Papers

Integrating environmental sensor data with leaf imagery is widely reported to boost crop disease classification accuracy. In this work, we reveal that these reported gains are often artifacts of dataset construction: because a single sensor reading is shared across many images collected in a single session (one farm on one date), multimodal networks can predict disease simply by memorizing session identities. Analyzing two widely used Korean datasets, the Crop Disease Diagnosis (CDD) benchmark and an AI Hub pest/disease dataset, we demonstrate that nearly all images share sensor values, with 91.9% of CDD test images having exact sensor duplicates in the training set. Remarkably, an image-free classifier given only timestamps matches or exceeds sensor-driven predictions across all seven evaluated crops, and matches the published macro-F1 of a state-of-the-art CDD fusion model. These results indicate that performance gains on standard random splits cannot be disentangled from session leakage. We propose that multimodal crop studies must evaluate on session-held-out splits and report performance against sensor-free date-time baselines to ensure genuine generalization.

Confluence is a fundamental property of nondeterministic computations, arising from parallelism, concurrency, or freedom in the evaluation order. It guarantees that such a computation always yields the same result, regardless of the order in which steps are taken. The decreasing diagrams technique of van Oostrom is one of the most versatile methods for establishing confluence of transition systems (abstract rewriting systems). It reduces global confluence to local confluence: a system is confluent whenever its transitions admit a locally decreasing labeling. Essentially all classical confluence criteria arise as corollaries. A central question, posed by van Oostrom in 1993, asks whether the decreasing diagrams technique is complete: Does every confluent transition system admit a locally decreasing labeling? This is Problem 56 of the RTA List of Open Problems. A positive answer was known only for countable systems, and recently up to the first uncountable cardinal $\aleph_1$. The general case remained open. We settle this thirty-three-year-old problem in full. We prove that every confluent transition system admits a locally decreasing labeling using only three labels. This bound is optimal, as two labels do not suffice even at the first uncountable cardinality. It follows that this single criterion can, in principle, certify the confluence of every confluent system, and hence of every confluent program. The entire development is machine-checked in the Isabelle/HOL and Lean proof assistants and relies only on classical logic and the axiom of choice.

We study higher moments of quantum fluctuations and microscopic correlation energy in the three-dimensional Gross–Pitaevskii regime. For a smooth, compactly supported, nonnegative radial interaction and an $N$-independent normalized initial condensate wave function in $H^6$, we propagate the third spectral moment of a positive correlated energy along the exact many-body evolution. A uniform initial bound controls the third moment of the depletion number and sixth moments of collective one-particle fluctuations on every compact time interval, independently of $N$. For a nonzero interaction and a smooth, compactly supported initial condensate, we also identify the excitation-energy measure at scale $N^2$, weighted by the first energy. This limit holds for norm-convergent pure-state families with a uniform bound on the initial third correlated-energy moment. Its positive-energy part is a spectral measure of the relative scattering operator $-2\Delta+v$, multiplied by a time-dependent dressed contact. We compute the radial density and prove strict positivity of the contact for nonzero references with finite kinetic energy and finite mean excitation number. The same evolving states have bounded physical fluctuation moments and excitation-energy moments of order $p>1$ bounded below by a positive multiple of $N^{2p-2}$, in the extended spectral sense. Inverse powers of the positive initial energy construct admissible pure and mixed families. For the norm-convergent pure-state class, we determine the scaled interaction-energy moments for $1\le p<2$ and bound the second moment by $O(N^2)$. A finite cubic approximation has norm error $O(N^{-3/16})$ on the energy form domain and $O(N^{-5/4})$ on a stronger initial domain of its generator.

Large Language Models (LLMs) are increasingly deployed for automated software vulnerability analysis. Binary classification alone is insufficient; practitioners need explanations to triage bugs and engineer patches. Standard practice relies on Chain-of-Thought (CoT) prompting, but free-form reasoning allows models to obscure logical leaps, hallucinated execution steps, and internal inconsistencies behind plausible prose. Our manual audit reveals that approximately 60% of correct vulnerability verdicts are accompanied by fabricated or unverifiable claims, and free-form explanations allow reasoning errors to evade LLM-as-a-judge evaluation. We present Vulnerability Explanation Reasoning Auditor (VERA), an automated framework for auditing LLM vulnerability reasoning. Rather than accepting free-form text, VERA asks models to output a Structured Reasoning Record (SRR) encoding tracked pointers, memory operations, and state transitions in machine-readable fields. A multi-stage judge audits each SRR against eight reasoning failure modes using deterministic checks, with LLM calls reserved for semantic interpretation. The standardized SRR schema also enables automated mutation testing to benchmark judges at scale without human annotation. Our evaluation shows reasoning flaws occur in correct verdicts just as frequently as incorrect ones, and VERA exposes 87% of reasoning errors that free-form LLM-as-judge systematically miss.

Sinkholes are a widespread geohazard in karst terrain. In Florida, soluble carbonate bedrock, shallow groundwater, and intense rainfall combine to make subsidence both common and spatially heterogeneous. Predicting where and when sinkholes will occur is difficult for two reasons. First, locations without reported sinkholes cannot be directly labeled or sampled as true negative locations. Second, the potential factors governing sinkhole risk span heterogeneous data modalities and therefore require careful integration within a unified modeling framework. We address both problems with our proposed model, a multimodal Cox proportional hazards framework for sinkhole susceptibility. Our contributions are threefold. First, we extend the proportional-hazards formulation to heterogeneous multimodal input through modality-specific encoders and a cross-modal fusion layer. Second, we treat unreported locations as right-censored rather than negative, avoiding hard-negative labeling and yielding continuous, time-aware susceptibility from the predicted survival function. Third, a statewide Florida case study with spatially blocked validation and ablation studies quantifies the benefit of multimodal integration. A Florida case study demonstrates that the proposed method effectively ranks sinkhole risk and produces a statewide susceptibility map that captures spatial variations in sinkhole occurrence.

Unstructured database search is a fundamental problem that requires finding one or more elements satisfying a specific property within a set of candidates. While Grover's algorithm provides a quadratic speedup for finding a marked element when the number of solutions is known, finding all solutions when their number is unknown presents additional challenges. In this paper, we thoroughly analyze this problem by considering all the different regimes of combinations of classical, Grover and generalized fixed-point quantum search instances. We unify these into an adaptive Bayesian approach that maximizes the expected success probability per unit execution time at each searching instance. For a problem with a known number of solutions, much lower than the database size, we prove that our proposed approach is asymptotically optimal within the considered search model. Furthermore, we prove that for any probability distribution characterizing the likely number of solutions, in regimes where the classical verification time is at most 25% of the quantum amplitude amplification time, hybrid classical and Grover approaches are preferred to generalized fixed-point. Outside of this regime, we derive an upper bound on the maximal improvement achievable by fixed-point search compared to the best Grover-based score. Additionally, we determine the optimal transition point between classical sampling and quantum searching using an integral approximation of the probability distribution of the number of solutions. The analytical results are also supported by numerical simulations of the proposed algorithm and by comparisons between the generalized fixed-point and Grover-based search policies.

We report the experimental observation of discrete ferroelectric switching down to 0.475 nm x 0.475 nm in HfO2-based ferroelectrics using correlated STEM electron beam induced current (EBIC) imaging and nanoscale voltage pulsing. These high-resolution measurements reveal single-domain switching events characterized by abrupt, bi-state transitions with no intermediate polarization states. By mapping polarization-voltage behavior and switching kinetics across thousands of domains, we extract spatially resolved switching thresholds (Emin), switching speeds (tsw), and remanent polarization (2Pr), uncovering robust scaling trends. Larger domains exhibit nearly twice the polarization and faster switching despite higher Emin, while smaller domains switch more slowly at the same field. Sub-domain imaging enables quantification of variation scaling: polarization variation increases linearly logarithmically with area, with inter-domain variation dominating intra-domain variation. Importantly, we show that multi-bit operation arises from the statistical distribution of domain-level switching, rather than partial polarization, enabling distinct and reliable states in devices as small as 0.01 um2. These findings provide a foundational experimental framework for designing scalable, multi-bit ferroelectric memory based on grain- and domain-level heterogeneity.

We study the problem of constructing highly nonlinear vectorial maps $F: \mathbb F_2^n \to \mathbb F_2^m$. Concretely, we want an $F$ and an $A = A(m,n)> 0$ as small as possible, so that for every affine map $L: \mathbb F_2^n \to \mathbb F_2^m$ (of the form $L(x) = M x + b $) we have: $$\mathrm{agree}(F, L) := |\{ x \in \mathbb F_2^n \mid F(x) = L(x) \}| \leq A.$$ Such questions have been studied by Nyberg (1991,1993), Carlet and Ding (2004,2007), Liu, Mesnager and Chen (2017), Nagy (2025), and Biryukov, Turecek, and Udovenko (2026). There is a classical method of constructing such functions from bent-functions and Fourier analytic ideas; the best bound achievable by this method is: $$ A(m,n) = \Theta(2^{n-m} + 2^{n/2}),$$ and in particular, is never smaller than $2^{n/2}$. In this work, we show how to construct highly nonlinear functions beyond this Fourier bound. Concretely, we show how to construct for every $\gamma>0$, a function $F: \mathbb F_2^n \to \mathbb F_2^m$ with $m = O_{\gamma}(n)$, achieving $$ A(m,n) \leq (1 + \gamma)^n.$$ Surprisingly, we even achieve the same quantitative behavior for the much harder question of having low agreement with $m$-tuples of degree $d$ polynomials $Q: \mathbb F_2^n \to \mathbb F_2^m$, with $m = O_{\gamma, d}(n)$. Here the previously best bounds were of the form $A(m,n) = O( 2^{-\frac{n}{2^{d+1}}} \cdot 2^n )$ of Ben-Sasson and Kopparty (2010), based on Gowers-norm-type arguments. All our results generalize to all finite fields $\mathbb F_q$ in place of $\mathbb F_2$. Our methods are based on a new connection to classical results on counting solutions to systems of polynomial equations via algebraic methods. This connection brings us to basic questions in combinatorics, about graphs and hypergraphs with simultaneously a small number of edges and independent sets.

Memory self-evolution uses task feedback to iteratively improve executable memory programs that store and retrieve information from past interactions. Existing approaches typically adopt holistic evolution, deriving revision directions from mixed feedback and judging progress by overall performance. This can obscure optimization directions and hide capability-specific gains offset by regressions elsewhere, leaving promising directions underexplored. We introduce capability-driven evolution, which extends search guidance from overall performance to individual capability dimensions, preserving promising revisions and expanding exploration beyond the boundaries of holistic evolution. We propose PrisMem, which uses dependency-aware capability selection to prioritize targets with potential cross-capability benefits and history-guided diagnosis to refine capability specialists. Trace-guided integration compares evaluated programs on paired differential cases, using their behavioral differences to consolidate complementary gains into a unified memory program. Experiments show that PrisMem outperforms the strongest baselines by 10.54 and 7.83 percentage points on BEAM-1M and LongMemEval-M, respectively, demonstrating its effectiveness on million-token histories.

Reinforcement learning post-training for language models relies on two reward designs: human preferences (RLHF, DPO) and binary verifiers (RLVR). Clinical question answering fits neither. Near-correct answers differ by a single substituted entity, and no executable check decides clinical correctness. We instantiate a soft verifier from a maintained controlled vocabulary: UMLS Concept Unique Identifier overlap (via scispaCy, set-level F1) gives a graded, externally specified reward computed without a model in the loop. We combine it inside GRPO with an entropy-normalised LLM judge, which covers the safety and evidence axes overlap cannot see, and a small consistency penalty on padding and repetition that keeps early-training samples scorable. This three-term composite improves over SFT on Phi-3-mini (3.8B) over MedQA by 2.9% on EM (0.700 vs 0.680) and 39% on Token-F1 (0.202 vs 0.145); on Llama-3.2-3B the corresponding gains are 14% on EM and 35% on Token-F1. We report Token-F1 as the primary metric because it credits partially-correct clinical content that EM discards at this open-generation scale. Main-table results are means over 3 seeds with standard deviations below 0.005. The method transfers to PubMedQA, where training on the PubMedQA train set with the same composite reward improves Token-F1 over SFT by 22% on Phi-3-mini and 17% on Llama-3.2-3B without retuning. A reward ablation on Phi-3, varying the judge-ontology split at a fixed consistency weight, attributes 3 EM points to the ontology term, the contribution that catches entity substitutions the judge cannot. Three negative findings constrain the design: DPO under random negatives underperforms SFT for strong-prior models but helps the weakest-prior one; PPO under a sparse neural reward diverges; GRPO with KL-in-loss collapses at 7B.

Landscape analysis has been successfully applied to understand complex optimisation problems, gain insights into algorithm behaviour, and automate algorithm selection and configuration. Although many landscape analysis techniques have been developed over the last decades, it remains difficult for researchers and practitioners to decide which approaches are appropriate and to implement them in practice. Some tools are available, but these are either restricted to particular problem domains (e.g., unconstrained black-box continuous optimisation), or are limited in what they model and measure. In addition, output from landscape analysis is often not easily interpretable, especially when computed landscape features do not correspond with aspects of problems that practitioners are familiar with. In this paper, we introduce a principled approach for explainable landscape analysis (XLA) with an associated Python package called pyXla. The approach is generic in that it applies to problems with different representations (continuous or combinatorial), with single or multiple objectives, with or without constraints. The extent of analysis provided by the XLA framework depends on the data available, with richer analysis offered as additional information is provided by the user. We demonstrate the explainable output produced by pyXla on a selection of hand-crafted problems with diverse landscape characteristics.

Edge video analytics with lightweight models is prone to accuracy degradation due to persistent distributional shifts in live video streams. While continuous learning (CL) addresses such data drift, it heavily strains the limited compute resources of edge servers originally provisioned for inference. Our empirical study reveals that emerging vision foundation models (VFMs) offer a practical, retraining-free alternative that delivers high average accuracy with remarkable compute savings. However, VFMs frequently misclassify specific rare classes, which often represent critical objects, as visually similar common classes. We design DIALER, a system that exploits the spare compute cycles freed by retraining-free VFM inference to mitigate rare-class misclassifications. Specifically, DIALER pre-builds multi-stage correction pipelines for dominant rare-to-common confusion pairs offline. At runtime, it routes correction candidates to the corresponding pipelines and executes as many stages as idle GPU headroom permits. Evaluation on four real-world driving datasets shows that DIALER improves rare-class accuracy by up to 14.0% without interfering with real-time VFM inference for multi-stream analytics.

Del Pezzo orbifolds are del Pezzo surfaces equipped with a strict normal crossing divisor, called boundary, such that the log anticanonical divisor is ample. We classify del Pezzo orbifolds of degree less than 6 in terms of components of the boundary, in the sense of Campana. This completes our previous work on classification of del Pezzo orbifolds with irreducible boundaries.

This paper introduces a dense upper mid-band Frequency Range (FR3) Channel Knowledge Map (CKM) dataset for Uncrewed Aerial Vehicles (UAVs) with an on-board base station (UxNB). It contains 16,180 CKM samples from 3,236 urban locations in 66 cities at 7.125 GHz and UxNB heights of up to 500 meters. Every 513x513 sample stores the building geometry, the line-of-sight (LOS) state, attenuation, delay spread, angular spread, and variable transmitter height. As a focused first use-case, we propose an interpretable height-aware attenuation model. Its LOS branch combines free-space loss, two-ray term, and compact data-based height/range calibration. Its non-LOS (NLOS) branch combines a COST 231-Hata basis with local environment-specific linear calibration. The proposed model reaches 1.93 dB overall root mean square error, with 1.74 dB in LOS and 3.54 dB in NLOS on over 500 unique locations in 14 unseen cities (2,590 samples in total). The result provides attenuation data for FR3 UxNB deployments and a physical anchor for future FR3 modeling efforts.

Forecasting suicide risk is difficult due to the high heterogeneity of patients and the low base rate of suicide-related events (SREs). We present Latent Similarity Gaussian Processes (LSGPs), which embed patients in a continuous latent space to jointly model similarity and forecast risk. By selectively drawing information from latent peers, LSGPs better capture individualized risk trajectories, generalizing nomothetic (pooled), idiographic (per-patient), and hierarchical frameworks. Our contributions are: (1) an identifiable two-channel Similarity Kernel; (2) proof that the standard model-fitting algorithm, mean-field variational inference, collapses LSGPs to nomothetic models, along with a fix; and (3) empirical results on intensive longitudinal suicide data showing LSGPs outperform nomothetic, idiographic, and hierarchical models for next-week risk forecasting, with the largest gains in forecasting first-occurrence SREs.

Large language models (LLMs) are increasingly explored for graph understanding and decision-making, while System One models such as Jev select directly from supplied options. However, the capabilities of System One models on graph-related tasks remain unclear. We introduce GraphDecisionBench, a model-independent benchmark that combines structural task profiles, matched graph-text input contrasts and heuristic-proposal controls to diagnose graph decision performance. We evaluate Jev and related choice-based models alongside language-model baselines, covering fourteen model-interface configurations. Jev's results illustrate the benchmark's central distinctions: accurate adjacency recognition does not guarantee broader structural correctness, joint graph-text input does not consistently improve prediction, and feasible construction does not establish high solution quality. Its task contracts, candidate interfaces and scoring rules support comparison across native selectors and language-model adapters. Code and aggregate results are available at https://github.com/VictorYXL/GraphDecisionBench.

We study positive solutions of a discrete Hénon equation on the integer lattice graph and on the half-space, with zero Dirichlet boundary conditions in the half-space case. The nonlinearity is governed by a Hénon-type potential with positive exponent. For sufficiently large nonlinearity exponents, we prove the existence of positive solutions both on the whole lattice in dimensions at least three and on the half-space in dimensions at least two. Thanks to the Hénon potential, the standard variational compactness is unavailable to obtain the positive solution. Our proofs combine weighted Banach spaces, two-sided Green kernel estimates and the Schauder fixed point theorem.

Performance analysis is essential for scalable MPI programs, yet tool and workflow complexity often relegates it to the end of Parallel Programming courses. EduMPI Suite lowers this entry barrier by automating cluster execution, measurement, and near-real-time analysis while visualizing MPI communication from the first program. This paper presents a three-year experience report on its integration into HPC education. We trace the transition of performance analysis from a last-week add-on to a recurring element of MPI development, using unpublished historical survey evidence and individual 2025 questionnaire data. Earlier cohorts perceived performance analysis as unnecessary, difficult, or unintuitive. In the final study, all students recommended introducing EduMPI Suite early in the course. Of 33 students, 29-33 rated it higher than conventional tools for understanding program behavior, interpreting communication, identifying bottlenecks, obtaining visual feedback, and navigating the tool. These findings support embedding performance analysis throughout MPI education before transitioning learners to professional environments.

We study the equational theory and subvariety structure of the ai-semiring variety $\V_\infty$ generated by all flat semirings $S(a_1\cdots a_k)$, where the letters \(a_i\) are pairwise distinct. Using interval semirings of posets, we characterize its subdirectly irreducible members and describe variety membership in terms of jointly separating families of strict order-preserving maps. We obtain explicit finite identity bases for \(\V_\infty\) and each $\V_k$ generated by $S(a_1\cdots a_k)$. Consequently, every flat semiring \(S(W)\) associated with a nonempty set \(W\) of linear words is finitely based. This yields finitely based ai-semirings with exactly \(k\)-nilpotent multiplicative reduct for each \(k\geq 1\). For each \(k\geq 1\), let \(\B_k\) be the subvariety of \(\V_\infty\) defined by the \((k+1)\)-nilpotent identity. We prove that each \(\B_k\) is generated by a finite interval semiring and that every proper subvariety of \(\V_\infty\) is contained in some \(\B_k\). The variety \(\B_3\) is a Cross variety with exactly \(11\) subvarieties, whereas \([\V_k,\B_k]\), \([\V_k,\V_{k+1}]\), and \([\B_{k-1},\B_k]\) each contain continuum many subvarieties for every $k\geq 4$. In particular, this provides infinitely many finitely based finite semirings $S(a_1\cdots a_k)$ whose generated variety has continuum many subvarieties for every \(k\geq 5\).

We study leakage from Shamir secret sharing when each device uses its share to produce one qubit from an initial quantum resource independent of the secret and sharing randomness. We prove exponentially small trace distance between the leakage states of any two secrets, when reconstruction requires a sufficiently large fraction of the shares, for fixed stationary chains satisfying an upper operator mixing condition and for resources generated by fixed finite quantum memories with primitive transfer channels. These guarantees permit arbitrary extensions of the device marginal as adversary side information and hold uniformly over prime fields larger than the number of shares. For independent device–reference pairs, which provide the quantitative input to the argument, we determine the optimal exponential base when reconstruction requires all shares: $2\sqrt2/\pi$ for a qubit and $2/\pi$ for a classical bit, in both cases allowing arbitrary finite references. A comparison of selected marginals with product states converts the bounds for independent device–reference pairs into security guarantees for the correlated resources.

Embodied world models predict the visual consequences of candidate actions before execution. However, existing action-conditioned world models often adopt uniformly weighted visual generation objectives that can be misaligned with embodied prediction needs. Even with explicit motion conditioning, these objectives can underemphasize spatially sparse changes that are critical to interaction. We propose KineWorld, a transport-aware world-modeling framework that extends robot kinematics from motion conditioning to the spatial allocation of generative supervision. Kinematic Transport Lifting (KTL) constructs renderer-derived, camera-aligned transport fields from commanded robot motion. Transport-Aware World Diffusion (TAWD) calibrates their motion support on the video-latent grid and reweights future-RGB flow matching through a normalized mixture of uniform and transport-focused distributions. We train KineWorld using ALOHA-AgileX bimanual manipulation data from RoboTwin 2.0. KineWorld achieves an EWMScore-P of 68.95 in single-view evaluation and a TWB-Score of 54.82 in multi-view evaluation. These results support a shift from appearance fitting toward action-consequence modeling for embodied decision-making.

Isogeometric analysis (IGA) solves partial differential equations accurately on exact NURBS geometry, whereas neural solvers are mesh-free but often orders of magnitude less accurate and typically trained by non-convex optimization without error control. We propose IGA-KAN, which uses local Kolmogorov-Arnold networks, fitted in closed form, to improve the IGA solution instead of replacing it. An IGA Galerkin solve produces u_h; on every knot-vertex patch a Kolmogorov-Arnold ridge model is fitted to the strong form of the equation, the exact boundary data and u_h, and the models are blended by IGA hat functions. With fixed inner functions the fit is one batched linear least-squares problem, without optimizer, learning rate or initialization. An a posteriori safeguard, motivated by a maximum-principle bound, decides where local models are used, keeping the IGA solution elsewhere. On eight benchmarks with exact solutions, five from the literature and one also posed on a domain fitted to a brain slice from MRI, the method reduces the error of IGA, at an unchanged number of Galerkin unknowns, by factors of 4.2 to 90 in L^2 and 4.1 to 220 in H^1 on the reference meshes, and its L^2 error is 6 to 6x10^4 times smaller than that of the best Kolmogorov-Arnold network trained from scratch on the same equations with a fixed budget. In an inverse problem it recovers an unknown constant source from one noise-free observation 167 times more accurately than IGA. The gain is attributed to the superconvergence of local averages of the Galerkin solution.

Adapting general-purpose large language models to specific tasks requires substantial human effort in designing data and training strategies. Sustaining improvement is especially challenging because model updates change the error distribution, requiring strategies to be continually refined. We introduce ImproveAnyTask, an autonomous post-training harness that improves task performance under a limited compute budget. Drawing inspiration from gradient-based parameter optimization, the harness organizes adaptation into error attribution, update-direction selection, and executable model updates. It combines metric-level and case-level analysis to identify a focal problem, then investigates research-backed strategies and compares their reported gains and reproduction difficulty. The selected strategy is translated into training data and a training configuration, with small-scale execution checks preceding full post-training. Subsequent evaluation guides model selection and further adaptation, while validated strategies and scripts are retained for reuse. Across 11 tasks, ImproveAnyTask achieves mean gains of 18.29 and 11.97 percentage points on the Base and Instruct models, respectively, with a maximum gain of 41.96 points, under a 24-hour budget with resources equivalent to eight H20 GPUs.

Iron sulfide (FeS) is a key refractory compound in astrophysical environments. It is commonly found in meteorites and evidence of FeS has only been reported in solid form in a protoplanetary environment. Furthermore, FeS is of astrobiological interest since it acts as a precursor to the formation of pyrite (FeS$_2$), which plays a key role in anaerobic metabolism. We present millimeter-wave spectroscopic calculations for gaseous FeS and report its tentative detection toward the massive disk Orion SrcI. If confirmed, this would constitute the first ever detection of gaseous FeS in the interstellar medium. Our data are consistent with a FeS column density of $\sim1.7 \times 10^{15}$ cm$^{-2}$. Comparing to other sulfur reservoirs, the amount of sulfur locked in FeS is more than three orders of magnitude lower than that contained in SO$_2$ and SiS. However, FeS emission may arise from a different region as it is the case for the metallic salt NaCl. Our results support the presence of FeS in interstellar grains and are consistent with grain destruction playing an important role in the origin of the FeS emission. The observations, however, are still insufficient to discern whether FeS is a main sulfur reservoir in molecular clouds or a primary carrier of refractory iron-bearing material.

In this paper, we evaluate open-source generative LLMs on legal Natural Language Inference (NLI). Legal inspectorial processes take place in specific domains and often deal with confidential data. This creates a need for working with local models that do not require labeled training data. We evaluate our models on the ContractNLI benchmark and two NLI4Wills datasets. We successfully reproduce the baseline for the task (Span NLI BERT) and we evaluate multiple open-source LLMs on the same task. We analyze the invalid rate of the models, and their stability across temperature settings and domains. Among the generative models, Gemma-4 26B performs the best, reaching an accuracy of 81.2%, even outperforming the supervised model on one metric. On accuracy, it is not possible to beat the supervised model with zero-shot approaches. Qwen-3.6 35B performs well on both ContractNLI and additional datasets in the legal wills domain. Our findings indicate that zero-shot, open-source, generative LLMs are a viable alternative for real-world legal NLI when no supervised data is available. Our code is available at https://github.com/fbaratov/contractnli-llms.

In deep graph neural networks, increasing depth enlarges the receptive field but often leads to over-smoothing, where node representations tend to align. We develop a unified, mode-wise stability framework for deep GNN propagation that provides a principled characterization of over-smoothing. By interpreting layer depth as time and layer updates as graph-coupled dynamics, over-smoothing can be understood as an undesirable dynamical synchronization of features, for which the master stability curve provides a theoretical tool to assess the stability of synchrony. Guided by this theory, we further propose Stability-Shaped Deep Graph Learning (SDGL) to mitigate over-smoothing in deep GNNs. SDGL has two complementary instantiations: one induces controlled Turing instability to replace synchronization with spatial pattern formation, and the other maintains stable near-critical propagation. Experiments on diverse node- and graph-level benchmarks demonstrate the improved depth scaling and consistent accuracy gains over strong baselines, including graphs exhibiting long-range dependencies.

In the continuity of [1, 2, 3], we study a class of constrained mean-field Langevin dynamics formulated as a Wasserstein gradient flow with an energy constraint. We show that the constrained evolution therefore defines a well-posed dissipative dynamics in the Wasserstein space $\mathcal{P}_2(\mathbb{R}^d)$. We prove that the flow preserves probability mass and the energy constraint, dissipates the free energy monotonically, and converges exponentially to a unique constrained equilibrium under geodesic convexity assumptions. Using synchronous coupling, under Lipschitz assumptions, we demonstrate the quantitative $L^2$-propagation of chaos with a Fournier-Guillin bound, and under conditions of sufficient dissipativity, we derive an explicit time-uniform bound. We also demonstrate exponential controls in the $\mathcal{W}_2$ Wasserstein metric and the contraction of the invariant measure map. Using log-Sobolev inequalities, we show that the mean-field entropies decay exponentially along the constrained flow. The results are applied to several concrete and original examples. Keywords and phrases: Wasserstein gradient flows $\bullet$ mean-field Langevin dynamics $\bullet$ constrained nonlinear Fokker-Planck equations $\bullet$ Lagrange multiplier $\bullet$ JKO scheme $\bullet$ propagation of chaos $\bullet$ synchronous coupling $\bullet$ exponential ergodicity $\bullet$ functional inequality $\bullet$ log-Sobolev inequality $\bullet$ transport inequality $\bullet$ Talagrand T 2 -inequality

While reinforcement learning with verifiable rewards provides reliable outcome supervision for VideoLLMs, sequence-level rewards offer limited token-level guidance. On-policy self-distillation addresses this limitation by conditioning a self-teacher on privileged information to provide dense token-level supervision. However, aggregating heterogeneous evidence within a single teacher context obscures cross-evidence agreement and conflict. A further challenge lies in determining whether teacher guidance should refine reward-based updates or provide corrective supervision for failed trajectories. To address these issues, we propose MeSD, a multi-evidence self-distillation framework for VideoLLMs. MeSD constructs three evidence-conditioned teachers with shared parameters, using the ground-truth answer as a common semantic context while separately incorporating temporal and spatial evidence. Given the same student-generated prefixes, MeSD evaluates evidence-specific preferences relative to the Answer Teacher and fuses teacher-common preferences with gated teacher-specific residuals. Furthermore, MeSD introduces Verification-Guided Optimization to classify trajectories as Success, Failure, or Indeterminate. For Success and Indeterminate trajectories, MeSD refines token-level advantage magnitudes while preserving reward-derived signs. For verified failure trajectories that contain the required evidence, MeSD applies failure-conditioned distillation, using reverse-KL correction toward the fused distribution. Experiments on multiple video benchmarks demonstrate consistent gains over reinforcement learning and self-distillation baselines.

We study the Euclidean Varadhan formula (EVF) and path laws for diffusions with critical divergence-free drifts in dimension $d\geq2$. For drifts given by smooth bounded skew-symmetric stream matrices, we prove a quantitative lower bound under a sector condition with a lower-order term. Its constants depend only on the dimension and the sector condition data. By approximation, the locally uniform Euclidean lower bound holds for all divergence-free $L^\infty_t{\rm BMO}^{-1}_x$ drifts. However, a time-dependent counterexample shows that EVF can fail even for a drift in $L^\infty_tL^d_x$. A complementary upper bound is given under a structural decomposition condition. In particular, for every time-independent $L^{d,\infty}$ drift (without any smallness assumption), and the decoupled diffusion associated with the two-dimensional vorticity equation, the EVF holds. Finally, we construct a time-independent $L^d$ drift whose SDE has a unique strong solution from the origin and whose path law is mutually singular with the corresponding driftless Brownian law. The same diffusion satisfies EVF, showing that Brownian short-time endpoint costs can persist despite singularity of the path law.

In this paper we construct new examples of diameter graphs and Reuleaux polyhedra in $\mathbb{R}^3$, obtaining a full characterization of their combinatorial structure. For a finite set of points $X\subset\mathbb{R}^d$, its diameter graph is the graph on vertex set $X$ where pairs forming a diameter pair are connected by an edge. Grünbaum, Heppes and Straszewicz independently proved that the diameter graph of $X\subset \mathbb{R}^3$ has at most $2|X|-2$ edges, answering a question of Vázsonyi. Their proof relied on ball polytopes. The ball polytope $\mathcal{B}(X)$ is the intersection of the unit balls centered at the points of $X$. We call a ball polytope a Reuleaux polyhedron if the centers form a family with $2|X|-2$ diameter pairs. Kupitz, Martini and Perles showed that the skeleton of a Reuleaux polyhedron must be a 2-connected strongly involutive self-dual graph. They conjectured that in the simple 3-connected case this is also sufficient. We not only confirm this conjecture, but we show that any 2-connected (not necessarily simple) strongly involutive self-dual graph arises as the skeleton of a Reuleaux polyhedron. To construct the new Reuleaux polyhedra we construct new diameter graphs. It was known that any 3-dimensional diameter graph is a subgraph of a non-bipartite quadrangulation of the projective plane. We show that the reverse holds. That is, for any such graph we construct a diameter realization. This also confirms and strengthens a conjecture of Montejano, Pauli, Raggi, Roldán-Pensado on metric embeddings of strongly involutive self-dual graphs. The construction relies on ideas from rigidity theory. We also discuss a number of applications of these results, such as the construction of bodies of constant width and connections to Steinitz's theorem and Borsuk's conjecture.