arXiv:2509.15254v3 Announce Type: replace
Abstract: In this study, we address the problem of in-flight object catching using a quadruped robot with a basket. Our objective is to accurately predict the impact point, defined as the object's landing position. This task poses two key challenges: the absence of public datasets capturing diverse objects under unsteady aerodynamics, which are essential for training reliable predictors; and the difficulty of accurate early-stage impact point prediction when trajectories appear similar across objects. To overcome these issues, we construct a real-world dataset of 8,000 trajectories from 20 objects, providing a foundation for advancing in-flight object catching under complex aerodynamics. We then propose the Object-Adaptive Impact Point Predictor (OIPP), consisting of two modules: (i) an Object-Adaptive Encoder (OAE) that extracts object-dependent representations from motion histories, and (ii) an Impact Point Predictor (IPP) that estimates the impact point from these representations. Two IPP variants are implemented: a Neural Acceleration Estimator (NAE)-based method that predicts trajectories and derives the impact point, and a Direct Point Estimator (DPE)-based method that directly outputs it. Experimental results show that our dataset is more diverse and complex than existing datasets, and that our method outperforms baselines on both 15 seen and 5 unseen objects. Furthermore, we show that improved early-stage prediction enhances catching success in simulation and demonstrate the effectiveness of our approach through real-robot experiments. The demonstration is available at https://sites.google.com/view/robot-catching-2025.
Science Journals
arXiv:2607.09235v1 Announce Type: new
Abstract: The current state of the art in AI/ML rests on deep neural architectures, which, in general, suffer from a lack of interpretability. Interpretability is crucial to gleaning insights while analyzing experimental data, where quantitative predictions may not be adequate for a scientist. We present a three layer neural architecture, SAMPAT (Smooth Approximation via Multivariate Polynomials and Analytic Transformations), that can provably learn a continuous, everywhere differentiable function, that can approximate any smooth function arbitrarily closely. SAMPAT's approximant can be expressed as a closed and compact algebraic, analytic expression, providing complete interpretability. Experiments on synthetic and benchmark datasets indicate that SAMPAT yields competitive performance with simpler representations. For many tasks, a two layer SAMPAT suffices. By imposing restrictions on the connectivity between neurons, SAMPAT may be used to provide a range of approximants, including regular and trigonometric polynomials, rational expressions, Gaussians, mixtures of Gaussians, as well as arbitrary combinations of the same; without restrictions, it learns a suitable structure. SAMPAT may be used to factorize polynomials and model nonlinear systems. With the addition of skip connections, a 4 to 6 layer SAMPAT is adequate to represent a substantive range of methods widely used in AI/ML, allowing the choice of a model's family, not just its parameters, to also be optimized as part of the learning process.
arXiv:2607.09236v1 Announce Type: new
Abstract: Machine unlearning in LLMs is the targeted removal of specific knowledge while preserving all other capabilities, critical for privacy and safety. Yet existing benchmarks measure it unreliably. They miss knowledge that resurfaces under paraphrased or indirect queries, a failure we call under-forgetting, and lack the semantic, syntactic, and lexical probes needed to verify that unrelated knowledge is preserved, a failure we call over-forgetting. Both failures reflect an asymmetric generalization problem. Forget evaluation must cover diverse query formulations of the same target facts, testing whether forgetting holds beyond exact training prompts. Retain evaluation must probe a far larger and implicitly defined set, namely every fact disjoint from the forget target. The retain set thus defines the effective forget set, yet current datasets provide no fine-grained annotation of this forget-retain boundary. We address this with SUITE, an evaluation protocol and training corpus that captures forget-retain structure for real-world factual domains. Methods trained on SUITE improve substantially, showing that training data is as important as algorithmic design. Building on the obtained insights, we introduce JensUn++, an unlearning algorithm that achieves the best forget-retain utility trade-off across three LLMs, in both sequential and joint unlearning settings. Code and datasets are available at https://amitpeleg.github.io/forget-narrowly-retain-broadly
arXiv:2607.09606v1 Announce Type: new
Abstract: Research on D\"urer's problem focuses on edge unfoldings of convex polyhedra that avoid overlap. We invert the goal and find unfoldings that overlap at some point to any given thickness t.
We have two main results. The first is that, if we allow unfolding cuts that do not follow polyhedron edges, then there is a convex polyhedron that can unfold with overlap of any given thickness. The second result is that for any given thickness, there is a convex polyhedron with an edge unfolding that overlaps to that thickness.
arXiv:2607.09253v1 Announce Type: new
Abstract: AI chatbots are increasingly used for answering health-related questions. This study examines the role of topic type discussed with an AI chatbot and individual characteristics on perceived benefits and risks, intention to use an AI chatbot, and willingness to self-disclose health information. We conducted an online experiment with a 2 (topic type: physical versus psychological, between-subjects) x 2 (topic sensitivity: low versus high, within-subjects) mixed design among a Dutch representative sample (N = 1,388). Results showed that perceived benefits were positively associated with intention and willingness to self-disclose, while perceived risks were negatively associated. Moreover, participants reported higher usage intentions for low-sensitive topics compared to high-sensitive topics. Furthermore, perceptions, intention, and willingness to self-disclose varied by individual characteristics. Overall, our findings suggest that intentions to use AI chatbots and self-disclosure of health-related information are primarily related to perceived benefits and risks and to personal characteristics rather than to topic type.
arXiv:2607.09257v1 Announce Type: new
Abstract: Non-binary successive cancellation list (NB-SCL) decoding expands each surviving path into $q$ candidate branches at every information symbol, which causes high path expansion, sorting, and pruning complexity. To address this issue, this paper proposes low-complexity list decoding algorithms for $2\times2$ kernel non-binary polar codes (NBPCs). First, we design a split-reduced non-binary successive cancellation list (SR-NBSCL) decoder that skips path splitting when the current symbol is sufficiently reliable. We then exploit the final Rate-1 node structure and switch the last group of information symbols to simplified non-binary successive cancellation (NB-SC) decoding, resulting in the enhanced split-reduced non-binary successive cancellation list (ESR-NBSCL) decoder. To further reduce branch expansion at unreliable symbols, we introduce an accumulated reliability-deviation (ARD) metric and propose an adaptive branch-pruning non-binary successive cancellation list (ABP-NBSCL) decoder, which prunes unreliable candidate branches before sorting and then reduces the dominant sorting complexity. Simulation results show that the proposed decoders achieve frame-error-rate (FER) performance close to that of conventional NB-SCL decoding with much lower complexity. In particular, the ABP-NBSCL decoder reduces the path splitting number (PSN) by more than $80\%$ at several tested signal-to-noise ratios (SNRs), with a negligible performance loss.
arXiv:2607.09261v1 Announce Type: new
Abstract: Virtual Reality (VR) offers a flexible and controllable platform for studying human-robot interaction. Prior work has explored VR for socially aware robot navigation. However, whether VR captures the multimodal interaction dynamics observed in real-world human-robot co-navigation remains insufficiently understood. In this work, we present a VR prototype and evaluate its suitability for studying multimodal human-robot interaction (HRI) in socially aware navigation. Specifically, we investigate whether VR preserves the multimodal interaction dynamics observed in real-world human-robot co-navigation. We conducted a within-subjects study (N = 21) in which participants interacted with a PR2 mobile manipulator robot in both a motion capture equipped arena and its virtual replica in an immersive VR environment. Two common co-navigation scenarios were examined : orthogonal crossing and pass-by interactions. Participants evaluated the robot's perceived social awareness and interaction comfort, while trajectory and head-orientation data were analysed to examine behavioral responses during the interaction. Our results show that participants perceive the robot's socially aware navigation similarly in VR and in the real world. Furthermore, VR captures human interaction behaviors in ways consistent with real-world observations. These findings suggest that VR can be a reliable and flexible platform for studying richer multimodal behaviors in social navigation and HRI.
arXiv:2607.09263v1 Announce Type: new
Abstract: Sign Language Retrieval (SLRet) enables efficient access to sign language content but remains fragile in fine-grained scenarios where visually similar signs must be distinguished. We show that this limitation does not stem from model capacity, but from ineffective hard negative supervision. Specifically, we formulate fine-grained retrieval failures as a negative distribution mismatch: semantically distinct yet visually confusable signs are rarely treated as hard negatives, while existing text-based mining strategies fail to capture such visual ambiguity. To address this issue, we propose Sign-Aware Hard Negative Mining (SAN), which constructs hard negatives based on visual confusability in the sign embedding space rather than linguistic similarity. Experiments on PHOENIX-2014T demonstrate that SAN substantially improves fine-grained retrieval performance while preserving coarse-grained accuracy, highlighting the importance of aligning negative supervision with visual ambiguity in sign language retrieval.
arXiv:2607.09266v1 Announce Type: new
Abstract: Per-layer diagnostics reveal that, at the prescribed learning rate, Lion's effective scale is 2.6-2.8x too high for attention and MLP parameters and ~2x too high for normalization layers on ViT-Tiny/CIFAR-100; this 32% cross-layer-type disparity cannot be reproduced by a single global rate. The measurement comes from LionVote, a per-layer learning rate mechanism in which each parameter tensor maintains a compound level, a persistent integer updated every c epochs by two diagnostics (gradient direction stability and momentum health) resolved by a validation loss tiebreaker. Voting thresholds derive from geometric identities, the EMA time constant, and a noise-floor estimate; cadence is bounded structurally and selected by ablation. On ViT-Tiny/CIFAR-100, LionVote achieves 69.7% top-1 accuracy vs. Lion's 69.0% (p < 0.02, Welch's t-test) and AdamW's 68.8%. Per-layer adaptation value depends on both architectural heterogeneity and task; on uniform CNN architectures tuned SGD with cosine annealing remains dominant, and on ViT architectures gains are task-dependent.
arXiv:2607.09491v1 Announce Type: new
Abstract: Centralized cryptocurrency exchanges (CEXes) enable fast off-chain conversions between hundreds of coins. It is an open question which algorithmic trading patterns occur on these platforms. A major challenge to measuring CEXes is that their public trade data does not contain addresses or trader identifiers allowing linkage. We propose a novel methodology to infer one-way arbitrage (OWA) trading in anonymized spot trade data from CEXes. We identify 402 M likely OWA sequences in 5 years of trading on Binance (and almost 2 M during 9 years on Kraken), accounting for 0.94 % and 0.13 % of the total traded volume, respectively. While we estimate total profits of $31.2 M on Binance and $975 k on Kraken, profits from individual OWA sequences are less than $1 on average after accounting for trading fees. We also observe that OWA has become faster over time, while the profitability of individual sequences has decreased. Our findings highlight that pricing discrepancies regularly occur in CEXes, and raise questions for future work to identify the precise circumstances that enable profitable OWA.
arXiv:2607.09510v1 Announce Type: new
Abstract: Large language model (LLM) coding agents are increasingly deployed to autonomously perform software engineering tasks in terminal-based environments, making their reliability a growing concern. Existing empirical studies investigate why coding agents fail, yet they largely treat failure as a final outcome rather than a temporal process, providing limited insight into how failures emerge, evolve, and become unrecoverable. We present the first large-scale empirical study of CLI coding-agent failure trajectories, introducing a process-oriented framework that analyzes failure through its onset, evolution, and recovery across execution trajectories. We first collect 3,843 execution trajectories generated by seven frontier models across three coding-agent scaffolds (OpenHands, MiniSWE, and Terminus2) on Terminal-Bench, then carefully filter them to obtain 1,794 complete and valid trajectories for manual annotation (over 63,000 execution steps), from which we derive 14 findings spanning failure occurrence, root causes, recovery, and cross-system consistency. Our findings show that coding-agent failures are predominantly driven by epistemic errors, typically begin within the first few execution steps, and often remain hidden until recovery is no longer possible, suggesting that improving coding-agent reliability requires earlier validation and intervention rather than relying solely on final-outcome evaluation.
arXiv:2510.07884v2 Announce Type: replace
Abstract: Weak-to-strong generalization provides a promising paradigm for scaling large language models (LLMs) by training stronger models on samples from aligned weaker ones, without requiring human feedback or explicit reward modeling. However, its robustness and generalization are hindered by the noise and biases in weak-model outputs, which limit its applicability in practice. To address this challenge, we leverage implicit rewards, which approximate explicit rewards through log-likelihood ratios, and reveal their structural equivalence with Contrastive Decoding (CD), a decoding strategy shown to reduce noise in LLM generation. Building on this connection, we propose Contrastive Weak-to-Strong Generalization (ConG), a framework that employs contrastive decoding between pre- and post-alignment weak models to generate higher-quality samples. This approach enables more reliable capability transfer, denoising, and improved robustness, substantially mitigating the limitations of traditional weak-to-strong methods. Empirical results across different model families confirm consistent improvements, demonstrating the generality and effectiveness of ConG. Taken together, our findings highlight the potential of ConG to advance weak-to-strong generalization and provide a promising pathway toward AGI.
arXiv:2607.09271v1 Announce Type: new
Abstract: For solid-state transformers (SSTs) in high-power grid-connected applications, improperly designed control loops can excite strong inherent AC-DC port coupling, leading to low-frequency oscillation issues, especially under weak grid conditions. To address this problem, this article establishes a multiport admittance matrix for the SST, encompassing its AC dq axes and primary DC port, to characterize its inherent dynamics. Subsequently, a multiport dissipativity analysis is conducted to evaluate the robust stability of the SST. By leveraging the decomposition of passivity conditions into distinct self- and coupling-dissipativity indices, the specific root causes of instability are diagnosed. This framework reveals that a severe coupling-dissipativity failure, induced by the internal dynamics of the synchronization loop, is the dominant instability mechanism rather than a localized self-dissipativity issue. Guided by this diagnosis, a stabilizing controller featuring dynamics-free orthogonal signal reconstruction is designed to reshape the admittance characteristics of the SST. This enhancement specifically targets the identified coupling-dissipativity deficiencies, thereby resolving the root cause of the instability. Finally, the stability analysis and the effectiveness of the enhancement strategy are validated on a down-scaled SST prototype. Experimental results demonstrate that the criterion accurately predicts the coupling-induced oscillations and that the enhanced controller guarantees stable operation under challenging weak-grid conditions.
arXiv:2607.08883v1 Announce Type: new
Abstract: Behavioral alignment in large language models often masks fragile internal safety representations. Recent work suggests that refusal behavior is mediated by low-dimensional directions in activation space. This raises questions about how such representations are structured, localized, and accessed by optimization. We study adversarial suffix attacks as a probe of representational alignment. We introduce Activation-Guided GCG, which replaces output-based objectives with losses that directly target a model's internal refusal direction. Across several objective variants, we find that suppressing refusal globally across all layers and positions is more effective than targeting a single layer-position pair. This suggests that safety representations are distributed across the forward pass rather than causally localized to a single site. We further introduce Soft-GCG, a continuous relaxation of discrete suffix optimization using Gumbel-Softmax. Soft-GCG achieves a 33 $\times$ speedup over standard GCG while improving attack success rates. Evaluating across model scales, we find that smaller models remain vulnerable while larger models resist both activation- and suffix-based attacks at our compute-constrained settings, consistent with larger and better safety trained models being harder to jailbreak. Together, our results clarify how safety mechanisms are encoded and can be broken in contemporary models. These insights provide concrete guidance for designing more robust and representation-aware alignment strategies.
arXiv:2607.09351v1 Announce Type: new
Abstract: Single Image Super-Resolution (SISR) reconstructs high-quality images from low-resolution inputs. While recent multi-modal methods improve perceptual quality, they remain sensitive to erroneous priors and require expensive annotations. To address these issues, we propose Simon-SR, a multi-modal SISR framework leveraging learnable prompts for efficient semantic mining and robust text-image fusion. Our approach combines Contrastive Prompt Learning with Prompt-Guided Spatially Adaptive Refinement to enhance multi-modal alignment. Experiments demonstrate that Simon-SR surpasses state-of-the-art methods, achieving maximum improvements of 0.50 dB in PSNR, 0.0133 in SSIM, and 0.0695 in LPIPS. Code will be released.
arXiv:2607.09365v1 Announce Type: new
Abstract: Video-based manipulation provides object-centric motion priors from human demonstrations, generated videos, or RGB-D observations, but such priors are typically embodiment-agnostic and cannot be directly executed by a specific robot. This paper presents \textbf{PhysV2A}, a reachability-gated and semantic-mask-constrained feasibility-completion framework for converting video-derived 6D object motion into robot-executable manipulation trajectories. The key idea is to treat grasp feasibility as trajectory-conditioned rather than local: each RGB-D-generated 6-DoF grasp candidate is rigidly coupled with the recovered object motion to form a grasp-conditioned TCP trajectory hypothesis. PhysV2A then performs hierarchical reachability-gated selection, where infeasible grasp--trajectory pairs are rejected by robot-centric kinematic checks and surviving candidates are ranked by downstream execution suitability. For the selected reachable trajectory, a VLM-assisted and rule-validated S-Mask identifies task-critical and relaxable Cartesian components, enabling semantic-mask-constrained manipulability refinement through redundancy-first optimization and bounded Cartesian relaxation. Real-robot experiments on four tabletop manipulation tasks show that PhysV2A improves task success over representative video-prior and IK-only baselines, reduces kinematic-feasibility failures, and produces better-conditioned trajectories with bounded semantic deviations.
arXiv:2607.09276v1 Announce Type: new
Abstract: Due to the use of PI-based d q current decoupling in the pulse rectifier of CRH5 high-speed trains, the PI parameters directly affect the traction system's control performance. Linearized control may have issues with reference trajectory changes or model mismatches, leading to a decrease in system performance, while nonlinear control may have problems with jitter and poor steady-state accuracy. This paper proposes a new control strategy that replaces all PI in the d q current decoupling control with a single intelligent agent. This method based on Deep Reinforcement Learning (DRL) can avoid various drawbacks of linearization and nonlinear control and ensure the stability of intermediate DC voltage. However, when EMUs are in different working conditions and switching, the Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm used in traction dual rectifiers does not have a good control effect. Focusing on the issue, Reward Shaping (RS) is added to re-design a nonlinear reward function, which can be combined with Prioritized Experience Replay (PER) to increase the convergence speed of the episode reward. The simulation results show that the improved control strategy can be effectively applied to EMUs working in multiple conditions. Finally, the stability analysis is carried out using Lyapunov's second method and the verification results of the hardware-in-the-loop (HIL) simulation platform show that the DRL control has a good effect.
arXiv:2601.10034v2 Announce Type: cross
Abstract: Decision making often exhibits context dependence that challenges classical probability theory. This paper develops a quantum-like extension of the Tug-of-War (QTOW) decision-making model to clarify when such context dependence can be represented by a single minimal internal state. The QTOW construction uses a qutrit internal state, conservation-preserving updates, and measurement-induced disturbance to model decision, learning, and probing operations within one coherent state space. Within this minimal representation, KCBS-type probing contexts can be constructed, yielding a witness of non-contextual classical non-embeddability. The main claim is not that quantum theory is uniquely or assumption-freely derived from decision making. Rather, a classical reconstruction of the same operation family requires additional contextual memory, history dependence, or an enlarged hidden-state representation. Thus, contextual probability appears as a resource signature of minimal decision dynamics, while quantum probability provides a compact, memory-efficient realization of this structure.
arXiv:2607.08861v1 Announce Type: cross
Abstract: In this article we investigate the theoretical convergence properties of the fictitious-play approximation procedure applied to coupled FBSDE systems for finite-player non-zero-sum stochastic differential games. Under one set of assumptions, the convergence is shown to be geometric. Under an additional structural assumption, the geometric convergence rate further improves to a super-exponential rate in a special class of games. To the best of our knowledge, this provides the first convergence analysis of fictitious play for fully coupled FBSDEs. A numerical experiment with a linear-quadratic interbank borrowing and lending problem confirms the geometric convergence.
arXiv:2607.08875v1 Announce Type: cross
Abstract: With the increased demand for spectrum usage in recent years, particularly with the expansion of NGSO satellite systems for broadband internet and cellular services, radio astronomy observatories located at remote sites have been faced with the challenge of increasingly detrimental RFI exposure from ubiquitous satellite downlinks. With the help of the U.S. NSF, NRAO and the radio astronomy community have spearheaded collaboration efforts with the commercial NGSO operators to develop different coordination techniques to alleviate the impacts of these downlink signals in radio astronomy scientific observations. This paper summarizes the ongoing coordination efforts, spectrum interference avoidance schemes, and a case study on community participation of the Operational Data Sharing (ODS) system between RAS and NGSO operators. We highlight some of the essential lessons learned from these collaborations and potential application of the ODS system to other potential spectrum stakeholders.
arXiv:2607.09416v1 Announce Type: cross
Abstract: We develop a statistical-mechanical theory of water in unsaturated soil whose outcome is a continuum field equation for the pore-occupancy g(r,x,t), the fraction of pores of radius r that are water-filled at position x and time t. The theory is built across three scales: microscopic inter-pore transfers set by Hagen-Poiseuille rates and a driving potential (the difference of pore-class chemical potentials, taken in capillary-gravitational form but open to adsorptive, osmotic, or thermal refinement); a mesoscale master equation relaxing the occupancy toward the equilibrium step g_eq=H(r*-r); and, on contracting the averaging volume to a point, the continuum balance d_t g + div F = C[g] - E - T, of which everything else is a limit, a moment, or a boundary resolution. The kinetic equation is an Onsager gradient flow descending the Gibbs free energy, with an H-theorem for the isothermal unforced system and mass conservation as its zeroth moment. A single dimensionless group, the pore-resolved Damkohler number Da(r,x), organizes the behavior and unifies phenomenologies long modelled separately. A Chapman-Enskog reduction identifies Richards' equation as the quasi-static (Da->0) limit, with matric potential and hydraulic conductivity K emerging only there and K vanishing below the percolation threshold; capillary-bundle and critical-path models are its diagonal and spectral limits. Hysteresis is the holonomy of a forcing bundle, a geometric phase rather than per-pore bistability, with a falsifiable loop-area law H ~ I^2. Preferential flow is what the same equation does where Da>1, so the Richards/preferential-flow dichotomy becomes a continuous Da-controlled crossover. Out of the quasi-static limit g(r) is the irreducible state variable. All inputs are geometric properties of the pore network, measurable from micro-CT and calibrated against no macroscopic data.
arXiv:2607.09423v1 Announce Type: cross
Abstract: In this paper, we study the problem of optimizing Markov processes that interpolate between two prescribed probability distributions while minimizing a given cost. The main computational challenge is the curse of dimensionality: in high-dimensional state spaces, representing the full distribution is intractable. To address this, we reformulate the problem in terms of sequential couplings and develop convex relaxations based on local marginals and cluster moments. These relaxations exploit locality and sparse interaction structure, provide computable lower bounds, and recover low-order statistics of the intermediate laws. We identify dynamic optimal transport as a special case of our Markov process optimization problem and develop a procedure for recovering the underlying Benamou--Brenier dynamics from the relaxed solution. We also show that the procedure extends to more general Markov processes and illustrate it with a constrained process between Ising models.
arXiv:2607.09129v1 Announce Type: new
Abstract: We derive a low-energy $\mathbf{k}\cdot\mathbf{p}$ effective Hamiltonian for monolayer osmium carbide (OsC) and ruthenium carbide (RuC) in a planar hexagonal configuration. First-principles calculations indicate that both monolayers are dynamically stable and exhibit features of a two-dimensional quantum spin Hall (QSH) phase, characterized by a nontrivial $\mathbb{Z}_2$ topological invariant. Using symmetry analysis at the $\Gamma$ point, we construct a multiband $\mathbf{k}\cdot\mathbf{p}$ Hamiltonian including spin-orbit coupling and reduce it to a four-band low-energy model through L\"owdin partitioning. The effective Hamiltonian has a block-diagonal form, with two blocks related by time-reversal symmetry, analogous to the Bernevig--Hughes--Zhang (BHZ) model. In contrast to the standard BHZ form, the symmetry-allowed off-diagonal coupling contains quadratic momentum-dependent terms, which modify the low-energy dispersion near the $\Gamma$ point. The fitted parameters reproduce the ab initio band structures in the low-energy region, yielding a compact model for analyzing the electronic and topological properties of monolayer OsC and RuC.
arXiv:2607.09442v1 Announce Type: new
Abstract: The exact domatic-number problem asks, for a fixed integer k, whether a given graph G satisfies dom(G) = k. Riege and Rothe proved DP-completeness for every fixed k >= 5, while the cases k = 3 and k = 4 remained open. We close this classification gap. The main ingredient is a polynomial-time reduction from 3SAT whose output graphs have domatic number 4 in the satisfiable case and domatic number 2 in the unsatisfiable case; in particular, the reduction never produces a graph of domatic number 3. This directly realizes the route suggested by Riege and Rothe for closing the remaining cases. Together with a simpler three-versus-two reduction, this yields DP-completeness of Exact-3-DNP and Exact-4-DNP. The proofs are constructive and give explicit graph gadgets whose local domination constraints encode truth assignments and clause satisfaction. The soundness arguments show conversely that any sufficiently large domatic partition enforces the intended consistency conditions and therefore yields a satisfying assignment. Consequently, Exact-k-DNP is DP-complete for every fixed k >= 3, completing the fixed-value classification from k = 3 onward.
arXiv:2607.09293v1 Announce Type: new
Abstract: In this work, we introduce a fifth-order well-balanced (WB) path-conservative A-WENO scheme with the central-upwind numerical fluxes (PCCU-5) for the Ripa model. The proposed scheme is capable of exactly preserving a variety of steady states, including still-water, moving-water, isobaric, and constant water height ones. This goal is achieved with the help of a flux globalization technique: The source terms are incorporated into the fluxes, resulting in a quasi-conservative system, for which central-upwind numerical fluxes are computed using the path-conservative integration. The proposed A-WENO scheme utilizes a WENO interpolation of the equilibrium variables rather than the conservative ones to ensure the WB property. In addition, we perform the WENO interpolation of the local characteristic equilibrium variables to mitigate numerical oscillations near discontinuities. We perform a series of numerical experiments, which demonstrate that the proposed fifth-order WB PCCU-5 scheme achieves high resolution and clearly outperforms its second-order counterpart. Our numerical results also demonstrate the importance of the local characteristic projection for significantly reducing (eliminating) numerical oscillations near discontinuities.