Mean-square convergence and stability of the backward Euler method for stochastic differential delay equations with highly nonlinear growing coefficients

Over the last few decades, the numerical methods for stochastic differential delay equations (SDDEs) have been investigated and developed by many scholars. Nevertheless, there is still little work to be completed. By virtue of the novel technique, this paper focuses on the mean-square convergence and stability of the backward Euler method (BEM) for SDDEs whose drift and diffusion coefficients can both grow polynomially. The upper mean-square error bounds of BEM are obtained. Then the convergence rate, which is one-half, is revealed without using the moment boundedness of numerical solutions. Furthermore, under fairly general conditions, the novel technique is applied to prove that the BEM can inherit the exponential mean-square stability with a simple proof. At last, two numerical experiments are implemented to illustrate the reliability of the theories

Stability of the numerical scheme for stochastic McKean-Vlasov equations

This paper studies the infinite-time stability of the numerical scheme for stochastic McKean-Vlasov equations (SMVEs) via stochastic particle method. The long-time propagation of chaos in mean-square sense is obtained, with which the almost sure propagation in infinite horizon is proved by exploiting the Chebyshev inequality and the Borel-Cantelli lemma. Then the mean-square and almost sure exponential stabilities of the Euler-Maruyama scheme associated with the corresponding interacting particle system are shown through an ingenious manipulation of empirical measure. Combining the assertions enables the numerical solutions to reproduce the stabilities of the original SMVEs. The examples are demonstrated to reveal the importance of this study

The sudden stratospheric warming in January 2021

Using the ERA5 reanalysis, sea surface temperature and sea ice observations, and the real-time multivariate Madden–Julian index, this study explores a sudden stratospheric warming (SSW) in January 2021, its favorable conditions, and the near surface impact. Wavenumbers 1 and 2 alternately contributed to the total eddy heat flux from mid-December 2020 to late January 2021, and the wavenumber 2 during the onset period nearly split the stratospheric polar vortex. In mid-December 2020 and during the 2021 New Year period (1–5 January 2021), a blocking developed over the Urals, which enhanced the local ridge and the climatological wavenumber 2. Composite results confirm that the Arctic sea ice loss in autumn and La Niña favor the deepening of the high latitude North Pacific low and the increase of the Urals height ridge, which together enhance the planetary waves and hence disturb the stratospheric polar vortex. However, the Madden–Julian oscillation (MJO) in the tropics was dormant in mid-to-late December 2020 and early January 2021, and the well-established statistical relationship between the MJO convection over the western Pacific and the SSW is not applicable to this special case. The cold air outbreak in China during the 2021 New Year period before the January 2021 SSW onset is not explained by the SSW signal which developed in the stratosphere. In contrast, the downward-propagating signal reached the near surface in mid-February 2021, which may contribute to the cold air outbreak in US and may help to explain the extreme coldness of Texas in middle February

Resveratrol Pretreatment Improved Heart Recovery Ability of Hyperglycemic Bone Marrow Stem Cells Transplantation in Diabetic Myocardial Infarction by Down-Regulating MicroRNA-34a

AIM: To examine the effect of resveratrol (RSV) on bone marrow mesenchymal stem cells (BMSCs) under hyperglycemic conditions and on BMSCs transplantation in diabetic rats with myocardial infarction (MI).METHODS:In vitro, BMSCs were isolated from 3-week-old male Sprague Dawley (SD) rats and cultured under hyperglycemic conditions for up to 28 days. Cell viability was analyzed by cell counting kit-8 (CCK-8) assays. The expression of miR-34a was measured by RT-qPCR. Western blotting was used to examine the protein expression of SIRT1, P21, P16, VEGF and HIF-1α. A senescence-associated β-galactosidase assay was used to examine the senescence level of each group. In vivo, a diabetes model was established by feeding rats a high-sugar and high-fat diet for 8 weeks, injecting the animals with streptozotocin (STZ) and continuing high-sugar and high-fat feeding for 4 additional weeks. Then, left anterior descending coronary artery (LAD) cessation was used to established the myocardial infarction (MI) models. Each group of rats was transplanted with differentially preconditioned BMSCs after myocardial infarction. Ultrasound was used to analyze cardiac function 1 and 3 weeks after the operation, and frozen heart sections were used for immunohistochemical analysis, Masson staining and CD31 measurement. In addition, ELISA analysis of serum cytokine levels was performed.RESULTS: This study showed that the viability of BMSCs cultured under hyperglycemic conditions was decreased, the cells became senescent. Besides, an obviously increased in the expression of miR-34a was detected. Moreover, RSV preconditioning reduced the expression of miR-34a in BMSCs after high glucose stimulation and rejuvenated BMSCs under hyperglycemic conditions. Further analysis showed that the transplantation of RSV-BMSCs were benefit to heart recovery following infarction in diabetic rats, promoted proangiogenic factor release and increased arteriole and capillary densities.CONCLUSION: RSV rejuvenated BMSCs after chronic hyperglycemia-induced senescence by interacting with miR-34a and optimized the therapeutic effect of BMSCs on diabetes with myocardial infarction

Prevalence of A2143G mutation of H. pylori-23S rRNA in Chinese subjects with and without clarithromycin use history

<p>Abstract</p> <p>Background</p> <p>A2143G mutation of <it>23S rRNA </it>gene of <it>H. pylori </it>results in clarithromycin (CLR) resistance. To investigate the prevalence of the CLR resistance-related A2143G mutation of the <it>H. pylori</it>-specific <it>23S rRNA </it>gene in Chinese subjects with and without CLR use history, 307 subjects received the treatment with amoxicillin and omeprazole (OA) and 310 subjects received a placebo in 1995, and 153 subjects received a triple therapy with OA and CLR (OAC) in 2000. DNA was extracted from fasting gastric juice at the end of the intervention trial in 2003. <it>H. pylori </it>infection was determined by <it>H. pylori</it>-specific <it>23S rRNA </it>PCR, ELISA, and¹³C-urea breath test assays. Mutations of the <it>23S rRNA </it>gene were detected by RFLP assays.</p> <p>Results</p> <p>The presence of <it>23S rRNA </it>due to <it>H. pylori </it>infection in the OA group remained lower than that in the placebo group 7.3 yrs after OA-therapy [51.1% (157/307) vs. 83.9% (260/310), p = 0.0000]. In the OAC group, the <it>23S rRNA </it>detection rate was 26.8% (41/153) three yrs after OAC-treatment. The A2143G mutation rate among the <it>23S rRNA</it>-positive subjects in the OAC group [31.7% (13/41)] was significantly higher than that in the OA group [10.2% (16/157)] and the placebo group [13.8% (36/260)]. The frequency of the AAGGG → CTTCA (2222–2226) and AACC → GAAG (2081–2084) sequence alterations in the OAC group was also significantly higher than those in the OA group and the placebo group.</p> <p>Conclusion</p> <p>Primary prevalence of the A2143G mutation was 10~14% among Chinese population without history of CLR therapy. Administration of CLR to eliminate <it>H. pylori </it>infection increased the prevalence of the A2143G mutation in Chinese subjects (32%) significantly.</p

Resolving Fine-Scale Surface Features on Polar Sea Ice: A First Assessment of UAS Photogrammetry Without Ground Control

Mapping landfast sea ice at a fine spatial scale is not only meaningful for geophysical study, but is also of benefit for providing information about human activities upon it. The combination of unmanned aerial systems (UAS) with structure from motion (SfM) methods have already revolutionized the current close-range Earth observation paradigm. To test their feasibility in characterizing the properties and dynamics of fast ice, three flights were carried out in the 2016–2017 austral summer during the 33rd Chinese National Antarctic Expedition (CHINARE), focusing on the area of the Prydz Bay in East Antarctica. Three-dimensional models and orthomosaics from three sorties were constructed from a total of 205 photos using Agisoft PhotoScan software. Logistical challenges presented by the terrain precluded the deployment of a dedicated ground control network; however, it was still possible to indirectly assess the performance of the photogrammetric products through an analysis of the statistics of the matching network, bundle adjustment, and Monte-Carlo simulation. Our results show that the matching networks are quite strong, given a sufficient number of feature points (mostly > 20,000) or valid matches (mostly > 1000). The largest contribution to the total error using our direct georeferencing approach is attributed to inaccuracies in the onboard position and orientation system (POS) records, especially in the vehicle height and yaw angle. On one hand, the 3D precision map reveals that planimetric precision is usually about one-third of the vertical estimate (typically 20 cm in the network centre). On the other hand, shape-only errors account for less than 5% for the X and Y dimensions and 20% for the Z dimension. To further illustrate the UAS’s capability, six representative surface features are selected and interpreted by sea ice experts. Finally, we offer pragmatic suggestions and guidelines for planning future UAS-SfM surveys without the use of ground control. The work represents a pioneering attempt to comprehensively assess UAS-SfM survey capability in fast ice environments, and could serve as a reference for future improvements

An ensemble study of turbulence in extended QSO nebulae at z≈0.5z\approx0.5--1

Turbulent motions in the circumgalactic medium (CGM) play a critical role in regulating the evolution of galaxies, yet their detailed characterization remains elusive. Using two-dimensional velocity maps constructed from spatially-extended [OII] and [OIII] emission, Chen et al. (2023b) measured the velocity structure functions (VSFs) of four quasar nebulae at $z\approx\!0.5$--1.1. One of these exhibits a spectacular Kolmogorov relation. Here we carry out an ensemble study using an expanded sample incorporating four new nebulae from three additional QSO fields. The VSFs measured for all eight nebulae are best explained by subsonic turbulence revealed by the line-emitting gas, which in turn strongly suggests that the cool gas ($T\!\sim\!10^4$ K) is dynamically coupled to the hot ambient medium. Previous work demonstrates that the largest nebulae in our sample reside in group environments with clear signs of tidal interactions, suggesting that environmental effects are vital in seeding and enhancing turbulence within the gaseous halos, ultimately promoting the formation of the extended nebulae. No discernible differences are observed in the VSF properties between radio-loud and radio-quiet QSO fields. We estimate the turbulent heating rate per unit volume, $Q_{\rm turb}$, in the QSO nebulae to be $\sim 10^{-26}$--$10^{-22}$ erg cm$^{-3}$ s$^{-1}$ for the cool phase and $\sim 10^{-28}$--$10^{-25}$ erg cm$^{-3}$ s$^{-1}$ for the hot phase. This range aligns with measurements in the intracluster medium and star-forming molecular clouds but is $\sim10^3$ times higher than the $Q_{\rm turb}$ observed inside cool gas clumps on scales $\lesssim1$ kpc using absorption-line techniques. We discuss the prospect of bridging the gap between emission and absorption studies by pushing the emission-based VSF measurements to below $\approx\!10$ kpc.Comment: 23 pages; 7 figures, and 4 tables in main text; 9 figures in Appendix; accepted by ApJ. Comments welcom

The first comprehensive study of a giant nebula around a radio-quiet quasar in the z<1z < 1 Universe

We present the first comprehensive study of a giant, $\approx \! \! 70$ kpc-scale nebula around a radio-quiet quasar at $z<1$. The analysis is based on deep integral field spectroscopy with MUSE of the field of HE$\,$0238$-$1904, a luminous quasar at $z=0.6282$. The nebula emits strongly in $\mathrm{[O \, II]}$, $\rm H \beta$, and $\mathrm{[O \, III]}$, and the quasar resides in an unusually overdense environment for a radio-quiet system. The environment likely consists of two groups which may be merging, and in total have an estimated dynamical mass of $M_{\rm dyn}\approx 4\times 10^{13}$ to $10^{14}\ {\rm M_\odot}$. The nebula exhibits largely quiescent kinematics and irregular morphology. The nebula may arise primarily through interaction-related stripping of circumgalactic and interstellar medium (CGM/ISM) of group members, with some potential contributions from quasar outflows. The simultaneous presence of the giant nebula and a radio-quiet quasar in a rich environment suggests a correlation between such circum-quasar nebulae and environmental effects. This possibility can be tested with larger samples. The upper limits on the electron number density implied by the$\mathrm{[O \, II]}$doublet ratio range from$\log(n_{\rm e, \, [O \, II]} / \mathrm{cm^{-3}}) < 1.2$to$2.8$. However, assuming a constant quasar luminosity and negligible projection effects, the densities implied from the measured line ratios between different ions (e.g.,$\mathrm{[O\,II]}$,$\mathrm{[O\,III]}$, and$\mathrm{[Ne\,V]}$) and photoionization simulations are often$10{-}400$times larger. This large discrepancy can be explained by quasar variability on a timescale of$\approx 10^4{-}10^5$ years.Comment: 19 pages, 9 figures, 3 tables; Submitted to MNRA

The Cosmic Ultraviolet Baryon Survey (CUBS) VIII: Group Environment of the Most Luminous Quasars at z≈1z\approx1

We investigate the group-scale environment of 15 luminous quasars (luminosity $L_{\rm 3000}>10^{46}$ erg s$^{-1}$) from the Cosmic Ultraviolet Baryon Survey (CUBS) at redshift $z\approx1$. Using the Multi Unit Spectroscopic Explorer (MUSE) integral field spectrograph on the Very Large Telescope (VLT), we conduct a deep galaxy redshift survey in the CUBS quasar fields to identify group members and measure the physical properties of individual galaxies and galaxy groups. We find that the CUBS quasars reside in diverse environments. The majority (11 out of 15) of the CUBS quasars reside in overdense environments with typical halo masses exceeding $10^{13}{\rm M}_{\odot}$, while the remaining quasars reside in moderate-size galaxy groups. No correlation is observed between overdensity and redshift, black hole (BH) mass, or luminosity. Radio-loud quasars (5 out of 15 CUBS quasars) are more likely to be in overdense environments than their radio-quiet counterparts in the sample, consistent with the mean trends from previous statistical observations and clustering analyses. Nonetheless, we also observe radio-loud quasars in moderate groups and radio-quiet quasars in overdense environments, indicating a large scatter in the connection between radio properties and environment. We find that the most UV luminous quasars might be outliers in the stellar mass-to-halo mass relations or may represent departures from the standard single-epoch BH relations.Comment: 18 pages, 8 figures, accepted for publication in Ap

Discovery of optically emitting circumgalactic nebulae around the majority of UV-luminous quasars at intermediate redshift

We report the discovery of large ionized, [O II] emitting circumgalactic nebulae around the majority of thirty UV luminous quasars at $z=0.4-1.4$ observed with deep, wide-field integral field spectroscopy (IFS) with the Multi-Unit Spectroscopy Explorer (MUSE) by the Cosmic Ultraviolet Baryon Survey (CUBS) and MUSE Quasar Blind Emitters Survey (MUSEQuBES). Among the 30 quasars, seven (23%) exhibit [O II] emitting nebulae with major axis sizes greater than 100 kpc, twenty greater than 50 kpc (67%), and 27 (90%) greater than 20 kpc. Such large, optically emitting nebulae indicate that cool, dense, and metal-enriched circumgalactic gas is common in the halos of luminous quasars at intermediate redshift. Several of the largest nebulae exhibit morphologies that suggest interaction-related origins. We detect no correlation between the sizes and cosmological dimming corrected surface brightnesses of the nebulae and quasar redshift, luminosity, black hole mass, or radio-loudness, but find a tentative correlation between the nebulae and rest-frame [O II] equivalent width in the quasar spectra. This potential trend suggests a relationship between ISM content and gas reservoirs on CGM scales. The [O II]-emitting nebulae around the $z\approx1$ quasars are smaller and less common than Ly$\alpha$ nebulae around $z\approx3$ quasars. These smaller sizes can be explained if the outer regions of the Ly$\alpha$ halos arise from scattering in more neutral gas, by evolution in the cool CGM content of quasar host halos, by lower-than-expected metallicities on $\gtrsim50$ kpc scales around $z\approx1$ quasars, or by changes in quasar episodic lifetimes between $z=3$ and $1$.Comment: 18 pages, 5 figures, 2 tables. Accepted for publication in the Astrophysical Journa