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Let $\mathcal{H}$ be a separable Hilbert space and $\mathcal{L}_{0}\subset B(\mathcal{H})$ a complete reflexive lattice. Let $\mathscr{K}$ be the direct sum of $n_0$ copies of $\mathcal{H}$ ($n_{0}\in\mathbb{N}$ and $n_0\geq 2$) or the direct sum of countably infinite many copies of $\mathcal{H}$ respectively. We construct two class of subspace lattices $\mathcal{L}$ on $\mathscr{K}$. Let $Alg\mathcal{L}$ be the corresponding subspace lattice algebra. We show that every local derivation from $Alg\mathcal{L} $ into $B(\mathscr{K})$ is a derivation.

Intermittent transitions, associated with critical dynamics and characterized by power-law distributions, are commonly observed during sleep. These critical behaviors are evident at the microscopic level through neuronal avalanches and at the macroscopic level through transitions between sleep stages. To clarify these empirical observations, models grounded in statistical physics have been proposed. At the mesoscopic level of cortical activity, critical behavior is indicated by the intermittent transitions between various cortical rhythms. For instance, empirical investigations utilizing EEG data from rats have identified intermittent transitions between $\delta$ and $\theta$ rhythms, with the duration of $\theta$ rhythm exhibiting a power-law distribution. However, a dynamic model to account for this phenomenon is currently absent. In this study, we introduce a network of sparsely coupled excitatory and inhibitory populations of quadratic integrate-and-fire (QIF) neurons to demonstrate that intermittent transitions can emerge from the intrinsic fluctuations of a finite-sized system, particularly when the system is positioned near a Hopf bifurcation point, which is a critical point. The resulting power-law distributions and exponents are consistent with empirical observations. Additionally, we illustrate how modifications in network connectivity can affect the power-law exponent by influencing the attractivity and oscillation frequency of the stable limit cycle. Our findings, interpreted through the fundamental dynamics of neuronal networks, provide a plausible mechanism for the generation of intermittent transitions between cortical rhythms, in alignment with the power-law distributions documented in empirical researches.

Recently released open-source pre-trained foundational image segmentation and object detection models (SAM2+GroundingDINO) allow for geometrically consistent segmentation of objects of interest in multi-view 2D images. Users can use text-based or click-based prompts to segment objects of interest without requiring labeled training datasets. Gaussian Splatting allows for the learning of the 3D representation of a scene's geometry and radiance based on 2D images. Combining Google Earth Studio, SAM2+GroundingDINO, 2D Gaussian Splatting, and our improvements in mask refinement based on morphological operations and contour simplification, we created a pipeline to extract the 3D mesh of any building based on its name, address, or geographic coordinates.

Many existing methods that use functional magnetic resonance imaging (fMRI) classify brain disorders, such as autism spectrum disorder (ASD) and attention deficit hyperactivity disorder (ADHD), often overlook the integration of spatial and temporal dependencies of the blood oxygen level-dependent (BOLD) signals, which may lead to inaccurate or imprecise classification results. To solve this problem, we propose a Spatio-Temporal Aggregation eorganization ransformer (STARFormer) that effectively captures both spatial and temporal features of BOLD signals by incorporating three key modules. The region of interest (ROI) spatial structure analysis module uses eigenvector centrality (EC) to reorganize brain regions based on effective connectivity, highlighting critical spatial relationships relevant to the brain disorder. The temporal feature reorganization module systematically segments the time series into equal-dimensional window tokens and captures multiscale features through variable window and cross-window attention. The spatio-temporal feature fusion module employs a parallel transformer architecture with dedicated temporal and spatial branches to extract integrated features. The proposed STARFormer has been rigorously evaluated on two publicly available datasets for the classification of ASD and ADHD. The experimental results confirm that the STARFormer achieves state-of-the-art performance across multiple evaluation metrics, providing a more accurate and reliable tool for the diagnosis of brain disorders and biomedical research. The codes will be available at: https://github.com/NZWANG/STARFormer.

We establish the spatial differentiability of weak solutions to nonstationary Stokes equations in divergence form with variable viscosity coefficients having $L_2$-Dini mean oscillations. As a corollary, we derive local spatial Schauder estimates for such equations if the viscosity coefficient belongs to $C^\alpha_x$. Similar results also hold for strong solutions to nonstationary Stokes equations in nondivergence form., Comment: 30 pages

Human-scene interaction (HSI) generation is crucial for applications in embodied AI, virtual reality, and robotics. While existing methods can synthesize realistic human motions in 3D scenes and generate plausible human-object interactions, they heavily rely on datasets containing paired 3D scene and motion capture data, which are expensive and time-consuming to collect across diverse environments and interactions. We present ZeroHSI, a novel approach that enables zero-shot 4D human-scene interaction synthesis by integrating video generation and neural human rendering. Our key insight is to leverage the rich motion priors learned by state-of-the-art video generation models, which have been trained on vast amounts of natural human movements and interactions, and use differentiable rendering to reconstruct human-scene interactions. ZeroHSI can synthesize realistic human motions in both static scenes and environments with dynamic objects, without requiring any ground-truth motion data. We evaluate ZeroHSI on a curated dataset of different types of various indoor and outdoor scenes with different interaction prompts, demonstrating its ability to generate diverse and contextually appropriate human-scene interactions., Comment: Project website: https://awfuact.github.io/zerohsi/

Decoding neural visual representations from electroencephalogram (EEG)-based brain activity is crucial for advancing brain-machine interfaces (BMI) and has transformative potential for neural sensory rehabilitation. While multimodal contrastive representation learning (MCRL) has shown promise in neural decoding, existing methods often overlook semantic consistency and completeness within modalities and lack effective semantic alignment across modalities. This limits their ability to capture the complex representations of visual neural responses. We propose Neural-MCRL, a novel framework that achieves multimodal alignment through semantic bridging and cross-attention mechanisms, while ensuring completeness within modalities and consistency across modalities. Our framework also features the Neural Encoder with Spectral-Temporal Adaptation (NESTA), a EEG encoder that adaptively captures spectral patterns and learns subject-specific transformations. Experimental results demonstrate significant improvements in visual decoding accuracy and model generalization compared to state-of-the-art methods, advancing the field of EEG-based neural visual representation decoding in BMI. Codes will be available at: https://github.com/NZWANG/Neural-MCRL.

Meeting growing demands for low latency and cost efficiency in production-grade large language model (LLM) serving systems requires integrating advanced optimization techniques. However, dynamic and unpredictable input-output lengths of LLM, compounded by these optimizations, exacerbate the issues of workload variability, making it difficult to maintain high efficiency on AI accelerators, especially DSAs with tile-based programming models. To address this challenge, we introduce XY-Serve, a versatile, Ascend native, end-to-end production LLM-serving system. The core idea is an abstraction mechanism that smooths out the workload variability by decomposing computations into unified, hardware-friendly, fine-grained meta primitives. For attention, we propose a meta-kernel that computes the basic pattern of matmul-softmax-matmul with architectural-aware tile sizes. For GEMM, we introduce a virtual padding scheme that adapts to dynamic shape changes while using highly efficient GEMM primitives with assorted fixed tile sizes. XY-Serve sits harmoniously with vLLM. Experimental results show up to 89% end-to-end throughput improvement compared with current publicly available baselines on Ascend NPUs. Additionally, our approach outperforms existing GEMM (average 14.6% faster) and attention (average 21.5% faster) kernels relative to existing libraries. While the work is Ascend native, we believe the approach can be readily applicable to SIMT architectures as well.

3D Gaussian Splatting (3DGS) has recently attracted wide attentions in various areas such as 3D navigation, Virtual Reality (VR) and 3D simulation, due to its photorealistic and efficient rendering performance. High-quality reconstrution of 3DGS relies on sufficient splats and a reasonable distribution of these splats to fit real geometric surface and texture details, which turns out to be a challenging problem. We present GeoTexDensifier, a novel geometry-texture-aware densification strategy to reconstruct high-quality Gaussian splats which better comply with the geometric structure and texture richness of the scene. Specifically, our GeoTexDensifier framework carries out an auxiliary texture-aware densification method to produce a denser distribution of splats in fully textured areas, while keeping sparsity in low-texture regions to maintain the quality of Gaussian point cloud. Meanwhile, a geometry-aware splitting strategy takes depth and normal priors to guide the splitting sampling and filter out the noisy splats whose initial positions are far from the actual geometric surfaces they aim to fit, under a Validation of Depth Ratio Change checking. With the help of relative monocular depth prior, such geometry-aware validation can effectively reduce the influence of scattered Gaussians to the final rendering quality, especially in regions with weak textures or without sufficient training views. The texture-aware densification and geometry-aware splitting strategies are fully combined to obtain a set of high-quality Gaussian splats. We experiment our GeoTexDensifier framework on various datasets and compare our Novel View Synthesis results to other state-of-the-art 3DGS approaches, with detailed quantitative and qualitative evaluations to demonstrate the effectiveness of our method in producing more photorealistic 3DGS models., Comment: 12 pages, 8 figures, 1 table

Graphical User Interface (GUI) agents, powered by Large Foundation Models, have emerged as a transformative approach to automating human-computer interaction. These agents autonomously interact with digital systems or software applications via GUIs, emulating human actions such as clicking, typing, and navigating visual elements across diverse platforms. Motivated by the growing interest and fundamental importance of GUI agents, we provide a comprehensive survey that categorizes their benchmarks, evaluation metrics, architectures, and training methods. We propose a unified framework that delineates their perception, reasoning, planning, and acting capabilities. Furthermore, we identify important open challenges and discuss key future directions. Finally, this work serves as a basis for practitioners and researchers to gain an intuitive understanding of current progress, techniques, benchmarks, and critical open problems that remain to be addressed.

\Graph similarity computation is an essential task in many real-world graph-related applications such as retrieving the similar drugs given a query chemical compound or finding the user's potential friends from the social network database. Graph Edit Distance (GED) and Maximum Common Subgraphs (MCS) are the two commonly used domain-agnostic metrics to evaluate graph similarity in practice. Unfortunately, computing the exact GED is known to be a NP-hard problem. To solve this limitation, neural network based models have been proposed to approximate the calculations of GED/MCS. However, deep learning models are well-known ``black boxes'', thus the typically characteristic one-to-one node/subgraph alignment process in the classical computations of GED and MCS cannot be seen. Existing methods have paid attention to approximating the node/subgraph alignment (soft alignment), but the one-to-one node alignment (hard alignment) has not yet been solved. To fill this gap, in this paper we propose a novel interpretable neural node alignment model without relying on node alignment ground truth information. Firstly, the quadratic assignment problem in classical GED computation is relaxed to a linear alignment via embedding the features in the node embedding space. Secondly, a differentiable Gumbel-Sinkhorn module is proposed to unsupervised generate the optimal one-to-one node alignment matrix. Experimental results in real-world graph datasets demonstrate that our method outperforms the state-of-the-art methods in graph similarity computation and graph retrieval tasks, achieving up to 16\% reduction in the Mean Squared Error and up to 12\% improvement in the retrieval evaluation metrics, respectively.

Text-to-video generation enhances content creation but is highly computationally intensive: The computational cost of Diffusion Transformers (DiTs) scales quadratically in the number of pixels. This makes minute-length video generation extremely expensive, limiting most existing models to generating videos of only 10-20 seconds length. We propose a Linear-complexity text-to-video Generation (LinGen) framework whose cost scales linearly in the number of pixels. For the first time, LinGen enables high-resolution minute-length video generation on a single GPU without compromising quality. It replaces the computationally-dominant and quadratic-complexity block, self-attention, with a linear-complexity block called MATE, which consists of an MA-branch and a TE-branch. The MA-branch targets short-to-long-range correlations, combining a bidirectional Mamba2 block with our token rearrangement method, Rotary Major Scan, and our review tokens developed for long video generation. The TE-branch is a novel TEmporal Swin Attention block that focuses on temporal correlations between adjacent tokens and medium-range tokens. The MATE block addresses the adjacency preservation issue of Mamba and improves the consistency of generated videos significantly. Experimental results show that LinGen outperforms DiT (with a 75.6% win rate) in video quality with up to 15$\times$ (11.5$\times$) FLOPs (latency) reduction. Furthermore, both automatic metrics and human evaluation demonstrate our LinGen-4B yields comparable video quality to state-of-the-art models (with a 50.5%, 52.1%, 49.1% win rate with respect to Gen-3, LumaLabs, and Kling, respectively). This paves the way to hour-length movie generation and real-time interactive video generation. We provide 68s video generation results and more examples in our project website: https://lineargen.github.io/., Comment: 20 pages, 20 figures

In this paper, we study the interaction between two closely spaced rigid inclusions suspended in a Stokes flow. It is well known that the stress significantly amplifies in the narrow region between the inclusions as the distance between them approaches zero. To gain deeper insight into these interactions, we derive high-order derivative estimates for the Stokes equation in the presence of two rigid inclusions in two dimensions. Our approach resonates with the method used to handle the incompressibility constraint in the standard convex integration scheme. Under certain symmetric assumptions on the domain, these estimates are shown to be optimal. As a result, we establish the precise blow-up rates of the Cauchy stress and its higher-order derivatives in the narrow region., Comment: 41 pages

MVImgNet is a large-scale dataset that contains multi-view images of ~220k real-world objects in 238 classes. As a counterpart of ImageNet, it introduces 3D visual signals via multi-view shooting, making a soft bridge between 2D and 3D vision. This paper constructs the MVImgNet2.0 dataset that expands MVImgNet into a total of ~520k objects and 515 categories, which derives a 3D dataset with a larger scale that is more comparable to ones in the 2D domain. In addition to the expanded dataset scale and category range, MVImgNet2.0 is of a higher quality than MVImgNet owing to four new features: (i) most shoots capture 360-degree views of the objects, which can support the learning of object reconstruction with completeness; (ii) the segmentation manner is advanced to produce foreground object masks of higher accuracy; (iii) a more powerful structure-from-motion method is adopted to derive the camera pose for each frame of a lower estimation error; (iv) higher-quality dense point clouds are reconstructed via advanced methods for objects captured in 360-degree views, which can serve for downstream applications. Extensive experiments confirm the value of the proposed MVImgNet2.0 in boosting the performance of large 3D reconstruction models. MVImgNet2.0 will be public at luyues.github.io/mvimgnet2, including multi-view images of all 520k objects, the reconstructed high-quality point clouds, and data annotation codes, hoping to inspire the broader vision community., Comment: ACM Transactions on Graphics (TOG), SIGGRAPH Asia 2024

Multimodal Large Language Models (MLLMs) have become increasingly important due to their state-of-the-art performance and ability to integrate multiple data modalities, such as text, images, and audio, to perform complex tasks with high accuracy. This paper presents a comprehensive survey on personalized multimodal large language models, focusing on their architecture, training methods, and applications. We propose an intuitive taxonomy for categorizing the techniques used to personalize MLLMs to individual users, and discuss the techniques accordingly. Furthermore, we discuss how such techniques can be combined or adapted when appropriate, highlighting their advantages and underlying rationale. We also provide a succinct summary of personalization tasks investigated in existing research, along with the evaluation metrics commonly used. Additionally, we summarize the datasets that are useful for benchmarking personalized MLLMs. Finally, we outline critical open challenges. This survey aims to serve as a valuable resource for researchers and practitioners seeking to understand and advance the development of personalized multimodal large language models.

We study a class of degenerate parabolic and elliptic equations in divergence form in the upper half space $\{x_d>0\}$. The leading coefficients are of the form $x_d^2a_{ij}$, where $a_{ij}$ are measurable in $(t,x_d)$ except $a_{dd}$, which is measurable in $t$ or $x_d$. Additionally, they have small bounded mean oscillations in the other spatial variables. We obtain the well-posedness and regularity of solutions in weighted mixed-norm Sobolev spaces., Comment: 42 pages

Contact-rich tasks present significant challenges for robotic manipulation policies due to the complex dynamics of contact and the need for precise control. Vision-based policies often struggle with the skill required for such tasks, as they typically lack critical contact feedback modalities like force/torque information. To address this issue, we propose FoAR, a force-aware reactive policy that combines high-frequency force/torque sensing with visual inputs to enhance the performance in contact-rich manipulation. Built upon the RISE policy, FoAR incorporates a multimodal feature fusion mechanism guided by a future contact predictor, enabling dynamic adjustment of force/torque data usage between non-contact and contact phases. Its reactive control strategy also allows FoAR to accomplish contact-rich tasks accurately through simple position control. Experimental results demonstrate that FoAR significantly outperforms all baselines across various challenging contact-rich tasks while maintaining robust performance under unexpected dynamic disturbances. Project website: https://tonyfang.net/FoAR/, Comment: 9 pages, 5 figures

We investigate higher derivative estimates for the Lam\'e system with hard inclusions embedded in a bounded domain in $\mathbb{R}^{d}$. As the distance $\varepsilon$ between two closely spaced hard inclusions approaches zero, the stress in the narrow regions between the inclusions increases significantly. This stress is captured by the gradient of the solution. The key contribution of this paper is a detailed characterization of this singularity, achieved by deriving higher derivative estimates for solutions to the Lam\'e system with partially infinite coefficients. These upper bounds are shown to be sharp in two and three dimensions when the domain exhibits certain symmetries. To the best of our knowledge, this is the first work to precisely quantify the singular behavior of higher derivatives in the Lam\'e system with hard inclusions., Comment: 37 pages

Addressing the challenge of ensuring safety in ever-changing and unpredictable environments, particularly in the swiftly advancing realm of autonomous driving in today's 5G wireless communication world, we present Navigation Secure (NavSecure). This vision-based navigation framework merges the strengths of world models with crucial safety-focused decision-making capabilities, enabling autonomous vehicles to navigate real-world complexities securely. Our approach anticipates potential threats and formulates safer routes by harnessing the predictive capabilities of world models, thus significantly reducing the need for extensive real-world trial-and-error learning. Additionally, our method empowers vehicles to autonomously learn and develop through continuous practice, ensuring the system evolves and adapts to new challenges. Incorporating radio frequency technology, NavSecure leverages 5G networks to enhance real-time data exchange, improving communication and responsiveness. Validated through rigorous experiments under simulation-to-real driving conditions, NavSecure has shown exceptional performance in safety-critical scenarios, such as sudden obstacle avoidance. Results indicate that NavSecure excels in key safety metrics, including collision prevention and risk reduction, surpassing other end-to-end methodologies. This framework not only advances autonomous driving safety but also demonstrates how world models can enhance decision-making in critical applications. NavSecure sets a new standard for developing more robust and trustworthy autonomous driving systems, capable of handling the inherent dynamics and uncertainties of real-world environments., Comment: 6 pages, 5 figures

In this paper, we introduce DINO-X, which is a unified object-centric vision model developed by IDEA Research with the best open-world object detection performance to date. DINO-X employs the same Transformer-based encoder-decoder architecture as Grounding DINO 1.5 to pursue an object-level representation for open-world object understanding. To make long-tailed object detection easy, DINO-X extends its input options to support text prompt, visual prompt, and customized prompt. With such flexible prompt options, we develop a universal object prompt to support prompt-free open-world detection, making it possible to detect anything in an image without requiring users to provide any prompt. To enhance the model's core grounding capability, we have constructed a large-scale dataset with over 100 million high-quality grounding samples, referred to as Grounding-100M, for advancing the model's open-vocabulary detection performance. Pre-training on such a large-scale grounding dataset leads to a foundational object-level representation, which enables DINO-X to integrate multiple perception heads to simultaneously support multiple object perception and understanding tasks, including detection, segmentation, pose estimation, object captioning, object-based QA, etc. Experimental results demonstrate the superior performance of DINO-X. Specifically, the DINO-X Pro model achieves 56.0 AP, 59.8 AP, and 52.4 AP on the COCO, LVIS-minival, and LVIS-val zero-shot object detection benchmarks, respectively. Notably, it scores 63.3 AP and 56.5 AP on the rare classes of LVIS-minival and LVIS-val benchmarks, improving the previous SOTA performance by 5.8 AP and 5.0 AP. Such a result underscores its significantly improved capacity for recognizing long-tailed objects., Comment: Technical Report

We revisit the problem of estimating the mean of a high-dimensional distribution in the presence of an $\varepsilon$-fraction of adversarial outliers. When $\varepsilon$ is at most some sufficiently small constant, previous works can achieve optimal error rate efficiently \cite{diakonikolas2018robustly, kothari2018robust}. As $\varepsilon$ approaches the breakdown point $\frac{1}{2}$, all previous algorithms incur either sub-optimal error rates or exponential running time. In this paper we give a new analysis of the canonical sum-of-squares program introduced in \cite{kothari2018robust} and show that this program efficiently achieves optimal error rate for all $\varepsilon \in[0,\frac{1}{2})$. The key ingredient for our results is a new identifiability proof for robust mean estimation that focuses on the overlap between the distributions instead of their statistical distance as in previous works. We capture this proof within the sum-of-squares proof system, thus obtaining efficient algorithms using the sum-of-squares proofs to algorithms paradigm \cite{raghavendra2018high}., Comment: Accepted at SODA 2025, 47 pages

Transformer model has gained prominence as a popular deep neural network architecture for neural language processing (NLP) and computer vision (CV) applications. However, the extensive use of nonlinear operations, like softmax, poses a performance bottleneck during transformer inference and comprises up to 40% of the total latency. Hence, we propose innovations at the circuit, architecture, and algorithm levels to accelerate the transformer. At the circuit level, we propose topkima-combining top-k activation selection with in-memory ADC (IMA) to implement a low-energy and low-latency softmax without any sorting latency. Only the k largest activations are sent to the softmax calculation block, reducing the huge computational cost of softmax. Using a modified training scheme with top-k only in the forward pass, experimental results demonstrate only a 0.4% to 1.2% reduction in accuracy across ViT, distilBERT, and BERT-base models when evaluated on CIFAR-10, CIFAR-100, and SQuAD datasets with k=5. At the architecture level, an improved scale-free technique is introduced to reduce the computational cost of attention. The combined system, dubbed Topkima-Former, enhances 1.8x-84x speedup and 1.3x-35x energy efficiency (EE) over prior In-memory computing (IMC) accelerators. Compared to a conventional softmax macro and a digital top-k (Dtopk) softmax macro, our proposed tokima softmax macro achieves about 15x and 8x faster speed respectively., Comment: 7 pages

Inferring object motion representations from observations enhances the performance of robotic manipulation tasks. This paper introduces a new paradigm for robot imitation learning that generates action sequences by reasoning about object motion from visual observations. We propose MBA (Motion Before Action), a novel module that employs two cascaded diffusion processes for object motion generation and robot action generation under object motion guidance. MBA first predicts the future pose sequence of the object based on observations, then uses this sequence as a condition to guide robot action generation. Designed as a plug-and-play component, MBA can be flexibly integrated into existing robotic manipulation policies with diffusion action heads. Extensive experiments in both simulated and real-world environments demonstrate that our approach substantially improves the performance of existing policies across a wide range of manipulation tasks. Project page: https://selen-suyue.github.io/MBApage/

As crucial additives and intermediate, alcohols, ethers, and aldehydes play a significant role in the combustion process. However, the chemistry of NOXhydrocarbon interactions and the rate rules governing these interactions remain largely unexplored in this combustion system. To address this gap, this study provides a comprehensive investigation of H-atom abstraction by NO2 from C1-C4 alcohols, aldehydes and ethers that leads to the formation of 3 HNO2 isomers (i.e., transHONO, HNO2, and cisHONO), encompassing 9 hydrocarbons and 45 reactions. Utilizing the DLPNO CCSD(T)cc pVDZ M06 2X 6 311g d,p method, the electronic structures, single point energies, C H bond dissociation energies and 1 D hindered rotor potentials of the reactants, transition states, complexes and products in each reaction are computed. Adding these H atom abstractions to the chemical kinetic model improves the model reactivity and advances the ignition, as indicated by the reduction in ignition delay time for species that initially lacked these reactions. Further sensitivity and flux analyses highlight the crucial role of H atom abstraction by NO2. The findings underscore the importance of accurately incorporating these kinetic parameters into newly developed chemical models for alcohols, aldehydes, and ethers. Additionally, the study highlights the need for future experimental efforts to investigate the effects of NO2 on the combustion systems of these compounds., Comment: 52 pages

Subwavelength resonance is a vital acoustic phenomenon in contrasting media. The narrow bandgap width of single-layer resonator has prompted the exploration of multi-layer metamaterials as an effective alternative, which consist of alternating nests of high-contrast materials, called ``resonators'', and a background media. In this paper, we develop a general mathematical framework for studying acoustics within multi-layer high-contrast structures. Firstly, by using layer potential techniques, we establish the representation formula in terms of a matrix type operator with a block tridiagonal form for multi-layer structures within general geometry. Then we prove the existence of subwavelength resonances via Gohberg-Sigal theory, which generalizes the celebrated Minnaert resonances in single-layer structures. Intriguingly, we find that the primary contribution to mode splitting lies in the fact that as the number of nested resonators increases, the degree of the corresponding characteristic polynomial also increases, while the type of resonance (consists solely of monopolar resonances) remains unchanged. Furthermore, we derive original formulas for the subwavelength resonance frequencies of concentric dual-resonator. Numerical results associated with different nested resonators are presented to corroborate the theoretical findings.

Muons, which play a crucial role in both fundamental and applied physics, have traditionally been generated through proton accelerators or from cosmic rays. With the advent of ultra-short high-intensity lasers capable of accelerating electrons to GeV levels, it has become possible to generate muons in laser laboratories. In this work, we show the first proof of principle experiment for novel muon production with an ultra-short, high-intensity laser device through GeV electron beam bombardment on a lead converter target. The muon physical signal is confirmed by measuring its lifetime which is the first clear demonstration of laser-produced muons. Geant4 simulations were employed to investigate the photo-production, electro-production, and Bethe-Heitler processes response for muon generation and their subsequent detection. The results show that the dominant contributions of muons are attributed to the photo-production/electro-production and a significant yield of muons up to 0.01 $\mu$/$e^-$ out of the converter target could be achieved. This laser muon source features compact, ultra-short pulse and high flux. Moreover, its implementation in a small laser laboratory is relatively straightforward, significantly reducing the barriers to entry for research in areas such as muonic X-ray elemental analysis, muon spin spectroscopy and so on.

Personalization of Large Language Models (LLMs) has recently become increasingly important with a wide range of applications. Despite the importance and recent progress, most existing works on personalized LLMs have focused either entirely on (a) personalized text generation or (b) leveraging LLMs for personalization-related downstream applications, such as recommendation systems. In this work, we bridge the gap between these two separate main directions for the first time by introducing a taxonomy for personalized LLM usage and summarizing the key differences and challenges. We provide a formalization of the foundations of personalized LLMs that consolidates and expands notions of personalization of LLMs, defining and discussing novel facets of personalization, usage, and desiderata of personalized LLMs. We then unify the literature across these diverse fields and usage scenarios by proposing systematic taxonomies for the granularity of personalization, personalization techniques, datasets, evaluation methods, and applications of personalized LLMs. Finally, we highlight challenges and important open problems that remain to be addressed. By unifying and surveying recent research using the proposed taxonomies, we aim to provide a clear guide to the existing literature and different facets of personalization in LLMs, empowering both researchers and practitioners.

Generalization in robotic manipulation remains a critical challenge, particularly when scaling to new environments with limited demonstrations. This paper introduces CAGE, a novel robotic manipulation policy designed to overcome these generalization barriers by integrating a causal attention mechanism. CAGE utilizes the powerful feature extraction capabilities of the vision foundation model DINOv2, combined with LoRA fine-tuning for robust environment understanding. The policy further employs a causal Perceiver for effective token compression and a diffusion-based action prediction head with attention mechanisms to enhance task-specific fine-grained conditioning. With as few as 50 demonstrations from a single training environment, CAGE achieves robust generalization across diverse visual changes in objects, backgrounds, and viewpoints. Extensive experiments validate that CAGE significantly outperforms existing state-of-the-art RGB/RGB-D approaches in various manipulation tasks, especially under large distribution shifts. In similar environments, CAGE offers an average of 42% increase in task completion rate. While all baselines fail to execute the task in unseen environments, CAGE manages to obtain a 43% completion rate and a 51% success rate in average, making a huge step towards practical deployment of robots in real-world settings. Project website: cage-policy.github.io., Comment: Submitted to ICRA 2025

We investigate the inhomogeneous boundary value problem for elliptic and parabolic equations in divergence form in the half space $\{x_d > 0\}$, where the coefficients are measurable, singular or degenerate, and depend only on $x_d$. The boundary data are considered in Besov spaces of distributions with negative orders of differentiability in the range $(-1,0]$. The solution spaces are weighted Sobolev spaces with power weights that decay rapidly near the boundary, and are outside the Muckenhoupt $A_p$ class. Sobolev spaces with such weights contain functions that are very singular near the boundary and do not possess a trace on the boundary. Consequently, solutions may not exist for arbitrarily prescribed boundary data and right-hand sides of the equations. We establish a natural structural condition on the right-hand sides of the equations under which the boundary value problem is well-posed., Comment: 39 pages

Non-Independent and Identically Distributed (non-IID) data in Federated Learning (FL) causes client drift issues, leading to slower convergence and reduced model performance. While existing approaches mitigate this issue in Centralized FL (CFL) using a central server, Decentralized FL (DFL) remains underexplored. In DFL, the absence of a central entity results in nodes accessing a global view of the federation, further intensifying the challenges of non-IID data. Drawing on the entropy pooling algorithm employed in financial contexts to synthesize diverse investment opinions, this work proposes the Federated Entropy Pooling (FedEP) algorithm to mitigate the non-IID challenge in DFL. FedEP leverages Gaussian Mixture Models (GMM) to fit local data distributions, sharing statistical parameters among neighboring nodes to estimate the global distribution. Aggregation weights are determined using the entropy pooling approach between local and global distributions. By sharing only synthetic distribution information, FedEP preserves data privacy while minimizing communication overhead. Experimental results demonstrate that FedEP achieves faster convergence and outperforms state-of-the-art methods in various non-IID settings.

This research addresses the need for high-definition (HD) maps for autonomous vehicles (AVs), focusing on road lane information derived from aerial imagery. While Earth observation data offers valuable resources for map creation, specialized models for road lane extraction are still underdeveloped in remote sensing. In this study, we perform an extensive comparison of twelve foundational deep learning-based semantic segmentation models for road lane marking extraction from high-definition remote sensing images, assessing their performance under transfer learning with partially labeled datasets. These models were fine-tuned on the partially labeled Waterloo Urban Scene dataset, and pre-trained on the SkyScapes dataset, simulating a likely scenario of real-life model deployment under partial labeling. We observed and assessed the fine-tuning performance and overall performance. Models showed significant performance improvements after fine-tuning, with mean IoU scores ranging from 33.56% to 76.11%, and recall ranging from 66.0% to 98.96%. Transformer-based models outperformed convolutional neural networks, emphasizing the importance of model pre-training and fine-tuning in enhancing HD map development for AV navigation.

Synthesizing human motions in 3D environments, particularly those with complex activities such as locomotion, hand-reaching, and human-object interaction, presents substantial demands for user-defined waypoints and stage transitions. These requirements pose challenges for current models, leading to a notable gap in automating the animation of characters from simple human inputs. This paper addresses this challenge by introducing a comprehensive framework for synthesizing multi-stage scene-aware interaction motions directly from a single text instruction and goal location. Our approach employs an auto-regressive diffusion model to synthesize the next motion segment, along with an autonomous scheduler predicting the transition for each action stage. To ensure that the synthesized motions are seamlessly integrated within the environment, we propose a scene representation that considers the local perception both at the start and the goal location. We further enhance the coherence of the generated motion by integrating frame embeddings with language input. Additionally, to support model training, we present a comprehensive motion-captured dataset comprising 16 hours of motion sequences in 120 indoor scenes covering 40 types of motions, each annotated with precise language descriptions. Experimental results demonstrate the efficacy of our method in generating high-quality, multi-stage motions closely aligned with environmental and textual conditions.

In the fields of affective computing (AC) and brain-machine interface (BMI), the analysis of physiological and behavioral signals to discern individual emotional states has emerged as a critical research frontier. While deep learning-based approaches have made notable strides in EEG emotion recognition, particularly in feature extraction and pattern recognition, significant challenges persist in achieving end-to-end emotion computation, including real-time processing, individual adaptation, and seamless user interaction. This paper presents the EEG Emotion Copilot, a system optimizing a lightweight large language model (LLM) with 0.5B parameters operating in a local setting, which first recognizes emotional states directly from EEG signals, subsequently generates personalized diagnostic and treatment suggestions, and finally supports the automation of assisted electronic medical records. Specifically, we demonstrate the critical techniques in the novel data structure of prompt, model pruning and fine-tuning training, and deployment strategies aiming at improving real-time performance and computational efficiency. Extensive experiments show that our optimized lightweight LLM-based copilot achieves an enhanced intuitive interface for participant interaction, superior accuracy of emotion recognition and assisted electronic medical records generation, in comparison to such models with similar scale parameters or large-scale parameters such as 1.5B, 1.8B, 3B and 7B. In summary, through these efforts, the proposed copilot is expected to advance the application of AC in the medical domain, offering innovative solution to mental health monitoring. The codes will be released at https://github.com/NZWANG/EEG_Emotion_Copilot., Comment: 10 pages, 12 figures, 2 tables

Data is crucial for robotic manipulation, as it underpins the development of robotic systems for complex tasks. While high-quality, diverse datasets enhance the performance and adaptability of robotic manipulation policies, collecting extensive expert-level data is resource-intensive. Consequently, many current datasets suffer from quality inconsistencies due to operator variability, highlighting the need for methods to utilize mixed-quality data effectively. To mitigate these issues, we propose "Select Segments to Imitate" (S2I), a framework that selects and optimizes mixed-quality demonstration data at the segment level, while ensuring plug-and-play compatibility with existing robotic manipulation policies. The framework has three components: demonstration segmentation dividing origin data into meaningful segments, segment selection using contrastive learning to find high-quality segments, and trajectory optimization to refine suboptimal segments for better policy learning. We evaluate S2I through comprehensive experiments in simulation and real-world environments across six tasks, demonstrating that with only 3 expert demonstrations for reference, S2I can improve the performance of various downstream policies when trained with mixed-quality demonstrations. Project website: https://tonyfang.net/s2i/., Comment: Project website: https://tonyfang.net/s2i/

In this paper, we discuss the birational invariance of the class of balanced hyperbolic manifolds., Comment: 20 pages, comments are welcome!

In this note, we use the intersection number to determine explicitly the balanced cone of the small resolution of the quintic conifold., Comment: 8 pages, 1 figure, published in Sci Sin Math

Advanced facial recognition technologies and recommender systems with inadequate privacy technologies and policies for facial interactions increase concerns about bioprivacy violations. With the proliferation of video and live-streaming websites, public-face video distribution and interactions pose greater privacy risks. Existing techniques typically address the risk of sensitive biometric information leakage through various privacy enhancement methods but pose a higher security risk by corrupting the information to be conveyed by the interaction data, or by leaving certain biometric features intact that allow an attacker to infer sensitive biometric information from them. To address these shortcomings, in this paper, we propose a neural network framework, CausalVE. We obtain cover images by adopting a diffusion model to achieve face swapping with face guidance and use the speech sequence features and spatiotemporal sequence features of the secret video for dynamic video inference and prediction to obtain a cover video with the same number of frames as the secret video. In addition, we hide the secret video by using reversible neural networks for video hiding so that the video can also disseminate secret data. Numerous experiments prove that our CausalVE has good security in public video dissemination and outperforms state-of-the-art methods from a qualitative, quantitative, and visual point of view., Comment: Submitted to ICLR 2025

Let $n \ge 2$ and $\Omega \subset \mathbb{R}^n$ be a bounded Lipschitz domain. In this article, we establish first-order global regularity estimates in the scale of BMO spaces on $\Omega$ for weak solutions to the second-order elliptic equation $\mathrm{div}(A \nabla u) = \mathrm{div} , \boldsymbol{f}$ in $\Omega$. This is achieved under minimal regularity assumptions on $\Omega$ and the coefficient matrix $A$, utilizing the pointwise multiplier characterization of the BMO space on $\Omega$. As an application, we also obtain global estimates of $\nabla u$ in the Lebesgue space $L^1(\Omega)$ when $\boldsymbol{f}$ belongs to the Hardy space on $\Omega$., Comment: 30 pages

Millimeter wave sensing provides people with the capability of sensing the surrounding crowds in a non-invasive and privacy-preserving manner, which holds huge application potential. However, detecting stationary crowds remains challenging due to several factors such as minimal movements (like breathing or casual fidgets), which can be easily treated as noise clusters during data collection and consequently filtered in the following processing procedures. Additionally, the uneven distribution of signal power due to signal power attenuation and interferences resulting from external reflectors or absorbers further complicates accurate detection. To address these challenges and enable stationary crowd detection across various application scenarios requiring specialized domain adaption, we introduce LLMCount, the first system to harness the capabilities of large-language models (LLMs) to enhance crowd detection performance. By exploiting the decision-making capability of LLM, we can successfully compensate the signal power to acquire a uniform distribution and thereby achieve a detection with higher accuracy. To assess the system's performance, comprehensive evaluations are conducted under diversified scenarios like hall, meeting room, and cinema. The evaluation results show that our proposed approach reaches high detection accuracy with lower overall latency compared with previous methods.

Reliability in cell type annotation is challenging in single-cell RNA-sequencing data analysis because both expert-driven and automated methods can be biased or constrained by their training data, especially for novel or rare cell types. Although large language models (LLMs) are useful, our evaluation found that only a few matched expert annotations due to biased data sources and inflexible training inputs. To overcome these limitations, we developed the LICT (Large language model-based Identifier for Cell Types) software package using a multi-model fusion and "talk-to-machine" strategy. Tested across various single-cell RNA sequencing datasets, our approach significantly improved annotation reliability, especially in datasets with low cellular heterogeneity. Notably, we established objective criteria to assess annotation reliability using the "talk-to-machine" approach, which addresses discrepancies between our annotations and expert ones, enabling reliable evaluation even without reference data. This strategy enhances annotation credibility and sets the stage for advancing future LLM-based cell type annotation methods.

In the context where social media is increasingly becoming a significant platform for social movements and the formation of public opinion, accurately simulating and predicting the dynamics of user opinions is of great importance for understanding social phenomena, policy making, and guiding public opinion. However, existing simulation methods face challenges in capturing the complexity and dynamics of user behavior. Addressing this issue, this paper proposes an innovative simulation method for the dynamics of social media user opinions, the FDE-LLM algorithm, which incorporates opinion dynamics and epidemic model. This effectively constrains the actions and opinion evolution process of large language models (LLM), making them more aligned with the real cyber world. In particular, the FDE-LLM categorizes users into opinion leaders and followers. Opinion leaders are based on LLM role-playing and are constrained by the CA model, while opinion followers are integrated into a dynamic system that combines the CA model with the SIR model. This innovative design significantly improves the accuracy and efficiency of the simulation. Experiments were conducted on four real Weibo datasets and validated using the open-source model ChatGLM. The results show that, compared to traditional agent-based modeling (ABM) opinion dynamics algorithms and LLM-based opinion diffusion algorithms, our FDE-LLM algorithm demonstrates higher accuracy and interpretability., Comment: Submitted to ICASSP 2025

It is well known that every solution of an elliptic equation is analytic if its coefficients are analytic. However, less is known about the ultra-analyticity of such solutions. This work addresses the problem of elliptic equations with lower-order terms, where the coefficients are entire functions of exponential type. We prove that every solution satisfies a quantitative logarithmic ultra-analytic bound and demonstrate that this bound is sharp. The results suggest that the ultra-analyticity of solutions to elliptic equations cannot be expected to achieve the same level of ultra-analyticity as the coefficients., Comment: 24 pages, submitted

We study the field concentration phenomenon between two closely spaced perfect conductors with imperfect bonding interfaces of low conductivity type. The boundary condition on these interfaces is given by a Robin-type boundary condition. We discover a \textit{new} dichotomy for the field concentration depending on the bonding parameter $\gamma$. Specifically, we show that the gradient of solution is uniformly bounded independent of $\varepsilon$ (the distance between two inclusions) when $\gamma$ is sufficiently small. However, the gradient may blow up when $\gamma$ is large. Moreover, we identify the threshold of $\gamma$ and the optimal blow-up rates under certain symmetry assumptions. The proof relies on a crucial anisotropic gradient estimate in the thin neck between two inclusions. We develop a general framework for establishing such estimate, which is applicable to a wide range of elliptic equations and boundary conditions., Comment: 38 pages. Symmetry assumption in Theorem 1.3 is removed, boundary regularity assumptions in Lemmas 2.1 and 2.2 are weakened. Exposition improved and references added

The Reverse Cuthill-McKee (RCM) algorithm is a graph-based method for reordering sparse matrices, renowned for its effectiveness in minimizing matrix bandwidth and profile. This reordering enhances the efficiency of matrix operations, making RCM pivotal among reordering algorithms. In the context of executing the RCM algorithm, it is often necessary to select a starting node from the graph representation of the matrix. This selection allows the execution of BFS (Breadth-First Search) to construct the level structure. The choice of this starting node significantly impacts the algorithm's performance, necessitating a heuristic approach to identify an optimal starting node, commonly referred to as the RCM starting node problem. Techniques such as the minimum degree method and George-Liu (GL) algorithm are popular solutions. This paper introduces a novel algorithm addressing the RCM starting node problem by considering both the eccentricity and the width of the node during the run. Integrating this algorithm with the RCM algorithm, we introduce RCM++. Experimental results demonstrate that RCM++ outperforms existing RCM methods in major software libraries, achieving higher quality results with comparable computation time. This advancement fosters the further application and development of the RCM algorithm.The code related to this research has been made available at https://github.com/SStan1/RCM\_PP.git.

We consider nonstationary Stokes equations in nondivergence form with variable viscosity coefficients and generalized Navier slip boundary conditions with slip tensor $\mathcal{A}$ in a domain $\Omega$ in $\mathbb{R}^d$. First, under the assumption that slip matrix $\mathcal{A}$ is sufficiently smooth, we establish a priori local regularity estimates for solutions near a curved portion of the domain boundary. Second, when $\mathcal{A}$ is the shape operator, we derive local boundary estimates for the Hessians of the solutions, where the right-hand side does not involve the pressure. Notably, our results are new even if the viscosity coefficients are constant., Comment: 33 pages, 1 figure / v2. revised introduction and simplifed arguments

Spatial reasoning in Large Language Models (LLMs) is the foundation for embodied intelligence. However, even in simple maze environments, LLMs still encounter challenges in long-term path-planning, primarily influenced by their spatial hallucination and context inconsistency hallucination by long-term reasoning. To address this challenge, this study proposes an innovative model, Spatial-to-Relational Transformation and Curriculum Q-Learning (S2RCQL). To address the spatial hallucination of LLMs, we propose the Spatial-to-Relational approach, which transforms spatial prompts into entity relations and paths representing entity relation chains. This approach fully taps the potential of LLMs in terms of sequential thinking. As a result, we design a path-planning algorithm based on Q-learning to mitigate the context inconsistency hallucination, which enhances the reasoning ability of LLMs. Using the Q-value of state-action as auxiliary information for prompts, we correct the hallucinations of LLMs, thereby guiding LLMs to learn the optimal path. Finally, we propose a reverse curriculum learning technique based on LLMs to further mitigate the context inconsistency hallucination. LLMs can rapidly accumulate successful experiences by reducing task difficulty and leveraging them to tackle more complex tasks. We performed comprehensive experiments based on Baidu's self-developed LLM: ERNIE-Bot 4.0. The results showed that our S2RCQL achieved a 23%--40% improvement in both success and optimality rates compared with advanced prompt engineering., Comment: Submitted to ICASSP

Current LiDAR point cloud-based 3D single object tracking (SOT) methods typically rely on point-based representation network. Despite demonstrated success, such networks suffer from some fundamental problems: 1) It contains pooling operation to cope with inherently disordered point clouds, hindering the capture of 3D spatial information that is useful for tracking, a regression task. 2) The adopted set abstraction operation hardly handles density-inconsistent point clouds, also preventing 3D spatial information from being modeled. To solve these problems, we introduce a novel tracking framework, termed VoxelTrack. By voxelizing inherently disordered point clouds into 3D voxels and extracting their features via sparse convolution blocks, VoxelTrack effectively models precise and robust 3D spatial information, thereby guiding accurate position prediction for tracked objects. Moreover, VoxelTrack incorporates a dual-stream encoder with cross-iterative feature fusion module to further explore fine-grained 3D spatial information for tracking. Benefiting from accurate 3D spatial information being modeled, our VoxelTrack simplifies tracking pipeline with a single regression loss. Extensive experiments are conducted on three widely-adopted datasets including KITTI, NuScenes and Waymo Open Dataset. The experimental results confirm that VoxelTrack achieves state-of-the-art performance (88.3%, 71.4% and 63.6% mean precision on the three datasets, respectively), and outperforms the existing trackers with a real-time speed of 36 Fps on a single TITAN RTX GPU. The source code and model will be released.

Current 3D single object tracking methods primarily rely on the Siamese matching-based paradigm, which struggles with textureless and incomplete LiDAR point clouds. Conversely, the motion-centric paradigm avoids appearance matching, thus overcoming these issues. However, its complex multi-stage pipeline and the limited temporal modeling capability of a single-stream architecture constrain its potential. In this paper, we introduce SiamMo, a novel and simple Siamese motion-centric tracking approach. Unlike the traditional single-stream architecture, we employ Siamese feature extraction for motion-centric tracking. This decouples feature extraction from temporal fusion, significantly enhancing tracking performance. Additionally, we design a Spatio-Temporal Feature Aggregation module to integrate Siamese features at multiple scales, capturing motion information effectively. We also introduce a Box-aware Feature Encoding module to encode object size priors into motion estimation. SiamMo is a purely motion-centric tracker that eliminates the need for additional processes like segmentation and box refinement. Without whistles and bells, SiamMo not only surpasses state-of-the-art methods across multiple benchmarks but also demonstrates exceptional robustness in challenging scenarios. SiamMo sets a new record on the KITTI tracking benchmark with 90.1\% precision while maintaining a high inference speed of 108 FPS. The code will be released at https://github.com/HDU-VRLab/SiamMo.