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This paper presents both a priori and a posteriori error analyses for a really pressure-robust virtual element method to approximate the incompressible Brinkman problem. We construct a divergence-preserving reconstruction operator using the Raviart-Thomas element for the discretization on the right-hand side. The optimal priori error estimates are carried out, which imply the velocity error in the energy norm is independent of both the continuous pressure and the viscosity. Taking advantage of the virtual element method's ability to handle more general polygonal meshes, we implement effective mesh refinement strategies and develop a residual-type a posteriori error estimator. This estimator is proven to provide global upper and local lower bounds for the discretization error. Finally, some numerical experiments demonstrate the robustness, accuracy, reliability and efficiency of the method.

Carbon- and Oxygen-rich stars populating the Thermally-Pulsing Asymptotic Giant Branch (TP-AGB) phase of stellar evolution are relevant contributors to the spectra of ~1 Gyr old populations. Atmosphere models for these types are uncertain, due to complex molecules and mass-loss effects. Empirical spectra are then crucial, but samples are small due to the short (~3 Myr) TP-AGB lifetime. Here we exploit the vastness of the MaNGA Stellar library MaStar (~60,000 spectra) to identify C,O-rich type stars. We define an optical colour selection with cuts of (g-r)>2 and (g-i)<1.55(g-r)-0.07, calibrated with known C- and O- rich spectra. This identifies C-,O-rich stars along clean, separated sequences. An analogue selection is found in V,R,I bands. Our equation identifies C- and O-rich spectra with predictive performance metric F1-scores of 0.72 and 0.74 (over 1), respectively. We finally identify 41 C- and 87 O-rich type AGB stars in MaStar, 5 and 49 of which do not have a SIMBAD counterpart. We also detect a sample of non-AGB, dwarf C-stars. We further design a fitting procedure to classify the spectra into broad spectral types, by using as fitting templates empirical C and O-rich spectra. We find remarkably good fits for the majority of candidates and categorise them into C- and O-rich bins following existing classifications, which correlate to effective temperature. Our selection models can be applied to large photometric surveys (e.g. Euclid, Rubin). The classified spectra will facilitate future evolutionary population synthesis models., Comment: 16 pages, 13 figures, MNRAS in press

Covert communication's effectiveness critically depends on precise channel state information (CSI). This paper investigates the impact of imperfect CSI on achievable covert communication performance in a two-hop relay system. Firstly, we introduce a two-hop covert transmission scheme utilizing channel inversion power control (CIPC) to manage opportunistic interference, eliminating the receiver's self-interference. Given that CSI estimation error (CEE) and feedback delay (FD) are the two primary factors leading to imperfect CSI, we construct a comprehensive theoretical model to accurately characterize their effects on CSI quality. With the aid of this model, we then derive closed-form solutions for detection error probability (DEP) and covert rate (CR), establishing an analytical framework to delineate the inherent relationship between CEE, FD, and covert performance. Furthermore, to mitigate the adverse effects of imperfect CSI on achievable covert performance, we investigate the joint optimization of channel inversion power and data symbol length to maximize CR under DEP constraints and propose an iterative alternating algorithm to solve the bi-dimensional non-convex optimization problem. Finally, extensive experimental results validate our theoretical framework and illustrate the impact of imperfect CSI on achievable covert performance.

Transforming a sentence into a two-dimensional (2D) representation (e.g., the table filling) has the ability to unfold a semantic plane, where an element of the plane is a word-pair representation of a sentence which may denote a possible relation representation composed of two named entities. The 2D representation is effective in resolving overlapped relation instances. However, in related works, the representation is directly transformed from a raw input. It is weak to utilize prior knowledge, which is important to support the relation extraction task. In this paper, we propose a two-dimensional feature engineering method in the 2D sentence representation for relation extraction. Our proposed method is evaluated on three public datasets (ACE05 Chinese, ACE05 English, and SanWen) and achieves the state-of-the-art performance. The results indicate that two-dimensional feature engineering can take advantage of a two-dimensional sentence representation and make full use of prior knowledge in traditional feature engineering. Our code is publicly available at https://github.com/Wang-ck123/A-Two-Dimensional-Feature-Engineering-Method-for-Entity-Relation-Extraction

Current methods to extract relational triples directly make a prediction based on a possible entity pair in a raw sentence without depending on entity recognition. The task suffers from a serious semantic overlapping problem, in which several relation triples may share one or two entities in a sentence. In this paper, based on a two-dimensional sentence representation, a bi-consolidating model is proposed to address this problem by simultaneously reinforcing the local and global semantic features relevant to a relation triple. This model consists of a local consolidation component and a global consolidation component. The first component uses a pixel difference convolution to enhance semantic information of a possible triple representation from adjacent regions and mitigate noise in neighbouring neighbours. The second component strengthens the triple representation based a channel attention and a spatial attention, which has the advantage to learn remote semantic dependencies in a sentence. They are helpful to improve the performance of both entity identification and relation type classification in relation triple extraction. After evaluated on several publish datasets, the bi-consolidating model achieves competitive performance. Analytical experiments demonstrate the effectiveness of our model for relational triple extraction and give motivation for other natural language processing tasks.

Deep learning models have shown promising performance for cell nucleus segmentation in the field of pathology image analysis. However, training a robust model from multiple domains remains a great challenge for cell nucleus segmentation. Additionally, the shortcomings of background noise, highly overlapping between cell nucleus, and blurred edges often lead to poor performance. To address these challenges, we propose a novel framework termed CausalCellSegmenter, which combines Causal Inference Module (CIM) with Diversified Aggregation Convolution (DAC) techniques. The DAC module is designed which incorporates diverse downsampling features through a simple, parameter-free attention module (SimAM), aiming to overcome the problems of false-positive identification and edge blurring. Furthermore, we introduce CIM to leverage sample weighting by directly removing the spurious correlations between features for every input sample and concentrating more on the correlation between features and labels. Extensive experiments on the MoNuSeg-2018 dataset achieves promising results, outperforming other state-of-the-art methods, where the mIoU and DSC scores growing by 3.6% and 2.65%., Comment: 10 pages, 5 figures, 2 tables, MICCAI

The iMaNGA project uses a forward-modelling approach to compare the predictions of cosmological simulations with observations from SDSS-IV/MaNGA. We investigate the dependency of age and metallicity radial gradients on galaxy morphology, stellar mass, stellar surface mass density ($\Sigma_*$), and environment. The key of our analysis is that observational biases affecting the interpretation of MaNGA data are emulated in the theoretical iMaNGA sample. The simulations reproduce the observed global stellar population scaling relations with positive correlations between galaxy mass and age/metallicity quite well and also produce younger stellar populations in late-type in agreement with observations. We do find interesting discrepancies, though, that can inform the physics and further development of the simulations. Ages of spiral galaxies and low-mass ellipticals are overestimated by about 2-4 Gyr. Radial metallicity gradients are steeper in iMaNGA than in MaNGA, a discrepancy most prominent in spiral and lenticular galaxies. Also, the observed steepening of metallicity gradients with increasing galaxy mass is not well matched by the simulations. We find that the theoretical radial profiles of surface mass density $\Sigma_*$ are steeper than in observations except for the most massive galaxies. In both MaNGA and iMaNGA [Z/H] correlates with $\Sigma_*$, however, the simulations systematically predict lower [Z/H] by almost a factor of 2 at any $\Sigma_*$. Most interestingly, for galaxies with stellar mass $\log M_*\leq 10.80 M_\odot$ the MaNGA data reveal a positive correlation between galaxy radius and [Z/H] at fixed $\Sigma_*$, which is not recovered in iMaNGA. Finally, the dependence on environmental density is negligible in both the theoretical iMaNGA and the observed MaNGA data.

Motivated by the recent work of Gimperlein and Goffeng on Calder\'on's commutator on compact Heisenberg type manifolds and the related weak Schatten class estimates, we establish the characterisation of $L^p$ boundedness for Calderon's commutator on stratified Lie groups. We further study related weak Schatten class estimates for second order commutators on two step stratified Lie groups, which include the Heisenberg groups. This latter result is obtained using double operator integral techniques which are novel in this area., Comment: simplified the proof

In this paper, a temporal nonuniform $L1$ type difference scheme is built up for the time fractional diffusion-wave equation with the help of the order reduction technique. The unconditional convergence of the nonuniform difference scheme is proved rigorously in $L^2$ norm. Our main tool is the discrete complementary convolution kernels with respect to the coefficient kernels of the L1 type formula. The positive definiteness of the complementary convolution kernels is shown to be vital to the stability and convergence. To the best of our knowledge, this property is proved at the first time on the nonuniform time meshes. Two numerical experiments are presented to verify the accuracy and the efficiency of the proposed numerical methods.

Strengthening the synergy between simulations and observations is essential to test galaxy formation and evolution theories. To achieve this goal, in the first paper of this series, we presented a method to generate mock SDSS-IV/MaNGA integral-field spectroscopic galaxy observations from cosmological simulations. In this second paper, we build the iMaNGA catalogue consisting of $\sim$1,000 unique galaxies from the TNG50 cosmological simulations, selected to mimic the SDSS-IV/MaNGA-Primary sample selection. Here we present and discuss the iMaNGA sample and its comparison to the MaNGA Primary catalogue. The iMaNGA sample well recovers the MaNGA-Primary sample in terms of stellar mass vs angular size relation and spatial resolution. The S\'ersic index vs angular size relation, instead, is not reproduced well by the simulations, mostly because of a paucity of high-mass elliptical galaxies in TNG50. We also investigate our ability to recover the galaxy kinematics and stellar population properties with full-spectral fitting. We demonstrate that 'intrinsic' and `recovered' stellar kinematics, stellar ages and metallicities are consistent, with residuals compatible with zero within 1$-{\sigma}$. Also`intrinsic' and `recovered' star formation histories display a great resemblance. We conclude that our mock generation and spectral fitting processes do not distort the `intrinsic' galaxy properties. Therefore, in the third paper of this series, we can meaningfully test the cosmological simulations, comparing the stellar population properties and kinematics of the iMaNGA mock galaxies and the MaNGA observational results., Comment: Published on MNRAS: 03 May 2023 https://doi.org/10.1093/mnras/stad1337

We present a stellar parameter catalog built to accompany the MaStar Stellar Library, which is a comprehensive collection of empirical, medium-resolution stellar spectra. We constructed this parameter catalog by using a multicomponent $\chi^{2}$ fitting approach to match MaStar spectra to models generated by interpolating the ATLAS9-based BOSZ model spectra. The total $\chi^{2}$ for a given model is defined as the sum of components constructed to characterize narrow-band features of observed spectra (e.g., absorption lines) and the broadband continuum shape separately. Extinction and systematics due to flux calibration were taken into account in the fitting. The $\chi^{2}$ distribution for a given region of model space was sampled using a Markov Chain Monte Carlo (MCMC) algorithm, the data from which were then used to extract atmospheric parameter estimates ($T_{eff}$, log g, [Fe/H], and [$\alpha$/Fe]), their corresponding uncertainties, and direct extinction measurements. Two methods were used to extract parameters and uncertainties: one that accepts the MCMC's prescribed minimum-$\chi^{2}$ result, and one that uses Bayesian inference to compute a likelihood-weighted mean from the $\chi^{2}$ distribution sampled by the MCMC. Results were evaluated for internal consistency using repeat observations where available and by comparing them with external data sets (e.g., APOGEE-2 and Gaia DR2). Our spectral-fitting exercise reveals possible deficiencies in current theoretical model spectra, illustrating the potential power of MaStar spectra for helping to improve the models. This paper represents an update to the parameters that were originally presented with SDSS-IV DR17. The MaStar parameter catalog containing our BestFit results is available on the SDSS-IV DR17 website as part of version 2 of the MaStar stellar parameter value-added catalog., Comment: 22 pages, 21 figures. A&A in press

The convergence of variable-step L1 scheme is studied for the time-fractional molecular beam epitaxy (MBE) model with slope selection.A novel asymptotically compatible $L^2$ norm error estimate of the variable-step L1 scheme is established under a convergence-solvability-stability (CSS)-consistent time-step constraint. The CSS-consistent condition means that the maximum step-size limit required for convergence is of the same order to that for solvability and stability (in certain norms) as the small interface parameter $\epsilon\rightarrow 0^+$. To the best of our knowledge, it is the first time to establish such error estimate for nonlinear subdiffusion problems. The asymptotically compatible convergence means that the error estimate is compatible with that of backward Euler scheme for the classical MBE model as the fractional order $\alpha\rightarrow 1^-$. Just as the backward Euler scheme can maintain the physical properties of the MBE equation, the variable-step L1 scheme can also preserve the corresponding properties of the time-fractional MBE model, including the volume conservation, variational energy dissipation law and $L^2$ norm boundedness. Numerical experiments are presented to support our theoretical results., Comment: 23 pages,21 figures,4 tables