Papers

Neuroimaging is a widely used modality for characterizing neurodegeneration in various health conditions. Brain age gap has emerged as a promising biomarker for monitoring brain health from neuroimaging data using machine learning algorithms. Recent studies have leveraged coVariance neural networks (VNN)-driven pipelines based on the advancements in graph signal processing for relatively transparent construction of brain age gap from neuroimaging data. In this paper, we focus on a longitudinal study of VNN-based brain age gap in conjunction with Alzheimer's Progression Score (APS) in individuals that are at a higher risk of neurodegeneration due to family history of Alzheimer's disease. APS is a multimodal marker of disease progression. The longitudinal analysis of APS and VNN-derived brain age gap metrics revealed that a higher risk of disease progression at baseline predicted a larger rate of increase in brain age gap in follow-up visits. Thus, our findings revealed potential stratification in the brain age gap modulated by clinical/biological risks of AD in the at-risk population.

Let $\Gamma<SO(4)$ be a nontrivial finite group acting freely on $S^3$, and let $M=S^3/\Gamma$. We prove that every smooth conformal class $C$ on $M$ satisfies \[ Y(M,C)\le |\Gamma|^{-2/3}Y(S^3), \] with equality for the quotient-round conformal class. Consequently, \[ \sigma(M)=|\Gamma|^{-2/3}Y(S^3). \] Our approach uses four-dimensional Poincaré–Einstein fillings of the ball. We first establish compactness for fillings whose conformal infinities range over a compact family of positive-scalar-curvature metrics. Since compactness alone does not guarantee continuation through degenerate Einstein metrics, we use equivariant Fredholm parity to obtain a filling with the prescribed boundary conformal class and group action. A common interior fixed point then makes the Li–Qing–Shi boundary test function invariant, and its descent to $M$ gives the sharp covering factor.

Frontier language-model agents can now improve robots on their own: they write control code, test it, and keep what works as skills and memories for the next task. We introduce SEAR (Self-Evolving Agentic Robotics), a framework and benchmark built around two questions. Is the agent really learning, or just trying more often? And does what it learns still help on new tasks, in a new simulator, and on a real robot? The framework runs an agent in three modes: it writes code that becomes the policy (code-as-policy), acts live in the control loop (agent-as-policy), or works as a researcher that fine-tunes a vision-language-action model (auto-research). The benchmark adds controls that separate retained experience from repeated attempts, familiar tasks, privileged simulator state, larger budgets, and luck. Across seven frontier language models, 330 simulated and five physical tasks, and over four years of agent runtime, we highlight three findings. First, the learning curve of a robotic agent depends both on the overall time budget and the task difficulty relative to model capability. Harder tasks make longer sessions worthwhile; on easier tasks, re-rolling short attempts does just as well. Second, control code and shared routines transfer across tasks and simulators, while task-specific solutions do not. On a real robot, we observe a performance gap between agent-designed practice and novel human-designed scenes. Third, different models evolve more effectively in different ways. Some do best acting live, others writing code first. And a text-only model keeps pace with a comparable multimodal one: perception helps with error assessment, but agentic reasoning and tool use can matter more. We release the benchmark and codebase to support future research.

Engineered transport architectures can improve electrolyte distribution and active-material utilization in porous electrodes, yet their implementation remains limited by fabrication methods that compromise precision, throughput, active-material preservation, or scalability. Here, an integrated embossing-calendering method is introduced to pattern Prussian blue analog (PBA) porous electrodes with embedded, micro-interdigitated flow fields (e$\mu$-IDFFs) for electrochemical desalination. This non-subtractive, roll-to-roll compatible method forms channels by controlling plastic deformation while simultaneously calendering the electrode, preserving active material and reducing patterning time by 100-fold relative to mechanical milling. Indentation experiments and a closed-form model further show that embossing requires 15-fold less force than stamping, while electrode microstructures show local densification beneath embossed channels. PBA electrodes are embossed with novel e$\mu$-IDFFs that use continuous width-tapering with isometric flow paths that promote uniform electrolyte distribution, increase rate capability, and reduce polarization. Compared with e$\mu$-IDFFs patterned using less scalable means and non-isometric flow paths, these e$\mu$-IDFFs desalinate seawater-salinity feeds near to potable levels with 1.5-fold of its thermodynamic energy efficiency and water recovery. Brackish desalination benefits similarly. Tapered, isometric e$\mu$-IDFFs and the embossing method introduced to pattern them are readily translated other electrochemical energy storage and separations systems.

Long-term robot autonomy depends on more than effective action generation: a policy must recognize when its behavior is no longer sufficiently supported and use assistance to improve. We introduce Equilibrium Energy Control (EqC), a framework for introspective lifelong robot learning built around an explicit conditional energy landscape. EqC casts generative action refinement as equilibrium-seeking optimization, while the geometry of the refinement process reveals whether the generated behavior remains consistent with the learned landscape. This competence signal enables Energy-Gated DAgger, where persistent energy-consistency violations trigger expert takeover and the resulting recovery trajectories are aggregated for subsequent policy updates. EqC integrates naturally into both Diffusion Transformer policies and flow-matching-based vision-language-action (VLA) policies. Across simulation and real-world bimanual manipulation, EqC matches or improves control performance and robustness while enabling timely intervention near the policy's competence boundary. A real-world study further shows how these interventions progressively expand the range of situations handled autonomously, providing a practical path from static generative controllers toward self-improving robot systems.

Agentic remote sensing is evaluated on how many questions it can answer, whereas crisis response depends on whether its answers can be relied on and how much of the decision can safely be handed to the agent. This paper argues that autonomy should be earned, not assumed: An Earth-Observation (EO) agent should be granted autonomy in proportion to demonstrated reliability, epistemic honesty and verifiability. The position is supported by an evidential meta-analysis of twelve agentic RS/EO/GIS benchmark studies from peer-reviewed venues. Only one repeats runs, three contain unanswerable tasks and none measures calibration. Their own tables show that completed workflows are often not correct (task success exceeds tool-call correctness by up to 54pp on identical queries), that the gap to an expert trajectory widens overall with trajectory length (from 7 to 56pp), and that capability does not predict abstention (Spearman r from -0.25 to 0.50, all n.s.). The paper then contributes three EO-specific trust properties, an autonomy ladder for crisis EO tasks, and a readiness protocol that replays archived emergency activations before any live use. In this context, current evidence justifies assistive roles only.

We study the invariant rank-four deformed Hermitian–Yang–Mills equation associated with the chain $\mathcal{O}(1)\to\mathcal{O}(2)^{\oplus2}\to\mathcal{O}(3)$ over $\mathbb P^1$, with vertical weights $(4,2,0)$ and a fixed product Kähler class and phase. For arbitrary linear arrows $\psi=Bz$ and $\phi=(Az)^T$, smooth strictly calibrated reduced solutions exist exactly when $A$ is invertible and $z^TA^TBz$ is not identically zero. The same condition characterizes stability, semistability and polystability in the specified equivariant coherent category. The classification includes all eleven nonempty coefficient strata and both coincident and distinct divisor points on the rank-one lower boundary. The analytic proof retains the ordered, noncommuting middle equation. After constructing positive-parameter solutions, it rules out unbounded metric values by combining the source budgets with moving spectral tests; on the rank-one lower boundary, the divisor mass must also be retained. Global value, gradient and symbol estimates then give a smooth strictly calibrated endpoint on the original chain. No equivalence with full coherent or derived-category stability, uniqueness, or estimate uniform across changing chains is asserted.

Existing malware detection approaches heavily rely on handcrafted features derived from static or dynamic analysis of the executable files. These methods require specialized domain expertise, dedicated analysis tools, and time-consuming analysis, which limits their scalability and robustness in the face of the increasing complexity and diversity of modern malware. Consequently, there is a growing interest in approaches that operate directly on raw bytes, which contain rich semantic and structural information. However, capturing long-range dependencies within executable files remains challenging for conventional static and CNN-based methods. This paper presents MalwareFormer, a transformer-based, byte-level malware detection framework that operates directly on raw bytes, without requiring domain knowledge or feature extraction. MalwareFormer achieves an accuracy of 98.35%, a balanced accuracy of 98.32%, a macro-F1 of 98.32%, and a false positive rate of 1.94%, outperforming both baselines across all threshold-dependent classification metrics and demonstrating that transformers provide a powerful and scalable approach for byte-level malware detection.

LLM ensemble gains are often measured against a single baseline, but the value attributed to additional candidates can change with the comparison used. We study an LLM aggregator under four matched conditions: Direct (no candidates), Single-slot (one candidate in a multi-slot interface), Duplicate (one candidate repeated), and Multi-candidate (separately generated candidates). Under either non-diverse control, overall candidate gain (CIV) splits algebraically into an additional-candidate contrast (DSV) and a candidate-context contrast (CCV); the split, but not CIV, depends on the chosen control. On MultiHopRAG model diversity (k=2), the repetition gap Rep=-8.33 pp [-13.25, -3.75] quantifies the difference between gains measured against Duplicate and Single-slot. On a matched FRAMES stronger-panel extension (n=200, k=3, aggregator output limit 4096), paired Delta Rep=+9.67 pp [+6.00, +13.50]; within panels, Rep changes sign (original -6.33; stronger +3.33). In FRAMES evidence aggregation, candidate-context contrasts remain strongly negative under both non-diverse controls. Our results show why ensemble evaluations should state the reference control before attributing gains to additional candidates.

We develop and analyze an entropic descent method for a nonconvex optimization problem on probability simplices arising in classical and quantum secure communication. The optimization variables describe a randomized encoder, allowing its input distribution and stochastic preprocessing to be optimized jointly. An exact relative-entropy identity yields a channel-independent majorization bound and an explicit mirror-descent iteration with a fixed unit step size. We establish quantitative descent, convergence of objective values, and stationarity of accumulation points on their support faces for arbitrary finite classical channels, without assuming degradedness or less noisiness. For strictly positive transition matrices, a square-root parametrization and a Kurdyka–Łojasiewicz argument establish finite length of the transformed trajectory and convergence of the entire sequence, including limits on the simplex boundary. For less-noisy channels, a restricted convex formulation admits global convergence with an explicit \(O(1/t)\) objective-error bound. We extend the relative-entropy construction to noncommuting quantum outputs and derive monotone alternating updates for covariant encoders, including correlated preprocessing over a fixed block. Numerical experiments compare the method with analytic benchmarks and constrained optimization, reveal multiple attracting values, and demonstrate strict improvements from stochastic preprocessing.

Long-horizon agents accumulate progress in persistent task state, yet repeatedly process interaction histories describing how that progress was achieved. This raises a natural question: can long-horizon context instead be organized around reusable progress rather than the history that produced it? In this paper, we introduce CarryOn, an object-oriented context runtime that organizes continuation around reusable task objects. Rather than treating compressed histories or reconstructed accounts of progress as the primary basis for continuation, CarryOn builds a context view from continuation carriers, complementary execution context, and a live tail of recent interactions. A core challenge is keeping this reusable basis valid after its surrounding history is retired: how can CarryOn update the basis without reconstructing the full representation at every fold? CarryOn maintains carrier records across folds, revising affected records against bound evidence and applicable environment checks while carrying forward unaffected records and jointly updating execution context. Experiments on OSWorld 2.0 and BrowseComp-Plus show improved gains of 5.8% and 7.0% while reducing total token usage by 51.9% and 22.9%, respectively. Project page: https://ethannju.github.io/carryon

In this short note we show the existence of stably exotic knotted surfaces in 4-manifolds in the sense that the embedded surfaces are topologically equivalent but are not smoothly equivalent even after any number of internal and external stabilisations.

We compute the one-loop gauge-field two-point functions analytically in scalar QED on dS$_{d+1}$ for general dimension and scalar mass, using the EAdS reformulation of the in-in formalism arXiv:2007.09993. The Dirichlet EAdS gauge field acquires a Schwinger-type mass, with its longitudinal mode supplied by a composite of charged scalars obeying opposite boundary conditions, while the Neumann mode remains protected by gauge invariance. In dS, the Dirichlet correction induces an anomalous dimension $\gamma_J$ for the boundary current and modifies the late-time falloff of the electric field. This bulk calculation reproduces the boundary multiplet-recombination result of arXiv:2509.18888. Summing over the in-in contour branches gives the retarded dS bubble kernel, making direct contact with the Bros-Moschella framework. We establish a spectral Cutkosky rule that expresses the discontinuity of this kernel across the principal-series cut in the Casimir plane in terms of a two-particle cut, with both internal scalar lines placed on shell. Although the full bubble coefficient involves a ${}_7F_6$ hypergeometric function, the cut collapses to a closed product of Gamma functions and determines the complete non-local part of the kernel through a dispersion relation. Analytic continuation of the same cut reproduces the complete one-loop result for $\gamma_J$. In the complex Casimir plane, the loop-corrected Dirichlet photon appears as a pole on the second sheet and is therefore naturally interpreted as a dS resonance, or quasinormal mode, whose frequency is shifted at one loop.

Design calculations let researchers gauge, before data is collected, whether a planned study is likely to detect an effect. In this paper, we develop such calculations for predictive models using ordinary least squares and ridge regression under leave-one-out cross-validation. To do so, we derive closed-form expressions relating the expected out-of-sample $R^2$ and the expected correlation between observed and predicted outcomes to four design-stage quantities: sample size, number of predictors, an assumed population $R^2$ ($\rho^2_{in}$) and a design efficiency factor $D^*$ (which summarizes how leverage is distributed across observations). Unlike the classical shrinkage formulas, which depend only on sample size and dimension, these are sensitive to how covariates are arranged – to imbalance and skew. A simulation study assesses the accuracy of the formulas against realized values under a variety of data generating mechanisms. We apply the methods to a published study predicting personality from smartphone behavior and show that the design formulas would have indicated, before any analyses were run, that least squares could not be expected to beat the sample mean while ridge could. An R package, predpower, implements the calculations.

Large language model multi-agent systems extend individual agents' capabilities through collaboration across specialized roles, tools, and workflows. Yet collaboration makes failures harder to diagnose: one agent may misinterpret a correct result while others carry the mistake forward. Failure attribution therefore seeks to identify the responsible agent and decisive error step. Recent methods trace dependencies, but knowing where information came from is not the same as knowing where it went wrong. We introduce BLADE (Blame Localization via Audited Dependency Evidence), a training-free framework that moves beyond tracing information to auditing its use. Using Jev for structured probabilistic judgments, BLADE uses dependency probabilities to select relevant source-decision handoffs for auditing. At these handoffs, it examines whether receiving decisions use their sources faithfully and within task requirements, distinguishing error introduction, propagation, and repair. These findings inform a global diagnosis that considers all execution steps. Without reference answers, BLADE achieves the best or tied-best step accuracy among eight strategies under a shared Jev decision interface on 1,228 failed runs across five Who&When and Who&When Pro subsets, outperforming All-at-once by 2.2-11.1 percentage points. Making responsibility evidence explicit offers a path toward more interpretable and reliable agentic systems.

Video diffusion models generate visually compelling short-term sequences but often struggle to preserve scene geometry and object structure over time. In this paper, we first demonstrate that current video attention cannot identify reliable correspondences across frames, with responses dispersed across multiple regions even after recognizable scene structure has emerged. We argue that reliable cross-frame associations are essential for information exchange as scene structure forms in video generation. Thus, we introduce Geometry Attention Distillation (GAD), which transfers correspondences from a frozen geometry model's attention to video attention. Extracted from clean videos, these correspondences link the same static surface or moving object across frames. Since structure formation begins in deeper layers at higher noise and shallower layers at lower noise, we apply attention distillation at a student layer selected according to the noise timestep. After training, video attention focuses more consistently on corresponding locations. Experiments across all three video backbones demonstrate improved long-range scene consistency and dynamic temporal consistency, with geometric gains across generation lengths. On Wan2.2 5B, GAD improves cross-frame matching accuracy by at least 30% over the Wan baseline on both long-range benchmarks. Notably, GAD achieves these gains without additional inference modules, offering a promising approach to efficient and consistent video-based world simulation. Project page: https://fantasy-amap.github.io/GAD/.

Multimode mechanical resonators offer a large set of densely packed, long-lived bosonic modes within a single compact device, making them attractive for quantum simulation, quantum information processing, and quantum-enhanced sensing. Many such applications rely on multipartite entanglement, yet deterministic mechanical entanglement has so far been largely limited to pairs of modes. Here we demonstrate the deterministic and programmable preparation of multipartite entangled states among the phonon modes of a high-overtone bulk acoustic wave resonator coupled to a superconducting transmon qubit. By sequentially applying optimal-control-engineered isometries between the qubit and successive modes, we generate matrix product states of bond dimension two, including $W$, Greenberger-Horne-Zeilinger (GHZ), and cluster states. We fully characterize these states via quantum state tomography and certify genuine multipartite entanglement among up to four modes. We further demonstrate correlated-noise sensing by exploiting the complementary decoherence responses of the stored $W$ and GHZ states, isolating inter-mode phase correlations from local decoherence and placing quantitative bounds on collective dephasing. Our results establish a scalable approach to preparing multipartite entangled states in mechanical systems, with promising applications in multiparameter sensing and tests of quantum mechanics with massive objects.

We study the randomised and deterministic demand-query complexity of approximate bipartite matching with few query rounds. The demand-query model, introduced in [Blumrosen and Nisan SICOMP 2009; Nisan SODA 2021], is inspired by combinatorial auctions and welfare maximisation, where an oracle returns the first neighbouring vertex (item) of a vertex u (agent) according to a given permutation pi (preference ordering of the agent over the items). For randomised algorithms, our main result gives a trade-off between the number of rounds k, the per-round query budget q=n^{1+\delta}, and the achievable approximation ratio. Let 1 <= k <= log n, and -1 <= delta <= 1/k. Every k-round randomised algorithm using O(q) demand queries per round has a worst-case expected-size approximation factor of Omega(n^{1/2k-delta/2}/k). Conversely, we give a randomised algorithm achieving approximation factor O(n^{(1-k*delta)/(k+1)}/k) in expectation. For deterministic algorithms, for k*q >= n, we show that the optimal deterministic approximation factor is ~Theta(n^2/(q*k^2)), thereby improving the previous lower bound of [Nisan SODA 2021] by a polynomial factor over a wide range of parameters. In particular, for q=Theta(n), we improve the deterministic round-complexity lower bound for constant-factor approximation from ~Omega(n^{1/3}) to ~Omega(sqrt n). Our algorithms produce matching and vertex-cover certificates; the deterministic trade-off also extends to minimum vertex cover and maximum fractional matching. We extend the randomised upper bounds to the weaker Demand-OR model [Nisan 2021]. We prove a non-adaptive simulation of uniform random-neighbour queries using known techniques, avoiding the O(log n)-round penalty of the trivial binary-search simulation. Consequently, our upper bounds yield the same k-round approximation guarantees using O(q * log^2 n) Demand-OR queries per round.

Massive mechanical oscillators couple directly to forces, accelerations and gravity, making them attractive probes of new physics and of quantum mechanics at macroscopic scales. Pushing sensitivities beyond the standard quantum limit for signals of unknown phase requires non-Gaussian quantum states, whose metrological advantage has so far been confined to lighter systems such as trapped ions. Here we operate a microgram-scale acoustic mode of a high-overtone bulk acoustic wave resonator as a phase-insensitive quantum-enhanced sensor. A transmon qubit prepares the mode in Fock states of up to seven phonons by optimal control, and resolves its phonon-number distribution after interaction with a weak resonant signal. Bayesian analysis yields a Fisher information five times the vacuum value, a 7.0 dB gain in signal-amplitude sensitivity over any classical probe state, irrespective of its energy, currently limited by state preparation infidelities. We then train a neural network on the measured sensor response to perform Bayesian estimation without any analytical model of the system, showing the same sensitivity gain with half the systematic bias. Our results establish acoustic resonators prepared in non-Gaussian states as quantum-enhanced probes for high-frequency gravitational waves, dark matter and wave-function collapse.

We consider solutions to the two-dimensional Euler equations with a logarithmically regularized velocity given by $u=\nabla^{\perp}(-\Delta)^{-1}\ln^{-\gamma}(|\nabla|+e)\omega$ and initial vorticity in $\dot{H}^1 \cap \dot{H}^{-1}(\mathbb{R}^2)$. We show that if $\gamma>1/2$, then global well-posedness holds.

A robot needs a world model that predicts how its actions will change the scene and a policy that chooses those actions. Models are usually built and evaluated for only one of these roles, and every robot records its actions in its own format. We ask whether one robot world model can serve both roles across different bodies, and what makes this work. We present GreenWAM, a world foundation model for robotics, together with the recipe that produces it: (1) a shared anatomical action space that describes 20 robot families, from bimanual arms to dexterous humanoids, in common joint coordinates; (2) joint training on these families in visual, action-conditioned and world-action modes; and (3) policies that split an action expert off the generator. As a world model, GreenWAM attains top-tier trajectory, depth and 3D accuracy on WorldArena 1.0, ahead of every world-action model and video generator in our comparison. As a policy, it scores among the top entries of the RoboTwin 2.0 leaderboard, reaches the highest zero-shot LIBERO-plus success among the compared methods and is competitive with dedicated vision-language-action and world-action policies on CALVIN and LIBERO. We further adapt GreenWAM to a real humanoid, where it succeeds more often than policies adapted from $\pi_{0.5}$ and from Cosmos 3 Edge, and distill it into a single-step policy for real-time control. Controlled experiments yield three findings: robot specialization improves world prediction and control together; an action expert helps when split off at the start of adaptation; and keeping world-model modes during policy adaptation preserves robustness to scene changes.

System one models enable direct, low-latency decision-making. Yet recent practice of predicting an answer from serialized text does not, by itself, respect the structure of a decision problem. We argue that current designs underemphasize four important structural requirements. (i) null-aware: Models should distinguish answer absence from uncertainty among candidates; (ii) permutation-invariant: Reordering alternatives should not change the decision; (iii) option-scalable: Growing candidate sets should not require redefining the output space; (iv) cacheable: Request-independent computation over recurring alternatives should be reusable across requests. We introduce Jeva, a decision-native architecture that addresses these requirements jointly. A shared encoder independently represents the request and each option, while a compact decision stack refines only the request state against immutable option memory. Symmetric aggregation yields permutation-equivariant probabilities; shared scoring accommodates variable-size candidate sets. A separate coverage estimate distinguishes answer absence from candidate competition, enabling explicit null outcomes. Request-independent option representations and layer projections support reuse across newly assembled sets. These mechanisms unify Choice, Noul, and Score outputs. Across evaluations, Jeva combines strong typed-decision performance with near-perfect null detection and no decision flips under any tested permutations. It scales to thousands of candidates and substantially reduces latency through cross-request reuse without changing decisions.

Limited battery endurance remains a major obstacle to persistent UAV missions. Existing energy-replenishment approaches typically rely on battery-swapping/charging infrastructure or on ground vehicles with accessible road networks - assumptions that may not hold in infrastructure-less regions (ILRs) such as remote wilderness, mountainous terrain, and disaster-stricken areas. We formulate energy resupply in ILRs as a distinct logistics problem, in which energy itself must be projected into a region with no pre-existing infrastructure, and proposes a Distributed Energy Relay Framework that enables cooperative energy delivery using porter drones. The framework introduces a Transportation-by-Relay-and-Cache (TRC) mechanism, in which drones relay battery resources toward a mission location. Additional models are developed to characterize battery transportation capacity, relay amplification, energy-delivery capability, operational cost, and reliability. Based on these models, stations independently evaluate their delivery capability and submit bids to a mission coordinator, which selects an energy-delivery coalition that satisfies mission requirements while minimizing cost. Analytical evaluation illustrates the impact of battery characteristics and drone capabilities on energy projection and demonstrates the effectiveness of the proposed framework for sustaining UAV missions in ILRs.

International challenges have become the standard for developing and benchmarking biomedical image analysis methods using centralized multi-institutional data. Federated learning (FL) describes a paradigm-shift on multi-institutional collaborations, where models are trained across institutions while their data are always retained locally. The Federated Tumor Segmentation (FeTS) challenge, first held in 2021, was the first challenge dedicated to FL in medical imaging and editions in 2022 and 2024 pushed the frontiers of real-world method validation. FeTS++ 2027 returns after a two-year gap with a substantially larger and more diverse cohort, and with the two "pluses" that name the challenge: an official classification task alongside segmentation, and a move of the infrastructure to NVIDIA FLARE (NVFlare). Built on the clinically acquired, multi-institutional multi-parametric MRI data of the BraTS 2025 Lighthouse challenge, FeTS++ spans gliomas and meningiomas across patient cohorts from institutions in North America, Europe, Asia, and Africa, and focuses on ranking submitted methodological approaches according to their model utility and an efficiency-aware score. Task 1 asks participants to find the best strategy for aggregating knowledge from per-institution segmentation models, while Task 2 asks them to distinguish glioma from meningioma under the same federated protocol, in which the entity label is heavily confounded with the site of origin.

We study plank coverings of cube annuli $Q\setminus\delta Q\subset\mathbb{R}^d$, where $Q$ is the $d$-dimensional unit cube and $\delta Q$ is a homothetic copy lying in its interior. A. Bezdek proved that, in dimension $2$, every plank covering of such an annulus has total width at least~1 whenever $\delta\le1-1/\sqrt2$. Smurov, Bogataya, and Bogatyi extended this result to all $d\ge2$ under the condition $\delta\le1-1/\sqrt d$. It is conjectured that the same lower bound holds for $\delta\le1-1/d$. We provide evidence for this conjecture in dimensions $2$ and $3$ by proving that there exist positive constants $\varepsilon_2$ and $\varepsilon_3$ such that the bound remains valid whenever $\delta\le1-1/\sqrt d+\varepsilon_d$.

Predicting spatial gene expression from standard H&E images could extend molecular analysis to tissues without spatial transcriptomic measurements. A standard Transformer applies self-attention over spots but ignores where each spot sits in the tissue, whereas a spot's molecular state depends on tissue context at multiple spatial scales. Building on this insight, we introduce MIST, a Multi-context Spatial Transformer that augments the self-attention backbone with two context pathways applied in every layer: a coordinate-invariant local pathway that attends over spatial k-nearest-neighbor spots, and a slide pathway that broadcasts a whole-slide summary to every spot; the model predicts all spots in a single forward pass. Because coordinates enter only through pairwise distances, the local pathway is invariant to translations, rotations, and reflections when image features are fixed. In intra-cohort evaluation across six human organ cohorts from HEST-1k, MIST improves mean Pearson correlation over the strongest evaluated baseline by 9.7%, 11.6%, and 11.4% for 10-, 50-, and 100-gene panels, respectively, with the lowest average MSE and MAE. MIST further improves leave-one-organ-out transfer by 6.0% over the next strongest baseline, attains the best expression-derived domain recovery (highest mean ARI and NMI at every clustering resolution, and higher NMI than the closest baseline on 84% of held-out slides), and reproduces spatial expression patterns of selected cancer-marker genes. Together, these results show that adding local and slide context to a vanilla Transformer backbone is an effective approach to spatial gene expression prediction from histology.

Gravitational waves (GWs) propagating across the Universe can be distorted by intervening lenses, producing characteristic wave-optics signatures. These effects are not incorporated into current matched-filtering searches and can therefore substantially reduce detection efficiency. The underlying mechanism is the signal-consistency test, which measures deviations between the observed and expected signal-to-noise ratio (SNR) distributions. We report a systematic study of the impact of gravitational lensing on signal-consistency tests, using a two-image interference model and representative signal-consistency statistics in both the time and frequency domains. We find that overlapping images produce sharply localized SNR residuals in the time domain, breaking the reflection symmetry of the autocorrelation about the merger time. Although interference fringes produce broadband SNR residuals in the frequency domain, both domains exhibit a minimum for high-mass signals when the fringe structure becomes comparable to the signal bandwidth. This highlights a limitation of current strategies that search for distorted lensed signals only among GW events detected by matched-filtering searches. Exploiting this asymmetry, we develop a statistic that separates selected down-ranked lensed injections from noise-background triggers and paired nonlensed injections, without extending the template bank. Our results establish the first connection between lensing observables and detection, paving the way for the discovery of lensed GWs.

In this paper, we study online paging with delay or deadlines. In online paging with delay, an online algorithm manages a cache of size $k$ and needs to serve incoming requests by adding the requested pages to the cache. In addition, it has the option to delay serving incoming requests at a cost that depends on the delay. We propose a new online algorithm, which combines a threshold rule with first-in, first-out (FIFO) replacement, and show that it is $(2k+2)$-competitive for cache size $k$. This result corrects a previously published claim that the competitive ratio is exactly $2k+1$ regardless of the number of holes (pages outside the cache). However, in the case of one hole, we show that the FIFO rule with a different threshold is indeed $(2k+1)$-competitive, giving a tight result. In the case of deadlines, the same analysis gives a deadline-triggered algorithm that is $(k+1)$-competitive in general and $k$-competitive if there is only one hole. Moreover, we show that the second hole makes paging with deadlines strictly harder than classical paging, where the competitive ratio is independent of the number of holes. For paging with deadlines, we prove a deterministic lower bound of $k+\tfrac12$, already for two holes. We show that, as a consequence, no threshold-triggered algorithm can achieve a competitive ratio less than $2k+\frac32$ in general.

Rubric-based reward models (RMs) evaluate responses against explicit criteria. However, existing methods often derive criteria from observed response candidates, introducing response-induced bias that may limit rubric generalizability. Their judges also struggle with mechanical constraints when relying on reading alone, and commonly used pairwise judges provide only relative preferences, complicating their direct use for policy optimization. We propose ReVeR, a pointwise rubric RM that derives hard rules and graded principles by reasoning about the instruction alone and evaluates responses independently through tool-augmented judging. Both components are trained through label-blind distillation, in which preference labels only filter a teacher's outputs, yielding ReVeR-Traces, a large-scale dataset of rubric-reasoning and judging trajectories. Experiments demonstrate that ReVeR outperforms pairwise rubric RMs in average preference accuracy, most clearly on instruction following, as well as in test-time scaling and downstream policy optimization. We further find that generator RL improves preference accuracy while reducing rubric fidelity, and that higher preference accuracy does not necessarily translate into better downstream policies. These findings highlight that rubric fidelity, preference accuracy, and downstream utility are distinct properties, shedding light on future RM research.

Human-AI Interaction is commonly evaluated by what an artificial agent enables during use, yet interaction can also alter the human who acts next. We introduce Residual Human States, a trajectory-based framework for representing the potentially multidimensional human state carried forward after interaction with AI, relative to a relevant alternative trajectory. The framework distinguishes assisted output from human-state transition and derives four empirical propositions: multidimensionality, interaction-policy dependence, horizon dissociation, and temporal persistence. Its central claim is that assisted performance does not by itself determine the human state carried forward. We examine these propositions through four empirical cases with different inferential roles. Published medical-training evidence illustrates how one AI interaction history can be associated with both slightly higher observed accuracy on some later unaided cases and transmission of a systematic decision bias on others. A second diagnostic-learning study shows that later unaided behaviour differs across AI-support policies, while also revealing that aggregate accuracy cannot by itself distinguish improved discrimination from a shifted response criterion. In a classroom experiment, generative-AI tutoring substantially improved assisted practice performance without a corresponding detectable gain on a subsequent unaided exam. A longitudinal reanalysis of personalised AI dialogue further shows that residual contrasts can evolve across post-interaction horizons and that such change may arise from the comparison trajectory as well as from the focal intervention. Evaluating interactive AI systems therefore requires attention not only to contemporaneous performance, but also to which human states alternative interaction trajectories produce, relative to which counterfactuals, and how durably.