Papers

We introduce a new criterion which guarantees that a conservative local diffeomorphism is both non-uniformly expanding (in particular has all its Lyapunov exponents positive) and stably ergodic. The criterion involves averaging expansion rates over preimages and allows us to construct explicit examples in a variety of homotopy classes, including those represented by linear endomorphisms with contracting directions.

We study the asymptotic behavior of extreme events in multivariate stationary sequences, with particular emphasis on stochastic processes generated by dynamical systems. We develop a general framework for describing the dependence structure of extremes through two complementary objects: the tail process and the spectral measure. We first extend the enriched point-process convergence of the univariate theory to the multivariate setting, proving that the decorated point process of exceedances converges to a marked Poisson cluster process whose marks retain the componentwise and temporal structure of extreme clusters. We then construct a spectral measure for stationary sequences, which assigns weight to distinct extremal profiles and characterizes the asymptotic dependence between components, and establish a de Haan-Resnick type representation. We also relate the spectral measure to the tail process, showing that its normalized profile distribution is recovered from the angular component of the tail process. Finally, we recover the classical univariate and multivariate exceedance processes as special cases. We illustrate the theory through applications to dynamical systems, using examples in which different dynamical mechanisms give rise to distinct extremal clustering patterns and cross-dependence structures. These applications demonstrate the ability of the proposed framework to capture genuinely multivariate features of extreme events and to extract information about the underlying dynamics that is not accessible through classical exceedance processes.

Deep search enables language agents to solve complex information-seeking tasks through iterative web exploration. However, developing robust open-source agents remains challenging for three reasons. First, opaque trajectory-construction pipelines make training data difficult to audit and reproduce. Second, context compression can create a substantial mismatch between training and inference. Third, agents may retrieve benchmark content from the open web during evaluation, contaminating the results and overstating their performance. To overcome these bottlenecks, we introduce Glasseek, a fully transparent deep search framework spanning the complete development lifecycle, releasing all data, model weights, training recipes, and code. Specifically, for data construction, we establish a verifiable trajectory curation pipeline that systematically generates high-quality exploration paths. For training, we propose Compaction-Managed GSPO (CM-GSPO), which uses the same policy for search and summarization while optimizing only execution sub-trajectories, enabling end-to-end search-policy training across context-compaction boundaries. For evaluation, we conduct the first systematic audit of test-set leakage in open-web agents and release a modular anti-leakage plugin that seamlessly integrates into existing evaluation harnesses. Under this rigorous evaluation protocol, our 9B agent outperforms frontier proprietary agents across almost all deep research benchmarks spanning diverse task types, and achieves the best overall performance among recent open-weight agents, setting a new state of the art at the 9B scale.

We give a construction of a body of constant width from a unit Reuleaux polyhedron that preserves all its symmetries. As opposed to the Meissner surgery, our construction modifies both edges of each dual pair and requires no choice between them. For the Reuleaux tetrahedron it recovers a previously known body of constant width with six elliptic edges and tetrahedral symmetry.

The penetration-resistant design of concrete structures requires the spatiotemporal evolution of the stress field within the target, whereas in design only the strength grade, the geometry and the projectile parameters are known, and the aggregate arrangement is not. Empirical formulae and scalar-output surrogates serve design screening, and mesoscale finite element models resolve the aggregate-scale response, but one solution cannot cover random aggregate samples at scale, and no framework links mesoscale heterogeneity to field-level prediction. A physics-coupled graph neural operator (PC-GNO) is proposed, which learns in function space the evolution of the mid-plane six-component stress tensor field. The training data are generated by full-scale, aggregate-resolved finite element models and comprise 359 cases at the impact velocities of 100, 135 and 165 m/s, corresponding to compressive strengths of 14, 23 and 48 MPa; the data source is verified by laboratory measurements. The coupling strength of message passing is constructed from the impedance contrast across the material interface, and the update is constrained by spectral normalization. Under the single-step primary setting, the mean accuracy of the three levels is 80.16% (91.45%, 77.80% and 71.22%), i.e. 27.81, 42.46 and 34.16 percentage points above the preceding-frame field of the same window; with 20 664 parameters it exceeds the 87.9% of the best Fourier neural operator configuration (about 812 times as many parameters) and the 71.0% of the closed-form linear regression. The output is the complete six-component tensor field rather than a fixed engineering quantity, so that strength criteria and energy indicators follow from one set of weights. For field-level response prediction in concrete penetration, this result provides a data-driven route, with conditions of applicability defined by the training and the evaluation.

Real data are often arbitrary, indirect observations of an unknown underlying process, and those observations can distort its geometry. Existing geometric methods equip data with the induced geometry of the ambient space, but this entangles the true geometry of the process with the distortion of the observation. To address this, we introduce Intrinsic Geometry Matching (IGM): a scalable approach to learn the intrinsic geometry of the underlying process. Specifically, we learn the carré du champ operator of the process, allowing us to recover its diffusion geometry. Our method uses the fact that data often come with natural perturbations, like steps in a time series, to recover the intrinsic carré du champ while transforming naturally with changes in observation: it is observation-equivariant. Furthermore, since this equivariance relates the geometry of different spaces, we can train a model using additional sources of data, even when that data lies in another space. We evaluate IGM on molecular dynamics, image, and video data and find better performance and scaling than existing neural and graph-based geometric tools.

Observables in complex biological systems are often reduced in their inherent complexity, resulting in abstract, a priori mathematical representations based on simple concepts such as points in spaces or interconnected nodes in lattices or networks. This reduction is relevant not only for the formulation of multiscale mathematical models and field theories but also for experimental planning and data collection to gain systematic evidence for the nature of such systems, thus extracting robust causal relationships that would lead to better control of the system. However, mathematical abstraction remains challenging and problematic, especially given the tightly intertwined elements between objects and their environment, the system's affordance, and the fact that all these aspects limit fundamental mathematical concepts such as set theory, thus hindering the definition of phase spaces in extreme cases. In this work, I introduce a potential axiomatic representing a nonreducible representation of high order structures representing entanglement between observables in complex systems and their environment, considering not only their coupling but also their affordance in relation to the overall system and context, and thus intend to formalize concepts already used in complex systems such as Kantian wholes. In light of this axiomatic, I identify states that are rather less elastic with respect to their environment, discuss how low elasticity enables the application of set theory, while high elasticity limits the mathematical representation of complex systems, and present an exemplary Ising model with a network of elastic states with respect to different contexts as a limiting case for mathematical modelling in this context.

A landmark result states that the expressive power of graph neural networks (GNNs) is bounded from above by the 1-dimensional Weisfeiler-Leman (1-WL) test. We ask whether a constant-depth GNN can match the expressive power of 1-WL while using only rational weights. We prove that this is the case when Schanuel's conjecture, a famous open problem from transcendental number theory, is taken to be true. Our GNN construction works even with integer weights, and more generally with a broad range of rational weights. As the activation function, it may use logistic sigmoid, hyperbolic tangent, or related functions. It is uniform across all graph sizes. We also prove a partial converse: if a GNN with exponentiation, hyperbolic sine or hyperbolic cosine as activation matches the expressive power of the 1-WL test in a slightly more expressive setting where graphs may contain certain auxiliary vertices, then this implies Schanuel's conjecture restricted to the numbers that arise in computations of the GNN. We also conduct experiments showing that the constructed GNNs indeed match the 1-WL test.

Bayesian optimisation (BO) is a powerful framework for sample-efficient optimisation of expensive black-box functions, but its application to high-dimensional discrete scientific design remains challenging. Local trust-region BO methods such as TuRBO address high dimensionality by restricting search to adaptively sized neighbourhoods. However, a direct discrete analogue based on edit distance can be poorly suited to structured discrete objects: neighbourhoods grow combinatorially, and metric proximity does not capture the dependencies that determine whether a design is plausible or useful. Motivated by the growing availability of pretrained generative models, we introduce GenTuRBO, which replaces the geometric trust region with an adaptively scaled proposal distribution defined by a pretrained generator. The generator provides a learned prior over discrete transformations, encoding coordinated changes without explicitly enumerating edit-distance neighbourhoods. GenTuRBO performs strongly across all three domains and achieves the highest mean final scores on Ehrlich sequence optimisation and Sokoban coordination.

We characterize the randomized component-oracle complexity of finite-sum nonconvex-concave optimization with a bounded dual domain. For $\Phi(x)=\max_{y\in Y}n^{-1}\sum_{i=1}^n f_i(x,y)$, the goal is to find an $\varepsilon$-stationary point of the Moreau envelope $\Phi_{1/(2L)}$ with probability at least $2/3$ and a fixed query budget. Let $A=L\Delta/\varepsilon^2$, $B=LD_Y/\varepsilon$, and $\bar B=\max\{1,B\}$, where $\Delta$ bounds the initial primal gap and $D_Y$ bounds the dual diameter. For $A$ above a universal constant, the worst-case complexity is \[ \widetilde\Theta\!\left(n+A\min\left\{ \sqrt n\,\bar B+\bar B^4,\ n^{3/4}\bar B\right\}\right). \] The bounds agree within constants for $B\le n^{1/4}$ and within one logarithm for larger $B$. Upper bounds require only mean-squared averaged smoothness and concavity of the average in the dual variable; lower bounds already hold under individual smoothness. The lower constructions cover adaptive component selection, arbitrary query norms, private randomization, and outputs that were never queried. A cone construction gives the small-diameter bound, while a serial branch construction and balanced replication give the remaining two regimes. On the upper side, a persistent estimator with primal averaging complements accelerated proximal dual steps equipped with an explicit primal certificate. The characterization takes the worst case over admissible known dual domains and finite dimensions.

Tabular data generation aims to synthesize realistic samples from limited observations while faithfully capturing the underlying data distribution. Tabular foundation models (TFMs), pretrained on diverse tabular tasks and adapted through in-context learning, have demonstrated strong predictive capabilities, suggesting the potential of extending this paradigm to tabular data generation. However, the strong predictive performance of TFMs often relies on sufficiently large context sets, whereas tabular generation is typically needed precisely when target data are scarce. Extending the foundation-model paradigm to generation therefore requires reliable distribution inference from only a limited context. To this end, we propose TabGift, a context-efficient tabular foundation model enabling both efficient distribution modeling and effective generation from only a few context samples. TabGift maps heterogeneous tables into a shared latent space with a pretrained tabular encoder, where an in-context diffusion model learns to denoise latent samples conditioned on a small set of clean examples. This design transfers generative priors across datasets and enables distribution inference from limited context, while a lightweight dataset-specific MLP decoder maps generated representations back to the original data space. Experiments on 7 classification and 11 regression datasets show that TabGift consistently outperforms representative baselines in synthetic data quality, with particularly strong gains under limited-context settings, while achieving substantially faster adaptation and generation.

We derive a Fredholm-Pfaffian formula for the one-time multi-point transition probabilities of half-space polynuclear growth with any nonnegative boundary nucleation rate and general deterministic upper semi-continuous initial profiles. We prove the formula by showing that it satisfies an integral Kolmogorov equation with a unique bounded solution. We also discuss the formal 1:2:3 scaling limit of the kernel and its relation to the half-space KPZ fixed point.

Visual features extracted from vision models like DINOv2 or Stable Diffusion enable high quality semantic correspondence between images. However, such features exhibit documented limitations that hinder accurate correspondence estimation such as the inability to disambiguate the left from right for categories exhibiting symmetries or repeated parts. Previous attempts to improve these features rely on using supervised data such as annotated keypoint pairs or camera pose information, or make restrictive topological assumptions, such as modelling the object of interest as a 3D sphere. We introduce a new self-supervised approach that allows us to learn features for topologically complex object categories using a simple prior. Instead of relying on an expensive instance-level analysis by synthesis pipeline, our approach makes use of contrastive learning and distribution matching at the global dataset-level to learn the coarse shape and appearance of a category. Combined with additional geometric losses, this enables us to replicate the global and local statistics of visual features which match those that are extracted from real images. Quantitative results are presented across several challenging object categories, demonstrating the effectiveness of our approach.

Multimodal decentralized learning enables collaboration across heterogeneous edge devices without sharing raw data, but differing modality sets create coupled computation and communication bottlenecks. Multimodal agents support cross-modal alignment while training more model components and sharing bandwidth across multiple modality overlays. Under bandwidth limits, these agents can become hot spots: transfers miss aggregation windows, and their updates become stale or underrepresented, degrading worst-agent accuracy. Asynchrony removes global blocking but does not by itself coordinate local cross-modal interaction with timely peer-update exchange. We present MODAIC (Modality-Decoupled Asynchrony with Interleaved Coordination), a wait-free system that coordinates local modality progress, peer-to-peer update delivery, and aggregation under heterogeneous compute and bandwidth. Hierarchical asynchrony lets modalities progress independently while enforcing reciprocal feature exchange; load-aware update fetching overlaps training with communication, limits concurrent serving load, and reuses late arrivals; and consensus-aware peer selection uses lightweight metadata to account for update availability, peer participation, and loss similarity without active probing. We implement MODAIC as a containerized multi-agent framework and evaluate it on local and cross-region cloud testbeds. Across AVE and KU-HAR, MODAIC improves average accuracy and multimodal worst-agent performance. On AVE at 200 Mbps per agent, it improves multimodal worst-agent accuracy by 11.0 percentage points at 1000 seconds over the strongest baseline. On the cloud testbed, it reduces time-to-accuracy by up to 30%. Ablations show that simpler load-balancing and delayed-aggregation variants leave a worst-agent accuracy gap, and stress tests show tolerance to WAN variability and partial tracker unavailability.

Let $X_N(t)$, $t\in[0,\pi]$, be a stationary Gaussian trigonometric polynomial, and let $\mathcal Z_N$ denote the number of zeros of the rescaled process $X_N(t/N)$ on $[0,N\pi]$. We establish the quantitative central limit theorem \[ d_{\mathrm W}\left( \frac{\mathcal Z_N-\mathbb E[\mathcal Z_N]} {\sqrt{\operatorname{Var}(\mathcal Z_N)}},Z\right) \le C\frac{(\log N)^2}{\sqrt N}, \] where $Z$ is standard Gaussian and $d_{\mathrm W}$ denotes the Wasserstein-1 distance. The proof combines Ornstein–Uhlenbeck regularization of the singular Kac representation with direct estimates of the covariance between the Malliavin–Stein factor and Stein test functions. A lattice lower bound of order $N^{-1/2}$ shows that the convergence rate is optimal up to logarithmic factors.

Vision-language-action (VLA) models show strong potential for end-to-end autonomous driving by leveraging world knowledge and understanding to excel in long-tail scenarios. However, current VLAs have two limitations: 1) Degeneration into vision-action (VA) models. For low latency, regression/flow-based methods directly generate actions but underuse VLM understanding, causing unsafe, unexplainable actions. 2) Autoregressive high latency. Autoregressive methods sequentially generate chain-of-thought (CoT) and action tokens, fully leveraging VLM understanding, but high latency hinders deployment. To enable low-latency deployment while using CoT to assist action generation, we propose AUGUstus, an Autonomous-driving VLA model with Unified Generation and Understanding. We unify diffusion-based action generation and autoregressive CoT understanding in one model, where understanding only serves generation. Joint CoT supervision preserves VLM spatial understanding in shared representation for safer, more accurate trajectories. AUGUstus-mode orders action generation before CoT, so CoT supervises reliable actions during training while inference needs only action output, enabling low latency. AUGUstus-GRPO, a unified GRPO algorithm, jointly optimizes action and CoT, improving action performance. Experiments show AUGUstus achieves 94.6 PDMS on NAVSIMv1 and 90.7 EPDMS on NAVSIMv2, SOTA planning without scorer module. On nuScenes, it achieves average L2 error 0.27 m and average collision rate 0.05%, best among compared methods. To validate AUGUstus practicality, we train on in-house data with 512 NVIDIA H800 GPUs for ~2 days, evaluate on an internal 1,000 km dataset, and preliminarily deploy on a real vehicle, achieving 12 Hz operation. Project page: https://augustus-ad.github.io

Offline reinforcement learning aims to learn effective policies from fixed datasets without environment interaction. Although generative models such as diffusion and flow matching enhance policy expressiveness, they typically start from uninformative Gaussian noise and generate actions through multi-step iteration, leading to high computational costs and failing to effectively leverage suboptimal trajectories in datasets. We propose MeanFlow2Better (MF2B), which reformulates offline RL as generative decision chunk optimization from current performance status to better performance status in a high-level latent decision space. MF2B maps trajectory chunks to high-level latent decision representations through an encoder, placing generation starting points within a structured decision space sculpted by behavioral data. The model learns a shared conditional mean velocity field in this space, constructing two flow mappings: from Gaussian-Induced Decision Sources toward positive behavioral decision regions, and from suboptimal decisions toward high-value decision regions. Both flow mappings complete decision refinement through one-step ODE integration over the unit time interval $\Delta t=1$, requiring neither multi-step iterative sampling nor backpropagation through time. Furthermore, we propose hierarchical chunk-level advantage to guide the flow direction toward high-return regions, where the high-level decisions cover multiple low-level actions, leading to sequence length compression from $T$ to $K \approx T/H$ and significantly lower computational overhead. On the D4RL Gym-MuJoCo benchmark, MF2B achieves an average score of 90.91, matching or surpassing strong baselines.

Most prior work on predicting mental health help-seeking treats it as post-hoc classification of users already active in clinical communities, which cannot tell whether someone approaching a transition can be identified in advance. We instead frame help-seeking as a time-to-event problem and ask which Reddit users will eventually seek mental health support, and how imminent that transition is. We build a two-arm cohort: a control frame of 6,337 ordinary users with genuine right-censoring (12.1% transition rate) to answer who will transition, and a clinical frame of 5,023 eventual transitioners to answer how soon. Features come only from posts written before any clinical activity, and user-grouped five-fold cross-validation plus a four-year temporal holdout guard against leakage. We compare TF-IDF, MentalBERT embeddings and behavioural activity features using Cox proportional hazards models, Random Survival Forests and an LSTM sequential model. Behavioural features alone outperform text for predicting who will seek help (C-index 0.797 vs. 0.763), and combining both is best (0.823 under cross-validation, 0.856 on the holdout). The pattern reverses for predicting how soon a known transition will happen: text remains a stable predictor (C-index 0.698) while behavioural features become unstable. Structural engagement patterns therefore carry information about future help-seeking beyond linguistic content, and separating who from when yields a cleaner analysis.

We use Gaia Data Release 3 (DR3) light curves to identify photometrically selected changing-state active galactic nucleus (CSAGN) candidates. We employ unsupervised deep learning and anomaly detection methods to identify unusual patterns of variability in the light curves of 872,228 AGNs with known variability. We find that 8,504 light curves show anomalous behavior. Among these, 682 sources show evidence for two-state photometric behavior during the Gaia DR3 observing baseline. These 682 CSAGN candidates were selected using an automated statistical pattern recognition approach based on Gaussian mixture models (GMMs) to identify sources whose magnitude distributions are consistent with two preferred brightness levels, substantially reducing the need for human visual inspection in selecting the CSAGN candidates. The candidates tend to have fainter absolute magnitudes and lower redshifts than the non-anomalous Gaia variable AGN sample, suggesting that some may be accreting at lower rates. Our approach builds a large candidate sample with less reliance on human visual selection. Follow-up observations of these sources can help identify what drives changing-state transitions and clarify their connection to accretion-disk physics and supermassive black hole (SMBH) fueling.

Tracing money flows in cryptocurrency transaction networks is challenging because funds can move across accounts, transactions, and token layers. We propose a transaction-aware graph in which nodes represent account–asset states within transactions, while edges encode observed transfers, inferred asset transformations, and temporal inter-transaction sequences. Applied to Aave borrow–repay flows, we compare graph construction and edge-pruning strategies and extract shortest paths using a heuristic weighting. Our results reveal a trade-off between reachability and interpretability and uncover frequent token sequences underlying how borrowed assets are transformed before repayment. This work lays a foundation for general, interpretable multi-token flow tracing.

Artificial Intelligence (AI) models are increasingly developed, published and used across scientific fields. Researchers, students and industry professionals who want to apply these models to their own research questions often lack the programming and data science expertise to do so. Existing guidelines cover single steps, but not the route from a published model to working predictions on one's own data. Here we present the hands-on workflow PRAISE, a Practical, Reproducible AI-model Implementation for Science and Education, that helps non-programmers implement published AI models step by step. Because implementations rarely work the first time, PRAISE anticipates common failures and provides a fallback route for each. As a proof of principle, three BSc chemistry students and their tutor applied PRAISE without prior programming or data science knowledge. They reproduced, validated and extended a state-of-the-art model that predicts enzyme-substrate interactions. This shows that with PRAISE, implementing an AI model from the literature becomes a learnable skill, one that turns non-programmer scientists from users into evaluators and improvers of AI models.

Generative retrieval (GR) offers a promising paradigm for industrial search by unifying candidate generation within an autoregressive framework. However, its effectiveness is limited by two key challenges. First, existing Semantic ID (SID) tokenizers struggle to incorporate collaborative signals while maintaining effective codebook utilization, limiting their ability to distinguish items and achieve high-quality retrieval. Second, existing reinforcement learning (RL) methods suffer from severe reward sparsity under exact SID matching, leaving many sampled trajectories without effective learning signals and hindering preference optimization. To address these challenges, we propose WeGR, a unified generative retrieval framework consisting of two complementary components. Specifically, the Collaborative and Collapse-free Tokenizer (CoCo-VAE) incorporates query-to-item and item-to-item collaborative signals while mitigating codebook collapse through codebook refresh and complementary regularization, enabling more informative and balanced SID representations. Building upon these SIDs, Dynamic Horizon Policy Optimization (DHPO) progressively expands both reward evaluation and policy optimization horizons, reducing learning difficulty while leveraging behavioral reward signals at different levels of the SID hierarchy, without relying on auxiliary reward models. Extensive offline experiments demonstrate the effectiveness of WeGR in improving retrieval and ranking performance. Moreover, a two-month online A/B test in WeChat E-commerce Search demonstrates relative improvements of 2.539% in orders, 1.508% in click-through rate, and 1.381% in conversion rate, while reducing online CPU and GPU usage by 25.5% and 26.1%, respectively. The system has been successfully deployed across multiple search scenarios in WeChat, serving billions of users, generating tens of millions of PVs daily.

Multiple second-order control barrier function constraints can exhaust their common control authority under bounded acceleration, even when the current state remains feasible. We define a signed local joint-feasibility margin whose sign exactly identifies whether the current barrier half-spaces intersect the admissible input set. For unit-scaled distance constraints, it has acceleration units and a support-function dual that identifies weighted constraint conflicts. We predict the margin one sample ahead for nine task-directed candidates, selecting either the least-deviating candidate that attains a desired margin or the candidate with the largest predicted margin before solving the same hard HOCBF quadratic program. A controlled one-step case shows that, at the state predicted under the hard-QP command, two constraints remain individually feasible but become jointly infeasible, whereas the margin-feedback controller retains a positive next margin. Separately, across 20 paired initial conditions, the margin-feedback controller retains the hard-QP command in a low-pressure task and acts at positive margin in a critical task before the hard-QP problem becomes infeasible; its trajectories remain feasible at that time and complete the task. Source code is publicly available. https://github.com/xirhxq/cbf/tree/robio2026-preventive-regulation

Visual in-context learning (ICL) enables vision-language models (VLMs) to adapt at test time via demonstration examples, but its effectiveness depends critically on the examples selected. Recent counterfactual selection methods improve ICL by constructing demonstrations that expose how individual attribute changes affect the answer. However, they require multi-stage pipelines involving attribute extraction, caption engineering, and composed image matching. We propose a simpler alternative grounded in a key observation: a model's own prediction errors are natural counterfactual demonstrations that directly encode its failure modes. Our method, SMILE (Self-Mined Visual In-Context Learning from Errors), builds a model-specific pool of hard negatives offline by recording the target VLM's own mistakes. At test time, the prediction serves as a direction signal that surfaces, in the semantic embedding space, the past mistakes most likely to recur for the current query. This prediction-conditioned identification provides a unified mechanism for both closed-set classification and open-ended visual question answering without task-specific design. Across four benchmarks and four VLMs, SMILE delivers an average task-score gain of +3.09 points over the SOTA baseline at 5x lower latency. Project page: https://tree-shu-zhao.github.io/SMILE/

The vortex structures in the momentum distributions of multiple particle-antiparticle pairs produced from the vacuum by a spatially uniform, time-varying electric field with arbitrary polarization are investigated using the Bogoliubov transformation. For linearly polarized fields, as the field strength increases, the nodal lines in the multi-pair momentum distribution break up into vortex-antivortex pairs in both the bosonic and fermionic cases. Each vortex carries a topological charge that is an integer multiple of the single-pair vortex topological charge. For circular polarization, a central vortex appears at all field strengths. For bosons, its topological charge is an integer multiple of the single-pair vortex topological charge; for fermions, it is an integer multiple of the vortex topological charge for single-pair production with zero total spin projection along the field propagation direction. For elliptical polarization with suitable ellipticity, discrete vortices coexist with a central vortex. In this case, however, the integer-multiple relation for fermions generally fails because the two-pair production amplitude is a determinant and spin-channel contributions are separated in momentum space. These results provide a theoretical basis for understanding the vortex topology of multi-pair production in strong-field QED and for its potential control.

Drug discovery remains a resource-intensive and time-consuming process, involving billions of dollars and a decade of development to advance a drug to market. While many in silico tools have accelerated this process, operating them still demands substantial time, effort, and expertise from medicinal chemists. Autonomous systems built on Large Language Models (LLMs) have emerged as a promising solution, yet current designs limit their performance. Existing single-agent systems scale poorly to long-horizon, multi-step, and realistic tasks, whereas multi-agent systems typically execute predefined workflows that cannot capture the iterative, non-linear nature of a real drug discovery campaign. Here, we present MADDIE, a multi-agent drug discovery engine. It comprises a central agent, Orchestrator, and four specialized worker agents: HitIdentifier, LeadOptimizer, Synthesizer, and Evaluator, each representing a critical step in a drug discovery campaign. Under Orchestrator's orchestration and coordination, these worker agents are composed into flexible workflows, enabling MADDIE to adapt its strategy and navigate the drug discovery pipeline end-to-end. Across 50 protein targets, MADDIE produces molecules satisfying key property requirements and their synthesis routes, outperforming existing agentic systems, generative models, and general-purpose LLMs by a wide margin. Our analysis reveals how these agents collaborate and that MADDIE can employ different strategies across targets to achieve the campaign's goal, while still being efficient in time and tokens. Together, they demonstrate MADDIE as a low-cost, effective, and efficient autonomous engine for accelerating drug discovery. Code and dataset is available via https://github.com/ninglab/MADDIE.

We study compact static manifolds with boundary from a spectral point of view, with particular emphasis on the relation between Dirichlet, Neumann, and Robin spectra and the nodal structure of static potentials. We establish comparison inequalities linking Dirichlet and Neumann eigenvalues with the scalar curvature and derive sufficient spectral conditions ensuring that a static potential changes sign. We also obtain bounds on the number of connected components of the zero set, sufficient conditions for its connectedness, and sufficient conditions ensuring that its components intersect the boundary. Finally, we study variational properties of Robin static triples and characterize compact Robin static triples whose metrics are critical for the first mixed Robin–Dirichlet eigenvalue under admissible volume-preserving deformations.

Black-hole interiors are hidden from exterior observers, yet their geometry can enter the high-overtone spectrum of linear perturbations. We study how this spectrum encodes metric and supporting-matter information in analytic Einstein–Maxwell–dilaton black holes. Coupling a neutral spectator to the dilaton at fixed UV dimension provides a matter-sensitive channel alongside the momentum response. For real-endpoint spacelike connections, the momentum response and mass-label dependence separate the metric exponents from the signed dilaton slope. Near the causal threshold, a complex endpoint controls the spectral family: the mass profiles approach a common value, producing a shared fractional correction, while regular propagation retains label dependence. This mechanism is present at criticality without an inner horizon and continues locally into timelike interiors. Exterior numerical spectra support the reconstruction and the leading complex-endpoint responses. Local scaling and probe coupling set the candidate responses, while wave connection determines their imprint on the exterior spectrum.

Near-ideal, field-free superconducting diode behavior is demonstrated in room-temperature-grown Mo$_2$N/FePt bilayers. The response is consistent with remanent FePt stripe domains producing polarity-dependent thresholds for flux entry and vortex motion. Micromagnetic simulations reveal a periodic stray-field modulation across the stripes and asymmetric field enhancement near their ends at the bridge edges. One current polarity remains nearly dissipationless up to a sizable fraction of the estimated depairing current, whereas the opposite polarity develops dissipation at much lower current, yielding diode efficiencies up to approximately 85% in the thinner bilayer. The nonreciprocity can be continuously tuned by the in-plane magnetic preparation angle and reversibly switched by reverse-field excursions through the hysteretic reversal of the FePt layer. These results support edge-controlled flux entry and vortex motion as a route to high-efficiency superconducting diodes.

Studying event memory requires defining events and their relationships within remembered experience. Autobiographical narratives provide evidence of this organization, but their analytical units must first be established. This study introduces a large language model framework for constructing event representations from narratives and modeling their structure and dynamics with excerpt-level traceability. Explicit boundary rules and a feature schema informed by hippocampal models of episodic memory and navigation guide event construction. In a proof-of-concept application to interviews from five participants, the framework constructed 256 event-states. Multiple correspondence analysis embedded these states in feature-based spaces, with analyses focused on a selected 4-D geometry and 10-D and 13-D reference geometries. Consecutive event-states were significantly closer than expected under randomized narrative order. In the selected 4-D ten-basin solution, similarity between basin-state feature profiles corresponded with similarity between one-step routing profiles; context, mechanism, and theme differentiated full-system pathway engagement. A successor representation modeled expected basin-state occupancy across successive steps. Correlations between basin-centroid distances and complete successor-profile distances were positive across all five basin solutions, with exploratory tests supporting correspondence in at least two solutions across all three geometries. These findings connect feature-based event representations with observed narrative transitions and modeled multistep organization. The framework translates hippocampal principles into source-linked event boundaries and state representations, providing an analytical basis for testing neural accounts of event segmentation and predictive organization during naturalistic recall.