Papers

Estimating two-sample comparison functionals within heterogeneous groups is challenging when outcomes are observed only for a small labelled subset while covariates are widely available. We develop semi-supervised estimation of group-specific two-sample comparison functionals and their prespecified aggregates. The proposed estimator combines single-index conditional imputation from labelled cross-arm pairs with averaging over all available covariate pairs. To handle index-score densities that may vanish at attainable endpoints, we use centred stabilization, with a smooth stabilizer in the profile criterion and a shrinking lower truncation of the kernel denominator (the hard floor) in the point estimator. The outer average retains all covariate pairs. Under a correctly specified single-index conditional-mean model and the stated regularity conditions, we establish consistency and asymptotic normality for bounded comparison functionals. A four-role original-observation influence representation accounts for sample overlap and identifies the variance component that unlabelled covariates can reduce relative to supervised estimation. We further establish conditional validity of observation-level multinomial perturbation resampling with complete refitting and shared labelled counts, distinguishing ideal variance consistency from finite-replicate variance estimation. Simulations show small bias and lower mean squared error than supervised estimation across the point-estimation settings, together with near-nominal coverage in the perturbation experiment. A descriptive NHANES 2011-2018 illustration comparing serum creatinine by hypertension history across age groups yields point estimates similar to their supervised counterparts and smaller semi-supervised standard errors for all reported comparisons.

Time Series Foundation Models (TSFMs) promise a paradigm shift toward zero-shot forecasting by eliminating task-specific training. However, existing works often overlook trade-offs between predictive accuracy and probabilistic calibration. This paper presents a benchmark study of six TSFMs evaluated on energy, traffic, and financial datasets. We contrast their performance against statistical baselines and a supervised DL model. The study reveals that while TSFMs outperform statistical methods and supervised models, they are subject to a fundamental trade-off between point accuracy and probabilistic reliability. Specifically, xLSTM architectures provide robust probabilistic calibration across horizons. In contrast, patch-based transformers offer competitive accuracy but face calibration issues at long horizons, while transformer-based models exhibit context saturation points for optimal zero-shot reasoning. These findings offer evidence-based guidance for balancing generalization and uncertainty quantification in real-world deployments.

Encryption hides IoT payloads, but traffic shape can still reveal device identity through packet sizes, timing, direction, and packetization. We present Adaptive Traffic Camouflage, a causal, leakage-aware controller that characterizes traffic-shape leakage without runtime device labels and selects a budget-feasible transformation for the next traffic window from previous-window context. The controller chooses among padding, packet splitting, timing, and composite transformations, or leaves traffic unchanged when camouflage is unnecessary. We evaluate the design on CIC-IoT-2022, IoT Sentinel, and UNSW using classical and sequence-based fingerprinting models under clean-trained, defense-aware, and incremental-exposure settings, with fixed, random, and mean-bandwidth-matched baselines. Under the Balanced profile, camouflage reduces mean Macro-F1 by 13.2-23.3% relative to clean traffic with 4.88-7.47% average bandwidth overhead and at most 0.64 ms added latency. Under the larger Privacy profile, the reduction increases to 28.0-43.5%. Defense-aware training recovers much of the lost attacker performance on CIC-IoT-2022 and UNSW, while IoT Sentinel retains a substantial privacy gap. A non-causal same-window reference provides only modest additional benefit over previous-window control, and metadata-rich attackers remain effective outside the targeted traffic-shape surface. These results show that causal, resource-aware camouflage can reduce IoT traffic-shape fingerprintability under explicit communication constraints, while the persistence of protection depends on how readily the defended distribution can be learned.

Large language models (LLMs) for code completion may generate deprecated APIs because their pre-training corpora contain code from historical library versions. Existing approaches use inference-time intervention, model editing, or machine unlearning, but multiple plausible completions make predefined replacements restrictive. Moreover, existing studies rarely verify whether models exhibit the targeted deprecated behavior or evaluate unintended changes to other APIs. We conduct a systematic empirical study of machine unlearning for deprecated API knowledge and construct MUDAPIBench, a behavior-grounded benchmark with over 7,000 model-specific instances derived from 145 deprecated-to-up-to-date API mappings across eight Python libraries. Instances are retained only when the original model generates the target deprecated API. We evaluate eight representative unlearning methods across three code LLMs on deprecated API forgetting, up-to-date API generation, preservation of other and unrelated API behaviors, general code-generation capability, and efficiency. Results show that Gradient Difference (GD) provides the best overall trade-off, suppressing deprecated APIs while preserving other capabilities with moderate computational costs. Further analyses reveal substantial variation across libraries and show that APIs deprecated after the model's training-data cutoff are harder to forget. Layer-wise analyses indicate that GD achieves effective forgetting with comparatively controlled internal changes.

Vision-Language-Action (VLA) models have emerged as general-purpose robotic manipulation policies. However, in dexterous hand manipulation, contact forces are typically provided as separate states or force-specific representations, making it difficult to explicitly represent the spatial correspondence between force and their corresponding visual locations. In this work, we propose VisForce, which visually grounds the current and desired forces at their corresponding fingertip locations. VisForce renders current and desired visual force cues on the current wrist image and a task-specific goal image, and combines the two representations through goal-conditioned cross-attention to generate force-aware actions. We evaluate VisForce using a real UR10 robot equipped with an RH56F1 dexterous hand through force-conditioned grasping and three multi-stage manipulation tasks. In force-conditioned grasping experiments, VisForce exhibited a consistent grip-force response as the desired force increased, and achieved grasp-and-lift success rates of 70% and 80% for an egg and a toothpaste tube, respectively. It further achieved final success rates of 70%, 55%, and 40% on cup insertion/bottle pouring, tong-assisted bread transfer, and slip-modulated peg-in-hole, respectively. These results show that fingertip-aligned visual force representations can be effectively used for force-aware conditioning in VLA-based dexterous hand manipulation.

Epsilon Indi Ab is currently the coldest, and one of the closest, directly imaged exoplanets (T_eff = 275 K, d=3.6 pc), offering a unique opportunity to test our understanding of the physical and chemical properties of gas giants across the full temperature range spanned by hotter directly imaged exoplanets and the cooler giants of the Solar System. We aim to characterize the atmosphere of Epsilon Indi Ab using infrared spectroscopic observations. We present JWST spectroscopic observations of Epsilon Indi Ab obtained with MIRI in the Medium Resolution Spectrograph mode (4.9-27.9 microns, October 2025) and NIRSpec in the Integral Field Unit mode (2.87-5.27 microns, May 2026). The data are highly contaminated by the stellar light from the bright host star. We therefore adopt a high-pass filtering and cross-correlation approach based on petitRADTRANS atmospheric models to detect the planetary signal and specific molecules. The cross-correlation analysis enables a robust detection of the planet with both instruments (up to S/N = 15.2). Using molecular mapping, we securely identify the presence of NH3 (maximum S/N = 15.6), H2O (maximum S/N = 10.8), CH4 (S/N = 3.8) and marginally detect CO2 (S/N = 2.5). These first results confirm the potential of infrared spectroscopy combined to cross-correlation techniques to characterize the atmosphere of directly imaged exoplanets with JWST, even the in case where the contamination by the host star is critical.

Purpose: To develop a wearable, stretchable radio-frequency (RF) coil that conforms to the extremities and improves the filling factor in low-field MRI. Methods: A stretchable solenoid RF coil was fabricated by stitching a sinusoidally arranged Litz-wire conductor onto an elastic textile. The coil was compared with four rigid coils, including two routinely used designs and two prototypes designed to isolate the effects of conductor material and stretchability. Performance was characterized through quality-factor, loading-factor, transmit-efficiency, and image-based signal-to-noise ratio (SNR) measurements. Phantom and in-vivo knee experiments for one volunteer were performed using two portable MRI systems operating at 3.53 and 3.04 MHz. Results: The electrical performance of the selected Litz wire decreased with increasing frequency, becoming a slight disadvantage at 3.53 MHz. Nevertheless, the stretchable coil provided the highest phantom SNR in both systems, exceeding that of the best-performing rigid coil by approximately 8 % at 3.53 MHz and 20 % at 3.04 MHz. In vivo, its global SNR was 5 % lower than that of the best rigid coil at 3.53 MHz and 19 % higher at 3.04 MHz. Compared with the larger rigid coil required when knee positioning is constrained, the corresponding SNR improvements were approximately 18 % and 80 %. Conclusion: Anatomical conformity can compensate for the frequency-dependent electrical limitations of Litz wire in stretchable low-field RF coils. The proposed design provided SNR comparable to or greater than the best rigid designs while facilitating coil placement in subjects for whom smaller rigid coils may be impractical.

Large language model (LLM) serving is increasingly agentic, with multi-turn sessions that idle between actions yet must retain their full context. Limited GPU memory capacity forces inactive KV states to be evicted, so resuming a session incurs either costly recomputation or slow interconnect transfers. To address this, high bandwidth flash (HBF)-an on-package 3D-NAND memory offering orders-of-magnitude greater capacity than high bandwidth memory (HBM) at comparable read bandwidth-has emerged as a strong candidate. However, its high read energy and limited write endurance make it impractical to serve all KV traffic. Fortunately, our analysis shows that agentic KV states exhibit distinct access patterns: a small hot set is read for every decoding step, while a large cold pool is read only when a paused session resumes. Exploiting this, we place the hot set in HBM and the cold pool in HBF, forming a hot-cold KV hierarchy within the GPU memory tier. On agentic workloads with Qwen3-Coder-30B-A3B, our design delivers 14 ms time-between-tokens (TBT) and adds only $\approx$0.1 ms of resume latency on top of prefill, while hosting $24\times$ more concurrent sessions per GPU. By confining HBM to the hot set, our design also cuts read power by 7.6 kW per 8-GPU node relative to serving all KV from flash-establishing HBF as a cold-tier complement to HBM rather than its replacement.

Graph Incremental Learning has garnered increasing attention as dynamic graph data continues to emerge across diverse fields. Conventional approaches primarily address catastrophic forgetting by preserving node-related knowledge through replay or distillation techniques; however, they often incur high computational costs and inefficiency. This issue is further exacerbated in real-world scenarios where labeled data for new classes is scarce. In this paper, we propose a novel lightweight plastic-memory framework specifically designed for few-shot incremental learning on graphs. The core idea of our framework is the construction of a plastic-memory module that evolves over time, continuously updating and expanding its memory to accommodate new classes while retaining previously learned knowledge. In contrast to existing techniques, our memory module is both lightweight and effective, featuring an innovative evolving micro-clustering structure that dynamically updates representations of class prototypes, sub-prototypes, and their interaction weights. Building on this memory module, we introduce a memory-driven meta-learning framework that enhances adaptability to new tasks in its inner loop while maintaining stability for earlier tasks in the outer loop. Extensive experiments on four benchmark datasets demonstrate the framework's superior performance in balancing stability for old knowledge and adaptability to new knowledge.

The impact parameter and transverse charge densities provide spatially resolved information on hadron structure and probe the interplay between dynamical chiral symmetry breaking and SU(3)-flavor symmetry breaking. We investigate the valence-quark distributions of the pion and kaon using their unpolarized vector GPDs at nonzero skewness $\xi$ within the covariant Nambu–Jona-Lasinio model, with ultraviolet divergences regulated by the Schwinger proper-time scheme. Increasing $\xi$ shifts the distributions toward smaller $x$, reduces their central magnitude at $b_\perp=0$, and broadens their transverse profiles. These results provide insight into the spatial structure of the pion and kaon and offer stringent tests of nonperturbative QCD dynamics, with relevance to forthcoming measurements at Jefferson Lab and the Electron-Ion Collider.

Nearest-neighbor graphs are discrete objects whose membership may change under small perturbations of the underlying coordinates. We establish an explicit stability guarantee for finite labeled configurations in an arbitrary metric space. If the gap between the kth and (k+1)st distances is positive, simultaneous per-label perturbations smaller than one quarter of that gap preserve the directed k-nearest-neighbor membership. The factor four is sharp under the stated uniform displacement assumptions, and every fixed deterministic construction based solely on the labeled neighbor family is consequently invariant. Under an interval-valid Lipschitz bound for labeled information-space trajectories, the same result yields a certified lower bound on the first possible rewiring time, with a refinement for label-specific motion bounds. We apply the finite theorem to frozen standardized Taylor-Green future-information coordinates [d_B, log A_B] for 585 particles at three observed time strata. Outward-rounded interval arithmetic certified a sufficient perturbation radius of approximately 1.023 x 10^-6, and a separately implemented checker within the same research workflow verified the rank and distance-margin calculations. An outcome-blind audit then examined whether the construction supported a numerical continuous-time horizon. Because the complete information map involved discrete clustering and boundary reconstruction and lacked an analytic derivative bound, validated dense-time bound, or certified modulus of continuity, the application was correctly classified as DISCRETE_ONLY with STOP_NO_INTERVAL_VALID_BOUND. Thus finite local structural invariance is proved and numerically certified for the frozen configuration, while temporal specialization and predictive generalization remain separate questions requiring additional evidence.

Memory constraints in artificial intelligence motivate accurate function approximation with fewer parameters. We study looping, which repeatedly composes one update function with shared parameters; each output becomes the next input. A looped Transformer, for example, reuses one block, whereas its conventional untied counterpart uses separately parameterized blocks. We compare their parameter requirements for a given worst-case approximation accuracy, or equivalently, their approximation accuracy under a common budget limiting distinct trainable coefficients. We then ask whether this representational parsimony improves statistical accuracy. For general likelihood models, we establish an upper squared Hellinger risk bound for looped sieve maximum likelihood and a minimax lower bound for the jointly tuned untied family. Further loop iterations improve the approximation bound without adding parameters, while increasing computation and the fitted-class complexity bound. For targets of known Hölder smoothness, looped residual feedforward networks and post-layer-normalized Transformers attain the minimax polynomial rate up to logarithmic factors with a fixed number of bounded real parameters. At sufficiently large fixed budgets, looped worst-case risk vanishes while optimal worst-case untied risk remains bounded away from zero. The loop-to-untied risk ratio also tends to zero under specified growing-budget conditions. Regression, binary response, and energy-based generative models illustrate the theory.

Accurate multi-step traffic forecasting remains challenging because observed traffic signals contain heterogeneous temporal dynamics with different characteristics and levels of predictability. Existing approaches typically model these dynamics within a unified representation or rely on predefined decomposition rules, which may limit their ability to flexibly separate persistent patterns from rapidly varying fluctuations. To address this issue, we propose the Adaptive Decomposition Network (ADNet), a component-specific forecasting framework that adaptively disentangles traffic dynamics into dominant and residual components. ADNet introduces a learnable complementary spectral decomposition mechanism that determines the contribution of each frequency bin to the two components. Unlike hard frequency partitioning, every frequency bin can contribute to both components with different learned proportions, allowing the decomposition to be optimized jointly with the forecasting objective. The reconstructed components are then modeled by two dedicated spatiotemporal forecasting branches, and their predictions are integrated to generate the final multi-step forecast. Experiments on the Alameda and Orange regions of the TraffiDent dataset show that ADNet achieves the best performance in 20 of the 24 reported region-horizon-metric comparisons, with particularly clear gains at longer forecasting horizons. Capacity-controlled ablation experiments further show that the learnable decomposition substantially outperforms a fixed decomposition and provides additional improvements beyond the dual-branch architecture alone. These results demonstrate the effectiveness of adaptive decomposition and component-specific modeling for multi-step traffic forecasting.

Nonlinear activations can create equivariant interactions between irreducible representations that linear maps cannot. We use the Gaussian degree decomposition to extend ordinary polynomial degree to such nonlinear maps, and prove that for a fixed coordinatewise equivariant layer each degree factors into a polynomial determined by the linear maps and a scalar determined by the activation. This separates three distinct obstructions, coming from symmetry, coordinates, and activation.

Recent advances in generative video models have enabled the synthesis of visually realistic content, posing significant challenges to synthetic video detection. Existing detectors often rely on appearance artifacts, semantic inconsistencies, and temporal patterns that may be generator-specific, limitating generalization to unseen synthesis models. We investigate whether responses to a pretrained generative model provide more transferable forensic cues. Our key observation is that real and AI-generated videos exhibit distinct velocity responses under a pretrained Flow Matching video model. This distinction persists when different pretrained video-generation backbones are used as probes, suggesting that velocity responses offer transferable forensic signals beyond visual artificts. Motivated by this observation, we propose TRACE (\emph{\underline{T}rajectory \underline{R}epresentation \underline{a}nd \underline{C}onsistency \underline{E}stimation}), a generation-process-aware framework for AI-generated video detection. TRACE leverages a pretrained video DiT as a velocity-field probe to extract representations at multiple flow time points, and models cross-frame consistency through velocity differences between adjacent frames. We further introduce a Real-Centered Trajectory Optimization objective that encourages generator-invariant representation learning. Extensive experiments on AIGVDBench demonstrate that TRACE generalizes effectively across diverse generators, substantially outperforming prior state-of-the-art methods on unseen open- and closed-source video generation models.

Large language models (LLMs) are emerging as scientific assistants, yet their computational demands and limited domain specialization constrain sustainable deployment in environmental engineering. Here, we investigate whether domain-specialized small-scale LLMs can combine scientific capability with sustainable deployment in biological wastewater treatment. We developed a benchmark evaluating three scientific capabilities of LLMs: retrospective cognition, comprehension fidelity, and prospective extrapolation. BioWater (8 billion parameters, fine-tuned on specialized domain knowledge) achieved higher comprehension-fidelity scores than participating human experts and performance comparable to a 397-billion-parameter general-purpose LLM in retrospective cognition and prospective extrapolation. Human-BioWater collaboration generated a scientific hypothesis that was subsequently supported by laboratory experiments, demonstrating its potential to contribute to prospective scientific research. We further evaluated the economic and environmental implications of LLM deployment across global wastewater treatment plants (WWTPs). Locally deployed small-scale LLMs became more sustainable than cloud-based large-scale LLMs as inference demand increased in intelligent WWTPs. These findings highlight domain-specialized small-scale LLMs as a promising pathway towards scientifically capable, computationally efficient, and sustainably deployable artificial intelligence for wastewater treatment.

HopChain has shown on still images that multi-hop data synthesis improves vision-language reasoning, because long chain-of-thought reasoning exposes errors that compound across steps, while most data used for reinforcement learning with verifiable rewards (RLVR) rarely demands a chain of visual evidence, so these weaknesses are likely to stay unexposed. We observe the same problem in video, where this framework has not yet been explored. We therefore build Video-HopChain, a dataset of 22,550 multi-hop video questions over 13,378 videos, together with a held-out benchmark of 1,000 questions. Each question chains three to six yes/no questions about moments in one video, and each yields one of two integers depending on its answer. The final answer is the sum of these integers, so an exact match on that sum gives the verifiable reward that RLVR needs. We first train Qwen3-VL-8B with GRPO on a standard video dataset, and a second stage on Video-HopChain then raises the mean over eight video understanding and reasoning benchmarks from 55.4 to 57.9 and improves every one of them. Training on such a dataset, however, exposes a known limitation of GRPO: its learning signal comes from the reward variance within a group, so hard questions whose rollouts are all incorrect and easy questions whose rollouts are all correct both leave the group with no gradient. To recover these groups at the same compute budget, we introduce Confidence-Gated Exploration (CGE). With 8 rollouts per question, CGE samples the first 4 as usual. If these 4 are either all correct or all incorrect, it samples the last 4 with the policy's most confident token masked inside the reasoning span, and removes the masked positions from the loss while all 8 rollouts enter the advantage. With CGE, the mean rises further to 59.3. We release the dataset, the checkpoint, and the data generation and training code.

Integrated sensing and communications (ISAC) spans radiofrequency (RF), visible-light, optical-fiber, power-line, and acoustic systems, yet technology transfer across these domains remains underexplored. This article examines bidirectional knowledge and technology transfers centred on RF-ISAC. It shows how VLC motivates power-domain sensing, fiber enables differential referencing and distributed processing, and PLC inspires topology-aware monitoring and adaptive probing. Conversely, RF-ISAC contributes joint signal design, nuisance suppression, and weak-return recovery. The article highlights transferable principles, required adaptations to improve ISAC, and information potentially lost across physical media.

This paper is concerned with stochastic Hamiltonian systems driven by Lévy processes. By employing the lent particle method developed by Bouleau and Denis in the framework of Malliavin calculus with jumps, we establish an explicit Bismut–Elworthy–Li type derivative formula for the associated Markov semigroup, as well as corresponding gradient estimates. The main novelty lies in extending the known results for Brownian-motion-driven degenerate systems to the nonlocal setting with jumps, where the presence of a pure jump noise and the degeneracy of the coefficients pose substantial difficulties. Our approach provides a systematic treatment of such nonlocal degenerate operators and fills a gap in the literature on derivative formulae for jump-type stochastic Hamiltonian systems.

Vision-language models (VLMs) have achieved strong performance on tasks such as visual question answering, yet small image resizes can turn correct answers into errors. We investigate whether changes in visual configuration, such as image tiling and token arrangement, contribute to this instability. Across seven checkpoints and four benchmarks, equally small resizes cause more correctness flips when they switch configurations. Surprisingly, in over half of these cases, models answer the question incorrectly but can still read the correct answer when told what to read. Furthermore, attention interventions in LLaVA-NeXT suggest that configuration changes can weaken the use of readable information during answering. We therefore guide models using field cues and their own transcriptions. With annotation assistance, these forms of guidance together correct 97.2% of errors with readable information. These findings show that configuration changes can affect how models use information they can still read.

Graphical User Interface (GUI) Agents autonomously interact with software to fulfill user requests, where GUI navigation stands out as the most critical and challenging capability. Mastering this capability demands a complex synergy of step-wise decision-making, state-action alignment, and long-horizon planning. While directly mixing these corresponding navigation tasks seems intuitive to simultaneously acquire these skills, such a direct combination is severely bottlenecked by inconsistent optimization objectives and profound data heterogeneity. To overcome these barriers, we propose the MaP (stands for “Masked Trajectory Prediction”), a unified framework that seamlessly harmonizes divergent GUI navigation tasks. By modeling multi-turn GUI interactions as a trajectory and defining training objectives through component masking and prediction, MaP shifts the optimization from task-specific marginal distributions to a consistent objective. Furthermore, to handle the data heterogeneity across multiple navigation tasks, we design a role-aware adapter learning module that dynamically routes each token to a specialized representation space. Extensive experiments on five representative GUI navigation benchmarks demonstrate that MaP effectively mitigates gradient conflicts and significantly outperforms the direct mixture training, establishing a robust paradigm for multi-task GUI navigation.

Let $1 \leq q < p$ and let $\lambda_1$ be the first eigenvalue of the $p$-Laplacian in a bounded domain $\Omega$. We study the energy functional $$ E_\lambda(u)=\frac{1}{p}\left(\int_\Omega|\nabla u|^p\,dx -\lambda\int_\Omega|u|^p\,dx\right)-\mathcal{F}(u), \quad u\in W_0^{1,p}(\Omega), $$ where $\mathcal{F}$ is positively $q$-homogeneous and vanishes along the first eigenspace. Assuming a suitable relation between $\mathcal{F}$ and the $\kappa$-th power of the principal part of $E_{\lambda_1}$ near this eigenspace, we describe the behavior of $E_{\lambda_1}$ according to the relations $p\kappa<q$, $p\kappa=q$, or $p\kappa>q$. In particular, the functional is unbounded from below in the first case, and has a negative infimum in the last case. We then study how sufficiently small $q$-homogeneous perturbations of $\mathcal{F}$ influence the geometry of $E_\lambda$. In this way, we describe assumptions guaranteeing the existence of three critical points in a left neighborhood of $\lambda_1$ and two critical points in a right neighborhood of $\lambda_1$, which indicates an $S$-shaped structure of the solution set. The results are applied to double-phase functionals and the nonlinear Fredholm alternative.

We develop a Poincaré duality theory for defects of nondegenerate sesquilinear pairings over Laurent polynomial rings. A key ingredient is a novel flat resolution of the character module, constructed from a triangulation of the sphere at infinity associated with a fan. The cup product on this resolution turns Poincaré duality on the sphere into canonical pairings between the resulting defect modules. In middle degrees, we construct distinguished quadratic refinements using equivariant cohomology of the sphere with the antipodal action. The effective replacement of the sphere with a projective space provides a geometric substitute for division by two. Applied to translation-invariant Pauli stabilizer codes, our results establish the nondegeneracy of higher-dimensional braiding pairings. They extend the two-dimensional T-junction formula for topological spin to higher dimensions, while giving it a geometric interpretation.

AI planning studies how an agent can reach a goal by executing a sequence of actions. To plan correctly, the agent needs an action model describing when each action can be executed and how it changes the world. Constructing such models by hand requires domain expertise, and can be costly and error-prone. Action models can instead be learned from available data using existing neurosymbolic approaches, but they currently assume access to complete traces of fully observable images . These approaches fail to learn action models under partial observability where some of the images might not be present or are not fully informative of the current state of the world. Hence, this paper proposes NeSyAM, a novel neurosymbolic modeling paradigm for action model learning under partial observability. In addition, the paper presents a unified variational framework for theoretically analysing the limitations of existing methods compared to our proposed approach. NeSyAM is then tested extensively on six visual planning domains and three observation regimes to show it consistently recovers relevant parts of the true action model under partial observability.

The Remote Point Problem (RPP) is an algorithmic problem that asks, given a linear subspace $L \subseteq \mathbb{F}^n$ of dimension $k$, to deterministically find a vector $v \in \mathbb{F}^n$ far in Hamming distance from $L$. This problem was introduced by Alon, Panigrahy and Yekhanin [APY09], motivated in part by the matrix rigidity approach for proving circuit lower bounds. An algorithm is said to achieve remoteness $d$ if it finds a vector $v$ whose Hamming distance from $L$ is at least $d$. We observe that over the rational numbers, the problem admits a deterministic polynomial-time algorithm that achieves optimal remoteness $n-k$. Over finite fields, we obtain a (modest) improvement of a result of Alon, Panigrahy and Yekhanin [APY09], and give an algorithm that achieves remoteness $\Omega\left(\frac{n}{\max\{k, \log n\}} \log n\right)$.

We extend the global existence results for critical parameters of [Bianchini and Leccese, J. Math. Anal. Appl. (2024)] to the multidimensional problem \begin{equation*} \partial_t u + \text{div } (b(t,x) u^{1+k}) = \Delta u \end{equation*} for $b:(0,\infty)\times\mathbb{R}^d\to\mathbb{R}^d$ non-autonomous fields, in the case \begin{equation*} b\in L^\infty_{\mathrm{loc}} \bigl((0,\infty),L^{p,\infty}(\mathbb{R}^d)\bigr), \qquad p>d\ge 2. \end{equation*} For the critical case, we study the difference between two ordered solutions whose conserved small mass absorbs the drift. Finitely many increments then reach an arbitrary solution.

In this work, we investigate the thermodynamics of arbitrary spherically symmetric surfaces in non-flat FLRW spacetimes within general relativity. Adopting the gravity-to-thermodynamics perspective, the Clausius relation and the unified first law follow directly from the gravitational field equations and matter dynamics, with a central role played by the matter-flux measure derived from energy-momentum conservation. The cosmological apparent-horizon and event-horizon thermodynamics are both recovered as special cases. In particular, the event-horizon temperatures derived from the gravitational dynamics satisfy both thermodynamic relations without introducing phenomenological modifications, and the corresponding temperature reduces to the Gibbons-Hawking temperature in the de Sitter limit. We further show that previous inconsistencies originate from incompatible temperature prescriptions rather than from any intrinsic deficiency in the thermodynamics of the cosmological event horizon. These results demonstrate that the gravity-thermodynamics correspondence is a generic feature of gravitational dynamics rather than a property unique to causal horizons.

We prove that a compact Brody-hyperbolic manifold carrying a strictly positive quasi-closed plurinegative $(1,1)$-current has nef canonical bundle, which is ample if every positive Lelong level set has complex dimension at most two. We also establish Kähler rigidity of the prescribed Hermitian metric for nonpositive constant Chern holomorphic sectional curvature on compact manifolds in Fujiki's class and for nonzero constant Chern holomorphic sectional curvature on compact complex threefolds. In complex dimension four, we prove that every balanced Hermitian metric with nonzero constant Chern holomorphic sectional curvature is Kähler, without assuming compactness or completeness. Under the same curvature assumption, dimension inequalities for the subspaces spanned by the image of the $(1,0)$ covariant derivative of the Chern torsion and its iterated images under Chern curvature endomorphisms imply Kählerness in dimensions at least five for balanced metrics and at least four without balancedness. At zero Chern holomorphic sectional curvature, we construct compact balanced examples in every complex dimension at least seven that are not Chern flat. However, on a compact connected Hermitian manifold with zero Chern holomorphic sectional curvature and vanishing first Chern–Ricci tensor, the prescribed metric is Kähler flat whenever the manifold admits a smooth semipositive plurinegative $(1,1)$-form positive definite at some point.

We determine the Gabriel spectrum of a category of sheaves of vector spaces in purely topological terms. For every topological space $X$, we prove that the Gabriel spectrum of ${\mathbf{Sh}}(X)$ is homeomorphic to ${\mathrm{Sk}}({\mathrm{Sob}}(X))$, where ${\mathrm{Sob}}(X)$ denotes the sobrification of $X$ and ${\mathrm{Sk}}$ indicates passage to the Skula topology. The proof is based on a classification of indecomposable injective sheaves and a characterization of localizing subcategories in terms of Skula-open subsets. We show that the Gabriel spectrum is always Hausdorff, zero-dimensional, and totally disconnected, and that it is compact if and only if $X$ is Noetherian. This leads to computations of Gabriel spectra arising in persistence theory. In particular, the Gabriel spectrum of the category of persistence modules over ${\mathbb R}^n$ is homeomorphic to the space of ideals of ${\mathbb R}^n$ with a natural topology.

Using large language models (LLMs) to simulate diverse human populations has the potential to transform many aspects of computational social science, yet many evaluations score the average response rather than the spread of opinion within real groups. Here, we develop a diagnostic framework that measures point accuracy alongside dispersion retention, the ratio of predicted to human standard deviation ($\dr$), on 10{,}000 respondent–question pairs from the World Values Survey (WVS) spanning twelve countries and six continents. We evaluate eleven zero-shot language models and five variants fine-tuned on WVS data with SFT, DPO, and GRPO. We identify a failure mode we term consensus collapse, where alignment training compresses outputs toward one stereotype per group. Along the post-training trajectory from the Llama~3.1 70B base to the Tulu~3 checkpoints, the first stage, supervised instruction tuning, removes half of the spread with minimal accuracy gain ($\dr$ 1.22 to 0.59; accuracy $+0.9$ points), the later stages do not restore it, and a gap opens between WEIRD and non-WEIRD countries that survey fine-tuning then deepens while pursuing higher point accuracy. The most accurate model (Tulu~3 70B-DPO fine-tuned on WVS, 57.9%) keeps half the human spread overall ($\dr = 0.50$) and 11% of it for Nigeria, against 0.70–0.87 for WEIRD countries. Raising the sampling temperature to 1.0 leaves the Wasserstein-1 distance ($\wone$) to human distributions unchanged for both fine-tuned DPO models, and GRPO on Qwen~3.5 9B does not restore the spread under either an accuracy reward or a distribution-shaped reward. Mixing the aligned model with an unaligned prior raises $\dr$ from 0.51 to 0.62 on a held-out split but leaves Nigeria at 0.36. Point accuracy alone therefore misjudges these simulators, and current post-training trades diversity for consensus.