Science & Mathematics

Recent studies have applied large language model (LLM) agent systems to computational simulation workflows. Such workflows are long-horizon, so the information generated can exceed what an LLM can reason over at once, its context window. Context management is therefore essential, yet existing systems have either neglected it or treated it as a supporting mechanism rather than a subject of study. This paper presents MarkovSim, an LLM agent harness for long-horizon computational simulation, whose core is a context management scheme built into the workflow. The workflow record is written to a memory system with a predefined schema, and at workflow-defined boundaries, namely the state transitions of a finite-state machine a compact representation of the solution progress is constructed from it as the agent's context. Instantiated on finite element analysis and evaluated on six benchmark problems, MarkovSim passed 16 of 18 runs and corrected its own faults in both the solver operations and the model physics. The engineer was consulted only where engineering judgement was needed. The context remained bounded throughout every run, regardless of its length.

A gapped Dirac cone in antiferromagnetic topological insulators (AFM-TIs) is essential for realizing the quantized anomalous Hall effect, yet its intrinsic magnitude remains controversial. In the prototypical AFM-TI MnBi2Te4, however, the observed Dirac gap is significantly smaller than theoretical predictions or nearly absent, highlighting a long-standing discrepancy. Here we demonstrate that NdBi hosts a spin-polarized topological surface Dirac cone with a sizable gap of 17 meV at the Dirac point, in excellent agreement with density functional theory predictions (12 meV). This direct observation is enabled by high-resolution 7 eV laser-based spin- and angle-resolved photoemission spectroscopy, which unambiguously disentangles the spin-polarized surface Dirac cone from bulk-derived states. Furthermore, through temperature dependence and controlled surface contamination, we establish a direct linkage between surface magnetism and the Dirac gap, demonstrating that the gap opens only in the presence of surface magnetic order. These results provide definitive spectroscopic evidence for an intrinsic Dirac gap in AFM-TIs and establish NdBi as a model platform to resolve the long-standing discrepancy between experiment and theory in AFM-TIs.

Electroencephalography (EEG) is widely used in clinical assessment, brain-computer interfaces, and cognitive-state analysis, yet EEG modeling remains fragmented across task paradigms. Recent multimodal large language models (MLLMs) provide a promising interface for flexible multimodal reasoning, but their ability to understand EEG inputs remains limited. In this work, we propose OneEEG, a unified EEG-MLLM framework for multi-task EEG understanding. By training on our curated OneEEG-Instruct, a multi-task EEG instruction-tuning dataset, OneEEG jointly models numerical EEG representations and visual EEG representations, and introduces a task-aware Mixture of Projectors (MoP) to align heterogeneous EEG features across different task families with the LLM embedding space. We further establish OneEEG-Bench, a benchmark for evaluating current MLLMs and our method on multi-task EEG understanding. Experiments show that existing MLLMs have limited ability to interpret EEG inputs, while OneEEG achieves stronger performance by integrating numerical and visual EEG representations with task-aware EEG-to-LLM projection. Extensive ablations and analyses further reveal the effects of visual EEG renderings, MoP variants, router behavior, and feature dispersion across EEG tasks.

Machine learning models in engineering are often used beyond their training conditions, where reliable uncertainty quantification (UQ) matters most. Existing comparisons of regression UQ methods rely on random splits, which assess calibration only in distribution. We introduce a three-rung shift ladder (in distribution, soft shift and hard shift) built along physically meaningful shift variables, and evaluate 12 methods from five families on seven public engineering datasets: five extrapolation settings, an unseen turbofan fault mode and a winter air-quality sensor deployment. All tuning uses source data only. In distribution, conformal methods cover at least 0.946 of test points on every dataset. Under hard shift, mean coverage falls to 0.40-0.75 across the 11 methods that always return an interval, and no systematic difference in method ranks is detected (Friedman p = 0.63). Weighted conformalised quantile regression stays near nominal on the points it answers, but abstains on 85\% of hard-shift points on average and covers only 0.67 of the few Concrete points it answers. Source-validation gains predict improvement in distribution and under soft shift, but not under hard shift (Spearman's rho = 0.04). Engineering evaluations should split calibration data by deployment unit, report subgroup coverage and sharpness, and treat abstention as an explicit operational outcome.

The Global Knowledge Graph (GKG) of the Global Database of Events, Language, and Tone (GDELT) characterizes news articles using named entities, topics, quantitative and temporal features, quotations, tone, and dictionary-based content measures. Its codebook defines the record format, but the software that produces the records is not public, so researchers cannot generate compatible records for articles they collect themselves. We built an open-source reconstruction, gdelt-regkg, and measured how closely it agrees with GDELT's archived (native) records for 193,550 English articles from 8,729 publishers (2020-2025) and 2,500 articles in five other languages. Agreement depends strongly on the field. English tone, the percentage of positive minus negative words, has a mean absolute error (MAE) of 1.79 points and a concordance correlation coefficient of 0.75. Identity agreement (F1) is 0.65 for persons, 0.42 for organizations, and 0.65 for locations. It is lower for date components (0.42), complete counts with their objects and locations (0.07), and quotations (0.07), while GCAM category presence reaches micro F1 0.84 within the implemented dictionaries. In subsets where retrieved and native titles and lengths match, tone error falls to 1.47 and organization F1 rises to 0.48, yet most disagreement remains. A larger gazetteer raises coverage of native places from 89.5% to 97.1% with little change in location F1. Tone computed on English translations of non-English articles is less accurate (MAE 2.10-2.64) than for English articles. The results are conditional on article pages that could still be retrieved, and the correspondence subsets do not isolate the effect of input differences. Reconstructed records should therefore be assessed field by field and not treated as completely interchangeable with native ones.

3D Gaussian Splatting (3DGS) has become a promising representation for real-time novel view synthesis and 3D scene reconstruction. For practical deployment, recent studies have explored pose-free feed-forward 3DGS, which reconstructs Gaussian representations directly from unposed input images. However, these methods remain sensitive to residual pose errors, which perturb canonical-space Gaussian transformation, introducing noisy supervision for geometry and attribute learning. To address this problem, we present SG-Splat, a pose-free feed-forward 3DGS framework that improves robustness to pose uncertainty and stabilizes the learning of Gaussian primitives. SG-Splat decouples geometry estimation and Gaussian attribute prediction into two dedicated branches, reducing error coupling between pose-sensitive geometry and Gaussian attributes. We further introduce a coarse-to-fine refinement pipeline, consisting of Flow-Guided Pose Refinement (FGPR) and Residual-Guided Geometry Correction (RGC), to improve geometric alignment before Gaussian attribute reconstruction. Specifically, FGPR refines camera poses with flow-based correlation features and differentiable bundle adjustment. RGC then corrects initial point maps using depth residuals derived from FGPR, producing more reliable Gaussian centers. To stabilize training, we introduce a dual-path strategy that mixes ground-truth and predicted poses for canonical transformation. It provides clean supervision for Gaussian attributes while improving geometry robustness to residual pose errors. Extensive experiments on DL3DV and RealEstate10K show that SG-Splat achieves state-of-the-art performance in both novel view synthesis and pose estimation.

Large sparse matrices---adjacency matrices of web and social graphs, feature matrices of machine-learning pipelines, the relations of graph databases---are routinely compressed to save space. Classical compressors, however, force the matrix to be decompressed before it can be used, so the space savings often yield a computational overhead. A recent line of work studies \emph{computation-friendly} compression: formats that are not only small, but let us carry out matrix--vector products, and in some cases matrix--matrix products, sums and closures, directly on the compressed representation {\em in time proportional to that compressed size}. This survey organizes that literature around the kind of redundancy each format exploits: spatial clustering of the nonzeros ($k^2$-trees and their variants), similarity between rows (Boldi--Vigna-style referencing and set-difference compression), repeated substrings (grammar compression), and dense bipartite substructures (bicliques). For each family we describe the representation, the algorithms, the theoretical guarantees and the empirical performance. Further, we show that the last three families are instances of a single general scheme, which we call a {\em sparse straight-line factorization} of the matrix, whose forward and backward substitutions evaluate right and left products in time proportional to the size of the representation, and that the product of two such factorizations is again one, which gives matrix--matrix products with a compressed output. An appendix reviews formats that must be decompressed (at least partially) before operating, for completeness. We close with a cross-family comparison and a list of open problems.

Tensor recovery spans heterogeneous data structures and observation processes, calling for a representation that can adapt across modalities and tasks. We propose DiffTR, an unsupervised framework that unifies tensor completion, denoising, and hyperspectral super-resolution through coordinate-conditioned diffusion. Shared factors indexed by tensor coordinates condition a compact score network, and score matching jointly learns the factors and an implicit tensor representation from the available observations. Scalar and vector-valued outputs accommodate individual entries and entire tubes, enabling a common formulation for tabular tensors, images, and videos. The framework separates representation learning from task-specific observation modeling: reverse diffusion recovers missing values; estimation via Tweedie's formula, soft thresholding, and optional spatial consistency support mixed-noise denoising; and measurement-guided sampling transfers a prior learned from low-resolution hyperspectral observations to high-resolution reconstruction, followed by post-sampling refinement with data consistency and spectral subspace regularization. This separation makes the representation compatible with different corruption models and permits task-specific constraints to be incorporated within the same recovery framework. Experiments across multiple tensor modalities and recovery tasks demonstrate competitive reconstruction quality and the flexibility of a unified conditional generative representation. The code is available at https://github.com/CZY-Code/DiffTR

Minimal binary linear codes play an important role in secret-sharing schemes and in the structural study of linear codes. We study the minimality of three classes of known constructions: codes from a single complete Hamming-weight layer, codes from arbitrary unions of such layers and graph cut-space codes. For the previously studied single-layer codes C, we give a complete minimality classification: C is minimal if and only if t is even. For t = 4, we determine the minimum and maximum weights, and show that the family strictly violates the binary Ashikhmin Barg sufficient condition for every k. We also calculate the minimum distance of the dual code. For arbitrary unions of complete Hamming-weight layers, we obtain an if-and-only-if classification of minimality and uniform criteria for evenness, self-orthogonality, the doubly even property and hull dimension. We further analyze the family for odd k. Finally, using the classical bond characterization of cuts, we translate minimality of graph cut space codes into a graph-theoretic condition: a nonempty simple graph has a minimal cut code precisely when it has one edge-containing component and that component is complete. We also give a graph-function realization of the known binary tetrahedron code and explicitly identify the resulting code equivalence.

Besides domination-based algorithms such as the NSGA-II, the decomposition-based MOEA/D is one of the most popular and successful optimization heuristic for multi-objective problems. It decomposes the problem into several, single-objective subproblems. By solving these in a co-evolutionary manner and archiving non-dominated solutions, it approximates or computes the Pareto front. Interestingly, so far no advantages from the co-evolutionary communication of subproblem solutions were proven. In this first mathematical runtime analysis addressing this research question, we investigate how the mutation-based MOEA/D solves the classic OneMinMax benchmark when solutions are exchanged among subproblems in different distances $r$. We show, for the first time, that the MOEA/D profits from an exchange of solutions, and that already very small communication radii $r$ are sufficient to maximally profit from this feature of the algorithm. More precisely, for all values $r \ge 1$ we prove a tight runtime guarantee of $Θ(n^2)$, where $n$ is the problem size. This is asymptotically faster than the known bound of $O(n^2 \log n)$ guarantee for $r=0$, which we complement with a matching bound of $Ω(n^2 \log n)$.

Single-Domain Generalized Object Detection (S-DGOD) aims to generalize from a single source domain to unseen domains under distribution shifts. Existing efforts mainly focus on simulating unseen domains or suppressing domain-specific factors. However, they largely overlook the intrinsic generalization capability embedded in Vision Foundation Models (VFMs). In this work, we show that unconstrained fine-tuning disrupts the geometric structure of pre-trained representations, which encodes domain-invariant semantics. Motivated by this, we propose Geometric-Invariance Fine-Tuning (GIFT), a geometric-aware fine-tuning method for VFMs. Specifically, we introduce a series of learnable Householder reflections to the pre-trained weights to encourage geometry-consistent adaptation under domain shift. In addition, we propose a lightweight channel-wise scaling to facilitate effective task-specific adaptation. Extensive experiments demonstrate that GIFT consistently outperforms state-of-the-art (SOTA) approaches on two S-DGOD benchmarks. Notably, by introducing fewer than 1% additional trainable parameters into the frozen backbone, the proposed method achieves improvements of +7.9% and +2.9% in mPC over the previous SOTA on the Cityscapes-C and Diverse Weather Dataset, respectively. This finding highlights that preserving representation geometry is crucial for robust cross-domain generalization, establishing GIFT as a principled and efficient solution to domain shift.

In the past few years, Vision Transformer (ViT) has achieved excellent performance in the field of computer vision. However, there still some problems remain. For instance, ViTs heavily rely on large-scale training data since they simply contain a large number of trainable parameters, which slows down their learning efficiency and limits their applicability in resource-constrained scenarios. In this paper, we propose a novel deep learning model, namely All-Convolutional Self-Attention Network (ACSAN), which applies convolution operations to replace fully-connected matrices multiplications in the ViT framework. To implement ACSAN, we firstly design Dynamic Convolutional Self-Attention (DCSA) as the basic module, which employs multi-scale dilated convolutions to generate Query, Key, and Value. We defined spatial self-attention and channel self-attention to generate attention features respectively. The two attention features are finally merged as the output of the DCSA module. Based on DCSA, we then construct the basic ACSAN block. Comparing with ViT, we use DCSA to replace the regular self-attention operations, and use convolution layers to replace MLPs. To evaluate the performance of the proposed method, we train ACSAN on three widely-used image classification databases, i.e. CIFAR-10, CIFAR-100 and ImageNet-1k, from scratch. Experimental results show that ACSAN achieves excellent classification accuracy comparing with standard ViT with comparable or fewer parameters, as well as other state-of-the-art methods. Ablation studies verify that each component contributes positively to the final performance.

Cross-dataset generalisation remains a major challenge for automated electrocardiogram (ECG) arrhythmia classification because of differences in patient populations, acquisition protocols, annotation practices, and class distributions. Learning representations that remain informative across independent datasets could reduce reliance on dataset-specific labelled data. We propose TransECG-SSL, a self-supervised framework for transferable heartbeat representation learning from unlabelled ECG data. A Transformer encoder is pretrained using a hybrid objective combining masked signal reconstruction and contrastive learning, then frozen and evaluated by linear probing under patient-disjoint evaluation. Experiments across three public ECG databases and seven source--target settings show that Hybrid SSL consistently outperforms randomly initialised Transformers and achieves higher balanced accuracy than architecture-matched source-supervised pretraining. Reconstruction-only SSL remains competitive with Hybrid SSL, whereas contrastive-only pretraining performs substantially worse, highlighting the importance of masked reconstruction for transferability. Cross-dataset transfer nevertheless reduces balanced accuracy relative to target-specific self-supervised pretraining, while minority arrhythmia classes remain challenging under severe class imbalance. These findings demonstrate the potential of label-efficient self-supervised learning for cross-dataset ECG representation transfer while highlighting persistent limitations from domain shift and class imbalance.

Embodied agents are expected to accomplish real-world goals by deciding for themselves how and when to interact with their surroundings. For many such goals, changing the physical state of the world is the means rather than the end: the agent changes the state of a system through interaction, observes the feedback, and explores until it either achieves the goal itself (e.g., discovering physical laws) or learns what the goal requires; it acts to know. Manipulation benchmarks stop at acting to change, with the target state given; scientific discovery benchmarks evaluate knowing but replace physical experimentation with symbolic actions or numerical queries. We introduce EmbodiedLab, a benchmark in which a robot must act to know. Quantitative science experiments make this setting controllable: the parameters of the system are resampled for every instance, so the result cannot be known in advance, yet it can be scored exactly. Across 30 experiments in five disciplines on 14 apparatus platforms, the agent receives an objective and the apparatus, chooses its own procedure, and operates a physics-based simulated laboratory, reading the instruments through its cameras. Evaluation checks what the agent came to know, grounded in readings recorded during the episode, as well as the physical state the task requires; every experiment is verified to be solvable. We evaluate six frontier models in their developers' coding agents with native observation and control, with added perception and motion planning, and with manipulation skills distilled from the strongest agents. With native control, even the strongest agent succeeds less than half the time; for every agent, most failures arise in interacting with the apparatus, and manipulation skills help weaker agents more than perception and planning. The benchmark and its evaluation code are available at https://github.com/HexaFuture/EmbodiedLab.

We develop a unified framework for assortment optimization and matching under multinomial logit (MNL) choice, yielding simple algorithms and analyses across a broad class of problems. The framework centers on a single-customer assortment problem in which the firm commits to eligible products before their independent availabilities are revealed. A simple threshold policy achieves a tight $1/2$ guarantee against a benchmark that selects its assortment after observing availability and may control dependence subject to the same marginal probability bounds. This guarantee accommodates cardinality constraints and adversarial removal of excess available products. Combined with problem-specific linear programming relaxations, the framework yields $1/2$ guarantees for standard two-sided assortment optimization, customization under mixtures of MNL models, ride-hailing notifications, multi-round broadcast matching, and MNL prophet inequalities, and a $1/4$ guarantee for fully static two-sided assortment optimization. Across these applications, we improve approximation factors, extend guarantees to more general revenues and cardinality constraints, and retain existing factors against stronger benchmarks.