Papers

In this paper we present synthetic Very Long Baseline Interferometry (VLBI) observations of M87 between a near-future configuration of the Event Horizon Telescope (EHT) and one or multiple 2.5 m-class balloon-borne VLBI stations on a northern transatlantic flight trajectory launching from Kiruna, Sweden. These balloon-borne VLBI stations have the advantage of operating above 99.5% of the atmosphere and their motion allows for efficient sampling of the uv-plane. Assuming frequency phase transfer between 230 and 86 GHz we run these simulations using a modified version of the ngehtsim software package. Our simulations demonstrate the ability of such a VLBI array to probe M87 at the jet base adding baselines down to 0.2 G$\lambda$ for a single balloon-VLBI station and 0.07 G$\lambda$ for three balloon VLBI stations. Using the Bayesian imaging software Comrade.jl, we demonstrate the recovery of jet structures up to 150 $\mu$as in size for a single balloon and up to 300 $\mu$as in size with three balloons. Finally, we test the improvement in jet image fidelity by computing the normalized cross-correlation (NXCOR) and normalized-root-mean-square error (NRMSE) between the image reconstruction and ground truth. We find a factor of 1.2 improvement in the jet NRMSE for a single balloon and a factor of 1.3 improvement for 3 balloons as compared to EHT-only simulations.

We compute the Euler characteristic of Bestvina-Brady kernels $\operatorname{BB}(\Gamma)$ for all Artin groups of spherical type. Our method involves discrete Morse theory to describe the cellular structure of a classifying space for the Bestvina–Brady kernel, through the action of $\operatorname{BB}(\Gamma)$ on non-integer level sets of the universal cover of the Salvetti complex. We extend the method of computation of $\chi(\operatorname{BB}(\Gamma))$ to Artin groups that satisfy the $K(\pi,1)$-conjecture and whose nerves are rationally acyclic, and we provide an example by realising the projective plane as the nerve of a Coxeter group.

Rare but severe failures of large language models can become practically significant at deployment scale. Estimating their probabilities with direct Monte Carlo sampling is highly inefficient, while proposal-based methods typically require auxiliary learning of an additional proposal distribution. We introduce Weighted Ensemble (WE), a training-free framework for rare-event estimation in language models. WE samples exclusively from the original language model and improves upon direct Monte Carlo by periodically reallocating the sampling budget toward prefixes that appear more likely to reach the target rare event. To guide this reallocation without learning a separate proposal distribution, we exploit internal LLM representations as prefix-level signals and empirically validate their effectiveness. We provide a theoretical analysis of the proposed algorithm. Experiments on safety-related tasks spanning both small-scale and modern large-scale LLMs demonstrate that WE improves the efficiency and reliability of rare-event probability estimation.

We present LidarVerse, a real-time unified LiDAR world model for sensor simulation across tasks and sensors. Existing LiDAR simulators largely follow one of two complementary paradigms: reconstruction-based methods preserve the geometry of a captured scene but require lengthy per-scene optimization, whereas generative methods amortize learning across data but lack the consistency needed for long-horizon rollouts. LidarVerse brings both paradigms into a single, unified conditional generative framework. A universal tokenizer maps LiDAR range sequences into a shared latent space, where a bidirectional teacher learns a common interface for conditioning on a LiDAR prefix, an HD-Map, a persistent spatial cache, and optionally, text. Varying the available scene evidence turns the same model into a generator of new worlds, a point-cloud forecaster, or a generalizable resimulator of observed scenes without per-scene optimization. We distill the teacher into a four-step autoregressive causal student and maintain both a rolling temporal K/V cache and a world-aligned spatial cache, enabling persistent long-horizon rollouts with real-time inference at 11 FPS on a single H100 GPU. LidarVerse achieves state-of-the-art performance on most reported metrics across all three evaluation protocols, while its tokenizer supports 32-, 64-, and 128-beam LiDAR and generalizes to an unseen scanning pattern. These results demonstrate that generative and reconstruction-grounded LiDAR simulation can be realized within one model, providing the core capabilities for future closed-loop sensor simulation.

We consider the problem of counting solutions to integer linear programming problems of the form $\{x \in \mathbb{Z}^n_{\geq 0} : Ax = b\}$ where $A \in \{-\Delta,\ldots,\Delta\}^{m \times n}$ and $b \in \mathbb{Z}^m$. We present an algorithm that counts solutions with $(n\Delta)^{m + o(1)}\! \cdot \log\lVert b\rVert$ arithmetic operations. This simplifies the algorithm of Gribanov and Malyshev, who considered the problem for the more general setting in which $A$ is $\Delta$-modular.

Much of what we know about human perception and cognition comes from austere experimental settings: static stimuli presented to sedentary observers on flat monitors, complex responses reduced to simple button presses, and brain activity recorded from immobilized heads using EEG or fMRI. These highly controlled paradigms have provided remarkable insights, but capture a small and often unusual slice of behavior, raising questions about how well the findings generalize to the real world. Extended reality (XR), spanning both immersive virtual reality (VR) and augmented reality (AR) that overlays digital content on the real world, offers a way beyond these constraints, supporting controlled, reproducible experiments in which participants actively engage with three-dimensional tasks. Drawing on a growing body of VR and AR studies of attention, memory, and language – our own and others', some involving EEG – we outline what XR makes newly possible for cognitive neuroscience and reflect on the practical and conceptual obstacles that remain. The opportunities are substantial, but realizing them requires solving practical problems of hardware, timing, and measurement, and being realistic about what a virtual or augmented world can and cannot stand in for.

With the growing number of LLMs available, selecting which one to use for a prompt has become a key question. A large part of the routing literature relies on semantically embedding prompts into a vector space and then applying a lightweight classifier to the embedded representations. These methods perform robustly in-distribution but they struggle to generalize to unseen tasks. By studying the geometry of semantic embeddings, we trace a clear failure mode: features that determine the neighbors of unseen prompts are an unreliable proxy for LLM selection. We therefore replace the semantic embedding with the following map: we run a partial forward pass of Qwen2.5-7B-Instruct on the prompt and use the hidden state of its last token at a deep layer as the representation. When applying kNN and other simple classifiers to this new representation, we obtain a clear result in generalization: on average across cost penalties, their performance improves. Moreover, kNN and another simple classifier that we propose outperform every evaluated semantic-embedding baseline. Our two simple methods also beat a recent SoTA hidden-states based router on RouterBench.

This note grew out of two questions arising in different settings. The first concerns recognizing holomorphic functions among continuous functions on an annulus. The second concerns what self-reproducing subsets can tell us about semigroups of functions arising in analysis. Our analytic starting point is a variation on the classical relation between holomorphy and invariance of contour integrals. It identifies the holomorphic functions as the largest class containing the constant function 1 for which a contour convolution is independent of the chosen curve for every pair of functions. On this class, convolution amounts to multiplying Laurent coefficients. We then study families $B$ satisfying $B\diamond B=B$. We show that expressing a function as a convolution product of $m$ holomorphic functions corresponds precisely to its extension to a wider annulus determined by $m$. This identifies the largest self-reproducing family as the functions extending holomorphically to the punctured plane. We also prove that uniform boundedness on a fixed subannulus surrounding the unit circle forces all members of such a family to have Laurent expansions supported on one common finite set. A general semigroup theorem describes the minimal self-reproducing families.

Planck-mean absorption coefficients of pure gases are calculated from line-by-line integrations of HITEMP and ExoMol spectra up to 5000 K for use in high-enthalpy radiative heat transfer simulations. The dataset extends beyond conventional combustion products, including high-temperature radicals, nitrogen-bearing species, soot precursors, metal oxides, metal hydrides, and halides: AlF, AlH, AlO, BH, C2, C2H2, CH, CH4, CN, CO, CO2, H2O, HBO, HCN, HF, MgH, MgO, N2O, NO, NO2, OH, SiO, TiH, TiO. New calculations are validated against historical correlations for overlapping species, demonstrating good agreement over their applicable temperature ranges. Strong visible opacities result in large Planck-mean absorption coefficients for many of the considered species, highlighting the need to account for their radiative contribution in extreme environments. A brute-force search over several candidate functional forms is performed to provide a common set of coefficients, establishing a standardized framework that can be easily integrated into production solvers and extended as additional high-temperature line lists become available.

For a Chern nontrivial Bloch bundle over the three torus, we construct an orthonormal Wannier basis with the optimal pointwise decay $\mathcal{O}(|x|^{-5/2})$. All but one of the generators decay exponentially. This resolves the question left open in arXiv:2505.01999.

Optimal Morse vector fields on closed surfaces, i.e.\ fields with the minimal possible number of critical points (a single source and a single sink), are classified up to topological trajectory equivalence by one-cycle signed chord diagrams in Kybalko, Prishlyak and Shchurko (2018). We recall this construction and the associated duality, which corresponds to reversing the direction of the flow, in a unified encoding in which both endpoints of a chord carry the same label, and we make it algorithmic. We give an explicit traversal procedure that detects one-cycle diagrams, a canonical form of an equivalence class under cyclic shifts, reversal and relabeling of chords, and a construction of the dual diagram. On this basis we describe an algorithm that enumerates all one-cycle signed chord diagrams with a given number of chords, both for orientable and for non-orientable surfaces, groups them into equivalence classes, pairs each class with its dual, and identifies the self-dual ones. The algorithm is implemented in Python and archived in Zenodo; its output is validated against the Harer–Zagier numbers in the orientable case and against orbit-size counts in both cases. We also note that, when a one-cycle diagram is read as a cellular embedding of a one-vertex graph, its dual diagram describes the embedding of the dual graph.

We construct an infinite family of solutions to the Mondrian art problem with absolute defect bounded above by $280$, of side lengths $n_0 = 315$, $n_1 = 106785$, and $n_{j+2} = 340n_{j+1} - n_j$, where $n_j$ is congruent to $315 \pmod{630}$. This absolute bound shows that the minimum defect does not necessarily increase with $n$, providing a counterexample to a conjecture which has been open since the problem's original proposal. Our design is derived from a well-known seven-rectangle dissection over the real quadratic field $\mathbb{Q}(\sqrt{19})$, with non-integer side lengths; we tailor the side lengths to be integers via an infinite Pell family. Using the same method, we devise a second family with defect $560$ that contains infinitely many side lengths which are divisible by any given positive integer, implying that for any $k$ there are infinitely many side lengths $n \equiv 0 \pmod{k}$ with defect bounded above by $560$. This constant bound offers a dramatic improvement on the previous quadratic bounds.

We analyze the KdV–ghost system arising from the BRST formulation of BF-type topological field theory, its symmetries, Lax pair, spectral problem, zero-curvature formulation and Darboux formalism. The system is invariant under shifts of the ghost field, whose generator does not commute with the BRST symmetry of the KdV–ghost system. Their generators allow the introduction of a systematic procedure for generating new solutions from a given one, and the corresponding expressions in the Grassmann algebra are obtained explicitly. We introduce a Grassmann-valued Lax pair and prove an isospectral theorem relating the spectral problem of the spatial Lax operator for the KdV equation to that of its KdV–ghost extension. We also construct a triangular zero-curvature representation and show that the Grassmann-valued spatial Lax operator is related to the KdV spatial Lax operator by a nilpotent conjugation. The natural variable for a local Darboux formulation is the differentiated ghost $v=C_x$, for which the ghost equation coincides with the Fréchet linearization of the KdV flow. We then construct a nilpotent lift of the scalar KdV Bäcklund–Darboux transformation. Using Riccati variables and off-shell factorization identities for the KdV residue and its Fréchet derivative, we prove that the transformation closes on the local KdV–ghost system. Successive Darboux transformations yield a recursive ghost extension of the bosonic Darboux chain, with a new odd homogeneous contribution introduced at each step. For the solitonic examples, the resulting local ghost fields are naturally identified with tangent directions associated with the soliton phase parameters. The construction provides a Darboux-theoretic interpretation of the ghost sector while remaining distinct from the standard supersymmetric KdV hierarchies.

Wildfire decisions are made in hours, yet most learned spread models predict daily on targets including burned area. We propose FireGraphNet which formulates 12-hour growth as node classification on directed H3 graphs, with candidates ahead of the front and wind alignment, terrain, fuel continuity and barriers on edges. On satellite perimeters it achieves average precision 1.7-1.9x the strongest distance baseline on test California fires and 1.62x out of state. We show this skill comes from message passing rather than cell features or the aggregator, is highest on young fires in state, is carried deep along the wind by its edges, and is hidden by pooling. A convolutional network matches this ranking once trained on new growth, at worse calibration, so candidate construction, target definition, and aggregation shape conclusions about model skill. Editing fuel and barrier attributes reduces predicted spread more under guided than random placement, extending FireGraphNet to operational intervention analysis.

Many sentiment datasets use one annotator for each item, so the test labels show the conventions of that person. We build a Nepali benchmark from two annotators who labelled the same sentences blind. They labelled 5,614 sentences from tweets of Nepali public figures on a five-point scale. We keep only the 3,189 sentences where both give the same polarity. On the three-class benchmark, NepBERTa with a fixed tokenizer gets a macro-F1 of 0.877 and IndicBERTv2 0.867. Three commercial large language models (LLMs) get 0.882 to 0.896 zero-shot, and these differences are not significant. On the five-point scale, 766 sentences have two adjacent labels, for example Pos and SPos. We accept both labels and train on both. On this task, Claude Opus 5.5 beats the best encoders by 0.10 to 0.12 macro-F1. A tokenizer audit adds a second result. The default tokenizers of three Nepali BERT models delete the non-spacing Devanagari vowel signs and the virama. When we restore the marks, macro-F1 increases by 0.084 for NepBERTa but decreases by 0.095 for a model pretrained on stripped text.

Scientific imaging data involving medical (e.g., 3D radiographic, microscopic images) and astronomical sensors pose different challenges from natural images. One key challenge is that these datasets are often orders of magnitude larger than natural images. Efficient training and inference on such data is challenging due to the increased hardware requirements, often needing bespoke solutions. Moreover, the relevant objects such as tumors and astronomical phenomena are sparsely distributed with respect to the background information. Standard efficiency techniques like quantization and pruning apply uniform scaling of all regions, potentially compromising the precision/fidelity of predictions. Thus, efficient methods that reduce computational requirements without losing resolution for relevant parts of the data and with uncertainty estimates on predictions are essential. We present Conformal Adaptation with risk guarantees for uncertainty-aware sparse computations. Our formalism is general, spanning dense pixel-level classification and regression tasks where hierarchical models predict at low resolution, certify the signal using conformal risk control, and refine the certified predictions. We benchmark our method on multiple tasks such as 3D medical image segmentation, 2D galaxy flux prediction, and 1D calcium spike rate prediction, achieving $2.5$–$72\times$ wall-clock speedup across the various tasks, including on commodity CPUs.

The behavior of AI systems increasingly depends on the extent to which agents cooperate or coordinate with one another, in ways that may be desirable or not depending on the situation. Conventional explanations for cooperative behavior distinguish between purely other-regarding preferences ("altruism") and instrumental reasons for self-interested agents to cooperate. The way that agents should enact these mechanisms for cooperation (or not) is complicated by the fact that there is not a clear or unambiguous locus of identity or selfhood for AI agents. For example, it is unclear whether agents involved in instances of misaligned collective behavior are motivated by goals at the level of the collective or by various forms of instrumental reasoning. We develop a framework for reverse-engineering why a given set of agents engage in a particular set of cooperation-related behaviors. We argue that many different mechanisms can often produce similar observed behaviors and introduce a set of experimental designs along with conditions under which they can successfully disentangle competing explanations for multiagent behavior. We apply this framework to interactions from a set of frontier models in a simulated environment and demonstrate that the behavior of different models arises from substantively different mechanisms.

Full waveform inversion (FWI) is a powerful tool for high-resolution subsurface model reconstruction, but it remains highly nonlinear and ill-posed, especially when the initial model is inaccurate or the acquired data are noisy and incomplete. Annealed Stein variational gradient descent (ASVGD) provides a particle-based Bayesian framework for FWI by approximating the posterior distribution with an ensemble of velocity models, thereby enabling uncertainty quantification beyond a single deterministic solution. However, conventional ASVGD-FWI commonly relies on simple handcrafted priors, such as Gaussian or smoothing assumptions, which are often insufficient to represent complex geological structures. To address this limitation, we introduce a learned diffusion model (DM) as an implicit regularization mechanism within the ASVGD-FWI framework. Instead of explicitly evaluating the diffusion prior density, the trained diffusion model acts as a learned geological projection operator that guides updated particles toward the distribution of plausible velocity models. In this way, the proposed method combines data consistency from FWI, posterior diversity from ASVGD, and structural realism from the diffusion prior. Numerical experiments demonstrate that the diffusion-regularized ASVGD-FWI produces more geologically consistent mean models, suppresses nonphysical artifacts, and yields uncertainty estimates that are more concentrated around structurally complex and poorly constrained regions. These results suggest that learned diffusion priors can effectively enhance Bayesian FWI by improving both inversion stability and the interpretability of posterior uncertainty.

Thermal constraints in heterogeneous multi-core systems can significantly degrade performance, as conventional techniques such as dynamic voltage and frequency scaling (DVFS) and task migration introduce overhead under high utilization. Approximate computing, particularly loop perforation, can mitigate this overhead by reducing computation at the cost of accuracy loss. However, existing approaches typically apply a uniform perforation rate across all loops, ignoring loop-specific sensitivity. We propose AMAX, an accuracy-aware multi-loop asymmetric perforation framework that reduces the combinational design space through loop-wise profiling and multi-objective configuration selection, and dynamically adapts the resulting configurations at runtime according to performance requirements. Experiments on PARSEC benchmarks show that AMAX achieves up to 0.85 improvement in normalized accuracy over symmetric perforation for the same performance targets.

Evaluation of large language models (LLMs) remains largely pre-scientific: it involves many design decisions, with little guidance on how to make them. These choices can substantially affect measured performance and, consequently, decisions about subsequent pretraining. To identify effective evaluation setups, we investigate 8 aspects, such as task formulation or the number of in-context examples. We compare the setups using three widely-used signal criteria, repurposed as normative meta-measures: monotonicity, non-randomness, and ranking consistency of the evaluation scores across intermediate checkpoints. In an early pretraining scenario, we evaluate these setups on 26 monolingual 2B-parameter models trained on different types of data, using 80 tasks in four languages. We also examine the setups on three larger LLMs ($\geq$7B) in the same four languages and explore how the preferred setups change with model scale. Our results yield concrete recommendations: some choices, such as the use of multiple prompts, are consistently useful, whereas others, such as task formulation, depend on model scale. More generally, our framework serves as a recipe for the choice of evaluation setups in new scenarios.

Harness optimization improves LLMs by refining reusable prompts and scaffolding, yet requires further adaptation for program generation tasks such as text-to-SQL and text-to-Python. Existing methods often rely on LLM reflectors to propose harness updates, which can fix observed failures but also disrupt previously correct behavior. Text-to-code tasks offer a natural way to mitigate this issue: we can execute generated outputs, allowing us to evaluate and verify the effects of proposed updates directly. Building on this signal, we introduce HERO (Harnessing Evidence for Refinement and Optimization), which combines offline and test-time harness optimization. At the first stage, \method{} learns reusable prompt updates from execution-verified successes and failures and validates candidate revisions before adoption. At test time, we treat the generated code as an instance-specific harness and refine it using execution feedback. Across four SQL, Cypher, and Python benchmarks, \method{} achieves the best offline performance, improving pass@1 by \(7.6\) points over the initial prompt, while test-time refinement adds another \(2.0\) points and improves execution efficiency.

Existing biomimetic lower-limb prosthesis controllers are commonly designed for discrete locomotion modes, requiring separate parameterizations for level walking, ramps, and stairs. We present a mode-unified prosthesis control framework that represents knee and ankle biomechanics continuously as functions of terrain slope and gait phase across those locomotion conditions. Locally optimized ascent and descent polynomial models were unified using radial basis function (RBF) interpolation, preserving the accuracy of the partitioned models while outperforming a global polynomial representation. The resulting biomechanics were transformed into continuous and slope-dependent impedance parameters and implemented within a single finite-state-machine (FSM) controller using bilateral sensing for gait-state estimation. Experiments with 10 individuals with transfemoral amputation demonstrated terrain-adaptive locomotion from level walking through ramps and stairs up to 35 degrees, including 13 degree ramp and 15 degree stair conditions absent from the underlying able-bodied (AB) dataset. Experimental results reproduced the principal slope-dependent biomechanical trends predicted by the unified model, with high agreement for knee-related measures (r-square = 0.82 - 0.99) and ankle kinematics (r-square= 0.78 - 0.96). These findings demonstrated that unified biomechanical parameterization enables a prosthesis control architecture across diverse terrain conditions while preserving key features of AB biomechanics without requiring independently tuned impedance parameter sets for each locomotion mode.

Outflows driven by active galactic nuclei (AGN) are widely considered a key mechanism for regulating and quenching star formation in massive galaxies. However, direct observational evidence linking outflows to quenching has remained elusive for decades. This article reviews recent findings for massive galaxies at cosmic noon ($z\sim 2$), based on sensitive James Webb Space Telescope (JWST) observations tracing both star formation histories (through Balmer absorption lines) and neutral outflows (through blueshifted NaID absorption). Neutral outflows are found in $\sim$ 25 - 50% of massive ($\log(M_*/M_\odot)>$ 10) galaxies, independent of star formation rate. Outflows from star-forming galaxies are consistent with being powered by star-formation and/or AGN activity, whereas outflows from quiescent systems are generally attributed to current or previous AGN activity. There is growing evidence that recent rapid quenching of star-formation is associated with powerful AGN-driven outflows with mass loading factors $\eta \gtrsim$ 1 - 10. The neutral gas dominates the outflow mass budget but in most cases its velocity is below the halo escape velocity, indicating that this gas may form part of a galactic fountain. Detections of neutral gas inflows and residual cold gas reservoirs in quiescent galaxies suggest that other feedback mechanisms such as AGN heating are required to keep galaxies quenched over long timescales. We highlight the potential of multiphase outflow measurements to constrain feedback models, describe the main systematic uncertainties in mass outflow rate measurements, and discuss how the $z\sim 2$ results inform our understanding of the formation of the earliest massive quiescent galaxies.

Dantzig-Wolfe reformulation applied to two-stage stochastic mixed-integer programs (SMIP) has been shown empirically to yield a formulation with strong bounds that can be solved via column generation. However, the time to solve the restricted master problem grows significantly with the number of scenarios due to the increasing number of nonanticipativity constraints (NACs). Moreover, the associated high-dimensional dual space can cause the dual multipliers to oscillate between iterations, further slowing convergence. We propose an aggregated column generation framework for solving a Dantzig-Wolfe reformulation. Applied to SMIP, this method partitions the NACs into groups and replaces each group with a weighted surrogate constraint, leading to a reduced size and providing implicit stabilization by restricting the dual space. While aggregation leads to a relaxation, we develop two strategies for recovering the standard Dantzig-Wolfe reformulation bound. The first iteratively refines the partition by splitting groups that contain violated constraints. The second keeps the partition fixed and adaptively updates the aggregation weights. We prove convergence of the two approaches and study their computational performance on two benchmark problem classes.

Dynamic nuclear polarisation transfers polarisation from electron to nuclear spins by relying on a dissipative channel. Here we introduce a cavity-based DNP mechanism which uses the radiative relaxation of the electronic spin through the Purcell effect to bring about the nuclear spin polarisation. We implement this protocol on an ensemble of bismuth donor spins (I=9/2, S=1/2) in isotopically purified silicon coupled to a superconducting resonator. A single cycle, combining adiabatic microwave and radio-frequency pulses with Purcell relaxation, increases a target ground state's population by a factor of $1.79\pm0.04$; a cumulative enhancement of $4.6\pm0.2$ is reached with additional cycles, to be compared with the theoretical limit of ninefold set by the degeneracy of the ground manifold. We explain this difference by the competition between Purcell and intrinsic relaxation on the one hand and a collective effect that slows down the electronic spin radiative decay as the nuclear spin population grows on the other hand. Our results place radiative DNP as an available mechanism at millikelvin temperatures where phonon-mediated relaxation is frozen.

We study packet routing in queuing systems where queues act as selfish, myopic agents that use no-regret learning algorithms to select servers with unknown service rates. To model the small buffers used in data centers, we assume that each server has a single-packet buffer. Even such a tiny buffer already captures the features of buffering: routers can exploit multiple servers while accepted packets remain in service, but packets can occupy servers for multiple rounds, complicating future service and learning. We first analyze a single queue routing packets to $m$ buffered servers with service rates $\mu_1, \dots, \mu_m$. This setting is equivalent to an instance of the recharging bandits problem with geometric recharge. We prove that any no-regret learner achieves a long-run average throughput of at least the Hamacher sum of the server rates, and that this bound is tight. Consequently, a single no-regret queue is stable if and only if its arrival rate is below the Hamacher sum of the server rates. Moreover, comparing against an optimal policy, we show that any no-regret learner is at least $0.77$-competitive, which is also tight. We then study multi-queue systems where $n$ queues with arrival rates $\lambda_1, \dots, \lambda_n$, each at most $\lambda_{\max}$, compete for service from $m$ buffered servers. We show that the smallest overprovisioning factor that guarantees the system to be stable under high-probability no-regret learning is $\frac{1}{1-\lambda_{\max}}$. Equivalently, in terms of the total arrival and service rates, the condition $\sum_{i=1}^n \lambda_i < (1-\lambda_{\max})\sum_{j=1}^m \mu_j$ is sufficient, and sometimes necessary, for stability under no-regret learning. In particular, for $\lambda_{\max} = 1/2$, this improves the upper bound of Abel et al. (EC 2026) from $3$ to $2$, matching their lower bound and resolving their open question.

Before deploying clinical prediction models, their reliability must be assessed to ensure safe use. Errors may arise from distribution shifts between training and deployment or from heterogeneous performance where the model systematically underperforms for certain patient subgroups. Yet most post-hoc diagnostic methods evaluate reliability only at the population level, checking whether the deployment data resemble the training data and whether the model performs well on average, without accounting for heterogeneity that may cause some patients to be disproportionately affected. We propose a unified diagnostic pipeline that combines both perspectives. MED3pa first discovers interpretable low-confidence patient profiles, and Detectron is then applied within each profile to test whether its degradation is associated with a detectable harmful covariate shift. Across three clinical prediction tasks and three injected subgroup shifts in MIMIC-IV, we find that shift detectability itself is informative. An injected age shift, undetectable at the population level, was nonetheless localized to specific degraded profiles, whereas sex- and race-related shifts were detected broadly and therefore offered little guidance for identifying the most affected patients.

A fundamental bottleneck for translating thoughts to speech is the high physical cost of motor input forcing a strict tradeoff between communication speed and expressivity. Generative AI offers a promising solution by expanding highly abbreviated text input into fluent sentences, significantly reducing the motor burden on the user. However, sparse inputs are inherently ambiguous; without sufficient context, AI models frequently misinterpret these abbreviations and generate outputs that fail to align with the user's true cognitive intent. We propose Cognitive Steering, a framework that can be leveraged to reconstruct user intent by grounding Large Language Models (LLMs) in multimodal context and applying AI control methods. We demonstrate that aligning frontier models with selected environmental referents, emotional states, and communication motives on simulated abbreviation benchmarks achieves up to $\sim$88% top-5 expansion accuracy, doubling no-context baselines. We also reveal that different types of context require distinct AI control techniques: while physical objects in a scene are best provided through explicit text prompts, abstract factors like emotion may be more effectively managed by directly altering the AI's internal activations. These findings suggest a hybrid architecture for future interfaces that leverage Cognitive Steering to help users communicate both quickly and accurately, recruiting multiple AI control methods simultaneously to perfectly capture their intended communication goals.

Reference solutions and question-specific rubrics are not always available to guide the teacher in self-distillation. A large language model's own solution attempts offer an alternative, but their quality is difficult to assess in open-ended tasks without automatic correctness checks, and even correct attempts can involve uncertain token predictions. We propose Reliability–Uncertainty Self-Distillation (\method{}) to learn from these attempts. The same model serves as teacher and student: the teacher receives the question and completed attempt, and the student matches the teacher's token-level predictions using a question-only prompt. \method{} weights each attempt's distillation loss by additively combining judged reliability, estimated from a self-judge's score and confidence, with student predictive uncertainty. Across eleven reasoning benchmarks, \method{} outperforms all five baselines in average accuracy, reaching 70.47% on Qwen3-4B and 76.69% on Qwen3-8B (8.90 and 2.10 percentage points above the base models). Data and code are available at https://github.com/JP-25/RUSD.

The secondary zeta function is defined by $$ Z(s)=\sum_{\gamma>0}\frac{1}{\gamma^{s}}, $$ where $\tfrac12+i\gamma$ runs over the non-trivial zeros of the Riemann zeta function with positive ordinate, and the Riemann hypothesis is assumed throughout. In this article, we derive convergent integral representations of $Z(s)$ at positive even and odd integer argument, expressed through a differential operator acting on the logarithm of the Riemann $\xi$-function. Define $$ L(x)=\log\left(\frac{\xi(x+\tfrac12)}{\xi(\tfrac12)}\right), \qquad \mathcal{E}=x\frac{\mathrm{d}}{\mathrm{d}x}, \qquad \mathcal{D}_k=\mathcal{E}\prod_{j=1}^{k}(\mathcal{E}-2j). $$ Then, for $k\geq1$, $$ Z(2k)=\frac{(-1)^k}{2^k(k-1)!}\int_{0}^{\infty}\frac{\mathcal{D}_k L(x)}{x^{2k+1}}\,\mathrm{d}x $$ and $$ Z(2k+1)=\frac{(-1)^k}{\pi\,(2k-1)!!}\int_{0}^{\infty}\frac{\mathcal{D}_k L(x)}{x^{2k+2}}\,\mathrm{d}x. $$ In the last part, we write these formulas out explicitly for $Z(k)$, $2\leq k\leq 7$, both in terms of $L(x)$ and in terms of $\xi(x+\tfrac12)$ for reference. We also derive a limit formula for $\gamma_1$, the ordinate of the first nontrivial zero, and demonstrate its convergence numerically.