arXiv:2605.27004v1 Announce Type: new
Abstract: Lattice Boltzmann methods are usually derived under the assumption of isotropy. In this work, we present a derivation of a Lattice Boltzmann method for anisotropic fluid flow. Starting from an anisotropic equilibrium distribution, we show a full derivation of the resulting lattice Boltzmann method. We ensure that our method correctly reproduces macroscopic behavior via Chapman-Enskog analysis for a single-relaxation time collision operator. As a result, we are able to show that a properly discretized anisotropic Maxwell-Boltzmann equilibrium does macroscopically in fact lead to an anisotropic variation of the Navier-Stokes equations. All desired properties of lattice Boltzmann methods, such as locality of the collision operator, isotropic discrete position and velocity space, or mass and momentum conservation are retained. While it is explicitly shown in the context of fluid flow, the presented scheme is straight-forward to adopt to advection-diffusion problems.
Science Journals
arXiv:2605.27360v1 Announce Type: new
Abstract: Cellular research and development (R&D) is throttled by six structural processes that each consume months of manual engineering work per iteration: (i) synthesizing new features from standards or research papers into production code; (ii) conformance and interoperability testing; (iii) hardening against field anomalies and diverse deployment environments; (iv) data-driven optimization of network functionalities; (v) discovering and prototyping novel waveforms, functionalities, and capabilities for future standards; and (vi) securing the stack against vulnerabilities. Although Large Language Models (LLMs) have compressed comparable R&D work in general software engineering from days to minutes, their known pitfalls worsen on Radio Access Network (RAN) use cases: they hallucinate Application Programming Interfaces (APIs) and mis-read specifications, which kills interoperability of RAN components at the first mistake, and they heavily rely on simulations for designing algorithms, which is notorious for breaking when transferred to real hardware. To address these challenges, we present GENESIS, an agentic Artificial Intelligence (AI) framework that converts intents (e.g., a specification clause, a telemetry anomaly, or a research hypothesis) into solutions validated with over-the-air experiments, fed back into a persistent knowledge base. GENESIS is built on three composable primitives (agents, skills, hooks) and a knowledge layer (SYNAPSE) that doubles as the source of ground truth and the recipient of every artifact the framework produces, making capabilities compound across runs.
arXiv:2605.27130v1 Announce Type: new
Abstract: We present DEI: Diversity in Evolutionary Inference, a distributed Quality-Diversity (QD) search framework that assigns heterogeneous large language models (LLMs) as mutation operators across peer nodes communicating with non-blocking collective operations. Unlike homogeneous parallel search, which replicates a single model's inductive biases across all workers, DEI treats each LLM's distinct creative prior as a complementary source of behavioral novelty. Extending the Digital Red Queen framework with DEI, nodes share local optimal solutions at the end of each round to seed the next round's population. This creates cross-model adversarial pressure that drives robustness beyond intra-model self-play. Evaluated on the Core War domain, a competitive programming benchmark in which Redcode warrior programs battle inside a simulated machine, a four-node heterogeneous ensemble (GPT-5.4-mini, Claude Sonnet 4.6, GPT-5.2, and Claude Haiku 4.5) achieves 124 percent higher merged-archive QD-Score (45.90 vs. 20.46) and 28 percent higher coverage (80.6 percent vs. 63.0 percent of cells) than a single-node baseline at equal total LLM-call budget. The heterogeneous ensemble also outperforms an equally-budgeted homogeneous ensemble on QD-Score, coverage, and held-out solution generality across all four model families. These results provide the first empirical evidence that model diversity, not merely parallelism, is the key driver of gain in distributed LLM-based QD search.
arXiv:2605.26235v1 Announce Type: new
Abstract: Identifying dense subgraphs known as quasi-cliques is pivotal in numerous graph mining tasks across domains such as social networks, biology, and e-commerce. While prior work has developed efficient algorithms for quasi-clique detection in static graphs, real-world networks are inherently dynamic, where edges appear and disappear continuously. This renders static methods inefficient and ill-suited for real-time analysis. In this paper, we initiate the study of the Dynamic Maximum Quasi-Clique Problem (DMQCP), which aims to maintain and update the largest quasi-clique in a graph under streaming graph updates. We propose DMI, a novel MinHash-based dynamic framework that supports fast, high-quality approximate maintenance of quasi-cliques. DMI leverages two update-efficient hashing schemes, i.e., $l$-buffered $k$-MinHash and Bottom-$k$ MinHash, to maintain candidate quasi-cliques incrementally. To ensure robustness and reduce bias, we further design a batch reconstruction strategy to periodically rebuild the candidate set, guaranteeing both stability and adaptability under frequent updates. Extensive experiments on real-world and synthetic datasets show that DMI achieves up to four orders of magnitude speedup over static baselines, while preserving solution quality. As a side product, we also propose a framework NSF that primarily uses the neighbor-search technique to maintain quasi-clique candidates while edge updating. This work establishes the first efficient algorithmic framework for dynamic quasi-clique extraction, enabling scalable and real-time dense subgraph mining in evolving networks.
arXiv:2605.26503v1 Announce Type: new
Abstract: Vision-Language Navigation (VLN) requires an agent to navigate 3D environments following natural language instructions. During navigation, existing agents commonly encounter perceptual uncertainty, such as insufficient evidence for reliable grounding or ambiguity in interpreting spatial cues, yet they typically ignore such information when predicting actions. In this work, we explicitly model three forms of perceptual uncertainty (i.e., geometric, semantic, and appearance uncertainty) and integrate them into the agent's observation space to enable informed decision-making. Concretely, our agent first constructs a Semantic Gaussian Map (SGM), composed of differentiable 3D Gaussian primitives initialized from panoramic observations, that encodes both the geometric structure and semantic content of the environment. On top of SGM, geometric uncertainty is estimated through variational perturbations of Gaussian position and scale to assess structural reliability; semantic uncertainty is captured by perturbing Gaussian semantic attributes to reveal ambiguous interpretations; and appearance uncertainty is characterized by Fisher Information, which measures the sensitivity of rendered observations to Gaussian-level variations. These uncertainties are incorporated into SGM, extending it into a unified 3D Value Map, which grounds them as affordances and constraints that support reliable navigation. Comprehensive evaluations across multiple VLN benchmarks show the effectiveness of our agent.
arXiv:2604.23541v3 Announce Type: replace-cross
Abstract: This paper presents a symmetric unified transport (UT) compact model for metal-oxide-semiconductor field-effect transistors (MOSFETs) that bridges drift-diffusion (DD) and ballistic transport (BT) regimes. The proposed model self consistently accounts for both current and charge across the DD-BT transition. Quantum capacitance and carrier transport are incorporated into the charge density formulation. Drain side velocity saturation and the source side thermal velocity limit are unified within a single framework using a physically motivated high field scattering length, enabling accurate modeling from DD square law behavior to the ballistic limit. In addition, a physical channel charge and capacitance model is developed to capture capacitance reduction in the quasi-ballistic regime, which is not considered in standard compact models. The model is verified using theoretical analysis and experimental data from MOSFETs with multiple channel lengths, achieving accurate fitting using only physically motivated model parameters. The formulation is continuous and symmetric, and it passes both DC and AC symmetry tests.
arXiv:2605.26148v1 Announce Type: new
Abstract: A rainbow is a captivating natural phenomenon resulting from the refraction, dispersion, and reflection of sunlight within water droplets. Traditional classroom demonstrations often focus on qualitative explanations of the formation of rainbows using prisms or water bowls. This study presents a simple experimental approach to analysing the process of rainbow formation through quantitative analysis using a cylindrical glass filled with water, graph paper, and three semiconductor laser sources emitting red, green, and blue light. By measuring the angles of minimum deviation for different wavelengths, we have found that the experimental values closely match the theoretical predictions. This method offers a hands-on, cost-effective approach to enhance students' understanding of the physics behind rainbows.
arXiv:2605.26549v1 Announce Type: new
Abstract: With the widespread application of location-based services, fingerprint-based localization has demonstrated advantages in environments with complex signal propagation. Deep learning has significantly improved the efficiency of both offline training and online matching in localization processes. However, existing fingerprints only contain terminal position information without capturing motion states, and neural network designs have not fully incorporated structural features such as fingerprint sparsity. In this paper, we propose a triple-beam fingerprint (TBF) incorporating Doppler information and design a Transformer-based localization and orientation awareness network (LOA-Net) to simultaneously estimate user position and motion direction in massive multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems. We first show the correlation between TBF and multipath information, and investigate the collinearity of different TBFs, demonstrating that TBF is an effective small-size sparse fingerprint. Then, we propose LOA-Net containing a mask-augmented detection Transformer for regression (MaskDETR-Reg) module and a fusion-enhanced Transformer for direction classification (Fusion-TDC) module to process angle-delay domain information and Doppler domain information, respectively. Finally, in the simulation of indoor scenarios defined in 3GPP 38.901, the proposed method achieves significantly better localization accuracy than weighted $K$-nearest neighbors (WKNN), 2D and 3D convolutional neural networks (CNNs), and achieves satisfactory motion direction estimation accuracy.
arXiv:2602.22190v2 Announce Type: replace
Abstract: Open-source native GUI agents still lag behind closed-source systems on long-horizon navigation tasks. This gap stems from two limitations: a shortage of high-quality, action-aligned reasoning data, and the direct adoption of generic post-training pipelines that overlook the unique challenges of GUI agents. We identify two fundamental issues in these pipelines: (i) standard SFT with CoT reasoning often hurts grounding, and (ii) step-wise RLVR-tyle training faces partial verifiability, where multiple actions can be correct but only a single demonstrated action is used for verification. This makes offline step-wise metrics weak predictors of online task success. In this work, we present GUI-Libra, a tailored training recipe that addresses these challenges. First, to mitigate the scarcity of action-aligned reasoning data, we introduce a data construction and filtering pipeline and release a curated 81K GUI reasoning dataset. Second, to reconcile reasoning with grounding, we propose action-aware SFT that mixes reasoning-then-action and direct-action data and reweights tokens to emphasize action and grounding. Third, to stabilize RL under partial verifiability, we identify the overlooked importance of KL regularization in RLVR and show that a KL trust region is critical for improving offline-to-online predictability; we further introduce success-adaptive scaling to downweight unreliable negative gradients. Across diverse web and mobile benchmarks, GUI-Libra consistently improves both step-wise accuracy and end-to-end task completion. Our results suggest that carefully designed post-training and data curation can unlock significantly stronger task-solving capabilities without costly online data collection. We release our dataset, code, and models to facilitate further research on data-efficient post-training for reasoning-capable GUI agents.
arXiv:2605.24387v2 Announce Type: replace
Abstract: We consider an initial boundary value problem of the space fractional Allen-Cahn equation with logarithmic Flory-Huggins potential. As an approximation technique, first-order weighted and shifted Grunwald difference formulae of the left and right fractional derivatives are used. The main focus of the present work is to study the spectral features of the underlying matrices and matrix sequences and to design proper preconditioners based on the spectral information. Then a computational and spectral analysis of the resulting preconditioned matrix sequences is performed. Numerical evidence and a short list of open problems complete the current study.
arXiv:2605.21617v2 Announce Type: replace
Abstract: Inference from interaction maps, such as centromere identification from genome-wide chromosome conformation capture techniques -- notably Hi-C -- can be formulated as a generic inverse problem: infer a set of parameters given a map summarizing pairwise interactions between entities through blocks of variable numbers and sizes. In this work, we introduce a data-driven approach that leverages shared structure between these maps, such as global alignment between localized patterns, while handling the variability in number and size of entities arising in real-world data. Our approach relies on a transformer architecture capable of handling such variability and a custom simulator to generate abundant, yet computationally cheap synthetic data for training. Applied to the problem of centromere localization, the method accurately recovers their genomic positions across a wide range of species of various genome sizes.
arXiv:2605.26557v1 Announce Type: cross
Abstract: Antimicrobial photodynamic therapy (aPDT) is a promising modality for inactivation of antibiotic resistant bacteria, relying on the activation of a photosensitizer (PS) by light of a specific wavelength. This process results in the formation of reactive oxygen species, which ultimately induce cell death. However, aPDT in its conventional form, is limited by the shallow penetration of visible light, restricting its effectiveness for treatment of soft tissue and orthopaedic tissues. To overcome this limitation, near-infrared (NIR) absorbing PS can be used. However, poor stability in vivo after injection, ineffective microbial targeting due to hydrophilic nature and off-site tissue damage are the issues with use of NIR absorbing bare PSs. This issue can be mitigated by combining NIR light with a upconverting nanoparticles (UCNPs), which mediate in conversion of NIR into visible light for effective PS activation. In this study, LaF$_3$:Er$^{3+}$,Yb$^{3+}$ nanoparticles were synthesized using a hydrothermal method and coated with Rose Bengal (RB), a promising hydrophilic PS for aPDT, to evaluate the potential for NIR-triggered aPDT. Characterization of the synthesized UCNPs confirmed the crystalline structure, size distribution and successful RB functionalization. Photophysical studies demonstrated efficient energy transfer between UCNPs and RB, leading to singlet oxygen ($^1$O$_2$) generation in vitro. Antibacterial studies against Methicilin resistant Staphylococcus aureus (MRSA), a superbug of implicated soft tissue and orthopaedic infections, revealed significant photo-bactericidal efficacy upon NIR irradiation, indicating the potential of RB-coated UCNPs for aPDT applications.
arXiv:2605.27261v1 Announce Type: new
Abstract: We present a pilot study on the collection and synchronisation of multimodal data for player experience investigation. We collected game telemetry, self-reported surveys, biometrics, and cued-retrospective think-aloud (C-RTA) data from 19 participants playing three Atari 2600 games. The study then uses the data to investigate difficulty in PX, showcasing a protocol for future multimodal research.
The dataset obtained from the experiment, which is publicly available, shows potential as a rich, transformative source that can be used to investigate dynamic difficulty adjustment algorithms, game balancing strategies or broader explorations of games user research. The study findings suggest that the experimental approach holds strong potential for generalisation in future player experience studies.
arXiv:2605.24219v2 Announce Type: replace
Abstract: Large Language Models (LLMs) are increasingly deployed as autonomous agents that reason, use tools, and act over multiple steps. Yet most hallucination benchmarks still evaluate only the final output, missing failures that originate in intermediate Thought-Action-Observation steps. We present Trajel, a dataset and evaluation framework for auditing trajectory-level hallucinations in multi-agent industrial workflows. Trajel introduces a five-type hallucination taxonomy (factual, referential, logical, procedural, and scope-based) over expert-annotated agent traces from AssetOpsBench. We benchmark supervised detection models at the subtask, trajectory, and long-context levels. Our results show that the most common failure modes are missed by existing benchmarks, that nearly half of hallucinated trajectories involve multiple types at once, and that automated detectors with high binary accuracy still misclassify the subtlest types. Trajectory-aware detection significantly outperforms standard post-hoc verification, making taxonomy-grounded evaluation necessary for safer agentic deployment.
arXiv:2605.26175v1 Announce Type: new
Abstract: Low-bit activation quantization remains a major bottleneck in efficient large language model (LLM) deployment. The difficulty is not only that activations contain outliers, but that their distributions are often poorly matched to a low-bit uniform quantizer. Existing post-training quantization (PTQ) methods suppress peaks, balance channels, or minimize reconstruction error, yet they rarely specify what activation distribution is actually easy to discretize. As a result, activations may appear numerically smoother while still incurring large quantization error because the quantization range remains wide or most values collapse into a few levels near the mean. We recast activation transformation as quantizer-facing distribution design and analyze quantization error from an information-theoretic perspective. Our analysis shows that quantization-friendly activations should jointly have a smaller numerical range and sufficient dispersion within that range. Guided by this analysis, we propose InfoQuant, a train-free method that employs Peak Suppression Orthogonal Transformation (PSOT) to shape activations into more quantization-friendly distributions. We further introduce adaptive outlier-token selection to improve the robustness of PSOT during optimization. Across multiple LLM families, InfoQuant consistently outperforms prior PTQ and end-to-end training baselines. Under W4A4KV4, it preserves 97% of floating-point accuracy on average and reduces the LLaMA-2 13B performance gap by 42% over the previous state of the art. Code is available at [https://github.com/LLIKKE/InfoQuant](https://github.com/LLIKKE/InfoQuant)
arXiv:2605.27076v1 Announce Type: new
Abstract: In many multi-agent applications, tasks yield rewards only when executed by a coalition meeting an unknown size threshold; otherwise, feedback is fully censored. This censorship creates an identifiability problem: agents cannot distinguish stochastic failure from insufficient coordination. We formalize this setting as the Threshold-Activated Cooperative Multi-Armed Bandit (TAC-MAB) and analyze it under both centralized and decentralized coordination. We show that a centralized algorithm (C-TAC) achieves cumulative regret O(log T), decomposed into a structural-search term that captures the cost of resolving feasibility under censored feedback and a statistical-monitoring term for value estimation. We then introduce D-TAC, a decentralized event-triggered protocol in which agents synchronize only when their structural beliefs change. Empirically, D-TAC achieves a 23x reduction in communication relative to the centralized baseline while preserving feasibility alignment under conservative belief fusion. These results characterize the coordination cost of learning under censored feedback and show that near-centralized communication efficiency is achievable without continuous synchronization.
arXiv:2605.26167v1 Announce Type: new
Abstract: We propose Lie group embedded dynamical neural networks (LieEDNN) and the corresponding learning algorithms based on gradient descent and metric projection on smooth manifold, where we treat Lie group as an intrinsic representation for continuous symmetry of manifold geometry. Thereby we achieve learnable and stable dynamics on the underlying manifold for general Lie group, and we are able to utilize the powerful representation capability of Lie group such as SO(3) and SE(3) to solve real world engineering problems in areas such as robotics, graphics, and control. Two core challenges are: (i) General Lie groups are incompatible with addition arithmetic, which is necessary for neural network interactions. (ii) The dynamics evolve in the nonlinear representation space of special algebra rather than the normal Euclidean space, which violates the paradigm of common neural ODEs. To address these two challenges, we firstly introduce adjoint Lie group action on the Lie algebra, which induces a linear mapping and transfer to the block-wise structure of weight matrices, such that addition could operate on the Lie algebra as a vector space. Then we parameterize the Lie algebra and the adjoint action as linear transformation so that the architecture is aligned with neural network perceptrons. Explicitly, this embedding appears as block-wise manifold constraints on weights, and we develop algorithms to learn the equilibrium with stability guarantees of the temporal neural network dynamics. Experiments are implemented on a specific Lie group SE(3), with the application scenario of telescopic manipulators.
arXiv:2603.03711v3 Announce Type: replace
Abstract: Local Differential Privacy (LDP) is the gold standard trust model for privacy-preserving machine learning by guaranteeing privacy at the data source. However, its application to image data has long been considered impractical due to the high dimensionality of pixel space. Canonical LDP mechanisms are designed for low-dimensional data, resulting in severe utility degradation when applied to high-dimensional pixel spaces. This paper demonstrates that this utility loss is not inherent to LDP, but from its application to an inappropriate data representation. We introduce LDP-Slicing, a lightweight, training-free framework that resolves this domain mismatch. Our key insight is to decompose pixel values into a sequence of binary bit-planes. This transformation allows us to apply the LDP mechanism directly to the bit-level representation. To further strengthen privacy and preserve utility, we integrate a perceptual obfuscation module that mitigates human-perceivable leakage and an optimization-based privacy budget allocation strategy. This pipeline satisfies rigorous pixel-level $\varepsilon$-LDP while producing images that retain high utility for downstream tasks. Extensive experiments on face recognition and image classification demonstrate that LDP-Slicing outperforms existing DP/LDP baselines under comparable privacy budgets, with negligible computational overhead.
arXiv:2605.26163v1 Announce Type: new
Abstract: Competitive resource allocation problems over frequency and space can be formulated as minimax interaction between transmit power and worst-case interference. This formulation naturally arises in multi-operator low Earth orbit (LEO) satellite spectrum sharing, where transmissions from competing constellations interfere in real-time. Under Gaussian channels, AWF is strongly convex--concave on nondegenerate active channels, whereas discrete constellations yield generally nonconvex mercury/water-filling formulations. In this paper we propose the Adversarial Water-Filling (AWF) problem with corresponding theory and algorithms for these real situations. In addition, we develop a wireless foundation model for AWF to learn the AWF search dynamics. The architecture incorporates permutation-invariant channel representations, a constraint-aware graph neural network (GNN) with sparse message passing, and global latent variables capturing the low-dimensional water level implied by the AWF optimality. Through learned projected extragradient iterations, the model approximates stationary solutions of the constrained minimax problem arising under mercury/water-filling. We further show that, under local regularity and contractivity conditions, the learned AWF dynamics converge locally linearly around regular stationary points. Experiments demonstrate empirical generalization across unseen problem sizes, different constraints, and multiple discrete constellations, while achieving more than one-order-of-magnitude runtime improvements over iterative baselines. The related code can be found at https://github.com/convexsoft/AWF.
arXiv:2605.26190v1 Announce Type: new
Abstract: This paper presents the HRVConformer, a novel deep learning architecture for the classification of hypoxic-ischemic encephalopathy (HIE) using the instantaneous heart rate (HR) signal. Unlike conventional approaches that rely on handcrafted features, HRVConformer directly processes raw HR signals in an end-to-end manner, capturing both local and long-range dependencies through a hybrid Convolution-Transformer framework. By integrating convolutional layers for local feature extraction and Transformer-based attention mechanisms for global context modelling, the architecture effectively enhances signal representation and classification performance. The model was trained using supervised learning on a large HR dataset consisting of 1,573 one-hour epochs, including 259 one-hour expert-annotated epochs and a substantial set of weakly labelled data. A 314-hour validation set provided a robust performance estimation, while an independent 215-hour dataset with expert annotations was reserved for final testing. HR signals were extracted from electrocardiogram (ECG) recordings using an improved Pan-Tompkins algorithm, which significantly enhanced both signal quality and data availability. Experimental results demonstrate that the HRVConformer achieves an AUC of 83.23\% and accuracy of 74.56\% on the test set. These results surpass the performance of the Transformer, ResNet50 and fully convolutional networks baselines, highlighting the advantages of integrating convolutional and Transformer-based components for HR-based HIE classification. The proposed method provides a promising step toward a more accurate and automated assessment of HIE using HR signals. The code is available at: https://github.com/syu-kylin/HRVConformer.
arXiv:2605.26609v1 Announce Type: new
Abstract: Software stack upgrades are a routine part of software maintenance and evolution, typically motivated by improved performance, stability, or functionality. Yet their impact on energy consumption - a growing concern for organizations pursuing sustainability - remains poorly understood. This paper presents a systematic method for measuring how different versions of core software stack components, such as Spring Boot and the Java Virtual Machine (JVM), influence the energy consumption of applications. Our approach evaluates combinations of framework versions, runtime versions, and execution platforms through automated benchmarking. Using a case study based on the Spring Petclinic REST application, we show that energy consumption varies substantially across Spring Boot and JVM versions, in some cases producing unexpected regressions. Notably, newer JVM releases and virtual threads (introduced in Java 21 and 23) yielded significant energy savings without requiring application changes. These results demonstrate that software upgrades can meaningfully affect energy usage and that measuring energy consumption provides valuable evidence for decision making in software maintenance and evolution.
arXiv:2604.27292v3 Announce Type: replace
Abstract: Every system that performs effects has two boundaries: what it can do (expressiveness) and what governance covers (governance). In nearly all deployed AI systems, these boundaries are defined independently, creating three regions: governed capabilities (the only useful region), ungoverned capabilities (risk), and governance policies that address non-existent capabilities (theater). Two of the three regions are failure modes. We focus on the governance of effects: actions that AI systems perform in the world (API calls, database writes, tool invocations). This is distinct from the governance of model outputs (content quality, bias, fairness), which operates at a different level and requires different mechanisms. We present a formal framework for analyzing this structural gap. Rice's theorem (1953) proves the gap is undecidable in the general case for any Turing-complete architecture that attempts to govern effects behaviorally: no algorithm can decide non-trivial semantic properties of arbitrary programs, including the property "this program's effects comply with the governance policy." We define coterminous governance: a system property where the expressivenessboundary equals the governance boundary. We show that coterminous governance requires an architectural decision (separatingcomputation from effect) rather than a governance layer added after the fact. We show that structural governance under this separation subsumes separate governance infrastructure: governance checks become part of the execution pipeline rather than a second system running alongside it. We propose coterminous governance as the testable criterion for any AI governance system: either the two boundaries are provably identical, or risk and theater are structurally inevitable. Proofs are mechanized in Coq (454 theorems, 36 modules, 0 admitted).
arXiv:2605.27098v1 Announce Type: new
Abstract: We consider the problem of dividing a set of indivisible goods among agents with additive valuations. This problem has been studied under various objectives in both the computer science and the operations research literature. Our main contribution is a novel dictator test using this problem, which can separate a dictator from any function sufficiently far from a dictator. We use this test to prove the following hardness results (assuming the unique games conjecture is true):
(1) We show that it is NP-hard to approximate the max Nash welfare by a factor better than $\sqrt[3]{\frac{81}{65}} - \varepsilon \approx 1.0761$. This improves on the previous best known inapproximability factor of $\sqrt{\frac87} - \varepsilon \approx 1.069$.
(2) We show that it is NP-hard to approximate the maximum budgeted allocation by a factor better than $\frac{243}{227} - \varepsilon \approx 1.07$. This improves on the previous best known inapproximability factor of $\frac{16}{15} - \varepsilon \approx 1.067$.
(3) We show that it is NP-hard to approximate the max generalized assignment problem (GAP) by a factor better than $\frac{145}{129} - \varepsilon \approx 1.124$. This improves on the previous best known inapproximability factor of $\frac{11}{10} - \varepsilon \approx 1.10$.
arXiv:2605.26618v1 Announce Type: new
Abstract: The Abbe diffraction limit, tied to the fundamental spatial bandwidth constraint imposed by any physical aperture, remains the primary barrier to achieving ultimate far-field optical resolution and precise light-matter interactions. However, current efforts to engineer structured light fields beyond this limit often come at the cost of massive sacrifices in energy efficiency. In this work, we mathematically complete the family of non-zero azimuthal-order Circular Prolate Spheroidal Wave Functions (CPSWFs), introducing them as a complete class of band-limited superoscillatory optical vortices carrying helical phase. Compared with classical Laguerre-Gaussian (LG) beams, we rigorously prove that these eigenmodes achieve the theoretical upper bound for extreme energy concentration under strict band-limited constraints. At the scale of light-matter interactions, this optimal concentration directly amplifies the intensity gradients and angular momentum densities that govern optical forces. This advantage translates directly into a 29.9% reduction in the trapping power threshold and a 2.3-fold increase in the subdiffraction orbital rotation speed of nanoparticles. Looking forward, this fundamental physical framework not only establishes strict mathematical boundaries for structured light fields but also serves as an absolute theoretical benchmark for deep-learning inverse design, and next-generation extreme optical micro-manipulation systems.
arXiv:2605.26619v1 Announce Type: new
Abstract: Reconstructing continuous state trajectories of chaotic dynamical systems from sparse, noisy observations remains a fundamental open problem in nonlinear science. We introduce the Physics-Informed Diffusion Model with Dormand-Prince Integration (PIDM-DP), which embeds a fully differentiable 5th-order Dormand-Prince (DP-RK45) ODE integrator directly into the reverse sampling loop of a Denoising Diffusion Probabilistic Model (DDPM). At each denoising step, physics residuals are back-propagated via automatic differentiation, constraining every generated trajectory to satisfy the system's governing equations to 5th-order accuracy. A linear-scheduled guidance mechanism that ramps the physics weight from zero at high noise levels to its full value near the clean-data limit prevents the gradient explosions that cause naive physics-informed approaches to fail on stiff systems with Jacobian eigenvalues of order $O(10^3)$. Evaluated across five benchmark systems of increasing complexity 3D Lorenz, 3D R\"ossler, 5D Hyperchaotic, 20D Lorenz-96, and the stiff 3D Rabinovich-Fabrikant at 10% observation density with additive Gaussian noise ($\sigma=0.05$), PIDM-DP achieves reconstruction RMSE improvements of up to $15.4\times$ over an unconstrained diffusion baseline and decisively outperforms the Ensemble Kalman Filter on stiff systems where ensemble covariance collapses. On the Rabinovich-Fabrikant out-of-distribution benchmark, PIDM-DP attains RMSE $0.1097 \pm 0.0269$ versus $0.9443 \pm 0.5288$ (unconstrained diffusion, $8.6\times$ worse) and $0.3561 \pm 0.3040$ (EnKF, $3.2\times$ worse), with $p<0.001$ in paired Wilcoxon tests ($N = 30$). Topological validation via the Rosenstein Lyapunov estimator confirms that PIDM-DP preserves the chaotic invariant measure.