Papers

Medication recommendations seek to deliver personalized drug combinations based on patients' clinical information, where ensuring transparent decision-making and personalized safety are of paramount importance. However, existing approaches predominantly operate as “black boxes”, offering limited interpretability and hindering clinician trust. Furthermore, they typically rely on fixed, patient-agnostic safety constraints, neglecting the heterogeneity of risk tolerance across individuals, which poses significant risks to vulnerable populations. To address these gaps, we propose RES-MR, a novel Risk-aware Reasoning framework for Explainable and Safe Medication Recommendation using LLMs. RES-MR follows a two-stage training paradigm: (1) an explainable clinical reasoning distillation stage to elicit diagnostic capabilities by fine-tuning on synthesized reasoning trajectories, grounded in patient-specific knowledge from graph retrieval; and (2) a risk-aware policy optimization stage to dynamically balance therapeutic efficacy with personalized safety. This stage employs disentangled drug factors to construct patient-specific reference prototypes that capture desired therapeutic drug features and risk features to avoid. These prototypes enable risk boundary calibration and guide the model toward safe recommendations via reward shaping and clipping. Extensive experiments on benchmark datasets demonstrate that RES-MR significantly outperforms state-of-the-art baselines in terms of accuracy, safety, and explainability. Our code and data are available at: https://github.com/wangcong2001/RES-MR.

We propose a new framework for banner ad auctions, leveraging diffusion models to allow for multiple bidders to co-win a single banner ad opportunity, and in particular influence the ad shown on the banner depending on the strength of their bids, enabling a far richer outcome space compared to standard banner ad auctions, where there is a single winner who shows their ad. In our framework, the outcomes are images (what ad to show) and each bidder expresses their preferences over outcomes by declaring their value per unit of alignment between the image chosen by the mechanism and a textual description of their desired image. Our proposed mechanism combines the advertisers' bids and textual descriptions into a score that drives the reverse process of a diffusion model. This is used to sample a set of candidate images from which the welfare maximizing one is eventually chosen. Extensive experimentation evaluates our proposed mechanism around the following axes: (1) efficiency improvements of our allocation rule relative to the single-winner allocation rule; (2) monotonicity of our allocation rule; and (3) approximate incentive compatibility when combining our allocation rule with Myerson lemma-based or Clarke rule-based payments. Improvements along all these axes are shown with the number of Monte Carlo samples. Meanwhile, these benefits are attained while preserving the image quality.

Trapped ion quantum computing based on the quantum charge coupled device (QCCD) architecture uses functional zoning and ion transport to enable high fidelity computation and all to all qubit connectivity. As trapped ion quantum processing units (QPU) scale, 90{\deg} X-junction turns account for an increasing fraction of total transport time. Frequent junction crossings, therefore, make transport speed and final phonon excitation direct determinants of quantum algorithm execution efficiency. However, complex electric fields in X-junctions complicate waveform design, making it difficult to achieve high speed and low final phonon excitation simultaneously. Here, we develop a waveform design method for low-phonon-excitation high-speed X-junction(LHX-T) transport. It integrates low barrier pseudopotential channel design using multiple radio frequency (Multi-RF), multidimensional shortcut to adiabaticity dynamics, and constrained DC voltage optimization over the entire transport sequence. This framework connects waveform design, control, and computational validation, with smooth multichannel waveforms computed rapidly through a Karush-Kuhn-Tucker(KKT) linear system. The resulting waveform transports a single $^{171}Yb^+$ ion through a 90{\deg} turn in $5\mu s$ at an average speed of 14.6 m/s. Over 50 consecutive round trips, the final equivalent coherent phonon number consistently stays below 0.001, with no noticeable accumulation over time. System level evaluations at the QCCD scale show that the median duration of a single execution cycle is reduced by about $30\%$ across various circuit types. The fraction of execution time spent on transport decreases from approximately $70\%$ to $55\%$. This approach offers a means of designing fast ion transport waveforms with low phonon excitation for scalable QCCD based QPUs and provides a technical basis for efficient execution of quantum algorithms.

Accurate emission-rate quantification of methane point sources is essential for inventory verification and leak detection. UAV-borne sensing provides high-resolution, near-source measurements, but existing quantification methods mostly follow a predefined trajectory and rely on a single UAV. Building on a source receptor matrix (SRM) estimator and empirical observability Gramian (EMGR)-based path planning, this paper proposes a spatial-temporal hybrid path planning strategy for multi-UAV methane emission rate quantification. Measurements are time-averaged, and the forward Gaussian plume model is calibrated against a filament-based plume simulator (MOABS) to reduce model mismatch. Cooperating UAVs first spread out spatially to locate the source quickly, then switch to sequentially retracing a leader trajectory with a time lag to reduce quantification variance. Simulations show that the spatial stage localizes the source markedly faster than a single-UAV baseline, the temporal stage yields the lowest variance but converges slowly, and the proposed hybrid strategy converges substantially faster than the purely temporal strategy while matching its steady-state accuracy, with a narrower error band than the purely spatial strategy. A window-length study further shows that longer time-averaging windows exhibit diminishing returns, justifying the balance between spatial coverage and temporal averaging.

Reconciliation systems decide, continuously, whether money the ledger expected has arrived at the bank. On an asynchronous stream that decision is taken against partial evidence: a credit that has not appeared may be missing, or may simply not have been posted yet. Deployed pipelines settle this with a timeout or a watermark, and the exceptions are treated as findings. We give a temporal correctness contract that says when such a verdict is admissible, relative to a declared per-source lateness bound, and a checker for it that needs no ground truth. The contract separates three things an operator otherwise sees only as a rising break rate: the reconciler decided too early, an input broke the bound it declared, or the money really is gone. On workloads from a published payment simulator, the standard remedy for a stalled streaming join, an idleness timeout, introduces contract violations on 5.42% of obligations (95% CI [3.94, 6.92]) on traffic where the same job without it is exactly sound, and violations vanish once the timeout reaches the slow source's posting period, as predicted. Under a lateness shift, all four identity-based reconcilers we test raise spurious breaks on between 18.3% and 23.0% of the credits the bank did settle, while their contract violation rate stays at or below 1.01%: the checker attributes the loss to 240 bank-side and 413 ledger-side bound violations rather than to the reconcilers. Tracking one horizon per source leaves break latency 12.7% lower on average and halves its tail (p99 224 against 446 ticks) at equal soundness, though it is not cheaper at every cost setting and we report where it loses. An Apache Flink interval join, written the ordinary way, violates the contract on 14.9–20.1% of obligations. The contract is expressible as SQL over the tables a reconciliation system already keeps, agreeing with the reference implementation on all 4,395 verdicts.

We establish an exact correspondence between the quasi-Wronskian and quasi-Grammian constructions for the anti-self-dual Yang–Mills (ASDYM) equations with complex \(2\times2\) matrix-valued fields. Starting from vacuum wave functions associated with \(2M\) pairwise distinct nonzero constant spectral parameters, we restrict attention to a nonempty local domain on which the corresponding interpolation matrix is invertible. We show that both constructions are governed by the same uniquely solvable matrix-polynomial interpolation problem. In particular, the quasi-Wronskian Darboux polynomial \(T(\lambda)\) and the quasi-Grammian rational dressing matrix \(W(\lambda)\) satisfy \[ T(\lambda)=q_\xi(\lambda)W(\lambda), \] where \(q_\xi(\lambda)\) is the monic scalar polynomial whose zeros are the prescribed poles of \(W(\lambda)\). This identity yields explicit relations between the corresponding Yang and potential matrices and shows that the two constructions generate identical ASDYM gauge potentials in the same gauge.

For an odd prime $p$, we prove a Smith inequality over $\mathbb{F}_p$ for exact Lagrangian Floer homology under a symplectic $\mathbb{Z}_p$-action, assuming an equivariant stable normal trivialization compatible with the Lagrangians and the required relative Pin data. As an application, we obtain a rank inequality between the symplectic Khovanov homology of a $p$-periodic link and that of its quotient. These results extend the involutive localization of Seidel and Smith. The main construction is a stabilized chain complex. At every invariant intersection point we adjoin the Morse complex of a finite-dimensional normal spectral sphere, whose generators lie in free $\mathbb{Z}_p$-orbits. The differential counts holomorphic strips coupled to sphere half-trajectories by a one-sided weighted asymptotic evaluation. We prove transversality, a uniform spectral cutoff, and the compactification and gluing statements needed for the chain identity. The stabilized complex is quasi-isomorphic to the ordinary Floer complex and contains the complex of the fixed data as a subcomplex with free quotient, so the algebraic Smith inequality applies.

We consider spin-coupled Grover walks on hypercubes within the framework of quantum Bernoulli noises (QBN). We identify parity-dependent harmonic subspaces generated by the central Hamming layers: in even dimension they give a fixed-point subspace, whereas in odd dimension the walk reduces on the harmonic subspace to an explicit eight-dimensional reduced dynamics. Using symmetric-group representation theory, we characterize the corresponding isotypic structure and determine the reduced spectrum. The harmonic reduction also yields explicit long-time probability behavior and shows that the resulting states may occupy an asymptotically vanishing fraction of the hypercube while still spanning its full Hamming diameter.

In this work, we develop a general memory-augmented phase-field (MAPF) framework based on Onsager's variational principle, in which memory effects are incorporated through a general relaxation kernel while preserving the thermodynamic consistency of the underlying system. Rather than treating fractional models as fundamental formulations, we show that they can be interpreted as reduced descriptions associated with specific power-law memory kernels. The proposed MAPF equations provide a unified modeling framework for non-Markovian phase-field dynamics. To facilitate analysis and computation, we further introduce an equivalent internal-variable representation that transforms the original nonlocal-in-time dynamics into an extended Markovian gradient system. This formulation preserves key structural properties, including energy dissipation and mass conservation, and enables the development of efficient structure-preserving numerical schemes. In particular, we construct an energy-stable scalar auxiliary variable approach combined with a fast rank-one implementation that exploits the relaxation-spectrum-induced coupling structure, resulting in a computationally efficient algorithm with reduced storage requirements. The proposed framework establishes a systematic connection between memory-dependent phase-field modeling, internal-variable thermodynamics, and structure-preserving numerical computation. Numerical experiments demonstrate the accuracy, stability, and efficiency of the proposed methods for phase-field dynamics with long-time memory effects.

Structured knowledge retrieval acquires task-relevant evidence from structured knowledge sources for downstream tasks. Existing methods rely on unconstrained retrieval or predefined query-rule supervision, such as author-paper rules for scientific discovery and anatomy-drug rules for precision medicine. Such supervision is rarely available in practice. We propose Co-Adaptive Rule Routing and Constraining Retrieval (CoRE), which jointly learns which reasoning rule to assign to each query and how to retrieve evidence under that rule, without predefined query-rule pairs. A routing agent selects a rule, and its corresponding retriever traverses the knowledge base and ranks evidence that satisfies the rule's constraints. Because routing and retrieval are interdependent, CoRE alternates between reinforcement learning for the routing policy and contrastive learning for the rule-constrained retriever. The selected rules provide supervision for retriever training, while retrieval performance rewards the routing policy. This closed-loop process enables both components to co-adapt without explicit query-rule supervision. Experiments on STaRK-QA datasets across scientific discovery, biomedical reasoning, and e-commerce knowledge management demonstrate CoRE's effectiveness. Ablations show the benefit of co-adapting the router and retriever. Generation-based routing transfers across datasets and benefits from multi-domain pretraining followed by target-specific fine-tuning. Analysis of rule usage across queries also informs automatic rule refinement and discovery.

In Chinese content governance, large language models are increasingly used to identify toxic and discriminatory expressions, yet both task operationalization and ironic expression can alter bias measurement readings. We conducted a preregistered multi-task behavioral audit of multiple Chinese large language models. In the content classification experiment, the core panel's classification error rate rose from 10.9% in the formal register to 23.5% in the yinyang (an echoic-irony register) version, a risk difference of +12.7 percentage points. (95% CI [+9.7, +15.7]). Inter-rater agreement was lower in the yinyang register (majority-vote kappa = 0.299), so the increase contains a component of label uncertainty propagation, but the direction of increase was consistent under both adjudicated and majority-vote reference standards. Explicit irony-aware prompts reduced the intervention panel's error rate by 9.6 percentage points. We operationalized the 29 shared proposition anchors into three task forms: social consensus estimation (Form A), high-stakes decision (Form B), and controlled association rating (Form C); independent manipulation checks found that all 58 A-C comparison units received unanimous agreement, whereas the low A-B convergence was confirmed by calibrated majority adjudication (87.8% supporting the minority judgment); on the irony-probe materials, the interactions of B and C relative to A were +0.577 and +1.121, respectively. Thus, when evaluating large language models for Chinese content governance, the effect of task operationalization on bias readings is an empirical question that requires data to answer, and safety evaluation should incorporate the ironic register as a test condition.

Searches for dense packings of congruent shapes move rigid pieces. Hardening starts each piece as its inscribed disk and deforms it into the target shape while the container is compressed. We ask whether it is a search worth running alongside existing ones, and test it at matched budget and comparable tuning against rigid starts, growth, simulated annealing and perturbation–compression on seven families of squares, triangles, hexagons and disks in squares, triangles and circles (188 instances), scoring each method by the lowest container size it reaches. Hardening is not a better default: tuned rigid starts reach the lowest size most often. It is a different search. On squares in a square it reaches packings the other four methods miss, including Trump's n = 11 and Wainwright's n = 19 in 32 runs per method, and in a targeted follow-up campaign at ten times the budget (16 runs per method) it is the only one to reach the best known packings for n = 17 and n = 26, while annealing alone reaches n = 27. In exploratory ablations, compressing disks and then switching to polygons at once, or growing rigid polygons along hardening's area schedule, shows no detectable difference from rigid starts, and hardening's unique packings contain more tilted pieces. The bias costs elsewhere: hardening is worse on triangles and on four families held out from all development, where the short-pilot policy we tested showed no detected advantage over always starting rigid. Shape continuation is an alternative search that reaches different packings, worth keeping beside rigid ones; we did not show that splitting a fixed budget between them pays, and we have no test that predicts where it helps. Search campaigns were planned before they ran, with amendments, exploratory analyses and post-hoc checks identified separately; every run is replayable and every number is generated from an event log.

Identifying bug-inducing commits (BICs) is important for studying software bugs and maintaining software, yet the accuracy of existing SZZ methods remains limited. Although various improvements have been proposed, many SZZ methods still rely on code tracing, which searches for BICs by tracing code changed in a bug-fixing commit (BFC) back to earlier commits. However, this approach may miss the actual BIC when the code responsible for introducing a bug differs from the code modified to fix it. To overcome this limitation, we investigate whether BIC identification can be improved by exploring search strategies that are not constrained to start with code tracing. We use Claude Code, a coding agent that has demonstrated high BIC identification accuracy in prior research, to explore such strategies. Rather than prescribing a search process or providing predefined candidate commits, we allow Claude Code to independently investigate a Git repository. We evaluate its identification accuracy and search behavior on 79 Java cases from 70 repositories. In 79.7% of runs, Claude Code reviewed commit histories before inspecting individual code diffs. It used commit messages to select changes for closer inspection. With this approach, Claude Code achieves an F1 score of 0.771, significantly outperforming all ten evaluated SZZ baselines. Our failure analysis also reveals incorrect oracle labels and ambiguities in BIC definitions in the studied evaluation dataset. After reconstructing the evaluation dataset to address these issues, Claude Code achieves an F1 score of 0.938. A key lesson from Claude Code for improving SZZ search strategies is to use semantic information to find relevant commits and then examine their code changes, rather than starting with code tracing.

Can a holographic theory be reconstructed from its equation of state? We investigate this question using physics-informed neural networks in the bosonic-mass sector of the Pilch–Warner model. We first validate the PINN approach against an analytic solution encoding the leading high-temperature corrections to the conformal equation of state. We then reconstruct nonlinear black-brane geometries and the scalar potential using thermodynamics, ultraviolet asymptotics, Ward identities, and horizon regularity. Independent solutions of the bulk Einstein-scalar equations demonstrate that accurately reproducing thermodynamics with a trained PINN does not guarantee an accurate reconstruction of the scalar potential. High-precision knowledge of the high-temperature equation of state constrains nonlinear interactions in the bulk scalar potential. Fixing the cubic coupling to its exact PW value, motivated by this high-temperature extraction, reduces the maximum sampled error in the reconstructed scalar self-interactions by a factor of $\sim 15$ compared with constraining only the bulk scalar mass. Adding knowledge of the bulk viscosity of the gauge theory plasma further reduces this error by an additional factor of $\sim 13$, with independent forward solutions reproducing the bulk viscosity within $0.09\%$.

Executable tests grade large language model (LLM) coding-agent patches for leaderboards, rewards and self-improvement. Two preregistered re-execution studies returned negative results. SWE-bench Pro v1's offline option rejected none of 59 accepted Go patches whose grading configuration changed. Their exploratory, unweighted upper confidence limit is 4.95% under candidate independence, leaving a 3% exposed-patch risk unresolved; the preregistered estimator uses inverse sampling-probability weights. An extension was inconclusive. In a selected stratum, a reconstructed module cache built from the reference solution's dependencies rejected accepted alternatives from four models that passed with their own dependencies. Re-executing 1,929 selected agent-version/task evaluations from the Darwin Gödel Machine's archive preserved best-agent selection and system-variant ranking, with search history and scores of evaluations not rerun fixed. Exploratory host, image and adapted-grader comparisons also preserved them. Seven of 23 disagreements with archived verdicts did not recur on a second host; rebuilt images changed 16 three-run majority verdicts (0.83%) under four-CPU execution. We provide an evidence-to-claim summary, lessons for grader audits and an anonymous replication package. These results concern accepted patches and fixed-history decisions; general policy safety and adaptive-learning robustness require broader evaluations.

We develop a finite-tree formalism for sharp inequalities on real-valued, mean-centered $\operatorname{L}^1$-BMO over homogeneous $q$-ary filtrations. A reduction theorem identifies local and global sharp constants with the supremum of finite-depth constants. Finite anchoring gives compact optimization problems and rational extremizers under rational piecewise-linear hypotheses, while stable centering shows that imposing zero root average preserves the supremum over all depths. The principal application is the absolute-value map: we construct centered examples in which taking absolute values increases the BMO seminorm and obtain bounds strictly below the universal factor $2$. Jensen-defect Carleson functionals and martingale-difference envelopes provide further applications, illustrating distinct anchoring mechanisms and the differences between finite-depth rationality, stabilization, and global attainment.

The Ramanujan bound states that the degree of the trace of the $\mathfrak{p}$-Hecke operator on a space of weight $k$ Drinfeld cusp forms is at most $d(k-2)/2$, where $\mathfrak{p}$ is a prime of degree $d$ in $\mathbb{F}_q[T]$. We prove the strong Ramanujan bound, which states that at level 1, this bound can be improved to $d(k-(q+1))/2$. In addition, we classify when the strong Ramanujan bound is sharp; surprisingly, this turns out to depend on $\mathfrak{p}$ only through the parity of its degree. We also prove results related to the smallest slope of the Atkin operator and mod $p$ distributions of Frobenius polynomials of Drinfeld modules over finite fields.

We establish inverse inequalities in Gaussian Sobolev norms for shallow $\mathrm{ReLU}^k$ trial spaces. The estimates identify the sharp regularity threshold and quantify the dependence on parameter separation and bias magnitude. Based on these estimates, we prove convergence of weighted least squares discretizations of linear PDEs on $\mathbb R^d$ using shallow networks with prescribed inner parameters and finitely many residual samples in an expanding ball. Under suitable stability and regularity assumptions, we obtain an error bound of order $h^{k+(d+1)/2-r}\delta_\pm^{-(S-r)}$ in the Gaussian Sobolev norm of order $S$, up to logarithmic factors, where $r$ is the PDE order, $h$ is the parameter fill distance, and $\delta_\pm$ is the antipodal separation. The convergence results cover deterministic and random sampling and extend to fixed bounded regions by restriction. We construct parameter sets with $\delta_\pm\asymp h$, yielding a convergence rate in terms of the network width that matches a lower bound up to logarithmic factors. Numerical experiments support the theoretical results and provide practical guidance on balancing accuracy and stability.

Looped transformers reuse a single block across iterations, raising a natural question: how far can a block trained at one depth be safely extrapolated to greater depths? We study this question for all-pairs graph connectivity, where harder graphs require longer-range information propagation. We show that under exchangeability and symmetric positive initialization, population training at depth K converges to an update rule governed by a single effective parameter that balances graph propagation against fitting structure unresolved at training depth. This trade-off creates a finite extrapolation window: too few test-time loops provide insufficient propagation, while too many eventually create false connections. We derive explicit endpoints for this window and bound the graph hardness solvable beyond training as a function of training depth and hardness. In particular, a test depth chosen solely from the training distribution can guarantee recovery on substantially harder graphs, with a certified depth gain that grows exponentially as training depth outpaces training hardness. Experiments validate the predicted windows and show how compute budget and initialization affect the optimal training depth.

We study a density heat flow associated with normalized Liouville systems on a closed connected Riemannian surface, and we show that this flow leads to the existence of solutions for the corresponding subcritical Liouville systems. The coupling matrix is symmetric and entrywise nonnegative, with no invertibility, irreducibility or inverse-matrix sign assumption. Under the strict subcriticality conditions $8\pi\sum_{i\in J}\rho_i>\sum_{i,j\in J}a_{ij}\rho_i\rho_j$ for every nonempty set of components $J$, every smooth positive initial density of masses $\rho_i>0$ generates a unique global smooth positive solution converging in every $C^m$ norm to a stationary density. The limiting potentials solve the stationary Liouville system. Our proof uses entropy coercivity and a gradient inequality in the density variables, which also yields algebraic or exponential convergence rates.

We show that a quantum reservoir computer optimized with its quantum Fisher information (QFI) has a quantum advantage over a classical reservoir of equal readout cost, provided by a quantum-information advantage: optimizing the quantum parameters with the QFI metric. On Mackey-Glass forecasting, a driven Jaynes-Cummings reservoir with one to three atoms beats a tuned echo-state network at every size from 4 to 30 trained weights, by 25-69% in held-out error, and is ahead of 99.5% of 10,000 random networks. After grid and Bayesian searches saturate, the QFI-aware stage lowers the error by 29-51% at 12-30 weights, beyond equal-budget black-box search or classical-parameter gradients alone, and at 30 weights turns a loss into a win. We then derive a fundamental QFI bound on the first-order rate of change of the retrained loss and factorize the gap to this bound into five link efficiencies that identify the physical mechanism limiting optimization.

Large language models (LLMs) may introduce security vulnerabilities into generated code, which can persist into production when verification focuses on functional correctness. Existing defenses act before, during, or after generation, but none inspects the code during generation. Security prompts and retrieved security knowledge act before any code exists, constrained decoding limits token choices but cannot guide repair, and post-hoc repair must regenerate the full response. Reasoning LLMs draft code early in their streamed chain of thought, and in this pre-delivery window the code exists only inside the reasoning stream. We present SecReason, an in-stream defense that monitors this window. Dual-track incremental scanning applies security rules, checking each statement as it is emitted and tracing dataflows across the accumulated code. When a security rule fires, SecReason interrupts generation, inserts an in-stream warning, and resumes decoding, so the model repairs the draft within the same reasoning trace without regenerating the full response. On tasks where unassisted generation introduces vulnerabilities, \system raises the share of runs delivering secure and functionally correct code from below 15% to 72.8%–98.1% on \tool{CWEval} and \tool{SecCodeBench}. \system consumes fewer tokens than post-hoc repair, and when security rules misfire on secure code, it limits the functional regressions from false warnings.

Ordinary angles and unsigned areas discard orientation, and much of the case analysis in plane geometry is the price of that loss. Signed quantities (directed angles, oriented areas and directed distances) keep the signs and so let one argument serve for every configuration. We illustrate this with results that hold uniformly for convex, concave and crossed quadrilaterals: the diagonal area formula, an identity expressing one diagonal in terms of the sides and the other diagonal, a test for a pair of parallel sides, a theorem on equidiagonal quadrilaterals (such a quadrilateral has a pair of equal opposite sides if and only if it has a pair of parallel opposite sides), and a single ratio of directed distances that decides whether the vertices lie on an ellipse, only on hyperbolas, or on a circle.

We present the concept of quadrature-detected zero-to-ultralow-field nuclear magnetic resonance (QD ZULF NMR). Two orthogonal sensors, atomic optically pumped magnetometers, are used to separately detect components of oscillating sample magnetization, which are then combined into a quadrature signal. This approach enables the distinction of positive and negative resonance frequencies with respect to the laboratory frame—such that absolute signs of gyromagnetic ratios can be determined. In addition, QD ZULF NMR reduces peak density and overlap compared to ZULF NMR with single-axis detection, while providing richer information about nuclear-spin dynamics. As an illustration, we present experimental $J$-spectra for thermally polarized [$^{13}$C]-formic acid and [$^{13}$C]-methanol, compounds commonly used in ZULF NMR which represent XA and XA$_3$ spin systems, respectively. A theoretical framework describing QD ZULF NMR signals is provided.

We generalize Christol's theorem—which characterizes algebraic power series over a finite field in terms of automatic coefficient sequences—to completions of domains of finite type over a finite field~$\mathbb{F}_{q}$. Let $A$ be such a domain of dimension~$d$ and $\mathfrak{a}$ an ideal of depth~$d$. In the $\mathfrak{a}$-adic completion $\hat{A}$, choose an $\hat{A}$-regular sequence $\boldsymbol{x}=\{x_{1},\dots,x_{d}\}\subset\hat{\mathfrak{a}}$ and a set of representatives $E$ of $\hat{A}/(\boldsymbol{x})$ that is an $\mathbb{F}_{q}$-vector subspace consisting of algebraic elements. Every element $y\in\hat{A}$ then admits a unique expansion $y=\sum_{u\in\mathbb{N}^{d}}a_{u}x^{u}$ with coefficients $a_{u}\in E$. We prove that $y$ is algebraic over $A$ if and only if the coefficient sequence $\{a_{u}\}_{u\in\mathbb{N}^{d}}$ is $q$-automatic. The proof relies on a careful study of henselizations, which are shown to coincide with the algebraic closures inside the completions under certain conditions. As an application, we obtain a complete characterization of the automaticity of $\beta$-expansions for formal Laurent series over $\mathbb{F}_{q}$, answering questions posed by Hbaib–Mkaouar and Scheicher–Sirvent.

Experiments with remote decision-making agents depend on more than the policy: the world may change during inference, the simulator determines which actions are available, and births and immigration alter who can act. We present Jevolution, an instrumented spatial predator-prey framework that makes these dependencies explicit. Its reference implementation separates the evolving world, asynchronous request scheduling, controller adapters, and experiment records. The model combines local observations, energy and resource constraints, predefined signals, and inherited scalar traits. We describe these mechanisms using the ODD protocol and distinguish implemented controls from research questions requiring additional interventions. Free synthetic fixtures exercise scheduling, signaling, and inheritance against the pinned implementation; they validate specified software behavior rather than model intelligence or ecological realism. A completed communication case study illustrates the end-to-end workflow using Jev to control both species. Across 6 complete habitat-seed pairs, the mean signals-on minus signals-off difference in normalized rabbit abundance was -0.0095 (nominal 95% pair-bootstrap interval [-0.0772, 0.0602]). This small study does not resolve the direction of the signal-system effect. The contribution is an inspectable experimental system and its evidence boundaries, not a new policy-learning algorithm or a demonstration of emergent language, adaptive selection, or biological predictive validity.

Asynchronous rollout improves the efficiency of reinforcement learning with verifiable rewards (RLVR) by reducing under-utilization during long-tail generation. Sustained concurrency also concentrates context processing into fewer decode steps, increasing the KV workload per step. We characterize this KV concentration and find that KV cache quantization delivers substantially greater acceleration than weight-only and weight-activation quantization in our matched-workload comparisons. However, INT4 KV rollout can degrade learning even with token-level truncated importance sampling (TIS). We propose KV4-RL, which combines calibration-free INT4 KV quantization with selective INT8 protection of attention sinks and recent context. Protecting a bounded number of positions reduces sampler mismatch while retaining most of the speedup from INT4. Across 400 iterations of Qwen3-8B-Base GRPO training, KV4-RL achieves $1.80\times$ cumulative rollout speedup and $1.27\times$ cumulative full-iteration speedup over BF16 rollout, reaching $1.97\times$ rollout speedup over the final 50 iterations. Under a common BF16 evaluator, its final six-benchmark mean accuracy is within 0.5 percentage points of BF16-rollout training for both Qwen3-4B-Base and Qwen3-8B-Base.

We develop and analyze a symmetric two-level preconditioner for the method of reflections for Laplace problems in perforated domains. Using constant boundary modes, we define a coarse correction through a symmetric coercive dual formulation. Combining this coarse correction with parallel reflection corrections gives a symmetric positive definite preconditioner for solving the dual system by the conjugate gradient method. Under a geometric separation condition, we prove a condition number bound independent of the number and sizes of the holes and the diameter of the ambient domain. We also derive geometry-dependent convergence estimates for the one-level methods that explain the need for a coarse correction.

We establish a compact-localization theorem for finite iterates of the Smyth power space. Successive union maps assign to every finite-level Smyth object a canonical least compact saturated carrier in the original space, and co-sobriety at each positive finite level is equivalent to co-sobriety of the corresponding iterates over all compact saturated carriers. Consequently, if every compact saturated subspace of a $T_0$-space $X$ is stably compact—in particular, if every such subspace is Hausdorff—then $\PS^n(X)$ is co-sober for every finite $n\geq 1$. This applies to every $k_1$-Hausdorff space and hence to every Hausdorff or metrizable space. For the first iterate, we also give a direct full-Vietoris argument, independent of stable compactness, which shows that each $k$-irreducible compact saturated family is generated by its union.

In film production, chroma keying composites an approved foreground performance into a new environment, but conventional workflows require coordinated background plates and dedicated harmonization. Recent generative methods often require pre-aligned backgrounds, focus on background-conditioned foreground relighting, or represent the environment only through an edited first frame. These restrictions limit background selection, scene composition, and camera motion while adding preparation or editing effort. We present FreeCHROMA, which adapts a pretrained video diffusion model in a parameter-efficient manner for generative video compositing from one to three unaligned background references. The model integrates the foreground into the referenced environment, preserving foreground identity, motion, and fine visual details while generating a spatiotemporally coherent background. Foreground-background harmonization occurs within the same generation process, without a separate relighting stage. Optional text instructions help disambiguate complex spatial relationships and camera behavior. To train the model, we construct pseudo-paired data from readily available real monocular videos through foreground-background separation and augmentation with existing foundation models. The original videos serve as training targets, while automated processing and quality verification enable scalable data construction. Across reference fidelity, foreground preservation, scene integration, harmonization, and overall video quality, FreeCHROMA consistently outperforms recent compositing and conditional video-generation baselines, with particularly clear gains under camera motion. FreeCHROMA relaxes the constraints of existing tools to enable end-to-end generative chroma keying from unaligned inputs, with exploratory experiments demonstrating its potential in robotics.