Papers

Grasping is a fundamental robotic capability that bridges perception and physical task execution. This paper studies grasp pose recovery under a perception-to-execution mismatch, where a grasp generated from visual perception may become spatially stale if the object moves before execution, using only sparse tactile interactions and no further visual observations. We propose DA-GRD, Decision-Aware Grasp-Relevant Disambiguation, which maintains a weighted planar belief over possible object configurations and selects tactile probes according to their ability to eliminate hypotheses and improve agreement among candidate task grasps. Rather than fully relocalizing the object, DA-GRD stops when the remaining hypotheses support a common executable grasp. In MuJoCo experiments on ten rigid objects with translations up to 5~cm and yaw perturbations up to $\pm45^\circ$, DA-GRD achieves an 84.7% physical lift success rate, compared with 9.1% for stale AnyGrasp, 21.2% for the original fix-scan baseline, and 63.7% for fix-scan method adapted with an SE(2) belief. DA-GRD also achieves a 57.3% Task conditioned Success rate. Across objects, it uses a success-average of 4.13 tactile probes over the ten per-object means, corresponding to a 72.5% reduction relative to the fixed 15-probe baselines. Real-world experiments on six objects achieve 71.7% physical lift success and 38.3% task-conditioned success with 4.20 probes on average. These results show that tactile sensing can recover task-relevant grasps under vision-off conditions with limited physical interaction, without requiring complete object localization.

The proliferation of photorealistic AI-generated images demands robust detection methods that generalize across diverse generative models. While existing approaches target manipulation-based forgeries with local artifacts, generation-based images (e.g., from diffusion models) lack such traces, posing a fundamental challenge. We observe that generative models prioritize global semantics at the expense of local texture fidelity, making low-texture regions key indicators of synthetic origin. To exploit this, we propose EIB-Net, an Entropy-guided Information Bottleneck Network. EIB-Net introduces a novel Image Entropy (IE) metric to automatically select the most informative (lowest-entropy) patch, then processes it with a Variational Information Bottleneck (VIB) to learn compact, generalizable features. Extensive experiments on DIFF, DiffusionForensics, and GenImage benchmarks demonstrate state-of-the-art performance: EIB-Net achieves 85.7% accuracy using only 2% of training data, outperforming full-image baselines by over 15%, and maintains robust cross-generator generalization (83.5% average accuracy on GenImage). Furthermore, our entropy-guided patch selection (EGPL) consistently enhances diverse backbones (CNNs and Transformers), proving its practical value for data-efficient detection.

Human-robot interaction (HRI) claims that people form attachments and social bonds with artificial agents, yet the terms are often applied without the behavioural and physiological criteria that give them content in their source disciplines. Without this empirical grounding, studies deploy widely divergent methods, frequently producing expansive relational claims that far outstrip their underlying evidence. To address this, we propose a standardised four-question procedure, grounded in criteria established in the developmental, ethological, and neuroendocrine literatures, that classifies a given human-robot tie as an attachment, an affective social bond, or no relationship, with intermediate classifications when evidence is incomplete. We specify minimum evidential requirements for each question, and provide candidate HRI study designs, adapted from validated human-human, human-animal, and animal-animal paradigms. We then demonstrate the procedure by applying it to a representative set of published HRI studies, showing how often relational claims outstrip what the reported designs can establish. Finally, we discuss the ethical and regulatory burdens created when artificial agents engage human biobehavioural systems. By replacing the divergent operationalisations with a unified, criterion-based classification, this paper gives HRI practitioners a standardised basis for evaluating, classifying, and comparing human-robot relationships, and sets out the experimental rigour that each classification demands. We therefore call on researchers of human-robot relationships to adopt such rigour, or to consider alternative terminology in their descriptions of these ties.

We study the quasinormal mode spectrum and wave-scattering properties of the four-dimensional rational regular black hole recently obtained in non-polynomial (quasi-topological) gravity. Using third-order WKB together with two independent cross-checks a Frobenius–Riccati shooting method and a time-domain evolution we compute the fundamental scalar, electromagnetic, and axial gravitational-type quasinormal frequencies, validating our approach against known Schwarzschild results. We find that as the geometry approaches extremality, its dimensionless ringing frequency is systematically suppressed relative to the Schwarzschild value, a direct and quantifiable imprint of the non-polynomial regularization that we trace, via the photon-sphere correspondence, to the response of the effective potential near the horizon. A Fisher-matrix estimate indicates that this suppression could in principle be resolved by a space-based detector such as LISA for a sufficiently massive and nearby source. We further compute, for the first time, the axial gravitational-type ringdown spectrum of this geometry using the Regge–Wheeler master equation, while noting that a full stability analysis of the underlying gravity theory remains an open problem requiring the linearized field equations of the modified action. Finally, we examine the greybody transmission factors across spins $s=0,1,2$ and show that they follow the same systematic ordering and near-extremal enhancement as the ringing-frequency suppression, pointing to a common physical origin. Together, these results give one of the first quantitative characterizations of the observational signatures and the remaining open theoretical questions of a regular black hole in modified gravity.

Automation systems must adapt to changing tasks, equipment states, and staffing conditions while providing evidence for human review. This study presents an intent-review framework integrating large language models, digital twins, and human decision-making, implemented for multi-line task adjustment. A Propose-Verify-Decide workflow translates operator intent into structured requirements, generates a bounded set of candidate strategies, and checks semantics, simulation execution, and operational constraints. Linked records preserve traceability from requests to verification evidence and decisions. Thirty fixed test records were evaluated using four virtual surgical-instrument sorting lines: 28 assessed the workflow and two assessed model generation. Eighteen workflow cases met expectations (64.29%); three of ten strategy-workflow requests completed autonomously (30%); and seven of eight invalid inputs were correctly intercepted (87.5%). Analysis by anomaly source showed that the framework rejected two candidate batches that failed throughput constraints and paused recommendations in two cases with incomplete evidence. A mistranslated priority rule nevertheless reached simulation. These findings demonstrate handling of specific invalid inputs, throughput violations, and evidence gaps, and identify consistency between original intent and execution specifications as a key improvement area. The effect on overall erroneous decisions remains to be evaluated through matched comparisons, together with the influence of digital-twin fidelity using independent physical references.

Transformers achieve remarkable performance by jointly learning broad families of tasks during pretraining and adapting to unseen tasks from only a short prompt. Yet a rigorous mathematical and statistical understanding of this phenomenon remains limited. This paper aims to study how Transformers exploit shared cross-task structure and how this structure affects the sample complexity of in-context learning (ICL). Specifically, we characterize task-space complexity through covering numbers under a prescribed metric, thereby quantifying the low-dimensional cross-task structure without requiring an explicit parametric representation. The resulting cover provides a set of anchor functions, which we use to introduce a task-identification-and-evaluation procedure: context observations localize an unseen task among the anchor functions, and the response at a query is predicted by aggregating the corresponding anchor function query evaluations. For approximation, we explicitly construct a Transformer with Softmax attention to approximate this procedure. For generalization, we derive an error bound that separates the effects of the number of pretraining tasks and the prompt length. The scaling with respect to the number of pretraining tasks is governed by the intrinsic dimensions of the task space and input domain; once sufficiently many tasks are available, the dependence on the prompt context length becomes dimension-free. To the best of our knowledge, this is the first work to quantify cross-task complexity for general nonlinear task families and explicitly construct a Transformer that exploits their low-dimensional structure to perform ICL. Our theory provides a quantitative explanation of how joint pretraining across related tasks improves in-context generalization.

This paper studies the time optimal control problem for the heat equation with singular inverse-square potentials under the Hardy critical condition. We first establish an observability inequality for the singular parabolic equation from general space-time measurable sets of positive Lebesgue measure. Rather than depending on the still-unknown Lebeau-Robbiano spectral inequality for the underlying singular operator, our proof combines Carleman-based observability results over open cylinders, real-analyticity estimates of solutions away from the singular origin, propagation of smallness estimates for real-analytic functions, and a telescoping-series technique. Using this observability result, we derive the null-controllability with controls supported on measurable subsets. Finally, we prove that the corresponding time optimal control is unique and obeys the bang-bang property almost everywhere over the control domain.

Links in projective space $\mathbb{R}P^3$ can be represented by diagrams in $\mathbb{R}P^2$ where the projective plane $\mathbb{R}P^2$ is represented by a disk with antipodal identifications on the boundary. In this context if we place an $n-$strand braid $\beta$ on this disk keeping its end points on the boundary then due to the identification of antipodal points it naturally represents a link diagram in $\mathbb{R}P^3$. We call this the projective closure of the braid $\beta$. In this paper we show that not all links in $\mathbb{R}P^3$ possess a diagram represented by projective closure of some braid.

This research establishes a connection between macroscopic urban commuting flows and thermal equilibrium. Using mobility data from around 30 million records across six Japanese cities over one year, we introduce the Gravity-based Home Swapping Model (GHSM). This model applies Metropolis dynamics to urban commuting by treating individuals as interacting particles. Within this framework, total commuting time dictates the system energy, and temperature controls how strongly mobility responds to cost savings. Consequently, urban commuting can be analyzed through an evaluable free energy and simulated similarly to physical systems of matter. The maximumentropy doubly constrained gravity model serves as the stationary state. We find that the residential dynamics exhibit glassy characteristics. Through calibration to observed data, we reveal that the system demonstrates signatures of kinetically constrained models, specifically ageing, hysteresis, and freezing near equilibrium. Simulations initialized from arbitrary states converge to empirical origin-destination matrices. This demonstrates that minimal physical mechanisms can reconstruct complex urban realities.

Emotion dynamics are critical for understanding crisis-support conversations, yet most computational work treats emotion as static utterance-level labels. We introduce EMPATH, a framework for understanding affective dynamics in mental health dialogues across three granularities: turn-level labels, transition probabilities, and global conversation archetypes. Applying EMPATH to text-based crisis conversations with self-identified Black texters discussing grief, we find persistent negative affect, gradual hope-ward transitions, distinct texter-volunteer emotional roles, and heterogeneous recovery trajectories. These results highlight the informative patterns that emerge from computationally understanding crisis support and expressions of grief as dynamic processes within conversations, as well as the overall value of emotion-dynamic analysis for analyzing and comparing affect in dialogues.

Several hundreds of gravitational wave events have been detected. They are good tools to investigate various fundamental problems, including tests of general relativity (GR) theory. Among the GR test schemes based on gravitational wave data, the parameterized scheme has been extensively studied by many groups including the LIGO-VIRGO-KAGRA collaboration (LVK). Existing results indicate that the deviation parameters from GR are small. In the current paper, we would like to estimate whether these deviation parameters are small enough to confirm GR. We transform the deviation parameters into mass–mass relations and, by comparing the resulting mass–mass relations from different parameters, we can estimate the probabilities that the data favor the GR theory. Applying our null test scheme to five O1/O2 binary black hole events, we find some GR deviation signatures but they are not conclusive yet. We also find no monotonic correlation between the network SNR and the strength of GR deviation, suggesting that the observed tensions are not simply driven by signal strength. Our null test scheme can be easily generalized and applied to all gravitational wave observation data.

The Zero Forcing (or corruption) of a graph is the problem of finding a minimum-size “corrupting” set. It corresponds to a subset of its vertices that can corrupt the whole graph by iterating the following rule: if a corrupted vertex has exactly one neighbor that is not yet corrupted, the neighbor gets corrupted. The iteration of this process comes from the fact that the corruption of a vertex might enable new corruptions (from itself or some of its neighbors). For this reason, one can consider a step of corruption, where all the possible instances of the corruption rule are applied at once. This paper investigates Zero Forcing on temporal graphs, where the topology of the graph evolves throughout the experiment. At each time step (or snapshot) of the graph, a step of corruption is resolved wherever possible. We study the problem of finding a minimum-size corrupting set such that the whole (temporal) graph is corrupted at the end of the experiment. We present a panorama of results, including NP-hardness in some not-so-restrictive scenarios, polynomial algorithms, and a solution to an open question when the whole graph must be corrupted in a single step.

Spatial correlations can suppress scattering in disordered chains and produce perfectly transmitting resonances. The practical value of this protection, however, depends not on the resonance peak itself but on the width of the surrounding transmission window and its sensitivity to local ordering errors. We show that a resonance can remain exactly transparent at its center while arbitrarily rare adjacent-swap errors restore an inverse localization length proportional to the square of the energy detuning. For lossless single-channel chains assembled from independent blocks of fixed length and composition, this positive quadratic term is guaranteed by a local scattering invariant and holds for every arrangement and every fixed swap probability between zero and one. With exact tuning and matched contacts, the central transmission remains unity. A microscopic quantum chain exhibits both higher-order suppression of scattering in the ideal recursive arrangement and the predicted response to local exchanges. These results reveal a limitation of spatial ordering that is invisible to a measurement at the resonance alone: spatial ordering protects the resonance peak, not the transport around it. The effect can therefore be tested experimentally by measuring transmission spectra before and after exchanges, without identifying microscopic defects.

Supplying a released predator with additional, non reproducing food is a standard lever in augmentative biological control, with a known drawback with nothing limiting the predators own numbers, the extra food lets its population grow without bound. Competition among the predators supplies the missing brake. Howthis self limitation reshapes the spatial arrangement of the two species has not been asked. We address it with a reaction diffusion model of a logistically growing prey and a predator feeding through a Holling type II response that also draws on additional food , the predators competing among themselves at strength. In the well mixed setting we locate the Hopf bifurcation of the coexistence state exactly and show the cycle born there is stable, so weak competition gives boom bust oscillations, not runaway growth. Allowing movement, we obtain the diffusion driven Turing threshold at which the uniform state breaks into stationary patches of high and low density, and find the uniform oscillation stable as it appears. With prey mobility and competition strength as control parameters, the pattern forming and oscillatory instabilities meet at a single point, where we compute the dynamics. Simulations confirm the sequence weak competition gives a wholefield oscillation, stronger competition with faster prey spread gives fixed patterns, and near the crossover the two combine into patterns that pulse in time. Predator self competition therefore sets the spatial structure of the community, which is what matters when additional food is used to steer a control agent in the field.

On-policy self-distillation (OPSD) has become a popular recipe for post-training LLM agents. It supervises the agent model at the token level with a stronger teacher view of the same model, obtained by conditioning on privileged information (PI). In this work, we show that in multi-turn agents, this paradigm teaches the student to act with confidence but without the information behind it. The trained agent behaves as if it had privileged information it never observed, and its performance falls well short of plain RL, in the worst case below the untrained base model. Therefore, we propose Privileged Self-Practice (PSP), which keeps the PI and moves it from the loss to the sampler. When the student's rollouts on a task mostly fail, we inject a short per-task instruction written by an analyzer model, sample the task again with the instruction in context, and train on the result with an unchanged GRPO objective. The privileged information stays in the prompt and never enters the loss. Across AppWorld and SWE-bench Verified, with three different student models, PSP obtains the best average score in every setting and is the only method that consistently outperforms plain GRPO, with relative improvements over GRPO of 7% to 58% in average score across settings. Project page: https://sux1ngyu.github.io/PSP/.

Tool-calling agents produce heterogeneous outputs, interleaving structured tool invocations with user-facing natural language summaries. This output heterogeneity presents a structural failure mode in standard on-policy Reinforcement Learning (RL): algorithms like GRPO indiscriminately broadcast a homogeneous trajectory-level scalar advantage to all tokens. Consequently, gradient noise from summary generation leaks into tool-decision tokens, causing cross-segment credit misattribution and brittle optimization. In this work, we propose SLCA-GRPO, a framework incorporating Segment-Locked Credit Assignment (SLCA). To enable scalable exploration without costly real APIs and stable training, we first construct the Schema-Guided LLM Simulator (SGLS) as foundational training infrastructure. Building on this, SLCA decouples advantage estimation at the structural segment level within a single group of rollouts, without requiring additional rollouts from intermediate states. Supported by Hierarchical Rewards (HierR), SLCA routes execution advantages to tool tokens and preference advantages to summary tokens, eliminating advantage contamination (the dominant cross-segment credit misattribution channel) within each policy update. On a 7B backbone, SLCA-GRPO accelerates convergence and outperforms standard GRPO, ToolPO, and RLTR by +2.53 pp on in-domain evaluation, +1.36 pp on the Berkeley Function-Calling Leaderboard (BFCL), and +9.15 pp on $\tau^2$-Bench under the same training budgets, achieving higher accuracy with reduced tool redundancy and costs.

This paper investigates communication-free bearing-only formation tracking control for multi-agent systems governed by Euler-Lagrange dynamics. Distinct from existing results that can only stabilize a stationary formation, this work considers a scenario where the leaders move with time-varying velocities while the inter-agent communication is absent. In this setup, the leaders' states (position and velocity) are unavailable to all followers and cannot be estimated via distributed observers. A novel adaptive distributed control scheme is developed to address this problem. The design exploits the fact that bearing rates contain the projected relative-velocity information, which, together with bearing rigidity, provides a rigidity-based damping mechanism for compensating the unavailable velocity error. Moreover, this damping mechanism is incorporated into a bearing-driven auxiliary variable to construct a surrogate velocity error, facilitating the adaptive control design for EL dynamics. Furthermore, since this damping mechanism necessitates sufficient bearing rigidity, we characterize a rigidity-preserving set and establish its forward invariance, thereby guaranteeing such rigidity via initial conditions. Via a Filippov-based Lyapunov analysis, the proposed scheme is shown to achieve local practical formation tracking in the sense that the velocity error converges to zero and the position error is uniformly ultimately bounded. As a corollary, for the constant-velocity case, asymptotic tracking is achieved without initial-condition restriction. The simulation results verify the effectiveness of the proposed control law.

Unified vision-language models (VLMs) that tokenize images through a vector-quantized (VQ) codebook routinely hallucinate objects on grounded yes/no benchmarks, yet existing decoding-time fixes treat this as generic miscalibration without an architectural account. Using activation patching across twenty-five models spanning eight LLM families, we identify an early-layer ($L_0$) attention routing circuit shared across VQ-tokenized VLMs and propose a three-gate diagnostic that distinguishes the models carrying it from those that do not. The diagnostic isolates ten positive models (five natural unified-VQ VLMs across three LLM families and five induced variants) and rejects the remaining fifteen. A single-variable architectural swap (LLaVA-1.6 CLIP+MLP $\rightarrow$ VQ+Linear) installs the circuit, while a matched-compute MLP control on identical data does not, isolating vector quantization as the source of the pathological signal; the routing pathway that carries it is one that the backbone already provides. Against tuned VCD and DoLA baselines, tuned DoLA wins on binary calibration, but \textbf{only $L_0$ ablation reduces object hallucination in open-ended generation} (CHAIR$_i$ reduces by $31\,\%$ relatively, whereas tuned DoLA and VCD leave it unchanged or worsen it). These results recast object hallucination in unified VQ VLMs as a property of architecture and pretraining, and yield a targeted intervention that mechanism-agnostic decoding cannot replicate.

We disprove almost everywhere convergence of the Schrödinger evolution on the standard torus \(\mathbb{T}^d\) for initial data \(f\in H^s(\mathbb{T}^d)\) when \(s<d/(d+2)\), in all dimensions \(d\ge2\). We construct normalized data with frequencies of size $N$ whose evolution attains size $N^{d/(d+2)}$ on a set of uniformly positive measure. The key ingredient in the construction is that the frequencies lie in an affine congruence class, so that at suitable rational times their phases coincide on a family of well-separated spatial points. The result matches the known estimate for $s>d/(d+2)$ with $d\geq2$. By integer dilation and uniform boundedness, we also obtain a single datum in $H^s$ whose evolution is unbounded along a sequence of times tending to zero whenever $s<d/(d+2)$. We also record a logarithmic upper bound in $2D$ at the critical frequency power and a lower bound on shrinking time intervals.

We investigate linear matter-density perturbations in full quadratic gravity. Working in the longitudinal gauge and adopting the sub-horizon and quasi-static approximations, we obtain an algebraic expression for the effective gravitational coupling in the theory and the equation for evolution of matter density perturbations. We identify the positive-real poles of this coupling and map their dependence on the quadratic couplings. In the formal infrared continuation, the reduced coupling recovers its general-relativistic value, whereas at large physical wavenumber it is suppressed when both quadratic couplings are nonzero; the single-coupling limits reproduce distinct behaviors. Numerical integrations of the growing mode are performed up to the first pole and show that pole-free regions of the reduced system can support regular matter-growth solutions, while poles obstruct a continuous late-time evolution. Our results show that quadratic gravity cannot generally reproduce the standard cosmological evolution of perturbations and in the regions where it can, it closely matches the behavior of $f(R)$ theories.

Open-weight LLMs give downstream users control over the inference stack, but this flexibility can undermine post-release guarantees that sensitive knowledge has been modified or removed. Model editing and machine unlearning are used to modify or remove targeted knowledge without retraining models from scratch. However, existing security evaluations of these techniques face two critical limitations. First, they typically require access to either the original pre-edit/unlearning model or auxiliary classifiers to detect modifications or reconstruct pre-edit behavior. Second, they evaluate modifications under the canonical tokenization of an input, implicitly treating tokenization as a benign preprocessing step. We show that this assumption creates a security gap: the same input string can be represented by alternative valid tokenizations that induce different computational trajectories, allowing an adversary to bypass localized modifications and recover information intended to be suppressed. We introduce Toketive, a simple yet powerful reference-free attack that exploits the tokenization-based side channel to (i) detect modified knowledge and (ii) reconstruct the corresponding pre-edit response. It operates solely on the released model and requires neither the pre-edit model, training data, shadow models, nor auxiliary classifiers. Across five LLMs, six datasets, and six editing and unlearning techniques, we find that 38.6% of alternative tokenizations bypass the modification and recover the pre-edit response. Toketive detects modified facts with an F1 score of 84.2%, a 26.2% relative gain over the strongest baseline, and reconstructs pre-edit responses with 74.5% top-5 accuracy, 21.7% higher than the best baseline. Our results show that localized modifications should not be treated as robust knowledge-control boundaries without adversarial evaluation over alternative representations.

Pilot-aided channel estimation is a decisive block in orthogonal frequency-division multiplexing (OFDM) receivers for both 5G New Radio (5G-NR) and Long-Term Evolution (LTE). A large body of estimators exists, from simple least-squares (LS) interpolation to statistically optimal linear minimum-mean-square-error (LMMSE) variants and, more recently, deep convolutional denoisers, yet no single estimator is uniformly best: the winner depends on the propagation scenario, the numerology, the operating signal-to-noise ratio (SNR), the mobility (Doppler), and the antenna configuration. In this paper, we quantify this fact through a unified study of eight literature estimators evaluated over the 3GPP TR~38.901 Urban-Macro (UMa), Urban-Micro (UMi), and Rural-Macro (RMa) channels generated with NVIDIA Sionna, for both 5G-NR and LTE numerologies, in single-input single-output (SISO) and $8\times2$ multiple-input multiple-output (MIMO) settings. We then propose a condition-adaptive multi-agent orchestrator that treats each estimator as an independent agent and dispatches, per operating condition, to the agent that is best on a validation split without any genie knowledge. The orchestrator tracks the per-realization oracle to within $1.07$~dB and improves the normalized mean-square error (NMSE) over the best fixed strategy by up to $3.6$~dB at high SNR, where the low-SNR champion is no longer optimal. Because the agents are independent, running them concurrently delivers this best-of-eight accuracy at essentially single-estimator latency: a data-parallel partition scales the wall-clock nearly as $1/K$ with $K$ workers (up to $6.9\times$), whereas naive by-algorithm partitioning is Amdahl-limited by the heaviest agent. The results substantiate multi-agent orchestration as a practical route to robust channel estimation across heterogeneous 5G-NR/LTE deployments.

General Purpose Service Robot (GPSR) tasks, as defined in the RoboCup@Home benchmark, require robots to interpret diverse natural language commands and generate multi-step action sequences in real home environments. Conventional Single Prompt (SP) approaches suffer from context bloat and the "Lost in the Middle" phenomenon, leading to unreliable task planning. We propose an LLM chaining architecture that separates instruction classification and action generation into two specialized stages, reducing per-inference prompt length by approximately 45% while improving planning consistency. We evaluate our method using 100 randomly generated GPSR commands across three language models spanning local open-source and frontier cloud deployment contexts. Results show consistent planning improvements over SP across all models, with gains of up to +37 percentage points on local models. Further, real-robot execution experiments on the Toyota Human Support Robot (HSR) reveal that planning success alone does not guarantee task completion, with 6 of 10 tasks completing successfully and execution-layer failures identified as the primary remaining bottleneck.

We develop a novel pathwise approach to study the convergence of the law of killed diffusion processes conditioned on non-absorption, towards a quasi-stationary distribution (QSD) as time goes to infinity. We start from the general observation that the dynamics of an absorbed Markov process conditioned upon survival up to time $T>0$ is the minimizer of the pathwise relative entropy with respect to its unconditioned dynamics, under a simple distributional constraint at that time; in other words, a Föllmer process. We then show how this result applies to a Brownian diffusion process softly-killed at a state-dependent regular rate, and characterize the minimizer and its drift change. In the case when the diffusion process is moreover reversible, we leverage these ideas and recent results on the propagation of weak log-concavity of HJB semigroups to prove that, under strict asymptotic convexity of the potential, the conditioned dynamics satisfies a contractivity property in $1$-Wasserstein distance, uniformly in $T>0$. We then establish the existence of a QSD with a large domain of attraction and deduce the exponentially fast convergence to it of the conditioned semigroup in the $1$-Wasserstein distance as $T$ goes to infinity. Finally, we deduce the exponentially fast convergence, also in $1$-Wasserstein distance, of the law of the corresponding Q-process towards its equilibrium.

3D Gaussian Splatting (3DGS) enables high fidelity novel view synthesis but suffers from excessive storage and bandwidth requirements due to its unstructured representation. To address this, a projection based video coding framework has emerged as a leading approach, supported by MPEG's ongoing standardization, where 3DGS attributes are converted into 2D maps to take advantage of efficient compression using established video codecs such as HEVC and VVC. However, the effectiveness of this approach depends heavily on the spatial coherence of the projected video, which current sorting strategies such as PLAS and Morton ordering fail to preserve adequately, either incurring high computational cost or achieving limited correlation retention. To overcome these limitations, we propose a dual phase Morton spatial sorting algorithm that improves both coding efficiency and processing speed. In the first phase, Morton based 1D indexing is applied to high dimensional attributes to enhance spatial locality. The second phase further refines layout continuity through a structured 2D Morton mapping table that enforces spatial adjacency. This hierarchical strategy generates highly regular, block wise feature maps with strong local correlation, making them well suited for compression via conventional block based coding tools. Experimental results show that our method significantly outperforms existing approaches in both compression performance and runtime efficiency, providing a practical and standard compatible solution for 3DGS data coding.

Neural audio watermarks are increasingly deployed in commercial speech generation systems to make AI-generated speech traceable, yet their robustness has been studied mainly under conventional signal distortions. Since a watermark can be regarded as imperceptible noise added to the speech signal, a natural question is whether speech enhancement (SE), as a denoising model, can remove it. In this paper, we cascade Gaussian noise with SE models as a black-box watermark removal attack, covering both discriminative and generative SE paradigms, against six neural watermarks: AudioSeal, WavMark, SilentCipher, Timbre, Perth, and AlignMark. Experimental results show that the proposed attack significantly outperforms existing neural re-synthesis methods in watermark removal. In particular, we find that generative SE, which reconstructs the harmonic regions of speech while denoising, is highly destructive to watermarks. These findings show that SE poses a serious threat to current audio watermarking methods, and we call for SE-aware robustness evaluation in watermark design.

Wetting transitions on textured substrates play a central role in the design of functional surfaces, but resolving their transition mechanisms requires efficient exploration of complex energy landscapes. In particular, saddle points are essential for revealing the connectivity among metastable states and transition pathways. In this work, we develop a diffuse-domain accelerated saddle dynamics (DD-ASD) framework for mass-constrained wetting transitions on complex textured substrates. The diffuse-domain formulation embeds complex solid geometries into a Cartesian grid, avoiding body-fitted mesh construction in repeated saddle-point searches. An orthogonal projection is applied consistently to the phase-field state and unstable-direction dynamics, preserving the prescribed droplet mass at the discrete level. Momentum acceleration is incorporated into the saddle dynamics to improve the efficiency of high-index saddle searches. Under the stated local spectral and exact-eigenspace assumptions, we establish a local convergence rate of $1-\mathcal{O}(1/\sqrt{\kappa})$ on the effective mass-conserving subspace. Numerical experiments demonstrate the effectiveness of the proposed method in resolving wetting solution landscapes, transition pathways, and energy barriers on textured substrates. We further extend the framework to fully three-dimensional wetting-landscape computations.

The eigenvalue problem for a probability measure $\mu$ with compact support in $\R$ is whether there exist a countable set $\Lambda$ and a nonzero real $t\ne 1$ such that both $\Lambda$ and $t\Lambda$ are spectra of $\mu$, that is, the family $$E_{a\Lambda}=\{e^{-2\pi i a\lambda x}:\lambda\in\Lambda\}$$ is an orthonormal base for $L^2(\mu)$ for $a=1, t$. The eigenvalue problem was discovered independently by Strichartz (Str00), Laba and Wang (LW02) for the Cantor measures $\mu_{4,\{0,1\}}$ and $\mu_{6,\{0,1,2\}}$, respectively. In this paper, we investigate the spectral eigenvalue problem for the general spectral Cantor measure $\mu_{b,\mathcal{D}}$. This topic is naturally related to elementary number theory. Unexpectedly, however, our main results depend on the theory of integers, especially Artin's primitive root conjecture. To some extent, our results suggest that Artin's primitive root conjecture may hold and confirms some viewpoints implied by Minkowski in (Min57).

Federated learning (FL) lets EEG decoders learn from recordings of several subjects without pooling them. We consider two light EEG decoders, the Riemannian SPDNet and the Euclidean EEGNet. Both split into a trunk, which builds a latent representation, and a head, which classifies it. Inter-subject variability, however, makes a single shared FL model a poor fit for each subject. Personalised FL addresses this: all subjects learn a common trunk, and each subject keeps its own head. We adapt it for SPDNet and study its effects against standard FL and centralised training, with EEGNet as a Euclidean baseline. Experiments cover three motor-imagery datasets that span diverse regimes in channels, subjects and classes. We observe that personalised SPDNet reaches higher accuracy than both standard FL and centralised training, while converging in fewer rounds and communicating fewer parameters than standard FL. It also outperforms every EEGNet configuration on two of the three datasets, although centralised EEGNet outperforms centralised SPDNet.

Based on a two-parameter perturbative framework, we derive perturbative formulae for the radii of massive particle spheres and massive shadow radii, where an extremal black hole is employed as the perturbative background. Adopting extremal black holes as the perturbative background enables energy-dependent scans to probe stronger gravitational regimes. Using these formulae, we perform perturbative analyses of the massive shadows for several non-standard black holes, and obtain the expansion expressions near the photon sphere of the extremal black hole. It is found that, although the dependence on the energy parameter $\epsilon$ is the same across models, the coefficients associated with the deviation parameter $\delta$ differ significantly, which can serve to distinguish among different black hole models. Furthermore, we construct a two-point Padé approximant in the form of a continued fraction which achieves a globally accurate approximation for the massive shadow radius of the black hole over the entire parameter range. Numerical tests show that the relative errors based on this approximant are small enough to provide a reliable foundation for model-independent reconstruction of metric parameters.