes and most of the plasmids. We found that despite having a low 16S rRNA sequence divergence, the four isolates exhibit considerable genome reorganizations and variation in gene content. Furthermore, three of the four isolates possess genes encoding vanadium (V)-nitrogenase (vnf), which is uncommon among diazotrophs and has not been previously reported in plant cyanobionts. In two cases, the vnf genes were found on plasmids, implying possible plasmid-mediated horizontal gene transfers. Comparative genomic analysis of vnf-containing cyanobacteria further identified a conserved gene cluster. Many genes in this cluster have not been functionally characterized and would be promising candidates for future studies to elucidate V-nitrogenase function and regulation

Two types of generalized integrable decompositions and new solitary-wave solutions for the modified Kadomtsev-Petviashvili equation with symbolic computation

The modified Kadomtsev-Petviashvili (mKP) equation is shown in this paper to be decomposable into the first two soliton equations of the 2N-coupled Chen-Lee-Liu and Kaup-Newell hierarchies by respectively nonlinearizing two sets of symmetry Lax pairs. In these two cases, the decomposed (1+1)-dimensional nonlinear systems both have a couple of different Lax representations, which means that there are two linear systems associated with the mKP equation under the same constraint between the potential and eigenfunctions. For each Lax representation of the decomposed (1+1)-dimensional nonlinear systems, the corresponding Darboux transformation is further constructed such that a series of explicit solutions of the mKP equation can be recursively generated with the assistance of symbolic computation. In illustration, four new families of solitary-wave solutions are presented and the relevant stability is analyzed.Comment: 23 page

Experimental Free-Space Distribution of Entangled Photon Pairs over a Noisy Ground Atmosphere of 13km

We report free-space distribution of entangled photon pairs over a noisy ground atmosphere of 13km. It is shown that the desired entanglement can still survive after the two entangled photons have passed through the noisy ground atmosphere. This is confirmed by observing a space-like separated violation of Bell inequality of $2.45 \pm 0.09$. On this basis, we exploit the distributed entangled photon source to demonstrate the BB84 quantum cryptography scheme. The distribution distance of entangled photon pairs achieved in the experiment is for the first time well beyond the effective thickness of the aerosphere, hence presenting a significant step towards satellite-based global quantum communication.Comment: 4 pages, 3 figure

Self-renewal of single mouse hematopoietic stem cells is reduced by JAK2V617F without compromising progenitor cell expansion

Recent descriptions of significant heterogeneity in normal stem cells and cancers have altered our understanding of tumorigenesis, emphasizing the need to understand how single stem cells are subverted to cause tumors. Human myeloproliferative neoplasms (MPNs) are thought to reflect transformation of a hematopoietic stem cell (HSC) and the majority harbor an acquired V617F mutation in the JAK2 tyrosine kinase, making them a paradigm for studying the early stages of tumor establishment and progression. The consequences of activating tyrosine kinase mutations for stem and progenitor cell behavior are unclear. In this article, we identify a distinct cellular mechanism operative in stem cells. By using conditional knock-in mice, we show that the HSC defect resulting from expression of heterozygous human JAK2V617F is both quantitative (reduced HSC numbers) and qualitative (lineage biases and reduced self-renewal per HSC). The defect is intrinsic to individual HSCs and their progeny are skewed toward proliferation and differentiation as evidenced by single cell and transplantation assays. Aged JAK2V617F show a more pronounced defect as assessed by transplantation, but mice that transform reacquire competitive self-renewal ability. Quantitative analysis of HSC-derived clones was used to model the fate choices of normal and JAK2-mutant HSCs and indicates that JAK2V617F reduces self-renewal of individual HSCs but leaves progenitor expansion intact. This conclusion is supported by paired daughter cell analyses, which indicate that JAK2-mutant HSCs more often give rise to two differentiated daughter cells. Together these data suggest that acquisition of JAK2V617F alone is insufficient for clonal expansion and disease progression and causes eventual HSC exhaustion. Moreover, our results show that clonal expansion of progenitor cells provides a window in which collaborating mutations can accumulate to drive disease progression. Characterizing the mechanism(s) of JAK2V617F subclinical clonal expansions and the transition to overt MPNs will illuminate the earliest stages of tumor establishment and subclone competition, fundamentally shifting the way we treat and manage cancers

Carbon-Chain Molecules in Molecular Outflows and Lupus I Region--New Producing Region and New Forming Mechanism

Using the new equipment of the Shanghai Tian Ma Radio Telescope, we have searched for carbon-chain molecules (CCMs) towards five outflow sources and six Lupus I starless dust cores, including one region known to be characterized by warm carbon-chain chemistry (WCCC), Lupus I-1 (IRAS 15398-3359), and one TMC-1 like cloud, Lupus I-6 (Lupus-1A). Lines of HC3N J=2-1, HC5N J=6-5, HC7N J=14-13, 15-14, 16-15 and C3S J=3-2 were detected in all the targets except in the outflow source L1660 and the starless dust core Lupus I-3/4. The column densities of nitrogen-bearing species range from 10$^{12}$ to 10$^{14}$ cm$^{-2}$ and those of C$_3$S are about 10$^{12}$ cm$^{-2}$. Two outflow sources, I20582+7724 and L1221, could be identified as new carbon-chain--producing regions. Four of the Lupus I dust cores are newly identified as early quiescent and dark carbon-chain--producing regions similar to Lup I-6, which together with the WCCC source, Lup I-1, indicate that carbon-chain-producing regions are popular in Lupus I which can be regard as a Taurus like molecular cloud complex in our Galaxy. The column densities of C3S are larger than those of HC7N in the three outflow sources I20582, L1221 and L1251A. Shocked carbon-chain chemistry (SCCC) is proposed to explain the abnormal high abundances of C3S compared with those of nitrogen-bearing CCMs. Gas-grain chemical models support the idea that shocks can fuel the environment of those sources with enough $S^+$ thus driving the generation of S-bearing CCMs.Comment: 7 figures, 8 tables, accepted by MNRA