Papers

Nearest neighbor search algorithms are widely used and have a long history, but we find that key implementation details are seldom reviewed in articles about them. These details can materially impact performance, and thus change the conclusions one makes about a given algorithm's superiority. In this article, we highlight these impacts by reviewing the Cover Tree as an example, producing RustKNN, a unified Rust implementation of three construction variants of the Cover Tree with three query modes. Our analysis reveals: (1) the optimal query strategy depends on $k$ and on the dataset (single-tree search is fastest at $k{=}1$ on three of our four largest datasets, while dual-tree search is fastest at $k{\ge}5$ on the three largest), and choosing the wrong query mode can cost up to a $7.5\times$ factor in runtime; (2) the cover tree base parameter, set to 2 in theory and 1.3 in practice, is not a safe default for dual-tree search: 1.3 is optimal on only one of seven datasets, and on covtype it is $1.6\times$ slower than the optimum; (3) among five micro-optimizations, only early-exit distance computation has a consistent effect, and that effect grows with dimension (none at $d{=}32$, $1.31\times$ at $d{=}54$, and $1.49\times$ at $d{=}784$); and (4) all-nearest-neighbor and held-out benchmarks yield different implementation rankings. All main timing tables report medians over 20 independent allocations with bootstrap 95% confidence intervals. RustKNN is open source at https://github.com/CrowdStrike/RustKNN.

The second quantum revolution is a revolution of information. Advances in quantum computation, communication, and sensing offer new capabilities while raising questions about how quantum infrastructures will be organised, accessed, and governed. We argue that their significance for governance lies not in transforming political principles, but in how their technical and infrastructural requirements may affect existing relationships of authority, responsibility, legitimacy, and power. This paper develops a quantum governance lens that connects governance scholarship with quantum information science, examining interactions between technical design, institutional arrangements, and infrastructural dependencies. We apply this lens to five areas: quantum computation, quantum key distribution, Quantum Byzantine Agreement, blind quantum computation, and dual-use quantum sensing. These applications illustrate how technical capabilities may influence access, trust, privacy, oversight, and accountability, while demonstrating that technical guarantees cannot resolve institutional questions independently. We conclude that quantum technologies do not necessarily introduce unique governance challenges or require entirely new governance frameworks. Rather, they provide a context in which established questions of legitimacy, accountability, and equity must be reconsidered in relation to emerging technological capabilities and institutional choices.

We study the determinant line bundle for a family of elliptic operators on compact manifolds with boundary with the associated Quillen metric and Bismut-Freed connection, and we prove the global anomaly formula in this context. This extends Witten's holonomy theorem to manifolds with boundary. Witten studied the limiting behavior of the eta invariant of a Dirac operator on the total space of a fibration over $\mathbb{S}^1$ when the metric in the base $\mathbb{S}^1$ is blown up in a certain manner, a process known as taking the adiabatic limit. In this paper, we construct the calculus of adiabatic $b$-pseudodifferential operators, which naturally synthesizes the $b$-calculus and the adiabatic calculus of pseudodifferential operators. Using this calculus, and assuming the fiber operators to be invertible, we compute the adiabatic limit of the natural eta invariant in this setting and relate it to the integral of the Bismut-Freed connection and new correction terms coming from the boundary of the fibers.

Tensor decoupling algorithms recover compact representations of multivariate functions by combining linear factor matrices with univariate internal nonlinearities. We identify two limitations of recent methods. First, their performance is not invariant to mismatched output or gradient magnitudes, and second, their spline internals require manual tuning of their degrees of freedom. We propose two lightweight fixes. The first is a preprocessing step that rescales the input Jacobian tensor, removing both the bias towards larger magnitude outputs and the ill-conditioning of certain factor updates caused by such a mismatch. The second replaces B-spline internals by penalized splines coupled with generalized cross-validation, making the method less dependent on the user selecting the right number of control points. Finally, we release an efficient open-source JAX implementation of our algorithm.

Diffuse X-ray emission in galaxies originates from stellar-feedback-heated gas and unresolved compact sources. We investigate its thermal component and the scaling of X-ray luminosity with star formation rate (SFR), including galaxies with very low SFRs. We analyzed eROSITA/SRG data from the four all-sky surveys (eRASS:4) for a blind, volume-limited sample of 140 galaxies within 25 Mpc from the Updated Nearby Galaxy Catalog (Karachentsev et al. 2013), cross-matched with HECATEv2 (Kyritsis et al. 2026b). Early-type galaxies were analyzed separately, while star-forming galaxies were divided into low-, medium-, and high-specific-SFR (sSFR) subsamples. We modeled the integrated X-ray spectra with thermal plasma and power-law components, stacked spectra for each subsample, and derived total and thermal X-ray luminosities. The stacked spectra show a stronger soft thermal component at high sSFR, whereas low-sSFR and early-type galaxies are increasingly dominated by the harder non-thermal continuum. For star-forming galaxies, the total 0.5-8 keV luminosity follows $\log L_X \sim 39.5 + 0.9\log\mathrm{SFR}$, with an intrinsic scatter of about 0.9 dex. The 0.5-2 keV thermal luminosity follows $\log L_X \sim 38.7 + 1.1\log\mathrm{SFR}$, with an intrinsic scatter of about 0.7 dex. The thermal luminosity remains well correlated with SFR down to $\sim 10^{-5}\,\mathrm{M}_\odot\,\mathrm{yr}^{-1}$ and is consistent with previous relations for star-forming galaxies. By contrast, the flatter and more scattered total X-ray luminosity-SFR relation suggests that unresolved X-ray binaries likely dominate at low SFR, while thermal X-ray emission remains a robust tracer of stellar feedback.

Dispersion requires a set of mobile agents to occupy distinct nodes of a graph such that each node contains at most one agent. We study deterministic dispersion of $k\le n$ agents on an $n$-node oriented square grid, where each node has globally consistent North, East, South, and West port labels, from arbitrary initial configurations. This includes both rooted configurations, where all agents are co-located initially, and general configurations, where agents are initially distributed arbitrarily across the nodes. On oriented square grids, Kshemkalyani, Molla, and Sharma~\cite{KMS20} gave an $O(\min(k,\Side))$-round algorithm in the local-communication model, where only agents on the same node can exchange information, and an $O(\sqrt{k})$-round algorithm in the global-communication model, where any two agents can communicate regardless of position, both using $O(\log k)$ bits per agent. The bound in the local communication model is optimal when $k=\Theta(n)$, but it remains open whether local communication alone can match the $\Omega(\sqrt{k})$ time lower bound when $k=o(n)$. We solve this by presenting Spread–Reverse–Collect (SRC), a deterministic algorithm that disperses any $k\le n$ agents in $O(\sqrt{k})$ synchronous rounds using $O(\log k)$ bits of persistent memory per agent, matching both time and memory lower bounds. SRC is based on a geometric primitive, a \sharpS-shaped parallel sweep, together with a simple priority rule. Unlike earlier grid algorithms that gather agents at the boundary and spread out from there, each SRC sweep starts from the agents' current position, and when it reaches the boundary the group simply reflects its sweep back inside and continues. SRC therefore needs no knowledge of the grid size and runs unchanged on an infinite oriented grid.

Online platforms often expose activity signals even when records of the underlying connections are incomplete or delayed. These activity responses may retain indirect evidence of connections that formed during the observation period but are absent from the recorded topology. Recovering such hidden structural changes can help keep network records aligned with evolving interactions and support downstream network analysis. However, the effects of a change propagate through the network and may overlap, making state changes difficult to associate with specific connections. We propose the Hierarchical Structural Context Ranker (HSCR), which combines visible network structure with node-state changes to infer connections that have formed but remain unrecorded. By jointly modeling the topological context of state responses and associations among potential connections, HSCR converts distributed activity changes into evidence for distinguishing potential connections without prespecified dynamical equations or parameters. Experiments on five temporal-network benchmarks and a real temporal Reddit network validate its effectiveness. Across observation spans and structural-record delays, true added connections achieve a 36%-50% reduction in mean true rank relative to the corresponding best baselines. This work provides a principled way to prioritize unrecorded additions for structural verification and record maintenance in online communities, information networks, and other networked systems.

Recent work has investigated Omni-modal Large Language Models (OLLMs), models which can take multiple modalities and their combinations as input, as a way forward to have systems really capable of interacting with their environment. Uncertainty quantification (UQ) for OLLMs, however, remains an open problem: existing methods largely target at most two modalities at a time, require access to model internals, or re-invocation of the evaluated model. We propose a model-agnostic UQ framework that scores a Chain-of-Thought response entirely through external omni-modal embeddings, measuring the grounding of the reasoning in the multimodal input and its internal coherence. Our contribution is the family of signals and an empirical characterisation of when it is reliable, rather than any single estimator: we find the geometric scores to be largely redundant with one another (mean within-split rank correlation 0.91-0.94) but strongly complementary to answer-dispersion baselines, and their reliability to depend on the generator and the modality. The resulting confidence estimates require no access to logits, hidden states or gradients of the evaluated model and no additional inference from it; they do require segmenting the reasoning trace with an auxiliary model and, for the aggregated score, a labelled calibration set that we show can be as small as 25 examples (although we also show that such a set buys little over fixing one signal a priori). On UNO-Bench, with both a closed and an open model, our scores yield small gains over self-consistency (systematic with the closed generator, mixed with the open one) and are competitive with self-verbalisation and internal-state baselines, especially in open-ended, omni-modal questions where previous state-of-the-art baselines struggle.

Gromov hyperbolicity measures the geometric complexity of metric spaces and metric graphs through geodesic triangles and four-point conditions. While calculating the exact continuous hyperbolicity constant $\delta^*(G)$ of a graph $G$ typically requires evaluating quadruples of points over an infinite metric continuum, discretizing this domain is a fundamental challenge in metric graph theory. In this paper, we study the continuous Gromov hyperbolicity constant via the Gromov product. Our main result, the Quarter-Point Theorem, establishes that the search space for quadruples $(x,y,z,w)$ attaining the exact hyperbolicity constant $\delta^*(G)$ can be reduced from the entire metric graph to a finite or discrete subset $J'(G)$, comprising solely the vertices, edge midpoints, and quarter-points of $G$. This result holds for every graph, finite or infinite. This theoretical result provides a considerably simplified combinatorial framework for calculating hyperbolicity in complex networks and metric graphs. Furthermore, we exploit this discretization to significantly improve classical results by establishing and structural bounds relating the global hyperbolicity constant $\delta^*(G)$ with its restrictions to vertices ($\delta_V^*(G)$) and midpoints ($\delta_J^*(G)$).

We show that microlocal Arthur packets can be reconstructed from an otherwise underdetermined system of linear equations arising from Kashiwara's local index theorem. The key is a geometric rigidity property of Arthur orbits which, together with Fourier symmetry, uniquely determines the microlocal multiplicities defining these packets. This realizes the associated Arthur distribution as the unique normalized element in the intersection of two filtered spaces of standard stable distributions related by Fourier transform. Under standard enhanced local Langlands hypotheses and Aubert compatibility, this gives an alternative representation-theoretic definition of microlocal Arthur packets for general connected reductive $p$-adic groups that does not use twisted endoscopy and ensures stability through the stability of tempered packet distributions. In the unipotent setting, we use this characterization to prove agreement between endoscopic and microlocal Arthur packets for split $\mathrm{SO}_{2n+1}$ when the residue characteristic is at least $6n+4$. We further use this characterization to compute all unipotent Arthur packets with unramified real infinitesimal character for inner-to-split adjoint exceptional $p$-adic groups. In this exceptional setting, we prove the microlocal weak Arthur packet conjecture and give counterexamples to the microlocal analogues of the least- and greatest-parameter conjectures.

The field of twistronics, recently extended to twisted bilayer cuprate systems, has generated considerable interest due to the prediction of $d+id'$ states close to a $45^\circ$ twist, as suggested by multiple experimental probes. Theoretical studies of these systems using a variety of models and many-body theoretical techniques have revealed multiple competing order parameters. The large variability in experimental results and theoretical predictions demands an accurate microscopic model for these systems, in particular a more realistic description of the interlayer tunneling. In this study, we fit the in-plane hopping and compute the interlayer tunneling amplitudes by calculating the orbital overlap between $d_{x^2-y^2}$ wave functions at each site of the twisted square-lattice model. We observe sign-changing tunneling amplitudes, a strong twist-angle dependence of the direct tunneling term, and long-range tunneling amplitudes that often dominate over direct tunneling. We investigate the band structure, Fermi surfaces, and spectral functions in comparison with those obtained from the phenomenological model and find a substantial redistribution of spectral weight that modifies the competition between different superconducting ground states. We determine the phase diagram as a function of twist angle, filling, and direct tunneling strength, which is controlled by the $c$-axis distance between the monolayers, and observe a reduction in the region of time-reversal-symmetry-breaking (TRSB) $d+id'$ states compared with the phenomenological model. Finally, we investigate the Josephson critical current across the phase diagram and find strongly suppressed critical currents close to a $45^\circ$ twist, consistent with experimental observations.

A digital twin is a virtual representation of a physical system, continuously updated with data from the physical system, enabling dynamic information exchange and decision-making. This bidirectional interaction, which distinguishes digital twins from conventional simulation models, introduces new challenges to simulation-based optimization, control, and learning. This paper reviews recent developments in decision-making methodologies motivated by digital twins. We focus on three interconnected areas: simulation optimization, sequential decision making, and risk-aware decision making. For simulation optimization, we discuss data-driven simulation optimization under input uncertainty, streaming input data, decision-dependent observations, and limited computational and data-collection resources. For sequential decision making, we review the connections among digital twins, stochastic optimal control, and reinforcement learning, with emphasis on Bayesian approaches that update models and policies as new information becomes available. For risk-aware decision making, we discuss distributionally robust and Bayesian risk formulations as alternative approaches for addressing model uncertainty. Throughout the paper, we emphasize the common problem of making decisions while the underlying model is being updated. We conclude by identifying research challenges and opportunities.

The expansion of the Internet of Things (IoT) in residential and local automation environments has highlighted the limitations of considering the internal network as an inherently trusted domain. Man-in-the-middle (MitM) attacks, such as ARP spoofing, can allow traffic interception or manipulation when communications lack appropriate confidentiality, integrity, and authentication mechanisms. This paper presents a systematized review of the security mechanisms used by two communication alternatives between ESP-family microcontrollers and the Home Assistant platform: MQTT protected through TLS 1.3 and the ESPHome Native API, whose encryption is based on the Noise Protocol Framework using the Noise_NNpsk0_25519_ChaChaPoly_SHA256 pattern. The analysis considers four dimensions: cryptographic robustness, attack surface, implementation complexity, and resource consumption. The review identifies significant differences resulting from the architecture and cryptographic model of each alternative. TLS 1.3 provides a standardized framework compatible with public-key infrastructure and formal identity management, though it introduces greater configuration complexity and computational overhead during session establishment. The ESPHome Native API employs a more specialized scheme with lower operational complexity, eliminates dynamic algorithm negotiation, and uses ChaCha20-Poly1305. The resource-consumption analysis relies on measurements published by the projects and manufacturers themselves, not on an experimental test bench, and this limitation is explicitly acknowledged. The results identify the conditions under which each mechanism is appropriate for local home-automation architectures and provide a basis for designing IoT systems that balance security, interoperability, and resource constraints.

Short-video search requires compact query rewriters that infer personalized intent from brief, ambiguous queries under strict latency constraints. The challenge is to decide when personalization is warranted and generate a reformulation that preserves the user's immediate information need. A rewriter optimized for fluency or engagement may still introduce unsupported details and redirect the search toward a different intent. Existing methods often underutilize users' actual reformulations and behavioral traces, relying instead on synthetic reasoning and indirect behavioral rewards that may produce more engaging candidates but cause intent drift. To build an effective rewriter that remains faithful to user intent, we propose WeFair, Fidelity-Aware Alignment from Human Feedback for Personalized Query Rewriting in WeChat short-video search. WeFair assigns real user behavioral signals to a progression from demonstration to preference to verification. We first mine actual human reformulations from search sessions, then apply multidimensional LLM screening and contextual verification to filter unsupported transitions without extensive manual annotation. During training, we begin with a supervised curriculum that progressively builds rewriting capabilities from large-scale human personalized query demonstrations, and then use direct preference optimization to align with users' subsequent consumption. In the final on-policy optimization stage, we construct a strict verification reward based on actual human reformulations to further boost performance with group relative policy optimization. Further analysis shows that auxiliary rewards can activate more rollout groups in GRPO but reduce intent fidelity. Online A/B testing in WeChat short-video search shows a 1.576% relative increase in effective clicked-query rate (VV>10s) and a 1.731% relative reduction in query reformulation rate.

We study the computational complexity of graph distortion distances, a family of graph metrics measuring how vertex distances differ between two graphs. Formally, these distances are defined in terms of standard matrix norms on the difference of distance matrices under an optimal vertex alignment. The resulting metrics have natural interpretations, corresponding to three ways of measuring the distortion of shortest-path distances: the maximum distortion among all vertex pairs (entrywise maximum norm), global aggregation (entrywise $p$-norms), and local aggregation (operator $p$-norms) of distortions. For maximum distortion, we show that approximation below a factor of two is NP-hard even for highly restricted trees. Due to the close connection to the Gromov-Hausdorff distance, we obtain a similar hardness result for the latter. In both cases, we show essentially optimal additive inapproximability. On the algorithmic side, we give a subcubic-time algorithm for optimal embeddings of connected graphs into paths, based on a structural decomposition along a diametral path. Additionally, we give a simple approximation algorithm when one input graph has a "relatively path-like" metric structure, i.e. has bounded pathlength. For local and global distortion, we derive various hardness results even for restricted inputs. Making use of a close connection between the global distortion distances and Gromov-Wasserstein distances, we give the first formal proof of NP-hardness of the latter, which has been claimed in the literature many times but has, to the best of our knowledge, never been correctly proven.

Keeling et al. [Keeling2026Generative] report on a case study recently conducted by Redgrave LLP in which they assert that Relativity's Generative AI Review tool (aiR) achieved 88% recall while Relativity Assisted Learning (RAL), its machine-learning tool, achieved 64% recall. These results are not comparable because the methods employed have different objectives, because of inter-assessor disagreement, and because they represent different recall-precision and cost-benefit trade-offs. Our analysis of the Redgrave data indicates that, when these differences are taken into account, aiR and manual review are comparable. Furthermore, established machine-learning models employing Continuous Active Learning (CAL) show state-of-the-art effectiveness, and superior efficiency, when trained only on a sample of 2,000 first-pass-reviewer responsiveness determinations.

Although spiking neural networks (SNNs) show promise in energy-efficient computing through event-driven computation and stateful temporal processing, their recurrent membrane dynamics render their training inherently sequential and inefficient for long sequences. Existing methods achieve full-sequence parallelism in SNNs through two main strategies: redesigning or approximating spiking dynamics to avoid reset-coupled temporal dependencies, or relying on iterative relaxed fixed-point solvers that suffer from excessive memory costs and iteration-dependent backward overhead. To address these limitations, we present FidLIF, a novel framework that reconciles the incremental update and hard-reset behavior of standard spiking LIF neurons with parallel forward propagation and BPTT-equivalent backward propagation. FidLIF iteratively recovers the full-sequence membrane-potential trajectory in parallel. By exploiting the lower bidiagonal structure induced by the local recurrence of LIF neurons, FidLIF formulates each forward trajectory correction and backward adjoint propagation as associative scans with an $O(\log T)$ temporal depth. This formulation also supports input-dependent neuronal parameters and allows the same neuron to perform full-sequence parallel training and incremental step-by-step inference at deployment. In our numerical convergence evaluation, FidLIF achieves a mean absolute error below $10^{-7}$ relative to the matched serial relaxed LIF dynamics, while yielding gradients numerically equivalent to exact BPTT. Our Triton implementation delivers favorable long-sequence latency and memory scaling, while achieving competitive performance on four sequential classification benchmarks. By reconciling parallel training with step-by-step execution, FidLIF enables high-fidelity spiking dynamics to benefit from parallel hardware without compromising incremental inference at deployment.

We develop a comprehensive theoretical analysis of Matrix Shampoo for tracking time-varying optima in nonstationary stochastic optimization. We derive finite-horizon high-probability bounds for average tracking error that disentangle initialization, optimizer drift, momentum-induced drift penalty, stochastic noise, and adaptive preconditioning, with explicit dependence on momentum parameter \(\beta_1\) and stabilization parameter \(\varepsilon\). These bounds reveal an explicit drift–noise and stability–geometry tradeoffs: noise-dominated regimes favor larger $\beta_1$, which provides stronger first-moment averaging and greater suppression of gradient noise, whereas drift-dominated regimes favor smaller $\beta_1$, allowing faster adaptation to moving optimizer. Larger $\varepsilon$ reduces the preconditioner-perturbation term while weakening Shampoo's ability to exploit matrix geometry, thereby reducing adaptivity. We establish a matching minimax lower bound under squared path-variation constraint, proving the information-theoretic optimality of Shampoo over the class of causal optimization procedures. Under a constant stepsize, we establish high-probability bounds for the average projected stationarity gap along general nonstationary nonconvex objectives. We validate our theoretical findings on both synthetic and multiple real-world problems.

For $H^1(\mathbb{R}^2)$-orthonormal families $\{u_n\}_{n=1}^N$ with one-body density $\rho=\sum_{n=1}^N |u_n|^2$, we prove the whole-space endpoint Moser–Trudinger inequality $$ \int_{\mathbb{R}^2}\frac{e^{4\pi\rho(x)}-1-4\pi\rho(x)}{\rho(x)}\,dx \le C\left(N-1+\int_{\mathbb{R}^2}\rho(x)\,dx\right), $$ where the integrand on the left-hand side is defined to be zero on $\{x: \rho(x)=0\}$. We develop a heat-semigroup refinement of Rumin's density method to treat both the endpoint coefficient $4\pi$ and the whole-space setting. Our inequality is sharp in two respects: the optimality of the coefficient $4\pi$ and the linear growth in the rank $N$. Moreover, through a semiclassical analysis of the density generated by normalized Dirichlet eigenfunctions, we establish the collective asymptotic behaviors of the quantities appearing in the inequality in various regimes. These semiclassical behaviors show that the rank-dependent term $N-1$ on the right-hand side is indispensable.

Online motor imagery-based brain-computer interfaces (MI-BCIs) typically decode continuous EEG using fixed-length sliding windows that may be misaligned with neural events. Existing window optimization methods often evaluate windows independently, overlooking temporal dependencies and potentially producing fragmented or physiologically implausible selections. We propose Temporal Structure Embedded Reinforcement Learning (TSE-RL), a framework that incorporates prior knowledge of MI event structure into a constrained Markov decision process for adaptive window optimization. First, TSE-RL assigns each window an explicit semantic role through Discard, Onset, Sustain, or Offset actions, extending binary retain/discard decisions to event-level alignment. Second, a finite-state machine masks invalid actions to enforce the temporal order of MI phases and promote physiologically plausible window sequences. Third, a Transformer-based history encoder captures dependencies across windows, improving training stability and computational efficiency compared with recurrent architectures. TSE-RL is plug-and-play and can be integrated with diverse MI classifiers. Experiments on multiple benchmark datasets demonstrate consistent improvements in decoding performance in both cross-session and cross-subject settings. Visualization analyses further suggest that the learned window selection policy aligns with neurophysiological principles.

Antibody therapeutics have transformed treatment across diverse therapeutic areas and have become central to modern medicine. While recent machine learning approaches aim to accelerate antibody discovery through structure-based design and target-affinity optimization, successful candidates must also satisfy broad developability constraints, including structural compatibility, low immunogenicity, and favorable biophysical properties, while remaining sufficiently diverse to provide sufficient coverage of design space to mitigate later-stage development failures. We introduce a preference-conditioned multi-objective generative flow network (GFN) fine-tuning pipeline for fixed-framework CDRH3 loop redesign that fine-tunes a biological sequence model against many inexpensive proxies covering backbone compatibility, sequence likelihood, immunogenicity risk, novelty, and developability liabilities. It combines up to fourteen predictive rewards in a single policy trained to sample CDRH3 loops across 623 SAbDab antibody structures, leveraging a reward reduction strategy to preserve Pareto dominance under this learned map. We also introduce a novel autoregressive span-in-filling variant of AMPLIFY-350M that serves both as a scaffold-conditioned CDRH3 generation prior and as a direct conditional likelihood scorer. We evaluated reward scores, diversity, and design quality on loops sampled on 45 held-out antibody complexes to assess structural consistency, confidence, aggregation propensity, stability, and antigen binding. Compared with the inverse-folding methods ProteinMPNN and ESM-IF, our approach produces roughly 10x more distinct acceptable candidates per design at 50% sequence identity, while holding 10% of the 14-objective Pareto front pooled across methods, trading per-sample quality for greater exploration of novel possible structures.

Machine learning engineering (MLE) agents are emerging as a new paradigm for automating end-to-end ML pipeline development. Using large language models for code generation and predictive performance as a machine-gradable feedback signal, these agents iteratively synthesize, execute, and refine pipeline code. Yet current systems are largely evaluated on pre-built, single-table benchmarks that abstract away key data management challenges. This tutorial introduces the foundations of MLE agents and highlights research opportunities for the database community. We cover how agents combine program synthesis with iterative and evolutionary optimization, and discuss open challenges in efficient pipeline execution, data discovery and augmentation over heterogeneous sources, reliability and debugging, as well as fairness and compliance. We connect these challenges to existing data management techniques and conclude with a hands-on session using contemporary MLE agents.

The rapid expansion of artificial intelligence (AI) is driving substantial growth in data center electricity demand. Interval-based energy blocks in day-ahead markets do not explicitly retain predictable intra-interval demand evolution, potentially creating mismatches with ramp-feasible generation trajectories and affecting settlement. This paper proposes a power-trajectory framework in which data centers declare predictable aggregate demand evolution through continuous demand-side power trajectories before market clearing. The declared trajectories are treated as exogenous inputs for constructing generation trajectories and the corresponding price trajectory. For feasible market-clearing outcomes, physical temporal consistency is established through continuous-time power balance and satisfaction of the modeled generation operating constraints, while economic temporal consistency is established by preserving the dispatch-price correspondence in energy settlement on a common temporal basis. Under the adopted settlement definitions, a trajectory-based settlement analysis separately quantifies the monetary magnitude of representation-induced power imbalances and the supply-side compensation that may remain under temporally consistent clearing and settlement. An illustrative 5-bus case demonstrates the elimination of representation-induced power imbalance and identifies the timing and physical sources of supply-side compensation. A modified IEEE RTS-GMLC case further illustrates these compensation effects across multiple generating units under workload-driven data center demand variations.

We generalize the second-order fluid constitutive model to accommodate a range of possible frame indifferent time derivatives. Using the Gordon–Schowalter derivative, which contains the upper-convected, lower-convected, and corotational (Jaumann-Zaremba) derivatives as subsets, we show how the subjective choice of derivative may change model predictions and we identify features that remain universal independent of this choice. Writing these models in terms of generic coefficients is non-universal and may lead to misinterpretations of flow predictions. However, writing the models in terms of zero-shear material functions or terminal relaxation time reveals universal and robust representations.

The European Union's Artificial Intelligence Act introduces a structured framework for governing high-risk AI systems, emphasizing transparency, risk management, and role-specific accountability. However, current assessment practices often rely on monolithic system views or disconnected checklists, limiting their ability to capture the socio-technical complexity of real-world deployments. We explore the use of the Information Flow Methodology (IFM), a modeling-based approach to AI Act compliance assessment. IFM represents decision systems – whether algorithmic, human, or hybrid – as networks of information sites and transformation channels, enabling structured analysis of how information, decisions, and responsibilities flow across organizational and technical boundaries. We apply IFM in a real-world case involving a recruitment support tool used by a public-sector organization, evaluating both the Provider's system and the Deployer's recruitment process. Our results demonstrate that IFM can serve as a scaffold to bridge both component-based and holistic perspectives, and how technical systems are situated within socio-technical contexts. In doing so, IFM supports transparency, identifies risk pathways, and enables alignment analysis between intended and actual use. We argue that such modeling provides a foundational tool for effective, context-sensitive AI governance and accountability – offering capabilities beyond conventional checklist-based assessments.

What quantum mutual information adds to conventional correlation functions is often unclear. We study the spin-1/2 $J_1$-$J_2$ Heisenberg chain, using DMRG on infinite chains and periodic rings and an SU(2) decomposition of the mutual information into correlation channels. For singlet ground states the two-site mutual information is an exact function of the spin correlator, so any additional content must come from blocks. In the dimerized phase, blocks resolve bond-energy correlations in the SU(2)-scalar channel without an independent asymptotic length: singlet and triplet correlation lengths agree to about 1%. The scalar channel dominates block mutual information at large distances in the commensurate regime up to $J_2/J_1=0.40$, but falls to a few percent beyond the disorder point, which coincides numerically with the Majumdar-Ghosh point $J_2/J_1=1/2$; the structure-factor peak splits only at the Lifshitz point $J_2/J_1=0.520622(2)$. On the gapless side we compare block mutual information on rings extrapolated to infinite size with the two-interval prediction of SU(2)$_1$ conformal field theory across the Kosterlitz-Thouless point $J_2/J_1=0.241167$. There, for block lengths $l\le6$, the correction decays as $l^{-p}$ with $p=1.96$-$2.07$, and any logarithmic term is at least 60 times smaller than in the Heisenberg chain. Expanding in the marginal coupling (from level spectroscopy) the first-order coefficient is consistent with $l^{-2}$ scaling and the second-order coefficient is positive for $x\le1/4$, suggesting that the mutual information relative to the field-theory value becomes stationary at the KT point for large blocks. The scalar-channel share approaches 1/4 at small cross ratio $x$, as expected from SO(4) symmetry; under two stated assumptions its first-order response to the coupling is $(3/8)\ln x-5/8$ at small $x$, matched by the $l=4$ data within 1-3% at $x\le1/9$.

Intraoperative frozen-section diagnosis of central nervous system (CNS) lesions guides surgical decisions but is challenged by artefacts, diagnostic complexity and time constraints. Most pathology foundation models have limited exposure to CNS frozen tissue. Here we present FOCUS, a subspecialty foundation model pretrained on 27,930 frozen-sections enriched for CNS tissue. FOCUS led 11 internal diagnostic and 12 biomarker-prediction tasks, with mean AUCs of 0.969 and 0.877, respectively, retaining leading performance in temporal and external cohorts. To provide more comprehensive diagnostic information, we further organized ten diagnostic tasks into a WHO-aligned diagnostic hierarchy and separately evaluated FOCUS for lymphoma detection, a critical task for intraoperative surgical decision-making. In reader assessments by six neuropathologists, FOCUS assistance enabled junior readers to approach or exceed unassisted senior readers in hierarchical diagnosis and raised junior readers' lymphoma sensitivity from 81.6% to 94.7%. FOCUS could improve diagnostic accuracy and granularity, inform lymphoma-related resection decisions and provide provisional molecular information. Such capabilities highlight the potential of FOCUS to provide robust, clinically actionable support for intraoperative CNS pathology.

Many dense matrices in scientific computing have hierarchically low-rank off-diagonal structure but are accessible only through routines that apply the matrix and, in general, its transpose or adjoint to vectors, that is, through matrix–vector products (matvecs). We present a fully matrix-free algorithm that compresses such a matrix into Hierarchically Semi-Separable (HSS) form and factorizes it simultaneously with the off-diagonal ranks chosen adaptively from a prescribed tolerance. The method uses $\mathcal{O}(k)$ matvecs with each operator, where $k$ is the largest off-diagonal rank found. Building on fixed-rank block nullification, it samples the matrix in small random batches and enlarges each local basis until a randomized error estimate falls below the tolerance. Unitary nullspace updates give $\mathcal{O}(k^3)$ local dense work, the same asymptotic cost as when the ranks are known in advance. Because compression and elimination proceed together, no separate factorization step is required. Excluding the matvecs, the factorization uses $\mathcal{O}(N)$ arithmetic and storage when the off-diagonal ranks are bounded, and its inverse is applied in $\mathcal{O}(N)$ time. Experiments on Poisson and Helmholtz Schur complements, Matérn covariance matrices, and a complex Lippmann–Schwinger equation demonstrate the factorization as both a direct solver and a preconditioner on problems with up to millions of unknowns.

An unknown ground excitation is recovered from the measured response of a rigid body sliding in two dimensions on an inclined surface under Coulomb friction, a system with no classical solution, whose sampled trajectories come from a time stepper. The Moreau stepper is shown to admit an exact inverse, explicit, non-iterative and vectorizable, giving the ground acceleration over each step in closed form, without regularization or an assumed source model. The inverse evaluates the friction direction at the end of the step, not its beginning. Inverting the continuous equation instead is not a secondary discretization choice: the two inverses differ by an exact identity proportional to the rotation of the sliding direction within the step, bounded by twice the frictional deceleration, which is of order one g for typical interfaces. The identity is inactive in one dimension, which explains why the sliding block literature has not confronted it. Verification against a manufactured reference solution recovers it to machine precision. On the field record, the discrepancy reaches 0.10g in root mean square, which exceeds the whole propagated uncertainty of the reported peak, and it suppresses 17% of the recovered travel, behaving as a bias, not noise, so root-mean-square agreement in acceleration understates it. The method is applied to surveillance video of a delineator post that slid in the 24 June 2026 La Guaira earthquake, yielding a peak ground acceleration of 0.912 +/- 0.047g, and a lower bound of 0.47g independent of the imagery. Displaced rigid bodies can therefore provide quantitative ground-motion information where instruments are absent.

Does providing additional context to automated AI auditors improve their effectiveness? Using the Petri tool to audit LLM coding agents, we test the impact of providing two types of resources (an external codebase and benchmark transcripts) to LLM auditors, across four auditor-target LLM pairs and three behaviours (harmful compliance, reward hacking, sycophancy). (1) External codebase: We provide the auditor LLM with a fixed, external open source codebase, which prior work finds improves the realism of synthetic audits. Providing this resource suppresses reward hacking in both auditor-target pairs whose baseline rate is above the floor (4.8 to 1.3 and 3.9 to 1.8 on Petri's default 1-10 scale); the remaining two pairs sit at the floor throughout. The suppression recurs in three of four pairs under a different scenario and resource bundle. (2) External benchmark transcripts: We provide the auditor with transcripts of the target's performance on benchmarks measuring similar behaviours, intended to inform the auditor about the target's behavioural patterns. Providing this resource raises reward hacking scores in all four pairs (from 1.7 to 6.1 in one case). However, subsequent experiments show that supplying only the related benchmark's abstract, without transcripts, also increases reward hacking, and the effect is absent under a different framing of the same behaviour. Overall, we find no consistent effect of either resource outside reward hacking, but we find substantial variability in judge-scored behaviour across conditions. Our results underscore the importance of careful piloting with tools such as Petri, as the measured rate of target behaviour is highly sensitive to configuration decisions. We hope our results inspire more research into the reliability and robustness of automated alignment auditing.