We consider a discrete-time formulation for a class of high-dimensional stochastic joint replenishment problems. First, we approximate the problem by a continuous-time impulse control problem. Exploiting connections among the impulse control problem, backward stochastic differential equations (BSDEs) with jumps, and the stochastic target problem, we develop a novel, simulation-based computational method that relies on deep neural networks to solve the impulse control problem. Based on that solution, we propose an implementable inventory control policy for the original (discrete-time) stochastic joint replenishment problem, and test it against the best available benchmarks in a series of test problems. For the problems studied thus far, our method matches or beats the best benchmark we could find, and it is computationally feasible up to at least 50 dimensions -- that is, 50 stock-keeping units (SKUs).

We present Empathic Prompting, a novel framework for multimodal human-AI interaction that enriches Large Language Model (LLM) conversations with implicit non-verbal context. The system integrates a commercial facial expression recognition service to capture users' emotional cues and embeds them as contextual signals during prompting. Unlike traditional multimodal interfaces, empathic prompting requires no explicit user control; instead, it unobtrusively augments textual input with affective information for conversational and smoothness alignment. The architecture is modular and scalable, allowing integration of additional non-verbal modules. We describe the system design, implemented through a locally deployed DeepSeek instance, and report a preliminary service and usability evaluation (N=5). Results show consistent integration of non-verbal input into coherent LLM outputs, with participants highlighting conversational fluidity. Beyond this proof of concept, empathic prompting points to applications in chatbot-mediated communication, particularly in domains like healthcare or education, where users' emotional signals are critical yet often opaque in verbal exchanges.

Over the last decade, machine learning has been extensively applied to identify malicious Android applications. However, such approaches remain vulnerable against adversarial examples, i.e., examples that are subtly manipulated to fool a machine learning model into making incorrect predictions. This research presents DeepTrust, a novel metaheuristic that arranges flexible classifiers, like deep neural networks, into an ordered sequence where the final decision is made by a single internal model based on conditions activated in cascade. In the Robust Android Malware Detection competition at the 2025 IEEE Conference SaTML, DeepTrust secured the first place and achieved state-of-the-art results, outperforming the next-best competitor by up to 266% under feature-space evasion attacks. This is accomplished while maintaining the highest detection rate on non-adversarial malware and a false positive rate below 1%. The method's efficacy stems from maximizing the divergence of the learned representations among the internal models. By using classifiers inducing fundamentally dissimilar embeddings of the data, the decision space becomes unpredictable for an attacker. This frustrates the iterative perturbation process inherent to evasion attacks, enhancing system robustness without compromising accuracy on clean examples.

We study the decoupled multi-armed bandit problem, where the learner separately selects one arm for exploration and one, possibly different, arm for exploitation at each round. In this setting, the loss of the explored arm is observed but not incurred, whereas the loss of the exploited arm is incurred without being observed. We propose an efficient Follow-the-Perturbed-Leader (FTPL) policy that achieves Best-of-Both-Worlds (BOBW) guarantee with constant regret in the stochastic regime and optimal $O(\sqrt{KT})$ regret in the adversarial regime. A key feature of our method is that it completely avoids both the convex optimization required by prior BOBW policies and the resampling procedures typically used in FTPL bandit policies. This allows FTPL to fully realize its computational efficiency advantages, leading to substantial reductions in computational cost. We empirically confirm that our policy not only improves the runtime but also demonstrates superior regret performance in both regimes.

Generative models frequently suffer miscalibration, wherein statistics of the sampling distribution, such as the fraction of generations in a given class, deviate from desired values. We frame calibration as a constrained optimization problem and seek the closest model in Kullback-Leibler divergence satisfying a calibration constraint. To address the intractability of imposing these constraints exactly, we introduce two surrogate objectives for fine-tuning: (1) the relax loss, which replaces the constraint with a miscalibration penalty, and (2) the reward loss, which converts calibration into a reward fine-tuning problem. We demonstrate that these approaches substantially reduce calibration error across hundreds of simultaneous constraints and models with up to nine billion parameters, spanning applications in protein design, image generation, and language modeling.

Large language models (LLMs) are increasingly used to help security analysts manage the surge of cyber threats, automating tasks from vulnerability assessment to incident response. Yet in operational CTI workflows, reliability gaps remain substantial. Existing explanations often point to generic model issues (e.g., hallucination), but we argue the dominant bottleneck is the threat landscape itself: CTI is heterogeneous, volatile, and fragmented. Under these conditions, evidence is intertwined, crowdsourced, and temporally unstable, which are properties that standard LLM-based studies rarely capture. In this paper, we present a comprehensive empirical study of LLM vulnerabilities in CTI reasoning. We introduce a human-in-the-loop categorization framework that robustly labels failure modes across the CTI lifecycle, avoiding the brittleness of automated "LLM-as-a-judge" pipelines. We identify three domain-specific cognitive failures: spurious correlations from superficial metadata, contradictory knowledge from conflicting sources, and constrained generalization to emerging threats. We validate these mechanisms via causal interventions and show that targeted defenses reduce failure rates significantly. Together, these results offer a concrete roadmap for building resilient, domain-aware CTI agents.

As cyber threats continue to grow in scale and sophistication, blue team defenders increasingly require advanced tools to proactively detect and mitigate risks. Large Language Models (LLMs) offer promising capabilities for enhancing threat analysis. However, their effectiveness in real-world blue team threat-hunting scenarios remains insufficiently explored. This paper presents CyberTeam, a benchmark designed to guide LLMs in blue teaming practice. CyberTeam constructs a standardized workflow in two stages. First, it models realistic threat-hunting workflows by capturing the dependencies among analytical tasks from threat attribution to incident response. Next, each task is addressed through a set of operational modules tailored to its specific analytical requirements. This transforms threat hunting into a structured sequence of reasoning steps, with each step grounded in a discrete operation and ordered according to task-specific dependencies. Guided by this framework, LLMs are directed to perform threat-hunting tasks through modularized steps. Overall, CyberTeam integrates 30 tasks and 9 operational modules to guide LLMs through standardized threat analysis. We evaluate both leading LLMs and state-of-the-art cybersecurity agents, comparing CyberTeam against open-ended reasoning strategies. Our results highlight the improvements enabled by standardized design, while also revealing the limitations of open-ended reasoning in real-world threat hunting.

Semi-supervised learning (SSL) arises in practice when labeled data are scarce or expensive to obtain, while large quantities of unlabeled data are readily available. With the growing adoption of machine learning techniques, it has become increasingly feasible to generate multiple predicted labels using a variety of models and algorithms, including deep learning, large language models, and generative AI. In this paper, we propose a novel approach that safely and adaptively aggregates multiple black-box predictions of uncertain quality for both inference and prediction tasks. Our method provides two key guarantees: (i) it never performs worse than using the labeled data alone, regardless of the quality of the predictions; and (ii) if any one of the predictions (without knowing which one) perfectly fits the ground truth, the algorithm adaptively exploits this to achieve either a faster convergence rate or the semiparametric efficiency bound. We demonstrate the effectiveness of the proposed algorithm through small-scale simulations and two real-data analyses with distinct scientific goals. A user-friendly R package, sada, is provided to facilitate practical implementation.

While robotic perception has advanced rapidly in vision and touch, enabling robots to reason about indoor fungal contamination from weak, diffusion-dominated chemical signals remains an open challenge. We introduce Scensory, a learning-based robotic olfaction framework that simultaneously identifies fungal species and localizes their source from short time series measured by affordable, cross-sensitive VOC sensor arrays. Temporal VOC dynamics encode both chemical and spatial signatures, which we decode through neural networks trained on robot-automated data collection with spatial supervision. Across five fungal species, Scensory achieves up to 89.85% species accuracy and 87.31% source localization accuracy under ambient conditions with 3-7s sensor inputs. These results demonstrate real-time, spatially grounded perception from diffusion-dominated chemical signals, enabling scalable and low-cost source localization for robotic indoor environmental monitoring.

We develop a new classification framework based on the theory of coherent risk measures and systemic risk. The proposed approach is suitable for multi-class problems when the data is noisy, scarce (relative to the dimension of the problem), and the labeling might be unreliable. In the first part of our paper, we provide the foundation of the use of systemic risk models and show how to apply it in the context of linear and kernel-based multi-class problems. More advanced formulation via a system-theoretic approach with non-linear aggregation is proposed, which leads to a two-stage stochastic programming problem. A risk-averse regularized decomposition method is designed to solve the problem. We use a popular multi-class method as a benchmark in the performance analysis of the proposed classification methods. We illustrate our ideas by proposing several generalization of that method by the use of coherent measures of risk. The viability of the proposed risk-averse methods are supported theoretically and numerically. Additionally, we demonstrate that the application of systemic risk measures facilitates enforcing fairness in classification. Analysis and experiments regarding the fairness of the proposed models are carefully conducted. For all methods, our numerical experiments demonstrate that they are robust in the presence of unreliable training data and perform better on unknown data than the methods minimizing expected classification errors. Furthermore, the performance improves when the number of classes increases.

Computed tomography (CT) is important in clinical diagnosis, but acquiring high-resolution (HR) CT is constrained by radiation exposure risks. While deep learning-based super-resolution (SR) methods have shown promise for reconstructing HR CT from low-resolution (LR) inputs, supervised approaches require paired datasets that are often unavailable. Zero-shot methods address this limitation by operating on single LR inputs; however, they frequently fail to recover fine structural details due to limited LR information within individual volumes. To overcome these limitations, we propose a novel zero-shot 3D CT SR framework that integrates diffusion-based upsampled 2D projection priors into the 3D reconstruction process. Specifically, our framework consists of two stages: (1) LR CT projection SR, training a diffusion model on abundant X-ray data to upsample LR projections, thereby enhancing the scarce information inherent in the LR inputs. (2) 3D CT volume reconstruction, using 3D Gaussian splatting with our novel Negative Alpha Blending (NAB-GS), which models positive and negative Gaussian densities to learn signed residuals between diffusion-generated HR and upsampled LR projections. Our framework demonstrates superior quantitative and qualitative performance on two public datasets, and expert evaluations present the framework's clinical potential at 4x.

We study local linear convergence of gradient descent for finite-width feedforward networks under the squared empirical loss. Prior work shows that GD can remain confined to a Locally Quasi-Convex Region (LQCR) around initialization, but only gives a sublinear rate. We show that if the empirical Neural Tangent Kernel is positive at initialization, Lipschitz stable on the LQCR, and compatible with the LQCR radius, then the squared loss satisfies a local Polyak-Łojasiewicz inequality with constant $μ= λ_0 - L_Θr(\Rcal) > 0$. Combined with fixed-step iterate containment in the LQCR, imposed as a hypothesis in the linear-rate theorem, this yields linear convergence on the region. The LQCR supplies localization; fixed-step containment is imposed as a hypothesis in the linear-rate theorem; and the PL inequality comes from NTK conditioning under squared loss. The result is therefore a sufficient local condition, not a claim that this mechanism is necessary or unique for fast convergence. Empirically, we probe the theory through NTK spectral gap, parameter drift, empirical PL ratio, and suboptimality decay. On binary MNIST, the NTK remains positive, the PL ratio has a positive lower envelope, and the loss shows geometric decay on the stable regime. In a width ablation, the fixed-step width-$1024$ run leaves the local regime; reducing the step size lowers final drift from $1.870$ to $0.158$, restores the observed local-regime diagnostics, and yields the largest empirical PL-ratio lower envelope observed in the study. A CNN robustness check on a CIFAR-10 subset shows the PL-ratio envelope remains positive across three seeds, with a positive lower envelope across all three seeds on the stable regime.

Digitization projects in humanities often generate vast quantities of page images from historical documents, presenting significant challenges for manual sorting and analysis. These archives contain diverse content, including various text types (handwritten, typed, printed), graphical elements (drawings, maps, photos), and layouts (plain text, tables, forms). Efficiently processing this heterogeneous data requires automated methods to categorize pages based on their content, enabling tailored downstream analysis pipelines. This project addresses this need by developing and evaluating an image classification system specifically designed for historical document pages, leveraging advancements in artificial intelligence and machine learning. The set of categories was chosen to facilitate content-specific processing workflows, separating pages requiring different analysis techniques (e.g., OCR for text, image analysis for graphics)

The burgeoning growth of the esports and multiplayer online gaming community has highlighted the critical importance of evaluating the Most Valuable Player (MVP). The establishment of an explainable and practical MVP evaluation method is very challenging. In our study, we specifically focus on play-by-play data, which records related events during the game, such as assists and points. We aim to address the challenges by introducing a new MVP evaluation framework, denoted as \oursys, which leverages Shapley values. This approach encompasses feature processing, win-loss model training, Shapley value allocation, and MVP ranking determination based on players' contributions. Additionally, we optimize our algorithm to align with expert voting results from the perspective of causality. Finally, we substantiated the efficacy of our method through validation using the NBA dataset and the Dunk City Dynasty dataset and implemented online deployment in the industry.

We study the problem of fairly allocating indivisible goods to agents in an online setting, where goods arrive sequentially and must be allocated irrevocably. Focusing on the popular fairness notions of envy-freeness, proportionality, and maximin share fairness (and their approximate variants), we investigate how access to future information changes what guarantees are achievable. Without any information, we prove strong impossibility results even for approximate fairness. With normalization information (agents' total values), we provide an algorithm that achieves stronger fairness guarantees than previously known results, and show matching impossibilities for stronger notions. With frequency predictions (value multisets without order), we design a meta-algorithm that lifts a broad class of offline ''share-based'' guarantees to the online setting, matching the best-known offline bounds. Finally, we provide learning-augmented variants of both models: under noisy totals or noisy frequency predictions, our guarantees are robust and degrade gracefully with the error parameters.

Differential privacy (DP) provides robust privacy guarantees for statistical inference, but this can lead to unreliable results and biases in downstream applications. While several noise-aware approaches have been proposed which integrate DP perturbation into the inference, they are limited to specific types of simple probabilistic models. In this work, we propose a novel method for noise-aware approximate Bayesian inference based on stochastic gradient variational inference which can also be applied to high-dimensional and non-conjugate models. We also propose a more accurate evaluation method for noise-aware posteriors. Empirically, our inference method has similar performance to existing methods in the domain where they are applicable. Outside this domain, we obtain accurate coverages on high-dimensional Bayesian linear regression and well-calibrated predictive probabilities on Bayesian logistic regression with the UCI Adult dataset.

Large Language Models (LLMs) have transformed artificial intelligence by advancing natural language understanding and generation, enabling applications across fields beyond healthcare, software engineering, and conversational systems. Despite these advancements in the past few years, LLMs have shown considerable vulnerabilities, particularly to prompt injection and jailbreaking attacks. This review analyzes the state of research on these vulnerabilities and presents available defense strategies. We roughly categorize attack approaches into prompt-based, model-based, multimodal, and multilingual, covering techniques such as adversarial prompting, backdoor injections, and cross-modality exploits. We also review various defense mechanisms, including prompt filtering, transformation, alignment techniques, multi-agent defenses, and self-regulation, evaluating their strengths and shortcomings. We also discuss key metrics and benchmarks used to assess LLM safety and robustness, noting challenges like the quantification of attack success in interactive contexts and biases in existing datasets. Identifying current research gaps, we suggest future directions for resilient alignment strategies, advanced defenses against evolving attacks, automation of jailbreak detection, and consideration of ethical and societal impacts. This review emphasizes the need for continued research and cooperation within the AI community to enhance LLM security and ensure their safe deployment.

As large language models (LLMs) increasingly engage in complex social interactions, ensuring that their behaviors align with human ethical principles and intentions, known as value alignment, has become a critical scientific challenge. Existing benchmarks often rely on static assessments and fail to capture the longitudinal dynamics of decision-making or the latent cognitive processes driving agent behavior. In this work, we propose FairMindSim, a realistic simulation benchmark rooted in social psychology that evaluates alignment through continuous economic games. To move beyond black-box observations, we introduce the Belief-Reward Alignment Behavior Evolution Model (BREM), a probabilistic framework that formalizes decision-making as a dynamic trade-off between maximizing extrinsic rewards and upholding intrinsic beliefs. We conducted a large-scale comparative study involving 1,017 human participants and ten LLMs, including GPT-5 and Gemini-3-Pro. Our experimental results reveal a capability linked non linear empirical trend in the Third Party Punishment (TPP) game. Mid capability models exhibit rigid and algorithmic aggression that is characterized by over punishment, while frontier models show a convergence of restraint and a shift toward human like leniency as reasoning capabilities scale. Furthermore, using BREM, we decompose agents longitudinal decision dynamics and find that more advanced models better balance conflicting objectives by reducing belief action inconsistency. Our contributions provide a standardized protocol for psychological stress testing and an interpretable mechanism for analyzing the longitudinal evolution of AI alignment in controlled social dilemma settings.

The Arab Spring was a historic set of protests beginning in 2011 that toppled governments and led to major conflicts. Collective memories of events like these can vary significantly across social contexts in response to political, cultural, and linguistic factors. While Wikipedia plays an important role in documenting both historic and current events, little attention has been given to how Wikipedia articles, created in the aftermath of major events, continue to evolve over years or decades. Using the archived content of Arab Spring-related topics across the Arabic and English Wikipedias between 2011 and 2024, we define and evaluate multilingual measures of event salience, deliberation, contextualization, and consolidation of collective memory surrounding the Arab Spring. Our findings about the temporal evolution of the Wikipedia articles' content similarity across languages has implications for theorizing about online collective memory processes and evaluating linguistic models trained on these data.

We introduce an evidence-driven Bayesian formulation of physics-informed neural networks that enables automatic optimization of loss weights between PDE residuals, boundary conditions, and observational data. Unlike existing Bayesian PINN approaches based on sampling or variational inference, the proposed method uses a Laplace approximation to compute model evidence analytically, enabling efficient hyperparameter tuning and model comparison without posterior sampling. We demonstrate the method on the heat, wave, and Burgers' equations, obtaining solutions in agreement with exact or reference results. In the Burgers' equation example, we further show that the framework naturally integrates information from governing equations and noisy measurements, providing predictive uncertainties within a unified Bayesian setting.

Global symmetry anomalies of a quantum field theory (QFT) can be packaged as specific couplings of a higher-dimensional symmetry theory (SymTh). In this work we show that for 5D superconformal field theories (SCFTs) engineered from M-theory backgrounds $X$ a Calabi-Yau cone, this data can be extracted from the path algebra of branes probing $X$. This provides a complementary algebraic approach compared with more geometric computations based on the explicit calculation of triple intersection numbers in a resolved geometry and / or $η$-invariants extracted from the boundary geometry $\partial X$. Our method applies in situations where the counterpart geometric computation is either unknown or combinatorially unwieldy. We illustrate with several toric threefold examples, including orbifolds $\mathbb{C}^{3} / Γ$ and more general non-orbifold Calabi-Yau cones of Sasaki-Einstein five-manifolds.

Non-singular gravitational theories are expected to be relevant in the early universe. In this paper, we derive a set of effective Friedmann equations describing the dynamics of matter shells in the presence of a gravitational regulator $\ell$. We find that such a regulator induces a primordial black hole mass gap such that below a certain mass $M_\text{gap}(\ell, R_H)$ no black holes can form. The order of magnitude of this mass gap is set by the regulator $\sim c^2\ell/G$, with subleading dependence on the horizon radius at time of formation $R_H$. Finally, we show that over a wide range of equation of state parameters $ω= 0 \dots 1/3$, the mass gap implies a Carr criterion of the form $δ_H > 2G M_\text{gap}/R_H - 1$. If the horizon size is of the same order of the regulator, $R_H \sim \ell$, this new criterion is stronger than the traditional Carr criterion for primordial black hole formation. This connects the primordial black hole abundance directly to the presence of gravitational regulators.

In this paper, we give a short Bayesian proof of Talagrand's celebrated majorizing-measure theorem (MMT). While the upper-bound direction of MMT follows relatively directly from standard arguments, the lower-bound direction is widely regarded as the more difficult part and has received several distinct proofs. Unlike previous approaches, our proof does not rely on existing Gaussian processes lower bounds techniques, nor on combinatorial, geometric, or coding-theoretic constructions. Instead, we derive the lower bound from two area identities for Gaussian additive models. We show that the Gaussian width of a finite set is the integrated mean-squared error of the maximum-likelihood estimator (MLE), while the integrated minimum mean-squared error (MMSE) is larger than the Fernique-Talagrand functional, up to a universal constant. Simply then comparing the MLE with Bayes-optimal estimation gives a direct proof of the hard direction of MMT.

Electron doped rhombohedral multilayer graphene at high displacement field features an exceptionally flat band minimum with near-ideal quantum geometry. Experiments in this regime observe the formation of a 'quarter metal,' in which the electron liquid condenses into a single spin- and valley flavor. Remarkably, recent experiments have found a zero resistance state in the same region of the density- and displacement-field-tuned parameter space, attributed to the formation of a chiral superconductor characterized by a finite-momentum Cooper pair condensate. Here, we use nanoSQUID-on-tip magnetometry to map the orbital magnetization of electron-doped rhombohedral graphene devices ranging in thickness between 3 and 13 layers. Magnetization within the quarter metal phases peaks at finite density, consistent with concentration of the Berry curvature in a finite-momentum 'ring of fire'. Correlating transport and local magnetometry data in a tetralayer sample reveals that the superconducting state has a finite orbital magnetic moment, providing direct evidence of its chiral nature. We further show that widely observed stochastic switching of the resistivity in the metallic regime arises from a density-tuned sign change in the valley-resolved total magnetic moment. This leads to the formation of metastable magnetic domains under typical gate control sequences and can also be harnessed for electric-field controlled switching of orbital moment across the entire device. Unexpectedly, we find magnetic inhomogeneity specific to the apparent normal state of the chiral superconductor, suggestive of a strain-tuned competition between magnetic and non-magnetic ground states. Our results point to a subtle energetic competition underlying the observation of chiral superconductivity in a narrow range of layer numbers.

Software engineering (SWE) agents are transitioning from code generation to full software development lifecycle automation. A critical phase in this lifecycle is specification design: transforming initial proposals into carefully considered requirements through expert review. Existing benchmarks such as SWE-Bench are implementation-focused by measuring the agent's ability to generate code given fixed, precise design requirements. This formulation assumes specifications are correct and complete. In real-world complex and critical software systems, initial specifications are often incomplete and flawed, requiring extensive expert reviews and revisions before being accepted for implementation. To fill this gap, we introduce SpecBench to evaluate specification-level reasoning: the ability to generate complete, unambiguous, consistent, and correct system specifications. SpecBench tasks are derived from the Request for Comments (RFC) process used by mature open-source projects. For each task, an agent is given an initial design proposal, the project codebase, and all past project RFC discussions. The agent is tasked with identifying specification deficiencies: omissions, ambiguities, inconsistencies, or incorrect assumptions in the initial proposal. We evaluate predictions against critiques raised by expert maintainers during historical RFC reviews. SpecBench contains tasks from 5 diverse repositories: Kubernetes, React, Rust, TVM, and vLLM. We evaluate state-of-the-art SWE agents on SpecBench, analyzing their capacity to reason about system design without execution feedback. The best performing agent, GPT-5.4, achieves 44.4% accuracy.

Differentially private (DP) image synthesis generates images that preserve the statistical characteristics of a sensitive dataset, enabling sensitive data analysis and usage while providing rigorous guarantees of privacy leakage. Existing methods fine-tune public models using DP Stochastic Gradient Descent (DP-SGD) on sensitive images to generate synthetic images. But full fine-tuning public models on sensitive images is computationally expensive, because current public models typically contain a large number of parameters. Recent work proposes heuristically using Low-Rank Adaptation (LoRA) on all attention-layer parameters of public models to reduce the number of trainable parameters. However, we argue that exhaustive LoRA coverage across all attention-layer parameters is suboptimal in a DP setting, as it leads to noise accumulation and collapse during private training. To address this issue, we propose DP-SAPF, which uses a saliency-aware strategy to identify specific target parameters for LoRA training under DP. DP-SAPF is inspired by the fact that larger gradients signify higher saliency, indicating that these parameters are most critical for the DP learning. Specifically, we feed the sensitive images into public models, compute gradients, and add noise to the gradients to satisfy DP. Then, DP-SAPF identifies the most salient parameters, those exhibiting high gradient magnitudes on sensitive images, for DP fine-tuning. Experiments on four sensitive image datasets show that DP-SAPF improves the utility and fidelity of synthetic images while requiring fewer computational resources than fine-tuning methods without parameter selection.

Modern table formats such as Apache Iceberg compute and store metadata-commit timestamps, record counts, and column-level statistics such as null counts and value bounds at write time as part of file writing. These statistics serve query planning, yet they overlap substantially with data quality (DQ) monitoring needs. We describe a metadata-first approach that repurposes write-time statistics for continuous DQ observability: anomaly detection, drift monitoring, null-rate tracking; without scanning any data. Deployed at LinkedIn across 200,000+ Iceberg tables (800+ PB), this approach satisfies approximately 60% of user-defined DQ rules at zero marginal compute cost and reduces profiling resource consumption by around 50%. Extending manifest statistics with lightweight counters (sum, zero-value counts, boolean counts) and incrementally mergeable sketches; Theta sketches for distinct counts, KLL sketches for quantiles; can further raise metadata-satisfiable coverage to close to 90% of production DQ rules. We validate sketch accuracy, mergeability, and storage overhead on production data and propose that table formats should store per-file sketches in Puffin sidecar files, following the same store-then-aggregate pattern used for existing manifest statistics.

Deciding periodicity of infinite words generated by morphisms is a classical result in combinatorics on words from 80's by Harju, Linna and Pansiot. In this paper, we are interested in this question in the abelian setting. Two words are called \textit{abelian equivalent} if they contain the same numbers of occurrences of each letter. An infinite word $s$ is called \emph{ultimately abelian periodic} if it can be factorized as $s=uv_1v_2v_3\cdots$, where $v_i$'s are abelian equivalent words. If $u$ is empty, then $s$ is called \emph{purely abelian periodic}. We provide the following characterization of binary morphisms generating abelian periodic words: A word generated by a binary morphism $f$ is abelian periodic if and only if either it is periodic or there exist an integer $K$ and words $u$, $v$, $u'$, $v'$ such that $f^K(a) = uv$, $f^K(b) = u'v'$, $u\sim_{ab} u'$, and $vu$ and $v'u'$ are abelian periodic with abelian equivalent periods. For the case of the purely abelian periodic words, we also provide an upper bound on $K$ which makes the obtained characterization algorithmic.

Galaxy redshift surveys encode a wealth of information generated by nonlinear gravitational evolution, galaxy bias, and redshift-space distortions, only part of which is accessible through standard two-point statistics. Motivated by the need for flexible and computationally efficient alternatives, we introduce the augmented correlation function, a general framework in which an arbitrary transformation of the galaxy field defines additional ``latent'' dimensions that extend the standard two-point correlation function and isolate clustering properties averaged out in conventional analyses. As a proof of concept, we study a latent variable constructed from the pairwise gradient of the inverse Laplacian of the galaxy density field, showing that the resulting statistics naturally distinguish clustering regimes associated with infalling and outflowing pairs. Using Fisher forecasts based on $z=1$ halo catalogues from the Quijote simulations within $νΛ\mathrm{CDM}$ cosmology, we find that the augmented correlation systematically yields tighter constraints on all cosmological parameters considered. Although these improvements should be regarded as indicative given the exploratory nature of the analysis and the limitations of Fisher forecasts and simulations, our results demonstrate the potential of augmented correlations as a flexible framework for extracting additional information from spectroscopic galaxy surveys.

We develop a straightforward analytical framework for the propagation of spatial light modes through a turbulent atmosphere. Built upon the split-step approach with the mode-based optical field representation, it directly assesses how turbulence-induced phase fluctuations deplete the optical power in the original mode and re-distribute it into neighboring spatial modes. Importantly, this power transfer scales linearly with the propagation distance in a uniform channel, yielding a simple solution for arbitrary distances in the form of a matrix exponential. The transfer rate is determined by the spatial spectral overlap between the turbulence spectrum and the acceptance spectrum for a pair of interacting spatial modes. The model predicts the average power in each spatial mode and is exact when a single mode strongly dominates all others. Our predictions show reasonably good agreement with simulations up to medium-to-strong turbulence levels. The model also confirms the scalings with mode order previously known as empirical observations.