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Uniform interpolation is the property that, for any formula and set of atoms, there exists the strongest consequence omitting those atoms. It plays a central role in knowledge representation and reasoning tasks such as knowledge update and information hiding. This paper studies the uniform interpolation property in epistemic modal logics with distributed knowledge, which captures agents' collective reasoning abilities. Building on the bisimulation-quantifier perspective, we extend the canonical-formula and literal-elimination framework of Fang, Liu, and van Ditmarsch to distributed knowledge settings and introduce the concept of collective $p$-bisimulation. We show that, for distributed knowledge modal logics $\mathsf{K}_n\mathbf{D}$, $\mathsf{D}_n\mathbf{D}$, and $\mathsf{T}_n\mathbf{D}$, every satisfiable canonical formula's uniform interpolant omitting an atom $p$ is exactly its remainder of eliminating $p$. Then, we provide a finer analysis for the transitive and Euclidean systems $\mathsf{K45}_n\mathbf{D}$, $\mathsf{KD45}_n\mathbf{D}$, and $\mathsf{S5}_n\mathbf{D}$, and prove that every formula of modal depth $k + 1$ has a uniform interpolant of modal depth $2 k + 1$. Thus, we

Retrieval-Augmented Generation enhances large language models by incorporating external knowledge, but deploying it in sensitive scenarios risks privacy leakage via malicious prompts. To address this, we propose a multi-agent framework that sanitizes retrieved content through semantic rewriting. By employing three specialized agents for privacy extraction, semantic analysis, and reconstruction, our approach collaboratively removes sensitive identifiers while preserving the semantic core. We evaluate the framework on the ChatDoctor and Wiki-PII datasets across six large language models. Experimental results demonstrate a significant reduction in privacy leakage under targeted attacks. For instance, we reduced targeted information exposure in LLaMA-3-8B from 144 instances in the baseline to just 1. Furthermore, we maintain strong contextual fidelity with a BLEU-1 score of 0.122, outperforming the existing SAGE method's 0.117. Finally, the framework operates as an asynchronous preprocessing module, introducing no additional latency to online inference, as all rewriting is executed as a one-time offline preprocessing step. To promote reproducibility, the source code of this work is pub

Automated agent workflows can enhance the problem-solving ability of large language models (LLMs), but common search strategies rely on stochastic exploration and often traverse implausible branches. This occurs because current pipelines sample candidate steps from generic prompts or learned policies with weak domain priors, yielding near-random walks over operators, units, and formats. To promote ordered exploration, this paper introduces SCULPT, a constraint-guided approach for Monte Carlo Tree Search (MCTS) that integrates domain-aware scoring into selection, expansion, simulation, and backpropagation. SCULPT scores and prunes actions using a combination of symbolic checks (dimensional consistency, type compatibility, magnitude sanity, depth control, and diversity) and structural pattern guidance, thereby steering the search toward plausible reasoning paths. Under matched LLM configurations, SCULPT yields stable improvements on multiple datasets; additional results with GPT-5.2 assess executor transferability and performance on frontier reasoning models. Overall, domain-aware constraints can improve accuracy while maintaining efficiency and reasoning stability.

Crop disease diagnosis from field photographs faces two recurring problems: models that score well on benchmarks frequently hallucinate species names, and when predictions are correct, the reasoning behind them is typically inaccessible to the practitioner. This paper describes Agri-CPJ (Caption-Prompt-Judge), a training-free few-shot framework in which a large vision-language model first generates a structured morphological caption, iteratively refined through multi-dimensional quality gating, before any diagnostic question is answered. Two candidate responses are then generated from complementary viewpoints, and an LLM judge selects the stronger one based on domain-specific criteria. Caption refinement is the component with the largest individual impact: ablations confirm that skipping it consistently degrades downstream accuracy across both models tested. On CDDMBench, pairing GPT-5-Nano with GPT-5-mini-generated captions yields \textbf{+22.7} pp in disease classification and \textbf{+19.5} points in QA score over no-caption baselines. Evaluated without modification on AgMMU-MCQs, GPT-5-Nano reached 77.84\% and Qwen-VL-Chat reached 64.54\%, placing them at or above most open-sou

We study the error exponents in quantum hypothesis testing between two sets of quantum states, extending the analysis beyond the independent and identically distributed case to encompass composite correlated hypotheses. In particular, we introduce and compare two natural extensions of the quantum Hoeffding divergence and anti-divergence to sets of quantum states, establishing their equivalence or quantitative relations. In the error exponent regime, we generalize the quantum Hoeffding bound to stable sequences of convex, compact sets of quantum states, demonstrating that the optimal Type-I error exponent, under an exponential constraint on the Type-II error, is precisely characterized by the regularized quantum Hoeffding divergence between the sets. In the strong converse exponent regime, we provide a general lower bound on the exponent in terms of the regularized quantum Hoeffding anti-divergence and a matching upper bound when the null hypothesis is a singleton. The generality of these results enables applications in various contexts, including (i) refining the generalized quantum Stein's lemma by [Fang, Fawzi & Fawzi, 2024]; (ii) exhibiting counterexamples to the continuity

Agricultural disease diagnosis challenges VLMs, as conventional fine-tuning requires extensive labels, lacks interpretability, and generalizes poorly. While reasoning improves model robustness, existing methods rely on costly expert annotations and rarely address the open-ended, diverse nature of agricultural queries. To address these limitations, we propose \textbf{Agri-R1}, a reasoning-enhanced large model for agriculture. Our framework automates high-quality reasoning data generation via vision-language synthesis and LLM-based filtering, using only 19\% of available samples. Training employs Group Relative Policy Optimization (GRPO) with a novel reward function that integrates domain-specific lexicons and fuzzy matching to assess both correctness and linguistic flexibility in open-ended responses. Evaluated on CDDMBench, our resulting 3B-parameter model achieves performance competitive with 7B- to 13B-parameter baselines, showing a +27.9\% relative gain in disease recognition accuracy, +33.3\% in agricultural knowledge QA, and a +26.10-point improvement in cross-domain generalization over standard fine-tuning. These results suggest that automated reasoning synthesis paired with

We experimentally demonstrate background-free, hyperfine-level-selective measurements of individual Cs atoms by simultaneous cooling to $5.3~μ\rm K$ and imaging on the $6s_{1/2}\rightarrow 5d_{5/2}$ electric-quadrupole transition. We achieve hyperfine resolved detection with fidelity 0.9993(4) and atom retention of 0.9954(5), limited primarily by vacuum lifetime. Performing state measurements in a 3D cooling configuration enables repeated low loss measurements. A theoretical analysis of an extension of the demonstrated approach based on quenching of the excited state with an auxiliary field, identifies parameters for hyperfine-resolved measurements with a projected fidelity of $\sim 0.9995 $ in $\sim 60~μ\rm s$.

Accurate and interpretable crop disease diagnosis is essential for agricultural decision-making, yet existing methods often rely on costly supervised fine-tuning and perform poorly under domain shifts. We propose Caption--Prompt--Judge (CPJ), a training-free few-shot framework that enhances Agri-Pest VQA through structured, interpretable image captions. CPJ employs large vision-language models to generate multi-angle captions, refined iteratively via an LLM-as-Judge module, which then inform a dual-answer VQA process for both recognition and management responses. Evaluated on CDDMBench, CPJ significantly improves performance: using GPT-5-mini captions, GPT-5-Nano achieves \textbf{+22.7} pp in disease classification and \textbf{+19.5} points in QA score over no-caption baselines. The framework provides transparent, evidence-based reasoning, advancing robust and explainable agricultural diagnosis without fine-tuning. Our code and data are publicly available at: https://github.com/CPJ-Agricultural/CPJ-Agricultural-Diagnosis.

In [8], Fang-Lan-Xiao proved a formula about Lusztig's induction and restriction functors which can induce Green's formula for the path algebra of a quiver over a finite field via the trace map. In this paper, we generalize their formula to that for the mixed semisimple perverse sheaves for a quiver with an automorphism. By applying the trace map, we obtain Green's formula for any finite-dimensional hereditary algebra over a finite field.

We study the problem of quantum channel discrimination between two channels with an adversary input party (a.k.a. a jammer). This setup interpolates between the best-case channel discrimination as studied by (Wang & Wilde, 2019) and the worst-case channel discrimination as studied by (Fang, Fawzi, & Fawzi, 2025), thereby generalizing both frameworks. To address this problem, we introduce the notion of minimax channel divergence and establish several of its key mathematical properties. We prove the Stein's lemma in this new setting, showing that the optimal type-II error exponent in the asymptotic regime under parallel strategies is characterized by the regularized minimax channel divergence.

Hamiltonian simulation becomes more challenging as the underlying unitary becomes more oscillatory. In such cases, an algorithm with commutator scaling and a weak dependence, such as logarithmic, on the derivatives of the Hamiltonian is desired. We introduce a new time-dependent Hamiltonian simulation algorithm based on the Magnus series expansion that exhibits both features. Importantly, when applied to unbounded Hamiltonian simulation in the interaction picture, we prove that the commutator in the second-order algorithm leads to a surprising fourth-order superconvergence, with an error preconstant independent of the number of spatial grids. This extends the qHOP algorithm [An, Fang, Lin, Quantum 2022] based on first-order Magnus expansion, and the proof of superconvergence is based on semiclassical analysis that is of independent interest.

Pre-trained Language Models (PLMs) have shown impressive results in various Natural Language Generation (NLG) tasks, such as powering chatbots and generating stories. However, an ethical concern arises due to their potential to produce verbatim copies of paragraphs from their training data. This is problematic as PLMs are trained on corpora constructed by human authors. As such, there is a pressing need for research to promote the generation of original content by these models. In this study, we introduce a unique "self-plagiarism" contrastive decoding strategy, aimed at boosting the originality of text produced by PLMs. Our method entails modifying prompts in LLMs to develop an amateur model and a professional model. Specifically, the amateur model is urged to plagiarize using three plagiarism templates we have designed, while the professional model maintains its standard language model status. This strategy employs prompts to stimulate the model's capacity to identify non-original candidate token combinations and subsequently impose penalties. The application of this strategy is integrated prior to the model's final layer, ensuring smooth integration with most existing PLMs (T5,

We formulate spin magnetohydrodynamics (MHD) by including the magnetic-flux and total angular momentum conservation laws in the hydrodynamic framework. To specify the local angular momentum conservation, we choose the totally antisymmetric spin current. The entropy-current analysis allows for ten dissipative first-order transport coefficients including anisotropic spin relaxation rates and the conversion rate between a vorticity (shear) to a symmetric stress (antisymmetric torque), as well as anisotropic viscosities and resistivities. By employing the linear-mode analysis, we solve the first-order spin MHD equations to determine the dispersion relations with the complete information of anisotropy retained. Our analytic solutions indicate that the small-momentum expansion is spoiled by blow up of the higher-order terms when the angle between the momentum and the magnetic field approaches the right angle. This also reveals the existence of another expansion parameter, and, in light of it, we provide solutions in an alternative series expression beyond the critical angle. We confirm that these two series expansions work well in the appropriate angle ranges as compared with numerical r