Unit commitment problem (UCP) is a critical component of power market decision-making. However, its computational complexity necessitates effi-cient solution methods. In this work we propose a framework to accelerate the solving process of the UCP, and the data collecting process for two dis-tinct graph neural network (GNN) policy. We at first train a Neural Initial Commitment Prediction policy to obtain an initial commitment for UCP. Sec-ond, a heuristic process is introduced to restore the feasibility of the initial commitment. Third, get the neighborhood based on the initial prediction then neighborhood search to improve the commitment. At last, we train a Neural neighborhood Prediction policy to predict the neighborhood of the incum-bent commitment at each iteration, continuously optimizing the commitment until the stopping condition is met. This approach produces high-quality ini-tial commitments that can be iteratively refined to meet higher accuracy re-quirements. The experimental results show that the GNN policies trained on the 80-unit system outperform commercial solvers on a 1080-unit system, and LNS performs better than commercial solver on more complex instanc-es.

Current medical image segmentation approaches have limitations in deeply exploring multi-scale information and effectively combining local detail textures with global contextual semantic information. This results in over-segmentation, under-segmentation, and blurred segmentation boundaries. To tackle these challenges, we explore multi-scale feature representations from different perspectives, proposing a novel, lightweight, and multi-scale architecture (LM-Net) that integrates advantages of both Convolutional Neural Networks (CNNs) and Vision Transformers (ViTs) to enhance segmentation accuracy. LM-Net employs a lightweight multi-branch module to capture multi-scale features at the same level. Furthermore, we introduce two modules to concurrently capture local detail textures and global semantics with multi-scale features at different levels: the Local Feature Transformer (LFT) and Global Feature Transformer (GFT). The LFT integrates local window self-attention to capture local detail textures, while the GFT leverages global self-attention to capture global contextual semantics. By combining these modules, our model achieves complementarity between local and global representations, alleviating the problem of blurred segmentation boundaries in medical image segmentation. To evaluate the feasibility of LM-Net, extensive experiments have been conducted on three publicly available datasets with different modalities. Our proposed model achieves state-of-the-art results, surpassing previous methods, while only requiring 4.66G FLOPs and 5.4M parameters. These state-of-the-art results on three datasets with different modalities demonstrate the effectiveness and adaptability of our proposed LM-Net for various medical image segmentation tasks.

This paper investigates the stratification of the discriminant hypersurface associated with a univariate polynomial via the number of its distinct complex roots. We introduce two novel approaches different from the one based on subdiscriminants. The first approach stratifies the discriminant hypersurface by recursively removing all the lowest-order points, while the second one stratifies the discriminant hypersurface by recursively removing all the smooth points. Both approaches rely solely on the discriminant itself instead of using high-order subdiscriminants. These results offer new insights into the intrinsic geometry of the discriminant and its connection to root multiplicity.

We have collected 10025 foreground-background quasar pairs with projected distances d_p<500 kpc from the large quasar catalog of the SDSS DR16Q. We investigate the properties of the Mg II absorption lines with W_r>0.15 Å around foreground quasars, including both the LOS (line-of-sights of foreground quasars) and transverse (TRA, perpendicular to the LOS) absorptions. Both the equivalent width (the correlation coefficient $\rho=-0.915$ and the probability P < 10^{-4} of no correlation) and incident rate ($\rho=-0.964$ and P < 10^{-6}) of TRA \Mgii\ absorption lines are obviously anti-correlated with projected distance. The incident rate of TRA \Mgii\ absorption lines is obviously (>4\sigma) greater than that of LOS \Mgii\ absorption lines at projected distances d_p<200 kpc, while the TRA and LOS \Mgii\ both have similar (<3\sigma) incident rates at scales d_p>200 kpc. The anisotropic radiation from quasars would be the most possible interpretation for the anisotropic absorption around quasars. This could also indicate that the quasar radiation is not obviously impacting the gas halos of quasars at scales d_p>200 kpc.

This paper studies the issues about the generalized inverses of tensors under the C-Product. The aim of this paper is threefold. Firstly, this paper present the definition of the Moore-Penrose inverse, Drazin inverse of tensors under the C-Product. Moreover, the inverse along a tensor is also introduced. Secondly, this paper gives some other expressions of the generalized inverses of tensors by using several decomposition forms of tensors. Finally, the algorithms for the Moore-Penrose inverse, Drazin inverse of tensors and the inverse along a tensor are established.

In this paper, a restricted memory quasi-Newton bundle method for minimizing a locally Lipschitz function over a Riemannian manifold is proposed, which extends the classical one in Euclidean spaces to the manifold setting. The curvature information of the objective function is approximated by applying the Riemannian version of the quasi-Newton updating formulas. The subgradient aggregation technique is used to avoid solving the time-consuming quadratic programming subproblem when calculating the candidate descent direction. Moreover, a new Riemannian line search procedure is proposed to generate the stepsizes, and the process is finitely terminated under a new version of the Riemannian semismooth assumption. Global convergence of the proposed method is established: if the serious iteration steps are finite, then the last serious iterate is stationary; otherwise, every accumulation point of the serious iteration sequence is stationary. Finally, some preliminary numerical results show that the proposed method is efficient.

We study extensions of the GD tensor inverse using the M-product. The aim of current research is threefold. In the first place, the tensor GD inverse under the M-product is introduced and considered. We give the several properties and representations of the GD inverse using the core nilpotent decomposition and then establish the reverse-order law rules for the GD inverse. Second, the tensor GDMP inverse is studied and the corresponding numerical algorithm is given. In addition, the reverse- and forward-order laws of the GDMP inverse are established. Third, the GD-Star tensor inverse under the M-product is introduced and studied. Finally, the GD inverse, GDMP inverse and GD-Star inverse solutions of multilinear equations are investigated. Illustrative numerical calculation is performed.

Aims. We aim to provide an explanation for the PA rotation in GRBs and find the physical conditions that lead to the rotation by 90 degrees in the toroidal magnetic-field (MF) model. Moreover, we present some observable polarization properties in the MF model that can be tested in the future. Results. We find that the PA rotation in the toroidal MF is primarily related to three critical factors: the viewing angle, the jet opening angle, and the jet Lorentz factor. Additionally, the PA can experience flips of 90 degrees twice. The conditions for the flips are $q \gtrsim 0.5$ (except for $q\simeq 1$) and $y_j =(\Gamma \theta_j)^2 \gtrsim 4$. However, the two flips in the PA might not be concurrently observable due to the constraint of flux. Taking these conditions into account and assuming a random orientation between the jet axis and the line of sight (LOS), we obtain a theoretical upper limit (without any constraints) for the observed rate of GRBs in the X-ray or $\gamma$-ray band displaying the flips in PA as $R_{ch} \lesssim 80\%$. We further constrain the observed rate as $R_{ch} \sim 16\%$ according to the maximal post-flip polarized flux level, where the observed rate of single and double flips each account for $\sim 8\%$. It should be noted that the observed rates are different in various wavebands. The observed rate of the second PA flip in the optical bands should be higher than that in the X-ray or $\gamma$-ray band since the flux in the optical band declines much slower than that in the X-ray or $\gamma$-ray band. Moreover, when the LOS is close to the jet edge ($q\to 1$), it is the easiest case in which to observe the 90-degree PA flip due to the relatively high post-flip polarized flux level.

In this paper, we will study the issue about the 1-$\Gamma$ inverse, where $\Gamma\in\{†, D, *\}$, via the M-product. The aim of the current study is threefold. Firstly, the definition and characteristic of the 1-$\Gamma$ inverse is introduced. Equivalent conditions for a tensor to be a 1-$\Gamma$ inverse are established. Secondly, using the singular value decomposition, the corresponding numerical algorithms for computing the 1-$\Gamma$ inverse are given. Finally, the solutions of the multilinear equations related 1-$\Gamma$ inverse are studied, and numerical calculations are given to verify our conclusions.

In this paper, a descent method for nonsmooth multiobjective optimization problems on complete Riemannian manifolds is proposed. The objective functions are only assumed to be locally Lipschitz continuous instead of convexity used in existing methods. A necessary condition for Pareto optimality in Euclidean space is generalized to the Riemannian setting. At every iteration, an acceptable descent direction is obtained by constructing a convex hull of some Riemannian $\varepsilon$-subgradients. And then a Riemannian Armijo-type line search is executed to produce the next iterate. The convergence result is established in the sense that a point satisfying the necessary condition for Pareto optimality can be generated by the algorithm in a finite number of iterations. Finally, some preliminary numerical results are reported, which show that the proposed method is efficient.

In active galactic nuclei, jet-driven feedback plays a significant role in influencing the properties of gas within their host galaxy and the circumgalactic medium. By combining observations from the Very Large Array Sky Survey, the Faint Images of the Radio Sky at Twenty-cm, the LOFAR Two Metre Sky Survey, and the Sloan Digital Sky Survey, we assembled a sample of 3,141 radio-loud quasars, among which 418 exhibit \mgii\ associated absorption lines in their Sloan spectra. We classify these quasars into evolutionary stages based on their radio spectral shapes. Our analysis reveals that evolved quasars exhibit a significantly higher incidence of \mgii\ associated absorption lines compared to younger sources, particularly among quasars with ``non-peaked'' radio spectra, which show an incidence of \mgii\ associated absorbers approximately 1.7 times greater than that of gigahertz-peaked spectrum sources. This observation can be explained effectively by jet-driven feedback. As quasars age, their jets expand and expel substantial amounts of gas from small scales to larger scales, ultimately reaching the circumgalactic medium. The gas expelled from the inner regions and distributed over larger scales results in a greater coverage fraction of absorbing gas. Consequently, evolved quasars exhibit a higher incidence of \mgii\ absorption lines.

Some optically selected quasars exhibit Mg II assoicated absorption lines (AALs), and its origin remains unclear. In this paper, we compile a sample of 1769 quasars, with or without Mg II AALs. Of which 1689 are Far-Infrared (FIR) detected quasars and the rest are not detected in FIR. For the FIR undetected quasars, we obtain stacks for both with and without Mg II AAL quasars. Then we estimate the star formation rates (SFRs) within quasar host galaxies based on their FIR luminosities derived from their FIR greybody components, and find that, although quasars with Mg II AALs have significantly redder median composite spectra than those without Mg II AALs, the SFR distributions of the two types of quasars are statistically indistinguishable. These results do not require an evolutionary link between the quasars with and without Mg II AALs, and would be reconciled if an orientation effect cannot be ignored among the quasars hosting different types of absorption lines.

In this paper, we develop a general mathematical framework for analyzing electostatics within multi-layer metamaterial structures. The multi-layer structure can be designed by nesting complementary negative and regular materials together, and it can be easily achieved by truncating bulk metallic material in a specific configuration. Using layer potentials and symmetrization techniques, we establish the perturbation formula in terms of Neumann-Poincar\'e (NP) operator for general multi-layered medium, and obtain the spectral properties of the NP operator, which demonstrates that the number of plasmon modes increases with the number of layers. Based on Fourier series, we present an exact matrix representation of the NP operator in an apparently unsymmetrical structure, exemplified by multi-layer confocal ellipses. By highly intricate and delicate analysis, we establish a handy algebraic framework for studying the splitting of the plasmon modes within multi-layer structures. Moreover, the asymptotic profiles of the plasmon modes are also obtained. This framework helps reveal the effects of material truncation and rotational symmetry breaking on the splitting of the plasmon modes, thereby inducing desired resonances and enabling the realization of customized applications.

Conventional wisdom in composite optimization suggests augmented Lagrangian dual ascent (ALDA) in Peaceman-Rachford splitting (PRS) methods for dual feasibility. However, ALDA may fail when the primal iterate is a local minimum, a stationary point, or a coordinatewise solution of the highly nonconvex augmented Lagrangian function. Splitting sequential quadratic programming (SQP) methods utilize augmented Lagrangian dual descent (ALDD) to directly minimize the primal residual, circumventing the limitations of ALDA and achieving faster convergence in smooth optimization. This paper aims to present a fairly accessible generalization of two contrasting dual updates, ALDA and ALDD, for smooth composite optimization. A key feature of our PRS-SQP algorithm is its dual ascent-descent procedure, which provides a free direction rule for the dual updates and a new insight to explain the counterintuitive convergence behavior. Furthermore, we incorporate a hybrid acceleration technique that combines inertial extrapolation and back substitution to improve convergence. Theoretically, we establish the feasibility for a wider range of acceleration factors than previously known and derive convergence rates within the Kurdyka- Lojasiewicz framework. Numerical experiments validate the effectiveness and stability of the proposed method in various dual-update scenarios.

In this new era of time-domain and multi-messenger astronomy, various new transients and new phenomena are constantly being discovered thanks to the rapid advances in observations, which provide the excellent opportunity to study the physics in the extreme environments. The enhanced X-ray Timing and Polarimetry mission (eXTP), planned to be launched in 2030, has several key advantages, including advanced polarimetry, high sensitivity & large effective area, and wide energy range coverage, which make it a groundbreaking project in high-energy astrophysics. In this article, we briefly introduce the potential time-domain and multi-messenger targets for eXTP, including gravitational-wave (GW) counterparts, gamma-ray bursts (GRBs), magnetars and fast radio bursts (FRBs), tidal disruption events (TDEs), supernovae, high energy neutrinos and TeV active galactic nucleus (AGNs), and so on. We discuss the advantages of future eXTP observations for detecting these sources, their detection capabilities, the abilities to distinguish theoretical models, and their applications in gravity and cosmology.

We construct a catalogue of stellar masses and ages for 696,680 red giant branch (RGB) stars, 180,436 primary red clump (RC) stars, and 120,907 secondary RC stars selected from the LAMOST\,DR8. The RGBs, primary RCs, and secondary RCs are identified with the large frequency spacing ($\Delta \nu$) and period spacing ($\Delta P$), estimated from the LAMOST spectra with spectral SNRs > 10 by the neural network method supervised with the seismologic information from LAMOST-Kepler sample stars. The purity and completeness of both RGB and RC samples are better than 95\% and 90\%, respectively. The mass and age of RGBs and RCs are determined again with the neural network method by taking the LAMOST-Kepler giant stars as the training set. The typical uncertainties of stellar mass and age are, respectively, 10\% and 30\% for the RGB stellar sample. For RCs, the typical uncertainties of stellar mass and age are 9\% and 24\%, respectively. The RGB and RC stellar samples cover a large volume of the Milky Way (5 < R < 20\,kpc and |Z| <\,5\,kpc), which are valuable data sets for various Galactic studies.

The nnUNet segmentation framework adeptly adjusts most hyperparameters in training scripts automatically, but it overlooks the tuning of internal hyperparameters within the segmentation network itself, which constrains the model's ability to generalize. Addressing this limitation, this study presents a novel Self-Adaptive Convolution Module that dynamically adjusts the size of the convolution kernels depending on the unique fingerprints of different datasets. This adjustment enables the MSA2-Net, when equipped with this module, to proficiently capture both global and local features within the feature maps. Self-Adaptive Convolution Module is strategically integrated into two key components of the MSA2-Net: the Multi-Scale Convolution Bridge and the Multi-Scale Amalgamation Decoder. In the MSConvBridge, the module enhances the ability to refine outputs from various stages of the CSWin Transformer during the skip connections, effectively eliminating redundant data that could potentially impair the decoder's performance. Simultaneously, the MSADecoder, utilizing the module, excels in capturing detailed information of organs varying in size during the decoding phase. This capability ensures that the decoder's output closely reproduces the intricate details within the feature maps, thus yielding highly accurate segmentation images. MSA2-Net, bolstered by this advanced architecture, has demonstrated exceptional performance, achieving Dice coefficient scores of 86.49\%, 92.56\%, 93.37\%, and 92.98\% on the Synapse, ACDC, Kvasir, and Skin Lesion Segmentation (ISIC2017) datasets, respectively. This underscores MSA2-Net's robustness and precision in medical image segmentation tasks across various datasets.

A recent study by Hon et al. reported that a close-in planet around the red clump star, 8 UMi, should have been engulfed during the expansion phase of its parent star's evolution. They explained the survival of this exoplanet through a binary-merger channel for 8 UMi. The key to testing this formation scenario is to derive the true age of this star: is it an old "imposter" resulting from a binary merger, or a genuinely young red clump giant? To accomplish this, we derive kinematic and chemical properties for 8 UMi using astrometric data from {\it Gaia} DR3 and the element-abundance pattern measured from a high-resolution ($R \sim 75,000$) spectrum taken by SOPHIE. Our analysis shows that 8 UMi is a normal thin-disk star with orbital rotation speed of $\it{V}_\mathrm{\phi}=\mathrm{244.96 km s^{-1}}$, and possesses a Solar metallicity ([Fe/H] $= -0.05 \pm 0.07$) and $\alpha$-element abundance ratio ([$\alpha$/Fe] $= +0.01 \pm 0.03$). By adopting well-established relationships between age and space velocities/elemental abundances, we estimate a kinematic age of $3.50^{+3.00}_{-2.00}$ Gyr, and a chemical age of $3.25^{+2.50}_{-1.50}$ Gyr from [C/N] and $3.47 \pm 1.96$ Gyr from [Y/Mg] for 8 UMi, respectively. These estimates are consistent with the isochrone-fitting age ($1.90^{+1.15}_{-0.30}$ Gyr) of 8 UMi, but are all much younger than the timescale required in a binary-merger scenario. This result challenges the binary-merger model; the existence of such a closely orbiting exoplanet around a giant star remains a mystery yet to be resolved.

The classical theory of Kosambi-Cartan-Chern (KCC) developed in differential geometry provides a powerful method for analyzing the behaviors of dynamical systems. In the KCC theory, the properties of a dynamical system are described in terms of five geometrical invariants, of which the second corresponds to the so-called Jacobi stability of the system. Different from that of the Lyapunov stability that has been studied extensively in the literature, the analysis of the Jacobi stability has been investigated more recently using geometrical concepts and tools. It turns out that the existing work on the Jacobi stability analysis remains theoretical and the problem of algorithmic and symbolic treatment of Jacobi stability analysis has yet to be addressed. In this paper, we initiate our study on the problem for a class of ODE systems of arbitrary dimension and propose two algorithmic schemes using symbolic computation to check whether a nonlinear dynamical system may exhibit Jacobi stability. The first scheme, based on the construction of the complex root structure of a characteristic polynomial and on the method of quantifier elimination, is capable of detecting the existence of the Jacobi stability of the given dynamical system. The second algorithmic scheme exploits the method of semi-algebraic system solving and allows one to determine conditions on the parameters for a given dynamical system to have a prescribed number of Jacobi stable fixed points. Several examples are presented to demonstrate the effectiveness of the proposed algorithmic schemes.

In this paper, we propose a quantum clock synchronization (QCS) network scheme with silicon-chip dual-pumped entangled photon source. This scheme couples two pump beams into the silicon-based waveguide, where degenerate and non-degenerate spontaneous four-wave mixing (SFWM) occurs, generating entanglement between one signal channel and three idler channels. The entangled photons are distributed to remote users through the wavelength division multiplexing strategy to construct an entanglement distribution network, and the round-trip QCS is adopted to realize a QCS network that can serve multiple users. A proof-of-principle QCS network experiment is implemented among the server and multiple users (Alice, Bob, and Charlie) for 11.1 hours, where Alice and Charlie are 10 km away from the server and Bob is 25 km away from the server. The lowest time deviations (TDEV) between the server and each user (Alice, Bob, and Charlie) are 1.57 ps, 0.82 ps and 2.57 ps at the average time of 8000 s, 8000 s and 800 s respectively. The results show that the QCS network scheme with dual-pumped SFWM photon source proposed by us achieves high accuracy, and the channel resources used by n users are reduced by about 30% compared with other round-trip QCS schemes.