Papers

Loss spikes are recurrent instabilities in neural-network training and can arise from multiple mechanisms. For Adam in particular, macroscopic loss spikes have been linked to optimizer dynamics, yet how its two momentum timescales govern them remains unclear. We investigate this dependence by mapping training dynamics across the $(\beta_1,\beta_2)$ plane. Across a range of model–task settings, an approximately linear boundary, $1-\beta_2=C(1-\beta_1)$, separates spiky from non-spiky dynamics, whereas a one-dimensional quadratic loss produces approximately cubic slope. A one-dimensional superquadratic loss $L(x)\propto|x|^n$ recovers the near-linear scaling and links the boundary coefficient to the effective loss exponent $n$. We further show that confident cross-entropy losses develop a core–wall landscape comprising a narrow quadratic core followed by a steep wall, which produces effective superquadratic behavior at the scale of an optimizer update. Together, these results connect Adam loss spikes to both the mismatch between momentum timescales and finite-scale superquadratic loss geometry beyond the Hessian.

Let $X\subset \mathbb{O}^n$ be a nodal hypersurface of degree $d$ with an ordinary $m$-fold point. Let $\delta_X$ be the largest value of $\delta$ such that $X$ is contained in the closure of the Severi variety of degree $d$ hypersurface in $\mathbb{P}^n$ with $\delta$ nodes. After recalling how the semicontinuity of the spectrum yields an upper bound for $\delta_X$, we produce various lower bounds for $\delta_X$. These bounds are given by polynomials in $m$ of degree $n$, with different leading coefficients. This improves previous bounds given by Ciliberto-Galati.

We study statistical variants of the classical largest average submatrix problem. For small submatrices (where the dimension is less than linearly proportional to the original matrix), the problem is typically well understood and believed to exhibit the statistical-computational gap (SCG). However, analytical treatment of both the information-theoretic and algorithmic aspects of the linear regime remains challenging, and no mathematically rigorous results have yet arrived anywhere close to proving or disproving SCG existence in this setting. Focusing on the linear regime, we make strong progress in several key directions: 1) We develop a generic Random Duality Theory (RDT) framework to characterize largest average submatrix values. 2) Using the plain RDT variant, we obtain closed-form upper bounds as explicit functions of dimensionality proportionality parameters. 3) We demonstrate that a lifted RDT variant strictly improves upon the plain RDT within a certain linear range of submatrix dimensions. 4) For small submatrices where the dimensional proportionality constants approach zero, we prove that our results match both the replica results from [34] (obtained via one-step replica symmetry breaking) and the sublinear results from [18,45].

Large Language Models (LLMs) have demonstrated remarkable performance in automatic code generation tasks, thereby encouraging new research in this area. Although numerous studies have explored LLM-based code generation, the impact of the natural language in input prompts remains unexplored (language bias). This study aims to (1) quantify how the natural language of input prompts influences LLM-based code generation performance and (2) evaluate a mitigation strategy to reduce language bias in code generation. We assess code generation Accuracy on AtCoder, LeetCode, and BigCodeBench. To quantify the language bias on code generation, each problem is presented in English, Japanese, and Chinese. We use seven LLMs (GPT-4o, o3-mini, DeepSeek-V3.2, Llama-3, Qwen2.5-Coder-14B, Qwen2.5-Coder-0.5B, and GitHub Copilot) and assess their performance in terms of Accuracy (the number of problems for which generated code passes all test cases). We compare Accuracy before and after translation to evaluate the effectiveness of translation as a mitigation strategy. We observed that the natural language of problem statements affects LLM-based code generation performance. Specifically, the languages officially supported by each dataset achieved the highest median Accuracy. Also, translation improved Accuracy, but its effectiveness was not consistent across datasets and model types. We found that AtCoder contained a particularly high proportion of narrative-style problem statements and longer problem statements. Natural language significantly affects LLM code generation accuracy. Translation can mitigate language bias in some settings, but its effectiveness depends on the dataset and model type. Furthermore, the narrative aspects and context length of input prompts are important factors related to language bias and the effectiveness of translation as a mitigation strategy.

We introduce Nemotron-SEA-LION-v4.8, a family of Southeast Asian Languages In One Network (SEA-LION) models built upon NVIDIA Nemotron 3. The family includes 30B-A3B and 120B-A12B models, with both continued-pretrained base checkpoints and post-trained variants. We adapt the models using Southeast Asian, reasoning, code, and multilingual parallel data, followed by post-training with supervised fine-tuning and online on-policy distillation. On SEA-HELM, the 30B-A3B model improves the overall SEA score from 46.06 to 51.57, while the 120B-A12B model improves from 49.30 to 63.44. Across seven Southeast Asian languages, we observe broad capability gains with the 120B-A12B model showing broader and more consistent improvements across tasks.

The round-robin procedure is a simple and well-studied fair division mechanism where agents pick goods in turns. Motivated by draft mechanisms in sports leagues, we investigate strategic behaviour in online round-robin for subadditive agents. This gives rise to an extensive-form game, and we study the computational problem of computing a subgame perfect Nash equilibrium (SPNE). We show that for just two submodular agents, computing an SPNE is $\mathsf{PSPACE}$-hard. Even for the class of $\mathit{OXS}$ utilities, which are a special case of submodular utilities, computing an SPNE remains $\mathsf{NP}$-hard for a small number of agents. We complement our computational results with normative results. We show that for just three additive agents, there exist instances where every equilibrium violates EF1. This separates the online and the direct revelation games. On the positive side, we show that for additive agents every equilibrium allocation is proportional up to one good (PROP1) and for two additive agents it is also EF1. Finally, by showing that round-robin is bossy at equilibrium, we prove that the number of equilibrium allocations can be exponential even if agents have lexicographic preferences.

It is mathematically proved that, for a grid under a boundary-preserving piecewise-smooth deformation, the positivity of the Jacobian determinant in each closed element is also a sufficient condition for the deformed grid to remain valid. Most of the proof is devoted to showing that the element-wise positivity of the Jacobian indeed induces a local isomorphism in the grid-deformation setting. This result provides users of ALE methods and of the generalized Lagrangian method with a clean answer: checking the Jacobian alone is enough to determine the validity of the deformed grid.

This paper studies predictive online control for linear dynamical systems with time-varying cost functions, motivated by applications such as real-time adaptive control of motorized LiDAR sensing systems, where the controller must adjust the sensing direction online to balance localization accuracy, scanning efficiency, and smooth actuation under changing environmental conditions. We propose a predictive online control (POC) algorithm that leverages short-term predictions of future cost functions while accounting for the memory effect induced by system dynamics. Using the disturbance-action controller (DAC) parameterization, the online control problem is transformed into an OCO-with-memory formulation over policy parameters. We develop a windowed receding-horizon update that incorporates short-term predictions and accommodates a total-variation regularizer to suppress abrupt policy variations. Theoretically, we prove that POC achieves a dynamic policy regret bound scaling with the path length of the comparator sequence, and provide sufficient conditions in terms of logarithmic prediction and memory horizons for the regret guarantee. The proposed method is evaluated on a motorized LiDAR sensing task, demonstrating improved localization accuracy together with a favorable trade-off between sensing accuracy and scanning completeness.

Large language models (LLMs) are increasingly deployed in applications involving interaction between agents, where their output plays a role in collective reasoning and decision-making processes. Despite significant research into the functioning of LLMs in such multi-agent systems, the processes of bias propagation in such systems are still a challenge. This work studies how biased opinions are propagated in the form of textual interaction in an environment of LLMs, in which a minority of agents maintain persistent extreme opinions, while the remaining agents iteratively update their beliefs through structured textual interactions. The findings show that even the presence of a small percentage of biased agents in such a system leads to significant shifts in the opinions of non-biased agents. It suggests that for the same percentage of biased agents, the shifts occur more quickly for the Llama~3.2 model when compared to a classical Friedkin-Johnsen (FJ) model. Further semantic analysis demonstrates that rhetorical consistency in textual explanations increases systematically with biased exposure and, importantly, is partially decoupled from numerical convergenumericalutral agents adopt the vocabulary employed by the biased agents even in configurations where their numerical opinion shifts remain moderate. The research helps explain how bias and language develop together in multi-agent language model ecosystems.

Conventional integrated sensing and communications (ISAC) systems primarily integrate communications and sensing through shared physical resources, without explicitly exploiting task-relevant semantic information. To move beyond such physical-level integration, we propose semantic ISAC (SemISAC), a general framework that unifies semantic communication (SemCom) and semantic sensing (SemS) to convey source meaning and acquire environmental meaning. Specifically, the transmitter combines source semantics and sensing task information with available side information to design the shared waveform and allocate radio resources, while the receiver-side communication and sensing task decoders recover the source meaning and infer the required environmental information, respectively. We also provide an information-theoretic interpretation to characterize the relationship between physical and task-relevant information and the resulting semantic trade-off in SemISAC. Building on this framework, we formulate the general SemISAC design problem and propose two realization methods, namely end-to-end (E2E) SemISAC optimization and modular SemISAC optimization. As a concrete realization, we apply modular SemISAC optimization to jointly design a learnable time-frequency (TF) precoder in an orthogonal frequency-division multiplexing (OFDM) system for representative SemCom and SemS tasks. Simulation results demonstrate that the proposed realization reduces sensing semantic distortion under a given communication requirement and achieves a more favorable communication-sensing trade-off than baseline designs.

Large language model (LLM) agents increasingly tackle long-horizon tasks through multi-step environment interaction, yet a single erroneous action can alter subsequent states and observations, causing errors to compound over time. Existing methods either correct the context without repairing altered environment states or restore earlier states while discarding useful experience, making it difficult to both eliminate failure conditions and avoid repeating past mistakes. We argue that reliable recovery should instead be treated as a rollback-boundary control problem that jointly determines when to intervene, where to resume, and what information should survive recovery. Based on this view, we propose Rollback-Induced Reflection (RIR), a unified recovery framework that restores execution to a selected prior state while carrying forward reusable knowledge distilled from the abandoned trajectory to guide subsequent decisions. We further characterize recovery through a unified operator over rollback depth and retained memory, providing a general view of state restoration and knowledge retention. Experiments on three long-horizon benchmarks show that RIR consistently improves average task performance across multiple LLM backbones, with structured reflection memory preserving useful experience and selective rollback enabling efficient recovery.

This study examines how the chemical-reaction timescale alters hypersonic wall-model predictions of heat and momentum transfer. A one-dimensional finite-rate-chemistry wall model for high-enthalpy air is evaluated over 3 <= Ma_e <= 25, 2 <= p_e <= 100 kPa, and a broad range of edge and wall temperatures. All forward and reverse reaction rates are multiplied by a common factor Gamma, which changes the chemical timescale while preserving the equilibrium constants and thereby connects the frozen and fast-chemistry limits within the same governing equations. Taking a 1 percent difference in wall heat flux between the frozen and finite-rate solutions as the threshold for retaining finite-rate chemistry, two quantities obtained from the frozen solution provide practical selection criteria: Da_fr = t_shear / t_ch >= 1.93 x 10^3 and T_max >= 3760 K. The wall heat flux does not generally vary monotonically with reaction rate; instead, it can decrease below both the frozen and fast-chemistry predictions before recovering at higher rates. The two limiting chemistry solutions therefore do not generally bound the finite-rate heat-flux response, and interpolation between them can be misleading. At Ma_e >= 20, the median wall-heat-flux errors of the frozen and fast-chemistry limits are 7.1 percent and 27.6 percent, respectively. Chemistry also produces substantial changes in wall heat flux and shear stress, whereas the Reynolds analogy factor responds much less because the momentum- and enthalpy-side wall-law shifts nearly cancel. These results show that finite-rate wall transfer cannot in general be inferred from its frozen and fast-chemistry limits and provide frozen-state indicators for determining when finite-rate chemistry should be retained in hypersonic wall modelling.

RAW-to-sRGB image signal processing (ISP) must recover perceptually faithful colors and fine details from sensor measurements, often under imperfect spatial alignment and missing camera metadata. This paper presents, to the best of our knowledge, the first application of visual autoregressive (VAR) next-scale prediction over a discrete image codebook to the RAW-to-sRGB ISP task. We adapt a frozen 1.10\,B-parameter VAR backbone for RAW-conditioned ISP with only 32.93\,M trainable parameters (2.99%), and propose a frequency-decomposed color loss that separately supervises low-frequency tone via wavelet LL cosine similarity and chromatic edges via detail-band $\ell_1$. On the Zurich RAW-to-sRGB benchmark, the method improves PSNR-Y from 21.31 to 21.89\,dB and reduces LPIPS from 0.276 to 0.218 on the full 1,204-image test set. Diagnostic experiments show that the VAR prior preserves structure well, but continuous color transfer remains the dominant bottleneck: oracle affine correction recovers 3.8\,dB, while learned color heads yield marginal gains.

This paper investigates the imaging–communication trade-off in very-low-Earth-orbit (VLEO) integrated sensing and communication synthetic aperture radar (ISAC-SAR) using cyclic-prefix orthogonal frequency-division multiplexing (CP-OFDM) as the shared waveform. We develop a unified analytical framework that jointly accounts for random communication payloads, range-dependent CP deficit across the swath, and slow-time-varying platform Doppler over the synthetic aperture. The resulting signal model separates the coherently retained component from inter-carrier interference (ICI) and inter-symbol interference (ISI) through common subcarrier-coupling coefficients. By propagating these effects through receive filtering, range compression, and azimuth focusing, we derive image-domain statistics for matched- and reciprocal-filter receivers. Based on the derived statistics, an effective noise-equivalent sigma zero (ENESZ) is formulated to characterize data-dependent sidelobes, ICI/ISI, and noise enhancement on a common backscatter-equivalent scale. The analysis reveals that the CP duration acts as a system-level design parameter bringing scalable trade-off. Increasing the CP improves coherent retention and suppresses range-dependent interference, but simultaneously reduces coherent processing gain and communication payload throughput. Accordingly, the sufficient-CP duration does not generally coincide with the imaging-optimal CP duration. End-to-end simulations for a representative VLEO scenario validate the derived image-domain statistics and demonstrate the resulting trade-off between ENESZ and communication throughput as a function of CP duration.

Blue large-amplitude pulsators (BLAPs) are rare, hot, short-period pulsating stars whose rapid oscillations provide a unique probe of stellar interiors and atmospheres. In this paper, we study two short-period BLAPs in the Galactic bulge, OGLE-BLAP-142 ($P \approx 6.6$ min) and OGLE-BLAP-148 ($P \approx 7.5$ min), by combining light curves from the OGLE, KMTNet, and DREAMS surveys, spanning 17 years with cadences ranging from minutes to hours to days. We perform Generalized Lomb-Scargle periodogram analyses of their light curves and identify, for each BLAP, three closely spaced pulsation modes separated by $\sim 1\%$. The dominant mode can switch within timescales of order a year, accompanied by a likely blueward color shift ($\sim 0.1$–$0.2$ mag). The yearly period excursions of the resolved mode families imply apparent $|\dot{P}/P|$ values of order $10^{-6}$–$10^{-4}\,\mathrm{yr^{-1}}$, large enough to mimic or exceed smooth evolutionary period changes. One mode family in OGLE-BLAP-148 shows a coherent decade-long drift at the $\sim10^{-5}\,\mathrm{yr^{-1}}$ level, but its failure to extrapolate to the earliest and latest epochs suggests a transient mode-family drift rather than secular evolution. Such close-spaced multiple pulsations and mode switching may be common among BLAPs with periods shorter than 10 min, and their physical origin remains unclear.

We study a fractional assignment setting where $n$ objects are to be assigned to $n$ agents with unit capacity, and each agent specifies an ideal distribution over the objects. Unlike in classic random assignment, these ideal distributions are not necessarily degenerate, as agents may prefer a mixture of objects rather than any single object. We assume that agents seek to minimize the $\ell_1$ distance between their ideal distribution and the distribution they receive, which is equivalent to maximizing the overlap between the two distributions. We propose two mechanisms, one based on water filling (WF) and the other on quadratic programming (QP), and show that both mechanisms are utilitarian-optimal (and hence Pareto efficient), envy-free, strategyproof, and satisfy equal treatment of equals. Moreover, we highlight a distinct advantage of each mechanism: while the WF mechanism satisfies the stronger property of group-strategyproofness, the QP mechanism is more robust in terms of egalitarian overlap welfare.

Agentic-AI based software development offers the promise of faster completion of the software, greater programmer efficiency, and more reliable code. The question is how can we verify these claims in an objective way? In this project, we attempted to answer this question based on three practices. First, we applied a typical best-practices agentic AI workflow for software development. Second, our target programs were ten well-known, release-quality human-written Linux utility programs so that we could compare the AI-generated code against a concrete ground truth. Third, we based our measure of reliability on a widely used testing technique, fuzz random testing. For this testing, we used both classic black box, generational testing and more modern coverage guided (gray box, mutational) testing using AFL++. We found that the AI-generated versions of the utility programs were typically as reliable - often more reliable - than the latest human-generated versions of these programs. While the AI-generated versions did have some failures, they were less common than the code from the standard repositories. Interestingly, the AI-generated code was less likely to have failures such as memory errors (such as buffer overflows) but more likely to have hangs such as infinite loops. In addition, we verified that generating robust and reliable software using agentic AI requires careful practice and human supervision. The quality of the code is highly dependent on the prompts and skills used, and how the human directing the process responds. We also demonstrated that using agentic AI workflow for software development (with its prompts and skills) can become a specification of the code that leads to cost-effective sustainability of the software.

Let $X$ be a genus $g\geq 0$ compact Riemann surface that admits an antiholomorphic involution $\iota$ with non empty fixed-point set, and let $D = \{p_1,\dots,p_k\}\subset \text{Fix}(\iota)$. At each puncture, we prescribe a Scherk map associated to a given real polynomial quadratic differential with even degree and negative leading coefficient. Here a Scherk map is the harmonic diffeomorphism from $\mathbb{C}$ to the interior of an ideal polygon in $\mathbb{H}^2$, whose Hopf differential is the given polynomial. We construct a harmonic map \[ h:X\backslash D \to \mathbb{H}^2 \] whose asymptotic behavior at each puncture matches the prescribed Scherk map. In particular, the image of $h$ tends to an ideal polygon near each end. The resulting $h$ covers harmonic maps obtained by taking the $\mathbb{H}^2$ factors of horizontal catenoids in $\mathbb{H}^2 \times \mathbb{R}$.

Traditional retrieval systems typically use multi-stage cascading architectures (MCA), where each module is optimized independently, leading to inconsistent objectives and the premature elimination of high-potential candidates. Recent LLM-based generation methods offer end-to-end solutions but use discrete semantic identifiers (SIDs) to retrieve ads, which are not learned by the base LLM and require memorization of numerous SID-to-ad mappings during SFT, suffering from limited generalization to unseen ads, high maintenance and update costs. The one-to-one mapping between SIDs and advertisements leads to inefficient decoding. Moreover, these methods rely on a small reward model (e.g. pctr) for relevance and ranking, limiting the LLM's ability to fully assess ads' commercial value. To address these challenges, we propose A uNified Generation-discriminative-ranking reaL-time rEtrieval (ANGLE) framework. ANGLE uses LLM-generated hierarchical textual representations, which consist of commercial intent that provide high-level overviews and ad abstract that deliver fine-grained details. Additionally, ANGLE integrates retrieval, relevance, and ranking directly within a single LLM, enabling precise and efficient ranking of ads by leveraging the full capabilities of the LLM. We applied ANGLE to the real-world search scenarios, achieving a 1.81% increase in consumption and a 2.16% increase in gross merchandise volume (GMV). We also conducted offline evaluations of ANGLE and seven baselines, with ANGLE outperforming all across key metrics such as HR and ACR.

We construct turbulent gravitational wakes in asymptotically AdS$_4$ spacetimes by solving the full non-linear Einstein equations in the characteristic formulation. Specifically, we show that a localized boundary deformation acting on a boosted black brane generates a wake whose boundary dynamics exhibit the formation of coherent vortical structures that are advected downstream by the background flow. Analysing a wake propagating along the x direction, we show that it displays the characteristic self-similar scaling of classical turbulent wakes. We then identify the geometric imprint of the wake on the horizon area density, the traceless horizon extrinsic curvature, and bulk metric perturbations, finding coherent structures that extend from the asymptotic boundary to the horizon. These results provide the first study of turbulent gravitational wakes in four-dimensional asymptotically AdS spacetimes.

In seismic exploration, the propagation of seismic waves naturally gives rise to long-range dependencies in seismic data. Capturing such global correlations can significantly improve the accuracies of seismic signal processing, inversion, and interpretation. Global modeling (GM) methods have therefore emerged as an effective paradigm for seismic exploration, offering a powerful means of exploiting the intrinsic global relationships within seismic data. However, the mainstream GM approaches, particularly Transformers, incur prohibitively high computational costs for their inherent quadratic complexity, which restricts the scalability of such methods to higher-dimensional data. To achieve efficient GM for three-dimensional (3D) seismic exploration, we propose a general framework, named lightweight Mamba-based global modeling (LMGM), to establish long-range dependencies at a relatively low computational cost. Specifically, LMGM fully leverages the linear complexity of Mamba. A three-directional scanning Mamba block is designed to exploit spatial correlations along the three dimensions of 3D seismic data. Meanwhile, a dual-domain-aware block is further developed to integrate time- and frequency-domain features for enhanced feature representation. In addition, a two-stage plug-and-play nonlinear normalization strategy is proposed to enhance the adaptability of LMGM to diverse seismic records while preserving signal characteristics. We employ 3D seismic data interpolation as a representative task to comprehensively evaluate LMGM. The results demonstrate that LMGM achieves superior processing performance while substantially reducing computational cost compared with U-Net-based and Transformer-based methods. Furthermore, experiments on random noise removal demonstrate the applicability of LMGM beyond interpolation, supporting its potential as a general GM framework.

Robotic data generation is a promising paradigm for scaling robot learning without collecting large-scale real-world data. However, generating geometrically diverse yet physically valid data for contact-rich tasks remains challenging, especially when success depends on precise geometric interfaces. Standard shape augmentation methods often distort task-critical interfaces, resulting in invalid contact relationships, e.g., fit mismatches or interpenetration, rendering downstream interactions infeasible. To address these limitations, we propose a function-preserving Real-to-Sim-to-Real framework that generates synthetic demonstrations from reconstructed assets without teleoperated source trajectories. Our method augments task-relevant object geometries through constraint-guided mesh deformation, together with physically consistent transfer of task poses and collision proxies. Visual domain randomization is further applied during simulation rollouts, enabling robust zero-shot policy deployment without real-world fine-tuning. Extensive experiments in both real-world and simulation settings demonstrate that our method enables robust generalization across unseen object geometries and diverse visual conditions in contact-rich and long-horizon tasks. Our method provides a practical path toward scalable robot learning for contact-rich tasks via shape deformation.

Sprays of scalar curvature constitute an important class of sprays, and such a class includes all two-dimensional sprays. In this paper, we consider the global metrizability of certain sprays on a manifold under some curvature and topological conditions. We prove that, for a regular spray G of scalar curvature with almost everywhere nonzero Ricci curvature on a manifold $M$ of dimension $n\ge 3$, G is globally metrizable if and only if it is locally metrizable, provided that $M$ has trivial first de Rham cohomology group. Further, we characterize the global metizability of a class of two-dimensional singular Berwald sprays on a manifold with trivial first de Rham cohomology group. Meanwhile, on a cylinder $S^1\times {\bf R}$ (with non-trivial first de Rham cohomology group), we construct a family of singular Berwald sprays which are locally metrizable but not globally metrizable. Finally, we construct some examples of two-dimensional sprays on cylinders or spheres with special properties.

Use case flows are important elements of use case modeling because they support downstream software engineering activities, including requirements analysis, architectural and detailed design, and test case generation. However, constructing them manually is costly and expertise-intensive, while existing automated approaches still struggle to preserve semantic consistency, control-flow logic, data-flow logic, and the intended system boundary, especially when identifying branch points and generating alternative flows. To address this problem, we propose FlowGen for complete use case flow construction. FlowGen uses LLM-based Semantic Information Processing (SIP) to extract semantic elements, constructs a Semantic Relational Graph (SRG) encoded by an enhanced R-GAT for basic flow generation (BFGen), and further supports branch point prediction through BPP and branch-conditioned alternative flow generation through AFGen. Evaluations on 13 public and 7 industrial datasets show that FlowGen consistently outperforms competitive baselines in all three core components. In particular, BFGen improves over the best baseline by 14% in Precision, 7-25% in Recall, 11-30% in F1, and 10-19% in AUC; BPP improves Precision by 30-110%, Recall by 33-91%, and F1 by 32-117%; AFGen improves Precision by 8-23%, F1 by 5-18%, and AUC by 0.6-2.5%. Moreover, we validate the effectiveness of the LLM-based SIP module and the attention preservation factor in BFGen, analyze the impact of requirement completeness on BFGen, and examine how different scopes of branch-related context affect AFGen.

We investigate the optimal endpoint $L^2$ restriction estimates of Laplace eigenfunctions on submanifolds of codimension 2 in a smooth closed Riemannian manifold $M$. For every fixed smooth codimension-two submanifold $\Sigma$, we prove a little-o improvement $o(\lambda^{1/2}\sqrt{\log\lambda})$ on the classical estimate $O(\lambda^{1/2}\sqrt{\log\lambda})$ of Burq–Gérard–Tzvetkov and Hu. Our proof uses the Bargmann transform and Tataru's phase-space representation to reduce the problem to Stein–Street's estimate for singular Radon transforms. The three-dimensional case can be handled directly by Ricci–Stein's estimate. Moreover, we construct explicit examples to show that the little-o improvement is optimal in general. These are closely related to earlier counterexamples for endpoint Strichartz estimates by Montgomery–Smith and Carbery–Hofmann. In particular, we establish the log-free estimate $O(\lambda^{1/2})$ when $(M,g)$ and $\Sigma$ are real analytic, whereas this estimate fails in general in the smooth setting.

This paper links all individuals who spoke in the German Bundestag between 1949 and 2021 to Wikidata, creating a longitudinal dataset that connects parliamentary speech transcripts with structured biographical metadata. We evaluate the coverage, composition, and potential biases of the retrieved properties and statements, with particular attention to gender, professional background, historical legacies, and transnational dimensions such as place of birth, languages, and foreign awards. The results demonstrate both the analytical potential of combining GermaParl with Wikidata and the importance of critically assessing uneven metadata coverage in open knowledge graphs.

Interacting dark energy (IDE) models, featuring interactions between dark matter (DM) and dark energy (DE), have received significant renewed interest. However, little attention has been devoted to understanding their genuine cosmological signatures, with comparisons against $\Lambda$CDM often carried out at fixed cosmological parameters. Considering the widely studied model with energy exchange rate proportional to the DE density, we carry out a three-level sequence of comparisons, starting from the naïve fixed-parameter comparison, then compensating for shifts in $\theta_s$ and $z_{\text{eq}}$, and then removing effects due to the modified background. We show that fixing $\theta_s$ and $z_{\text{eq}}$ leads to pre-recombination evolutions of the Weyl potential, photon monopole, and baryon velocity which are nearly identical to their $\Lambda$CDM counterparts, and hence virtually indistinguishable Cosmic Microwave Background (CMB) temperature power spectra. Comparing IDE to a non-interacting $w$CDM model with the same background, we find small scale-dependent signatures in CMB lensing. We find larger differences in the matter power spectrum, reflecting the different values of $\Omega_m$ resulting from the different partition of the dark sector into DM and DE, with only percent-level differences remaining once we compare $\Omega_m^2P_m(k)$, indicating the importance of high-fidelity determinations of $\Omega_m$. Our controlled comparison strategy can be a powerful tool for a wide range of models beyond $\Lambda$CDM.

We perform a detailed study of a principal–agent problem in a continuous time version of the celebrated Holmström–Milgrom model (Econometrica 55 (2), 1987) where we add limited liability for the Agent. We develop a probabilistic methodology to prove that the Principal's value function is the unique bounded classical solution to a fully nonlinear and fully degenerate partial differential equation (PDE) with Cauchy-Dirichlet boundary conditions on $[0,T]\times[0,\infty)$. Indeed, we also prove infinite continuous differentiability of the solution in the interior of the domain. The strength of our regularity result is such that we can ensure existence of optimal controls in strong form—a rare occurrence in dynamic contracting—and we obtain fine properties of the optimal control map, including a characterisation via a further nonlinear degenerate PDE.

Chess has long served as a model domain for studying search, expertise, decision-making, and artificial intelligence. The emergence of large language models (LLMs) has renewed the relevance of chess as a controlled environment for investigating strategic reasoning and comparing human and artificial decision-making. We present a systematic mapping study of recent research spanning human players, classical chess engines, neural and reinforcement-learning systems, LLMs, and hybrid approaches. The final map comprises 84 core study families, classified according to agent type, strategic-reasoning stages, and evaluation dimensions. The map reveals a literature strongly concentrated on situation assessment, evaluation, and action selection, while explicit planning, explanation, metacognition, and human–AI collaboration remain less explored. LLM research places particular emphasis on state representation and generalization, whereas grounded explanation appears more frequently in hybrid approaches combining language models with engines, expert knowledge, or other external structures. Two distinctions emerge that the map aggregates rather than resolves: hybrid systems differ in where and when heterogeneous capabilities combine, and evaluations that show improved human performance do not thereby establish human–AI synergy. We propose both as extensions of the mapping framework. We argue that chess provides a useful bridge between cognitive and computational perspectives on strategic reasoning, and identify explicit planning, grounded and faithful explanation, metacognitive calibration, and human–AI complementarity as directions for future research.

Among the crowd of dark matter candidates, light scalar and vector particles have been the focus of intense theoretical and experimental investigations over the past 15 years. However, those are always described as scalar or vector fields. Instead, we investigate their embedding as antisymmetric rank-three and rank-two tensor fields. By reconciling theoretical investigations, regarding the nature of the dualities relating the standard and tensorial descriptions and their different possible Stueckelberg gauge representations, and phenomenological examinations considering the effective interactions between tensor fields and the Standard Model, we prove these tensor fields to provide a completely distinct framework. This alternative set allows for different couplings and therefore different experimental signatures for the detection or production of dark matter at both low energy and colliders.