Papers

In this note we investigate the construction of near-group fusion categories via building explicit representations of them in certain graph planar algebras. To achieve this we first give a presentation for a cyclic near-group fusion category. Our presentation is “subfactor-centric” in the sense that we use a Q-system as one of our generating morphisms. Using this presentation we then obtain a rational system of equations, a solution of which corresponds to a faithful embedding of a near-group fusion category into a certain 2-coloured graph planar algebra. We end the note by providing solutions to these systems of equations for the odd cyclic groups up to order 13. This gives an alternate construction to the Evans-Gannon construction of the corresponding near-group fusion categories.

Accurately predicting fast solar wind conditions is challenging, as uncertainties are large and unquantified by traditional single-value prediction models. In particular, the risks of high-speed solar wind streams (HSSs), which can cause damage to technological infrastructure, cannot be reliably assessed without probabilistic forecasts. We present PROSWIN, a probabilistic machine learning model that forecasts the hourly solar wind speed (SWS) at Earth with a four-day lead time. The approach combines solar images and magnetograms using a deep neural network coupled to a distributional regression algorithm. Because standard error metrics underweight the relevance of HSS peaks, we further introduce the prediction score, a model-selection metric that jointly rewards timeline and HSS peak accuracy. On 14 years of data, our forecast achieves very well-calibrated uncertainties (<1% average deviation). Using the continuous ranked probability score (CRPS), a metric that assesses distributional accuracy, we obtain a timeline CRPS of 41.0 km/s, an HSS peak CRPS of 45.3 km/s, and a prediction score of 42.3 km/s. We find that the 171 Å channel is an important complement to the typically used 193 Å and 211 Å channels and that the prediction score for model selection improves the applicability of the model. Compared to selected models from the literature, ours is the only one that is accurate for both timeline and HSS peak values, rather than trading one off against the other. These results support the advantages of probabilistic over single-value solar wind models. The introduced methods are also transferable to other forecasting problems.

Generative AI (GenAI) applications have flourished enabling users to chat with large language models, and to create agents to act on their behalf for a variety of tasks. The pace of development of capabilities in this field is incredibly fast with security and safety taking a back seat. Unfortunately, the slower pace at which security and safety mechanisms have evolved has led to real incidents. Policy enables the definition of desirable behavior of applications, and for that reason, it is a cornerstone of making systems secure and compliant. Policy however means different things to different practitioners creating confusion and siloed solutions that are not adequate for compliance. This paper takes a tour of the good, the bad and the ugly when it comes to policy enforcement in GenAI applications. We propose a methodology to systematically analyze and dissect existing approaches to define and enforce policy found in the wild. Based on this principled analysis, we provide recommendations and call for action for the community to address. This paper is a companion extension of USENIX Security 2026 Enigma talk titled "From Alignment to Access Control: A Unified View of GenAI Policy Enforcement" by the author Nathalie Baracaldo.

The rationalization of protein hydrogel design is essential in creating bespoke and functional materials for a range of medical and healthcare applications, such as tissue engineering, wound healing and bio-sensors. The dynamic process of protein unfolding can significantly influence the resultant gel structure and behaviour - conformational changes in individual protein building blocks affect the bulk gel, whilst changes to bulk conditions influence how individual proteins move and respond. In order to characterize and control protein hydrogels, a multi-lengthscale picture must be built so that this complex interplay can be understood. We develop a coarse-grained computational model to investigate fundamental aspects of dynamic unfolding within chemically crosslinked protein hydrogels, focussing on the mesoscale structure during and after gelation. In simplifying protein unfolding to a single dynamic step, we are able to create a heterogeneous network formed of coarse-grained proteins. We observe evolving hydrogels consisting of regions of high-density protein clusters with a low degree of unfolding due to local crowding effects, interconnected by low-density stranded regions with a higher concentration of unfolded proteins. Systematically varying the barrier height for single protein unfolding demonstrates a weak influence on the mesoscale structure as characterised by fractal dimension and correlation length. Conversely, the measured changes in these parameters are greater after the gel experiences sustained conformational relaxation. This work demonstrates the effectiveness of coarse-grained modelling in capturing the heterogeneous mesoscale network of crosslinked unfoldable proteins. A greater predictive understanding of the structure and behaviour of protein hydrogels is gained through this model and will accelerate the design of novel biomaterials.

Even though privacy policies are the primary mechanism organizations use to disclose how they collect, process, and share personal data, they are difficult for average users to interpret, perhaps by design, due to their verbosity and dense legal language. Importantly, there is a lack of standardized metrics that characterize key qualities of a privacy policy beyond regulatory requirements. Recent advances in large language models (LLMs) make it feasible to automatically structure and analyze these documents at scale. In this study, we develop and evaluate an end-to-end, LLM-enabled system that converts raw privacy policies into fine-grained structured representations and a set of quantitative measures. Our pipeline applies a detailed taxonomy to extract specific data elements and governing practices, capturing relational links that connect each practice to the data elements it references. We apply our framework to a diverse corpus of 10,000 website privacy policies, yielding, to the best of our knowledge, the most comprehensive dataset of its kind to date. Building on our structured representations, we introduce the first standardized and repeatable quantitative metrics for evaluating privacy policies along four dimensions: completeness, transparency, commitment to user protection, and emphasis on business-driven data practices. This allows us to compare policies within and across industry sectors, and to assess the tension between user protection and business interests.

In grokking an early fit to the training data separates from a much later improvement in generalization. During this delay, training can move from a fixed neural tangent kernel (NTK) regime to one in which task-relevant kernel eigendirections continue to evolve. We provide a quantitative theory for how this transition from lazy to rich learning can produce delayed generalization. For homogeneous networks trained with squared loss and $L_2$ weight decay, we show that a finite residual remains after memorization, with larger residual fractions in target components associated with smaller NTK eigenvalues. These residuals feed back into the dynamics of the NTK itself, and projecting the resulting dynamics onto task-relevant spectral directions yields a reduced system in which residual-driven kernel growth competes with weight decay. This system predicts that the grokking timescale is controlled by the product of learning rate and weight decay, that feature learning slows logarithmically near a critical decay above which task-aligned NTK structure can no longer support generalization, and that stronger decay can prevent fitting altogether. We test these predictions in modular addition. In a homogeneous MLP, task-aligned Fourier structure continues to emerge in the NTK after training accuracy has saturated, and an 84$\times$90-grid of trained networks across varying learning rate and weight decay recovers the predicted phase geometry and inverse-product scaling of the generalization time with learning rate and weight decay. A one-block Transformer shows similar macroscopic phase structure in a 42$\times$45-grid, as well as the same transition-time scaling despite violating exact homogeneity. Together, these results provide a mechanistic derivation connecting post-fit feature learning to both the onset of generalization and its phase structure in the learning rate and weight decay plane.

Quantum strong direct-product theorems for specific functions have been known for nearly two decades. These have been extended to general results for function computation and state generation. The proofs of these results use a version of the multiplicative adversary method that does not naturally extend to relations. Standard strong direct-product theorems apply when algorithms must correctly answer every given question. Prior work extended them to equivalent threshold direct-product theorems, which require answers to all questions but only require that most answers are correct. We focus on two further generalizations. Strong selective direct-products apply to algorithms that adaptively choose, based on what they learn from queries, which questions from a large list to answer. This generalization is relational and useful for proving time-space tradeoffs. We prove a quantum strong selective direct-product theorem for all functions using a relational formulation of the multiplicative adversary method by Jeffery and Zur which we prove, via an equivalent formulation, satisfies a strong selective direct product property and captures any query lower bound for functions proven by negative-weights adversaries. The second generalization is list-decoding direct product problems introduced by Ben-David and Blais for classical query complexity. These allow an algorithm to produce a large list of possible output vectors such that one of them is fully correct. They proved that such theorems hold for randomized complexity of all Boolean functions. We prove a quantum analogue of this theorem for all partial Boolean-valued functions. We show that strong list-decoding direct-product theorems are implied by a special case of multiplicative adversaries which we show, via a new reduction, can be obtained from negative-weights adversaries for any Boolean-valued function.

Understanding the resources required to generate approximately random unitaries over various groups is a natural goal of quantum information theory. With respect to one notion of approximation, that of a design, it is known that the full unitary group can be approximated in logarithmic depth by one-dimensional circuits of nearest-neighbour 2-local gates. On the other hand, remarkably, circuits with this connectivity cannot form designs over the matchgate group in sublinear depth. Here we show that this dramatic slowdown can disappear when using a general qubit connectivity graph $\mathsf{G}$ of routing number ${\rm rt}(\mathsf{G})$. Indeed, in this setting one can obtain (strong) $\varepsilon$-approximate relative error matchgate $k$-designs in depth $\mathcal{O}(k^2{\rm rt}(\mathsf{G})\log n\log(n/\varepsilon))$. For all-to-all connectivity, ${\rm rt}(\mathsf{G})=2$. Our construction is conceptually simple, involving a random walk on the matchgate group, and no ancillae. As a technical byproduct, we improve upon the state of the art for fermionic routing, obtaining an $\mathcal{O}({\rm rt}(\mathsf{G})\log n)$ depth router. Additionally, for $k=3$, we obtain an exact strong matchgate design in $\mathcal{O}({\rm rt}(\mathsf{G})\log n)$ depth, again without ancillae. Under all-to-all connectivity, our fermionic router and 3-designs are optimal. Notably, our results imply that quantum algorithms for fermionic tomography which require drawing from a matchgate 3-design may be exponentially sped up on quantum computers with all-to-all connectivity, relative to their strictly one-dimensional counterparts.

We compute the linear magnetoelectric conductivity of a two-band vortex nodal-ring (VNR) semimetal and a three-band Hopf semimetal (HSM) within the semiclassical Boltzmann formalism, in the relaxation-time approximation, for three inequivalent planar-Hall configurations, with the electric ($\boldsymbol E$) and magnetic ($\boldsymbol B$) fields oriented differently relative to the nodal-ring plane and the Berry-curvature (BC) dipole axis. Unlike Weyl and multifold semimetals with point-monopole BC flux, the HSM carries a single, point-like BC-dipole fixed at its node, while the VNR hosts a continuous ring of such sources around the nodal loop. Both have vanishing Chern numbers. Working consistently to cubic order in $\boldsymbol B$, we evaluate the Drude, BC, orbital-magnetic-moment (OMM), anomalous-Hall, and Lorentz-force contributions. In both systems, the dipolar BC and OMM activate out-of-plane and odd-in-$\boldsymbol B$ in-plane response-channels that are symmetry-forbidden for a BC-monopole. Mirror symmetry confines the odd longitudinal terms to $B_z$, the field component along the dipole axis. The internode-scattering conductivity of the HSM vanishes identically, since the dipolar BC and OMM are even in momentum and no charge is pumped between two conjugate Hopf nodes, which carry oppositely oriented BC-dipoles. Comparisons with a $\mathcal{PT}$-broken gapped nodal-ring and a pseudospin-1 triple-point semimetal confirm the dipolar-BC origin of these features.

Row-sparse projection provides a useful tool in machine learning (ML) when it comes to, for example, feature selection, aiming to choose most relevant features for various ML objectives. One way to seek a high quality row-sparse projection is to combine an ML objective, such as the ones for PCA, LDA, and OCCA, with the matrix $(2,1)$-norm regularization which is nonsmooth. Such combinations result in challenging optimization problems on the Stiefel manifold that need to be solved efficiently. In this paper, a unifying NEPv framework is established to efficiently deal with optimization on the Stiefel manifold with the $(2,1)$-norm regularization. The effect of the $(2,1)$-norm regularization is also investigated. The wide applicability of the framework is demonstrated through the combinations of common learning objectives in today's data science applications with the $(2,1)$-norm regularization. Numerical experiments are presented to illustrate the use of the NEPv approach and to gain insights as to what a proper regularizing parameter should have in real-world applications.

Photon statistics have moved to the forefront of modern optics, as intensity fluctuations and correlations shape multiphoton interactions and reveal information beyond mean-intensity measurements. Developing high-quality photon sources with pronounced correlations is a fundamental necessity in these fields. Here we demonstrate fluctuation-driven nonlinear statistical amplification of quantum light in spontaneous four-wave mixing using filtered amplified spontaneous emission (ASE). Extending the coherent-pump framework to fluctuating fields, we show how nonlinear weighting of pump intensity combines with bosonic bunching to amplify quantum statistics and reshape temporal correlations. In a SiN microring, ASE pumping increases the zero-delay unconditional second-order correlation from 2.01 to 7.58 and extends the Hanbury Brown–Twiss correlation time by a factor of approximately 2.4. The super-bunched quantum source nevertheless retains heralded single-photon behaviour with $g_H^{(2)}(0)\simeq0.04$, while the same ASE pump supports time–energy entanglement in a silicon waveguide with a raw Franson visibility of 89.84%. These results establish driving-field statistics as a design dimension for quantum light, broadening the horizons for research into higher-order correlations and nonlinear physics.

Footnotes can be powerful tools to aid understanding, providing information that augments the reading experience. However, static footnotes cannot address every reader question. Current reading tools allow readers to view curated footnotes, allow personal and social annotation, and link dictionaries to reading material. Many other existing tools and natural language processing (NLP) techniques–such as generative AI, summarization and translation–could be used to address any reader question. However, no one has yet explored which of these features readers actually want. To bridge this gap, we conducted thirteen semi-structured interviews with readers from various backgrounds, followed by a thematic analysis of their responses. We develop themes describing the types of footnotes readers prefer and how to determine the quality of footnotes–specifically focusing on what sources of information a system considers, what the footnotes contain, and how the footnotes are presented to the reader.

Training vision-language-action (VLA) models for high-precision manipulation typically requires task-specific, high-quality data (e.g., teleoperation), which is slow and expensive to collect. To reduce this burden without compromising manipulation precision, we propose $\varepsilon$4P (Imperfection for Precision), a simple yet effective method that "upcycles" two otherwise discarded data sources: (1) low-precision data from the target task and (2) high-precision data from mismatched tasks. Rather than naively mixing these imperfect data sources throughout co-training, $\varepsilon$4P controls where each source contributes along the flow-matching trajectory. Specifically, low-precision, target-task data is used at high noise to preserve high-level task context and high-precision, task-mismatched data is used at low noise to transfer low-level action precision. Through real-robot experiments on both sub-millimeter, high-precision tasks and coarse-grained tasks, we demonstrate that the proposed method (1) effectively leverages additional imperfect data to improve policy performance by up to 31.7 percentage points, and (2) can replace an equal amount of task-specific, high-quality data with an average performance drop of only 4.2 percentage points. Overall, $\varepsilon$4P points toward a scalable paradigm for high-precision manipulation, in which heterogeneous, imperfect data can be systematically repurposed to reduce reliance on costly task-specific, high-quality data. More details are available at https://varepsilon4p.github.io/.

In the unrestricted max–min metric $T$-join problem, one seeks an even terminal set $T$ maximizing the cost of a minimum $T$-join. Iwata and Ravi gave a factor-$3/2$ approximation for this problem. We show that this guarantee is tight under the Unique Games Conjecture: no polynomial-time approximation with factor strictly smaller than $3/2$ exists under UGC. We then consider the exact-cardinality variant, which prescribes an even number \(k\) of terminals. Writing \(p:=k/n\), we give a deterministic polynomial-time \(\rho(p)\)-approximation for every feasible cardinality, where \[ \rho(p)= \begin{cases} 7/2, & \makebox[1.5em][r]{$0$}<p\le2/7,\\ 1/p, & 2/7\le p\le2/3,\\ 1/[2(1-p)], & 2/3\le p\le7/8,\\ 4, & 7/8\le p<1. \end{cases} \] In particular, a factor-\(4\) approximation holds throughout the entire feasible cardinality range, the factor is at most \(7/2\) whenever \(0<k\le 6n/7\), and equals \(3/2\) at \(k=2n/3\). The algorithmic framework is based on optimal laminar cut packings, their weighted tree representations, exact-cardinality rounding, and tree dynamic programming.

Increasingly, resource allocation games are being proposed to model team coordination in denied communication environments. Of particular interest is understanding the impact of communication denial on the quality of emergent team coordination. In this work, we consider the situation with an arbitrary communication network and use the Price of Anarchy to quantify the quality of emergent behavior. Our main result is a computationally efficient algorithm that calculates a minimal communication network that has the same performance guarantee as the full information case. Additionally, we provide efficient algorithms that compute a Nash and a strict Nash equilibrium in the full information setting. Finally to support these algorithms, we provide sufficient conditions for the existence of a strict Nash equilibrium, characterize strict Nash equilibria across all communication networks, and show that each strict Nash equilibrium in the full information case has a necessary and sufficient set of communication links that induce it. We conclude by giving an execution time experiment of the proposed algorithm and examine several example games.

We study the dispersionless limit of the Manakov system, the integrable two-component generalization of the nonlinear Schrödinger equation. We derive the resulting four-component genus-zero Manakov-Whitham system, characterize its hydrodynamic structure, and show that it passes the Haantjes tensor test for integrability. We show that the branch points of the spectral curve associated with plane wave solutions of the Manakov system are the local Riemann invariants of the dispersionless system. We also use the characteristic speeds to classify the baseband modulational stability/instability of the plane waves, and we study a direct linearization of the Manakov system to characterize their finite-wavenumber stability and verify agreement with the Whitham prediction in the long-wave limit. Finally, we validate the predictions by comparing them with the results of direct numerical simulations.

For every positive sequence that tends to zero faster than every fixed exponential, we construct a Hausdorff topological Vector Group topology on the additive group of real numbers. It lies strictly between the minimal Hausdorff topological Vector Group topology and the usual topology. The construction is illustrated by factorial powers, quadratic exponential decay, and prime radicals divided by a quadratic exponential. We also record a finite scalar covering criterion for comparing two such topologies.

Collaboration topology shapes both the performance and execution cost of LLM-based multi-agent systems. Because tasks differ in complexity and required capabilities, recent approaches generate task-specific collaboration graphs that specify agent participation and information flow. However, representative topology generators use either individual agents or predefined groups throughout an organization, overlooking differing collaboration needs across subtasks. Our key insight is to select granularity locally for each functional role, combining fine-grained control with reusable collaboration patterns within one organization. Learning such organizations requires exploring a combinatorial construction space with limited intermediate feedback from final-answer rewards. Therefore, we propose MAGIC, a dense-reward reinforcement learning framework for mixed-granularity graph generation. Specifically, MAGIC constructs a mixed-granularity agent graph by sequentially selecting a functional role, instantiating it as a single agent or reusable group, and connecting it to existing units. We directly optimize the construction policy using returns from trajectories sampled under the current policy and use potential-based reward shaping to provide intermediate feedback from probe-based utility and structural signals while preserving the cumulative task reward. MAGIC outperforms state-of-the-art baselines across eight benchmarks and demonstrates strong inference efficiency in our efficiency study.

We provide a purely geometric necessary and sufficient condition, in terms of a certain Cesàro mean of the volume function, for the existence of the Maz'ya-Shaposhnikova functional limit with respect to Gagliardo seminorms on metric measure spaces (under a mild measure condition). As an application, we establish the Maz'ya-Shaposhnikova convergence on the unbounded Sierpiński gasket. We also show that Ahlfors regularity does not imply the existence of this functional limit by constructing a concrete example.

We prove that every closed cooriented hypersurface immersion in $\R^{n+1}$, $n\ge 2$, with positive definite first Newton transformation bounds a compact immersed manifold with the prescribed boundary map and outward coorientation. Combined with the rigidity results of Ros and Pinkall, this filling theorem implies that every closed connected hypersurface immersed in $\R^{n+1}$ with constant scalar curvature is a round sphere.

Astrometry is the oldest method used to search for extrasolar planets. This technique provides key information about a planetary system, like the true mass of planets and its three-dimensional orbital architecture. Nowadays, the space-based mission Gaia, on one hand, and ground-based interferometry at infrared and radio wavelengths, on the other hand, can achieve astrometric accuracies of tens of micro-arseconds. Thanks to this unprecedented level of accuracy, the number of astrometrically discovered exoplanets has started to grow. In this chapter, I review the basic principles for orbital characterization of unseen planetary companions using astrometric data. I also review the properties of the exoplanets discovered so far with astrometric methods and comment on the contributions that this technique can make to the exoplanet field.

We present a new algorithm to compute a stream for the length spectrum of an oriented, finite-volume hyperbolic 3-manifold $M$. The advantage over the existing algorithm by Hodgson-Weeks is that our algorithm does not require finding a Dirichlet domain and thus can use interval arithmetic to verify the result. Our algorithm is also significantly faster in some cases. We also present a new algorithm to compute the optimal Margulis number of $M$. The authors have made these algorithms available in SnapPy.

Purposes: To characterize longitudinal retinal vascular changes in myopic children treated with orthokeratology (OK) or multifocal defocus lenses (Defocus) and to examine their association with axial elongation. Methods: In this retrospective cohort study, 43 myopic children underwent comprehensive clinical examination and fundus photography at baseline, 12 months, and 24 months. Axial length (AL) and spherical equivalent refraction (SER) were recorded at baseline, 6, 12, and 24 months. An automated segmentation model extracted vascular parameters, main vessel angle (MA), branching angle (BA), bifurcation edge angle (BEA), crossover point (COP), and terminal vessel count (TVC). Repeated-measures ANOVA assessed temporal changes. Pearson or Spearman correlations evaluated associations between AL and vascular metrics. Results: Over 24 months, the OK group exhibited significantly slower axial elongation than the Defocus group (0.214 mm and 0.522 mm, p < 0.01). In the OK group, MA and BA decreased modestly, BEA in arteries declined gradually, but COP and TVC remained relatively stable. The Defocus group demonstrated more pronounced decreases in MA and BA, an increase in BEA, and significant reductions in COP and TVC (p < 0.05). Correlation analysis revealed stronger associations between AL and vascular parameters, especially COP and TVC, in the Defocus group at all time points, whereas only BA and BEA correlated with AL in the OK group. Conclusions: OK lenses mitigate axial elongation and induce milder retinal vascular remodeling compared to Defocus lenses. Distinct temporal patterns of vascular metrics changes were observed between the two interventions, and correlate differentially with axial growth.

Artificial-intelligence (AI) agents are beginning to enter experimental laboratories, automating experiments and accelerating scientific discovery. Herein, we introduce an AI-driven workflow in which an AI agent performs multi-step, multi-day quantum transport measurements end-to-end. Specifically, given brief instructions, the agent starts by planning the multi-step measurements, then safely operates the cryogenic instruments, analyzes the data, and concludes with a final report. We demonstrate this AI workflow on multiple monolayer and bilayer MoS2 devices. Through autonomous measurement campaigns lasting up to six days, the agent determined the conduction-band spin-orbit coupling energy in monolayer MoS2, and mapped a layer- and valley-resolved phase diagram in bilayer MoS2. This experimental workflow is implemented through the FermiLink agent harness, which emphasizes instrumental safety and the reliability of the measurement and analysis. The framework is general and can be readily adapted to other types of experiments, representing a step toward self-driving laboratories.

Bosonic codes offer a promising approach towards hardware-efficient fault tolerance, with many leading examples such as the cat-code and the GKP code organized by an underlying symmetry. We build on a representation-theoretic framework of quantum error correction to formalize the construction and analysis of multimode symmetric bosonic codes, focusing on finite groups. Here, a physical, logical representation and an initial seed state together define the codewords via a covariant encoding. A central observation is that QEC matrices can be viewed as morphisms of group representations, so that Schur's lemma forces entire irreducible representations blocks to vanish. We recover several known single- and two-mode bosonic codes and build and analyze the error protection capabilities of three codes based on finite subgroups of SU(2). We analyze the impact of reducibility of the logical representation and optimize the seed state using the near-optimal fidelity.

The Milky Way has about 220 cataloged globular clusters. This number is far smaller than what is found in a similar galaxy such as Andromeda, which has about 600 globular clusters. Two possible reasons for this large difference might be observational bias and cluster dissolution. The infrared photometric survey VISTA Variables in the Via Lactea Extended has discovered many globular cluster candidates toward the Galactic bulge that need confirmation. We confirm the globular cluster nature of four candidates from the Galactic bulge based on radial velocities from MUSE data. Following our previous experience and method, we searched for a peak in the radial velocity distribution by deconvolving the radial velocity distribution into its bulge, disk, and potential cluster components. For Minni 23, we confirm the previously found parameters: this is an old and metal-rich bulge globular cluster. Additionally, we found a radial velocity peak associated with the candidate globular cluster Minni 07, with $\mu_{RV,cl}=80^{+26}_{-22}$ ${\rm km\ s}^{-1}$, $\sigma_{RV,cl}=48^{+15}_{-15}$ ${\rm km\ s}^{-1}$. We also derived $A_V=1.5$ and [Fe/H]$\approx-0.27$ for Minni 07. On the other hand, we were unable to reliably confirm the globular cluster nature for the candidates Minni 10 and Minni 19 with the currently available data. The devised strategy has proven to be efficient for the proposed goals, and it is worth repeating it for the larger sample of candidate globular clusters.

Integrating heterogeneous datasets within data lakes is a critical challenge, particularly for semantically related tables that lack the explicit attributes needed to be joined. We study Discovery-Driven Integration, where the relevant sources and their missing relational structure must be discovered before integration. In this setting, unstructured text provides the evidence that connects otherwise disjoint tables. The fundamental challenge is to discover the relationships at a fine-grained level that connect individual rows from different tables through specific sentences. We formalize this task as Text-Mediated Join Path Discovery and propose a horizontal bidirectional cross-attention architecture called LOKI Latent-space Optimization for Knowledge Integration) that learns contextualized representations of table rows and sentences. Through a global table-text contrastive objective, fine-grained row-sentence associations emerge without explicit local supervision. Existing multi-modal discovery methods largely retrieve coarse-grained column-text associations, whereas integration systems assume supplied row-text links, schemas, or queries. LOKI instead transforms these implicit associations into explicit, interpretable join paths, organizes them into relation-consistent groups, and materializes them as typed integrated tables with sentence-level provenance. Comprehensive evaluations on real-world benchmarks demonstrate that LOKI consistently outperforms state-of-the-art multi-modal data discovery approaches, and materializes typed integrated tables with 0.982 macro typed-pair precision while being up to 40 times cheaper in LLM API cost than direct prompting.

Interatomic potentials underpin MD and govern predictive atomistic-model fidelity for metals, semiconductors, oxides, liquids, and reactive systems. A potential has limited practical value until reliably implemented in production MD code. Slow, expertise-intensive implementation requires more than equation-to-C++ translation: it must select the neighbor-list architecture, evaluate and distribute many-body derivatives, manage interprocessor communication, and preserve host-code energy, force, and virial conventions. We introduce Agent-E2MD, a knowledge-guided agentic workflow that translates user-specified interatomic models into executable LAMMPS pair styles. It combines architectural classification, code generation, autonomous build-test-fix cycles, simulation execution, and hierarchical physical validation. We test Agent-E2MD on seven material-potential pairs: Lennard–Jones Ar, EAM/FS Ag, MEAM Bi, Tersoff Si, GAP Ni, ReaxFF C/H/N/O, and a recently developed Symbolic Regression EAM (Symb EAM) model for Al, currently unavailable in LAMMPS. Single-point results match reference energies and forces for all seven models. Five crystalline many-body benchmarks recover reference relaxed lattice properties, vacancy formation energies, and elastic constants. Ag, Bi, Si, and Ni are stable at finite temperature in nanosecond-scale simulations; ReaxFF extends validation to reactive dynamics with evolving bond order and charge equilibration. Results demonstrate that the software architecture for an interatomic potential can be inferred from its physical and mathematical structure. Agent-E2MD does not replace scientific judgment; it shifts users' effort from routine implementation to model definition, rigorous validation, and physical interpretation. The framework provides a practical, traceable bridge between emerging AI-driven potential discovery methods and production-scale atomistic simulations.

Cytoplasmic streaming is believed crucial to large developing cells, such as oocytes, where flow provides a much faster route to transport and mixing of cellular components than molecular diffusion. Molecular motors carrying cargoes on cytoskeletal elements are known to drive streaming in a variety of biological systems and, in Drosophila oocytes, cell-spanning vortical flows are tied to kinesin motors moving on dense beds of microtubules. Recent theories and simulations suggest such streaming self-organizes through interacting microtubules, motors, and flow. Whether these theoretically derived flows are adequate to the tasks of transport and mixing has been unclear. Here we report on new observations of coherent waves traveling persistently through microtubule beds during streaming, and investigate their impact on fluid transport and mixing. Leveraging recent advances in simulating the complex fluid-structure problems of cellular environments, we probe a biophysical model set in an oocytal geometry. Our simulations identify previously unknown waving states that show concordance with our experimental observation and the capacity for functional transport and mixing.

We prove that every spanning subgraph $H$ of an $n$-vertex $(p,\beta)$-bijumbled graph, satisfying $\delta(H)\geq(1/2+\varepsilon)pn$, where $\varepsilon > 0$ is arbitrarily small yet fixed, admits a rainbow Hamilton cycle under any globally $\mu pn$-bounded colouring, provided that $\beta\leq cpn$ and $pn\geq M$, where $\mu$, $c$, and $M$ are positive constants depending solely on $\varepsilon$; in particular, $pn$ may be taken to be a sufficiently large constant. This answers a question of Coulson, Keevash, Perarnau and Yepremyan for random graphs and extends it to deterministic pseudorandom hosts. In fact, we prove that $H$ admits at least $(apn)^n$ rainbow Hamilton cycles, where $a > 0$ is a constant depending solely on $\varepsilon$. If $pn\geq D\log n$, then, upon fixing a coloured $H$, retaining each edge independently with probability $D\log n/(pn)$ preserves rainbow Hamiltonicity asymptotically almost surely. The logarithmic degree requirement is needed only for this percolation conclusion. All three conclusions also hold with rainbowness replaced by avoidance of prescribed pairs of edges, provided that each edge has at most $\mu pn$ conflicting partners. Our proofs use spread measures and the lopsided local lemma.