Papers

Strassen showed that two 2x2 matrices can be multiplied with 7 multiplications instead of 8. Applied recursively, his algorithm multiplies two nxn matrices with O(n^2.807) multiplications, beating the naive O(n^3). The best known 3x3 recursive matrix multiplication algorithm uses 23 multiplications O(n^2.854). The best published lower bound of 21 (on algorithms with integer constants) leaves room for an algorithm with O(n^2.771) multiplications, and thus does not rule out the possibility of an algorithm that would beat Strassen's. We prove a lower bound of 22 multiplications for any 3x3 recursive algorithm with integer constants, proving that no such algorithm can do better than O(n^2.814) multiplications, and eliminating the possibility of a 3x3 algorithm that beats Strassen's 2x2 method. The proof builds on a recent decomposition method from Wang, who approached the problem by turning it into 496 subproblems. We provide exact solutions for 359 of them. The proof is in Lean; verification requires auditing only a few short files. The Lean formalization directly encodes statements about the limitations of recursive algorithms for matrix multiplication, as opposed to just a statement about the rank of the problem.

Federated learning (FL) on heterogeneous edge devices must jointly accommodate unequal resource budgets and domain-shifted local data. Existing resource-adaptive methods decide how much of a model each client trains but not where retained capacity should reside or how it should be shared, whereas federated domain-generalization methods usually assume a shared full architecture. Uniform compression can therefore discard high-utility channels, and a single aggregation path can mix transferable features with domain-sensitive updates. We propose FedSAP, a domain-aware heterogeneous FL framework that casts structured pruning as budget-constrained tri-state channel allocation. FedSAP converts each keep ratio into non-uniform layer budgets, assigns stable channels to a Global pool, useful domain-sensitive channels to pseudo-domain-specific Private pools, and low-utility channels to a Dropped state. This partition lets broadly useful features benefit from cross-client pooling while isolating domain-sensitive updates from incompatible clients. Domain-Guided Assignment infers pseudo-domains from shallow-gradient similarity, while Type-Matched Aggregation restricts each channel to its intended sharing scope. Across three random seeds, FedSAP reaches 76.00% and 72.67% mean global accuracy on Digits and Office-Caltech, exceeding the strongest baseline by 1.70 and 4.92 percentage points while supporting client pruning ratios of up to 80% across heterogeneous clients.

In recent decades, artificial intelligence has made significant progress in understanding and interacting with images. One of the important applications of this technology is Visual Question Answering (VQA), a research field that requires computers to understand and answer questions about images in a natural manner. Despite extensive research and development in VQA for English, there have been very few similar efforts made for other languages, especially Vietnamese. This gap presents a significant challenge and opportunity for the advancement of VQA technology in the Vietnamese language context. By bridging this gap, the field of Vietnamese VQA not only enriches the diversity of research in artificial intelligence but also enables practical applications in various domains, such as education, healthcare, and entertainment, catering to Vietnamese-speaking populations worldwide. Thus, the exploration and development of Vietnamese VQA systems hold immense potential for advancing both research and practical applications in the intersection of computer vision and natural language processing. In this paper, we propose a Multi-layer Fusing Transformer model utilizing a cross attention module to combine multiple modality features of images and texts from different layers in an aggregated representation. Our architecture allows us extract information from low level to high level. Through detailed experiments and ablation studies, our model achieves promising results against the competitive baselines in ViVQA dataset for Vietnamese language.

The next-generation matrix method is a powerful tool for computing the basic reproduction number in compartmental mathematical models of infectious diseases. The method has been recently extended to mathematical biochemistry, where it can be used to establish parameter regions of stability and instability for boundary steady states. Several significant challenges in its application remain, however, particularly around establishing conditions under which the method is mathematically valid, computationally tractable, and biologically meaningful in the biochemical setting. In this paper, we address these challenges by shifting the interpretation from new infections in the epidemiological setting to autocatalysis in the biochemical setting. We introduce a graph, called the ALT-graph (autocatalysis-leak-transition graph), which decomposes the contribution of each reaction to the Jacobian as autocatalytic, leak, or transition edges. We then present a systematic algorithm for splitting the ALT-graph, which is guaranteed to produce a valid reproduction number, $\rho(FV^{-1})$, while also decreasing computational complexity by lowering the rank of $FV^{-1}$. We apply the method to models of both biochemical reaction networks and infectious disease spread.

Direct to device D2D connectivity from low Earth orbit LEO satellites is moving to Ku band, where a handheld terminal must obtain directional gain from several small phased array panels distributed around the chassis. Beam management then becomes a joint satellite panel beam selection problem with hundreds of candidates, and ordinary hand motion can change the best candidate within one decision interval. This paper proposes a low overhead predictive beam management scheme for a multiband LEO D2D downlink in which a low frequency anchor link carries control signalling and fallback traffic, and a Ku band link carries broadband data. The handset inertial measurement unit IMU reports attitude and angular rate with a known delay; the scheme extrapolates the delayed attitude to the current orientation, scores all satellite panel beam candidates analytically from the satellite ephemeris and panel geometry, and trains only a small candidate set built with a satellite panel diversity rule under a fixed pilot budget. The Ku band link is activated only when its predicted post training rate exceeds the anchor rate by a margin. Trace driven Monte Carlo simulations with a four panel handset and two visible satellites show that, with six pilots 0.3 percent training overhead, the proposed scheme improves mean goodput by 21.2 percent and reduces broadband outage by 57.6 percent at 90 degrees per second relative to an equal budget delayed attitude baseline, and operates within 3.8 percent of a zero overhead oracle.

Yorùbá is a widely spoken tonal language that depends on diacritics to avoid lexical ambiguity. However, it is often written without these diacritics, thereby hindering downstream Natural Language Processing (NLP) tasks. In this paper, we introduce Yo-ByT5, a byte-level Automatic Diacritic Restoration (ADR) model fine-tuned from ByT5-small. We evaluate Yo-ByT5 alongside five publicly released Yorùbá ADR models and one open-weight large language model (LLM) on the YAD benchmark under a consistent protocol. Our results demonstrate that Yo-ByT5 matches the performance of the strongest existing model, mT5-base, with a DER of 10.14% and a CER of 3.48%. Furthermore, it exhibits superior text fidelity despite using approximately half the parameter count of mT5-base. We also release our training code and model outputs, as well as call for the development of a larger, purpose-built benchmark for Yorùbá diacritic restoration.

Explaining generalization and training dynamics in neural networks remains a challenge, and various approaches have been developed to study different aspects of these phenomena. In this paper, we introduce the idea of magnitude potential – a quantity based on the theory of metric magnitude – that reflects how well an arbitrary point is represented by a given set. We find that this basic quantity can be applied to examine various features in neural generalization. The ratio between the magnitude potential with respect to a class and with respect to the entire data, computed at the logit layer, is informative of the representation of the point. In experiments, these ratios for individual training points are found to be correlated with the Feldman memorization scores. Magnitude potential ratios aggregated across points detect structural changes in the decision boundaries and provide a geometric indicator of grokking in modular arithmetic. Although the magnitude potential ratio and neural collapse are both closely associated with intra-class and inter-class geometric structure, the magnitude potential ratio remains informative even when neural collapse is explicitly suppressed.

Recent 3GPP releases have extended 5G New Radio (NR) Sidelink (SL) to support device-to-device (D2D) relay and multi-hop capabilities. This paper presents SL-RFSIM, a component-based experimentation framework extending OpenAirInterface (OAI) with scalable multi-hop NR SL capabilities. SL-RFSIM replaces the legacy OAI RF simulator with a broker-based publish/subscribe architecture enabling arbitrary peer-to-peer connectivity while preserving compatibility with the OAI protocol stack. The framework further integrates pluggable mobility, propagation, reception, and monitoring services, and supports Layer-2 mesh networking through BATMAN-adv. Experimental evaluation on the SLICES-RI research infrastructure validates the proposed architecture through representative mesh networking scenarios and identifies the current software bottlenecks limiting scalability. SL-RFSIM provides an open-source foundation for reproducible experimental research on 5G NR SL and future multi-hop cellular mesh networks.

Optical inter satellite links ISLs are becoming the backbone of modern LEO constellations offering high capacity and low latency but introducing stringent geometric and physical layer constraints Routing in such networks must therefore account for time varying topology jitter induced outage and the heterogeneous reliability of intra and inter plane optical links aspects that classical shortest path or existing learning based schemes do not fully capture This paper develops a joint geometric and QoS aware routing framework for optical LEO networks We derive a closed form outage expression under Gaussian beam propagation with pointing errors and obtain analytical maximum feasible link ranges for different ISL classes These relations remove beam divergence from the optimization variables and embed optical feasibility directly into the routing layer leading to a latency reliability capacity constrained routing formulation that is proved to be NP hard To enable scalable decision making we cast snapshot routing as a Markov decision process and introduce an angle constrained masked deep Q network AC MDQN that integrates optical feasibility masks potential based latency shaping and a geometry aware corridor filter around the source destination great circle path This design significantly reduces the effective action space complexity while preserving near optimal routing choices Simulations on a Starlink like constellation demonstrate that AC MDQN achieves end to end latency within 1 to 2 percent of constrained shortest path solutions remains robust under varying pointing jitter and supports controllable hop latency trade offs through reward design The results confirm that the proposed framework provides an efficient and physically consistent routing solution for large scale optical LEO networks

Cooperative MARL is commonly evaluated through cooperation discovery from random initialization, leaving open whether continued optimization can destabilize learned cooperation. Actor-critic comparisons can also conflate critic presence with value gradients entering shared actor representations. We study cooperation maintenance, defined as the survival of a behaviorally verified cooperative policy under continued training. We formulate maintenance as a right-censored event-time problem and compare matched warm starts: X0 allows value loss gradients to update shared actor features, X1 retains the critic while blocking those gradients, and X5 removes the learned critic as a critic-free reference. This isolates direct value-gradient access while controlling initialization, critic computation, and evaluation. Positive reward scaling preserves strategic preferences and equilibria while perturbing learning dynamics. Gradient audits confirm the intended routing pathways, and frozen-policy torso perturbations probe whether route-induced updates align with local cooperation boundaries. In confirmatory MinEx and CleanUp-lite experiments, higher scales selectively increase maintenance sensitivity in X0; X1 remains near the censoring ceiling, and X5 has no confirmed events in the tested settings. In CleanUp-lite, route-by-scale displacement is associated with reduced local cooperation margins; MinEx shows a weaker, optimizer-dependent effect. These results identify a conditional, scale-sensitive maintenance risk associated with direct value-gradient routing rather than a universal failure of critics.

Subcritical bubbles can form an appreciable population during weak first-order phase transitions, but are usually treated as isolated fluctuations. This raises the question of whether spatial overlap between neighboring subcritical bubbles can modify their evolution. We address this question by combining analytic free-energy calculations for composite Gaussian profiles with Langevin simulations of overlapping configurations. We find that the overlap lowers the free-energy cost and generally increases the lifetime of subcritical bubbles, with the enhanced persistence potentially feeding back on their abundance. Such overlap can therefore generate collective effects and should be incorporated into kinetic descriptions of subcritical-bubble populations.

We study the Banach space and operator factorization structure of Janson-Sobolev and Janson-Sobolev-Hardy spaces. This new class of martingale spaces is determined by a $q$-adic filtration, a subspace $V\subset \mathbb{R}_0^{l\times q}$, and a rearrangement invariant function space $X$. Our main result shows that, for every bounded diagonal operator $D$, the operator $S = \sum_{t=1}^s \lambda_{\mathcal U}^{k_t}(D)Q_{\mathcal K_t}^{\mathcal B}$ determined by the linear functionals $\lambda_{\mathcal U}^{k_t}(D)$ and the canonical projections $Q_{\mathcal K_t}^{\mathcal B}$, almost projectionally factors through $D$ with constant $1^+$. As consequences, we obtain factorization results for diagonal operators both under a natural boundedness condition on the canonical projections and for all spaces equipped with the $L^1$-norm.

Difficulty is one of the most fundamental properties of a question: it determines whether the question can meaningfully discriminate between models of differing ability. Although a variety of methods can now estimate or predict difficulty automatically, they yield only a single descriptive number, with no account of the underlying factors that make a question difficult in the first place. In this work, we propose a data-driven approach that automatically generates and validates natural-language hypotheses explaining what makes one question harder than another. We first estimate each item's difficulty from the responses of a large pool of LLMs using Item Response Theory. We then sample contrasting sets of easy and hard questions and prompt an LLM to propose candidate explanations of the difference, which are subsequently validated and selected on held-out questions. Experimental results across three datasets spanning mathematical, logical, and commonsense reasoning show that our method produces interpretable and predictive hypotheses. On their own, they predict the difficulty of unseen questions competitively with, or better than, advanced black-box difficulty regressors; used as additional features, they further improve those regressors, implying that they discover difficulty signals that existing models fail to capture. Moreover, we demonstrate that editing questions according to a hypothesis can shift their measured difficulty in the expected direction, indicating that the discovered hypotheses are causally valid difficulty factors rather than post-hoc descriptions. Our approach thus turns a purely descriptive difficulty score into actionable statements.

Action chunking improves the performance of policies learned by behavioural cloning, and several mechanisms have been proposed to explain why, including temporal consistency, horizon reduction, representation learning, and reduced error compounding. We instead study what happens to an action error once it enters the system. At each state, we inject a small action error and measure how fast it grows or shrinks under two execution regimes: open-loop, where the rest of the chunk is replayed without replanning, and closed-loop, where the policy replans after the perturbation. The fitted rate labels each state as contracting, expanding, or unresolved. Across twelve manipulation tasks from three benchmark suites, we find that confidently stable states are rare, while error amplification is common among states whose propagation rate can be resolved. We further find that the measured propagation rate depends strongly on the fitting horizon: amplification is typically front-loaded, so short windows can overestimate longer-horizon propagation. Finally, we train predictors on these labels and find that a state's open-loop regime can be recovered from camera frames and proprioception alone, while its closed-loop propagation is only partially recoverable because it also depends on how the policy acts after the perturbation. These results suggest that error-compounding arguments alone do not provide a complete account of action chunking: neither passive open-loop dynamics nor policy replanning consistently contracts an injected error, and replanning rarely turns open-loop amplification into confident contraction. This suggests that closed-loop reactivity should be trained explicitly, using perturbation- and tree-coverage-oriented training to expose policies to deviations they must recover from, rather than expected to emerge reliably from standard imitation learning.

Federated parameter-efficient fine-tuning enables distributed clients to adapt pretrained vision-language models without sharing raw data or updating the full backbone. Its effectiveness, however, is limited by domain heterogeneity across clients. Existing personalized methods separate globally shared knowledge from client-specific style, but they largely treat each domain as a class-agnostic transformation. We show that this abstraction is insufficient: the cross-domain displacement associated with a fixed domain varies across semantic classes, and only a subset of these class-domain residuals damages the image-text decision margin. We therefore propose Margin-Oriented Semantic-Appearance Interaction Correction (MOSAIC), which first constructs a decision-aware harmfulness score that measures whether a training-derived class-domain residual favors a competing text prototype over the true class. It then models fine-grained class-domain interactions with a low-rank residual adapter whose class factors and residual basis are globally shared while domain factors remain client-private. An image-conditioned gate further controls candidate-wise correction, and harmful-pair-aware reweighting prioritizes decision-relevant residuals during local optimization. Extensive experiments on Office31, OfficeHome, and DomainNet100 demonstrate that MOSAIC consistently improves macro-client top-1 accuracy across all evaluated domain-shift and joint domain-label-shift settings.

Several ad hoc dispersion models for density-functional theory are based on the use of Hirshfeld (or "stockholder") partition of a molecular charge density, which provides an in situ definition of atomic size. We show that a recently introduced "optimized" quantum Drude oscillator model for dispersion admits a closed-form solution in terms of the Lambert $W$ function, whose branches identify the compact and diffuse oscillator solutions. The compact solution determines the $C_8$ (dipole-quadrupole) dispersion coefficient analytically from the free-atom polarizability, $C_6$ coefficient, and van der Waals radius, without any reference $C_8$ data. Next, we provide a formal basis for a relativistic version of the atoms-in-molecule Hirshfeld partition. Using four-component Dirac-Hartree-Fock densities for isolated atoms defines a strictly positive deformation field that carries the relativistic changes in atomic density into the Hirshfeld partition. A uniqueness theorem for the non-relativistic case is extended to relativistic Hirshfeld atoms and admits an asymptotic expansion through quadratic order in the fine-structure constant. Normalization requires the relativistic density correction to reshape the reference atom while preserving its population. Finally, four-component polarizabilities and C6 coefficients are reported for closed-shell atoms and ions, which supply the reference data required to extend atoms-in-molecules dispersion models into the heavy-element regime. Periodic trends are observable in a scalar contraction factor that measures relativistic effects.

Wearable ultrasound probes must transfer increasingly large acquisition payloads while maintaining compact, low-power electronics. In TinyProbe, the current bottleneck in data transfer occurs between the acquisition FPGA and the wireless system controller. This work presents an open-source, multi-wire SPI readout interface that uses serial command and address phases followed by a build-time-selectable dual- or quad-lane payload phase that is intended to address this bottleneck by increasing the potential bandwidth over the wifi limit while retaining compatibility with the Microcontroller-centric wearable US architecture. The interface emulates a serial flash memory, enabling compatibility with a broad range of microcontroller families and their existing peripheral interfaces. On the FPGA, the data path connects the existing acquisition FIFOs to the SPI interface through clock-domain crossing, sample reshaping, and packing into 32-bit words. Dual-SPI readout is integrated into the existing IGLOO2/SiWG917 TinyProbe architecture and verified at an SCLK frequency of 5 MHz. A separate Kria K26 testbed is used to characterize the FPGA SPI interface independently of the acquisition and wireless subsystems, demonstrating error-free transfers at SCLK frequencies up to 66 MHz. These measurements identify the SiWG917 multi-lane SPI implementation as the next bandwidth-limiting component and motivate a future upgrade of the system controller. The HDL and MCU implementations are released under a permissive open-source license.

We construct the Buchholz algebra without a Fock representation, as the bounded inverse limit of intrinsic particle-cutoff quotients of the gauge-fixed resolvent algebra, with isometric particle-degree coordinates. Its finite matrix corners carry canonical traces, KMS states, and trace-norm product formulas, together with closed-path expansions that lay the groundwork for path-integral representations. The known Fock-space description and a proper quasilocal subalgebra arise as realizations.

Dense melts of nonconcatenated ring polymers exhibit anomalous dynamics and nonlinear rheology, in some cases linked to long-lived inter-ring threading entanglement. Detecting these geometric constraints remains computationally demanding, with different methods being based on different geometric features tuned to specific models. Here, we introduce a machine-learning framework that detects threading directly from the writhe of ring conformations and we demonstrate its broad generalisability. Trained on simulations of isolated, distance-constrained pairs of short rings, a one-dimensional convolutional neural network (CNN1D) operating on the writhe profile classifies threading states with over 98% accuracy on held-out ring pairs. Remarkably, this model generalises without retraining to equilibrium dense melts spanning a wide range of densities and chain lengths (N = 100 to 1600), maintaining true-positive rates above 91% with false-positive rates near zero. Misclassified conformations are limited to physically ambiguous, shallow threading events which are arguably not impacting the dynamics of the rings. Effectively, writhe captures the interaction between the two rings, allowing writhe-based classifiers to improve the topological analysis of large ring-polymer systems with a 3-fold speed-up over the state-of-the-art minimal-surface detection. These results establish the writhe-trained neural networks as an accurate, scalable tool for characterising entanglement in ring polymer melts.

Federated training of foundation models is constrained by client memory and communication costs. LoRA-based methods reduce these costs through low-rank adapters, but their fixed rank budget can limit adaptation. Gradient low-rank optimization offers greater flexibility, yet independently chosen client subspaces create a problem we term subspace fragmentation: local projections interact with data heterogeneity to bias aggregated directions, while aggregation can increase update rank and communication cost. Thus, accurate local gradient compression need not preserve global descent. We propose FedLore, which shares a low-rank optimization basis within each round and refreshes it across rounds. The shared basis enables exact aggregation in low-rank coordinates and eliminates the identified projection bias. Subspace refresh allows the accumulated model update to exceed the per-round rank budget. We characterize the aggregation bias and establish an $O(T^{-1/2})$ stationarity bound for the projected-SGD variant under a global-gradient coverage condition and standard smoothness and variance assumptions, with bounded gradient heterogeneity. Experiments on vision and language tasks, including federated pre-training, show that FedLore outperforms the evaluated low-rank adapter baselines and matches or exceeds full-parameter training, while reducing communication and optimizer-state memory.

The environmental impact of deep learning has attracted increasing attention over the past decade. Existing studies mainly focus on the energy and carbon emissions of model training and inference, while the whole development phase is often overlooked. Yet, architecture prototyping and intensive experiments are conducted during this stage, which is highly energy-demanding. In this article, we propose a methodology to estimate these costs, based on activity logs from the Grid5000 shared computing platform used by the LORIA laboratory. As a case-study, we focus on audio projects developed in the Multispeech research team. We evaluate the overall energy cost of four projects, and we compare them to those of training the reported models. Our results show that the energy required for the development phase is 3 to 256 times greater than that required to train the best-performing model alone. These results advocate for a more systematic reporting of energy consumption across the entire life cycle of deep learning-based audio projects.

Agent evaluations increasingly go beyond a single success rate, reporting metrics such as cost, consistency, and robustness. Yet they typically treat the agent itself as fixed. In practice, an agent is a configurable system: users decide what to tell it, how long to let it run, and which model to use, and each of these choices can change how well and how consistently it performs. We study these choices on a new benchmark of four scientific tasks, where a coding agent must find and correctly operate a published specialist model. We investigate five parts of the agent's configuration: task information, reasoning, self-verification, time budget, and backbone model. We find substantial run-to-run variability, with approximately 54% of the outcome variance coming from repeating the same configuration rather than changing it. Across configurations, the information provided to the agent has the largest effect, exceeding both time budget and model size, while also reducing cost and improving calibration. Configuration choices also interact: additional time helps only when the agent has sufficient information or a capable enough model to use it. Finally, a trajectory-based taxonomy of agent behavior reveals that prompting an agent to verify its answer has little effect on its verification behavior, whereas providing a dedicated verification tool changes that behavior substantially. These results suggest that agents should be evaluated as configurable systems themselves, and that some desired behaviors are more effectively implemented in the system than requested through prompting. We release the benchmark and more than 18,000 agent trajectories.

We prove that the product of chains $\mathbf m\times\mathbf n$ is not Schur positive whenever $n\ge4$ and $m\ge3n-1$. Writing $m=n+k$, we exhibit a negative Schur coefficient indexed by $(2n+k-1,2n+k-3,\ldots,k+5,k,k,4)$ and evaluate it explicitly as $(n-2)!$ times a polynomial of degree three in $k$. Together with earlier results, this establishes the two-case interpretation of the conjecture of Li, Qiu, Yang, and Zhang: these products are not Schur positive when $n=2$ and $m\ge8$, or when $n\ge3$ and $m\ge n+5$.

The emergence of foundation models for molecular property prediction requires a high degree of AI data readiness, including reliable metadata annotation. However, both public repositories and industrial screening databases suffer from missing, inconsistent, or conflated assay annotations. In this work, we quantify the extent of missing annotations in PubChem for the BioAssay Ontology (BAO) assay format and physical detection method fields and investigate whether open-source and proprietary large language models (LLMs) can reliably predict and audit metadata annotations directly from the assay text. In our assessment, we found that the annotation coverage across PubChem's $\sim$2 million bioassays is critically sparse, 36% lacking an assay format, 89% a BioAssay type, and >99.9% any BAO-mapped assay format or detection technology term. This motivates the need for automated test-metadata curation. Using evaluation sets derived from PubChem and ChEMBL, we assess the agreement of seven open-source and proprietary LLMs with existing silver labels. Recall is at least 0.96 for biochemical and cell-based assay formats, with a similar pattern for detection technology, although disagreements increase on under-represented classes. Manual inspection shows that many of these disagreements trace back to inconsistencies between silver sources rather than to LLM error. Moreover, in a qualitative study with a senior industrial curator, LLM-generated evidence prompted the expert to revise some of their own labels, showing LLMs can flag potentially mislabeled assays. Across the study, performance differences between proprietary and open-source models were small. Together, these results suggest LLMs can support the large-scale annotation and auditing of assay metadata, though per-class reliability estimates and targeted human review remain necessary before such labels enter downstream ML pipelines.

Let $B_3=B(0,3)\subset\mathbb{R}^3$. For every sufficiently large integer $k$, we construct a nonzero real function $u_k\in C^2(\overline{B_3})$ and a real potential $V_k\in L^\infty(B_3)$ such that $\Delta u_k=V_ku_k$, $u_k|_{\partial B_3}=0$, $\mathrm{ord}_0u_k=k$, and $\|V_k\|_\infty\le Ck^{3/2}$. Consequently, for every sufficiently large $N$, there is such a Dirichlet solution with potential norm smaller than $N$ and vanishing order at least $cN^{2/3}$. The construction extends directly to higher dimensions and to spheres. Together with previous results, this example indicates that $C(1+\|V\|_\infty^{2/3})$ is the sharp bound for the vanishing order in the real-valued case. It also indicates that the bound conjectured independently by Kukavica \cite{Kukavica1998} and Kenig \cite{Kenig2006} is not attainable in general.

Generative video world models can now synthesize open-ended environments that agents can navigate and interact with in simple ways. Yet open-ended generation does not imply full interaction: as a generated world expands, newly created content through navigation should expand what the agent can act upon, and as the agent changes the world, those changes should become persistent parts of the environment rather than transient visual effects. We characterize these two requirements as Open-World Interactivity, where newly generated or encountered entities are incorporated into the actionable world, and Persistent State, where interaction outcomes are committed to the world state and continue to influence subsequent observations and interactions. We present Oneira, an interactive video world model that closes the loop between generation and interaction through an explicit, extensible world state managed by a coding agent. Given the current observation and an action or high-level goal, the agent reads the world state, grounds the relevant entities, plans the interaction, and writes its outcome back into a world state table. When exploration reveals new objects, the agent incorporates them from generated observations, allowing the interaction space to expand with the generated world. Meanwhile, previously induced state changes are carried across video segments, making the consequences of interaction persistent parts of subsequent world evolution. The updated world state is rendered along the camera action trajectory into a coarse conditioning video, from which a video generator fills in the appearance, motion, and interaction details not represented in the state. Experiments show that Oneira enables direct and consistent interaction with newly generated objects, while preserving the effects of prior interactions over long horizons. Project page: https://madaoer.github.io/projects/oneira

The recently reported LUX-ZEPLIN (LZ) event has renewed interest in inelastic Higgsino dark matter. While a weak-scale Higgsino provides a simple interpretation of the event, such a scenario is in tension with the IceCube bound from dark-matter capture and annihilation in the Sun. This tension can be avoided for a much heavier Higgsino, with a mass of order $10^5$ GeV and a neutral-state mass splitting of $\simeq 400$ keV, which in turn points to gaugino masses around $10^7$ GeV. Such a heavy supersymmetric spectrum is often thought to be unfavorable for supersymmetric grand unified theories (GUTs), since it tends to worsen gauge coupling unification and lower the unification scale, potentially leading to excessively rapid proton decay. In this work, we revisit this expectation in minimal supersymmetric SU(5), taking into account the GUT-scale threshold corrections. We show that the resulting unification conditions allow the SU(5) gauge bosons to remain sufficiently heavy when the adjoint-Higgs self-coupling is small, thereby suppressing dimension-six proton decay. At the same time, the color-triplet Higgs mass can remain near the conventional GUT scale, $M_{H_C}\sim 10^{16}$ GeV, particularly when the gluino is significantly heavier than the wino. Remarkably, in this region the dimension-five decay mode $p\to K^+\bar\nu$ can have a lifetime within the reach of next-generation proton-decay searches, including Hyper-Kamiokande, JUNO, and DUNE. We also discuss supersymmetry-breaking scenarios that can give rise to the required supersymmetric mass spectrum.

Continuous legged manipulation requires accurate end-effector tracking while the base keeps walking. Combining reinforcement learning (RL) with model predictive control (MPC) suits this task: the learned policy provides robust locomotion, while MPC coordinates the base and arm to compensate for tracking errors. However, MPC can compensate only for base motion that it can predict, and a learned policy's command response varies with gait phase, contact, and payload. We present ReCo, a framework that couples response-consistent locomotion with policy-aware MPC for legged manipulation. Response shaping trains the policy to respond to commands consistently and repeatably across randomized dynamics. An identified closed-loop response model then lets MPC jointly plan locomotion commands and arm motion. On the simulation benchmark, ReCo reduces position and orientation root-mean-square error (RMSE) by 28.7% and 27.4% relative to the best baseline for each metric. Real-world experiments demonstrate onboard continuous legged manipulation with coordinated base and arm motion.

Context. Architectural degradation undermines software maintainability, evolvability, and quality. However, existing research remains fragmented across measurement approaches, metrics, tools, and remediation strategies, limiting our understanding of how these elements relate across the degradation lifecycle. Aim. We consolidate the state of the art on architectural degradation by examining how researchers measure it, which metrics and tools support its assessment, and how existing approaches address remediation. Method. We conducted a Multivocal Literature Review of 284 peer-reviewed and grey-literature studies. We supported screening, data extraction, and classification with a locally executed LLM-assisted pipeline combining Retrieval-Augmented Generation, multi-model validation, and human adjudication. We then analyzed the resulting taxonomies and their cross-dimensional relationships. Results and Conclusions. We identified 277 measurement approaches, 357 metrics, 238 tools, and 395 remediation approaches. Research strongly concentrates on static and structural analysis, structural metrics, and detection-oriented tools. In contrast, remediation spans heterogeneous code-level, architectural, and organizational interventions and shows substantially less consolidation. Overall, the field has developed a mature diagnostic apparatus but has made less progress in connecting degradation detection with effective remediation. Our results provide a structured view of the available techniques and identify the diagnosis-remediation gap as a key direction for future research.

We develop a growth model with an R&D sector in which the elasticity of innovation with respect to existing knowledge can be negative. We investigate the existence and uniqueness of a balanced growth path (BGP) and derive closed-form growth factors, showing that productivity and output growth are semi-endogenous and population-driven. We also establish the global stability under a general production function. Under testable parameter restrictions, the economy converges to the BGP. However, when the knowledge elasticity is sufficiently low, a Jacobian-based condition implies instability, and an N-period innovation cycle can emerge. Comparative statics are conducted to explore the impact of several factors, including research efficiency, input elasticity, and population growth. Numerical simulations map out transitions and mark the points at which stability is lost. They make clear when innovation frictions endanger balanced growth and provide practical guidance for R&D and demographic policy.