Omnimodal large language models (OmniLLMs) jointly process audio and visual streams, but the resulting long multimodal token sequences make inference prohibitively expensive. Existing compression methods typically rely on fixed window partitioning and attention-based pruning, which overlook the piecewise semantic structure of audio-visual signals and become fragile under aggressive token reduction. We propose Dynamic Audio-driven Semantic cHunking (DASH), a training-free framework that aligns token compression with semantic structure. DASH treats audio embeddings as a semantic anchor and detects boundary candidates via cosine-similarity discontinuities, inducing dynamic, variable-length segments that approximate the underlying piecewise-coherent organization of the sequence. These boundaries are projected onto video tokens to establish explicit cross-modal segmentation. Within each segment, token retention is determined by a tri-signal importance estimator that fuses structural boundary cues, representational distinctiveness, and attention-based salience, mitigating the sparsity bias of attention-only selection. This structure-aware allocation preserves transition-critical tokens while reducing redundant regions. Extensive experiments on AVUT, VideoMME, and WorldSense demonstrate that DASH maintains superior accuracy while achieving higher compression ratios compared to prior methods. Code is available at: https://github.com/laychou666/DASH.

Safety alignment in large language models is typically evaluated under isolated queries, yet real-world use is inherently multi-turn. Although multi-turn jailbreaks are empirically effective, the structure of conversational safety failure remains insufficiently understood. In this work, we study safety failures from a state-space perspective and show that many multi-turn failures arise from structured contextual state evolution rather than isolated prompt vulnerabilities. We introduce STAR, a state-oriented diagnostic framework that treats dialogue history as a state transition operator and enables controlled analysis of safety behavior along interaction trajectories. Rather than optimizing attack strength, STAR provides a principled probe of how aligned models traverse the safety boundary under autoregressive conditioning. Across multiple frontier language models, we find that systems that appear robust under static evaluation can undergo rapid and reproducible safety collapse under structured multi-turn interaction. Mechanistic analysis reveals monotonic drift away from refusal-related representations and abrupt phase transitions induced by role-conditioned context. Together, these findings motivate viewing language model safety as a dynamic, state-dependent process defined over conversational trajectories.

We introduce a framework for analyzing topological tipping in time-evolutionary point clouds by extending the recently proposed Topological Optimal Transport (TpOT) distance. While TpOT unifies geometric, homological, and higher-order relations into one metric, its global scalar distance can obscure transient, localized structural reorganizations during dynamic phase transitions. To overcome this limitation, we present a hierarchical dynamic evaluation framework driven by a novel topological and hypergraph reconstruction strategy. Instead of directly interpolating abstract network parameters, our method interpolates the underlying spatial geometry and rigorously recomputes the valid topological structures, ensuring physical fidelity. Along this geodesic, we introduce a set of multi-scale indicators: macroscopic metrics (Topological Distortion and Persistence Entropy) to capture global shifts, and a novel mesoscopic dual-perspective Hypergraph Entropy (node-perspective and edge-perspective) to detect highly sensitive, asynchronous local rewirings. We further propagate the cycle-level entropy change onto individual vertices to form a point-level topological field. Extensive evaluations on physical dynamical systems (Rayleigh-Van der Pol limit cycles, Double-Well cluster fusion), high-dimensional biological aggregation (D'Orsogna model), and longitudinal stroke fMRI data demonstrate the utility of combining transport-based alignment with multi-scale entropy diagnostics for dynamic topological analysis.

The nature of personalized text-to-image models poses a unique safety challenge that generic context-blind methods are ill-equipped to handle. Such global filters create a dilemma: to prevent misuse, they are forced to damage the model's broader utility by erasing concepts entirely, causing unacceptable collateral damage.Our work presents a more precisely targeted approach, built on the principle that security should be as context-aware as the threat itself, intrinsically bound to the personalized concept. We present IDENTITYGUARD, which realizes this principle through a conditional restriction that blocks harmful content only when combined with the personalized identity, and a concept-specific watermark for precise traceability. Experiments show our approach prevents misuse while preserving the model's utility and enabling robust traceability. By moving beyond blunt, global filters, our work demonstrates a more effective and responsible path toward AI safety.

Hardware design errors discovered after fabrication require costly physical respins that can delay products by months. Existing electronic design automation (EDA) tools enforce structural connectivity rules. However, they cannot verify that connections are \emph{semantically} correct with respect to component datasheets. For example, that a symbol's pinout matches the manufacturer's specification, or that a voltage regulator's feedback resistors produce the intended output. We present DRCY, the first production-ready multi-agent LLM system that automates first-pass schematic connection review by autonomously fetching component datasheets, performing pin-by-pin analysis against extracted specifications, and posting findings as inline comments on design reviews. DRCY is deployed in production on AllSpice Hub, a collaborative hardware design platform, where it runs as a CI/CD action triggered on design review submissions. DRCY is used regularly by major hardware companies for use-cases ranging from multi-agent vehicle design to space exploration. We describe DRCY's five-agent pipeline architecture, its agentic datasheet retrieval system with self-evaluation, and its multi-run consensus mechanism for improving reliability on safety-critical analyses

Classical Monte Carlo methods for pricing catastrophe insurance tail risk converge at order reciprocal root N, requiring large simulation budgets to resolve upper-tail percentiles of the loss distribution. This sample-sparsity problem can lead to AI models trained on impoverished tail data, producing poorly calibrated risk estimates where insolvency risk is greatest. Quantum Amplitude Estimation (QAE), following Montanaro, achieves convergence approaching order reciprocal N in oracle queries - a quadratic speedup that, at scale, would enable high-resolution tail estimation within practical budgets. We validate this advantage empirically using a Qiskit Aer simulator with genuine Grover amplification. A complete pipeline encodes fitted lognormal catastrophe distributions into quantum oracles via amplitude encoding, producing small readout probabilities that enable safe Grover amplification with up to k=16 iterations. Seven experiments on synthetic and real (NOAA Storm Events, 58,028 records) data yield three main findings: an oracle-model advantage, that strong classical baselines win when analytical access is available, and that discretisation, not estimation, is the current bottleneck.

We introduce an optimized protocol of fracture pattern classification using an artificial neural network to identify the solvent involved in the desiccation cracking process of starch-liquid slurries, even after it has been completely evaporated. For this purpose, image analysis techniques were used to characterize patterns obtained from drying suspensions using single solvents (water, ethanol, acetone) and two-component solvents (water-ethanol mixtures at different concentrations). Frequency histograms were generated based on nine morphological features, taking into account their size, shape, geometry and orientational ordering. Subsequently, we used these histograms as input data into artificial neural network variants to determine the set of features that lead to the higher accuracy in solvent identification. We obtained an average accuracy of $96(\pm 1)\%$ considering all solvents in the analysis. The highest accuracy was obtained with sets of features that include the crack area distribution. The proposed protocol can help to determine the combination of features that optimize pattern recognition in other fields of science and engineering.

This paper presents a federated learning framework secured by quantum key distribution (QKD) for wireless channel estimation and radar spectrum sensing in the next generation networks (NextG or Beyond 6G). A BB84-style protocol abstraction and pairwise additive masking are utilized to train clients' local models (CNN for channel estimation, U-Net for radar segmentation) and upload only masked model updates. The server aggregates without observing plain parameters; an eavesdropper without QKD keys cannot recover individual updates. Experiments show that secure FL achieves NMSE of 0.216 for channel estimation and 92.1\% accuracy with 0.72 mIoU for radar sensing. When an eavesdropper is present, QBER rises to $\sim$25\% and all rounds abort as intended; reconstruction error remains below $10^{-5}$, confirming correct aggregation.

AI is transforming pharmaceutical search, where traditional systems struggle with multimodal content and manual curation. Finder is a scalable AI-powered framework that unifies retrieval across text, images, audio, and video using hybrid vector search, combining sparse lexical and dense semantic models. Its modular pipeline ingests diverse formats, enriches metadata, and stores content in a vector-native backend. Finder supports reasoning-aware natural language search, improving precision and contextual relevance. The system has processed over 291,400 documents, 31,070 videos, and 1,192 audio files in 98 languages. Techniques like hybrid fusion, chunking, and metadata-aware routing enable intelligent access across regulatory, research, and commercial domains.

Translating single-cell RNA sequencing (scRNA-seq) data into mechanistic biological hypotheses remains a critical bottleneck, as agentic AI systems lack direct access to transcriptomic representations while expression foundation models remain opaque to natural language. Here we introduce ELISA (Embedding-Linked Interactive Single-cell Agent), an interpretable framework that unifies scGPT expression embeddings with BioBERT-based semantic retrieval and LLM-mediated interpretation for interactive single-cell discovery. An automatic query classifier routes inputs to gene marker scoring, semantic matching, or reciprocal rank fusion pipelines depending on whether the query is a gene signature, natural language concept, or mixture of both. Integrated analytical modules perform pathway activity scoringacross 60+ gene sets, ligand--receptor interaction prediction using 280+ curated pairs, condition-aware comparative analysis, and cell-type proportion estimation all operating directly on embedded data without access to the original count matrix. Benchmarked across six diverse scRNA-seq datasets spanning inflammatory lung disease, pediatric and adult cancers, organoid models, healthy tissue, and neurodevelopment, ELISA significantly outperforms CellWhisperer in cell type retrieval (combined permutation test, $p < 0.001$), with particularly large gains on gene-signature queries (Cohen's $d = 5.98$ for MRR). ELISA replicates published biological findings (mean composite score 0.90) with near-perfect pathway alignment and theme coverage (0.98 each), and generates candidate hypotheses through grounded LLM reasoning, bridging the gap between transcriptomic data exploration and biological discovery. Code available at: https://github.com/omaruno/ELISA-An-AI-Agent-for-Expression-Grounded-Discovery-in-Single-Cell-Genomics.git (If you use ELISA in your research, please cite this work).

Emerging AI regulations assign distinct obligations to different actors along the AI value chain (e.g., the EU AI Act distinguishes providers and deployers for both AI models and AI systems), yet the foundational terms "AI model" and "AI system" lack clear, consistent definitions. Through a systematic review of 896 academic papers and a manual review of over 80 regulatory, standards, and technical or policy documents, we analyze existing definitions from multiple conceptual perspectives. We then trace definitional lineages and paradigm shifts over time, finding that most standards and regulatory definitions derive from the OECD's frameworks, which evolved in ways that compounded rather than resolved conceptual ambiguities. The ambiguity of the boundary between an AI model and an AI system creates practical difficulties in determining obligations for different actors, and raises questions on whether certain modifications performed are specific to the model as opposed to the non-model system components. We propose conceptual definitions grounded in the nature of models and systems and the relationship between them, then develop operational definitions for contemporary neural network-based machine-learning AI: models consist of trained parameters and architecture, while systems consist of the model plus additional components including an interface for processing inputs and outputs. Finally, we discuss implications for regulatory implementation and examine how our definitions contribute to resolving ambiguities in allocating responsibilities across the AI value chain, in both theoretical scenarios and case studies involving real-world incidents.

Scaling cooperative multi-agent reinforcement learning (MARL) is fundamentally limited by cross-agent noise. When agents share a common reward, the actions of all $N$ agents jointly determine each agent's learning signal, so cross-agent noise grows with $N$. In the policy gradient setting, per-agent gradient estimate variance scales as $Θ(N)$, yielding sample complexity $\mathcal{O}(N/ε)$. We observe that many domains, including cloud computing, transportation, and power systems, have differentiable analytical models that prescribe efficient system states. In this work, we propose Descent-Guided Policy Gradient (DG-PG), a framework that utilizes these analytical models to provide each agent with a noise-free gradient signal, decoupling each agent's gradient from the actions of all others. We prove that DG-PG reduces gradient variance from $Θ(N)$ to $\mathcal{O}(1)$, preserves the equilibria of the cooperative game, and achieves agent-independent sample complexity $\mathcal{O}(1/ε)$. On a heterogeneous cloud scheduling task with up to 200 agents, DG-PG converges within 10 episodes at every tested scale, from $N{=}5$ to $N{=}200$, directly confirming the predicted scale-invariant complexity, while MAPPO and IPPO fail to converge under identical architectures.

The rise of large language models (LLMs) has introduced a new type of programming: natural language programming. Users write prompts, which are instructions in natural language, to direct LLMs to perform tasks such as natural language processing, code generation, reasoning, etc. An emerging area of research enables interoperability between prompts and programs. We present a novel programming abstraction, shared program state, that removes the manual work required to enable interoperability between prompts and program states. With shared program state, programmers can write prompts that directly access program variables, compute with program objects, and implement control flow in the program. We present a schema for specifying natural function interfaces that extend programming systems to support programs with prompts and leverage this schema to specify shared program state as a natural function interface. We implement shared program state in the Nightjar programming system. Nightjar enables programmers to write Python programs containing prompts that share the Python program state. We show that Nightjar programs achieve comparable or higher task accuracy than manually written implementations (+4-19%), while decreasing the lines of code by 39.6% on average. The tradeoff is that Nightjar may incur runtime overhead (0.4-4.3x manual implementations).

Generative models of 3D cardiovascular anatomy can synthesize informative structures for clinical research and medical device evaluation, but face a trade-off between geometric controllability and realism. We propose CardioComposer: a programmable, inference-time framework for generating multi-class anatomical label maps from interpretable ellipsoidal primitives. These primitives represent geometric attributes such as the size, shape, and position of discrete substructures. We specifically develop differentiable measurement functions based on voxel-wise geometric moments, enabling loss-based gradient guidance during diffusion model sampling. We demonstrate that these losses can constrain individual geometric attributes in a disentangled manner and provide compositional control over multiple substructures. Finally, we show that our method is compatible with a broad range of anatomical systems containing non-convex substructures, spanning cardiac, vascular, and skeletal organs. We release our code at https://github.com/kkadry/CardioComposer.

With the rising popularity of 3D Gaussian splatting and the expanse of applications from rendering to 3D reconstruction, there comes also a need for geometry processing applications directly on this new representation. While considering the centers of Gaussians as a point cloud or meshing them is an option that allows to apply existing algorithms, this might ignore information present in the data or be unnecessarily expensive. Additionally, Gaussian splatting tends to contain a large number of outliers which do not affect the rendering quality but need to be handled correctly in order not to produce noisy results in geometry processing applications. In this work, we propose a formulation to compute the Laplace-Beltrami operator, a widely used tool in geometry processing, directly on Gaussian splatting using the Mahalanobis distance. While conceptually similar to a point cloud Laplacian, our experiments show superior accuracy on the point clouds encoded in the Gaussian splatting centers and, additionally, the operator can be used to evaluate the quality of the output during optimization.

Phase transitions appear all over science, and are familiar from everyday life, as water boiling, sugar melting into caramel or as nematic molecules turning smectic in liquid-crystal displays. The dynamics of phase transitions can be extremely slow, as for example when fog in winter does not lift, that is when the coarsening takes much time from many tiny water droplets to fewer but larger rain drops that feel the pull of gravity. The dynamics of phase transitions is relevant also for the performance of computer algorithms. In the ubiquitous Metropolis Monte Carlo algorithm, the mixing dynamics towards equilibrium leads towards the solution of a sampling problem. It is governed by the same reversibility and detailed-balance principles as the overdamped physical dynamics of fog. For the phase-separated Lennard-Jones system, we describe here how the coarsening dynamics of non-reversible "lifted" variants of the Metropolis algorithm proceeds on much faster time scales, with the microscopic non-reversibility translating into large-scale relative motion of droplets that is impossible under the Ostwald-ripening condition of reversibility. A density-displacement coupling moves droplets relative to each other through a lensing effect. Efficient implementations of the long-range Metropolis algorithm and its non-reversible lifting (event-chain Monte Carlo) allow us to show that, in consequence, the coarsening growth exponent is larger under lifting. For large system sizes, the computing problem is thus solved infinitely faster than before, with the outcome strictly unchanged with respect to the Metropolis algorithm. We also discuss the larger setting of our findings, namely that "lifted" non-reversible algorithms can be set up for generic reversible sampling methods, with applications going much beyond our example of lifting fog.

Per- and polyfluoroalkyl substances (PFAS) are typically encountered as mixtures of distinct chemicals with distinct effects on multiple health outcomes. Estimating joint causal effects using spatially-dependent observed data is challenging. We propose a spatial causal tensor completion framework that jointly models multiple exposures and outcomes within a low-rank tensor structure, while adjusting for observed confounders and latent spatial confounders. This method combines a low-rank tensor representation to pool information across exposures and outcomes with a spectral adjustment step that incorporates graph-Laplacian eigenvectors to approximate unmeasured spatial confounders, implemented via a projected-gradient descent algorithm. This framework enables causal inference in the presence of unmeasured spatial confounding and pervasive missingness of potential outcomes. We establish theoretical guarantees for the estimator and evaluate its finite-sample performance through extensive simulations. In an application to national PFAS monitoring data, our approach yields more conservative and credible causal relationships between PFOA and PFOS exposure and 13 chronic disease outcomes compared with existing alternatives.

Recent cosmological observations show hints for possible deviations from the standard $Λ$CDM paradigm at late times. To study such deviation, we introduce a minimal phenomenological framework in which the total equation of state of the Universe, $w_{\rm T}(z)$, follows a logistic evolution motivated by a renormalization group like flow between cosmological fixed points. This approach directly reconstructs $w_{\rm T}(z)$ probed by background observables, without assuming a specific dark energy model. Using DESI-DR2 baryon acoustic oscillation measurements, DES-Dovekie latest supernova data, and CMB distance priors, we find that the logistic parametrization provides an improved fit compared to $Λ$CDM and remains competitive with standard dynamical dark energy models. The inferred expansion history exhibits noticeable deviations from $Λ$CDM at low redshifts, reflected in the reconstructed jerk parameter. While the statistical significance of these deviations is model-dependent, our results highlight the potential of flow-inspired parametrizations as a complementary and physically interpretable framework for probing late-time cosmic dynamics.

We propose a data-driven linear modeling framework for controlled nonlinear hereditary systems that combines Koopman lifting with a truncated Grunwald-Letnikov memory term. The key idea is to model nonlinear state dependence through a lifted observable representation while imposing history dependence directly in the lifted coordinates through fixed fractional-difference weights. This preserves linearity in the lifted state-transition and input matrices, yielding a memory-compensated regression that can be identified from input-state data by least squares and extending standard Koopman-based identification beyond the Markovian setting. We further derive an equivalent augmented Markovian realization by stacking a finite window of lifted states, thereby rewriting the finite-memory recursion as a standard discrete-time linear state-space model. Numerical experiments on a nonlinear hereditary benchmark with a non-Grunwald-Letnikov Prony-series ground-truth kernel demonstrate improved multi-step open-loop prediction accuracy relative to memoryless Koopman and non-lifted state-space baselines.

We present a general protocol for estimating $M$ observables from only $\mathcal{O}(\log (M)/\varepsilon^2)$ copies of a Gibbs state whose Hamiltonian is accessible. The protocol uses single-copy, nonadaptive measurements and uses a total Hamiltonian simulation time of $\widetilde{\mathcal{O}}(βM/\varepsilon^2)$; we show that the sample complexity is optimal in a black-box setting where exponential time Hamiltonian simulation is prohibited. The key idea is a new interpretation of quantum Gibbs samplers as \textit{detailed-balance measurement channels}: measurements that preserve the Gibbs state when outcomes are marginalized. Consequently, shadow tomography of thermal states admits a general efficient algorithm when the Hamiltonian is known, substantially lowering the readout cost in quantum thermal simulation.

Accurate probabilistic modeling of the power system restoration process is essential for resilience planning, operational decision-making, and realistic simulation of resilience events. In this work, we develop data-driven probabilistic models of the restoration process using outage data from four distribution utilities. We decompose restoration into three components: normalized restore time progression, total restoration duration, and the time to first restore. The Beta distribution provides the best-pooled fit for restore time progression, and the Uniform distribution is a defensible, parsimonious approximation for many events. Total duration is modeled as a heteroskedastic Lognormal process that scales superlinearly with event size. The time to first restore is well described by a Gamma model for moderate and large events. Together, these models provide an end-to-end stochastic model for Monte Carlo simulation, probabilistic duration forecasting, and resilience planning that moves beyond summary statistics, enabling uncertainty-aware decision support grounded in utility data.

The primary objective of this paper is to establish several sharp results concerning the Bohr inequality, the refined Bohr inequality, and the improved Bohr inequality for the classes of analytic functions and harmonic mappings defined on the shifted disks \[ Ω_γ=\left\{z\in\mathbb{C}:\left|z+\fracγ{1-γ}\right|<\frac{1}{1-γ}\right\}\quad\text{for}\quadγ\in[0,1).\]

We develop LENORI, a Large Event Number of Outages Resilience Index measuring distribution system resilience with the number of forced line outages observed in large extreme events. LENORI is calculated from standard utility outage data. The statistical accuracy of LENORI is ensured by taking the logarithm of the outage data. A related Average Large Event Number of Outages metric ALENO is also developed, and both metrics are applied to a distribution system to quantify the power grid strength relative to the extreme events stressing the grid. The metrics can be used to track resilience and quantify the contributions of various types of hazards to the overall resilience.

We introduce a postprocessing procedure that recovers sub-cell wave geometry from a standard one-dimensional Euler shock-capturing computation using differentiated Riemann variables (DRVs) -- characteristic derivatives that separate the three wave families into distinct localized spikes. Filtered DRV surrogates detect the waves, plateau sampling extracts the local states, and a pressure-wave-function Newton closure completes the geometry. The entire pipeline adds less than $0.25\%$ to the cost of a baseline WENO--5/HLLC solve. For Sod, a severe-expansion problem, and the LeBlanc shock tube, wave locations are recovered to within roundoff or $O(10^{-4})$ and the contact is sharpened to one cell width; a pattern-agnostic extension handles all four Riemann configurations with errors at the $10^{-6}$--$10^{-8}$ level. Direct comparison with MUSCL--THINC--BVD and WENO-Z--THINC--BVD shows that neither reproduces the combination of sharp contacts, small contact-window internal-energy error, and elimination of the LeBlanc positive overshoot achieved by the DRV reconstruction.

Recent experiments in rhombohedral graphene report an unusual superconducting phase emerging from a spin- and valley-polarized quarter-metal state. The prevailing interpretation invokes chiral topological superconductivity, but the role of the `Fulde-Ferrell' phase factor due to intra-valley pairing has remained largely unexplored. Here we show, via a gauge transformation, that this phase is equivalent to an ordinary chiral topological superconductor on the triangular lattice, while simultaneously forming an extraordinary Majorana crystal on the dual honeycomb lattice reminiscent of the Haldane model.

We study for the first time the action of the Hilbert matrix $$\mathcal H=(c_{n,k})_{n,k\geq 0}, \quad c_{n,k}=\frac{1}{n+k+1}$$ on the analytic tent spaces $AT^q_p, 1<p,q <\infty,$ of the unit disc $\mathbb D$ of the complex plane. They were proposed by Triebel as the natural analytic version of the tent spaces of measurable functions defined by Coifman, Meyer and Stein. The $AT_p^q$ spaces are consisted of those analytic functions $f$ in $\mathbb D$ such that $$ \|f\|_{AT_{p}^{q}}= \left\{\int_{\mathbb T} \left(\int_{Γ_{1/2}(ξ)} |f(z)|^p \ \frac{dA(z)}{1-|z|^2} \right)^{q/p}\ |dξ|\right \}^{1/q}<+\infty, $$ where $$ Γ_{1/2}(ξ) =\bigl\{ z\in \mathbb{D} : |z|< 1/2 \bigr\} \cup \bigcup_{|z|<1/2}[z,ξ), $$ $dA(z)$ is the normalized area Lebesgue measure in $\mathbb D$ and $|dξ|$ is the arc length in the unit circle $\mathbb T$. The Bergman spaces $A^p, p>1,$ stand among the $AT_{p}^{q}$ and correspond to the case $p=q$. The multiplication of the Hilbert matrix with the column matrix with entries the Taylor coefficients of an $f(z)=\sum_{k\geq 0} a_k z^k $ analytic in $\mathbb D$ introduces the series $$ \mathcal H (f)(z)= \sum_{n=0}^{\infty}\left(\sum_{k=0}^{\infty} \frac{a_k}{n+k+1}\right)z^n\,, \quad z\in \mathbb D\,\, $$ known in the literature as Hilbert operator. We prove that it is a bounded operator on the $AT_{p}^{q}$ when $1/p + 1/q <1,\, p>2$. This is a natural range for the values of the indices $p,q$ compared to what is known in the special case of the Bergman spaces. We confront the question under discussion through a more general point of view by studying an associated integral operator defined with respect to a positive Borel measure $μ$ on $[0,1)$. Finally, we provide an estimation of the norm of the Hilbert operator. Our work extends in a non-trivially way previous results on the Bergman spaces to the analytic tent spaces.

We introduce a model for directed spatial networks. Starting from an age-based preferential attachment model in which all arcs point from younger to older vertices, we add \emph{reciprocal} connections whose probabilities depend on the age difference between their end-vertices. This yields a directed graph with reciprocal correlations, a power-law indegree distribution, and a tunable outdegree distribution. We consider two versions of the model: an infinite version embedded in $\mathbb{R}^d$, which can be constructed as a weight-dependent random connection model with a non-symmetric kernel, and a growing sequence of graphs on the unit torus that converges locally to the infinite model. Besides establishing the local limit result linking the two models, we investigate degree distributions, various directed clustering metrics, and directed percolation.

Fluid gels are soft materials formed by shearing biopolymer solutions during the sol-gel transition. Their ability to yield and flow beyond a critical stress makes them attractive for designing versatile, biocompatible materials in food, health care and medical applications. Although it is well established that both microstructure and mechanical properties depend on the shear applied during gelation, a unified physical framework linking these features remains lacking. Here, using $κ$-carrageenan gels as a model system, we use a combination of rheology and confocal microscopy to tackle their shear-induced structuring in fluid gels. We identify a thermo-rheological memory in $κ$-carrageenan gels formed under flow and show that it arises from a competition between shear and interparticle adhesion, captured by an Adhesion number. The resulting microstructural evolution is reminiscent of the behavior of attractive particulate dispersions under simple shear flow, thereby bridging gels made of macromolecules and particulate gels. This framework provides a route to tune fluid gel properties without altering their composition.

The automorphism group of a regular locally finite tree is shown to admit irreducible Banach representations that are not admissible. The dense subspace of smooth vectors contains no algebraically irreducible component.

Incident management is essential to maintain the reliability and availability of cloud computing services. Cloud vendors typically disclose incident reports to the public, summarizing the failures and recovery process to help minimize their impact. However, such reports are often lengthy and unstructured, making them difficult to understand, analyze, and use for long-term dependability improvements. The emergence of LLMs offers new opportunities to address this challenge, but how to achieve this is currently understudied. In this paper, we explore the use of cutting-edge LLMs to extract key information from unstructured cloud incident reports. First, we collect more than 3,000 incident reports from 3 leading cloud service providers (AWS, AZURE, and GCP), and manually annotate these collected samples. Then, we design and compare 6 prompt strategies to extract and classify different types of information. We consider 6~LLM models, including 3 lightweight and 3 state-of-the-art (SotA), and evaluate model accuracy, latency, and token cost across datasets, models, prompts, and extracted fields. Our study has uncovered the following key findings: (1) LLMs achieve high metadata extraction accuracy, $75\%\text{--}95\%$ depending on the dataset. (2) Few-shot prompting generally improves accuracy for meta-data fields except for classification, and has better (lower) latency due to shorter output-tokens but requires $1.5\text{--}2\times$ more input-tokens. (3) Lightweight models (e.g., Gemini~2.0, GPT~3.5) offer favorable trade-offs in accuracy, cost, and latency; SotA models yield higher accuracy at significantly greater cost and latency. Our study provides tools, methodologies, and insights for leveraging LLMs to accurately and efficiently extract incident-report information. The FAIR data and code are publicly available at https://github.com/atlarge-research/llm-cloud-incident-extraction.