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Monge-Amp\`{e}re equation is a prototype second-order fully nonlinear partial differential equation. In this paper, we propose a new idea to design and analyze the $C^0$ interior penalty method to approximation the viscosity solution of the Monge-Amp\`{e}re equation. The new methods is inspired from the discrete Miranda-Talenti estimate. Based on the vanishing moment representation, we approximate the Monge-Amp\`{e}re equation by the fourth order semi-linear equation with some additional boundary conditions. We will use the discrete Miranda-Talenti estimates to ensure the well-posedness of the numerical scheme and derive the error estimates.

We prove that for a finite set of points $X$ in the projective $n$-space over any field, the Betti number $\beta_{n,n+1}$ of the coordinate ring of $X$ is non-zero if and only if $X$ lies on the union of two planes whose sum of dimension is less than $n$. Our proof is direct and short, and the inductive step rests on a combinatorial statement that works over matroids.

Let $(R,m,k)$ be a Golod ring. We show a recurrent formula for high syzygies of $k$ interms of previous ones. In the case of embedding dimension at most $2$, we provided complete descriptions of all indecomposable summands of all syzygies of $k$.

Text-to-SQL systems, which convert natural language queries into SQL commands, have seen significant progress primarily for the SQLite dialect. However, adapting these systems to other SQL dialects like BigQuery and PostgreSQL remains a challenge due to the diversity in SQL syntax and functions. We introduce SQL-GEN, a framework for generating high-quality dialect-specific synthetic data guided by dialect-specific tutorials, and demonstrate its effectiveness in creating training datasets for multiple dialects. Our approach significantly improves performance, by up to 20\%, over previous methods and reduces the gap with large-scale human-annotated datasets. Moreover, combining our synthetic data with human-annotated data provides additional performance boosts of 3.3\% to 5.6\%. We also introduce a novel Mixture of Experts (MoE) initialization method that integrates dialect-specific models into a unified system by merging self-attention layers and initializing the gates with dialect-specific keywords, further enhancing performance across different SQL dialects.

Edge states of a topological insulator can be used to explore fundamental science emerging at the interface of low dimensionality and topology. Achieving a robust conductance quantization, however, has proven challenging for helical edge states. Here we show wide resistance plateaus in kink states - a manifestation of the quantum valley Hall effect in Bernal bilayer graphene - quantized to the predicted value at zero magnetic field. The plateau resistance has a very weak temperature dependence up to 50 Kelvin and is flat within a dc bias window of tens of mV. We demonstrate the electrical operation of a topology-controlled switch with an on/off ratio of 200. These results demonstrate the robustness and tunability of the kink states and its promise in constructing electron quantum optics devices., Comment: 21 pages, 5 main figures, with Supplementary Materials

In this paper, we propose and analyze both conforming and nonconforming virtual element methods (VEMs) for the fully nonlinear second-order elliptic Hamilton-Jacobi-Bellman (HJB) equations with Cordes coefficients. By incorporating stabilization terms, we establish the well-posedness of the proposed methods, thus avoiding the need to construct a discrete Miranda-Talenti estimate. We derive the optimal error estimate in the discrete $H^2$ norm for both numerical formulations. Furthermore, a semismooth Newton's method is employed to linearize the discrete problems. Several numerical experiments using the lowest-order VEMs are provided to demonstrate the efficacy of the proposed methods and to validate our theoretical results.

Monolayer WSe$_2$ (ML WSe$_2$) exhibits high second harmonic generation (SHG) efficiency under single 1-photon (1-p) or 2-photon (2-p) resonance conditions due to enhanced second-order susceptibility compared with the off-resonance state \cite{lin2021narrow,wang2015giant}. Here, we propose a novel strain engineering approach to dramatically boost the in-plane second-order susceptibility ($\chi_{yyy}$) by tuning the biaxial strain to shift two K-valley excitons (the A-exciton and a high-lying exciton (HX)) into double resonance. We first identify the A-exciton and HX from the 2D Mott-Wannier model and compare the enhanced $\chi_{yyy}$ at single 1-p and 2-p resonance states. The strongest enhancement arises from the 2-p resonance state of HX. By applying a small uniform biaxial strain (0.16%), we observe an excitonic double resonance state ($E_{\rm{HX}}$ = 2$E_{\rm{A}}$, $E_{\rm{HX}}$ and $E_{\rm{A}}$ are the exciton absorption energies). Strain-tuning can yield up to a $50$X enhancement in $\chi_{yyy}$ compared to the single 2-p resonance state of HX, resulting in a further three orders of magnitude enhancement in SHG efficiency. Further exploration of strain states near 0.16\% reveals double resonance also occurs at other wavevectors near the K valley, leading to a further increase in $\chi_{yyy}$, confirming that strain engineering is an effective methodology for enhancing $\chi_{yyy}$. Our findings suggest new avenues for strain engineering the optical properties of 2D materials for novel nonlinear optoelectronics applications.

For the class of nonlinear input-affine systems with polynomial dynamics, we consider the problem of designing an input-to-state stabilizing controller with respect to typical exogenous signals in a feedback control system, such as actuator and process disturbances. We address this problem in a data-based setting when we cannot avail ourselves of the dynamics of the actual system, but only of data generated by it under unknown bounded noise. For all dynamics consistent with data, we derive sum-of-squares programs to design an input-to-state stabilizing controller, an input-to-state Lyapunov function and the corresponding comparison functions. This numerical design for input-to-state stabilization seems to be relevant not only in the considered data-based setting, but also in a model-based setting. Illustration of feasibility of the provided sum-of-squares programs is provided on a numerical example.

Digital human models of motion sickness have been actively developed, among which models based on subjective vertical conflict (SVC) theory are the most actively studied. These models facilitate the prediction of motion sickness in various scenarios such as riding in a car. Most SVC theory models predict the motion sickness incidence (MSI), which is defined as the percentage of people who would vomit with the given specific motion stimulus. However, no model has been developed to describe milder forms of discomfort or specific symptoms of motion sickness, even though predicting milder symptoms is important for applications in automobiles and daily use vehicles. Therefore, the purpose of this study was to build a computational model of symptom progression of vestibular motion sickness based on SVC theory. We focused on a model of vestibular motion sickness with six degrees-of-freedom (6DoF) head motions. The model was developed by updating the output part of the state-of-the-art SVC model, termed the 6DoF-SVC (IN1) model, from MSI to the MIsery SCale (MISC), which is a subjective rating scale for symptom progression. We conducted an experiment to measure the progression of motion sickness during a straight fore-aft motion. It was demonstrated that our proposed method, with the parameters of the output parts optimized by the experimental results, fits well with the observed MISC.

A gradient enhanced ADMM algorithm for optimal transport on general surfaces is proposed in this paper. Based on Benamou and Brenier's dynamical formulation, we combine gradient recovery techniques on surfaces with the ADMM algorithm, not only improving the computational accuracy, but also providing a novel method to deal with dual variables in the algorithm. This method avoids the use of stagger grids, has better accuracy and is more robust comparing to other averaging techniques.

Twist engineering of magnetic van der Waals (vdW) moir\'e superlattices provides an attractive way to achieve precise nanoscale control over the spin degree of freedom on two-dimensional flatland. Despite the very recent demonstrations of moir\'e magnetism featuring exotic phases with noncollinear spin order in twisted vdW magnet chromium triiodide CrI3, the local magnetic interactions, spin dynamics, and magnetic phase transitions within and across individual moir\'e supercells remain elusive. Taking advantage of a scanning single-spin magnetometry platform, here we report observation of two distinct magnetic phase transitions with separate critical temperatures within a moir\'e supercell of small-angle twisted double trilayer CrI3. By measuring temperature dependent spin fluctuations at the coexisting ferromagnetic and antiferromagnetic regions in twisted CrI3, we explicitly show that the Curie temperature of the ferromagnetic state is higher than the N\'eel temperature of the antiferromagnetic one by ~10 K. Our mean-field calculations attribute such a spatial and thermodynamic phase separation to the stacking order modulated interlayer exchange coupling at the twisted interface of the moir\'e superlattices. The presented results highlight twist engineering as a promising tuning knob to realize on-demand control of not only the nanoscale spin order of moir\'e quantum matter but also its dynamic magnetic responses, which may find relevant applications in developing transformative vdW electronic and magnetic devices.

We prove a sharp bound for the regularity of a squarefree monomial ideal with a linear presentation. This result also answers in positive a question on the cohomological dimension of squarefree monomial ideals satisfying Serre's $S_2$-condition proposed by Dao and Takagi.

Detecting defects and vulnerabilities in the early stage has long been a challenge in software engineering. Static analysis, a technique that inspects code without execution, has emerged as a key strategy to address this challenge. Among recent advancements, the use of graph-based representations, particularly Code Property Graph (CPG), has gained traction due to its comprehensive depiction of code structure and semantics. Despite the progress, existing graph-based analysis tools still face performance and scalability issues. The main bottleneck lies in the size and complexity of CPG, which makes analyzing large codebases inefficient and memory-consuming. Also, query rules used by the current tools can be over-specific. Hence, we introduce QVoG, a graph-based static analysis platform for detecting defects and vulnerabilities. It employs a compressed CPG representation to maintain a reasonable graph size, thereby enhancing the overall query efficiency. Based on the CPG, it also offers a declarative query language to simplify the queries. Furthermore, it takes a step forward to integrate machine learning to enhance the generality of vulnerability detection. For projects consisting of 1,000,000+ lines of code, QVoG can complete analysis in approximately 15 minutes, as opposed to 19 minutes with CodeQL.

Large language models (LLMs) have emerged as important components across various fields, yet their training requires substantial computation resources and abundant labeled data. It poses a challenge to robustly training LLMs for individual users (clients). To tackle this challenge, the intuitive idea is to introduce federated learning (FL), which can collaboratively train models on distributed private data. However, existing methods suffer from the challenges of data heterogeneity, system heterogeneity, and model size, resulting in suboptimal performance and high costs. In this work, we proposed a variant of personalized federated learning (PFL) framework, namely FDLoRA, which allows the client to be a single device or a cluster and adopts low-rank adaptation (LoRA) tuning. FDLoRA sets dual LoRA modules on each client to capture personalized and global knowledge, respectively, and only the global LoRA module uploads parameters to the central server to aggregate cross-client knowledge. Finally, an adaptive fusion approach is employed to combine the parameters of the dual LoRAs. This enables FDLoRA to make effective use of private data distributed across different clients, thereby improving performance on the client without incurring high communication and computing costs. We conducted extensive experiments in two practice scenarios. The results demonstrate that FDLoRA outperforms six baselines in terms of performance, stability, robustness, computation cost, and communication cost.

Lensless cameras, innovatively replacing traditional lenses for ultra-thin, flat optics, encode light directly onto sensors, producing images that are not immediately recognizable. This compact, lightweight, and cost-effective imaging solution offers inherent privacy advantages, making it attractive for privacy-sensitive applications like face verification. Typical lensless face verification adopts a two-stage process of reconstruction followed by verification, incurring privacy risks from reconstructed faces and high computational costs. This paper presents an end-to-end optimization approach for privacy-preserving face verification directly on encoded lensless captures, ensuring that the entire software pipeline remains encoded with no visible faces as intermediate results. To achieve this, we propose several techniques to address unique challenges from the lensless setup which precludes traditional face detection and alignment. Specifically, we propose a face center alignment scheme, an augmentation curriculum to build robustness against variations, and a knowledge distillation method to smooth optimization and enhance performance. Evaluations under both simulation and real environment demonstrate our method outperforms two-stage lensless verification while enhancing privacy and efficiency. Project website: \url{lenslessface.github.io}., Comment: under review

As the importance of comprehensive evaluation in workshop courses increases, there is a growing demand for efficient and fair assessment methods that reduce the workload for faculty members. This paper presents an evaluation conducted with Large Language Models (LLMs) using actual student essays in three scenarios: 1) without providing guidance such as rubrics, 2) with pre-specified rubrics, and 3) through pairwise comparison of essays. Quantitative analysis of the results revealed a strong correlation between LLM and faculty member assessments in the pairwise comparison scenario with pre-specified rubrics, although concerns about the quality and stability of evaluations remained. Therefore, we conducted a qualitative analysis of LLM assessment comments, showing that: 1) LLMs can match the assessment capabilities of faculty members, 2) variations in LLM assessments should be interpreted as diversity rather than confusion, and 3) assessments by humans and LLMs can differ and complement each other. In conclusion, this paper suggests that LLMs should not be seen merely as assistants to faculty members but as partners in evaluation committees and outlines directions for further research.

Workshop courses designed to foster creativity are gaining popularity. However, even experienced faculty teams find it challenging to realize a holistic evaluation that accommodates diverse perspectives. Adequate deliberation is essential to integrate varied assessments, but faculty often lack the time for such exchanges. Deriving an average score without discussion undermines the purpose of a holistic evaluation. Therefore, this paper explores the use of a Large Language Model (LLM) as a facilitator to integrate diverse faculty assessments. Scenario-based experiments were conducted to determine if the LLM could integrate diverse evaluations and explain the underlying pedagogical theories to faculty. The results were noteworthy, showing that the LLM can effectively facilitate faculty discussions. Additionally, the LLM demonstrated the capability to create evaluation criteria by generalizing a single scenario-based experiment, leveraging its already acquired pedagogical domain knowledge., Comment: The final version appears in the proceedings of the 32nd International Conference on Computers in Education (ICCE 2024)

Combining high-throughput first-principles calculations and experimental measurements, we have identified a novel family of fast lithium-ion chalcogenide conductors in Li$_2$BMQ$_4$ (2114, B = Ca, Sr and Ba; M = Si, Ge and Sn; Q = O, S and Se) systems. Our calculations demonstrate that most of the thermodynamically and kinetically stable sulfides and selenides in this new system exhibit ultralow Li$^+$ ion migration activation energy (0.16 eV ~ 0.56 eV) and considerable bandgaps varying between ~ 2 eV and 3.5 eV. We have successfully synthesized Li$_2$BaSnS$_4$ and Li$_2$SrSiS$_4$, and they exhibit excellent moisture stability through H$_2$S gas measurements. Electrochemical impedance measurements indicate 2114 systems show the typical features of solid ionic conductors, with a room-temperature Li$^+$ conductivity close to 5$\times$10$^{-4}$ mS/cm aligning with our molecular dynamics simulations. Furthermore, we have theoretically investigated the substitution of Cl$^-$ at S$^{2-}$ site. The doped compounds display significantly higher conductivity, with an increase of about three orders of magnitude (up to a maximum of 0.72 mS/cm) compared to the undoped compounds. These findings offer valuable insights for the further exploration of potential chalcogenide solid electrolyte materials with robust air stability and enhanced ionic conductivity for practical applications in lithium-ion batteries.

Optically active spin defects in wide band-gap semiconductors serve as a local sensor of multiple degrees of freedom in a variety of "hard" and "soft" condensed matter systems. Taking advantage of the recent progress on quantum sensing using van der Waals (vdW) quantum materials, here we report direct measurements of spin waves excited in magnetic insulator Y3Fe5O12 (YIG) by boron vacancy $V_B^-$ spin defects contained in few-layer thick hexagonal boron nitride nanoflakes. We show that the ferromagnetic resonance and parametric spin excitations can be effectively detected by $V_B^-$ spin defects under various experimental conditions through optically detected magnetic resonance measurements. The off-resonant dipole interaction between YIG magnons and $V_B^-$ spin defects is mediated by multi-magnon scattering processes, which may find relevant applications in a range of emerging quantum sensing, computing, and metrology technologies. Our results also highlight the opportunities offered by quantum spin defects in layered two-dimensional vdW materials for investigating local spin dynamic behaviors in magnetic solid-state matters.

This paper presents an innovative continuous linear finite element approach to effectively solve biharmonic problems on surfaces. The key idea behind this method lies in the strategic utilization of a surface gradient recovery operator to compute the second-order surface derivative of a piecewise continuous linear function defined on the approximate surface, as conventional notions of second-order derivatives are not directly applicable in this context. By incorporating appropriate stabilizations, we rigorously establish the stability of the proposed formulation. Despite the presence of geometric error, we provide optimal error estimates in both the energy norm and $L^2$ norm. Theoretical results are supported by numerical experiments.

This paper reviews the NTIRE 2024 low light image enhancement challenge, highlighting the proposed solutions and results. The aim of this challenge is to discover an effective network design or solution capable of generating brighter, clearer, and visually appealing results when dealing with a variety of conditions, including ultra-high resolution (4K and beyond), non-uniform illumination, backlighting, extreme darkness, and night scenes. A notable total of 428 participants registered for the challenge, with 22 teams ultimately making valid submissions. This paper meticulously evaluates the state-of-the-art advancements in enhancing low-light images, reflecting the significant progress and creativity in this field., Comment: NTIRE 2024 Challenge Report

The field of meteorological forecasting has undergone a significant transformation with the integration of large models, especially those employing deep learning techniques. This paper reviews the advancements and applications of these models in weather prediction, emphasizing their role in transforming traditional forecasting methods. Models like FourCastNet, Pangu-Weather, GraphCast, ClimaX, and FengWu have made notable contributions by providing accurate, high-resolution forecasts, surpassing the capabilities of traditional Numerical Weather Prediction (NWP) models. These models utilize advanced neural network architectures, such as Convolutional Neural Networks (CNNs), Graph Neural Networks (GNNs), and Transformers, to process diverse meteorological data, enhancing predictive accuracy across various time scales and spatial resolutions. The paper addresses challenges in this domain, including data acquisition and computational demands, and explores future opportunities for model optimization and hardware advancements. It underscores the integration of artificial intelligence with conventional meteorological techniques, promising improved weather prediction accuracy and a significant contribution to addressing climate-related challenges. This synergy positions large models as pivotal in the evolving landscape of meteorological forecasting., Comment: 5 pages

Government development projects vary significantly from private sector initiatives in scope, stakeholder complexity, and regulatory requirements. There is a lack of empirical studies focusing on requirements engineering (RE) activities specifically for government projects. We addressed this gap by conducting a series of semi-structured interviews with 12 professional software practitioners working on government projects. These interviewees are employed by two types of companies, each serving different government departments. Our findings uncover differences in the requirements elicitation phase between government projects, particularly for data visualization aspects, and other software projects, such as stakeholders and policy requirements. Additionally, we explore the coverage of human and social aspects in requirements elicitation, finding that culture, team dynamics, and policy implications are critical considerations. Our findings also pinpoint the main challenges encountered during the requirements elicitation phase for government projects. Our findings highlight future research work that is important to bridge the gap in RE activities for government software projects.

Bound states in the continuum (BICs) are spatially localized states with energy embedded in the continuum spectrum of extended states. The combination of BICs physics and nontrivial band topology theory giving rise to topological BICs, which are robust against disorders and meanwhile of the merit of conventional BICs, is attracting wide attention recently. Here, we report valley edge states as topological BICs, which appear at domain wall between two distinct valley topological phases. The robustness of such BICs is demonstrated. The simulations and experiments show great agreement. Our findings of valley related topological BICs shed light on both BICs and valley physics, and may foster innovative applications of topological acoustic devices., Comment: A revised version has been accepted by Science Bulletin

As modern HPC computing platforms become increasingly heterogeneous, it is challenging for programmers to fully leverage the computation power of massive parallelism offered by such heterogeneity. Consequently, task-based runtime systems have been proposed as an intermediate layer to hide the complex heterogeneity from the application programmers. The core functionality of these systems is to realize efficient task-to-resource mapping in the form of Directed Acyclic Graph (DAG) scheduling. However, existing scheduling schemes face several drawbacks to determine task priorities due to the heavy reliance on domain knowledge or failure to efficiently exploit the interaction of application and hardware characteristics. In this paper, we propose INSPIRIT, an efficient and lightweight scheduling framework with adaptive priority designed for task-based runtime systems. INSPIRIT introduces two novel task attributes \textit{inspiring ability} and \textit{inspiring efficiency} for dictating scheduling, eliminating the need for application domain knowledge. In addition, INSPIRIT jointly considers runtime information such as ready tasks in worker queues to guide task scheduling. This approach exposes more performance opportunities in heterogeneous hardware at runtime while effectively reducing the overhead for adjusting task priorities. Our evaluation results demonstrate that INSPIRIT achieves superior performance compared to cutting edge scheduling schemes on both synthesized and real-world task DAGs., Comment: 11 pages

Semantic correspondence remains a challenging task for establishing correspondences between a pair of images with the same category or similar scenes due to the large intra-class appearance. In this paper, we introduce a novel problem called 'Small Object Semantic Correspondence (SOSC).' This problem is challenging due to the close proximity of keypoints associated with small objects, which results in the fusion of these respective features. It is difficult to identify the corresponding key points of the fused features, and it is also difficult to be recognized. To address this challenge, we propose the Keypoint Bounding box-centered Cropping (KBC) method, which aims to increase the spatial separation between keypoints of small objects, thereby facilitating independent learning of these keypoints. The KBC method is seamlessly integrated into our proposed inference pipeline and can be easily incorporated into other methodologies, resulting in significant performance enhancements. Additionally, we introduce a novel framework, named KBCNet, which serves as our baseline model. KBCNet comprises a Cross-Scale Feature Alignment (CSFA) module and an efficient 4D convolutional decoder. The CSFA module is designed to align multi-scale features, enriching keypoint representations by integrating fine-grained features and deep semantic features. Meanwhile, the 4D convolutional decoder, based on efficient 4D convolution, ensures efficiency and rapid convergence. To empirically validate the effectiveness of our proposed methodology, extensive experiments are conducted on three widely used benchmarks: PF-PASCAL, PF-WILLOW, and SPair-71k. Our KBC method demonstrates a substantial performance improvement of 7.5\% on the SPair-71K dataset, providing compelling evidence of its efficacy.

Human pose and shape (HPS) estimation with lensless imaging is not only beneficial to privacy protection but also can be used in covert surveillance scenarios due to the small size and simple structure of this device. However, this task presents significant challenges due to the inherent ambiguity of the captured measurements and lacks effective methods for directly estimating human pose and shape from lensless data. In this paper, we propose the first end-to-end framework to recover 3D human poses and shapes from lensless measurements to our knowledge. We specifically design a multi-scale lensless feature decoder to decode the lensless measurements through the optically encoded mask for efficient feature extraction. We also propose a double-head auxiliary supervision mechanism to improve the estimation accuracy of human limb ends. Besides, we establish a lensless imaging system and verify the effectiveness of our method on various datasets acquired by our lensless imaging system., Comment: Accepted to CVPR 2024. More results available at https://cic.tju.edu.cn/faculty/likun/projects/LPSNet

In this paper, we introduce StableGarment, a unified framework to tackle garment-centric(GC) generation tasks, including GC text-to-image, controllable GC text-to-image, stylized GC text-to-image, and robust virtual try-on. The main challenge lies in retaining the intricate textures of the garment while maintaining the flexibility of pre-trained Stable Diffusion. Our solution involves the development of a garment encoder, a trainable copy of the denoising UNet equipped with additive self-attention (ASA) layers. These ASA layers are specifically devised to transfer detailed garment textures, also facilitating the integration of stylized base models for the creation of stylized images. Furthermore, the incorporation of a dedicated try-on ControlNet enables StableGarment to execute virtual try-on tasks with precision. We also build a novel data engine that produces high-quality synthesized data to preserve the model's ability to follow prompts. Extensive experiments demonstrate that our approach delivers state-of-the-art (SOTA) results among existing virtual try-on methods and exhibits high flexibility with broad potential applications in various garment-centric image generation.

The integration of artificial intelligence (AI) with radiology marks a transformative era in medicine. Vision foundation models have been adopted to enhance radiologic imaging analysis. However, the distinct complexities of radiologic 2D and 3D radiologic data pose unique challenges that existing models, pre-trained on general non-medical images, fail to address adequately. To bridge this gap and capitalize on the diagnostic precision required in radiologic imaging, we introduce Radiologic Contrastive Language-Image Pre-training (RadCLIP): a cross-modal vision-language foundational model that harnesses Vision Language Pre-training (VLP) framework to improve radiologic image analysis. Building upon Contrastive Language-Image Pre-training (CLIP), RadCLIP incorporates a slice pooling mechanism tailored for volumetric image analysis and is pre-trained using a large and diverse dataset of radiologic image-text pairs. The RadCLIP was pre-trained to effectively align radiologic images with their corresponding text annotations, creating a robust vision backbone for radiologic images. Extensive experiments demonstrate RadCLIP's superior performance in both uni-modal radiologic image classification and cross-modal image-text matching, highlighting its significant promise for improving diagnostic accuracy and efficiency in clinical settings. Our Key contributions include curating a large dataset with diverse radiologic 2D/3D radiologic image-text pairs, a slice pooling adapter using an attention mechanism for integrating 2D images, and comprehensive evaluations of RadCLIP on various radiologic downstream tasks.

Aerosol-cloud interactions (ACI) pose the largest uncertainty for climate projections. Among many challenges of understanding ACI, the question of whether ACI is deterministic or stochastic has not been explicitly formulated and asked. Here we attempt to answer this question by predicting cloud droplet number concentration Nc from aerosol number concentration Na and ambient conditions. We use aerosol properties, vertical velocity fluctuation w', and meteorological states (temperature T and water vapor mixing ratio q_v) from the ACTIVATE field observations (2020 to 2022) as predictor variables to estimate Nc. We show that the climatological Nc can be successfully predicted using a machine learning model despite the strongly nonlinear and multi-scale nature of ACI. However, the observation-trained machine learning model fails to predict Nc in individual cases while it successfully predicts Nc of randomly selected data points that cover a broad spatiotemporal scale, suggesting the stochastic nature of ACI at fine spatiotemporal scales.

$k$-diagonal circulant matrices and cyclic banded matrices are widely used in numerical simulations and signal processing of circular linear systems. Algorithms that directly involve or specify linear or quadratic complexity for the inverses of these two types of matrices are rare. We find that the inverse of a $k$-diagonal circulant matrix can be uniquely determined by a recursive formula, which can be derived within $O(k^3 \log n+k^4)$. Similarly for the inverse of a cyclic banded matrix, its inverse can be uniquely determined by a series of recursive formulas, with the initial terms of these recursions computable within $O(k^3 n+k^5)$. The additional costs for solving the complete inverses of these two types of matrices are $kn$ and $kn^2$. Our calculations enable rapid representation with most processes defined by explicit formulas. Additionally, most algorithms for inverting $k$-diagonal circulant matrices rely on the Fast Fourier Transform, which is not applicable to finite fields, while our algorithms can be applied to computations in finite fields.

Recent text-to-image (T2I) models have had great success, and many benchmarks have been proposed to evaluate their performance and safety. However, they only consider explicit prompts while neglecting implicit prompts (hint at a target without explicitly mentioning it). These prompts may get rid of safety constraints and pose potential threats to the applications of these models. This position paper highlights the current state of T2I models toward implicit prompts. We present a benchmark named ImplicitBench and conduct an investigation on the performance and impacts of implicit prompts with popular T2I models. Specifically, we design and collect more than 2,000 implicit prompts of three aspects: General Symbols, Celebrity Privacy, and Not-Safe-For-Work (NSFW) Issues, and evaluate six well-known T2I models' capabilities under these implicit prompts. Experiment results show that (1) T2I models are able to accurately create various target symbols indicated by implicit prompts; (2) Implicit prompts bring potential risks of privacy leakage for T2I models. (3) Constraints of NSFW in most of the evaluated T2I models can be bypassed with implicit prompts. We call for increased attention to the potential and risks of implicit prompts in the T2I community and further investigation into the capabilities and impacts of implicit prompts, advocating for a balanced approach that harnesses their benefits while mitigating their risks.

The metallurgy and materials communities have long known and exploited fundamental links between chemical and structural ordering in metallic solids and their mechanical properties. The highest reported strength achievable through the combination of multiple metals (alloying) has rapidly climbed and given rise to new classifications of materials with extraordinary properties. Metallic glasses and high-entropy alloys are two limiting examples of how tailored order can be used to manipulate mechanical behavior. Here, we show that the complex electronic-structure mechanisms governing the peak strength of alloys and pure metals can be reduced to a few physically-meaningful parameters based on their atomic arrangements and used (with no fitting parameters) to predict the maximum strength of any metallic solid, regardless of degree of structural or chemical ordering. Predictions of maximum strength based on the activation energy for a stress-driven phase transition to an amorphous state is shown to accurately describe the breakdown in Hall-Petch behavior at the smallest crystallite sizes for pure metals, intermetallic compounds, metallic glasses, and high-entropy alloys. This activation energy is also shown to be directly proportional to interstitial (electronic) charge density, which is a good predictor of ductility, stiffness (moduli), and phase stability in high-entropy alloys, and in solid metals generally. The proposed framework suggests the possibility of coupling ordering and intrinsic strength to mechanisms like dislocation nucleation, hydrogen embrittlement, and transport properties. It additionally opens the prospect for greatly accelerated structural materials design and development to address materials challenges limiting more sustainable and efficient use of energy., Comment: 16 pages, four figures

Networked systems are increasingly the target of cyberattacks that exploit vulnerabilities within digital communications, embedded hardware, and software. Arguably, the simplest class of attacks -- and often the first type before launching destructive integrity attacks -- are eavesdropping attacks, which aim to infer information by collecting system data and exploiting it for malicious purposes. A key technology of networked systems is state estimation, which leverages sensing and actuation data and first-principles models to enable trajectory planning, real-time monitoring, and control. However, state estimation can also be exploited by eavesdroppers to identify models and reconstruct states with the aim of, e.g., launching integrity (stealthy) attacks and inferring sensitive information. It is therefore crucial to protect disclosed system data to avoid an accurate state estimation by eavesdroppers. This survey presents a comprehensive review of existing literature on privacy-preserving state estimation methods, while also identifying potential limitations and research gaps. Our primary focus revolves around three types of methods: cryptography, data perturbation, and transmission scheduling, with particular emphasis on Kalman-like filters. Within these categories, we delve into the concepts of homomorphic encryption and differential privacy, which have been extensively investigated in recent years in the context of privacy-preserving state estimation. Finally, we shed light on several technical and fundamental challenges surrounding current methods and propose potential directions for future research., Comment: 16 pages, 5 figures, 4 tables