Science & Mathematics

Understanding the three-dimensional (3D) quantum Hall effect, characterized by a Chern vector rather than a single Chern number, has been a central pursuit in topological physics. While quantized Hall transport is established for the special case with one nonzero Chern component, recent realizations of more general Chern-vector states raise a fundamental question: how does such topology protect quantized transport? Here, we predict a distinct 3D quantized Hall effect protected by $\mathbf{C}=(0,m,n)$. For samples with dimensions $L_y$ and $L_z$, global topology enforces collective quantization of $mL_y+nL_z$, despite the fragility of individual edge modes to disorder. This reveals a novel transport regime in which robust quantization emerges as a holistic property of a unified chiral network,rather than of its constituent modes. Crucially, this collective response manifests as a quantized Hall conductance $G_{xy}=\pm(mL_y+nL_z)e^2/h$, with a distinctive dependence on both Chern-vector components and sample dimensions. We propose candidate materials to facilitate experimental observation.

Maximum-likelihood (ML) decoding of linear block codes is NP-hard, so neural decoders are evaluated by how closely they approach it. We observe that proving a candidate optimal can be far easier than finding it, and build a decoder that does both. We cast decoding as a search over an absorbing-state discrete diffusion model, whose sequential commitment of coordinates turns generation into a tree, and run a probability beam search over it. A dual bound from a linear-programming relaxation and a distance-based test, both derived from the code, then certify per frame that the current candidate is the global ML solution; because both are theorems, certified frames incur no accuracy-computation trade-off. Across $15$ codes and five operating points we certify up to $99.9\%$ of frames, the two tests dividing the space as their derivations predict, one strong for sparse parity-check matrices and the other for codes with a large minimum distance. Certification also behaves as a per-frame reliability signal, with $96.7$-$100\%$ of all frame errors falling on uncertified frames. Against an exact ML reference at $5$ dB the decoder is within one standard deviation on three of the four codes where the reference is uncensored, and against four neural baselines it attains the best bit-error rate in $71$ of $75$ cells.

Distinguishing atomic species is an ongoing challenge in the field of scanning probe microscopy. Typically, atomic force microscopy makes use of electrostatic interactions to perform atomic identification. Here we perform lateral force microscopy (LFM) measurements with a CO terminated tip of a partially oxidized Cu(110) surface and show clear differences between the metal and oxygen sites over a large z-range. This allows for atomic identification on a typical metal oxide. Density functional theory based calculations show that the tip-sample interaction is dominated by short-ranged orbital interactions and that the electrostatic contribution is negligible. At small tip-sample distances, LFM can probe the Prandtl-Tomlinson stick-slip mechanism on the single-atom scale. It is visible as a striking asymmetry in the forward and backward scan directions, experimentally revealing this fundamental model for nanotribology on the single-atom scale.

Speculative decoding accelerates autoregressive (AR) language models by letting a small model draft tokens serially and a large model verify them in parallel. We reverse these roles. Starting from a standard AR checkpoint, we fine-tune the large model into a proposer that predicts a block of future tokens in a single forward pass, then use one additional forward pass to verify the proposed block. This gives ProVe, Proposer-Verifier decoding. The verifier can be a smaller AR model or the proposer itself; the latter gives ProVe-lossless, which reproduces the proposer's greedy AR decoding. Block proposals already provide substantial room for acceleration: with a block size of 16, the proposed block has an average AR-matching prefix of 6.6 tokens on GSM8K. Across six benchmarks with a 32B proposer, ProVe-lossless reaches 2.5x average AR throughput without training a separate draft head. With a small 3B verifier, ProVe reaches 2.7x average throughput at 2.6 accuracy points below AR on the six-task average, providing a controllable tradeoff between speed and accuracy.

Retrieval-Augmented Generation (RAG) has become the dominant paradigm for grounding the outputs of large language models (LLM) in external knowledge. However, practitioners are faced with a vast configuration space comprising chunking, embedding, retrieval, reranking, prompting and generation models, and there is limited guidance on how these components interact. We present RAG-NIMBF, a modular benchmarking framework that attaches to existing RAG pipelines as a non-invasive evaluation layer. It evaluates the configuration space through controlled ablation with end-to-end experiment tracking. The evaluation combines LLM-based answer quality scores, retrieval correctness measures, and runtime indicators. This study validates the framework across multiple generation models on the SQuAD dataset. This process reveals non-obvious interactions and demonstrates how the experiments are tracked. The findings indicate that the retrieval balance of relevance and diversity substantially enhances the relevance and coverage of retrieved context in comparison to a conventional similarity search, with MMR raising nDCG@5 by +4 to +11 percentage points across the swept models. More detailed prompt instructions meaningfully increase how faithfully generated answers stick to the retrieved evidence, especially for capable and reasoning models (+10 to +13pp on Qwen3.6-27B, GPT-4o-mini and Qwen3.5-think, but negligible on the 20B generator). Overall, RAG-NIMBF transforms the configuration space of RAG into reproducible, comparable experiments. By attaching to existing production pipelines in a non-invasive way, it enables practitioners to systematically evaluate and improve deployed systems without disrupting existing workflows. This replaces ad hoc choices with evidence-based decisions.

Every prompt sent to a hosted language model is readable by whoever runs it. We study whether the prompt can remain on the client while the host receives transformed vectors that stand in for it. A language model converts text to vectors exactly once, with a public lookup table; we perform that step locally and pass the vectors through a small trained network (55.6M parameters) before they leave the perimeter. The host runs a frozen 27B model (Qwen3.8-27B) on the transformed vectors and never receives text or token ids. We train the transform against the frozen model as a fixed judge, combining a forward-KL utility term with an auxiliary term that pushes each vector away from its original direction. On 1,490 MMLU questions held out from training, the transform costs 1.5 points of accuracy (80.7% vs. 82.3%), breaking 68 of the 1,226 questions the unmodified model answers correctly (5.5%), while 30.1% of content tokens no longer decode to their original token under a nearest-neighbour lookup.

LLM routing aims to select a capable model at low cost, but specialized routers can require updates as models and tasks change. We propose COMPASS, an agentic router in which an LLM follows a routing recipe, gathers performance and cost evidence through tools, and optionally inspects candidate answers before selecting a model. Our evaluations on LLMRouterBench and DeepSWE show that agentic routing can improve accuracy and lower model-call cost relative to specialized and trained routing baselines, without routing-specific training. On LLMRouterBench, COMPASS reaches 69.85% accuracy at \$139.57, compared with RLCascadeRouter's 69.14% at \$180.22. On DeepSWE under fixed five-fold cross-validation, it reaches 78.1% at \$215, compared with 74.1% at \$500 for the best single model. COMPASS also supports routing across benchmarks and adapts to an expanded model pool by reading new evaluation records, without changing the router's weights or prompt.

Complex concentrated alloys (CCAs) combining elements from 3d transition and refractory groups, specifically Cu-Ni-Ti-Zr-Hf-based shape memory systems, exhibit excellent functional properties but present significant manufacturing challenges via powder metallurgy. In this study, a non-equimolar Cu15Ni35Ti25Zr12.5Hf12.5 (at. %) alloy was successfully produced by induction melting, followed by atomization and subsequent consolidation via Spark Plasma Sintering (SPS) at temperatures ranging from 850 to 1100 C. Although global equilibrium phase diagrams predict solid-state stability up to 1260 C, localized melting unexpectedly occurred during SPS at 1100 C. By combining retrospective Scheil-Gulliver solidification simulations with 2D local equilibrium heat maps, we demonstrate that this early-stage melting is not driven by macroscopic thermal gradients, but by microsegregation inherited from atomization. During solid-state heating, thermally activated short-range diffusion, accelerated by high defect densities at particle interfaces, partitions Ti towards the interparticle network, leaving Cu-enriched regions (up to ~41 at. %) within the particle interiors. Owing to the strongly negative mixing enthalpy of Cu with Hf (-19.2 kJ/mol for $ΔH_{mix}^{l-l}$) and, to a lesser extent, with Ti, the local solidus of these Cu-rich regions is dramatically depressed. Upon heating to 1100 C, these regions cross their local solidus and form a liquid phase, whose solidification produces the Cu-Hf co-segregation. This framework accounts for localized melting phenomena in rapidly solidified CCA powders containing low-melting constituents with strong negative mixing enthalpies.

Despite decades of progress in model-based methods and tools for embedded real-time systems, there is still no integrated environment that supports the entire development lifecycle. This paper presents MIMOS-Tools, a comprehensive toolchain spanning the key phases of development, including modeling, simulation, formal verification, real-time scheduling, schedulability and end-to-end latency analysis, and code generation for heterogeneous multicore platforms. All phases are grounded in a single, coherent, and deterministic model of computation, the MIMOS model, for which we present a formal operational semantics and establish both functional and timing determinism. This semantic foundation ensures that properties verified at the model level are preserved throughout the development process and in the generated implementation. A distinguishing feature of MIMOS-Tools is its support for not only deterministic but also modular, compositional design. Unlike synchronous design environments such as SCADE and Simulink, which rely on a global base clock and offline static scheduling, MIMOS-Tools supports time-triggered asynchronous communication together with flexible real-time scheduling of computation. This removes the tight global coupling of the synchronous paradigm: components can be added, modified, or updated without recomputing a system-wide schedule, enabling scalable and incremental design and dynamic updates throughout the system lifecycle. However, MIMOS-Tools also supports Simulink models when the deadlines of tasks are set to zero to emulate the zero-time semantics of synchronous design. The toolchain is available at uu-mimos.github.io.

Continuous fuzzing is used for vulnerability detection in Open Source Software (OSS). Large-scale services such as Google's OSS-Fuzz fuzz over 1,300 projects and have revealed more than 10,000 vulnerabilities. Despite this, a considerable time lag often exists between when a vulnerability is introduced and when it is detected (i.e., the window of exposure). Given the computational cost of additional fuzzing, we aim to allocate fuzzing resources efficiently using vulnerability-risk estimates. We propose RAISE (Risk-Aware Intensive Supplemental Execution Framework), a Just-In-Time (JIT) framework that prioritizes additional fuzzing for high-risk project-days. RAISE performs binary classification at the project-day granularity to estimate whether a vulnerability is introduced on a given day. We construct a dataset combining vulnerability-introducing commits from the OSV database with daily coverage and change metrics from OSS-Fuzz, covering 15 C/C++ projects and 15,210 project-days, of which 347 (2.28%) are vulnerability-introducing. In a cross-project validation setting, our best model, a Random Forest combining VCCFinder-based static features with dynamic fuzzing features, achieves a ROC-AUC of 0.74, substantially outperforming a random baseline; coverage metrics, led by PatchCoverage, are the most important features. In a simulation over 968 vulnerabilities comparing five allocation strategies, Simple-Regression was significantly more cost-efficient than the prediction-agnostic heuristics, spending 91.60 additional fuzzing sessions per detected vulnerability, roughly half the cost of the Median heuristic (171.89). RAISE shows that JIT vulnerability prediction with coverage-aware fuzzing features can effectively guide risk-aware allocation of continuous fuzzing resources.

Multimodal retrieval-augmented generation over visually rich documents requires evidence at a finer granularity than entire pages. Existing visual retrievers typically index or return full pages, whereas training region-level retrievers often requires costly query-to-region annotations or noisy model-generated labels. We introduce GARRET, a region-retrieval framework trained from (page, question, answer) triplets through differentiable generative feedback. A shared context-preserving retriever produces page and region multi-vector representations. During training, their retrieval scores define a soft routing distribution over candidate region crops. An auxiliary vision-language model attends to each crop separately, aggregates crop-specific contexts using the routing weights, and predicts the question followed by the answer under a next-token prediction objective. Gradients through the routing distribution assign query-conditioned credit to the indexed region representations, without requiring query-to-region annotations. At inference, the auxiliary model is removed. GARRET also reuses the contextualized region representations, together with page summary tokens, to construct a compact page representation. We introduce ViDoRe-V3-Region, a corpus-wide benchmark containing 200,682 fixed candidate regions across eight domains. GARRET achieves a macro nDCG@10 of 0.4126, outperforming the strongest visual baseline by 2.94 points. On page retrieval, it remains comparable to ColQwen2.5-v0.2 while indexing 47.8% fewer vectors per page.

The residual maximum matching problem asks for a maximum matching whose deletion leaves a graph with the largest possible matching number. For unweighted graphs, previous work provides a $1/2$-approximation guarantee in general graphs and a $2/3$ guarantee in graphs with a perfect matching. We present a $2/3$-approximation algorithm running in $O(n^5)$ time, extending the latter guarantee to general graphs. The algorithm improves the residual matching number through single-edge exchanges involving free vertices. We prove that, for any maximum matching that admits no further improvement by such exchanges, the residual matching number is at least $2/3$ of the optimum, and we give an example showing that this bound is tight.

Online Continual Learning (OCL) requires models to learn from non-stationary data streams under a strict single-pass constraint, making them highly susceptible to catastrophic forgetting. While existing studies have explored various strategies from data, architecture, and optimization perspectives, the optimizer often directly uses generic approaches such as SGD and AdamW. In this work, we reveal a new link between optimization dynamics and OCL needs by recasting Polyak-Ruppert averaging as the engine of "plasticity" and Primal averaging as the anchor of "stability". This inspires our novel optimizer, SPIN (Stability-Plasticity INterpolation), which explicitly decouples plasticity and stability by interpolating between a fast-moving "plasticity" sequence and an adaptive "stability" sequence. We theoretically demonstrate that SPIN implicitly employs an inverse Hessian approximation, providing crucial Tikhonov regularization to damp noisy, single-sample Hessian estimates and mitigate forgetting. More importantly, SPIN can be seamlessly integrated into existing OCL methods by taking resulted gradients as input and replacing standard optimizers. Extensive experiments show that using SPIN instead of standard optimizers yields consistent and significant performance gains across multiple OCL approaches, including the challenging rehearsal-free setting and under strict memory constraints.

Car-following (CF) models is a fundamental component of microscopic traffic simulation and underpin the analysis of collective traffic dynamics, while its modeling becomes more challenging due to diverse human driving behaviors and the increasing presence of automated vehicle. Analytical CF models offer interpretable representations of longitudinal vehicle interactions, but their prescribed functional structures may limit the representation of heterogeneous driving behavior. This study proposes an agent-centered, physics-aware framework for the empirical discovery of CF laws from multi-source trajectory data. The framework iteratively combines agent-guided hypothesis generation, informed by traffic flow knowledge and state-dependent reconstruction errors, with evolutionary symbolic search and physics-aware multi-objective evaluation. Using NGSIM US-101, highD, and exiD, the framework discovers the Adaptive Equilibrium Response Model (AERM), which couples state-dependent relative-speed response with spacing-dependent equilibrium-speed restoration. AERM admits analytical equilibrium speed-spacing and flow-density relationships; its stability conditions are derived for the zero-delay formulation, and platoon simulations examine disturbance propagation. Evaluated against seven classical CF models on Shanghai naturalistic driving data, NGSIM I-80, and Waymo trajectories, AERM attains the lowest spacing and speed reconstruction errors under trajectory-specific calibration, reducing spacing RMSE by 9.11%, 7.59%, and 21.73% relative to the strongest baselines, and remains competitive under dataset-level shared parameters. These results demonstrate the fitting flexibility and analytical tractability of the discovered CF law, providing an interpretable basis for microscopic traffic simulation.

The Minimum Shared-Power Edge Cut (MSPEC) problem seeks to disconnect two designated terminals with minimum total power by assigning powers to graph vertices and deleting every edge for which the sum of the powers at its endpoints reaches its edge weight. Previous work gave a fully polynomial-time approximation scheme for this problem, while its exact computational complexity remained open. We prove that general MSPEC with nonnegative edge weights can be solved exactly in polynomial time. Specifically, we first use linear programming duality for each fixed cut to reformulate MSPEC as minimizing the maximum terminal-relaxed matching weight over all $s$-$t$ cuts. Then, we construct a terminal-copy extended graph that transforms the maximum-weight matching model with unconstrained terminal capacities for a fixed cut into an equivalent ordinary maximum-weight matching model. Next, we extend the submodularity of the unweighted maximum-matching cut function to nonnegative edge weights and prove that the restriction obtained by fixing the terminal copies on prescribed sides remains submodular. Consequently, MSPEC reduces to exact submodular function minimization. Once an optimal cut is obtained, a corresponding optimal power assignment can be recovered. This result resolves the open question concerning the exact computational complexity of general MSPEC.