Papers

This paper establishes the existence of local martingale solutions for a three-dimensional stochastic fluid–structure interaction (FSI) problem coupling a viscous compressible isentropic fluid with an elastic shell through Navier-slip boundary conditions. The fluid and shell are perturbed by compatible Stratonovich transport noise. A stochastic-flow transformation removes the stochastic transport integrals and produces a pathwise random FSI system whose pullback coefficients are only Hölder continuous in time. We combine a multi-layer approximation scheme with localization on bounded-flow events and freezing of the random coefficients on short deterministic time subintervals. The shell transport fields are not required to generate isometries: the bending-energy martingale and Itô correction are controlled at the natural $H^2$ level by commutator identities without derivative loss. Tightness is obtained in Jakubowski spaces, pressure compactness is proved through localized effective viscous flux, and the final artificial-pressure and penalty limit uses boundary-pressure tightness and $H^2$-graph trace tools. For $\gamma>3/2$ and non-colliding initial data, we obtain a martingale solution up to an almost surely positive stopping time.

We prove that for all real numbers $\kappa,\tau$ with $\kappa>8\tau^2$ and $\tau\neq 0$, the Berger sphere $\mathbb{E}^3(\kappa,\tau)$ contains smooth closed embedded rotational surfaces of genus one with constant mean curvature which are contained in an open hemisphere. This disproves a conjecture of Fernández and Mira. The main result of this paper is obtained by generative AI, particularly GPT-5.6-sol, Fable 5, and the Danus system, and then verified by the authors.

Humanoid loco-manipulation faces two prominent limitations: controllers using continuous velocity commands cannot precisely regulate individual footholds, while specialized foothold-tracking modules are difficult to integrate with whole-body manipulation. Furthermore, standard action-based imitation distillation primarily transfers expert actions, without explicitly encouraging a shared representation of heterogeneous skills. This paper introduces STRIDER, a hierarchical multi-gait framework to bridge these gaps. The framework integrates terrain-aware 3D stepping logic, Adversarial Motion Priors (AMP)-based natural walking, and Cartesian upper-body control: its stepping expert selects feasible footholds in the stance-foot frame and generates clearance-aware swing trajectories. To fuse distinct walking and stepping experts into one executable student policy, we propose Latent Distillation Proximal Policy Optimization (LD-PPO), a distillation algorithm augmented with teacher-conditioned latent alignment. By jointly optimizing on-policy reinforcement learning, DAgger-based action reconstruction, and latent alignment, LD-PPO transfers expert actions while encouraging a shared skill representation across heterogeneous modes. Simulation and real-robot evaluations on the TianGong Omni humanoid show that LD-PPO outperforms vanilla distillation-PPO in foothold-tracking and posture-tracking accuracy. Deployed on hardware, STRIDER realizes multi-gait loco-manipulation with accurate foothold and end-effector tracking.

Background: During the navigation of Rosetta's first Earth flyby in 2005, a small yet unexplained asymptotic velocity increase was detected in the departing leg, necessitating inserting an artificial prograde delta-V at perigee in the orbit determination. Similar instances of this phenomenon have been observed in several missions. However, subsequent Rosetta Earth flybys did not exhibit this effect. Despite numerous investigations of the - so called Earth flyby anomaly - over the last decades, the underlying cause remains unresolved. Idea: To address the problem, we perform an Orbit Determination using ESOC's new system for Deep Space orbit determination, utilising the original radiometric tracking data and spacecraft model. This approach enables the incorporation of additional physical effects in the flight trajectory, with the aim of identifying the root cause of the anomaly. Results: We successfully reproduced the anomaly using the new orbit determination software. Subsequent analysis ruled out explanations involving Earth ephemeris errors, gravitational field modelling, relativistic contributions, and propagator configurations. Additional dynamical variations, such as the solar radiation pressure or albedo radiation, were evaluated but found insufficient to account for the observed discrepancy. Outlook: During investigations of Earth's albedo effect, a possible explanation for an artificial velocity increase was identified. Albedo-induced illumination on thermally sensitive spacecraft surfaces could have triggered outgassing, consistent in direction and magnitude with documented outgassing events during Rosetta's cruise phase. A detailed attitude analysis further strengthens this theory and provides conclusive results, also in comparison to Rosetta's other Earth flybys.

We study the nonlinear evolution equation $$ \partial_t u+(G+G^\delta)u=I_\alpha(|u|^\rho) \quad\text{on }\mathbb{R}^{N+k}, $$ where $G$ is the nonnegative self adjoint realization of Grushin operator, $0<\delta<1$, and $I_\alpha$ is the potential operator with kernel $|z|^{-\alpha}$, $0<\alpha<N+k$. We develop a well-posedness theory for initial data in Marcinkiewicz spaces, allowing singular profiles outside the corresponding Lebesgue spaces. Using spectral calculus, subordination, and interpolation, we establish Lebesgue and Lorentz smoothing estimates for the mixed semigroup $e^{-t(G+G^\delta)}$, which distinguish the second-order behaviour at short times from the fractional decay at large times. In the subcritical regime, considering $$ \frac1\beta=\frac2Q+1-\frac{\alpha}{d}, \qquad \frac1{\beta_\delta}=\frac{2\delta}{Q}+1-\frac{\alpha}{d}, $$ where $Q$ is homogenous dimension, we prove local existence, uniqueness, Lipschitz dependence on the initial data, and a blow-up alternative in $L^{p,\infty}$ when $$ \rho<1+\frac{p}{\beta}. $$ At the critical relation $\rho=1+p/\beta$, a Yamazaki-type estimate and Lorentz duality yield global mild solutions for sufficiently small data in $L^{p,\infty}$. In the supercritical regime $\rho>1+p/\beta$, well-posedness is recovered in higher-integrability Marcinkiewicz spaces $L^{q,\infty}$ satisfying $$ \beta(\rho-1)<q<\beta_\delta(\rho-1), $$ with global existence for sufficiently small initial data. In all cases, the solutions attain their initial data in the weak-$*$ sense. These results extend the Marcinkiewicz-space theory to mixed Grushin diffusion with a spatially nonlocal potential source and reveal the role of the two competing diffusion scales in determining the admissible integrability regimes.

The influence of photon fields of local sources (LS) on the formation of the cosmic ray (CR) energy spectrum (E0) is considered. A model for the formation of irregularities in the CR spectrum, based on the local source model, is proposed. It is shown that the CR spectrum can be formed as a sum of partial spectra formed near local CR sources during the passage of primary cosmic radiation (PCR) through the photon fields of the sources. Local sources can be the most active stars of various types of variability in the stellar population, - from dwarfs to hypergiants. Studies have shown that the so-called "bump" near E0 = 100 PeV is formed in the photon fields of Mira-type variable stars, which are typically multiple stellar systems, consisting of a red giant and a white dwarf.

Ambisonics Upscaling (AU) aims to enhance the spatial resolution of sound fields by estimating high-order Ambisonics (HOA) components from low-order observations. While deep learning and model-based strategies have been considered for AU, both approaches exhibit significant performance degradation in realistic scenarios, where reverberant sound fields violate the directional sparsity inherent to discriminative mappings. In this work, we address AU as a generative task rather than a deterministic reconstruction, expanding generative modeling to specifically target the recovery of spatial information in reverberant speech. We investigate two dominant continuous-time generative paradigms, adapting both Score-based Generative Model and Flow Matching to these complex acoustic settings. We provide an extensive numerical study comparing our methods against state-of-the-art baselines in various acoustic scenarios. Additionally, we conduct subjective listening tests to evaluate the perceived quality and spatial accuracy of the proposed generative framework across various reverberant scenarios. The studies reveal that Flow Matching consistently outperforms both its discriminative counterparts and Diffusion-based paradigms in all reverberant settings.

Latent action models infer a code for the transition between two frames of action-free video. Recent methods regularise this code to compose additively and reverse antisymmetrically, and report order-of-magnitude reductions in the resulting errors as a label-free certificate that the code has captured temporal structure. We show that this conclusion does not follow. Reconstruction drives the decoded transition toward a difference of state features, for which both identities hold for any pairing, a solution the metric cannot distinguish from one encoding nuisance state or a coordinate convention. Across five source domains, a trained but unconstrained counterpart already achieves 83-97% of the reduction relative to an untrained anchor. The residual fold is governed as much by the decoder family as by what is learned. A constrained model retrained after its temporal pairing is destroyed still reaches, in each domain, a lower error than the unconstrained model on real data. Downstream, preserving the temporal pairing yields no consistent advantage on LIBERO-GOAL or LIBERO-SPATIAL, and across the tested arms the code's mean linear action decodability falls as the algebraic error improves. We also test the most direct repair, a violation-contrastive objective that requires the algebra to fail on destroyed pairings: in the tested configurations it yields only a marginal separation within the reconstruction budget, on training and test triples alike. We recommend a validation protocol that these methods currently lack: a baseline-corrected metric, retraining on destroyed pairings, and a seed-budget analysis.

We propose that the $248\,\mathrm{keV}$ nuclear-recoil candidate reported by LUX–ZEPLIN can arise from the endothermic hyperfine excitation of composite dark matter. Rather than requiring two distinct dark-sector particles, the inelasticity of scattering arises from a hyperfine transition between the pseudoscalar and vector states of a single dark hadron. In a PQ-augmented dark QCD framework, the parity-conserving vacuum suppresses dangerous elastic scattering, while axion emission depletes the relic excited-state population. Endothermic excitation near the Galactic kinematic edge then naturally produces a localized high-energy recoil peak. We find that sub-TeV-scale dark matter with a hyperfine splitting of a few hundred keV can yield an order-one event rate in the LZ high-recoil window. This interpretation offers a possible form of dark-matter hyperfine spectroscopy, with complementary tests from dark-photon searches and future recoil-spectrum measurements.

A potential path forward is Quantum Machine Learning (QML), which aims to leverage quantum computing in conjunction with classical machine learning to enhance computing efficiency and the expressiveness of models. In this paper, two different quantum classifiers - Variational Quantum Classifier (VQC) and Quantum Kernel Support Vector Machine (QSVM) - are compared with three classical classifiers as baseline classifiers - Logistic Regression, Support Vector Machine (SVM), and a Multi-Layer Perceptron (MLP) - on the Breast Cancer Wisconsin dataset. The quantum circuits were created in the PennyLane framework and simulated on a classical backend. However, in terms of accuracy, classical Logistic Regression performed better with an accuracy of 97.8%, classical SVM and QSVM with an accuracy of 95.6% each, although the Quantum VQC achieved a lower accuracy of 88.9% and had a recall of 100% for the benign class, though it correctly identified only 12 of the 17 malignant cases (a malignant-class recall of approximately 70.6%). The drawback of quantum models is the higher training time; however, since the quantum circuit needs to be classically simulated, the quantum SVM took 23.29 seconds compared to less than 0.01 seconds for the classical linear models. These results indicate that for small structured datasets, classifiers based on quantum computing have not yet surpassed well-tuned classical counterparts. In some respects (e.g., benign-class recall), they perform competitively, though not on malignant-class recall, where the VQC in particular performed worse than the classical baselines, which is worth further investigation on real quantum computers.

The dark photon $A'$ is widely considered as the mediator of dark matter $\chi$. In the conventional non-resonance benchmark scenario with $m_{A'}/m_\chi=3$, the kinetic mixing $\epsilon$ required to match the observed dark matter relic density is typically ruled out by the combined constraints from the direct detection, indirect detection, collider, and other relevant experiments. However, if a delayed decay of the inflaton creates the low-temperature reheating, the additional entropy production dilutes the dark matter relic density. As a result, a significantly smaller $\epsilon$ becomes sufficient to match the observation, which allows the dark matter to escape the present multi-experimental bounds. In this paper, we investigate the dark matter production under the influence of a low reheating temperature $T_{\rm rh}$ within the dark photon $A^\prime$ portal framework, where $A^\prime$ mediates the interaction between dark matter $\chi$ and the SM particles. We systematically explore the viable and promising parameter space for complex scalar, Dirac, and Majorana fermion dark matter under the combined experimental constraints, and compare the distinctions among these three scenarios.

We provide a complete algebraic characterization of homogeneous self-affine measures whose Fourier transform does not tend to $0$ at infinity. Moreover, we prove that an integral self-affine measure has power Fourier decay if and only if it is absolutely continuous. For a given integral affine IFS, we also provide an algorithm for determining those probability vectors for which the associated self-affine measure is absolutely continuous.

Evaluating treatment effects in clinical trials with time-to-event outcomes is complicated by intercurrent events (ICEs), e.g., treatment discontinuation or competing events. While the ICH E9 (R1) addendum outlines five strategies to address these challenges, accessible software implementing these methods is limited. This article introduces the \pkg{tteICE} package for \proglang{R}, which implements five strategies to facilitate valid causal inference in the presence of ICEs. \pkg{tteICE} enables researchers to either nonparametrically or semiparametrically efficiently estimate potential cumulative incidence functions under both treatment and control conditions. The treatment effect is assessed by contrasting these functions, with statistical uncertainty quantified using pointwise confidence intervals and $p$-values. The package supports data from randomized controlled trials and observational studies, including settings with competing risks and semi-competing risks. To reduce barriers for applied researchers, \pkg{tteICE} features integrated plotting functions and an accompanying interactive Shiny application that provides a user-friendly graphical interface with step-by-step instructions.

We identify a directional tangency mechanism responsible for anomalous far-field decay in Schrödinger equations. For constant-coefficient operators, we introduce a directional decomposition of the limiting resolvent based on the geometry of the Fermi surface and the observation direction. In two dimensions, we show that an analytic source produces a super-algebraically small tangency contribution, whereas a transverse non-analyticity located on the directional tangency set generates an algebraic contribution of order \(R^{-(2\alpha+1)}\). Shifting the singularity away from the tangency set restores super-algebraic decay, showing that geometric alignment is essential to the anomalous behavior. We further construct a bounded, decaying real-valued potential for which the same mechanism occurs in the first Born correction through the effective source \(Vu_0\). In a suitable long-range regime, the resulting tangency contribution decays more slowly than the conventional two-dimensional far-field term.

A Yau-type gradient estimate is proved for positive $p$-harmonic functions on complete Riemannian manifolds with compact boundary, under a Ricci lower bound on the Riemannian manifold and a mean curvature lower bound on the boundary, assuming the Dirichlet condition and a sign condition on the outward normal derivative. The result extends the estimate for harmonic functions by Kunikawa and Sakurai to the full range of $p$-Laplace operators and yields a Liouville theorem when the curvature hypotheses are nonnegative. The cutoff method of the linear theory does not extend when the exponent differs from two, since it requires a directional Hessian of the distance to the boundary that Laplacian comparison cannot control. That cutoff is replaced here by a radial barrier at the boundary and an intrinsic maximum principle in the interior.

For connected closed Lagrangian submanifolds of the homogeneous nearly Kähler sphere $\mathbb S^6(1)$, we first establish a new integral inequality. Then, as applications we prove sharp pinching theorems for the scalar curvature $\tau$ and Ricci curvature Ric, respectively: $\tau \ge \tfrac{23}{8}$ implies either $\tau=6$ with it totally geodesic, or $\tau=\tfrac{23}{8}$ with it congruent to the embedded Berger sphere of Dillen–Verstraelen–Vrancken; whereas ${\rm Ric}\geq\frac18$ implies that the submanifold is either totally geodesic, or has constant sectional curvature $K=\tfrac{1}{16}$, or is congruent to the embedded Berger sphere of Dillen-Verstraelen-Vrancken.

Using N. Honda's construction of twistor spaces, bimeromorphic invarince of $\partial\bar\partial$-lemma for threefolds and embedded resolution, we find a smooth compact complex threefold satisfying the $\partial\bar\partial$-lemma that contains a smooth compact surface for which the lemma fails. This disproves heredity in the smallest possible ambient dimension and yields counterexamples to L. Alessandrini's modification question in every complex dimension at least four. We establish a derived blow-up formula for generalized Bott–Chern complexes with coefficients, compatible with the comparison maps to coefficient cohomology. We also obtain a Dolbeault blow-up formula with bounded derived coefficients. For compact complex manifolds, we introduce a relative $\partial\bar\partial$-property, characterize it using the Frölicher spectral sequence and Hodge filtrations, and prove a blow-up criterion. Finally, counterexamples show the limitations of the classical formulae for coherent coefficients and singular ambient spaces, and the failure of the naive Bott–Chern Künneth formula.

We study exact sign recovery for PCA connectivity analysis in mixture models, using the projection onto the first $(K-1)$ principal components. For any fixed number of components with affinely independent means, we derive the oracle signal projection explicitly. Under anisotropic sub-Gaussian noise, with a random number of observations in each component, a rowwise eigenspace bound yields a sufficient condition, governed by the weakest signal direction, for recovering all connectivity signs without requiring a bounded condition number of the nonzero signal spectrum. Under isotropic Gaussian noise, when the configuration of the component means is fixed up to scaling and orthogonal transformations, we identify an asymptotically sharp threshold for the signal strength: exact sign recovery succeeds above the threshold and fails below the threshold, with probability tending to one when the signal strength stays a fixed relative distance from the threshold. The threshold has an explicit formula when the mixing proportions are equal and the means form a regular simplex.

We establish a resolvent factorization of the hyperbolic projection associated with the finite-range dual operators, by a kernel with exponential off-diagonal decay. As an application, we prove that, for every irrational frequency and every analytic potential, each subcritical Type I energy satisfying the gap-labelling condition is an endpoint of an open spectral gap. This confirms the conjecture of Ge–Jitomirskaya–You [GJY,You] in the subcritical regime.

Long-running LLM agents require memory that persists and evolves across sessions. Text-based memory retrieves and reconstructs past interactions at every query, making long-horizon performance increasingly dependent on retrieval quality and contextual reasoning as histories grow. Parametric memory encodes experience directly into model computation, but existing approaches provide limited support for cross-session memory evolution. Their coupling to a specific backbone further restricts memory reuse after model replacement. We introduce RPMem, a two-stage architecture that compiles each session into a model-independent latent memory through forward computation and selectively integrates it with retained memory via a task-trained recurrent gate. The consolidated memory is then mapped to backbone-specific low-rank adaptation (LoRA) parameters, allowing the encoding capability to transfer when the backbone is replaced. Evaluation across three long-term memory benchmarks and five diverse backbones demonstrates broad generalization with near-constant update cost and memory footprint. With Qwen3-8B on PERMA, RPMem reaches 85.52%, outperforming the strongest parametric and text-based baselines by 5.32 and 12.98 percentage points, respectively. Ablations validate the complementary roles of session compilation and cross-session consolidation, while dynamics analyses reveal that the gate acquires task-specific memory integration strategies. These results establish RPMem as a lifecycle-independent parametric memory framework that maintains evolving cross-session memory that remains reusable across backbone replacements. Our implementation is available at https://github.com/Quark-Medical/rpmem/tree/main.

Memory enables language model agents to use information beyond their context windows, but maintaining and accessing this information reliably remains difficult. Long-horizon conversational memory is especially challenging in multi-actor settings, where relevant evidence is distributed across participants and contexts, and previously established information may later be revised. We introduce EGMEMORY, a training-free agentic memory framework centered on evidence chains that preserve message-level evidence and provenance while tracking active states and their revision histories. At write time, adaptive memory inspection and an evidence-grounded propose-verify-commit protocol govern state updates. At read time, adaptive evidence navigation iteratively identifies the state and supporting evidence required for a query, using conversational structure to narrow the search space and lexical-semantic relevance to rank candidates. The system operates through prompting and tool use without memory-specific policy training. EGMEMORY achieves 68.2% on GroupMemBench and 77.9% on EverMemBench, outperforming the strongest evaluated baselines by 22.7 and 21.4 percentage points, respectively. It further reaches 73.6% on the dyadic LoCoMo benchmark, supporting its applicability beyond multi-actor conversations.

Given any norm $\|\cdot\|_{\mathbb R^2}$ on $\mathbb R^2$, we prove that the Lagrange spectrum for $2$-vectors contains a Hall ray. Equivalently, every sufficiently small $\rho\ge0$ occurs as $\liminf_{q\to\infty}q^{1/2}\min_{p\in\mathbb Z^2}\|qx-p\|_{\mathbb R^2} $ for some $x\in\mathbb R^2\setminus\mathbb Q^2$. Combined with a recent result of Kleinbock \cite{Kleinbock}, this implies that the $2$-dimensional Lagrange spectrum is either a ray, mirroring the behavior for Dirichlet spectra, or a ray preceded by a dense part.

Federated learning lets multiple parties train a shared model without pooling their data, but a client with far less data than the others can end up poorly served even when the group's average accuracy looks fine. We ask whether the choice of pretrained backbone affects this under LoRA fine-tuning, and whether per-word perplexity on the target text predicts which backbone helps the worst-off client before federated training starts. We ran 313 experiments across three text-classification datasets and three similarly sized backbones (RoBERTa, BERTweet, PubMedBERT), each compared against a task-specific baseline on identical data splits. Lower-perplexity backbones consistently produced larger gains for the worst-performing client, with a rank correlation of -0.87 across nine dataset-backbone pairs; a backbone held out of the analysis confirmed the pattern. Personalization with Ditto recovered only 4-12% of the gap between training alone and full federation, and removing aggregation entirely erased the benefit. A client's update also showed no sign of conflicting with the group's update; the two are close to orthogonal, ruling out one proposed explanation for this failure. Practically: measure perplexity on a sample of task text before choosing a backbone, and do not rely on personalization to protect a data-poor client. We release our code, predictions, and full results for others to test.

Non-verbal vocalizations (NVVs) carry important paralinguistic information but are often omitted by conventional automatic speech recognition (ASR) systems. The ISCSLP NVVSpeech Challenge requires joint transcription of lexical content and 16 NVV categories under limited and highly imbalanced supervision. We present a data-centric NVV-aware ASR pipeline based on cross-dataset label harmonization and a two-stage sampling schedule. We map heterogeneous source labels to the official taxonomy and exclude samples without a reliable mapping. Our schedule first uses square-root category sampling to moderate the long-tailed distribution and then applies uniform-category fine-tuning. On a fixed local validation split, square-root category sampling performs best among the tested single-stage settings. The final two-stage system obtains an official score of 63.86 and ranks fourth in Track 1.

Two-dimensional irregular bin packing combines combinatorial bin-assignment decisions with difficult geometric feasibility constraints, making exact optimization challenging. This paper develops an exact combinatorial Benders decomposition framework for the two-dimensional irregular bin packing problem with convex polygons, coupling a pattern-based master problem with an exact single-bin geometric feasibility oracle. The dynamically strengthened Benders master is solved by a tailored exact branch-and-price procedure that incorporates objective-layered search and adaptive exact pricing. Geometric information obtained from the oracle is further fed back to the master and pricing processes through dynamically generated Benders feasibility cuts, which progressively restrict the subsequent pricing problems. Computational experiments are conducted on 540 benchmark instances from 18 classes. The proposed method obtains the optimal solution for 318 instances across 12 classes within a 3600-second time limit. On these classes, the proposed method solves more instances than a direct mixed-integer programming formulation and a baseline combinatorial Benders decomposition approach.

Deep learning has advanced automated electrocardiogram (ECG) diagnosis, but the field's most accurate models, foundation models pretrained on millions of recordings, are not decision-pathway auditable: a clinician cannot trace a diagnosis to a physiological pathway or intervene on one. We propose TRACE, a Tractable Routing Autoencoder for Clinical ECG, whose 32-dimensional clinical latent space is specified in advance from domain knowledge rather than discovered by optimization. TRACE partitions this space into perfusion, structure, and conduction subspaces, routes each to its own diagnostic head by design, regularizes the partition with an orthogonality penalty, and reconstructs the ECG through a decoder that permits latent perturbation. On PTB-XL and Georgia, TRACE exceeds unconstrained classifiers and stays ahead of an ECG foundation model pretrained on ten million recordings, evaluated by linear probe on frozen features, at roughly an eighth of the parameter count. On the nine-label CPSC2018 cohort, which carries no structural class, the framework transfers with only the routing table re-specified to a perfusion/rhythm/conduction partition. Joint probe, erasure, and perturbation analyses verify the routing contract, and perturbing the depolarization and repolarization pathways modulates the reconstructed waveform. Removing the specified partition and its orthogonality penalty costs 1.70 AUC and 11.30 macro-F1 points on PTB-XL, and 2.76 AUC and 16.92 macro-F1 points on Georgia. A capacity-matched permutation control places arbitrary assignments within 0.34 AUC points of the ontology routing and leaves macro-F1 statistically level (p=0.619): the ontology supplies decision-pathway auditability at no macro-F1 cost.

Quantum teleportation and Bell measurements are considered in a noisy relay setting. We introduce two quantum relay-channel models with closed-form capacity formulas, motivated by the canonical quantum communication protocols of teleportation and superdense coding. In both models, the sender transmits a qubit, while the relay observes side information about the Pauli errors that occur in the channel and communicates with the receiver through an orthogonal rate-limited link. We develop a compress-forward coding scheme in which the relay compresses the Pauli-error sequence into bins and sends the bin index to the receiver. The receiver uses this partial error information to reduce the effective channel noise before quantum decoding. We show that this strategy is optimal by establishing matching converse bounds for both models.

For a fixed integer $r\geq4$, the $K_r-e$-free graph sandwich problem asks whether, given graphs $G_1\subseteq G_2$ on the same vertex set, there is an induced-$K_r-e$-free graph $H$ between them. We give a deterministic algorithm taking $O(n+\alpha(G_2)^{r-3}m_2)$ time and space, where $m_2=|E(G_2)|$ and $\alpha(G_2)$ is the arboricity of $G_2$. In particular, the diamond-free case takes $O(n+\alpha(G_2)m_2)$ time. This improves the direct $O(n^r m_2)$ implementation of the previously known forced-edge closure. Our implementation maintains components of common neighborhoods indexed by $(r-3)$-cliques. A filtered frontier supports their merges within the clique-listing bound, while completion events avoid repeatedly searching for affected cliques. On feasible instances the output is contained in every feasible sandwich, independently of processing order. Applying the closure to $(G,K_n)$ gives an $O(n^{r-1})$-time bound for partitioned and nonpartitioned probe $K_r-e$-free recognition, improving the $O(n^{r+2})$ bound obtained from the direct sandwich closure. We also describe a direct static recognizer based on the same local characterization.

Reinforcement Learning with Verifiable Rewards (RLVR) is expanding from tasks with well-defined correctness signals, such as mathematics and code, toward multifaceted quality requirements specified by multi-dimensional rubrics. Since policy optimization consumes one scalar per rollout, rubric-based pipelines must map multiple criterion scores into a scalar reward. This aggregation is often treated as score scaling, but it implicitly determines how quality dimensions trade off during training. The prevailing practice, normalizing each criterion and taking a linear combination, assumes that cardinal score differences are comparable across criteria and that gains on one criterion compensate for failures on another; both assumptions are unreliable when criteria are semantically heterogeneous. We propose Reinforcement Learning with Verifiable Rubric-based Ranking (RLVR$^2$), a verifiable ranking paradigm for rubric-based RLVR. For each criterion, RLVR$^2$ converts rubric scores into criterion-specific within-group ordinal outcomes, recovers a latent utility from the resulting comparison matrix, and merges these utilities into one training signal. By retaining only within-group ordering and discarding raw score magnitudes, RLVR$^2$ avoids calibrating heterogeneous rubric scales. It further supports objective-preserving attribute adjustment: auxiliary attributes that correlate with observed rankings but are not training objectives can enter the estimation without expanding the rubric or rewarding them directly. Across three model scales and 16 benchmarks, RLVR$^2$ consistently outperforms representative rubric-based baselines, achieving the best overall performance on most benchmarks at every scale. Analysis shows it controls systematic effects tied to reasoning efficiency and response formatting while preserving the quality objective.

High-precision positioning using the global navigation satellite system (GNSS) embedded in smartphones is demanded for sidewalk-level pedestrian navigation and pinpoint location-based applications. However, current smartphone positioning accuracy for pedestrians remains at the meter level. This is mainly because limitations of the compact linearly polarized (LP) antenna in smartphones increase GNSS observation noise and hinder stable carrier phase tracking. In this paper, we propose an external GNSS signal re-radiation system that boosts smartphone GNSS observation quality while still using the smartphone's built-in GNSS receiver and antenna. The system directly connects a compact active helical antenna and a thin passive patch antenna for re-radiation, and is designed to be attached directly to the smartphone. The proposed GNSS booster achieves (1) reduced thermal noise and stable signal tracking via increased received signal strength, (2) improved multipath robustness compared with a LP antenna, and (3) stabilization of antenna phase center variation. Static experiments confirm a substantial improvement in the observation quality of GNSS carrier phase measurements compared with standard smartphone positioning. Furthermore, in pedestrian experiments, the proposed booster enabled stable carrier phase integer ambiguity resolutions, achieving centimeter-level positioning using a smartphone.