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We survey quadratic Hessian equations: definition, background, rigidity of entire solutions, regularity of viscosity solutions, a priori Hessian estimates, and open problems.

This manuscript presents a comparative analysis of two software packages, MC X-ray and PENELOPE, focusing on their accuracy and efficiency in simulating k-ratios for binary compounds and comparing their spectra with experimental data for pure elements and compounds. Based on the Pouchou database, MC X-ray slightly outperforms PENELOPE in k-ratio calculations, achieving a root mean square error (RMSE) of 2.71\% compared to 2.87\%. Discrepancies between the two programs emerge at lower beam energies (3 keV and 5 keV) when comparing simulated spectra with experimental data; however, at higher energies (20 keV and 30 keV), both software packages exhibit consistent and reliable performance across a range of atomic numbers. While both tools are effective for analyzing homogeneous bulk samples, MC X-ray offers significant advantages in processing speed and user-friendliness. This study underscores the strengths and limitations of each package, providing valuable insights for researchers engaged in X-ray simulation and microanalysis., Comment: 11pages,16figures

Large Language Models (LLMs) have shown remarkable capabilities in various natural language processing tasks. However, LLMs may rely on dataset biases as shortcuts for prediction, which can significantly impair their robustness and generalization capabilities. This paper presents Shortcut Suite, a comprehensive test suite designed to evaluate the impact of shortcuts on LLMs' performance, incorporating six shortcut types, five evaluation metrics, and four prompting strategies. Our extensive experiments yield several key findings: 1) LLMs demonstrate varying reliance on shortcuts for downstream tasks, significantly impairing their performance. 2) Larger LLMs are more likely to utilize shortcuts under zero-shot and few-shot in-context learning prompts. 3) Chain-of-thought prompting notably reduces shortcut reliance and outperforms other prompting strategies, while few-shot prompts generally underperform compared to zero-shot prompts. 4) LLMs often exhibit overconfidence in their predictions, especially when dealing with datasets that contain shortcuts. 5) LLMs generally have a lower explanation quality in shortcut-laden datasets, with errors falling into three types: distraction, disguised comprehension, and logical fallacy. Our findings offer new insights for evaluating robustness and generalization in LLMs and suggest potential directions for mitigating the reliance on shortcuts. The code is available at \url {https://github.com/yyhappier/ShortcutSuite.git}.

In recent years, with rising consumer demand, fresh products have gained increasing attention, leading to rapid growth in the fresh food market. However, due to their perishable nature and sensitivity to storage conditions, fresh products are vulnerable to damage during transportation. Improper handling, excessive transit times, and physical impacts can result in significant losses. As a result, enhancing the efficiency of fresh product distribution while maintaining quality has become critical to the further development of the fresh food industry. Using Y chain supermarket as a case study, this paper investigates the logistics of fresh product distribution, identifying current challenges and inefficiencies. Through literature review, expert interviews, and comparative analysis, the study offers strategic recommendations for optimizing fresh product delivery routes to improve distribution efficiency and product quality., Comment: It optimizes fresh product delivery routes to improve distribution efficiency and product quality

High dynamic range (HDR) capture and display have seen significant growth in popularity driven by the advancements in technology and increasing consumer demand for superior image quality. As a result, HDR image compression is crucial to fully realize the benefits of HDR imaging without suffering from large file sizes and inefficient data handling. Conventionally, this is achieved by introducing a residual/gain map as additional metadata to bridge the gap between HDR and low dynamic range (LDR) images, making the former compatible with LDR image codecs but offering suboptimal rate-distortion performance. In this work, we initiate efforts towards end-to-end optimized HDR image compression for perceptually optimal storage and display. Specifically, we learn to compress an HDR image into two bitstreams: one for generating an LDR image to ensure compatibility with legacy LDR displays, and another as side information to aid HDR image reconstruction from the output LDR image. To measure the perceptual quality of output HDR and LDR images, we use two recently proposed image distortion metrics, both validated against human perceptual data of image quality and with reference to the uncompressed HDR image. Through end-to-end optimization for rate-distortion performance, our method dramatically improves HDR and LDR image quality at all bit rates.

Due to the fascinating generative performance of text-to-image diffusion models, growing text-to-3D generation works explore distilling the 2D generative priors into 3D, using the score distillation sampling (SDS) loss, to bypass the data scarcity problem. The existing text-to-3D methods have achieved promising results in realism and 3D consistency, but text-to-4D generation still faces challenges, including lack of realism and insufficient dynamic motions. In this paper, we propose a novel method for text-to-4D generation, which ensures the dynamic amplitude and authenticity through direct supervision provided by a video prior. Specifically, we adopt a text-to-video diffusion model to generate a reference video and divide 4D generation into two stages: static generation and dynamic generation. The static 3D generation is achieved under the guidance of the input text and the first frame of the reference video, while in the dynamic generation stage, we introduce a customized SDS loss to ensure multi-view consistency, a video-based SDS loss to improve temporal consistency, and most importantly, direct priors from the reference video to ensure the quality of geometry and texture. Moreover, we design a prior-switching training strategy to avoid conflicts between different priors and fully leverage the benefits of each prior. In addition, to enrich the generated motion, we further introduce a dynamic modeling representation composed of a deformation network and a topology network, which ensures dynamic continuity while modeling topological changes. Our method not only supports text-to-4D generation but also enables 4D generation from monocular videos. The comparison experiments demonstrate the superiority of our method compared to existing methods.

We demonstrate a CMOS-foundry-fabricated piezo-optomechanical photonic integrated circuit platform for ultraviolet and blue wavelengths, using alumina waveguides that are strongly mechanically coupled to monolithically integrated aluminum nitride piezoelectric actuators. Low waveguide losses are measured down to at least 320 nm, where we achieve 1.6 dB/cm. This allows us to demonstrate broadband amplitude modulators based on piezoelectrically actuated MEMS cantilever phase-shifters down to 320 nm, with a high extinction ratio of 30 dB. We further demonstrate the versatility of the platform by designing and demonstrating a modulator that can work with high extinction and low loss at 320 nm and 420 nm, simultaneously, demonstrating control of multiple, disparate wavelengths in one device. We also demonstrate narrow-band resonant racetrack modulators with quality factors of 4.7E5 and a tuning rate of 27.5 MHz/V. These results should open doors for a range of novel applications in UV photonics, quantum science, sensing and spectroscopy.

The China Space Station Telescope (CSST) is a two-meter space telescope with multiple back-end instruments. The Fine Guidance Sensor (FGS) is an essential subsystem of the CSST Precision Image Stability System to ensure the required absolute pointing accuracy and line-of-sight stabilization. In this study, we construct the Main Guide Star Catalog for FGS. To accomplish this, we utilize the information about the FGS and object information from the Gaia Data Release 3. We provide an FGS instrument magnitude and exclude variables, binaries, and high proper motion stars from the catalog to ensure uniform FGS guidance capabilities. Subsequently, we generate a HEALPix index, which provides a hierarchical tessellation of the celestial sphere, and employ the Voronoi algorithm to achieve a homogeneous distribution of stars across the catalog. This distribution ensures adequate coverage and sampling of the sky. The performance of the CSST guide star catalog was assessed by simulating the field of view of the FGS according to the CSST mock survey strategy catalog. The analysis of the results indicates that this catalog provides adequate coverage and accuracy. The catalog's performance meets the FGS requirements, ensuring the functioning of the FGS and its guidance capabilities., Comment: published on RAA

Constant rank theorems are obtained for saddle solutions to the special Lagrangian equation and the quadratic Hessian equation. The argument also leads to Liouville type results for the special Lagrangian equation with subcritical phase, matching the known rigidity results for semiconvex entire solutions to the quadratic Hessian equation.

Leakage out of the computational subspace is a major limitation of current state-of-the-art neutral-atom quantum computers and a significant challenge for scalable systems. In a quantum processor with cesium atoms, we demonstrate proof-of-principle circuit-based conversion of leakage errors to erasure errors via Leakage Detection Units (LDUs), which non-destructively map information about the presence or absence of the qubit onto the state of an ancilla. With a standard LDU circuit, we successfully convert leakage errors to erasure errors for all major leakage pathways while preserving the quantum information in the case that no leakage occurred. We benchmark the performance of the LDU using a three-outcome low-loss state detection method and also explore the advantages of three-outcome measurements for LDUs. We find that the LDU detects atom-loss errors with ~93.4% accuracy, limited by technical imperfections of our apparatus. We further compile and execute a SWAP LDU, wherein the roles of the original data atom and ancilla atom are exchanged under the action of the LDU, providing 'free refilling' of atoms in the case of leakage errors. This circuit-based leakage-to-erasure error conversion is a critical component of a neutral-atom quantum processor where the quantum information may significantly outlive the lifetime of any individual atom in the quantum register.

As XR technology continues to advance rapidly, 3D generation and editing are increasingly crucial. Among these, stylization plays a key role in enhancing the appearance of 3D models. By utilizing stylization, users can achieve consistent artistic effects in 3D editing using a single reference style image, making it a user-friendly editing method. However, recent NeRF-based 3D stylization methods encounter efficiency issues that impact the user experience, and their implicit nature limits their ability to accurately transfer geometric pattern styles. Additionally, the ability for artists to apply flexible control over stylized scenes is considered highly desirable to foster an environment conducive to creative exploration. To address the above issues, we introduce StylizedGS, an efficient 3D neural style transfer framework with adaptable control over perceptual factors based on 3D Gaussian Splatting (3DGS) representation. We propose a filter-based refinement to eliminate floaters that affect the stylization effects in the scene reconstruction process. The nearest neighbor-based style loss is introduced to achieve stylization by fine-tuning the geometry and color parameters of 3DGS, while a depth preservation loss with other regularizations is proposed to prevent the tampering of geometry content. Moreover, facilitated by specially designed losses, StylizedGS enables users to control color, stylized scale, and regions during the stylization to possess customization capabilities. Our method achieves high-quality stylization results characterized by faithful brushstrokes and geometric consistency with flexible controls. Extensive experiments across various scenes and styles demonstrate the effectiveness and efficiency of our method concerning both stylization quality and inference speed.

The emergence of 3D Gaussian Splatting (3DGS) has greatly accelerated the rendering speed of novel view synthesis. Unlike neural implicit representations like Neural Radiance Fields (NeRF) that represent a 3D scene with position and viewpoint-conditioned neural networks, 3D Gaussian Splatting utilizes a set of Gaussian ellipsoids to model the scene so that efficient rendering can be accomplished by rasterizing Gaussian ellipsoids into images. Apart from the fast rendering speed, the explicit representation of 3D Gaussian Splatting facilitates editing tasks like dynamic reconstruction, geometry editing, and physical simulation. Considering the rapid change and growing number of works in this field, we present a literature review of recent 3D Gaussian Splatting methods, which can be roughly classified into 3D reconstruction, 3D editing, and other downstream applications by functionality. Traditional point-based rendering methods and the rendering formulation of 3D Gaussian Splatting are also illustrated for a better understanding of this technique. This survey aims to help beginners get into this field quickly and provide experienced researchers with a comprehensive overview, which can stimulate the future development of the 3D Gaussian Splatting representation.

Neural implicit representations, including Neural Distance Fields and Neural Radiance Fields, have demonstrated significant capabilities for reconstructing surfaces with complicated geometry and topology, and generating novel views of a scene. Nevertheless, it is challenging for users to directly deform or manipulate these implicit representations with large deformations in the real-time fashion. Gaussian Splatting(GS) has recently become a promising method with explicit geometry for representing static scenes and facilitating high-quality and real-time synthesis of novel views. However,it cannot be easily deformed due to the use of discrete Gaussians and lack of explicit topology. To address this, we develop a novel GS-based method that enables interactive deformation. Our key idea is to design an innovative mesh-based GS representation, which is integrated into Gaussian learning and manipulation. 3D Gaussians are defined over an explicit mesh, and they are bound with each other: the rendering of 3D Gaussians guides the mesh face split for adaptive refinement, and the mesh face split directs the splitting of 3D Gaussians. Moreover, the explicit mesh constraints help regularize the Gaussian distribution, suppressing poor-quality Gaussians(e.g. misaligned Gaussians,long-narrow shaped Gaussians), thus enhancing visual quality and avoiding artifacts during deformation. Based on this representation, we further introduce a large-scale Gaussian deformation technique to enable deformable GS, which alters the parameters of 3D Gaussians according to the manipulation of the associated mesh. Our method benefits from existing mesh deformation datasets for more realistic data-driven Gaussian deformation. Extensive experiments show that our approach achieves high-quality reconstruction and effective deformation, while maintaining the promising rendering results at a high frame rate(65 FPS on average)., Comment: 11 pages, 7 figures

Aiming at improving the survey efficiency of the Wide Field Survey Telescope, we have developed a basic scheduling strategy that takes into account the telescope characteristics, observing conditions, and weather conditions at the Lenghu site. The sky area is divided into rectangular regions, referred to as `tiles', with a size of 2.577 deg * 2.634 deg slightly smaller than the focal area of the mosaic CCDs. These tiles are continuously filled in annulars parallel to the equator. The brightness of the sky background, which varies with the moon phase and distance from the moon, plays a significant role in determining the accessible survey fields. Approximately 50 connected tiles are grouped into one block for observation. To optimize the survey schedule, we perform simulations by taking into account the length of exposures, data readout, telescope slewing, and all relevant observing conditions. We utilize the Greedy Algorithm for scheduling optimization. Additionally, we propose a dedicated dithering pattern to cover the gaps between CCDs and the four corners of the mosaic CCD array, which are located outside of the 3 deg field of view. This dithering pattern helps to achieve relatively uniform exposure maps for the final survey outputs., Comment: 14 pages, 7 figures, 1 table. Accepted for pubulication in Research in Astronomy and Astrophysics

Great progress has been made in the field of quantum inertial sensors, from the laboratory to the real-world use, which will ultimately require sensor miniaturization and ruggedization for dynamic motion. However, lateral atomic movement with respect to the sensing axis limits inertial sensing, which inspires the atom guides to ensure transverse atomic confinement. Compared to a relatively large free-space optical mode, an evanescent field (EF) mode with an advantageously small mode area allows for stronger atom-light interactions and lower optical power requirements for the atom guides. We study EF atom guides in nanofibers and waveguides with traveling evanescent waves, rather than EF optical lattices with standing evanescent waves. Our preliminary demonstration of an EF atom guide takes place on a nanofiber using 685 nm and 937 nm lights, and we experimentally show that the atomic coherence of the EF atom guide (685/937 nm) is similar to the EF optical lattice. By replacing the 685 nm light with 793 nm light, we further demonstrate the sub-5mW EF atom guide (793/937 nm) on nanofibers and assess relative power reduction of 61$\%$ on nanofibers and 78$\%$ on membrane waveguides, compared to nanofibers (685/937 nm), for the same optical potential depth. Power reduction is beneficial for reducing total optical power requirements and improving heat dissipation in vacuum for atom guiding on chip-based membrane-photonic devices. To connect this work with EF-guided atom interferometry, we evaluate the viability and potential benefits of using the low-power light configuration on membrane waveguides, presenting fabricated linear and circular waveguides for future demonstrations. This is a promising step towards a chip-scale quantum inertial sensor array with reduced size, weight, and power., Comment: 12 pages, 9 figures

Job-shop scheduling problem (JSP) is a mathematical optimization problem widely used in industries like manufacturing, and flexible JSP (FJSP) is also a common variant. Since they are NP-hard, it is intractable to find the optimal solution for all cases within reasonable times. Thus, it becomes important to develop efficient heuristics to solve JSP/FJSP. A kind of method of solving scheduling problems is construction heuristics, which constructs scheduling solutions via heuristics. Recently, many methods for construction heuristics leverage deep reinforcement learning (DRL) with graph neural networks (GNN). In this paper, we propose a new approach, named residual scheduling, to solving JSP/FJSP. In this new approach, we remove irrelevant machines and jobs such as those finished, such that the states include the remaining (or relevant) machines and jobs only. Our experiments show that our approach reaches state-of-the-art (SOTA) among all known construction heuristics on most well-known open JSP and FJSP benchmarks. In addition, we also observe that even though our model is trained for scheduling problems of smaller sizes, our method still performs well for scheduling problems of large sizes. Interestingly in our experiments, our approach even reaches zero gap for 49 among 50 JSP instances whose job numbers are more than 150 on 20 machines.

Pure electric vehicles (PEVs) are increasingly adopted to decarbonize the transport sector and mitigate global warming. However, the inadequate PEV charging infrastructure may hinder the further adoption of PEVs in the large-scale traffic network, which calls for effective planning solutions for the charging station (CS) placement. The deployment of charging infrastructure inevitably increases the load on the associated power distribution network. Therefore, we are motivated to develop a comprehensive multi-objective framework for optimal CS placement in a traffic network overlaid by a distribution network, considering multiple stakeholders' interested factors, such as traffic flow, PEV charging time cost, PEV travel distance, and the reliability of the distribution network. We leverage a cross-entropy-based method to solve the optimal CS placement and evaluate our method in a real-world 183-node traffic network in Chengdu, China, overlaid by a 26-region distribution network. It is demonstrated that our work provides various viable planning options favoring different objectives for the stakeholders' decision-making in practice., Comment: IEEE I&CPS Asia 2023 (2023 IEEE IAS Industrial and Commercial Power System Asia Conference)

The Rydberg dipole-blockade has emerged as the standard mechanism to induce entanglement between neutral atom qubits. In these protocols, laser fields that couple qubit states to Rydberg states are modulated to implement entangling gates. Here we present an alternative protocol to implement entangling gates via Rydberg dressing and a microwave-field-driven spin-flip blockade [Y.-Y. Jau et al, Nat. Phys. 12, 71 (2016)]. We consider the specific example of qubits encoded in the clock states states of cesium. An auxiliary hyperfine state is optically dressed so that it acquires partial Rydberg character. It thus acts as a proxy Rydberg state, with a nonlinear light-shift that plays the role of blockade strength. A microwave-frequency field coupling a qubit state to this dressed auxiliary state can be modulated to implement entangling gates. Logic gate protocols designed for the optical regime can be imported to this microwave regime, for which experimental control methods are more robust. We show that unlike the strong dipole-blockade regime usually employed in Rydberg experiments, going to a moderate-spin-flip-blockade regime results in faster gates and smaller Rydberg decay. We study various regimes of operations that can yield high-fidelity two-qubit entangling gates and characterize their analytical behavior. In addition to the inherent robustness of microwave control, we can design these gates to be more robust to thermal fluctuations in atomic motion as well to laser amplitude, and other noise sources such as stray background fields.

We derive a priori interior Hessian estimates and interior regularity for the $\sigma_2$ equation in dimension four. Our method provides respectively a new proof for the corresponding three dimensional results and a Hessian estimate for smooth solutions satisfying a dynamic semi-convexity condition in higher $n\ge 5$ dimensions.

Chiral light-matter interactions supported by topological edge modes at the interface of valley photonic crystals provide a robust method to implement the unidirectional spin transfer. The valley topological photonic crystals possess a pair of counterpropagating edge modes. The edge modes are robust against the sharp bend of $60^{\circ}$ and $120^{\circ}$, which can form a resonator with whispering gallery modes. Here, we demonstrate the asymmetric emission of chiral coupling from single quantum dots in a topological resonator by tuning the coupling between a quantum emitter and a resonator mode. Under a magnetic field in Faraday configuration, the exciton state from a single quantum dot splits into two exciton spin states with opposite circularly polarized emissions due to Zeeman effect. Two branches of the quantum dot emissions couple to a resonator mode in different degrees, resulting in an asymmetric chiral emission. Without the demanding of site-control of quantum emitters for chiral quantum optics, an extra degree of freedom to tune the chiral contrast with a topological resonator could be useful for the development of on-chip integrated photonic circuits., Comment: 13 pages, 4 figures