Papers

Business intelligence (BI) is a cornerstone of enterprise decision-making and is widely used by enterprise users in software such as Power BI and Tableau. In traditional BI workflows, users need to prepare data by (1) identifying relevant tables, (2) performing data transformations, and (3) building join relationships, before they can (4) answer their business questions. These steps can be complex and time-consuming, making BI challenging. Given the strong capabilities of large language models (LLMs) in working with data, we study their ability to answer BI questions end-to-end, without requiring users to manually perform the tedious preparation steps. To do this, we harvest a large collection of real-world BI projects from public sources, and manually extract pairs of (questions, ground-truth answers) from real user dashboards. The resulting benchmark, BI-Bench, is the first benchmark to systematically study LLMs' ability on end-to-end BI. We find that even frontier LLMs perform poorly on BI-Bench, with less than 50% accuracy. To address their limitations, we design a tool-augmented BI-Agent that decomposes BI workflows into subtasks on structured data, such as search, join, and transform, and orchestrates specialized data management methods across BI stages. Furthermore, we develop a post-training framework that synthesizes training trajectories from real BI projects, enabling BI-Agent to be further post-trained using both supervised fine-tuning (SFT) and reinforcement learning (RL). BI-Agent achieves substantial accuracy gains of up to 40 percentage points with vanilla LLMs, and post-trained BI-Agent yields gains of up to 30 points. Our results highlight the importance of combining tool-augmented reasoning with domain-specific post-training in complex BI workflows, and point to promising directions for future research.

We investigate the one-dimensional Coulomb problem on the positive half-line for a fourth-order Schrödinger equation generated by a commonly used realization of the Generalized Uncertainty Principle (GUP). The problem is treated directly in position space by a higher-order Bethe–Ansatz construction, with the wave function represented as a polynomial multiplied by an exponential factor. The resulting residue conditions yield an analytic quantization condition and explicit polynomial solutions for the first three bound states. We identify the branch that is continuously connected to the ordinary Coulomb problem and show that its energies, decay constants, polynomial factors, and Bethe–Ansatz roots recover the ordinary half-line Coulomb results in the vanishing-deformation limit. On this Coulomb-connected branch, the deformation produces a lower admissibility bound on the principal quantum number, while arbitrarily high quantum numbers remain admissible. We also discuss the physical interpretation of the deformation strength: for ordinary microscopic systems, the weak-GUP regime is the conservative expectation in Planck-scale motivated models, whereas intermediate and strong regimes are primarily theoretical regimes in the present analysis. Since the differential equation is truncated at first order in the GUP parameter, quantitative predictions outside the weak-deformation regime should be interpreted with care.

Generative Artificial Intelligence (GenAI) has rapidly evolved from an experimental technology into a foundational component of modern software systems. However, as its adoption grows, protecting sensitive personal data becomes increasingly challenging. Specifically, GenAI systems not only amplify traditional privacy threats but also introduce new inference-based risks, such as constructing detailed user profiles from seemingly harmless inputs. In response, privacy threat modeling frameworks are beginning to capture GenAI-specific privacy threats with finer granularity. At the same time, a growing number of mitigation techniques have been proposed to address these threats. However, although knowledge of both threats and mitigations continues to mature, the problem- and solution-space have developed largely independently. This position paper argues that the primary challenge in GenAI privacy engineering is not the lack of knowledge about privacy threats or mitigation techniques, but the missing bridge between them. We decompose this gap into three sub-problems: (i) lack of fine-grained threat-to-mitigation mapping for GenAI systems, (ii) inapplicable solution-space assumptions in the GenAI context, and (iii) prioritization difficulty under GenAI constraints. We derive four recommendations for future mitigation-selection approaches, and outline a suggested approach that extends established threat-to-mitigation mapping methods to GenAI-specific threat characteristics. We propose a research agenda toward more systematic privacy mitigation selection for GenAI-based systems.

Despite the widespread use and success of generative AI techniques today, theoretical guarantees on learning a distribution supported in $d$ dimensions from $n$ samples degrade as $O(n^{-1/\Theta(d)})$, though shown to be minimax optimal. We hypothesize that present bounds are too pessimistic because smoothness assumptions are not enough to capture the structure of distributions that often appear in real applications. Consequently, we introduce the class of sparse priors and define the "Sparse Dimension" as a measure of sparsity of a prior over the space of all distributions. We show that distribution learning under a $k$-sparse prior achieves a Bayesian risk lower bound of $\Omega(\sqrt{k/n})$ under common distance metrics, and show a matching (up to logarithmic terms asymptotically in $n,k$) upper bound for the TV distance under mild additional assumptions. We show the statistical equivalence of distribution learning and learning to sample in the Bayesian setting so that our results apply to learning to sample as well. While $k$ can still depend on the dimension $d$, or a notion of intrinsic dimension, our results show that learning under an appropriate prior overcomes the curse of dimensionality with respect to the dependence on $n$.

We distinguish two regimes in task-oriented quantization with a known deterministic oracle action. For an unconstrained interior oracle and a smooth strongly concave utility, quantizing the oracle action by vector Lloyd-Max minimizes a mean-squared-error surrogate and achieves a $\beta/\alpha$ approximation to the optimal $K$-level task quantizer. The reduction is exact for isotropic quadratic loss, and the corresponding task rate–distortion function is bracketed by two ordinary rate–distortion functions. Budget-constrained quadratic scheduling is different: the oracle satisfies a variational inequality, so quantizing water-filled actions is not generally optimal. We derive the exact Lloyd-type conditions for this case. The optimal action for a quantizer cell is water-filling evaluated at the cell's conditional-mean load, and the optimal encoder partitions load space into affine power-diagram cells. Thus the correct prescription is to quantize the load and water-fill its centroid. The distinction is material whenever a cell crosses water-filling active-set boundaries.

Word-representable graphs are a class of graphs that can be represented by words, where edges and non-edges are determined by the alternation of letters in those words. The tensor product $G \times H$ (also known as the direct product or Kronecker product) is one of the four standard graph products. Problem 7.2.5 in Kitaev and Lozin's book Words and Graphs (Springer, 2015) raised three open questions regarding the word-representability of tensor products. Despite extensive research on word-representable graphs, the word-representability of tensor products seems to have received no attention. This paper not only answers 2.5 of the questions posed by Kitaev and Lozin in Problem 7.2.5, but also initiates a systematic study, focusing on four fundamental families: wheel graphs $W_n$, complete graphs $K_n$, the Mycielskian of the cycle graph $\mu_n$, and the extended Mycielskian of the cycle graph $\mu'_n$. Among our main results, we prove that $W_{2n} \times G$, $\mu_{2n} \times G$, and $\mu'_{2n} \times G$ are always word-representable for any graph $G$; that $K_n \times K_m$ is word-representable if and only if $\min\{n,m\} \leq 3$; and that tensor products $G \times H$ containing $W_{2n+1} \times W_{2m+1}$ or $\mu_{2n+1} \times \mu_{2m+1}$ or $\mu'_{2n+1} \times \mu'_{2m+1}$ as induced subgraphs are non-word-representable. Our proofs exploit the hereditary nature of non-word-representability and the presence of non-comparability neighbourhoods.

Direct imaging of exoplanets is limited by the extreme contrast between the star and the planets, which is mitigated using a coronagraph. However, optical aberrations cause starlight leakage through the coronagraph, producing speckles that obscure the planetary signal. Achieving the required contrast levels demands wavefront control with subnanometric precision. Deep reinforcement learning offers a promising alternative to traditional focal-plane wavefront control techniques by enabling adaptive correction strategies learned directly from interaction with the system. In this work, we present a fully data-driven method for post-coronagraphic aberration correction in a simulated high-contrast imaging testbed. The agent controls a deformable mirror using observations consisting of focal-plane measurements (images) and physics-informed wavefront sensing information derived from these images. We evaluate different observation representations and control strategies, and the method is validated on simplified simulations of a high-contrast imaging testbed, where it successfully creates dark holes, i.e., regions of the focal plane in which residual starlight is strongly suppressed, while approaching the performance of conventional wavefront control methods.

We study the action of quantum channels on states on a von Neumann algebra $\mathcal{M}$ with conserved quantities encoded by a subalgebra $\mathcal{N}$. We define a phase as an equivalence class of normal states on $\mathcal{M}$ under the action of quantum channels preserving $\mathcal{N}$. First, we establish a relative quasi-entropic characterization of phase equivalence using the Petz recovery map. We further introduce the operator algebra (OA) symmetry of a state and define an equivalence relation between OA symmetries via bishifts of biprojections. When $\mathcal{N}\subseteq\mathcal{M}$ is an irreducible finite-index subfactor of type II$_1$, we prove that phase equivalence implies OA symmetry equivalence. Consequently, OA symmetry breaking provides a sufficient mechanism for detecting phase transitions. Furthermore, combining finite-index subfactor theory with quantum Fourier analysis, we prove that the cardinality of each phase is finite and obtain an explicit upper bound depending only on the Jones index.

Projects of orbital mirrors reflecting sunlight towards Earth raise reasonable concerns regarding photochemical and thermal retinal hazards and detrimental effects on visual performance (disability glare). This paper addresses these issues based on some current eye safety and glare standards. Telescopic observations of single mirrors appear to pose a significant risk of photochemical retinal hazard. The risk is higher for vulnerable populations. Unaided eye viewing of a mirror keeps the retinal risks low, both photochemical and thermal; however, disability glare may be unacceptably high, affecting awareness and response in critical visual operations. The simultaneous presence of several mirrors in the visual field of the observer, seen with the unaided eye or through optical instruments, will significantly increase all types of hazards. The kind and severity of their combined effects will depend on the angular distance between them. Additional information is needed to evaluate the effects of the transient flashes of light during mirror slewing operations.

We propose an information-theoretic authentication protocol based on a finite supply of long quadratic-stabilizer public-key states over an odd-prime field, where the effective key length after one signature exposure is the residual dimension $r=n-\ell$. A computationally unbounded adversary observes one valid classical signature and may jointly process $N$ public-key copies, while verification uses one additional independent copy. We show that, conditioned on the exposed signature, the security problem reduces to a partial-prediction game for a uniform stabilizer ensemble on these $r$ residual qudits, with a partial query along $d=\operatorname{rank}(Y-Y')$ directions, where $Y$ and $Y'$ denote the honestly signed and target-forged messages, respectively. Surprisingly, although the target requires only partial information, there is no first-order reduction in the required copy rate when $d/r\to\beta\in(0,1]$. The optimal average forgery probability for the specified target tends to zero for $N/r\to\alpha<1$ and to one for $\alpha>1$, revealing a sharp threshold at $\alpha=1$. Thus, long stabilizer public keys resist finite-copy forgery attacks under a single-signature-exposure model whenever the adversarial copy rate remains below one.

A 2021 proof of a special case of the Union-Closed Conjecture, by Aaronson, Ellis and Leader, has been formalised in the proof assistant Isabelle/HOL. Our discussion involves sketching their proof and displaying snippets from the Isabelle version of the proof, illustrating the extent to which mathematical reasoning can be rendered clearly in a formal language.

Parkinson's disease (PD) often manifests through speech impairments, facilitating accessible, non-invasive, and cost-effective severity assessment for early diagnosis and progression tracking. Despite advances in speech foundation models (SFMs), their cross-lingual generalization for PD severity multi-class classification remains underexplored due to limited labeled data, a lack of explainable methods and variability across languages and datasets. In this work, we evaluate pre-trained embeddings from four state-of-the-art open-source SFMs across three datasets in zero-shot and k-shot cross-lingual settings for multi-class PD severity assessment. Our results show that pre-trained speech embeddings enable meaningful cross-lingual transfer, although performance is sensitive to dataset properties, preprocessing, and adaptation strategy. Misclassifications under these conditions related to inter-speaker variability and atypical speech patterns highlight the need for more robust feature extraction and modeling for PD severity assessment while emphasizing the importance of explainability for reliable clinical insights.

Large language model (LLM) inference deployed on Kubernetes faces an autoscaling challenge that conventional web services do not: new serving replicas take two to ten minutes to start because multi-gigabyte model weights must be loaded, which makes purely reactive scaling structurally late. We ask a sharp question: among the components of a predictive autoscaler, which ones actually matter under such long actuation delays? We answer it by decomposing predictive autoscaling into four factors—token-aware demand tracking, startup-delay lookahead, a bounded uncertainty margin, and plant-state observation—and measuring each factor's contribution in isolation on production-derived heavy-tailed workloads generated by ServeGen. Our main finding is that a simple exponentially weighted moving average (EWMA) predictor with delay-aware lookahead and an upper confidence bound (UCB) margin captures most of the benefit, reducing time-to-first-token (TTFT) service-level-objective (SLO) violations from 53% (reactive, queries-per-second based) to 0.5% across five random seeds; lookahead alone is the single largest factor, a 14$\times$ reduction. Kalman filter variants do not consistently improve the cost–SLO tradeoff. Controlled experiments isolate the reason token granularity is necessary: context length, through key–value cache pressure, degrades TTFT far more than request rate at matched throughput. Finally, a validation on a real Kubernetes cluster (Qwen2.5-7B, A100, vLLM) confirms the central mechanism: a delay-aware lookahead controller cuts TTFT violations from 63.5% to 3.7% relative to reactive KEDA scaling. We distinguish throughout which findings are specific to Kubernetes actuation and which are general to LLM serving.

Synthesis pipelines increasingly claim not just that a program is correct, but that it is optimal. Such a claim has two halves with radically different verification stories. The upper bound, "a program of size m exists", is witnessed by an artifact that can be re-executed, proved equivalent to its specification, and shipped with a machine-checked certificate. The lower bound, "no program of size m-1 exists", has no witness and is discharged by running a solver until it reports UNSAT. Combinatorial optimization has known this asymmetry for decades and has largely addressed it: certifying algorithms make it explicit (McConnell et al., 2011), and pseudo-Boolean proof logging can certify optimality end to end with a formally verified checker (Bogaerts et al., 2023; Koops et al., 2025). That discipline has not reached circuit minimization. We call this the refutation gap: published gate counts for minimal XOR circuits provide no certificate for either half of the claim, and neither did 121 optimality results we ourselves produced. We close the gap with a pipeline that synthesizes minimal linear straight-line programs over GF(2), where every decisive UNSAT answer emits a DRAT proof checked by an independent third-party checker. We certify all 121 optimality results established by the project, across n = 6 to 9: 111 carry independently verified refutations, 10 are closed by a free counting bound, and none disagrees with the uncertified value. The median proof is 1.1 MB and checking costs 1.9x solving. We give five case studies where verification caught defects that code review did not, report two interface obstacles that push practitioners toward the uncertified path, and describe an adversarial audit that revealed a failure tail we were about to attribute to the problem was actually caused by our own budget.

Feature importance is central to interpretable machine learning, but the term "importance" encompasses several fundamentally different notions of relevance. We develop a unified perspective based on null importance: a population-level characterization of when a feature is irrelevant under a specified notion of relevance. We consider standard notions of null importance arising from marginal and conditional statistical relevance, predictive risk, functional invariance, and causal effects, and show how these notions answer different scientific questions. We illustrate the framework in two applications in which the distinction is particularly consequential: algorithmic fairness, where common fairness criteria correspond to different notions of null importance, and genomic perturbation modeling, where different notions of relevance lead to different conclusions about what a prediction model has learned. The framework connects three aspects of feature analysis: the scientific question defining relevance, the data and model assumptions that shape how different null notions relate, and the methods used to assess importance. We establish sufficient conditions under which null notions coincide and give counterexamples showing how they diverge when those conditions fail. We then characterize which nulls different method families target and when their zero-importance statistics identify those targets. Finally, simulations spanning feature dependence, redundancy, nonlinearity, hidden features and other standard phenomena, along with case studies on image and multiomics data, provide empirical evidence for these theoretical distinctions and their practical consequences. Taken together, these results provide a common statistical language for relating scientific questions, data-generating assumptions, and algorithms, and clarify the conclusions that feature-importance analyses can support.

A fundamental assumption in robotic perception is that the sensor's field of view (FoV) is fixed relative to the robot body. Motion-decoupled sensors, such as gimbal-mounted cameras and MEMS-based LiDARs, instead allow sensing direction to be controlled independently at runtime. This freedom creates a computational challenge: efficiently selecting useful viewing directions online in feature-dense environments. We propose PIVOT, a lightweight iterative method that optimizes sensor viewing direction along a fixed translation trajectory to maximize feature visibility. Under a conical FoV model, visibility depends only on the optical axis, yielding a two-degree-of-freedom optimization on the viewing sphere $S^2$. Coordinate-free $SO(3)$ exponential-map updates enable efficient continuous optimization without explicit angular parameterizations or exhaustive viewing-sphere search. Monte Carlo evaluations retain 98.1–99.6% of brute-force visibility with a 76–85x speedup. Photorealistic simulation and real-world experiments further demonstrate improved visual localization robustness and practical viewpoint control on a quadruped robot.

Addressing open questions such as the effect of galaxy cluster mergers on the evolution of galaxies and the self-interaction cross-section of dark matter requires the construction of a large, diverse sample of disturbed galaxy clusters. One contribution to such a sample is the extreme Disturbed Galaxy Cluster Sample (eDGeS), an ongoing spectroscopic study of massive disturbed and merging galaxy clusters selected from complementary surveys. Here, we present our first results from the eROSITA-selected subsample (eDGeS-eROSITA): a dynamical state analysis for the merging cluster candidate 1eRASS J025859.4-193727. We present the first spectroscopic redshift measurements for 76 galaxies in the direction of the cluster, confirming 51 as cluster members. The cluster displays a line-of-sight velocity dispersion of $\sigma_{\rm{cl}}=808^{+59}_{-66}~\rm{km~s^{-1}}$ and a dynamical mass of $M_{200}=4.47^{+0.94}_{-0.93} \times 10^{14}~M_{\rm{Sun}}$. While the cluster shows no evidence for substructure along the line of sight, the projected distribution of member galaxies reveals three subclusters, only one of which appears associated with the cluster's X-ray contours. Phase-space analysis reveals a large fraction of recently infallen member galaxies. Together, this evidence suggests a cluster merger along the plane of the sky. Assuming that the two most massive subclusters are on outgoing (incoming) trajectories after their first pericentric passage, a two-body Monte Carlo model predicts that the two subclusters collided $0.50^{+0.20}_{-0.22}~\rm{Gyr}$ ($1.24^{+0.96}_{-0.38}~\rm{Gyr}$) ago.

The controlled dynamical generation of radial dam break flows (DBFs) is demonstrated in two-dimensional droplet environments. These ultracold mixtures feature competing mean-field and quantum fluctuation effects and are initialized on a disk-shaped uniform density. Depending on the value of the latter, reflecting also the dominance of attractive or repulsive interactions, three dynamical response regimes are identified. At small densities a moving wavetrain of bright ring solitons is observed (dubbed ring DBF), at intermediate densities a ring kink-dispersive shock wave, while at large densities the flows encompass composite ring kink-rarefaction waves moving towards the center. The emergence of these patterns, whose formation would be prohibited in two-dimensional Kerr media due to wave-collapse, is rooted in the competition between attraction and repulsion inherent to droplet environments, modeled by the extended Gross-Pitaevskii equation. The characterization of the ensuing nonlinear waveforms is further corroborated by reduced models based on the cubic-quintic nonlinear Schrödinger equation. The different wave patterns emanating from dam break flows can be experimentally realized using current state-of-the-art ultracold atom experiments.

The most energetic coherent structure of a hovering full-scale quadcopter is associated with a self-organizing process in which the individual rotor vortices synchronize their frequencies while undergoing merging events, yielding a globally correlated structure. We identify and characterize this phenomenon by applying spectral modal and conditional analyses to assimilated three-dimensional velocity data acquired via Shake-The-Box Lagrangian particle tracking. The dataset captures a high-Re, turbulent flow further complicated by time-varying rotor speeds stemming from active flight control, low-frequency vehicle drift, finite spatio-temporal resolution, and measurement uncertainty. Most coherent structures recover established single-rotor features such as tip vortices and their subharmonic pairing. The globally synchronized vortex merging manifests as a spectral peak at an incommensurate frequency below the rotor band, which cannot be explained by single-rotor aerodynamics, subharmonic instabilities, or band-to-band triadic interactions. Instead, conditional averaging provides evidence of the aforementioned intermittent, distinctly non-subharmonic vortex-merging process involving all four rotor wakes. Establishing whether or not this phenomenon is observed across different flight conditions and configurations remains speculative; however, the consistent characterization of the globally synchronized vortex merging using complementary frequency- and time-domain analyses despite experimental complexities, in particular rotor speed variations, demonstrates its robustness.

For any $0\le\gamma<1/3$ we construct weak solutions $(v,B,p)$ of the ideal MHD equations with $v,B\in C^\gamma(\mathbb T^3\times\mathbb R)$, which conserve neither the total energy nor the cross-helicity and have nontrivial magnetic helicity. We also establish anisotropic Hölder bounds with distinct velocity and magnetic exponents and stronger regularity along every magnetic field line. The admissible exponents connect the Goldreich–Sridhar \cite{GoldreichSridhar1995} spatial and parallel pair $1/3, 1/2$ with the $1/4$ spatial scaling of the Iroshnikov–Kraichnan weak-turbulence picture \cite{Iroshnikov1963,Kraichnan1965}. In the spirit of Arnold's formulation of ideal hydrodynamics, a solution is regarded as a path of volume-preserving diffeomorphisms; the proof is then based on the interplay between classical convex integration techniques and geometric constructions at the level of the Lie algebra of this Lie group. Our work substantially extends the recent result of Enciso, Peñafiel-Tomás and Peralta-Salas \cite{EnPePe} and can be used to reprove \cite{GiRa} of Giri and Radu without a Newton iteration.

Recognizing technical errors in movement is a perceptual skill important to motor learning, but it is challenging for beginners in fast, complex sports like fencing to develop it. A coach's attention is scarce, live demonstrations vary from repetition to repetition, and video review is limited to whatever camera angle was used to record it. Coaches and advanced fencers reviewing a recording face a related problem. They can see an error, but have no way to anchor their feedback to the movement itself, and are left describing it in words the learner must map back onto their own body. We present FenceXR, an augmented reality system that reconstructs 3D movement replays from monocular smartphone video to address both problems. A Trainee module trains novices to detect common lunge errors while a Reviewer module lets coaches and advanced fencers attach text or voice annotations to a specific joint and moment in a replay, which can be shared asynchronously with a trainee. In a study with 18 novice fencers, unaided error-detection accuracy rose from near-chance (37.5%) before training to 64.1% after a single session, with interviews showing a shift from broad visual scanning toward targeted inspection of specific joints and their timing. In a video-based study with four fencing experts, all four viewed the Reviewer module as a valuable complement to their existing coaching tools, particularly for feedback that is difficult to convey through standard video. We end with a discussion of implications for designing AR systems that ground movement-based training and feedback in the movement itself.

As model-generated content is increasingly consumed by other model instances in automated workflows, a practically important question arises: can a model embed a signal in natural language that an independent instance of the same model can detect, relying only on shared pre-training and task instructions, without any shared memory or coordination-specific training? We introduce For Your Eyes Only, a cooperative signalling game designed to evaluate this directly. A Sender produces free-form descriptions for two words, one of which is a hidden target; an isolated Receiver must identify it. We evaluate seven contemporary models from four architectural families on 300 word pairs from established psycholinguistic corpora, using the Double-Pass Success Rate to control for output biases. We find that most models struggle to maintain coordination once they are required to avoid detectable signals, while one frontier model retains near-perfect performance even after such filtering. We further show that models can direct this capability toward deliberate misdirection, and that coordination is consistently weaker across architectures than within them.

The Total Coloring Conjecture (TCC) is a challenging unsolved problem posed by Behzad and Vizing independently, which states that every simple graph $G$ admits a ($\Delta(G)$ +2)-total-coloring, where $\Delta(G)$ denotes the maximum degree of $G$. This conjecture has been confirmed for graphs with $\Delta(G)\leq 5$. However, for planar graphs, the only open case is $\Delta(G)=6$. It was known that planar graphs with maximum degree 6 and without 4-cycles are 7-totally-colorable. In this paper, we improve this result by showing that any planar graph $G$ of maximum degree 6, which does not contain some special 4-cycles, is 7-totally-colorable.

Agents can now externalize experience into memory, consolidating historical traces into semantic knowledge and procedural shortcuts that persist between sessions. Such memory is typically private to a single agent. We argue that agentic memory benefits from being collective, because trustworthy knowledge of the shared environment—the data sources, services, and tools agents depend on—cannot be established by any single agent, only corroborated across many independent observers. We present Cairn, a community reputation platform that captures collective knowledge, allowing agents to query the community's opinion of a resource before use and to submit evidence-backed ratings afterward. Cairn aggregates observations via a time-decayed Beta model with confidence shrinkage and supports semantic discovery over reviewer rationales. We evaluate Cairn's reputation engine under adversarial simulation (e.g., lying, collusion, camouflage), benchmark its retrieval performance, and report a case study of rating heterogeneous agents in production.

We present a simple argument providing a very general Bombieri–Taylor-type result to compute Bragg peaks in diffraction theory as limits. At its abstract core the argument relies on considering the Eberlein convolution as an inner product. This inner product gives an abstract version of a Cauchy–Schwarz type inequality which implies the Bombieri–Taylor-type result as well as generalizations.

Ultra-light dark matter, composed of bosons behaving as classical waves, can resonantly excite stellar oscillations. In this work, we investigate this phenomenon in relativistic stars, showing that $\ell=0$ fluid modes can be excited. We derive a framework for calculating the mode amplitude and apply it to neutron stars to predict the associated surface temperature fluctuations; the resulting signal lies beyond current observational sensitivities. We discuss prospects for extending this approach to other compact objects.

Test-time scaling can improve large language model reasoning by generating and combining multiple candidate responses. In sampling-based methods, the inference budget is often described by the number of generated candidates, N. However, N tells us how many candidates are generated, not how they are executed. The same candidate budget can be produced in one batched generation call or split across several sequential calls with smaller batch sizes. We first study the effect of increasing N on reasoning accuracy using Phi-3-mini and Qwen2.5-1.5B on 500 GSM8K prompts. As expected, increasing N from 1 to 8 improves accuracy by 8.4 percentage points for Phi-3-mini and 18.4 points for Qwen2.5-1.5B. However, accuracy alone does not show the systems cost of using a larger candidate budget. We therefore fix N = 8 and compare four generation schedules: 1x8, 2x4, 4x2, and 8x1, where axb denotes a generation calls with b candidates per call. We measure latency, throughput, GPU-hours, and gross GPU-device energy while keeping the total candidate count fixed. On A100 GPUs, eight serial calls use 4.64-4.86x as much gross GPU-device energy and have 5.77-6.12x the P95 latency of one batched call with eight candidates. The same pattern appears across three independently scheduled A100 nodes per model and in short-output SciQ/V100 experiments. These results show that candidate count alone is not enough to describe the systems cost of multi-candidate test-time scaling. When candidates are independent and memory allows it, fewer generation calls with larger batch sizes are more efficient. Evaluations should therefore report not only candidate count and accuracy, but also generation schedule and GPU-level systems metrics.

We study a finite-domain event for the mirror model on the Manhattan lattice: every boundary-to-boundary trajectory crosses a marked connector an even number of times, while internal cycles are unrestricted. Our main theorem gives a finite-scale confinement criterion: if this event's probability reaches a universal threshold in one even two-square rectangle, then almost surely every trajectory in the plane is periodic. We construct an exactly normalized three-color tensor representation and prove deterministic bounds for approximate contractions using the signed partial-permutation structure of directed continuations. These tools turn numerical evaluations into rigorous finite-volume statements. At mirror density \(p=2/5\), we prove that the boundary-parity probability is nonmonotone in the rectangle width, with a decrease followed by a certified increase. These values remain below the sufficient confinement threshold and do not resolve planar localization at this density. Further experiments track how the measured finite-size minimum varies with density, compare matching-based and entrywise error bounds, and exhibit endpoint-sensitive and cooperative responses to local mirror changes.

This paper continues the study of the $K$-theory of monoid schemes, using it to give a useful definition of the higher $K$-theory of a matroid via its Bergman fan.

Dimensionality plays a central role in determining the collective behavior of interacting quantum systems. Engineering strongly interacting ensembles of solid-state spin defects in reduced dimensions remains a significant challenge at the interface between the applied and fundamental sciences. Here, we create and characterize a positionally disordered, quasi-one-dimensional spin chain in diamond, consisting of optically dark substitutional nitrogen defects (P1 centers) and optically addressable probe nitrogen-vacancy (NV) centers. Our approach exploits the preferential incorporation of nitrogen along step bunches formed during chemical vapor deposition to achieve both lateral and vertical confinement. Combining spatially resolved materials characterization with nanoscale quantum sensing, we establish the one-dimensional character of the optically dark, unpolarized P1 spin ensemble. We then use correlation spectroscopy to probe local spin autocorrelations and investigate infinite-temperature dipolar spin transport. Our results establish a materials-based route for engineering low-dimensional quantum spin systems.