Papers

On-device learning is necessary when the model encounters user-,sensor-, or environment-specific shifts after deployment. Although parameter-efficient fine-tuning (PEFT) methods, particularly Low-Rank Adaptation (LoRA) variants, enable efficient adaptation at the edge, the limiting resource for Convolutional Neural Network (CNN) adaptation is often not the number of trainable parameters but the activation state that must be retained until the backward pass. This paper introduces Memory-Floor LoRA (MemFLoRA), a low-rank CNN adapter built around a memory-first design principle rather than a direct application of transformer-oriented LoRA. Instead of merely reducing trainable weights, we define an activation-memory-floor criterion: trainable backward computations must not depend on full-width layer inputs. The resulting adapter freezes the down-projection, trains a scale-matched up-projection, and combines eval-mode backbone normalization with activation-minimal backward rules, reducing saved state to the low-rank branch. Evaluated on three Human Activity Recognition (HAR) datasets and two CNN backbones under subject, body-location, and sensor-placement shifts, MemFLoRA reduces saved-activation memory by 98.5-98.7% and peak training-state memory by 94.9-97.3% relative to full fine-tuning, while matching or exceeding CNN PEFT baselines.

Behavioral watermarking embeds an owner identifier in an LLM agent's high-level action choices, giving provenance without touching output tokens. Prior agent watermarks break in two ways. First, all three prior schemes bind the watermark to the exact action symbol, so renaming a tool desynchronizes decoding even when the observation is untouched; in AgentMark's own robustness test, paraphrasing the observation alone drops bit-recovery to 16.8%. Second, every prior agent watermark studies only removal: none asks whether an adversary can forge a trajectory that verifies as someone else's, a question answered affirmatively for text watermarks (Jovanović et al., 2024). We present Semantic Behavioral Watermarking (SBW): watermarking over semantic action clusters under history conditioning, with the public-cluster bin replaced by keyed collision-resistant binning whose fresh-bucket assignment is provably unpredictable in the random-oracle model. Across five agent models (3B-14B, four vendors) and three encoders the ordering holds on both benchmarks: on ToolBench (600 trajectories per model) detection under rewriting is 0.49-0.66 for cluster-level versus 0.05-0.17 for exact-symbol at a permutation-calibrated 1% FPR, at 72-83% choice agreement against 22-27% for logit biasing; on ALFWorld (100 episodes per model) it is 0.92-0.97 versus 0.00-0.01. Keyed binning takes adaptive forgery from 100% to the false-positive floor at the primary operating point (bge, r=64). We also mark the boundary that guarantee does not cover: when the adversary copies the victim's own steps, shuffled splicing is neutralized (0.000 on Qwen2.5-3B) but chained replay remains at 0.76-0.98 across the five models, reported as open. Paraphrase robustness costs about half of the per-step watermark capacity. Code is available at https://anonymous.4open.science/r/SBW-Agent-Watermark.

Recent advances in algorithms for simulating Lindblad dynamics have clarified their theoretical potential for state preparation, but their practicality in the early fault-tolerant regime and beyond remains uncertain. In this work, we address this by investigating the cost of preparing ground states of the fermionic Hubbard model, following the single-ancilla approach of [Phys. Rev. Research 6, 033147 (2024)]. We derive rigorous error bounds including constant prefactors, and compare to empirical error behavior and practical convergence parameters obtained from circuit-level simulations. We find that empirically chosen parameters can reduce the required resources by orders of magnitude, resulting in an estimated $7.7 \times 10^8$ T gates to perform one unit of time evolution targeting the low-energy subspace of a 36-site fermionic Hubbard model. We identify the accurate filtering of energy transitions as the main source of this cost.

The Nancy Grace Roman Space Telescope launched on August 30th, 2026 and is expected to begin its science mission in 2027. Although Roman's core science will focus primarily on faint and distant sources, as a survey telescope, it will also observe many bright sources that can saturate the detector pixels. Our goal is to study the behavior caused by bright sources dispersed through the grism and to assess how detector properties may impact scientific analysis. We analyze detector saturation behavior in Roman's Wide Field Instrument (WFI) using Thermal Vacuum Test 2 (TVAC2) bright-source grism data. When bright sources are dispersed through the grism, we find that the faint and diffuse combined orders cause significant structured stray light. We also find that pixels neighboring saturated pixels continue to exhibit linear growth behavior before reaching saturation limits, in contrast to the non-linearity reported for non-dispersed bright point sources.

In this paper, we prove the strict Faber-Krahn inequality for non-negative-mass Dirac operators on simply connected domains with infinite-mass boundary condition. Denoting the first positive eigenvalue of the corresponding Dirac operator with mass $m\geq 0$ as $\lambda_1^{+}(\Omega;m)$, our main result shows that \begin{equation*} \lambda_1^{+}(\Omega;m)\geq \lambda_1^{+}(B_{|\Omega|};m), \end{equation*} where $B_{|\Omega|}$ is the disk with the same area as the domain $\Omega$, and the equality is strictly valid if and only if $\Omega=B_{|\Omega|}$. The key observation leading to the proof is that the upper component of the Dirac spinor associated with $\lambda_1^{+}(\Omega;m)$ is non-vanishing over $\Omega$, which is proved by exploiting its Dirac current and the associated stream function. Based on this global non-vanishing property, we construct a sphere-valued spinor map of degree one, which allows a sharp comparison with the radial disk profile using the planar isoperimetry.

We give an algorithm that samples uniformly random linear codes of any hull dimension and type over finite fields of odd characteristic, implying the first algorithm for sampling uniformly random self-orthogonal codes of any rate, including self-dual codes. Our algorithm is a re-visitation of the algorithm given by Albrecht, Benčina and Lai (EC'25), using the mass formulae proven by Li, Shi and Ling (IEEE Trans. Inf. Theory 71(1)). This allows us to instantiate code-based cryptographic schemes that rely on the hardness of Permutation Code Equivalence (PCE) on `random' self-dual codes for security and that were previously unable to sample them. Building on the observation by Bardet, Otmani and Saeed-Taha (ISIT'19) that Euclidean orthogonality is insufficient when considering PCE over finite extension fields due to non-trivial Galois automorphisms, we study the behaviour of what we call total orthogonality, that is orthogonality with respect to all induced Galois geometries simultaneously. We characterise total orthogonality of vectors and codes, and give an algorithm that samples linear codes with a total hull of a prescribed dimension; a subcode that acts as the hull in all Galois geometries of the ambient space. The algorithm incurs a rate decrease by a factor equal to the extension degree, however, we argue why this may be necessary in the context of PCE and explore how it limits the practicality of our algorithm. We consider the notion of Galois type of a linear code when Galois hulls are symmetric and show that all linear codes have constant Hermitian type.

Video gaze prediction is led by gaze-trained models, yet gaze-free priors carry signal those models have not absorbed, if one knows when to trust them. We propose FocusGate, a gated ensemble of gaze-free priors whose members may abstain. A per-frame gate reads three shape statistics of a defocus map and selects the frames on which the estimator is above chance on average, so rejected frames reduce to the base exactly, while midrank normalisation lets an all-zero prior abstain at zero parameters. Gated fusion is significantly positive on film, sports and web video, whereas unconditional fusion is harmful on sports and null on web. Added to four supervised predictors, the NTIRE 2026 champion among them, FocusGate improves all sixteen model-domain cells in shuffled AUC, fifteen significantly, one domain pre-registered and scored once, while adding only 1% to the champion's latency. Alone, it surpasses TASED-Net and UNISAL in shuffled AUC on film with a 16-frame causal mean.

As coding agents increasingly undertake real-world work autonomously, judging whether their risk treatments are warranted has become important. Existing work evaluates related agent behaviors from separate perspectives, but lacks a systematic framework for unifying these behaviors. To bridge this gap, we introduce ParanoiaEval, the first benchmark for unified evaluation of risk-treatment capabilities in coding agents. Grounded in the well-established Avoidance-Transfer-Mitigation-Acceptance framework in software engineering risk management, ParanoiaEval operationalizes its 4 fundamental treatments for coding-agent settings and contains 200 evidence-controlled repository-level task pairs, each differing only in treatment-defining evidence. We further introduce dedicated metrics for risk-treatment violations and evidence responsiveness, using a human-calibrated agentic judge for reliable evaluation. Large-scale experiments on 8 representative models and a post-hoc human study reveal that (I) unnecessary risk treatment occurs in 11.2%-58.7% of runs despite explicit evidence, with substantial variation across agent configurations; (II) stronger task capability does not ensure more appropriate risk treatment, while treatment violations substantially harm developers' experience, establishing risk treatment as an independent capability dimension; and (III) agents exhibit systematic patterns consistent with established risk-management findings, suggesting that knowledge from human practice can guide the diagnosis and improvement of this capability.

We show that distinct pure-strategy Nash equilibria typically have different utilitarian welfare values in sufficiently rich classes of $C^2$ games with open strategy sets. Here, typical means both generic and finitely prevalent, while rich means that the class admits a finite-dimensional family of perturbations that can independently move payoff values and first derivatives in any direction at any two distinct strategy profiles (for example, polynomial perturbations of degree at most three). Consequently, a welfare-maximizing equilibrium, if one exists, is unique. The result extends to each fixed $C^1$ payoff aggregator whose derivative with respect to the payoff vector is everywhere nonzero. In the full $C^2$ utility space, we also treat scalar criteria depending on strategies, payoffs, and payoff derivatives, subject to a nonvanishing condition in payoff-level or cross-player derivative directions. Finally, adjoining arbitrarily small perturbations from a suitable finite-dimensional space makes welfare separation typical in the augmented family, with separation holding for almost every perturbation of each fixed base game.

Background: Biomedical AI can generate plausible explanations without reliably verifying whether each statement is supported by patient-specific evidence. We developed a neuro-semantic verification framework that converts radiomic measurements into addressable evidence records and machine-checkable claims. Methods: UPenn-GBM radiomics were aligned with de novo CaPTk extraction from standardized MRI and expert-validated segmentations in an independent multicenter cohort. The shared space comprised 1,728 features from T1, T1GD, T2, and FLAIR MRI across three tumor regions. Reference-defined semantic states were derived from 611 UPenn cases. We evaluated cross-cohort transportability, model-linked provenance, deterministic verification, controlled predictive degradation, and an LLM claim-extraction pilot; MGMT prediction served only as a transport stress test. Results: Median semantic-state agreement was 0.786 (weighted kappa 0.709), ranging from 0.918 for morphologic to 0.252 for intensity features. The external evidence ledger contained 1,655 model-linked records for 331 patients. The verifier achieved 100% exact-set accuracy in a 6,620-claim corruption benchmark. In a 24-case pilot, GPT-5.6 Sol reproduced 72/72 prespecified atomic claims, and the frozen verifier recovered 24/24 expected conditions. During controlled degradation, ROC AUC declined from 0.899 to 0.500 while verification accuracy remained 1.000. External MGMT discrimination was weak (ROC AUC 0.543). Conclusions: Verifiability can be engineered and evaluated independently of predictive performance. LLMs may structure explanations, while final evidence-consistency checking remains deterministic.

Model merging provides a training-free way to transfer reasoning capabilities from language models to vision-language models (VLMs), but endpoint-based transfer can conflate pre-existing model differences with changes acquired during reasoning post-training. We instead formulate capability transfer around the training-stage update, isolating the parameter changes induced by reinforcement learning (RL). Yet transferring this update in full remains suboptimal: we find that its components differ substantially in cross-model transferability, with dominant directions transferring more effectively than the complete update. Based on this finding, we introduce Selective-RL, which isolates the RL-stage update, retains its dominant matrix-wise directions with magnitude preservation, and transfers them to the language modules of a VLM. Across three model families and five visual-reasoning benchmarks, Selective-RL improves full-update interpolation in 12 of 15 comparisons, including an 8.55 percentage-point MathVision gain on the Qwen recipient. Matched controls show that update magnitude or arbitrary low rank alone does not reproduce these gains. These results highlight a distinction between what is acquired during post-training and what remains transferable across models, providing a training-stage perspective on cross-model capability transfer. Code is available at https://anonymous.4open.science/r/selective-rl.

We establish a global large-data existence theory for the Bhatnagar–Gross–Krook equation in a slab with the physical collision frequency given by the local density. We consider both inflow and Maxwell boundary conditions and assume only finite mass, kinetic energy, and entropy of the initial data, together with the corresponding inflow flux bounds. The data need not be small or pointwise bounded, and we impose neither positive lower bounds on the density or temperature nor prescribed velocity moments above order two. To our knowledge, this is the first nonperturbative global existence result for this initial and boundary value problem under these assumptions. The central obstacle is the simultaneous loss of energy compactness and integrability of the unrenormalized collision operator. Finite energy alone does not give uniform integrability of the second velocity moment, while the density dependent collision frequency prevents separate local $L^1$ control of the gain and loss terms. We overcome these difficulties through a compensated estimate uniform in the truncation of the collision frequency, a de la Vallée Poussin weight determined by the data, and two successive renormalizations using entropy production. This yields the compactness of the macroscopic energy, local Maxwellians, and nonlinear collision term, and hence global renormalized solutions.

Multiscale, parameter-dependent partial differential equations (PDEs) pose severe computational challenges due to strong coefficient heterogeneity and high-dimensional parameter spaces. We develop a geometric interpolation approach within the multiscale generalized finite element method (MS-GFEM) that targets the most expensive component: computing parameter-dependent optimal local approximation spaces. Leveraging the spatial localization of MS-GFEM and assuming local parameter dependence, we decompose the global problem into parametrically low-dimensional local subproblems. The optimal subspaces for each parameter are identified as points on a Grassmann manifold and approximated via Grassmann interpolation on sparse grids, which preserves the geometric structure of these spaces while efficiently handling high-dimensional parameter spaces. The resulting localized model reduction method inherits the nearly exponential spatial convergence of MS-GFEM and the parametric convergence rates of sparse grids. Numerical experiments for elliptic problems confirm the theoretical convergence results.

Anisotropic Voronoi diagrams, in which each cell is the region first reached by an ellipse growing from its site, generate non-convex cells whose integral geometry can be described using Minkowski tensors of arbitrary order. In this work, we derive semi-analytical formulas for Minkowski tensors of arbitrary order of the 0th, 1st and 2nd kind for planar anisotropic Voronoi cells that are star convex at their nucleation point. The resulting formulas involve integrals of contact functions, which describe the cell boundary through a diffeomorphic transformation. This transformation renders the geometry amenable to analytical treatment, enabling us to obtain expressions for the desired Minkowski tensors. Although most of the integrals lack closed-form solutions, they can be efficiently approximated numerically once the contact function and its derivatives are known along the boundary of the cell of interest.

Let $S_E$ be the surface in Xiao's degree-four family identified by Polizzi as a smooth divisor in $E(3)$. Starting from Polizzi's branch model and Xiao's classification of the thirteen singular fibers, we derive the local spherical braids and their Picard–Lefschetz lifts, including the colored $3+3$ partitions at the seven reducible fibers. We identify the normalization of each bisection with $E/\{\pm1\}$ and its degree-two ruling map with the quotient by the involution induced by translation by a nonzero two-torsion point. We prove $\pi_1(S_E)\cong\mathbb Z^2$, compute the elementary-divisor-$4$ Albanese kernel of a regular genus-two fiber, and show that the six nonseparating Picard–Lefschetz transformations represent the six cusps of $\Gamma(4)$. We also prove that the natural product tori near an elliptic section are nullhomologous and cannot lower $b_1$ below $2$ by torus surgery. As a separate application of the degree-three monodromy, we give a twisted-double construction of an exotic $\mathbb CP^2\#7\overline{\mathbb CP}^{\,2}$.

We investigate how spatially uniform, time-modulated heating can be used to stabilize a thin liquid mirror in microgravity. Periodic heating generates oscillatory thermocapillary flows that suppress the instability associated with sustained heating, allowing the free surface to relax through the combined effects of thermal radiation, thermocapillary transport, and capillarity. Using multiple-scale analysis of a long-wave model, we derive the coupled surface-temperature evolution over many heating cycles. A subsequent linear stability analysis yields the stability criteria and decay times of individual surface modes. Numerical simulations validate the analytical predictions and demonstrate stabilization of meter-scale surface deformations over timescales of days.

Autonomous robots can increase uptime and reduce human exposure in Big Science facilities, but strong magnetic fields needed for their operation corrupt sensors and induce pose-dependent mechanical wrenches that destabilize robots and challenge conventional reactive controllers. This paper presents a control framework for modeling, estimating, and dynamically compensating for spatially varying magnetic wrenches acting on legged robots to improve robustness in these fields. We introduce a custom physics plugin for the MuJoCo simulator to model magnetic forces on rigid-body elements, alongside an inverse field-estimation framework to infer the latent magnetic field directly from quadruped dynamic responses and any number of sensor readings. Furthermore, we develop a Magnet-Aware Model Predictive Control (MPC) and Whole-Body Control (WBC) architecture that predicts and counteracts magnetic perturbations during locomotion to increase the range of magnetic fields in which the robot can operate. The effectiveness of the framework is validated through both simulation and physical hardware experiments. We show our method increases the the maximum rejectable disturbances from magnetic field in the force space by a factor of 2.5 and and between 1.6-2 times in torque space compared to a non-compensated system. Within the proposed magnetic field, this constitutes an increase in the area in which the robot can operate by 29,34% of which 10,84% would have previously caused an immediate collapse to non-compensated controllers.

Diffusion models are increasingly used as surrogates for expensive simulators in weather prediction, molecular dynamics, and materials design. In these models, computing the probability $p_0[E]$ of an event $E$ is difficult, especially when the event of interest is rare. A stable estimate using Monte Carlo becomes computationally intractable, requiring a growing sample size $\propto\!1/p_0[E]$ to compensate for an increasing rarity. In this paper, we present Diffusion rare event sampling with Sequential Monte Carlo (DireSMC), a sequential Monte Carlo scheme that guides a population of weighted samples towards the rare event, giving access not only to samples but also to a calibrated estimate of its probability. We set up our guidance using an analytical relaxation of the event set, allowing the method to easily extend to a wide range of user-defined rare events. We validate our method on a toy problem with analytical solutions and on a score-based climate emulator, where we obtain accurate rare-event probabilities on a range of rarities from $10^{-3}$ to $10^{-5}$, achieving net speed-ups of $9\times$ to $1413\times$ over Monte Carlo.

Software-engineering agents can enable people without formal software training to build systems they could not otherwise implement and simultaneously can produce more code than even experts can meaningfully inspect. In both cases, exhaustive code review is not reliable as the sole basis for human control. We report a case study of a production healthcare platform built through coding agents and governed by an operator without formal software-engineering training. Over time, its workflow grew into a human-led meta-agent system where one agent wrote code, other agents supervised and reviewed it, and project rules carried lessons forward. The operator found that tests, monitors and reviewing agents used to supervise the system were fallible. Some monitors measured proxies rather than outcomes, some audits failed silently, missing checks disappeared from reported results and one automated repair caused operational disruption. In this case, human control depended on keeping the intended outcome, the evidence used to judge it, the agents' permissions and the final human decision were all tied to the same underlying objective.

When learning probabilistic policies from human demonstrations, data-efficient learning and fast adaptations to new scenarios are key requirements. One popular way to achieve intuitive and reliable adaptations is through non-parametric, typically kernel-based, methods. However, existing solutions either fail to account for the geometry of manifolds common in robotics, limiting data efficiency, or, when geometry-aware, provide unreliable uncertainty estimates or require retraining to adapt. We propose a non-parametric approach leveraging geometric priors in scenarios of data scarcity and heteroscedastic uncertainties for probabilistic modeling. We utilize the method to formulate policies based on time or robot state, where non-separable diagonal kernels allow capturing uncertainty relations between degrees of freedom for same-sized in- and outputs. Fast updates, requiring less than 3 ms for a trajectory involving both position and orientation are possible through an optimized formulation. Our approach supports both manifold-valued input and manifold-valued output with large orientation changes. Using task parameterization, adaptation to different object poses is easily possible. We evaluate the approach on a set of toy examples and on real robot manipulation tasks both in autonomous execution and in shared control scenarios.

Video-language models are ranked by multiple-choice accuracy on frames from a uniform grid. The grid has two parameters, a rate and a phase, and benchmarks report only the rate. The phase moves answers: two deployed samplers differing only by a half-step phase offset answer 23.6% of questions differently while scoring within a point, and across four releases from two families shifting only the phase changes roughly one answer in five after controlling option order. PHASEFUSION decodes three offset grids and averages the option posteriors. The grids are the polyphase components of the dense grid. Fusion matches a 32-frame single pass in accuracy within a prespecified margin (logit-scored) and cuts the answers a half-step shift of all three grids changes from 18.2% to 10.1%. Option order, which changes only the presentation, is flagged instead by a one-pass answer margin. Report the phase convention with the budget, or marginalize it.

We investigate whether the high-energy nuclear recoil recently reported by LZ can probe dark matter (DM) whose relic abundance is set by coscattering, or conversion-driven freeze-out. We consider a singlet-doublet fermion DM model coupled to a light dark photon, in which the predominantly singlet-like DM state is separated from a more strongly interacting doublet-like state by a $\sim 100\,{\rm keV}$ mass splitting. In the small mixing regime, conversion into the doublet sector becomes the bottleneck controlling the relic abundance, realising coscattering, while the same small mixing would ordinarily suppress direct detection. A light dark photon enhances the endothermic transition $\chi_1 N\to\chi_2 N$, allowing the conversion-driven region to be probed by high-energy nuclear recoils. We find that for $m_{A'}=250~{\rm MeV}$ the LZ-sensitive region can cover essentially the full relic-compatible parameter space, including the dominantly conversion-driven regime. As the mediator mass is increased, the LZ sensitivity progressively shifts towards larger singlet-doublet mixing, reducing its overlap with the coscattering region. Combining the relic density and recoil requirements selects DM masses extending approximately from $750~{\rm GeV}$ to $1.6~{\rm TeV}$ for the mediator masses considered. The LZ recoil can therefore directly test the same interaction and physical parameters that dominantly set the DM relic abundance, providing a probe of the same conversion mechanism across vastly different cosmological epochs.

LLM-based agents solve complex multi-step tasks, but sequential execution incurs substantial latency. In principle, parallelizing work across multiple agents should yield near-linear speedups. Yet existing parallel multi-agent systems often run slower than a single-agent baseline. We attribute this gap to two hidden costs that parallel execution incurs but a serial agent avoids. First, there is a re-exploration cost: redundant effort spent by parallel workers reconstructing context that the orchestrator already possesses, such as prior decisions, that would otherwise be inherited implicitly in a serial execution. Second, there is an alignment cost: the overhead required to reconcile inconsistencies across independently generated outputs. We thus derive a principled decision criterion: a layer should be parallelized only when its critical-path cost, plus re-exploration and alignment overheads, is lower than the corresponding serial cost. While this criterion is naturally expressed in wall-clock time, we observe that LLMs are poorly calibrated when asked to estimate task duration. To address this, we instead measure cost in predicted output tokens, which we empirically find LLMs can estimate substantially more reliably than wall-clock time. Building on this token-based criterion, we propose SquidAgent. It estimates all token budgets in a single planning step, forks each worker directly from the orchestrator's session to eliminate re-exploration cost, and replaces post-hoc reconciliation with a pre-generated shared convention block that converts alignment into a bounded upfront cost. A deterministic scheduler then applies the criterion layer by layer. Empirically, SquidAgent achieves a 2.2$\times$ mean throughput improvement and a 2.6$\times$ mean wall-time speedup over Claude Code, and a 2.0$\times$ throughput improvement over the strongest multi-agent baseline.

This paper presents a model-free method for turbine repositioning control in floating offshore wind farms. The method uses a distributed online optimization framework to mitigate the wake effect. Conventional approaches rely on centralized, model-based control architectures, which suffer from poor practical feasibility. To overcome this limitation and address nonconvexity and inaccessible gradient information, we incorporate physics-informed knowledge of wake dynamics into the control system design. We demonstrate the effectiveness of the proposed method by comparing it with a centralized, model-based baseline in mid-fidelity simulations. Results indicate that the proposed method achieves slightly better performance while significantly reducing computational cost.

When optimizing computing architecture for specific computationally intensive tasks, such as evaluating or training a neural network, it is important to identify what computational subtasks will offer the greatest decrease in cost (e.g., wall clock time or energy usage). This problem is known as Hardware-Software (HS) Partitioning, and it has a variety of formulations, many of which are NP-Hard. In this paper, we will define a family of HS Partitioning formulations which admit an exact fixed parameter tractable algorithm based on the directed pathwidth of the given task graph and show that this family of problems contains multiple existing formulations such as makespan minimization. Finally, we examine task graphs with small directed pathwidth that arise in real world applications and show that our algorithm can provide a speed up of up to 200x over a comparable linear programming approach utilizing the Gurobi ILP Library.

We determine the complete relative isoperimetric profile of the three-dimensional unit cube and classify all minimizing sets, including the equality cases at both transition volumes. Up to cube isometries and complementation, the minimizers are corner eighth-balls, edge quarter-cylinders, and coordinate slabs, with transitions at $4\pi/81$ and $1/\pi$. Building on this classification, we prove that the perimeter deficit at each fixed volume controls the squared $L^1$ distance to the full minimizing family, with optimal exponent two. Near either transition, a uniform estimate combines the distance to each adjacent phase with its excess perimeter and identifies the linear degeneration, at neighboring volumes, of the best constant for distance to the actual minimizers. As consequences, we resolve the isoperimetric conjecture in Milman's formulation (Conjecture~1.1) for all cuboids $(0,\beta)\times(0,1)^2$, $0<\beta\leq1$, and the three-dimensional case of Brezis's Open Problem~10.1.

We prove a sharp $L^\infty$ bound for the density of an infinite convolution in terms of $L^2$ norms of convolution powers of the summand densities. The bound may be finite even when every summand density is unbounded and the products arising from Young's inequality diverge.

Contact with contaminated objects can spread hazards through a household robot's grippers, tools, and shared surfaces, while new contacts can make an existing plan unsafe. Existing benchmarks do not jointly assess how planners identify hygiene risks from contact history and plan safe continuations after new contact events. Planners must do so within time and resource limits while respecting user priorities. We introduce HygieneRoboBench, with 624 instances across 134 task families, to evaluate safe resolution of household tasks from a given execution history. Tasks capture contamination through two grippers and shared objects, treatment costs, and user priorities. We combine controlled history, profile, and event comparisons with independent plan evaluation. These assess safe resolution, cost efficiency under user priorities, and responses to contact events. Evaluation of LLM-based and symbolic planners shows that safely completing a task does not guarantee the lowest execution costs under the user's priorities. To address this problem, we introduce Hygiene-NSP. It combines LLM-based grounding, contact-history reconstruction, and CP-SAT to jointly plan hygiene treatment and task execution under user priorities. Hygiene-NSP achieves safe resolution and optimal safe resolution rates of 94.4% and 90.4%, respectively. Both rates are higher than those of the evaluated baseline planners on the full dataset. Project page: https://euron-zc.github.io/HygieneRoboBench/.

A comprehensive multi-satellite analysis of the dynamically confirmed black hole candidate GS 1354-64 during its highly active 2025-2026 outburst is presented. Leveraging simultaneous broadband spectroscopy, fast timing, and X-ray polarimetry, I map the evolution and geometry of the accretion flow. During the initial Compton-dominated hard state rise, strong, narrow Type-C quasi-periodic oscillations (QPOs) evolving from 0.08 Hz to 1.73 Hz with high fractional RMS (~8-10%) are detected, showing a strong anti-correlation with the inner disk radius (R_in) and a linear correlation with the coronal photon index (Gamma), supporting disk migration driving the precessional frequency while cooling the corona. An anomalous, highly ionized (Fe XXVI) equatorial disk wind is also observed, suggesting strong localized radiation pressure prior to the state transition. In the luminous, thermal-dominated soft state, individual-epoch reflection modeling indicated a rapidly spinning black hole (a* ~ 0.94-0.99) at inclination i ~ 45-53 deg; joint spectral modeling across these epochs refines this to i ~ 51 deg and a* ~ 0.998, with the disk pinned to the ISCO. The QPOs shifted to higher frequencies (~4.7-6.2 Hz) and weakened (RMS ~3-6%). Joint spectro-polarimetric modeling of this epoch reveals a steep, energy-increasing polarization degree, ruling out a spherical or lamppost geometry in favor of a highly asymmetric, radially extended slab-like corona. The suppression of the high-RMS QPO, combined with the strict energy-independence of the polarization angle, indicates the corona stabilized into an extended, symmetric slab, consistent with the collapse of the puffed-up spherical corona seen in the hard state.

Long-horizon urban navigation requires sequential local decisions whose errors can compound over time. Imitation learning (IL) rarely learns from failures, while physical trial-and-error reinforcement learning (RL) is costly. Action-conditioned world models can provide imagined feedback by predicting visual consequences for candidate actions. However, a frozen world model may become less reliable as the policy evolves. In this paper, we introduce RIWANAV, a post-training framework that casts the coupled adaptation of a world model and an action model (policy) as task-specific recursive self-improvement (RSI). Each cycle alternates two updates. The world model evaluates policy actions through imagined outcomes, providing comparative feedback for group-relative policy optimization (GRPO). The improved policy then constructs a grounded self-curriculum, selecting expert-consistent action-video pairs by behavioral novelty and prediction error. The refined world model supplies feedback for the next policy update, closing the recursive self-improvement loop. Experiments show that RIWANAV outperforms training baselines and prior methods, validating the proposed recursive self-improvement loop between the policy and world model. Real-world trials further demonstrate its practical applicability.