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In 2018 the EDGES experiment claimed the first detection of the global cosmic 21cm signal, which featured an absorption trough centered around $z \sim 17$ with a depth of approximately -500mK. This amplitude is deeper than the standard prediction (in which the radio background is determined by the cosmic microwave background) by a factor of two and potentially hints at the existence of a radio background excess. While this result was obtained by fitting the data with a phenomenological flattened-Gaussian shape for the cosmological signal, here we develop a physical model for the inhomogeneous radio background sourced by the first galaxies hosting population III stars. Star formation in these galaxies is quenched at lower redshifts due to various feedback mechanisms, so they serve as a natural candidate for the excess radio background hinted by EDGES, without violating present day measurements by ARCADE2. We forward-model the EDGES sky temperature data, jointly sampling our physical model for the cosmic signal, a foreground model, and residual calibration errors. We compare the Bayesian evidences obtained by varying the complexity and prior ranges for the systematics. We find that the data is best explained by a model with seven log-polynomial foreground terms, and that it requires calibration residuals. Interestingly, the presence of a cosmic 21cm signal with a non-standard depth is decisively disfavored. This is contrary to previous EDGES analysis in the context of extra radio background models, serving as a caution against using a ''pseudo-likelihood'' built on a model (flattened Gaussian) that is different from the one being used for inference. We make our simulation code and associated emulator publicly-available., Comment: 17 pages, 9 figures, 1 table, version submitted to A&A

Kolmogorov-Arnold Networks(KANs), as a theoretically efficient neural network architecture, have garnered attention for their potential in capturing complex patterns. However, their application in computer vision remains relatively unexplored. This study first analyzes the potential of KAN in computer vision tasks, evaluating the performance of KAN and its convolutional variants in image classification and semantic segmentation. The focus is placed on examining their characteristics across varying data scales and noise levels. Results indicate that while KAN exhibits stronger fitting capabilities, it is highly sensitive to noise, limiting its robustness. To address this challenge, we propose a smoothness regularization method and introduce a Segment Deactivation technique. Both approaches enhance KAN's stability and generalization, demonstrating its potential in handling complex visual data tasks.

Crop production management is essential for optimizing yield and minimizing a field's environmental impact to crop fields, yet it remains challenging due to the complex and stochastic processes involved. Recently, researchers have turned to machine learning to address these complexities. Specifically, reinforcement learning (RL), a cutting-edge approach designed to learn optimal decision-making strategies through trial and error in dynamic environments, has emerged as a promising tool for developing adaptive crop management policies. RL models aim to optimize long-term rewards by continuously interacting with the environment, making them well-suited for tackling the uncertainties and variability inherent in crop management. Studies have shown that RL can generate crop management policies that compete with, and even outperform, expert-designed policies within simulation-based crop models. In the gym-DSSAT crop model environment, one of the most widely used simulators for crop management, proximal policy optimization (PPO) and deep Q-networks (DQN) have shown promising results. However, these methods have not yet been systematically evaluated under identical conditions. In this study, we evaluated PPO and DQN against static baseline policies across three different RL tasks, fertilization, irrigation, and mixed management, provided by the gym-DSSAT environment. To ensure a fair comparison, we used consistent default parameters, identical reward functions, and the same environment settings. Our results indicate that PPO outperforms DQN in fertilization and irrigation tasks, while DQN excels in the mixed management task. This comparative analysis provides critical insights into the strengths and limitations of each approach, advancing the development of more effective RL-based crop management strategies., Comment: 10 pages

This study introduces the Hybrid Multi-modal VGG (HM-VGG) model, a cutting-edge deep learning approach for the early diagnosis of glaucoma. The HM-VGG model utilizes an attention mechanism to process Visual Field (VF) data, enabling the extraction of key features that are vital for identifying early signs of glaucoma. Despite the common reliance on large annotated datasets, the HM-VGG model excels in scenarios with limited data, achieving remarkable results with small sample sizes. The model's performance is underscored by its high metrics in Precision, Accuracy, and F1-Score, indicating its potential for real-world application in glaucoma detection. The paper also discusses the challenges associated with ophthalmic image analysis, particularly the difficulty of obtaining large volumes of annotated data. It highlights the importance of moving beyond single-modality data, such as VF or Optical Coherence Tomography (OCT) images alone, to a multimodal approach that can provide a richer, more comprehensive dataset. This integration of different data types is shown to significantly enhance diagnostic accuracy. The HM- VGG model offers a promising tool for doctors, streamlining the diagnostic process and improving patient outcomes. Furthermore, its applicability extends to telemedicine and mobile healthcare, making diagnostic services more accessible. The research presented in this paper is a significant step forward in the field of medical image processing and has profound implications for clinical ophthalmology.

This paper proposes a medical literature summary generation method based on the BERT model to address the challenges brought by the current explosion of medical information. By fine-tuning and optimizing the BERT model, we develop an efficient summary generation system that can quickly extract key information from medical literature and generate coherent, accurate summaries. In the experiment, we compared various models, including Seq-Seq, Attention, Transformer, and BERT, and demonstrated that the improved BERT model offers significant advantages in the Rouge and Recall metrics. Furthermore, the results of this study highlight the potential of knowledge distillation techniques to further enhance model performance. The system has demonstrated strong versatility and efficiency in practical applications, offering a reliable tool for the rapid screening and analysis of medical literature.

The Chasing All Transients Constellation Hunters (CATCH) space mission is focused on exploring the dynamic universe via X-ray follow-up observations of various transients. The first pathfinder of the CATCH mission, CATCH-1, was launched on June 22, 2024, alongside the Space-based multiband astronomical Variable Objects Monitor (SVOM) mission. CATCH-1 is equipped with narrow-field optimized Micro Pore Optics (MPOs) featuring a large effective area and incorporates four Silicon Drift Detectors (SDDs) in its focal plane. This paper presents the system calibration results conducted before the satellite integration. Utilizing the data on the performance of the mirror and detectors obtained through the system calibration, combined with simulated data, the ground calibration database can be established. Measuring the relative positions of the mirror and detector system, which were adjusted during system calibration, allows for accurate installation of the entire satellite. Furthermore, the paper outlines the operational workflow of the ground network post-satellite launch.

We study the influence of a rotation on the string tension and the temperature of the confinement-deconfinement transition of gluodynamics by gauge/gravity duality. We explore two distinct approaches, global transformation and local transformation, to introduce rotation and compare the results. It is shown that the string tension extracted from the free energy in the presence of a heavy quarkonium decreases with the increasing angular velocity, while the transition temperature determined by the Polyakov loop increases with increasing angular velocity, which is in line with lattice simulations., Comment: 23 pages, 3 figures

Time cost is a major challenge in achieving high-quality pluralistic image completion. Recently, the Retentive Network (RetNet) in natural language processing offers a novel approach to this problem with its low-cost inference capabilities. Inspired by this, we apply RetNet to the pluralistic image completion task in computer vision. We present RetCompletion, a two-stage framework. In the first stage, we introduce Bi-RetNet, a bidirectional sequence information fusion model that integrates contextual information from images. During inference, we employ a unidirectional pixel-wise update strategy to restore consistent image structures, achieving both high reconstruction quality and fast inference speed. In the second stage, we use a CNN for low-resolution upsampling to enhance texture details. Experiments on ImageNet and CelebA-HQ demonstrate that our inference speed is 10$\times$ faster than ICT and 15$\times$ faster than RePaint. The proposed RetCompletion significantly improves inference speed and delivers strong performance, especially when masks cover large areas of the image.

KIC 10685175 is a roAp star whose polar magnetic field is predicted to be 6 kG through a non-adiabatic axisymmetric pulsation theoretical model. In this work, we aim to measure the magnetic field strength of KIC 10685175 using high-resolution spectropolarimetric observations, and compare it with the one predicted by the theoretical model. From the study of two high-resolution unpolarized spectra, we obtained [$T_{\rm eff}$, $\log g$, [Fe/H], [$\alpha$/Fe], $V_{mic}$]=[8250 $\pm$ 200\,K, 4.4 $\pm$ 0.1, -0.4 $\pm$ 0.2, 0.16 $\pm$ 0.1, 1.73 $\pm$ 0.2\,km~s$^{-1}$]. Although the Fe absorption lines appear relatively weak in comparison to typical Ap stars with similar $T_{\rm eff}$, the lines belonging to rare earth elements (Eu and Nd) are stronger than that in chemically normal stars, indicating the peculiar nature of KIC~10685175. The mean longitudinal magnetic field $\langle B_\ell \rangle=-226\pm39$\,G has been measured in the polarized spectrum, but magnetically split lines were not detected. No significant line profile variability was evident in our spectra. Also the longitudinal magnetic field strengths measured using line masks constructed for different elements have been rather similar. Due to a poor rotation phase coverage of our data, additional spectroscopic and polarimetric observations are needed to allow us to conclude on the inhomogeneous element distribution over the stellar surface. The estimated polar magnetic field is $4.8 \pm 0.8$\,kG, which is consistent with the predicted polar magnetic field strength of about 6\,kG within 3$\sigma$. This work therefore provides support for the pulsation theoretical model.

GRB 230812B, detected by the Gamma-Ray Integrated Detectors (GRID) constellation mission, is an exceptionally bright gamma-ray burst (GRB) with a duration of only 3 seconds. Sitting near the traditional boundary ($\sim$ 2 s) between long and short GRBs, GRB 230812B is notably associated with a supernova (SN), indicating a massive star progenitor. This makes it a rare example of a short-duration GRB resulting from stellar collapse. Our analysis, using a time-evolving synchrotron model, suggests that the burst has an emission radius of approximately $10^{14.5}$~cm. We propose that the short duration of GRB 230812B is due to the combined effects of the central engine's activity time and the time required for the jet to break through the stellar envelope. Our findings provide another case that challenges the conventional view that short-duration GRBs originate exclusively from compact object mergers, demonstrating that a broader range of durations exists for GRBs arising from the collapse of massive stars., Comment: 10 pages, 3 tables, 11 figures

This paper delves into the challenges and advancements in the field of medical image segmentation, particularly focusing on breast cancer diagnosis. The authors propose a novel Transformer-based segmentation model that addresses the limitations of traditional convolutional neural networks (CNNs), such as U-Net, in accurately localizing and segmenting small lesions within breast cancer images. The model introduces an axial attention mechanism to enhance the computational efficiency and address the issue of global contextual information that is often overlooked by CNNs. Additionally, the paper discusses improvements tailored to the small dataset challenge, including the incorporation of relative position information and a gated axial attention mechanism to refine the model's focus on relevant features. The proposed model aims to significantly improve the segmentation accuracy of breast cancer images, offering a more efficient and effective tool for computer-aided diagnosis.

LSMR is a widely recognized method for solving least squares problems via the double QR decomposition. Various preconditioning techniques have been explored to improve its efficiency. One issue that arises when implementing these preconditioning techniques is the need to solve two linear systems per iterative step. In this paper, to tackle this issue, among others, a modified LSMR method (MLSMR), in which only one linear system per iterative step needs to be solved instead of two, is introduced, and then it is integrated with the idea of flexible GMRES to yield a flexible MLSMR method (FMLSMR). Numerical examples are presented to demonstrate the efficiency of the proposed FMLSMR method., Comment: 19 pages, 2 figures

Carnivores interact with herbivores to indirectly impact plant populations, creating trophic cascades within plant-herbivore-carnivore systems. We developed and analyzed a food chain model to gain a mechanistic understanding of the critical roles carnivores play in ecosystems where plants face intense herbivory. Our model incorporates key factors such as seed production rates, seed germination probabilities, local plant interactions, herbivory rates, and carnivore predation rates. In the absence of carnivores, herbivores significantly reduce plant densities, often driving plants to extinction under high herbivory rates. However, the presence of carnivores suppresses herbivore populations, allowing plants to recover from herbivore pressure. We found that plant densities increase with carnivore predation rates, highlighting top-down effects and underscoring the importance of conserving carnivores in ecosystems where plants are at high risk of extinction from herbivory. Our results also show that carnivore density increases with seed-production rates, while herbivore density remains constant, indicating that plants benefit carnivores more than herbivores. This increase in carnivore density driven by high seed-production rates reflects bottom-up effects in the system. Overall, our study demonstrates that plants, herbivores, and carnivores can coexist even under intense predation stress. It suggests that carnivores play a crucial role in regulating plant and herbivore populations, with significant potential for maintaining biodiversity within ecosystems.

In this paper, Pro-HRnet-CNN, an innovative model combining HRNet and void-convolution techniques, is proposed for disease prediction under lung imaging. Through the experimental comparison on the authoritative LIDC-IDRI dataset, we found that compared with the traditional ResNet-50, Pro-HRnet-CNN showed better performance in the feature extraction and recognition of small-size nodules, significantly improving the detection accuracy. Particularly within the domain of detecting smaller targets, the model has exhibited a remarkable enhancement in accuracy, thereby pioneering an innovative avenue for the early identification and prognostication of pulmonary conditions., Comment: 7 pages

In this paper, an image recognition algorithm based on the combination of deep learning and generative adversarial network (GAN) is studied, and compared with traditional image recognition methods. The purpose of this study is to evaluate the advantages and application prospects of deep learning technology, especially GAN, in the field of image recognition. Firstly, this paper reviews the basic principles and techniques of traditional image recognition methods, including the classical algorithms based on feature extraction such as SIFT, HOG and their combination with support vector machine (SVM), random forest, and other classifiers. Then, the working principle, network structure, and unique advantages of GAN in image generation and recognition are introduced. In order to verify the effectiveness of GAN in image recognition, a series of experiments are designed and carried out using multiple public image data sets for training and testing. The experimental results show that compared with traditional methods, GAN has excellent performance in processing complex images, recognition accuracy, and anti-noise ability. Specifically, Gans are better able to capture high-dimensional features and details of images, significantly improving recognition performance. In addition, Gans shows unique advantages in dealing with image noise, partial missing information, and generating high-quality images.

IGR J17091-3624, in addition to GRS 1915+105, is the only black hole X-ray binary that displays ``heartbeat"-like variability characterized by structured flares with high amplitudes. In this study, we conduct a detailed phase-resolved analysis of the recently identified ``heartbeat"-like Class X variability in IGR J17091-3624 during its 2022 outburst, utilizing data from NICER and NuSTAR observations. A shortage in the high-energy (>20 keV) X-ray flux is detected at peak phases of the soft X-ray flare at a ~15 sigma confidence level from the phase-folded light curves. Furthermore, our phase-resolved spectral analysis reveals variations in the spectral shape, particularly showing significant synchronous variations in the disk temperature and flux with the count rate. These findings imply that the flare is primarily driven by instabilities within the accretion disk, consistent with previous studies on the well-known Class rho variability in GRS 1915+105. However, we also observe a positive correlation between the disk temperature and flux over the flare cycle, which differs from a loop relation between the two parameters found in the Class rho variability. This could suggest differences in underlying physical processes between the two variability classes. Variations in the Componization component during flares are also observed: the electron temperature and covering fraction show anti-correlations with the disk flux, revealing potential interactions between the accretion disk and the corona during these flares., Comment: Accepted for publication in The Astrophysical Journal

Low-frequency quasi-periodic oscillations (LFQPOs) are commonly observed in X-ray light curves of black hole X-ray binaries (BHXRBs); however, their origin remains a topic of debate. In order to thoroughly investigate variations in spectral properties on the QPO timescale, we utilized the Hilbert-Huang transform technique to conduct phase-resolved spectroscopy across a broad energy band for LFQPOs in the newly discovered BHXRB Swift J1727.8-1613. This is achieved through quasi-simultaneous observations from Neutron star Interior Composition ExploreR (NICER), Nuclear Spectroscopic Telescope ARray (NuSTAR), and Hard X-ray Modulation Telescope (Insight-HXMT). Our analysis reveals that both the non-thermal and disk-blackbody components exhibit variations on the QPO timescale, with the former dominating the QPO variability. For the spectral parameters, we observe modulation of the disk temperature, spectral indices, and reflection fraction with the QPO phase with high statistical significance (>5\sigma). Notably, the variation in the disk temperature is found to precede the variations in the non-thermal and disk fluxes by ~0.4-0.5 QPO cycles. We suggest that these findings offer further evidence that the type-C QPO variability is a result of geometric effects of the accretion flow., Comment: Accepted for pulication in The Astrophysical Journal

Image-text matching is a key multimodal task that aims to model the semantic association between images and text as a matching relationship. With the advent of the multimedia information age, image, and text data show explosive growth, and how to accurately realize the efficient and accurate semantic correspondence between them has become the core issue of common concern in academia and industry. In this study, we delve into the limitations of current multimodal deep learning models in processing image-text pairing tasks. Therefore, we innovatively design an advanced multimodal deep learning architecture, which combines the high-level abstract representation ability of deep neural networks for visual information with the advantages of natural language processing models for text semantic understanding. By introducing a novel cross-modal attention mechanism and hierarchical feature fusion strategy, the model achieves deep fusion and two-way interaction between image and text feature space. In addition, we also optimize the training objectives and loss functions to ensure that the model can better map the potential association structure between images and text during the learning process. Experiments show that compared with existing image-text matching models, the optimized new model has significantly improved performance on a series of benchmark data sets. In addition, the new model also shows excellent generalization and robustness on large and diverse open scenario datasets and can maintain high matching performance even in the face of previously unseen complex situations., Comment: arXiv admin note: text overlap with arXiv:2405.17460 by other authors

This paper establishes a variant of Stewart's theorem (Theorem~6.4 of Stewart, {\em SIAM Rev.}, 15:727--764, 1973) for the singular subspaces associated with the SVD of a matrix subject to perturbations. Stewart's original version uses both the Frobenius and spectral norms, whereas the new variant uses the spectral norm and any unitarily invariant norm that offer choices per convenience of particular applications and lead to sharper bounds than that straightforwardly derived from Stewart's original theorem with the help of the well-known equivalence inequalities between matrix norms. Of interest in their own right, bounds on the solution to two couple Sylvester equations are established for a few different circumstances.

Model reduction is a powerful tool in dealing with numerical simulation of large scale dynamic systems for studying complex physical systems. Two major types of model reduction methods for linear time-invariant dynamic systems are Krylov subspace-based methods and balanced truncation-based methods. The methods of the second type are much more theoretically sound than the first type in that there is a fairly tight global error bound on the approximation error between the original system and the reduced one. It is noted that the error bound is established based upon the availability of the exact controllability and observability Gramians. However, numerically, the Gramians are not available and have to be numerically calculated, and for a large scale system, a viable option is to compute low-rank approximations of the Gramians from which an approximate balanced truncation is then performed. Hence, rigorously speaking, the existing global error bound is not applicable to any reduced system obtained via approximate Gramians. The goal of this paper is to address this issue by establishing global error bounds for reduced systems via approximate balanced truncation., Comment: 35 pages

Optimal transport has been an essential tool for reconstructing dynamics from complex data. With the increasingly available multifaceted data, a system can often be characterized across multiple spaces. Therefore, it is crucial to maintain coherence in the dynamics across these diverse spaces. To address this challenge, we introduce Synchronized Optimal Transport (SyncOT), a novel approach to jointly model dynamics that represent the same system through multiple spaces. With given correspondence between the spaces, SyncOT minimizes the aggregated cost of the dynamics induced across all considered spaces. The problem is discretized into a finite-dimensional convex problem using a staggered grid. Primal-dual algorithm-based approaches are then developed to solve the discretized problem. Various numerical experiments demonstrate the capabilities and properties of SyncOT and validate the effectiveness of the proposed algorithms.

Underdetermined generalized absolute value equations (GAVE) has real applications. The underdetermined GAVE may have no solution, one solution, finitely multiple solutions or infinitely many solutions. This paper aims to give some sufficient conditions which guarantee the existence or nonexistence of solutions for the underdetermined GAVE. Particularly, sufficient conditions under which certain or each sign pattern possesses infinitely many solutions of the underdetermined GAVE are given. In addition, iterative methods are developed to solve a solution of the underdetermined GAVE. Some existing results about the square GAVE are extended., Comment: 27 pages

Utilizing NICER observations, we present an analysis of the soft X-ray re-brightening event of GRS 1915+105 observed in 2021. During this event, we observed the emergence of a stable, long-lasting low-frequency quasi-periodic oscillation (LFQPO) with frequencies ranging from 0.17 to 0.21 Hz. Through a careful spectral analysis, we demonstrate that a low-temperature Compton-thick gas model well characterizes the emitted radiation. By examining the spectrum and identifying numerous absorption lines, we discerned a transition in the wind properties. This transition was marked by a shift from a state characterized by low speed, high column density, and high ionization degree to one featuring still low speed but low column density and ionization degree. Intriguingly, the presence or absence of the QPO signal is perfectly correlated with these distinct wind characteristics. The low-speed wind observed could be indicative of a 'failed wind', while the observed shift implies a transition from a magnetically to a thermally driven wind. Notably, this QPO signal exclusively manifested itself during the magnetically driven phase, suggesting the possibility of a novel perturbation associated with magnetic effects.

Stellar flares are critical phenomena on stellar surfaces, which are closely tied to stellar magnetism. While extensively studied in main-sequence (MS) stars, their occurrence in evolved compact stars, specifically hot subdwarfs and white dwarfs (WDs), remains scarcely explored. Based on Cycles 1-5 of TESS photometry, we conducted a pioneering survey of flare events in $\sim12,000$ compact stars, corresponding to $\sim38,000$ light curves with 2-minute cadence. Through dedicated techniques for detrending light curves, identifying preliminary flare candidates, and validating them via machine learning, we established a catalog of 1016 flares from 193 compact stars, including 182 from 58 sdB/sdO stars and 834 from 135 WDs, respectively. However, all flaring compact stars showed signs of contamination from nearby objects or companion stars, preventing sole attribution of the detected flares. For WDs, it is highly probable that the flares originated from their cool MS companions. In contrast, the higher luminosities of sdB/sdO stars diminish companion contributions, suggesting that detected flares originated from sdB/sdO stars themselves or through close magnetic interactions with companions. Focusing on a refined sample of 23 flares from 13 sdB/sdO stars, we found their flare frequency distributions were slightly divergent from those of cool MS stars; instead, they resemble those of hot B/A-type MS stars having radiative envelopes. This similarity implies the flares on sdB/sdO stars, if these flares did originate from them, may share underlying mechanisms with hot MS stars, which warrants further investigation., Comment: 25 pages, 11 figures, 5 tables, accepted for publication in ApJS

The Chasing All Transients Constellation Hunters (CATCH) space mission is an intelligent constellation consisting of 126 micro-satellites in three types (A, B, and C), designed for X-ray observation with the objective of studying the dynamic universe. Currently, we are actively developing the first Pathfinder (CATCH-1) for the CATCH mission, specifically for type-A satellites. CATCH-1 is equipped with Micro Pore Optics (MPO) and a 4-pixel Silicon Drift Detector (SDD) array. To assess its scientific performance, including the effective area of the optical system, on-orbit background, and telescope sensitivity, we employ the Monte Carlo software Geant4 for simulation in this study. The MPO optics exhibit an effective area of $41$ cm$^2$ at the focal spot for 1 keV X-rays, while the entire telescope system achieves an effective area of $29$ cm$^2$ at 1 keV when taking into account the SDD detector's detection efficiency. The primary contribution to the background is found to be from the Cosmic X-ray Background. Assuming a 625 km orbit with an inclination of $29^\circ$, the total background for CATCH-1 is estimated to be $8.13\times10^{-2}$ counts s$^{-1}$ in the energy range of 0.5--4 keV. Based on the background within the central detector and assuming a Crab-like source spectrum, the estimated ideal sensitivity could achieve $1.9\times10^{-12}$ erg cm$^{-2}$ s$^{-1}$ for an exposure of 10$^4$ s in the energy band of 0.5--4 keV. Furthermore, after simulating the background caused by low-energy charged particles near the geomagnetic equator, we have determined that there is no need to install a magnetic deflector.

We are concerned with efficient numerical methods for stochastic continuous-time algebraic Riccati equations (SCARE). Such equations frequently arise from the state-dependent Riccati equation approach which is perhaps the only systematic way today to study nonlinear control problems. Often involved Riccati-type equations are of small scale, but have to be solved repeatedly in real time. Important applications include the 3D missile/target engagement, the F16 aircraft flight control, and the quadrotor optimal control, to name a few. A new inner-outer iterative method that combines the fixed-point strategy and the structure-preserving doubling algorithm (SDA) is proposed. It is proved that the method is monotonically convergent, and in particular, taking the zero matrix as initial, the method converges to the desired stabilizing solution. Previously, Newton's method has been called to solve SCARE, but it was mostly investigated from its theoretic aspect than numerical aspect in terms of robust and efficient numerical implementation. For that reason, we revisit Newton's method for SCARE, focusing on how to calculate each Newton iterative step efficiently so that Newton's method for SCARE can become practical. It is proposed to use our new inner-outer iterative method, which is provably convergent, to provide critical initial starting points for Newton's method to ensure its convergence. Finally several numerical experiments are conducted to validate the new method and robust implementation of Newton's method.

In this paper, the problem of joint user scheduling and computing resource allocation in asynchronous mobile edge computing (MEC) networks is studied. In such networks, edge devices will offload their computational tasks to an MEC server, using the energy they harvest from this server. To get their tasks processed on time using the harvested energy, edge devices will strategically schedule their task offloading, and compete for the computational resource at the MEC server. Then, the MEC server will execute these tasks asynchronously based on the arrival of the tasks. This joint user scheduling, time and computation resource allocation problem is posed as an optimization framework whose goal is to find the optimal scheduling and allocation strategy that minimizes the energy consumption of these mobile computing tasks. To solve this mixed-integer non-linear programming problem, the general benders decomposition method is adopted which decomposes the original problem into a primal problem and a master problem. Specifically, the primal problem is related to computation resource and time slot allocation, of which the optimal closed-form solution is obtained. The master problem regarding discrete user scheduling variables is constructed by adding optimality cuts or feasibility cuts according to whether the primal problem is feasible, which is a standard mixed-integer linear programming problem and can be efficiently solved. By iteratively solving the primal problem and master problem, the optimal scheduling and resource allocation scheme is obtained. Simulation results demonstrate that the proposed asynchronous computing framework reduces 87.17% energy consumption compared with conventional synchronous computing counterpart.

We introduce the supervised Gromov-Wasserstein (sGW) optimal transport, an extension of Gromov-Wasserstein by incorporating potential infinity patterns in the cost tensor. sGW enables the enforcement of application-induced constraints such as the preservation of pairwise distances by implementing the constraints as an infinity pattern. A numerical solver is proposed for the sGW problem and the effectiveness is demonstrated in various numerical experiments. The high-order constraints in sGW are transferred to constraints on the coupling matrix by solving a minimal vertex cover problem. The transformed problem is solved by the Mirror-C descent iteration coupled with the supervised optimal transport solver. In the numerical experiments, we first validate the proposed framework by applying it to matching synthetic datasets and investigating the impact of the model parameters. Additionally, we successfully apply sGW to real single-cell RNA sequencing data. Through comparisons with other Gromov-Wasserstein variants on real data, we demonstrate that sGW offers the novel utility of controlling distance preservation, leading to the automatic estimation of overlapping portions of datasets, which brings improved stability and flexibility in data-driven applications.

The energy released from dark matter annihilation leads to additional ionization and heating of the intergalactic gas and thereby impact the hydrogen 21-cm signal during the cosmic dawn. The dark matter annihilation rate scales as density-squared and it becomes inhomogeneously boosted along with structure formation. This paper examines the inhomogeneity in DM annihilation rate induced by the growth of DM halo structures, and we show that this effect can significantly enhance the spatial fluctuations in gas temperature, gas ionization fraction and consequently the 21-cm brightness temperature. Compared to previous homogeneous calculations, inhomogeneous dark matter annihilation can enhance the 21-cm power spectrum by orders of magnitude across the scales of $k \in [0.05, 3]\ {\rm{Mpc^{-1}}}$. For a DM annihilation rate of $\left<\sigma v\right>/m_\chi \sim 10^{-27} {\rm cm^3 s^{-1} GeV^{-1}}$, the corresponding signatures in the 21-cm power spectrum signal can be detected by upcoming radio observatories such as the SKA., Comment: 8 pages, 3 figures