AI answer engines are a relatively new kind of information search tool: rather than returning a ranked list of documents, they generate an answer to a search question with inline citations to sources. But reading the cited sources is costly, and citation links themselves offer little guidance about what evidence they contain. We present attribution gradients, a technique to boost the informativeness of citations by consolidating scent and information prey in place. Its first feature is bringing evidence amounts, supporting/contradictory excerpts, links to source, contextual explanation into one place. Its second feature is the ability to unravel second-degree citations in place. In a lab study we demonstrate usage of the full gradient in a critical reading task and its support for deep engagement that increased the depth of what readers took away from the sources versus a standard citation and document QA design.

Social narratives help autistic children understand and navigate social situations through stories. To ensure effective practice, however, they often require significant time and effort from parents in customizing the narrative materials and delivering repeated instructions on them. We present AutiHero, a generative AI (GenAI)-based social narrative system, which supports parents to create personalized, multi-path stories targeting specific behavior of their autistic children, while enabling them to explore behavioral choices and causal consequences together in reading. A two-week deployment study with 16 autistic child-parent dyads showed that parents actively created, adapted, and read stories with their children, with increased confidence in everyday behavioral guidance. Our work contributes real-world-contextualized text+image content creation approaches harnessing GenAI, ensuring user-aligned application in sensitive contexts involving autistic children and their parents.

Just-in-Time software defect prediction (JIT-SDP) plays a critical role in prioritizing risky code changes during code review and continuous integration. However, existing datasets often suffer from noisy labels and low precision in identifying bug-inducing commits. To address this, we present ReDef (Revert-based Defect dataset), a high-confidence benchmark of function-level modifications curated from 22 large-scale C/C++ projects. Defective cases are anchored by revert commits, while clean cases are validated through post-hoc history checks. Ambiguous instances are conservatively filtered out via a GPT-assisted triage process involving multiple votes and audits. This pipeline yields 3,164 defective and 10,268 clean modifications, offering substantially more reliable labels than prior resources. Beyond dataset construction, we provide a systematic evaluation of how Code Language Models (CLMs)-specifically CodeBERT, CodeT5+, UniXcoder, and Qwen2.5-reason about code modifications. We first investigate which input encodings most effectively expose change information under five different strategies. We then design four counterfactual perturbation strategies (e.g., swapping added/deleted blocks, inverting diff polarity) to serve as diagnostic probes. We posit that if models genuinely capture change semantics, such distortions should lead to a clear decline in predictive performance. Our results show that compact diff-style encodings consistently outperform whole-function formats across all CLMs, supported by rigorous statistical confirmation. However, under counterfactual tests, performance remains effectively stable, revealing that what appears to be robustness in fact reflects a reliance on superficial cues rather than true semantic understanding.

When faced with new data, we often conduct a cluster analysis to obtain a better understanding of the data's structure and the archetypical samples present in the data. This process often includes visualization of the data, either as a way to discover or verify clusters. However, the increases in data complexity and dimensionality has made this step very tricky. To visualize data, nonlinear dimension reduction methods are the de facto standard for their ability to non-uniformly stretch and shrink space in order to preserve local clusters. Because this process requires a drastic manipulation of space, however, nonlinear dimension reduction methods are known to produce false structures, especially when mishandled. A common consequence that often goes undetected by the untrained eye is over-clustering of the data. In efforts to deal with this phenomenon, we developed an interactive tool that empowers analysts to distinguish false clusters and better interpret their high-dimensional clustering results. The tool uses various analytical plots to provide a multi-faceted perspective on the data's global structure as well as local inter-cluster relationships, helping users determine the legitimacy of their high-dimensional clustering results. The tool is available via an R package named DRtool.

A quantum thermodynamic system is described by a Hamiltonian and a list of conserved, non-commuting charges, and a fundamental goal is to determine the minimum energy of the system subject to constraints on the charges. Recently, [Liu et al., arXiv:2505.04514] proposed first- and second-order classical and hybrid quantum-classical algorithms for solving a dual chemical potential maximization problem, and they proved that these algorithms converge to global optima by means of gradient-ascent approaches. In this paper, we benchmark these algorithms on several problems of interest in thermodynamics, including one- and two-dimensional quantum Heisenberg models with nearest- and next-nearest neighbor interactions and with the charges set to the total x, y, and z magnetizations. We also offer an alternative compelling interpretation of these algorithms as methods for designing ground and thermal states of controllable Hamiltonians, with potential applications in molecular and material design. Furthermore, we introduce stabilizer thermodynamic systems as thermodynamic systems based on stabilizer codes, with the Hamiltonian constructed from a given code's stabilizer operators and the charges constructed from the code's logical operators. We benchmark the aforementioned algorithms on several examples of stabilizer thermodynamic systems, including those constructed from the one-to-three-qubit repetition code, the perfect one-to-five-qubit code, and the two-to-four-qubit error-detecting code. Finally, we observe that the aforementioned hybrid quantum-classical algorithms, when applied to stabilizer thermodynamic systems, can serve as alternative methods for encoding quantum information into stabilizer codes at a fixed temperature, and we provide an effective method for warm-starting these encoding algorithms whenever a single qubit is encoded into multiple physical qubits.

The 3D characterization of microstructures is crucial for understanding and designing functional materials. However, the scanning electron microscope (SEM), widely used in scientific research, captures only 2D electron intensity distributions. Existing SEM 3D reconstruction methods struggle with textureless regions, shadowing artifacts, and calibration dependencies, whereas advanced learning-based approaches fail to generalize to microscopic SEM domains due to the lack of physical priors and domain-specific data. We introduce NFH-SEM, a neural field-based hybrid framework that reconstructs high-fidelity 3D surfaces from multi-view, multi-detector SEM images. NFH-SEM integrates coarse multi-view geometry with photometric stereo cues from detector signals through a continuous neural field, incorporating a learnable forward model that embeds SEM imaging physics for self-calibrated, shadow-robust reconstruction. NFH-SEM achieves precise recovery across diverse specimens, revealing 478 nm layered features in two-photon lithography samples, 782 nm surface textures on pollen grains, and 1.559 $μ$m fracture steps on silicon carbide particles, demonstrating its accuracy and broad applicability. Our code and real-world dataset are available at https://github.com/zju3dv/NFH-SEM.

Research, innovation and practical capital investment have been increasing rapidly toward the realization of autonomous physical agents. This includes industrial and service robots, unmanned aerial vehicles, embedded control devices, and a number of other realizations of cybernetic/mechatronic implementations of intelligent autonomous devices. In this paper, we consider a stylized version of robotic care, which would normally involve a two-level Reinforcement Learning procedure that trains a policy for both lower level physical movement decisions as well as higher level conceptual tasks and their sub-components. In order to deliver greater safety and reliability in the system, we present the general formulation of this as a two-level optimization scheme which incorporates control at the lower level, and classical planning at the higher level, integrated with a capacity for learning. This synergistic integration of multiple methodologies -- control, classical planning, and RL -- presents an opportunity for greater insight for algorithm development, leading to more efficient and reliable performance. Here, the notion of reliability pertains to physical safety and interpretability into an otherwise black box operation of autonomous agents, concerning users and regulators. This work presents the necessary background and general formulation of the optimization framework, detailing each component and its integration with the others.

Conventional galaxy generation methods rely on semi-analytical models and hydrodynamic simulations, which are highly dependent on physical assumptions and parameter tuning. In contrast, data-driven generative models do not have explicit physical parameters pre-determined, and instead learn them efficiently from observational data, making them alternative solutions to galaxy generation. Among these, diffusion models outperform Variational Autoencoders (VAEs) and Generative Adversarial Networks (GANs) in quality and diversity. Leveraging physical prior knowledge to these models can further enhance their capabilities. In this work, we present GalCatDiff, the first framework in astronomy to leverage both galaxy image features and astrophysical properties in the network design of diffusion models. GalCatDiff incorporates an enhanced U-Net and a novel block entitled Astro-RAB (Residual Attention Block), which dynamically combines attention mechanisms with convolution operations to ensure global consistency and local feature fidelity. Moreover, GalCatDiff uses category embeddings for class-specific galaxy generation, avoiding the high computational costs of training separate models for each category. Our experimental results demonstrate that GalCatDiff significantly outperforms existing methods in terms of the consistency of sample color and size distributions, and the generated galaxies are both visually realistic and physically consistent. This framework will enhance the reliability of galaxy simulations and can potentially serve as a data augmentor to support future galaxy classification algorithm development.

Subseasonal-to-seasonal forecasting is crucial for public health, disaster preparedness, and agriculture, and yet it remains a particularly challenging timescale to predict. We explore the use of an interpretable AI-informed model analog forecasting approach, previously employed on longer timescales, to improve S2S predictions. Using an artificial neural network, we learn a mask of weights to optimize analog selection and showcase its versatility across three varied prediction tasks: 1) classification of Week 3-4 Southern California summer temperatures; 2) regional regression of Month 1 midwestern U.S. summer temperatures; and 3) classification of Month 1-2 North Atlantic wintertime upper atmospheric winds. The AI-informed analogs outperform traditional analog forecasting approaches, as well as climatology and persistence baselines, for deterministic and probabilistic skill metrics on both climate model and reanalysis data. We find the analog ensembles built using the AI-informed approach also produce better predictions of temperature extremes and improve representation of forecast uncertainty. Finally, by using an interpretable-AI framework, we analyze the learned masks of weights to better understand S2S sources of predictability.

In the era of AI, neural networks have become increasingly popular for modeling, inference, and prediction, largely due to their potential for universal approximation. With the proliferation of such deep learning models, a question arises: are leaner statistical methods still relevant? To shed insight on this question, we employ the mechanistic nonlinear ordinary differential equation (ODE) inverse problem as a testbed, using the physics-informed neural network (PINN) as a representative of the deep learning paradigm and manifold-constrained Gaussian process inference (MAGI) as a representative of statistically principled methods. Through case studies involving the SEIR model from epidemiology and the Lorenz model from chaotic dynamics, we demonstrate that statistical methods are far from obsolete, especially when working with sparse and noisy observations. On tasks such as parameter inference and trajectory reconstruction, statistically principled methods consistently achieve lower bias and variance, while using far fewer parameters and requiring less hyperparameter tuning. Statistical methods can also decisively outperform deep learning models on out-of-sample future prediction, where the absence of relevant data often leads overparameterized models astray. Additionally, we find that statistically principled approaches are more robust to accumulation of numerical imprecision and can represent the underlying system more faithfully to the true governing ODEs.

As Large Language Models (LLMs) become integral to software development workflows, their ability to generate structured outputs has become critically important. We introduce StructEval, a comprehensive benchmark for evaluating LLMs' capabilities in producing both non-renderable (JSON, YAML, CSV) and renderable (HTML, React, SVG) structured formats. Unlike prior benchmarks, StructEval systematically evaluates structural fidelity across diverse formats through two paradigms: 1) generation tasks, producing structured output from natural language prompts, and \textbf{2)} conversion tasks, translating between structured formats. Our benchmark encompasses 18 formats and 44 types of task, with novel metrics for format adherence and structural correctness. Results reveal significant performance gaps-even state-of-the-art models like o1-mini achieve only 75.58 average score, with open-source alternatives lagging approximately 10 points behind. We find generation tasks more challenging than conversion tasks, and producing correct visual content more difficult than generating text-only structures.

Routing problems are canonical combinatorial optimization tasks with wide-ranging applications in logistics, transportation, and supply chain management. However, solving these problems becomes significantly more challenging when complex constraints are involved. In this paper, we propose LMask, a novel learning framework that utilizes dynamic masking to generate high-quality feasible solutions for constrained routing problems. LMask introduces the LazyMask decoding method, which lazily refines feasibility masks with the backtracking mechanism. In addition, it employs the refinement intensity embedding to encode the search trace into the model, mitigating representation ambiguities induced by backtracking. To further reduce sampling cost, LMask sets a backtracking budget during decoding, while constraint violations are penalized in the loss function during training to counteract infeasibility caused by this budget. We provide theoretical guarantees for the validity and probabilistic optimality of our approach. Extensive experiments on the traveling salesman problem with time windows (TSPTW) and TSP with draft limits (TSPDL) demonstrate that LMask achieves state-of-the-art feasibility rates and solution quality, outperforming existing neural methods.

As data marketplaces become increasingly central to the digital economy, it is crucial to design efficient pricing mechanisms that optimize revenue while ensuring fair and adaptive pricing. We introduce the Maximum Auction-to-Posted Price (MAPP) mechanism, a novel two-stage approach that first estimates the bidders' value distribution through auctions and then determines the optimal posted price based on the learned distribution. We establish that MAPP is individually rational and incentive-compatible, ensuring truthful bidding while balancing revenue maximization with minimal price discrimination. On the theoretical side, we establish a statistical viewpoint that recasts revenue optimization as a valuation density estimation problem: we show that revenue regret can be controlled by uniform error in estimating the valuation density. MAPP achieves a regret of $O_p(n^{-1}(\log n)^2)$ when incorporating historical bid data, where $n$ is the number of bids in the current round. For sequential dataset sales over $T$ rounds, we propose an online MAPP mechanism that dynamically adjusts pricing across datasets with varying value distributions. Our approach achieves no-regret learning, with the average cumulative regret converging at a rate of $O_p(T^{-1/2}(\log T)^2)$. We validate the effectiveness of MAPP through simulations and real-world data from the FCC AWS-3 spectrum auction.

How has the public responded to the increasing prevalence of artificial intelligence (AI)-based technologies? We investigate public perceptions of AI by collecting over 12,000 responses over 12 months from a nationally representative U.S. sample. Participants provided open-ended metaphors reflecting their mental models of AI, a methodology that overcomes the limitations of traditional self-reported measures by capturing more nuance. Using a mixed-methods approach combining quantitative clustering and qualitative coding, we identify 20 dominant metaphors shaping public understanding of AI. To analyze these metaphors systematically, we present a scalable framework integrating language modeling (LM)-based techniques to measure key dimensions of public perception: anthropomorphism (attribution of human-like qualities), warmth, and competence. We find that Americans generally view AI as warm and competent, and that over the past year, perceptions of AI's human-likeness and warmth have significantly increased ($+34\%, r = 0.80, p < 0.01; +41\%, r = 0.62, p < 0.05$). These implicit perceptions, along with the identified dominant metaphors, strongly predict trust in and willingness to adopt AI ($r^2 = 0.21, 0.18, p < 0.001$). Moreover, we uncover systematic demographic differences in metaphors and implicit perceptions, such as the higher propensity of women, older individuals, and people of color to anthropomorphize AI, which shed light on demographic disparities in trust and adoption. In addition to our dataset and framework for tracking evolving public attitudes, we provide actionable insights on using metaphors for inclusive and responsible AI development.

Precision medicine in musculoskeletal imaging requires scalable measurement infrastructure. We developed a modular system that converts routine MRI into standardized quantitative biomarkers suitable for clinical decision support. Promptable foundation segmenters (SAM, SAM2, MedSAM) were fine-tuned across heterogeneous musculoskeletal datasets and coupled to automated detection for fully automatic prompting. Fine-tuned segmentations yielded clinically reliable measurements with high concordance to expert annotations across cartilage, bone, and soft tissue biomarkers. Using the same measurements, we demonstrate two applications: (i) a three-stage knee triage cascade that reduces verification workload while maintaining sensitivity, and (ii) 48-month landmark models that forecast knee replacement and incident osteoarthritis with favorable calibration and net benefit across clinically relevant thresholds. Our model-agnostic, open-source architecture enables independent validation and development. This work validates a pathway from automated measurement to clinical decision: reliable biomarkers drive both workload optimization today and patient risk stratification tomorrow, and the developed framework shows how foundation models can be operationalized within precision medicine systems.

Transferable Targeted Attacks (TTAs) face significant challenges due to severe overfitting to surrogate models. Recent breakthroughs heavily rely on large-scale training data of victim models, while data-free solutions, \textit{i.e.}, image transformation-involved gradient optimization, often depend on black-box feedback for method design and tuning. These dependencies violate black-box transfer settings and compromise threat evaluation fairness. In this paper, we propose two blind estimation measures, self-alignment and self-transferability, to analyze per-transformation effectiveness and cross-transformation correlations under strict black-box constraints. Our findings challenge conventional assumptions: (1) Attacking simple scaling transformations uniquely enhances targeted transferability, outperforming other basic transformations and rivaling leading complex methods; (2) Geometric and color transformations exhibit high internal redundancy despite weak inter-category correlations. These insights drive the design and tuning of S$^4$ST (Strong, Self-transferable, faSt, Simple Scale Transformation), which integrates dimensionally consistent scaling, complementary low-redundancy transformations, and block-wise operations. Extensive evaluations across diverse architectures, training distributions, and tasks show that S$^{4}$ST achieves state-of-the-art effectiveness-efficiency balance without data dependency. We reveal that scaling's effectiveness stems from visual data's multi-scale nature and ubiquitous scale augmentation during training, rendering such augmentation a double-edged sword. Further validations on medical imaging and face verification confirm the framework's strong generalization.

One of the current principal defenses against weaponized synthetic media continues to be the ability of the targeted individual to visually or auditorily recognize AI-generated content when they encounter it. However, as the realism of synthetic media continues to rapidly improve, it is vital to have an accurate understanding of just how susceptible people currently are to potentially being misled by convincing but false AI generated content. We conducted a perceptual study with 1276 participants to assess how capable people were at distinguishing between authentic and synthetic images, audio, video, and audiovisual media. We find that on average, people struggled to distinguish between synthetic and authentic media, with the mean detection performance close to a chance level performance of 50%. We also find that accuracy rates worsen when the stimuli contain any degree of synthetic content, features foreign languages, and the media type is a single modality. People are also less accurate at identifying synthetic images when they feature human faces, and when audiovisual stimuli have heterogeneous authenticity. Finally, we find that higher degrees of prior knowledgeability about synthetic media does not significantly impact detection accuracy rates, but age does, with older individuals performing worse than their younger counterparts. Collectively, these results highlight that it is no longer feasible to rely on the perceptual capabilities of people to protect themselves against the growing threat of weaponized synthetic media, and that the need for alternative countermeasures is more critical than ever before.

Quantum neural networks are expected to be a promising application in near-term quantum computing, but face challenges such as vanishing gradients during optimization and limited expressibility by a limited number of qubits and shallow circuits. To mitigate these challenges, an approach using distributed quantum neural networks has been proposed to make a prediction by approximating outputs of a large circuit using multiple small circuits. However, the approximation of a large circuit requires an exponential number of small circuit evaluations. Here, we instead propose to distribute partitioned features over multiple small quantum neural networks and use the ensemble of their expectation values to generate predictions. To verify our distributed approach, we demonstrate ten class classification of the Semeion and MNIST handwritten digit datasets. The results of the Semeion dataset imply that while our distributed approach may outperform a single quantum neural network in classification performance, excessive partitioning reduces performance. Nevertheless, for the MNIST dataset, we succeeded in ten class classification with exceeding 96\% accuracy. Our proposed method not only achieved highly accurate predictions for a large dataset but also reduced the hardware requirements for each quantum neural network compared to a large single quantum neural network. Our results highlight distributed quantum neural networks as a promising direction for practical quantum machine learning algorithms compatible with near-term quantum devices. We hope that our approach is useful for exploring quantum machine learning applications.

Galaxies evolve in tandem with their environments -- mergers and gas inflows drive galaxy growth while galactic outflows launched by supernovae may seed the galactic environment with gas, metals, and energy, fueling star-formation far from the main bodies of galaxies. The formation histories of young stars in the stellar halos of nearby galaxies can help understand this interplay. We thus present the most detailed map to date of young stars in the stellar halo of M82, a starburst galaxy in the M81 Group that hosts a prototypical outflow, using Hubble Space Telescope (HST) and Subaru Hyper-Suprime Cam observations. We find widespread extraplanar populations of stars with ages $\lesssim630$ Myr, with clear detections of stars up to $\sim5$ kpc to the south in unique arc-like stellar features (Southern Arcs) and in a new stellar trail up to $\sim20$ kpc to the east (M82's Tail), originating from the Southern Arcs. We estimate a total halo star formation of $\sim4\times10^6\,M_\odot$ in the last $630$ Myr. Overall, the star formation history (SFH) of the M82 Tail is correlated with periods of heightened star cluster formation in the M82 disk, which suggests the influence of the starburst outflow. Further, the fraction of young stars decreases as we move away from M82 to the east. We forward a picture where the M82 Tail formed from ram pressure stripped gas arising from M82's westward motion, triggered by shocks from the outflow.

Optical atomic clocks provide exceptionally accurate and precise signals for timekeeping and precision measurements, but they require high-power, free-space laser configurations that limit scalability. We introduce and explore a scalable infrastructure for strontium (Sr) optical-lattice clocks that incorporates co-design of atomic-beam slowing and a magneto-optical trap (MOT) from an effusion source, generation of complex, three-dimensional free-space laser configurations with a photonic integrated circuit (PIC) and metasurface (MS) optics, and laser stabilization to a frequency-comb supercontinuum generated with integrated nonlinear photonics. With these elements, we realize MOTs of all stable strontium isotopes ($^{84}$Sr, $^{86}$Sr, $^{87}$Sr, $^{88}$Sr) with populations commensurate with natural abundances, demonstrating precise beam control and robustness. Access to laser-cooled alkaline-earth atoms with scalable integrated photonics enables system engineering for optical clocks, quantum sensing, and quantum information, and our experiments demonstrate extensible technologies that advance toward a Sr optical clock largely free of bulk optics.

We determine the semisimplicity criterion for even partition algebras over the complex field. Specifically we prove that the even/2-tonal partition algebras $P_n^2(δ)$ over $\mathbb{C}$ are semisimple for all $n$ if and only if parameter $δ\not\in \mathbb{N}_0$ .

Let $A \bowtie^{f,g} (J,J')$ be the bi--amalgamation of a commutative ring $A$ with $(B,C)$ along the ideals $(J,J')$ with respect to the ring homomorphisms $(f,g)$. In this article, we study the basic homological properties of the bi--amalgamated algebra construction. We first calculate the dimension and depth of the bi--amalgamated algebra under fairly general circumstances and derive necessary and sufficient conditions for Cohen--Macaulayness in terms of maximal and big Cohen--Macaulay modules of $A$. Furthermore, we characterize the Gorenstein property of the bi--amalgamated algebra through the canonical modules of $f(A)+J$ and $g(A)+J'$. We apply our results to the theory of curve singularities by constructing Gorenstein algebroid curves through bi--amalgamated and amalgamated algebras. We also give a brief remark concerning the universally catenary property of $A\bowtie^{f,g}(J,J')$.

We propose a generalization of quantum field theory within Schrodinger's functional representation, inspired by Nambu's proper-time formulation of quantum mechanics. The key motivation for this generalization is to incorporate a fundamental, Lorentz-invariant minimum scale, which in this formulation is played by a minimal proper time $τ_{\min}$. The introduction of $τ_{\min}$ leads to several significant effects at very high energies: it modifies the Heisenberg uncertainty principle, induces a controlled violation of unitarity, and suppresses high-energy modes. This minimal scale renders the theory asymptotically safe through a mechanism akin to dimensional reduction, while reproducing all the standard results at low energies, where quantum field theory emerges. Remarkably, the same framework can accommodate a deterministic regime at energies approaching the Planck scale. These features suggest that a minimal proper-time formulation renders the quantum field theory an effective but finite theory, superseded at trans-Planckian energies.

In this article, we study orientably-regular maps of Euler characteristic $-2p^2$ and classify those that admit a group of orientation-preserving automorphisms of order $10p^2$, where $p$ is a prime number. Along the way, we classify all compact Riemann surfaces (or complex algebraic curves) of genus $1+p^2$ endowed with a group of conformal automorphisms of order $5p^2$.

Belief propagation (BP) provides a scalable heuristic for contracting tensor networks on loopy graphs, but its success in quantum many-body settings has largely rested on empirical evidence. Developing upon a recently introduced cluster-expansion framework for tensor networks, we rigorously study the applicability of BP to many-body quantum systems. For a state represented as a PEPS satisfying a ``loop-decay" condition, we prove that BP supplemented by cluster corrections approximates local observables with exponentially small relative error, and we give explicit formulas expressing local expectation values as BP predictions dressed by connected clusters intersecting the observable region. This representation establishes a direct link between cluster corrections and physical correlation functions. As a result, we show that ``loop-decay" \emph{necessarily implies} exponential decay of connected correlations, yielding sharp, rigorous criteria for when BP can and cannot succeed, and ruling out its validity at critical points. Numerical simulations of the two- and three-dimensional transverse field Ising model at zero and finite temperature confirm our analytical predictions, demonstrating quantitative accuracy deep in gapped phases and systematic failure near criticality.

This work continues the author's earlier work (2026, Studia Mathematica) on Picard's problem: is every meromorphic function on a complete noncompact Kähler manifold with nonnegative Ricci curvature necessarily a constant, if it avoids 3 distinct values? In that prior work, a positive answer was obtained under a growth condition for non-parabolic manifolds. In this paper, we give a full solution to the non-parabolic case by removing this growth condition via a global Green function approach. For the parabolic case, to overcome the obstacle arising from the absence of a positive global Green function, we introduce a heat kernel approach to Nevanlinna theory. Based on it, we develop a Carlson-Griffiths theory, which gives the first systematic result in Nevanlinna theory for parabolic Kähler manifolds. As a direct application, we confirm the parabolic case of Picard's problem under a weak growth condition.

We prove that the relative p-adic monodromy theorem holds over a dense open subset. Moreover, we establish the equivalence of the following two statements: the local constancy of the Newton polygon function associated with a de Rham local system around rank-1 points, and the relative p-adic monodromy theorem near rank-1 points. We demonstrate how to extend the relative p-adic monodromy conjecture from the neighborhood of rank-1 points to the entire interiors of Newton partitions.

Suppose we observe data from a distribution $P$ and we wish to test the composite null hypothesis that $P\in\mathscr P$ against a composite alternative $P\in \mathscr Q\subseteq \mathscr P^c$. Herbert Robbins and coauthors pointed out around 1970 that, while no batch test can have a level $α\in(0,1)$ and power equal to one, sequential tests can be constructed with this fantastic property. Since then, and especially in the last decade, a plethora of sequential tests have been developed for a wide variety of settings. However, the literature has not yet provided a clean and general answer as to when such power-one sequential tests exist. This paper provides a remarkably general sufficient condition (that we also prove is not necessary). Focusing on i.i.d. laws in Polish spaces without any further restriction, we show that there exists a level-$α$ sequential test for any weakly compact $\mathscr P$, that is power-one against $\mathscr P^c$ (or any subset thereof). We show how to aggregate such tests into an $e$-process for $\mathscr P$ that increases to infinity under $\mathscr P^c$. We conclude by building an $e$-process that is asymptotically relatively growth rate optimal against $\mathscr P^c$, an extremely powerful result.

We study the Hitchin morphism for higher dimensional varieties and show that, for a certain class of varieties which we call r-small, the set-theoretic image of the Hitchin morphism from the Dolbeault moduli space coincides with the spectral base. In other words, a stronger version of the conjecture of Chen and Ngô holds for this class of varieties, which includes K-trivial varieties. As part of the proof, we slightly modify the construction of spectral covers to obtain normal spectral covers.

This paper introduces a novel measure to quantify the directional dependence of extreme events between two variables. The proposed approach is designed to capture asymmetric tail dependence by studying conditional tail expectations of rank-transformed variables, thereby quantifying the behavior of one variable when the other takes extreme values. We investigate the theoretical asymptotic behavior of the associated estimator. The effectiveness of the approach is demonstrated through an extensive simulation study. In addition, we discuss the use of the proposed coefficient for the detection of causal effects in extreme events. Finally, we apply the method to an oceanographic dataset, where the results highlight the strong asymmetric nature of extreme events and identify the dominant directions of extremal influence among key oceanographic variables. As a directional measure of tail dependence, our approach provides a natural tool for exploring causal-effect relationships in extreme-value settings.