Papers

Dissipative algorithms approach the problem of ground state preparation by mimicking the natural thermalization of a quantum system in contact with a large, low-temperature thermal environment. The environment can be efficiently simulated by a single ancilla qubit with a variable energy gap that is repeatedly coupled to the system qubits to generate a dissipative channel, and then reset after each interaction. Here we present an adaptive implementation of the dissipative algorithm, RL-Adapt, that uses single-shot reinforcement learning to optimize the selection of ancilla frequency and system-bath interaction operator to maximize energy dissipation without relying on a priori knowledge of the system spectrum. The adaptive implementation results in significantly reduced convergence times and can successfully find the ground state even for non-ideal operator pools that fail to converge using non-adaptive, uniform random operator and ancilla frequency selection.

We study a fully discrete approximation theory for the two-dimensional incompressible Euler equations on $\mathbb{T}^{2}$, in vorticity form, driven by Kraichnan-type transport noise and with $\mathbb{H}^{-1}(\mathbb{T}^2)$-valued initial vorticity. The main new ingredient is a finite-dimensional coercivity estimate for the torus Kraichnan model, which captures at the discrete level the regularizing mechanism induced by the rough transport noise. Together with a new compactness strategy based on continuous equation-based interpolants and localized discrete estimates, this coercivity estimate gives tightness of the approximations and shows that subsequential limit is a weak martingale solution of the Euler equations.

Tree-Adjoining Grammars (TAGs) have recently been introduced to Nonlinear System Identification (NLSI) as a means of encoding an entire model class as a finite set of grammatical rules, from which candidate models are assembled as trees. Existing TAG-based identifiers rely on evolutionary optimisation and return point estimates of the model structure. This paper instead proposes the TAG framework within a Bayesian setting. A generative prior is defined over tree structures and their parameters, and a Reversible-Jump MCMC sampler with structure-preserving tree moves is used to infer the joint posterior over model structure, parameters and predictions. Two training objectives are considered; that is, a one-step-ahead objective with conjugate parameter proposals, and a simulation-based objective handled by likelihood-free inference. The approach is validated on a simulated polynomial NARX system, the Silverbox benchmark, and wave-loading data from the Christchurch Bay Tower, where embedding Morison's equation as a fixed initial tree yields a grey-box model that outperforms the physics-driven baseline. The results demonstrate that Bayesian TAGs are well suited to quantifying uncertainty in equation discovery for dynamical systems and to fitting physics-informed models.

Grain boundaries influence hydrogen transport in polycrystalline metals by acting as both trapping sites and interconnected diffusion pathways. Conventional interpretations of thermal desorption spectroscopy (TDS) and permeation experiments often treat traps as isolated defects, neglecting grain boundary connectivity and potentially misinterpreting experimental data. Here, we develop a quantitative phase-field model for hydrogen diffusion, grain boundary trapping, and grain boundary-assisted transport. The formulation preserves the physical grain boundary volume independently of the numerical interface thickness and accounts for anisotropic diffusion parallel and perpendicular to grain boundaries. Benchmark simulations verify quantitative behavior under interface upscaling. The model shows that grain boundary diffusion can significantly shift TDS peaks, making Kissinger-type analyses unreliable when grain boundary transport is significant. Effective diffusion coefficients are also shown to depend strongly on grain size, trapping free energy, temperature, and grain boundary mobility. These results highlight the coupled role of trapping thermodynamics, bulk diffusion, and grain-boundary transport.

Quantum electrodynamics in strong background electromagnetic fields or strong-field QED (SFQED) has been investigated in great detail at the tree level. The study of SFQED at higher loops has not been carried out in a correspondingly systematic way, with the notable exception of strong background atomic fields. Here, we investigate the renormalization of SFQED by writing the standard unrenormalized SFQED Lagrangian density, which differs from the vacuum-QED Lagrangian density by the additional interaction term of the Dirac four-current density with the background four-vector potential, in terms of renormalized quantities and counterterms. Within this framework, we confirm the necessity of renormalizing the background field as an electric charge rather than as a photon field. We compare this approach with an alternative one which features a different renormalized Lagrangian density and we show that they are physically equivalent. As a byproduct, it will become clear that the renormalizability of SFQED directly derives from the renormalizability of vacuum QED. Also, we obtain that the renormalized SFQED Lagrangian density features a new counterterm as compared to the vacuum Lagrangian density. This counterterm is necessary to renormalize the electron self energy, which undergoes a new contribution as compared to vacuum QED, physically due to the electromagnetic field produced by the four-current density induced in the vacuum by the background electromagnetic field. The vacuum-induced electromagnetic field diverges and needs to be renormalized. We show how the renormalization of the vacuum-induced electromagnetic field is implemented explicitly at one loop and at two loops. The renormalization at all loops is shown to be more easily deduced at the level of the Lagrangian density. Finally, some subtleties concerning the renormalization procedure in the case of a free background field.

In this work, we define $(3+1)$-dimensional topological quantum field theories (TQFTs) and their lattice realizations with input data given by a pivotal fusion 2-category; more precisely, our framework applies in wider generality to presemisimple locally fusion pivotal tensor $2$-categories, which are equipped with a so-called shadow trace. We introduce a decoration of triangulated manifolds by the input data, and develop a $20j$-symbol formalism for computing 4-simplex scattering amplitudes. We verify the topological invariance of 20$j$-symbol summations under the 4-dimensional Pachner moves. Furthermore, we also construct explicitly a 3-dimensional Levin-Wen-type lattice Hamiltonian model realizing the state-sum invariant. Our construction can be understood as a higher-dimensional analogue of the spin-networks construction for the Turaev-Viro invariant. Examples arising from $2$-groups are discussed from the perspective of higher gauge theory.

Predicting human gaze is a core capability for applications ranging from web/UI design analysis to robotics and human-computer interaction. Yet, most visual attention modeling methods output only a dense saliency map, which is often insufficient for action: practitioners need to connect attention peaks to discrete elements in the scene (what) and understand the drivers of those peaks in context (why), while remaining robust to domain shift across natural images, commercial content, and UI/web layouts. We, therefore, introduce OpenVAM (Open-world Visual Attention Modeling with VLMs), a unified framework that jointly addresses universality and explainability across heterogeneous domains (natural scenes, commercial imagery, and UI/web layouts) and supervision modalities. OpenVAM adopts a decoupled-but-aligned design: a dedicated dense visual pathway provides stable, spatially precise localization, while an instruction-following vision–language semantic head generates grounded what/why explanations conditioned on the same image and data-type prompts. A three-stage training strategy preserves strong localization priors while progressively introducing language grounding and improving explanation alignment via parameter-efficient adaptation without perturbing the saliency branch. We further propose a scalable pipeline to generate multi-domain saliency-reason annotations for training and systematic evaluation. Experiments across diverse datasets show that OpenVAM improves robustness under domain shift while producing image-grounded explanations that make saliency predictions more interpretable.

Distributionally robust optimization (DRO) provides a principled framework for learning under distribution shift, but its practical use is hindered by the difficulty of evaluating worst-case risks for nonconvex loss functions. We study a penalized DRO formulation in which the adversary may choose any distribution but incurs a Wasserstein penalty for deviating from the empirical distribution. We show that the adversary's problem can be reformulated as an optimization problem over transport maps that push empirical samples to adversarial ones, and we prove that optimal maps are cyclically monotone. We also show that standard adversarial training—based on per-sample local optimization—violates cyclical monotonicity and wastes transport costs unless the adversary is severely restricted. We propose two remedies. First, we introduce multi-start particle ascent, which alternates parallel gradient ascent with reassignment to enforce cyclical monotonicity across samples. Second, we parameterize adversarial maps as gradients of input-convex neural networks, which guarantees cyclical monotonicity by construction. Experiments on robust regression, image classification, and robust control show that our methods consistently outperform standard adversarial training and state-of-the-art baselines, achieving improved robustness and better generalization under distribution shift.

We aim to expand the sample of RSGs with direct measurements of circumstellar gas through millimeter observations of two of the largest coeval RSG populations in the Galaxy: the open clusters RSGC1 and RSGC2. We present an interferometric molecular line study of 28 RSGs in RSGC1 and RSGC2 with ALMA. The primary targeted emission is CO $J=2-1$ and continuum, with additional thermal and maser SiO lines observed for RSGC2 targets. We measure terminal expansion velocities, systemic velocities, emission-region sizes, and provide updated dust models and luminosities using the new long-wavelength constraints. Finally, we perform 1D radiative transfer modeling of CO rotational-line emission to estimate mass-loss rates. We detect $^{12}$CO toward six RSGs in RSGC2 and five in RSGC1. Except for DFK 52, the spatial distribution of all $^{12}$CO emission is relatively compact or unresolved. The obtained mass-loss rates range from $\log(\dot{M}/M_\odot\,\mathrm{yr}^{-1})=-5.5$ to $-3$, but are highly uncertain due to a lack of stringent constraints on the envelope sizes and temperatures. The lower-limit $\dot{M}$-values we obtain are high compared to standard empirical prescriptions and favor dust models assuming a radiatively driven wind. DFK 49 is a clear outlier: its revised luminosity is the lowest in both clusters, yet it harbors a strong wind with $\dot{M}>10^{-5}\,M_\odot\,\mathrm{yr}^{-1}$. The CO emission regions are much smaller than expected from nearby RSGs and theoretical models, and suggest a unique phase structure for the CSM around RSGs in cluster environments. This work demonstrates the mutual utility of molecular line and dust observations for constraining RSG winds, while highlighting the need for future spatially resolved, multi-tracer observations of RSGC targets to establish the physical structure of their circumstellar environments and improve mass-loss determinations.

High-frequency industrial cyber-physical systems (CPS) stream continuous sensor telemetry at sub-10-second intervals. Multi-horizon forecasting over hours is required for predictive maintenance and operational control. However, deploying machine learning models over extended horizons (H = 2,160 steps at dt = 5 s) encounters the Dual-Timescale Forecasting Dilemma: the trade-off between short-horizon kinetic momentum and long-horizon diurnal thermodynamic equilibrium. Autoregressive rollouts suffer from compounding error drift, while direct multi-output projectors exhibit variance explosion and noise extrapolation. In this work, we prove that autoregressive mutual information decays exponentially toward zero over extended lead times, and that the optimal minimum-variance estimator converges asymptotically to the periodic diurnal baseline (Lemma 1 and Theorem 1). Guided by these bounds, we propose the Dynamic Asymptotic Decomposition (DAD) framework. The architecture couples a continuous sigmoidal authority transition schedule \(\alpha(h)\) with monotonic L2 regularization scaling \(\lambda(h)\), transferring prediction authority from kinetic autoregression to diurnal equilibrium while enforcing physical non-negativity. Evaluated across a 30-day industrial telemetry stream (N = 518,400 steps) over 16 walk-forward test windows, DAD achieves an overall Mean Absolute Error (MAE) of 0.1764, representing a 78.3% error reduction over Deep LSTM (0.8143), 60.2% over PatchTST (0.4431), and 20.8% over DLinear (0.2227). Computational profiling demonstrates edge execution in 0.72 ms with 0.203 MFLOPs and 72k parameters on a single CPU core (over 3400x faster than Transformer baselines), validated by an automated dual-stage CI/CD quality assurance harness and physical fail-safe architecture.

Inference in LLMs is conventionally a fixed-depth, fixed-order forward pass through every layer, regardless of how difficult the input is. The human brain does not work this way. Using the thalamus as a central hub, it routes information flexibly to all regions of the cortex according to demand. Li et al. (2026) recently showed, with program-of-layers (PoLar), that transformers can be given an analogous flexibility if their layers are treated as a library of functions rather than a fixed sequence. Performance improves over the standard forward pass when each input is dynamically routed through an adaptive sequence of skipped or repeated contiguous layer blocks. Reconstructing PoLar's diagnostic Monte Carlo Tree Search in more detail across 6 models, we reproduce several of its findings: skipping outperforms the standard pass, repeating outperforms skipping, and combining both outperforms either alone. Shorter programs suffice for easier questions, while harder questions require more layer repeats. For their main claim, the learned router's gain, we find what drives it. Under their setup, the router gains by repairing the format of the model's answers, which a single fixed program, selected on validation questions, does better. In our setup, with a prompt that already fixes the format, a larger data split and our search, its top prediction collapses to the standard pass on every model, although its top-5 programs together still gain. Beyond reproduction, we find in our setup that a small fixed menu of programs solves far more questions than the standard pass, and that programs which correct errors are brittle: undoing a single edit typically breaks the correction. PoLar mirrors principles of thalamo-cortical coordination between cortical-area-like transformer layers, although a working thalamus analogue, a router that picks a better program per input, remains to be found.

With the prevalence of Attention Deficit Hyperactivity Disorder (ADHD) over the past decades, healthcare systems across the globe face critical diagnostic challenges due to long diagnostic waiting times and a reliance on subjective behavioural assessments that cannot distinguish ADHD from comorbid psychiatric disorders, especially for adult patients. This exploratory study investigates whether EEG-based word association paradigms show promise as a complementary approach to screening for ADHD in adults. Using a mixed-method approach, the study examines neurological and cognitive differences between neurotypical individuals (NT), clinically diagnosed ADHD participants (ND), and self-reported ADHD cases awaiting formal diagnosis (SR) across three word association tasks. While established EEG biomarkers (ERP N400, Theta/Beta Ratio, and Alpha Suppression) show no significant group differences, semantic distance analysis reveals a statistically significant main effect ($p=0.003$), with the SR group showing the most divergent associations. These preliminary findings suggest that word association paradigms may capture cognitive differences not detected by standard EEG metrics and encourage further large-scale investigation as a potential complement to existing adult ADHD screening tools.

The Model Context Protocol (MCP) provides a common interface through which AI applications discover and use external resources and tools. It allows language-model agents to ground their reasoning in current system state and interact with heterogeneous services. In medical environments, however, exposing device state and action affordances requires deterministic constraints on possible effects. We present an IEEE 11073 Service-Oriented Device Connectivity (SDC)-to-MCP gateway that exposes metrics, alarms, context references, and semantic metadata as read-only resources, while representing selected action affordances as policy-validated dry-run tools. The term safety-bounded denotes a narrow no-execution property: agent-facing requests dispatch no SDC device operation. A Python prototype supports simulated fault and lifecycle experiments, a software-reference protocol path spanning independent Java and Python implementations, deterministic baselines, representation ablations, and multi-model agent evaluation. The results show semantically explicit resource exposure, visible rejection of invalid or outdated state, and preservation of the no-execution boundary across resource, proposal, and authorization paths. Explicit semantic metadata improved conformity to required metric identifiers in structured alarm outputs relative to a generic representation, while retained structured-output failures reveal a distinction between plausible narrative answers and task-compliant machine-readable results.

To be able to perform inspection or digitization tasks, mobile robots on construction sites must be able to localize themselves reliably with respect to a global reference frame that is shared with a building map. Similar room layouts and low-texture surfaces pose a challenge for existing LiDAR- and vision-based localization methods. We approach this problem with a LiDAR-based global relocalization system that estimates the robot's pose relative to a building mesh and combines a PointNet++ encoder with a place recognition decoder, whose outputs serve as a learned observation model within a Monte Carlo Localization (MCL) framework. The pipeline is trained exclusively on synthetic LiDAR scans obtained by simulating the robot's sensors inside the building mesh. Our approach is robust in ambiguous environments due to an uncertainty-aware decoder that scales positional likelihoods and a resampling strategy that injects model hypotheses into the particle set, enabling recovery from potential particle depletion. Evaluations on real-world datasets show that our method outperforms both diffusion-based and ScanContext++ baselines while maintaining fast inference (18 ms per call), demonstrating the practicality of synthetic-data training for mesh-referenced global localization in construction robotics.

Vision-Language Models (VLMs) exhibit remarkable zero-shot generalization, yet they often encode unwanted or hazardous stylistic domains such as idealized textbook diagrams in medical AI or cartoon vehicles in autonomous driving. Approximate Domain Unlearning (ADU) aims to selectively erase a model's recognition of a target visual domain while preserving accuracy on the remaining domains. However, existing ADU methods operate under a flawed closed-vocabulary assumption: they evaluate unlearning solely on the specific object classes seen during the unlearning fine-tuning phase. Consequently, these methods do not unlearn the domain itself; they merely overfit to seen class-domain pairs, leaving the domain easily recognizable for unseen classes and providing a false sense of removal. We argue that true domain erasure must be class-agnostic. To address this, we formalize Open-Vocabulary Domain Unlearning (OVDU), a rigorous protocol that mandates domain forgetting must transfer to held-out classes. To solve the OVDU challenge, we propose a surgical parameter-editing framework. First, a Fisher Information mask isolates domain-sensitive weights, mathematically protecting foundational zero-shot generalization. Second, our Targeted Manifold Scattering (TMS) objective uses preference-based mining to locally scatter the forget domain's stylistic geometry. Evaluated across PACS, OfficeHome, and DomainNet, our method vastly improves open-vocabulary generalization over existing baselines. Crucially, it delivers exceptional sample efficiency, outperforming peak 8-shot baseline results with only 4 shots.

Motivated by Brouwer's conjecture, Ashraf, Omidi and Tayfeh-Rezaie proposed the following Brouwer-type conjecture that for every graph $G$ on $n$ vertices with $m$ edges, the sum $S_k^+(G)$ of its $k$ largest signless Laplacian eigenvalues satisfies $S_k^+(G)\le m+\binom{k+1}{2}$ for $k=1, \ldots, n$. In this paper, we prove that the above conjecture holds. Moreover, the equality holds if and only if $k=1$ and $G$ is either star $K_{1,a}$ or triangle $K_3$ with adding some isolated vertices. For split graphs, properties of block signless Laplacian matrices based on clique and independent set are adapted. While for non-split graphs, some spectral graph substructure are used to control the sum of signless Laplacian eigenvalues.

Contemporary large language model (LLM) chat systems treat conversation history as an immutable sequence of turns that defines the model's working context. However, user intent in real interactions is not static: it evolves through correction, refinement, and shifting constraints. This mismatch between dynamic intent and static transcripts can result in context pollution, where outdated or irrelevant information persists and continues to influence subsequent responses. We introduce mutable transcripts, a new interaction paradigm that enables users to revise prior turns through natural language edit requests, allowing the conversation history itself to be updated rather than appended. This reframes the transcript from a passive record into an editable representation of conversational state. We present a working prototype that integrates transcript-level revision into a standard chat interface and evaluate its feasibility through a controlled user study (n=17) and an illustrative transcript analysis of representative interaction scenarios. Participants significantly preferred mutable transcripts over standard chat across measures of clarity, confidence, and ease of use, with reduced intent to restart conversations. Transcript analysis of representative user study conversations shows that mutable transcripts can reduce conversation length and eliminate obsolete retained context. These findings provide initial evidence that user-driven revision of conversational history can improve interaction quality and help maintain a more current representation of user intent. The source code and prototype can be accessed at https://github.com/QxLabIreland/ReChat

We study the Wasserstein lift of nonlinear Poisson systems with inhomogeneous Neumann boundary conditions. We establish the existence of minimizers using new estimates involving the $p$-moments of measure-valued traces. We also derive the optimality conditions, which turn out to be matrix-valued generalizations of pressureless Euler equations. While deterministic minimizers exist under suitable convexity assumptions and for one-dimensional source domains, we show that genuinely measure-valued minimizers arise in higher dimensions. In particular, we construct examples in which the lifted and classical variational problems have different minimum values, thereby precluding the solutions to the lifted problem from being deterministic, despite the absence of any a priori mechanism enforcing measure-valued behavior. To the best of our knowledge, this phenomenon is new in the nonlinear elliptic theory.

The goal of this paper is to refine methods in computable analysis and to employ them in the study of solutions of an optimization problem posed by Bellman. This problem asks how to find optimal (shortest) paths which do not fit into given plane figures. We show that each instance of Bellman's problem has an arbitrarily small uniformly computable perturbation for which the minimal length of path is computable, and thus the class of optimal paths is a $\Pi_1^0$ class, and there are uniformly computable paths which escape with arbitrarily small length greater than the minimum possible.

Time-series carry structure simultaneously at multiple scales (fine-grained variation, mid-range motifs, and global properties) and downstream tasks operate at correspondingly different scales. Most existing self-supervised learning approaches supervise representations globally via instance-level contrastive losses and limited temporal neighborhood supervision, but do not explicitly exploit the structural hierarchy. We propose a learning framework that explicitly enforces a structural hierarchy across three scales independently: a local objective for token alignment, a mid-range objective for window-level motifs, and a global objective for sequence-level agreement. Realizing this framework requires the backbone to expose a representation at each scale; we introduce Progressive Memory Transformer (PMT), which augments a transformer with writable, window-aligned memory that exposes the mid-range scale alongside the token and sequence-level representations conventional transformers already provide. Across eight UCR/UEA/UCI classification benchmarks, a cue-retention probe, and forecasting benchmarks, PMT learns representations that probe well at the global, mid-range, and local scales—strong low-label classification (1–5% labels), competitive forecasting performance across multiple horizons, and quantitative and qualitative evidence that memory states capture mid-range motifs.

We study the three-parameter family of quantum conditional Rényi entropies $H_{\alpha,z}^\lambda$ introduced in Commun. Math. Phys. 407, 180 (2026). We prove that the previously established data-processing region is sharp. We then characterize the club-sandwiched family through a classical coarse-graining principle: within the full data-processing region, universal monotonicity under deterministic coarse-graining of the classical conditioned register holds if and only if $z = \alpha$. Finally, we establish rigidity of entropic duality by showing that any universal duality relation for finite-dimensional tripartite pure states must satisfy the known parameter relations. Thus, the data-processing region, the club-sandwiched subfamily, and the duality transformation are each uniquely characterized by their respective universal properties.

Large video diffusion models offer expressive priors for embodied prediction and learning, yet their many-step sampling remains costly for interactive downstream use. Distribution Matching Distillation (DMD) enables few-step video generation, but can suppress robot–object motion while preserving visual quality. Examining DMD's teacher and fake-score signals, we find that weak re-noising keeps the teacher posterior concentrated near motion-deficient rollouts, limiting motion-restoring guidance. Meanwhile, stronger-motion rollouts tend to incur larger fake-score fitting errors, which can hinder the generator's learning of interaction dynamics. We propose DyMD, a DMD framework that adapts both teacher supervision and critic fitting to the evolving student. Temporal affinity–conditioned re-noise sampling adapts the timestep distribution to each rollout's current interaction fidelity by mixing the base schedule with a teacher prior motivated by local posterior variation, thereby balancing motion recovery and appearance refinement. To better track stronger-motion rollouts, dynamics-guided fake-score tracking uses a noise-conditioned predictor to estimate noise-relative fitting difficulty from latent temporal dynamics, then upweights predicted-hard rollouts in the critic loss. Using DyMD, we distill a 14B teacher into a four-step 1.3B student with no auxiliary modules at inference. On embodied-video benchmarks, the student improves R-Bench task adherence by $9.6$ percentage points and PAI-Bench-G Domain score by $5.1$ points over Base DMD while maintaining comparable visual quality. As a backbone for downstream action planning, our student achieves 34% mean success across two WorldArena tasks, compared with 16% for Base DMD.

In this paper, we discuss the dynamics of test particles in the space-time of spherically symmetric, charged boson stars and their frozen states. These latter objects consist of a de Sitter core and a black hole exterior with a shell of finite thickness interpolating between the two. We discuss charged and uncharged massive particles, find the ISCOs and determine whether collisions of massive particles close to the core of (frozen) boson stars can lead to large center of mass energies. We also discuss massless test particles and find that photons rings as well as light points are possible in the space-time of frozen boson stars. We compare our results with those in the corresponding Reissner-Nordstroem space-time and point out differences.

Gradient-based optimization (GBO) of problems constrained by partial differential equations is central to parameter identification and structural design in solid mechanics. Lattice Boltzmann method (LBM) schemes for linear elastic solids have only recently been derived. Combined with automatically generated discrete adjoint collision kernels, they make GBO possible with a purely LBM-based primal and adjoint solver. We propose, to our knowledge, the first optimization benchmarks for solid LBM: three inverse problems, each with a manufactured solution of the forward problem and a known reference control. These are the identification of two scalar amplitudes of a body force field on a periodic domain, the distributed control of the same field with up to $12800$ degrees of freedom, and the identification of Young's modulus on an elliptic plate with Dirichlet and Neumann boundaries. The primal scheme converges with second order on the periodic domain and with first order on the elliptic plate. The recovered controls follow these rates, with experimental orders of convergence of $1.92$ and $1.06$, respectively. Gradients obtained via forward-mode automatic differentiation (f-AD) and the discrete adjoint LBM (ALBM) require the same number of optimization steps and yield control errors agreeing to at least eleven significant digits. The ALBM gradient is further validated node-wise against a finite difference quotient, with deviations decreasing under mesh refinement. The benchmarks are implemented in the open-source LBM framework OpenLB and provide a verification basis for optimization in LBM-based solid mechanics and its extension to fluid-structure interaction.

The diffusion synthetic accelerated (DSA) source iteration is a standard solver for the radiative transfer equation. Using Fourier analysis, a convergence rate \(\rho_\infty(c)\le0.2247\,c\) with \(c\) the maximum ratio of scattering to total cross section has been established for an infinite homogeneous medium. For slab geometry with inflow boundary conditions and arbitrary bounded cross sections we prove that the spectral radius of the DSA iteration is at most \(\rho_\infty(c)\). We show that this convergence rate carries over to a variational discretization of the DSA iteration on every conforming tensor-product Galerkin space whose angular factor contains the constants. The analysis rests on an exact min–max characterization of the spectral radius. From it we derive a checkable sufficient condition for a given rate. We verify this condition using a suitable energy-stable projection, a weighted angular average whose weight is chosen so that the condition holds with the rate \(\rho_\infty(c)\). Since the projection maps discrete spaces into discrete spaces, the argument applies verbatim to the discrete iteration. As a consequence, the condition number of the preconditioned system is uniformly bounded by \(1+0.29\,c\), which implies rapid convergence of the preconditioned conjugate gradients method.

This article is concerned with the asymptotic shape of quantile surfaces, defined as the set of quantiles at a given level $\alpha$ generated by a controlled one-dimensional distribution. Specifically, when the distribution arises as a linear combination of log-normal random variables and the control is a vector of positive coefficients, we prove that quantile surfaces are globally concave in the left tail ($\alpha\to0$) and globally convex in the right tail ($\alpha\to1$). Moreover, these surfaces exhibit asymptotic separation of scale and shape.

The decay of a density wave, the Fourier component of the adparticle density seen by a coherent probe, obeys in an interacting adlayer an exact memory equation of Mori's form, determined by the local rate and the memory function. Because the density is conserved, the correlation function is a characteristic function, and the kernel is built from that of a single jump; positivity and normalization then make the local rate and the memory function equilibrium averages, whatever the interaction. The local rate obeys an exact sum rule, which makes de Gennes narrowing a theorem on the lattice and gathers the interaction into one effective hop rate. Detailed balance makes the decay a superposition of relaxation modes, approached from below by a convergent hierarchy of closed forms. The theory fixes the local rate, the memory function and the relaxation spectrum. The experiment provides the static structure factor and the decay, recorded from the instant of scattering through a ballistic regime, a jump regime in which the memory acts, and a diffusive regime. A single exponential fitted, as experiments do, over a time interval in the diffusive regime gives the slowest relaxation rate, the constant rate of that regime, and not the local rate. The correlation time, defined as the area beneath the normalized decay, needs no time interval and is the mean inverse relaxation rate. Under a standard condition on the jump rates, met in one-dimensional diffusion when the rate of leaving a site is independent of the site reached, the correlation time, the static structure factor and the lattice geometry give the effective hop rate at long wavelength, with no model or fit and with a parameter-free test. There the sum rule becomes a Darken-type relation.

We prove that at any nondegenerate neck pinch singularity of Lagrangian mean curvature flow of surfaces the mean curvature becomes unbounded, with control on the blow-up rate.

Retrieval-augmented generation (RAG) is often used to address outdated knowledge by providing external evidence. But retrieval helps only when that evidence is still valid. We identify a temporal alignment failure, stale-document poisoning, in which outdated evidence makes a model wrong despite answering correctly without retrieval. We construct a benchmark of 317 verified knowledge reversals across medicine, law, software, and platform policy, grounded in dated official sources. Across 12 models, recent medical reversals are harder than long-established ones. More importantly, outdated retrieval flips 30% of Llama and 37% of Qwen answers even without instructions to trust the document; explicit follow instructions raise these rates to 66% and 75%. Across four open models and four domains, poisoning ranges from 17-91%, while matched up-to-date evidence is followed in 97-100% of trials. To isolate temporal applicability, we keep the historical evidence unchanged across 50 reversals and vary only the evaluation date. A clear pattern emerges: dates alone produce only modest adaptation, but when models are explicitly told when the old evidence stops applying, the larger models switch to the appropriate answer almost perfectly. Causal interventions confirm that this validity information directly shapes the final decision. The same internal components also support broader comparison tasks, suggesting that temporal applicability can recruit a general reasoning mechanism used for other comparisons. Finally, a fixed recency-aware hybrid re-ranker reduces poisoning by 4.6-10.0 points when dates are accurate, with gains that depend on reliable temporal metadata. Reliable RAG therefore requires selective trust: models must determine not only what retrieved evidence says, but whether it still applies.

Whether an information extraction pipeline should process page images or parsed text depends on the document, and the answer flips across the layout spectrum. We study this trade-off under a constraint that rules out (closed) cloud services: privacy-sensitive documents processed on-premise by small ($\le 8\mathrm{B}$ parameter) text-only and vision–language models, evaluated on both accuracy and energy over a design space spanning input representation, model family, and inference configuration. Benchmarking on the near-plain-text Kleister-NDA contracts and the layout-rich VRDU forms, we find that batching is the dominant energy lever, cutting energy per page by 38-85% at no cost in accuracy, while FP8 quantization saves 27-32% when requests are served one at a time but less than 1mWh per page (9-19%) once batching is applied. Preprocessing dominates what remains: neural OCR costs $17\times$ more energy per page than classical OCR and never reaches the Pareto frontier. Which representation wins flips with the type of document: vision–language models on layout-rich documents and small text-only models with a cheap parser on near-plain text, where they are both more accurate and cheaper than any vision–language configuration. Our work yields concrete guidelines for energy-efficient, privacy-compliant local information extraction.