Papers

We propose a general approach to enharmonicism within syntactic music theory; that is, we formalize several abstract structures of enharmonicism without any acoustic considerations. The structures of concern to this paper are constructed from diatonics, chromatics, and enharmonics, and we seek to present a general enharmonic theory that builds upon Hook's enharmonic theory published in "Enharmonic Systems: A Theory of Key Signatures, Enharmonic Equivalence and Diatonicism" (2007). We also propose that the two criteria of reflection and maximal evenness can be used to determine whether an arbitrary enharmonic system is musically practical. Moreover, we argue that preferential treatment of the standard enharmonic system (SES) can be motivated from an abstract mathematical perspective divorced from pitch consideration and conventional acoustic constructions of SES.

We show that a (stronger) version of random resolution has the feasible disjunction property. This is the first instance of a proof system not known to have feasible interpolation, which nevertheless has the feasible disjunction property.

Compound AI pipelines chain LLM calls, retrievers, and tools and are nondeterministic: sampling, model updates, and volatile tool responses make one input yield different outputs across runs. Such pipelines increasingly run across edge, cloud, and orbital nodes owned by no single party, whose optimizations discard intermediate results before inspection. Verifying reproduction there means tolerating nondeterministic outputs, a node that may not report honestly, and intermittent access to any shared record; existing work addresses at most two at once. We give a protocol covering all three: it commits digests of each stage's inputs, outputs, and context under a policy digest pinning the metric and threshold, anchors them without trusting the executing node, defers under partition, and decides a challenge on the median of $k$ re-executions, with no quorum. Where that procedure breaks is the main result. On a synthetic HotpotQA pipeline a calibrated fixed threshold accepts 44 of 45 honest reproductions and rejects 104 of 105 divergent pairs, yet lets same-input fabrication through in 27 of 29 trials at k=5, more samples being no help since sampling sharpens an estimate without moving it. Holding that metric and this pipeline's re-execution spread fixed, the binding constraint is the threshold rather than the sample size: one derived per execution detects 19 of 29 where the best constant matched to the same zero honest rejections reaches 9, rejects no honest commitment at k=5 though 3 of 15 at k=3, and catches 11 of 15 of an attacker built against it, which has to aim at a target drawn only after its commitment exists. That rule is measured rather than deployed.

Classical panic-mode recovery skips a failed scan forward by convention, promising progress but no repair-universal boundary guarantee for where it lands. We choose the resume position by theorem, via a committed-prefix lemma over certificates posted for parallel lexing (arXiv:2608.03473, arXiv:2608.09761): a position is a sound recovery point when every prefix repair whose scan commits through the certificate's returned evidence places a token boundary there. This quantifier is strictly stronger than its complete-repair special case, and at a sound recovery point the inclusion is strict precisely when no repair completes while some scan commits through the evidence. The evidence-returning interface pairs each answer with the interval it rests on, so a caller who knows what the scanner cannot check decides whether the boundary transfers to the intended input. The search provably terminates; the guarantee is relative to the active mode's automaton. For an automaton of n states the quantifier is decided exactly from the preserved tail by at most n + 1 representative repairs, and a shortest reaching repair has at most n - 1 symbols and a shortest counterrepair at most n, both tight. Every anchor of an m-byte input is profiled in $O(nm + n|\Sigma|)$ time. The shipped repair routines are the complete-repair case, which proves their contracts. In a deterministic corruption study of munch's procedure beside skip-one and delimiter recovery, every certified answer whose evidence survives the damage passes its landing check on every move, 40,885 of 40,885, while the 5,595 first answers resting on evidence the damage reached land 1,589 times, reported, not asserted. Of the 16,808 trials labeled beyond repair, 13,522 resume on a suffix that tokenizes whole, where both quantifiers are provably empty, and 3,286 stay undetermined, their damaged inputs not archived.

Several public-key schemes base their security on the belief that inverting a unit of a group ring is hard. A recent result showed that this belief is false on a quantum computer when the group is abelian. To restore security, designers moved to non-abelian groups, especially dihedral groups, believing that the hardness of the dihedral hidden subgroup problem (HSP) would protect the scheme. This paper shows that unit inversion is a different problem and does not require an HSP solver. Instead, it can be solved by a change of basis that splits the group ring into small matrix blocks. We prove that unit inversion is polynomial-time, classically and quantumly, when an efficient generalized Fourier transform exists, the group ring is semisimple, and the largest matrix block has polynomial size. Dihedral group rings satisfy these conditions because their irreducible representations have dimension at most 2 and an efficient Fourier transform exists. We give an explicit reversible quantum circuit for the block-inversion step and validate it in a register-level simulator. We also identify the exact structural boundary where the method stops and propose a candidate construction in the surviving regime under a new, clearly stated security assumption. The constructive results are supported by reproducible software artifacts and experiments.

The adoption of generative AI in software-intensive systems is proceeding rapidly, but current analytical instruments - principally unidimensional maturity models - compress important configurational variation into a single progressive axis. Drawing on an inductive interview study of eighteen senior practitioners across telecommunications, automotive, defence, aviation, banking, energy, government, and enterprise software services, this paper presents the Trustworthy Autonomy Health Check Model: a structured, multidimensional instrument for characterizing how organizations establish trust in GenAI-assisted software engineering. The model organizes eight empirically grounded dimensions into a system layer (Scope of Agent Authority, Assurance Mechanisms, Data Trustworthiness, Architectural Containment, Traceability & Comprehensibility) and an organizational layer (Governance, Human Oversight Posture, Workforce Capability Sustainability), each on a five-level ordinal scale. A cross-cutting overlay of four trust paradigms - operational, engineering, statistical, and containment-based - captures how trust is established, complementing the dimensions capturing what must be trustworthy. The model is diagnostic rather than prescriptive: it supports cross-organizational comparison, surfaces configurational trade-offs, and locates an organization in a shared space without imposing a single progression path. Higher levels are not inherently better; the goal is alignment across dimensions appropriate to the organization's domain and chosen trust paradigm. This is formalized as the alignment hypothesis: effective trustworthiness is constrained by the fit between the scope of agent authority and the dimensions enabling it, with misalignment producing pathological risk or unnecessary friction. We discuss how practitioners can apply the model and outline directions for empirical validation.

Expert evaluation of jailbreak responses is costly and difficult to scale, so the community increasingly relies on automated evaluators to determine whether an attack succeeds. However, jailbreak studies typically validate their chosen evaluator independently, repeatedly spending resources on similar evaluation efforts while making results across papers difficult to compare. Different evaluators also encode different definitions of jailbreak success, meaning that reported attack strength and apparent progress can depend substantially on which evaluator is used. We systematically compare six evaluators that recur in recent jailbreak attack and defense research: HarmBench, JailbreakBench, JailbreakRadar, StrongReject, JADES, and JailMeter. To our knowledge, no prior study has evaluated all six on the same human-labeled data under a controlled setup. We evaluate them on JailbreakQR and JailMeter-Eva, using human judgments as the reference, and measure agreement with humans, error types, and consistency across attack families. For evaluators that require a general-purpose LLM judge, we use a shared backbone to control for model-specific variation. We found that JADES exhibits the best overall performance, while HarmBench and StrongReject also demonstrate good performance.

Choosing a deferral policy for a frozen classifier requires more than ranking uncertain cases: confidence may be miscalibrated, errors have unequal costs, reviewers can err, and deployment data can leave calibration support. We study these interactions through EcoTrust, a post-hoc framework that compares automatic action with review using a six-group error-risk estimator, class-asymmetric costs, reviewer accuracy, and an optional support gate. On a Columbia River thermal-stress testbed, the learned estimator improves error-ranking area under the receiver operating characteristic curve from 0.869 to 0.889, but Chow's confidence rule has lower in-distribution cost (0.416 versus 0.567 per day). Across 12 off-the-shelf backends, learned risk and a calibration-matched, class-aware confidence estimator each beat raw Chow on six; a paired year-block bootstrap does not resolve their mean cost difference. In transfer to ten river stations, the gate flags every case and becomes an always-review fallback, attaining the lowest cost on eight stations only when review is perfect and unconstrained. These results characterize decision boundaries on one controlled task: richer risk signals do not reliably improve on calibrated confidence, and detected extrapolation does not imply transferable case-level ranking.

Vision-guided reinforcement learning for Unmanned Aerial Vehicles (UAVs) remains challenging due to unstable policy optimisation, aggressive exploration, and the cost of high-dimensional visual perception. In this work, we investigate long-horizon UAV visual servoing using compact target-centric cues combined with low-dimensional sensor measurements. Rather than learning directly from RGB images, lightweight target segmentation provides image-space offsets and relative depth, which are combined with quadrotor velocity and projected-gravity measurements into a compact 12D policy observation. We compare Direct PPO with three matched-budget curriculum strategies: a Visual curriculum that progressively expands target placement difficulty, a Dynamics curriculum that gradually relaxes action constraints and smoothing, and a Joint curriculum that combines both progressions. All strategies reach comparable nominal performance, with complementary advantages across tracking metrics. Observation ablations show that proprioceptive measurements are critical for stable flight and image-space cues for target alignment, while explicit depth is not necessary for strong performance in the evaluated setting. Against tuned classical visual-servo controllers, learned policies show greater robustness to strong control and visual perturbations, while the Visual curriculum exhibits the smallest degradation under unseen target motion. Overall, the results demonstrate that compact target-centric representations can support robust long-horizon aerial visual servoing and that visual curriculum training can improve robustness to dynamic distribution shifts despite limited gains in nominal performance.

How can language model agents effectively leverage libraries of reusable knowledge to solve long-horizon tasks? Recent work has increasingly focused on agent skills: reusable capabilities represented as skill packages, i.e., multi-file bundles containing instructions, scripts, and other resources that help agents perform specific tasks. Agent skills are typically executed by loading their skill instructions into an agent's context and relying on the agent to follow them. As task horizons grow, however, this approach becomes increasingly brittle, because reasoning quality degrades as more information accumulates in the context window. We investigate an alternative approach in which skill packages are instead invoked as subagents. Rather than loading skill instructions into the main context, subagent execution spawns fresh context windows dedicated to solving individual subtasks. We show that subagent execution outperforms agent-skill execution when skill packages expose clear input-output contracts and their instructions encode the procedural knowledge needed to fulfill those contracts. The tradeoff is additional communication overhead, as extra tokens are required to coordinate between the main agent and its subagents. Our results show that the benefit of reusable knowledge depends not only on its content, but also on how it is organized and invoked.

Additional inference compute can increase the number of correctly resolved security-assurance tasks, but repeated success, unique coverage, accepted evidence, and operational protection are different quantities. We develop a resource-constrained framework that separates them. For repeated conditionally independent attempts with latent success probability $\Theta$, coverage is $C_n = 1 - E[(1-\Theta)^n]$, and its limiting value is $1 - P(\Theta = 0)$. Positive pairwise outcome correlation does not by itself imply a ceiling below one: we construct two models with the same mean success and pairwise correlation but different limiting coverage. We distinguish this result from the effective sample size used to estimate a mean, and show why finite-budget observations cannot generally identify an asymptotic support ceiling. We then connect coverage to fallible evidence checking, proper scoring of factual grounding, complete resource accounting, service capacity, and a response model that includes mitigation delay. A conceptual defensive architecture separates evidence analysis, adjudication, and operational authority. An evaluation protocol specifies held-out tasks, paired comparisons, negative cases, and uncertainty reporting. The contribution is a consistent theoretical synthesis and a set of counterexamples to invalid extrapolations, rather than an empirical scaling law. All numerical illustrations are analytic; no model-parity result, hardware benchmark, or general attacker-defender equilibrium is claimed.

Understanding the brain's mechanisms is crucial in neuroscience, particularly for simulating natural intelligence and advancing artificial general intelligence (AGI). Liu et al. (2024) and Deco et al. (2025) propose that quantum entanglement may underlie the synchronization of millions of neurons, introducing the Liu-Chen-Ao (LCA) hypothesis of entangled nerve fibers. However, directly testing this idea remains challenging. Here we employ a nonlocal many-body wave equation, introducing a generalized probability-wave framework to model collective behaviors among adaptive, interacting agents, particles, or neurons. This approach enables testable eigenmodes, offering an indirect means of examining the LCA hypothesis by observing patterns in collective trading behaviors. These patterns, rooted in behavioral psychology, are thought to mirror the internal brain's decision-making and underlying mechanisms. Our analysis of Chinese intraday stock market data shows that adaptive entangled game modes explain 82%-94% of decision patterns, sharply contrasting neoclassical finance predictions assuming independent rational agents. Additionally, 2-12% of actions adapt to news, events, and environmental changes, marked by rapid equilibrium shifts, while truly independent behaviors make up less than 5%. These results empirically support the LCA hypothesis and underscore the need to simulate the brain's mechanisms and generate adaptive, entangled modules for AGI. They also expose the shortcomings of conventional artificial neural networks (ANNs) that depend on vast, opaque parameters. By combining ANN-based AI with probability-wave-based entangled brain simulations, machine learning enables the creation of human-like processing units (HPUs). Such HPUs promise more efficient and robust AGI, particularly for embodied intelligence and robotics.

This book develops algebraic and combinatorial methods for studying discrete structures. It brings together graph theory, Boolean functions, Fourier analysis on finite groups, coding theory, perfect colorings and perfect codes, association schemes, Latin squares, and related topics. A central theme is the interaction between different representations of the same object: combinatorial, algebraic, spectral, and coding-theoretic. The main mathematical object studied in this book is a perfect coloring of a graph, or, equivalently, an equitable partition of a graph. The book is intended for advanced undergraduate and graduate students in mathematics and computer science, as well as for researchers in discrete mathematics, combinatorics, coding theory, and related fields.

AI research agents combine public information and experimental feedback to produce measurable results. The Discovery Certification Protocol (DCP) turns an outcome claim into an executable audit under a registered model, information boundary, and budget. Gate 1 validates useful improvement. Gate 2 tests recovery by matched agents given the starting information and observed Web content, with run history and new measurements withheld. Core requires adequate registered controls, zero recoveries, and a finite-sample recovery bound. Optional Gate 3 compares truthful and neutral feedback from a shared checkpoint; Evidence adds a supported effect and a null-policy equivalence check. Controlled SQLite and virtual catalyst audits pass both decision kernels. On real-data response surfaces, Yacht and Ionosphere pass the Core kernel after zero recoveries in 96 attempts, with an upper bound of 0.0468. Each target combines ten observed utilities and six predictions into a 16-entry data product. Yacht scores 0.7677 on reconstruction of all 32 switch effects, with utility-prediction MAE 0.0315 on its six unmeasured configurations. Fresh truthful continuations recover the target level in 9/30 and 16/30 trials, respectively, separating achieved utility from process repeatability. A deterministic verifier reproduces these local decisions from frozen records.

Acidophilic proteins that remain stable and functional under highly acidic conditions, are important for industrial biocatalysis, acid-related bioprocessing, and the discovery of acid-stable enzymes. However, their identification relies heavily on time-consuming experimental screening methods. With the rapid growth of protein sequence databases, the need for computational identification methods that are both accurate and efficient has become stronger. The emergence of protein language models (PLMs) has significantly improved the sequence representation of downstream biological prediction tasks. This paper proposes MI-PEFT, a mixture-of-experts integrated parameter-efficient fine-tuning framework. Built on the ESM C-600M backbone, the framework incorporates LoRA-based PEFT methods and a DeepSeekMoE-based classification head to resolve the limitations of PEFT and significantly improve computational efficiency. Notably, this task is characterized by a significant class imbalance in the dataset, making high specificity particularly challenging. The experimental results demonstrate that MI-PEFT on PLMs, especially {\text{C}}^{\text{3}}\text{A}, serves as an efficient tool for identifying acidophilic proteins and a constrained pathway that helps resolve class-imbalance by preserving the pretrained representations.

Let $R=\mathbb{Z}/(2^n-1)\mathbb{Z}$, where $n\geq 3$, and let $S_w\subseteq R$ be the residues whose canonical $n$-digit binary expansion has Hamming weight $w$. We obtain, in particular, an asymptotic formula for the additive energy of $S_w$ \[ E(S_w)=\frac{\left|S_w\right|^4}{|R|}+ \mathcal{O}\left(|R|^3 n^{-3} \right), \] which holds uniformly in $w$. The error term is optimal in order, with a matching lower bound for $w=\lfloor n/2+\sqrt{n} \rfloor$. It follows that triple sums of arbitrary unit dilates have asymptotically uniform representation counts when $\prod_{j=1}^{3} \left|S_{w_j} \right| /\left(|R| n^{-3/5}\right)^3\to\infty$, and that double sums have asymptotically full support when $\left|S_{w_1}\right| \left|S_{w_2} \right|/\left(|R| n^{-3/4}\right)^2\to\infty$. In the proof, modular collisions are represented using a cyclic binary carry automaton; this appears to be a novel approach in this area of problems.

Many scientific graphs attach several variables to each node, so a single scalar edge weight cannot describe direction-dependent interactions. We model each edge by a symmetric positive-definite (SPD) matrix and infer a posterior over matrix-valued graph geometries, which we call the Bayesian matrix-valued graph (BMVG). We ask how these interactions reconfigure across contexts: how large the change is and which multivariate directions strengthen or weaken. The geodesic distance induced by the affine-invariant Riemannian metric (AIRM) quantifies deformation magnitude and generalized eigenvalues resolve its signed directions.Against fused graphical lasso, Bayesian multiple-GGM, and common principal components, BMVG is competitive on global precision recovery while retaining identifiable matrix-valued edge structure and accurately recovering edge-level deformation directions. In controlled known-truth experiments, it resolves structural change with increasing sample size, including orientation changes that leave ordinary eigenvalues unchanged. In one year of Bay Area weather data, the geometry of 12-hour change reconfigures spatial coupling about as much as whole seasons differ. In TCGA-BRCA, estrogen-receptor (ER)-associated reconfiguration concentrates on specific gene-module pairs and persists under graph-scaffold sparsification and removal of subgroup mean differences. These results establish posterior matrix-valued edge geometry as a unified framework for quantifying and interpreting context-dependent multivariate reconfiguration.

An expository essay containing some new results. A learner holds a prior belief over Boolean maps that answer a finite set of $Q$ questions, and receives answers one by one. Each answer carries surprisal and can clear predictive uncertainty about both the question asked and questions still unasked. We quantify this effect by the leverage: table entropy cleared per bit of surprisal received. Taking expectations over the truth prior and the question order, define the aggregate leverage as the ratio of expected uncertainty cleared to expected surprisal received. It equals one for independent answers and can exceed one for correlated answers. At finite size, this ratio is determined exactly by a single sequence: the mean entropy $G_\ell$ of the answers to $\ell$ questions. As the number of input bits grows at fixed asked fraction $t=\ell/Q$, a limiting increment profile $\gamma(t)$ determines the macroscopic learning curve. With $\eta_0$ the limiting initial entropy per question, the leverage becomes $L(t)= \frac{\eta_0-(1-t)\gamma(t)} {\int_0^t\gamma(x),dx}$. For exchangeable priors, de Finetti's representation gives a constant bulk profile $\gamma(t)$: deduction is confined to a boundary layer at $t=0$, and the leverage is forced to a hyperbolic form, as surprisal grows linearly. By contrast, we construct a simplicity prior with nontrivial bulk learning by grading Boolean maps by their polynomial degree over $\mathbb{F}_2$ and allocating weight across degree classes through a CDF $F$. Reed-Muller capacity then yields $\gamma(t)=1-F(t)$. This realizes any nonincreasing profile taking values in $[0,1]$, together with the corresponding macroscopic leverage curve.

Large language models (LLMs) are rapidly emerging as a new paradigm for modeling social networks by representing users and their relationships and interactions through natural language. Unlike classical network models or deep learning approaches, LLMs can simulate context-aware social behavior and language-driven interactions, enabling more realistic modeling of network formation and dynamic social processes. However, existing studies are scattered across different research communities and lack a unified perspective. This survey presents the first comprehensive review of LLMs for social network modeling by organizing the literature into two broad categories: network generative models and dynamic process models. Network generative models are further classified into selection-based and interaction-based approaches, while dynamic process models are categorized into opinion dynamics, information diffusion, and rumor propagation, each with their underlying modeling mechanisms. LLMs enable rich textual social interactions and decision-making, but they also exhibit many limitations, including inherent social biases and prompt sensitivity. We outline these open research challenges and discuss future directions in LLM-based social network modeling.

Bone-selective synthesis from digitally reconstructed radiographs (DRRs) requires separating skeletal signal from overlying tissue while preserving anatomical detail. U-Net skip connections supply fine encoder features, but their transfer is independent of decoder context. We introduce RFS-UNet, which lets the decoder participate in high-resolution channel recalibration. Pooled encoder and decoder features jointly predict a bounded residual scale, initialized to preserve the original skip transfer. The module operates at the two finest resolutions and integrates directly into the backbone. On a rebuilt patient-unique cohort, RFS improves test PSNR over U-Net-64 by 0.10 dB. A three-seed comparison with encoder-only recalibration supports the contribution of decoder context. RFS also offers a lower-latency alternative to CBAM, with 2.25 times faster inference in matched profiling. Decoder-conditioned reuse thus improves bone-selective synthesis through a compact architectural change.

Deep learning has achieved state-of-the-art performance in echocardiographic video segmentation, with an increasing number of models incorporating temporal information. However, quantitative evaluation of temporal explainability remains largely unexplored. We propose a quantitative framework for evaluating Grad-CAM explanations using four complementary metrics measuring temporal consistency, saliency motion, anatomical overlap, and temporal overlap. Using EchoNet-Dynamic, we compare a baseline 2D U-Net with ConvLSTM U-Net models trained across multiple temporal strides. While segmentation performance remained comparable across all models, intermediate ConvLSTM explanations exhibited substantially lower saliency consistency and greater centroid motion than final prediction explanations. Temporal Bottleneck explanations were significantly more stable than Encoder Bottleneck explanations across all strides, while final ConvLSTM Decoder3 explanations were broadly comparable to those of the 2D U-Net. Importantly, conventional frame-wise explanation metrics cannot determine whether variation in intermediate explanations reflects meaningful temporal feature evolution or explanation instability. These findings establish a preliminary quantitative framework for temporal explainability and motivate temporal-aware XAI methods that explicitly account for evolving representations in medical video models.

As an emerging framework, movable antenna (MA)-enabled wireless powered networks (WPNs) have attracted growing attention. WPNs integrate wireless communication and energy transfer. MA can dynamically adjust the position of antenna units by introducing additional spatial degrees of freedom, so as to make full use of channel gain, optimize the effect of energy beamforming, and further improve the performance of WPNs. In this article, we first classify the implementations of MA by driving architectures, and review the fundamental principles of WPNs. We then highlight the key advantages of MA-enabled WPNs in enhancing wireless power transfer efficiency, realizing flexible and adaptive beamforming, and improving system robustness and interference resilience. Furthermore, four representative application scenarios and three key enabling technologies are discussed. A case study is also presented to show the reduction in transmit power brought by MA for WPNs. Finally, we discuss the challenges and future directions of MA-enabled WPNs, aiming to provide reference for future research and practice.

Many pedestrian trajectory prediction algorithms have been proposed to improve the safety of navigation for mobile robots working in human-robot coexistence environments. Some pedestrian trajectory prediction algorithms extract information about obstacles near pedestrians from top-down view images to improve the accuracy of trajectory prediction. However, mobile robots typically create local occupancy maps using LiDAR, rather than top-down view images. Meanwhile, the vision sensors on board robots provide egocentric view images, which contain fine-grained behavioral information about the pedestrians near the robot. To better use the information collected by LiDAR and on-board vision sensors, we propose MamMA, a Mamba-based pedestrian trajectory prediction algorithm considering occupancy maps and pedestrian awareness states. MamMA divides the occupancy map by patches and extracts obstacle features from each patch to create map features. Pedestrian awareness states are divided and considered, as some studies show that awareness states affect the perception and speed of pedestrians. Furthermore, a Mamba-based model is proposed to predict the future trajectories of pedestrians based on different types of features. Experiments on the STCrowd, SiT, JRDB, ETH, and UCY datasets show that MamMA achieves better average displacement error and final displacement error than the state-of-the-art algorithms.

The software supply chain has become an increasingly exposed attack surface because of its reliance on intricate yet fragile dependencies. Existing defenses such as GitHub Dependabot often raise many false alerts because their coarse-grained matching cannot determine whether a vulnerable dependency is actually exploitable. Security analysts typically spend substantial time assessing vulnerability exploitability case by case. Recent LLM agents have emerged as promising candidates for this task given their advanced capabilities in coding and cybersecurity, yet no existing benchmark evaluates them on it. Prior benchmarks target zero-day settings, where agents detect and exploit previously unknown vulnerabilities. In contrast, software supply chain security focuses on how known vulnerabilities in upstream dependencies affect downstream projects. This requires agents to reason across repositories and determine whether an upstream vulnerability is exploitable in the downstream project. To address this gap, we introduce VEX-Bench, the first benchmark for evaluating LLM agents' ability to assess the exploitability of software supply chain vulnerabilities. It contains 75 real-world cases mined from GitHub and labeled by security experts, covering Python, Java, and Go. We evaluate nine models across three agent harnesses. While GPT-5.5 and Claude Opus 4.6 reach approximately 80% F1 on binary vulnerability-status classification, only GPT-5.5 surpasses 70% macro-F1 on fine-grained justification classification. This gap highlights the challenge of moving beyond binary exploitability assessment to identifying fine-grained exploitability reasons. Code and data: https://github.com/steven1518/vex-bench

Smart healthcare monitoring systems require precise action recognition to ensure well-being and timely intervention in critical situations such as falls, particularly for mobility-challenged individuals. Existing datasets are often clip-based, lacking the frame-level detail needed to recognize actions online, as they unfold. To address this, we introduce SAFER-Activities, a dataset for fall detection and physical activity monitoring, with a dedicated subset for wheelchair use scenarios. It comprises over 66 hours of video data captured by multiple cameras, with 85,310 action instances and frame-level annotations for 30 action classes. We benchmark action recognition on SAFER-Activities with 2D and 3D skeleton models, RGB models with frozen backbones, and multimodal fusion strategies, and evaluate on in-lab, out-of-distribution, and cross-dataset test sets. Skeleton-based models generalize best under domain shift; fusing frozen RGB features with the skeleton stream improves in-domain recognition over the baseline CNN1D, most clearly on the wheelchair subset, but degrades out of distribution. Cross-dataset and qualitative evaluations confirm that models trained on SAFER-Activities transfer well to unseen environments and external fall data. To support research on robust fall detection and activity monitoring, we release the dataset and code at https://safer-activities.github.io/.

Representational fidelity is routinely treated as a single abstract-realistic continuum, a simplification that limits how it is described and compared across research and design contexts. We introduce a multidimensional design space of representational fidelity for didactic visualization in science & engineering, inductively derived from a 175-item corpus spanning several disciplines, modalities, and instructional aims. The resulting design space specifies five dimensions: Morphological, Dynamic, Cueing, Contextual, and Interactive Fidelity, with seven sub-dimensions. We demonstrate the design space's descriptive power through successive rounds of expansion and refinement and analyze the corpus to reveal relationships among dimensions and implications for design and research. We further validate the design space through a pilot focus group in which participants applied the dimensions in an open-ended design exercise. Resulting sketches and verbal rationales informed a single-designer applied case study, offering preliminary evidence of the design space's generative potential as a structured aid to design exploration. Together, these contributions lay the groundwork for future research and more intentional design practice.

We present GridapGeosciences$.$jl, a new parallel distributed-memory Julia package for the numerical approximation of partial differential equations on general manifolds. Our abstract approach to generating discrete manifold domains relies on mesh refinement in general, and is implemented within the Gridap finite element library, whose high-level interface enables seamless definition of both intrinsic and extrinsic variational formulations. GridapGeosciences$.$jl features the cubed sphere manifold, which is used in this study to showcase the functionality of GridapGeosciences$.$jl in different applications. The first application involves scalar transport where we develop intrinsic formulations of common stabilisation terms, which are shown to be equivalent to well-known extrinsic stabilisation formalisations. Such stabilisation terms are used to develop an intrinsic formulation of the two-dimensional thermal shallow water equations that includes upwinded numerical fluxes. The final application is a linearisation of the Boussinesq equations where we demonstrate the capacity of GridapGeosciences$.$jl to capture both surface and vertical dynamics on a three-dimensional manifold.

Localized dimensionality reduction improves the scalability of operator learning for high-dimensional partial differential equations (PDEs), but independently decoded local patches can introduce block offsets, interface mismatches, and spurious high-wavenumber content. We introduce Two-Scale Localized PCA-Net, which decomposes the solution into a coarse-global component and local residual corrections. A compact global PCA basis captures domain-scale structure, while nonoverlapping local PCA bases represent the remaining fine-scale residual. A block-balanced latent objective couples the two representations, and optional interface-aware fine-tuning further promotes continuity through reconstruction and trace losses. On Poisson benchmarks, the two-scale representation substantially reduces reconstruction error and visible block artifacts relative to plain and overlap-based localized PCA-Net while approximately halving PCA fitting cost relative to overlap. On heterogeneous Darcy flow, it strongly reduces interface and discrete-residual errors, with more modest reconstruction gains. Ablations show that the primary improvement arises from the two-scale output representation, while interface-aware fine-tuning provides complementary continuity refinement. Overall, separating globally coherent structure from localized residual detail provides an efficient representation for artifact-reduced PDE operator learning.

Current LLM-based multi-agent systems (MAS) periodically compress intermediate states to reduce inference-time token consumption, thereby attempting to incorporate more agents. However, naive scaling strategies face challenges. For example, in economic simulations, large-scale MAS typically discard semantically rich economic states, i.e., agent behavioral trajectories, which are key drivers of macroeconomic fluctuations. In this paper, we reveal a phenomenon in which agent heterogeneity gradually decreases during simulation, and propose Prospect-State Propagation for Multi-Agent Systems (PspMAS). Inspired by prospect theory, PspMAS decouples each agent's micro state into a compact Prospect State and an expressive Semantic State. The former records psychological traces through a lightweight, parallelizable propagator and continuously injects heterogeneity into the system. The latter leverages the strong perception, reasoning, planning, and decision-making abilities of LLMs. These two components work complementarily, providing a scalable LLM-based multi-agent simulation solution.

We introduce FlexMoGen, a novel framework for flexible human motion synthesis conditioned on both natural language descriptions and motion style references. Text prompts are effective at defining semantic content, but they are often limited in capturing fine-grained style details such as timing, limb articulation, and expressive dynamics. A style example clip supplements the text by conveying these nuanced motion characteristics directly, enabling the model to preserve high-level intent while reproducing the desired stylistic traits. Given a text prompt and a style example clip, FlexMoGen generates high-quality motions that preserve semantic content while faithfully reflecting the target style, offering users greater control over the animation generation process. Unlike prior methods that rely on discrete style labels and do not generalize to long or multi-style generation, FlexMoGen learns a variational style encoder without style supervision and supports long, time-varying, multi-style synthesis. Our framework jointly pre-trains the style encoder and a text-to-motion latent diffusion model within a unified architecture, modulating motion style through a lightweight adaptation module. It integrates an efficient relative positional encoding scheme and is trained on both stylized and non-stylized datasets, enabling strong generalization to unseen text-style combinations. Experiments show that FlexMoGen achieves the best balance between content fidelity and style reflection.