Papers

We initiate the study of quantum leakage resilience of unmodified Shamir secret sharing over prime fields. A well-studied leakage model for Shamir's secret sharing classically is single-bit local leakage from each share. We consider its quantum analogue where, for each party, a local leakage channel takes as input the party's share and outputs a leaked qubit. Without preshared entanglement, we show that the distinguishing advantage is $2^{-\Omega(n)}$ when the threshold rate $t/n=\tau$ exceeds $\tau_\star\approx0.73339$ by a fixed positive margin. More generally, we allow disjoint entangled blocks of any fixed maximum size where there is no entanglement between different blocks or with the adversary, and each block emits at most a fixed number of qubits. Security holds when the threshold rate is high enough (sufficiently close to one). We then allow a specified set of devices to share entanglement with the adversary. We show that security holds even when a linear number of devices ($\alpha n$ for small $\alpha>0$) share entanglement with each other and with the adversary for a large enough threshold rate. As a complementary negative result, we also show that even classical single-bit leakage makes Shamir scheme insecure if we allow arbitrarily large entanglement between the leakage devices. A GHZ state shared by exactly $t$ leakage devices makes even classical one-bit leakage insecure, without any entanglement with the adversary. In this attack, each participating device emits only one classical bit, and their joint parity distinguishes any chosen pair of secrets with a constant advantage. Thus, for fixed threshold rates above $\tau_\star$, the maximum number of devices that may share arbitrary entanglement with one another and with the adversary while preserving security is linear in $n$ up to constant factors, although the optimal support fraction remains open.

We propose that, at criticality, equilibrium dynamics effectively evolves on a fractal subspace rather than throughout the full Euclidean space. Starting from Fisher's formulation of the order-parameter correlation function, we interpret the anomalous critical exponent $\eta$ geometrically through a correlation fractal dimension associated with this effective subspace. Using fractional-calculus tools, we derive a form of the correlation function that recovers critical behavior below the upper critical dimension and obtain an explicit relation between $\eta$ and a fractal dimension $d_R$ linked to the Riesz fractional derivative. We also examine the Rushbrooke scaling relation and investigate critical behavior in non-integer-dimensional and disordered systems. In the disordered case, controlled by a parameter $\sigma$, we test the range over which the proposed geometric interpretation remains valid. The results connect scaling laws, critical exponents, correlations, and fractal geometry, suggesting that the anomalous behavior observed at criticality can be understood as a consequence of dynamics constrained to an effective fractal subspace.

In this paper we deal with a nonlinear elliptic problem in the whole space $\mathbb{R}^N$ involving the $p$-Laplacian operator with $p>N$. Under suitable assumptions on the potential term and on the nonlinearity, we establish the existence of at least three distinct weak solutions. Our approach is variational and relies on two different three critical points theorems. The results extend to higher dimensions some recent multiplicity theorems for one-dimensional $p$-Laplacian equations on the real line, and provide explicit ranges for the parameter $\lambda > 0$ ensuring the existence of multiple solutions, which are nonnegative under additional sign conditions. The nontriviality of the solutions is also discussed. Finally, applications to problems whose nonlinearities have separated variables are presented.

Scenario analysis is widely used to stress test financial portfolios, yet conventional approaches often summarize scenario gains using point estimates that overlook dependence between stressed and unstressed risk factors. We develop a machine learning framework for quantifying uncertainty in realized next-day scenario gains through prediction intervals whose widths can be calibrated online. Adaptive conformal scenario analysis (ACSA) calibrates scenario-specific quantile predictions and provides a long-run empirical coverage guarantee over realized scenarios. Our main method, kernel scenario analysis (KSA), estimates scenario-conditional quantiles directly from the specified stress and current market information. KSA can also be combined with ACSA to obtain online-calibrated prediction intervals. In experiments designed to reflect real-world markets, conventional scenario analysis can substantially understate risk, including for portfolios that appear safe under standard stress tests. Our proposed methods achieve better calibration and sharper intervals than empirical-quantile baselines. Overall, the framework moves scenario analysis beyond point estimates by quantifying predictive uncertainty and providing tools for statistically validating scenario gains.

Non-injective mappings in neural networks map distinct inputs to the same representation, thereby implicitly inducing equivalence relations in the input space. However, the input differences eliminated by these mappings may still be required by downstream tasks, creating a mismatch between operator-induced indistinguishability and task-required distinctions. For non-injective linear operators realized in the current forward pass, their null spaces exactly characterize these invisible input variations. We propose Task-Relevant Null-Space Residuals (NSR), a general residual framework for non-injective linear mappings. NSR combines null-space component extraction from pre-mapping representations, member-level encoding and gating, and application-specific integration to exploit potentially task-relevant information under downstream supervision while preserving the original aggregation or merging rules. We evaluate NSR in two structurally different settings: token merging and graph aggregation. In token merging, NSR achieves higher semantic segmentation performance than the corresponding compressed baselines in 34 out of 36 evaluated configurations, with a maximum observed gain of 31.51 mIoU points under strong compression. In graph aggregation, NSR achieves 100% training accuracy on Tree-NeighborsMatch at depths d=2–6 across three backbones, alongside gains on heterophilic node classification and molecular graph regression. Together, these results support null-space residuals as a practical complement to non-injective linear mappings, enabling downstream models to learn from input distinctions invisible in the original operator's output.

For any Tychonoff space $X$, let $D(X)$ denote either the space $C(X)$ of all continuous real-valued functions on $X$ or the space $C^*(X)$ of all bounded continuous real-valued functions on $X$. We write $D_p(X)$ when $D(X)$ is endowed with the topology of pointwise convergence. In our recently published paper [8, Theorem 1.6], we obtained the following result: if $T: D_{p}(X) \to D_{p}(Y)$ is a linear continuous surjection, where $X$ is a metrizable space and $Y$ is a perfectly normal space, then $Y$ inherits a given topological property $\mathcal{P}$ from $X$. A linear continuous surjection $T: E_{p}(X)\to E_{p}(Y)$ is said to be densely defined if $E(X)$ and $E(Y)$ are dense linear subspaces of $D_{p}(X)$ and $D_{p}(Y)$, respectively, and $E(X)$ is correct (see Definition 1.5(a)). In the present paper, we establish sufficient conditions under which the above statement remains valid for a densely defined linear continuous surjection $T: E_{p}(X) \to E_{p}(Y)$. In particular, $\mathcal{P}$ can be zero-dimensionality, $\sigma$-compactness or strong countable-dimensionality. Additionally, for arbitrary Tychonoff spaces $X$ and $Y$, assuming that $T: E_p(X)\to E_p(Y)$ is a densely defined linear continuous operator, we show that $X\in\mathcal P$ implies $Y\in\mathcal P$, where $\mathcal P$ is the property $(\kappa)$, the strong $\sigma$-scatteredness, or the property of being a $\Delta_1$-space.

We develop a completely positive and trace-preserving non-Markovian transmon model with longitudinal Markovian dephasing and transverse renewal events motivated by a glassy two-level-system environment. A microscopic Hamiltonian identifies coupling subspaces; a normalized Prabhakar waiting-time law phenomenologically coarse grains slow defect reconfigurations. Forward chronological renewal histories yield an exact map-level Volterra equation, a noncommuting kernel–resolvent master equation, and an equivalent drift-conjugated Caputo-type representation with its required initial-value term. Without energy relaxation, Pauli-space dynamics splits into two one-dimensional subspaces and a coupled $(\sigma_y,\sigma_z)$ subspace supporting directional transfer between coherence and longitudinal polarization; $\sigma_x$ polarization is renewal-insensitive. For heavy-tailed waiting times with $0<\alpha<1$, branch-cut analysis gives a generic $t^{-\alpha}$ storage tail in longitudinal polarization generated from initial coherence and $O(t^{-1-\alpha})$ reverse transfer; constant-rate Poisson renewal yields pole-generated exponential decay. Independent zero-temperature relaxation at finite $T_1$ exponentially cuts off these tails when its rate is below twice the pure-dephasing rate. We compare independent inverse-Laplace reconstructions of the waiting-time density, memory kernel, and selected qubit-response components to assess numerical accuracy. For the studied parameters, Prabhakar renewal gives larger forward-transfer magnitudes at the prescribed readout than both a scale-matched constant-rate Poisson reference and an inhomogeneous Poisson reference matching the full expected-count profile, including finite-$T_1$ tests. Both Poisson references yield larger evaluated finite-window peaks. Disorder-motivated renewal memory reshapes transmon decoherence selectively by state and direction.

The two-fluid model provides a powerful phenomenological framework for superfluids, where components interact through vortex-induced mutual friction. Quantum turbulence in such coupled two-fluid systems has become a central theme in low-temperature physics. However, the fundamental incompatibility between discrete vortex-line and continuum descriptions has historically forced reliance on phenomenological parameters. Here, we present an ab initio holographic simulation of this active two-fluid dynamics. Using a fully backreacted gravitational model, we intrinsically incorporate reciprocal momentum exchange and finite-temperature dissipation without empirical inputs. Contrasting continuously driven and freely decaying turbulence, we uncover pronounced non-Gaussian tails and spatial anisotropy in the normal-fluid velocity statistics, arising directly from the dynamical quantized vortex backreaction. Raising the temperature suppresses normal-fluid velocity fluctuations despite increasing the vortex density. This suppression is unambiguously traced to the thermal depletion of the superfluid condensate. Our results establish holographic duality as a rigorous first-principles framework for quantum turbulence, revealing the active role of the normal fluid far from equilibrium and yielding predictions for ongoing cold-atom and superfluid experiments.

We study well-formed weighted projective threefolds $X=\mathbb P(w_0,w_1,w_2,w_3)$ that admit a $\mathbb Q$-Gorenstein smoothing to a smooth Fano threefold of Picard number one. For del Pezzo threefolds $V_d$ and prime Fano threefolds $Y_g$, we derive three necessary numerical and local conditions: the anticanonical volume equation, an identity obtained from the linear term of the anticanonical Hilbert polynomial, and a global section condition for smoothing the transversal $A$-singularities along coordinate curves. A computer search using these conditions determines all numerical candidates, apart from the known infinite family for $V_5$, with $w_0+w_1+w_2+w_3\leq 5000$. We construct $\mathbb Q$-Gorenstein smoothings to $V_1, V_2, Y_6, Y_{10},$ and $Y_{12}$ from numerical candidates of weighted projective threefolds, and prove that $\mathbb P(2,5,8,25)$, although a numerical candidate for $V_4$, is not $\mathbb Q$-Gorenstein smoothable. To identify the smooth fibers, we also give a vanishing-cycle criterion ensuring that Picard number one is preserved under the smoothing.

Proactive LLM agents can turn idle compute into useful support before users ask. Yet even correct work can misread user context, impose review costs, or undermine trust. This work proposes foundations for designing, realizing, and evaluating proactive LLM agents around three joint principles (3T): Task Capability, anticipating relevant needs and correctly performing useful work; Temporal Allocation, allocating compute according to resource availability and when results are needed; and Trust, sustaining users' confidence and appropriate reliance on the agent. We connect these objectives to a design space organized around five dimensions: task scope, anticipation horizon, activation trigger, processing timing, and intervention depth, and specify the situation and system modeling needed to support its choices, including user and environment representations, backbone LLMs, and agent harnesses. Lastly, we propose PROACTIVITY-GYM, a simulation-based evaluation testbed including multi-day scenarios, stateful environments, and persona-conditioned simulated users that can evaluate the consequences of proactive assistance across interactions. Evaluations across 23 model-harness configurations uncover substantial performance gaps across 3T and reveal that LLM judges often conflate task capability and trust. A human study with 30 participants demonstrates the importance of the joint 3T optimization: participants show sharp trust declines after intervention misalignment despite correct outcomes, and prefer sleep-time assistance, even when imperfect, to preserve ongoing focus. Together, these findings support designing and evaluating proactive agents through the joint consideration of useful work, compute allocation, and evolving user trust.

We evaluate the road safety implications of Low Traffic Neighbourhoods (LTNs) and blanket 20 mph speed limits in London using injury-collision records (2020-2024). Because London implemented 20 mph limits primarily via sign-only orders without physical traffic calming, this work evaluates the blanket statutory model rather than lower urban speeds in principle. For LTNs, we apply a causal pipeline combining naive pre/post comparisons, Empirical Bayes shrinkage for Regression to the Mean (RTM), and spatial Difference-in-Differences. Naive comparisons suggest substantial crash reductions, but Empirical Bayes adjustment reveals much of this reflects mean reversion. After correction, only one zone exhibits a statistically significant inside-area reduction. We find no consistent evidence of boundary-road crash displacement nor uniform inside safety gains. Given the modest corrected benefits, small journey-time increases on boundary roads (approximately 10 seconds per vehicle) monetarily negate safety gains. For 20 mph versus 30 mph roads, five associational methods across 14 contexts show that the aggregate difference in the fatal or serious (KSI) collision share is negligible (0.6 percentage points). Controlling the false discovery rate, four contexts display robustly higher KSI shares on 20 mph roads: A-roads, junctions, pedestrian crossings, and single carriageways, with no context showing a robust reduction. In movement corridors where road geometry cues higher speeds, sign-only limits fail to self-enforce. These findings highlight a structural "wrong-road problem." Indiscriminate sign-only limits impose economic drag without proportionate safety returns. Transport authorities should move away from blanket statutory defaults and return to targeted physical engineering on high-harm corridors.

Nearly $\mathrm{G}_2$ manifolds are positive Einstein seven-dimensional manifolds whose associated cone metric has special holonomy equal to, or contained in, $\mathrm{Spin}(7)$. We study nearly parallel $\mathrm{G}_2$-structures invariant under a cohomogeneity-one action of $\mathrm{SO}(4)$, and construct the first inhomogeneous nearly parallel $\mathrm{G}_2$-structure on the Berger space $\mathrm{SO}(5)/\mathrm{SO}(3)$. The cone over this metric has full holonomy $\mathrm{Spin}(7)$. The existence of the solution is established by a rigorous computer-assisted shooting argument. We also establish a local desingularisation of a finite quotient of the sine cone over $S^3\times S^3$ by gluing in the asymptotically conical $C_7$ bubble constructed by Foscolo–Haskins–Nordström. We show that as the singular orbit of a family of nearly parallel $\mathrm{G}_2$ manifolds collapses, away from the singular orbit the desingularising family converges to the sine cone quotient, while the natural blow-up converges to the AC torsion-free $\mathrm{G}_2$-metric of $C_7$.

Affordance perception aims to localize actionable regions supporting embodied interaction, yet 2D and 3D affordance grounding have evolved as separate problems, with different task definitions, supervision formats, datasets, and evaluation protocols. This fragmentation limits the learning of transferable object-affordance semantics across visual and geometric spaces. We propose Token Router for Tasks, a multitask training paradigm for MLLM-based systems that routes contextual hidden states to task-specific branches without requiring the language head to generate predefined markers. Routed states are supervised directly by branch-specific objectives, enabling dense prediction losses to shape shared MLLM representations. We instantiate this paradigm as UniAfford, a unified framework for generalizable 2D-3D affordance perception, together with UniAfford-Data, a dataset integrating pixel-level 2D annotations, point-level 3D annotations, and language instructions under a shared object-affordance taxonomy, supporting heterogeneous supervision through semantic-level 2D-3D pairing. UniAfford adopts an MLLM as a shared semantic hub and a modality-aware token router to produce image- and point-cloud-affordance queries. These queries respectively condition a SAM-style pixel decoder and a SONATA-based point decoder, enabling flexible 2D, 3D, and joint affordance inference from image-only, point-cloud-only, or paired multimodal inputs. Experiments demonstrate strong zero-shot generalization across 2D and 3D affordance benchmarks without target-specific fine-tuning, alongside state-of-the-art branch-wise performance under modality-isolated protocols. Ablations validate token routing, joint 2D-3D supervision, and decoder coupling, while language-head diagnostics show that routed latent states carry meaningful object-affordance semantics. Project page: https://4dvlab.github.io/UniAfford

While Large Vision-Language Models (LVLMs) achieve remarkable success, hallucinations remain a significant barrier to their reliable deployment. Recent studies primarily attribute these issues to cross-modal attention imbalances; most solutions therefore focus on reweighting visual tokens or suppressing language priors. However, such approaches often overlook the spectral characteristics of the visual information flow and frequently rely on Contrastive Decoding (CD), which doubles inference time. Instead of following conventional approaches, we identify two distinct hallucination patterns-Perceptual-Semantic Dissociation and Localized Fixation-and propose FLASH (Frequency-Localized Attention SHaping), a training-free and CD-free framework. FLASH utilizes a Spectral Vortex Score to detect vision heads within multi-head attention layers and applies adaptive spectral modulation to rectify the visual information flow during decoding. Empirical results demonstrate that FLASH achieves a superior balance between performance and efficiency compared to SOTA methods.

Let $E_2$ be the extraspecial group of order $3^5$ and exponent three. We prove that $d(E_2\times C_3^r)=2r+10$ for $0\le r\le3$. The upper bounds follow from signed zero-block identities and two finite statements in the four-dimensional symplectic space over $\mathbb F_3$. The first supplies edge weights for all completable balanced triangles on any indexed list of at most sixteen nonzero vectors. The second supplies weights for the direction families that can occur in a critical list with no central terms. We give complete coverage arguments, exact certificate files, and separately implemented checking programs. A compression argument removes any need for an induction through smaller list lengths in the sixteen-term potential theorem. The formula for $r\ge4$ remains open.

Softmax attention is ubiquitous in modern machine learning, but its quadratic scaling with sequence length makes it costly. To reduce this cost, attention is often approximated with fast algorithms, which incur error but can still perform well in practice and on some inputs. At the same time, the growing diversity of attention applications makes approximation guarantees that do not depend on particular input structure a compelling target. For such uniform guarantees over all inputs, known runtime lower bounds rule out fast algorithms for near-exact attention, but leave open the practically important regime: is there an efficient algorithm with even a modest uniform approximation guarantee? We answer this question negatively. Under standard complexity-theoretic assumptions, no truly subquadratic algorithm can approximate attention with any nontrivial additive or relative guarantee uniformly over all inputs. This impossibility holds in the mildest parameter regime for which known algorithms do not already achieve strong approximation guarantees in near-linear time, and extends to practically relevant relaxations: even after polynomial preprocessing of the KV cache, no efficient algorithm can obtain a nontrivial uniform approximation guarantee, or identify a small set of keys receiving substantial attention under sparsity. Overall, our results settle the computational limits of uniform attention approximation.

Object-centric scene reconstruction requires completing partial object observations while preserving metric alignment and avoiding collisions with the surrounding. Existing generation-based methods are often image-conditioned and suffer from scale ambiguity and insufficient geometric constraints. We propose COOL, a framework for COllision-aware and Observation-aLigned reconstruction. Based on an object generation model, COOL conditions the generation on instance and background point clouds. Instance geometry anchors generation in scene coordinates, while background geometry provides local context for scene-consistent completion. We further introduce an explicit collision loss and use joint optimization and resampling to reduce collisions during inference. Experiments on 3D-Front and Scan2CAD demonstrate strong scene-level fidelity, observation alignment, and collision reduction. Moreover, additional studies validate its robustness to mask errors and its applicability to real-world scene replicas.

It is widely accepted that water vapor forms clouds by heterogeneous nucleation (condensation on pre-existing dry nuclei). Homogeneous nucleation (directly from water vapor, without a pre-existing nuclei) is theoretically possible, but it requires high levels of supersaturation and so it is not considered a viable cloud formation process under real atmospheric conditions. Here, we show that introducing homogeneous nucleation in a meteorological model of Mars allows to successfully reproduce the unique characteristics of the Arsia Mons Elongated Cloud, a remarkable water ice cloud that occurs recurrently on Mars and which had remained impossible to model under conventional cloud microphysics. This finding demonstrates that homogeneous nucleation happens on Mars, provides the first evidence of homogeneous nucleation of water vapor in a planetary atmosphere, and challenges current assumptions about cloud formation processes, which is also relevant for certain clouds on Earth and potentially on other planets.

This paper is concerned with a capillary $L_p$ Christoffel–Minkowski-type problem involving the prescription of a class of $L_p$ geometric measures formed by the $k$-th capillary area measure and the $q$-th dual curvature measure. By establishing a gradient estimate, we prove the existence of an even, smooth, strictly convex solution in the parameter range $1<p<q\leq k+1$, where $1\leq k\leq n$.

Plasmas sustain strong energy and momentum flux, yet this activity is typically treated as a dissipative loss channel rather than a usable resource, and its conversion into macroscopic work remains challenging. Here we demonstrate a plasma-powered active engine by coupling self-propelled micromotors to ratchet rectification. Dielectric microspheres in the plasma sheath spontaneously develop asymmetric surface charging and undergo a Quincke rotational instability, forming fast micromotors that extract energy directly from the plasma. Their stochastic impacts are rectified by a sawtooth rotor into a directed angular-momentum flux that drives steady rotation, while an outer asymmetric gear organizes the active bath into coherent circulation to amplify torque transfer. Operating in an inertia-relevant regime, the engine achieves orders-of-magnitude enhancements in both power output and end-to-end efficiency compared with liquid-phase active engines, and remains functional down to the single-micromotor limit. More broadly, our results establish a general route to rectify nonequilibrium plasma activity for macroscopic work.

The usage of chemical dispersant to promote the breakup of oil droplets remains one of the crucial response strategy towards controlling the rapidly rising droplets during an underwater oil spillage disaster like the Deepwater horizon. However, the detrimental effects of dispersant on the marine life are now well recognized. Here, we demonstrate that vortex ring presents an environmental friendly alternative to the debatable usage of chemical dispersant that primarily aids droplet break-up. We propose two mitigating strategies through the application of vortex rings: (i) atomization of large oil droplets into smaller droplets, which enhances natural dispersion and biodegradation (ii) targeted relocation of spilled oil droplets from ecologically sensitive regions to safer remote locations during minor spill events. This proof-of-concept study demonstrates that vortex rings can efficiently atomize underwater oil droplets while simultaneously transporting them over long distances. The efficiency strongly depends on the droplet size distribution and the strength of the vortex ring. Using time scale analysis and force balances arguments, we propose droplet response and atomization criteria by a traversing vortex ring. Beyond atomization and droplet transport which are center to many engineering processes, the work finds high relevance in the area of bubble turbulence, agricultural industry, multiphase reactors, combustion process, atmospheric fluid dynamics and oil extraction from rocks, to name a few.

Time series foundation models (TSFMs) are pretrained on heterogeneous collections containing billions of observations, yet their training windows are typically sampled without estimating whether they provide useful learning signal. We introduce a static data-selection framework that scores each window with a reference forecaster and retains an intermediate interval within every source dataset. Specifically, we connect forecasting loss to optimization difficulty by showing that normalized squared loss controls the per-sample gradient norm under a local Jacobian condition. We then define a reference loss score and apply dataset-stratified selection to preserve the diversity of samples. Across various TSFM architectures, our method outperforms random selection by an absolute margin and even improves both relative MASE and CRPS over full-data pretraining by retaining fewer candidate pretraining windows. Further analyses show strong cross-scale and cross-architecture score correlations, indicating that a small reference model can often select data for larger targets, provided that the reference and target share compatible difficulty orderings.

Simulation-based inference and other field-level weak-lensing analyses require intrinsic-alignment (IA) models generating realistic intrinsic-ellipticity fields across two-point and non-Gaussian observables. We develop a halo-based IA prescription with separate central and satellite components and test it against intrinsic galaxy shapes in FLAMINGO. We jointly fit two-point and higher-order statistics involving the IA, lensing, and density fields, including correlations between the intrinsic shapes of distinct galaxies, and compare against field-level nonlinear-alignment and density-weighted NLA prescriptions. We first evaluate the models at the positions of the original FLAMINGO galaxies, fixing the galaxy–matter connection and isolating the IA response. NLA and $\delta$NLA leave substantial discrepancies on nonlinear scales and across higher-order observables, whereas the halo model provides a simultaneous description of all statistics. We then remove the FLAMINGO galaxy catalogue and regenerate the source population from the halo field using a low-dimensional halo occupation model; the agreement is preserved even when the detailed occupation is only approximately reproduced. Much of this performance can be retained with a compact four-parameter portable model, and the same architecture transfers successfully to an independent gravity-only N-body realization with different halo definitions and shape measurements. These results show that nonlinear field-level IA modelling can be substantially improved over simple NLA-like prescriptions without introducing a large nuisance-parameter space. The halo model therefore provides a promising route for incorporating intrinsic alignments into simulation-based weak-lensing inference, although further validation across halo masses, hydrodynamical simulations, and realistic survey selections will be needed before application to data.

Early, simultaneous, and late fusion combine network layers at different stages of community detection. Their modularity values consequently need not measure the same property of a partition. For normalized shared-node multiplexes, a unified comparison extends an existing two-layer identity: early fusion equals simultaneous fusion plus a weighted variance of community degree volumes. An elementary simplex argument explains simultaneous fusion's preference for single-layer weights. For a specified late-fusion construction, an additional transformation correction separates changes to the graph from changes to the objective. Exact small-network experiments and Louvain and Leiden experiments illustrate these distinctions. On label-free Cora, all objective-selected weights favor citations alone, while the fixed equal-weight mixtures achieve higher median adjusted Rand agreement with subject categories. The analysis provides a diagnostic for interpreting fusion objectives; higher objective values alone do not establish better recovery of externally defined communities.

Let $p$ be an odd prime number. Based on recent work of Zhang, we prove that for a finite set $S$ of primes of $\Q$ containing $\infty$ but not $p$, any continuous odd representation $G_{\Q,S} \to \GL_2(A)$ over a complete Noetherian local ring $A$ with finite residue field of characteristic $p$ has finite image, where $G_{\Q,S}$ denotes the Galois group of the maximal extension of $\Q$ unramified outside $S$. This proves the two-dimensional odd case of Boston's strengthening of the unramified Fontaine–Mazur conjecture over $\Q$. Furthermore, we show that for an imaginary quadratic field $K$, any continuous conjugate self-dual two-dimensional $p$-adic representation of its pro-$p$ Galois group $G_{K,S}(p)$ has finite image, provided the primes in $S$ satisfy a modest condition. As an application, we resolve the sufficiency direction of McLeman's $(3,3)$-conjecture on $p$-class field towers for $p>3$. Namely, we prove that if $K$ is an imaginary quadratic field with $p$-class rank two and the Galois group $G_{K,\varnothing}(p)$ of the maximal unramified $p$-extension of $K$ has Zassenhaus type $(3,3)$, then the $p$-class field tower of $K$ is finite. For $p=3$, the results of Ahlqvist and Pink give the same finiteness conclusion in ten of the thirteen possible cases for the fourth Zassenhaus quotient.

Bilateral data from paired body parts are common and correlated in clinical studies. Classical frequentist methods perform poorly in small or sparse datasets. This paper develops a Bayesian framework for bilateral data with multiple groups under Dallal's model. We derive three objective priors (uniform, Jeffreys', and Bernardo's reference priors) and propose a range-based posterior testing procedure, combined with a decision rule, to test the homogeneity of risk differences, with the equivalence margin calibrated. Monte Carlo simulations evaluate empirical Type I error rates, powers, and interval estimation properties. Results show that the Bayesian methods achieve accurate coverage probabilities, narrower confidence intervals, and better Type I error control than the frequentist Wald approach, especially in small-sample and sparse-data settings. We illustrate the methodology with two real datasets. The proposed framework provides a robust and flexible tool for multi-group bilateral data analysis.

World-action models (WAMs) couple future visual-state prediction with action generation. By adapting video generators or image-editing models pretrained at scale, a prominent line of recent WAMs inherits both predictive knowledge and the models in which it was learned. We ask whether a predictive visual latent space induced by large-scale predictive pretraining can instead provide a sufficient foundation for effective WAM learning without inheriting a complete pretrained visual generative model. To answer this question, we introduce V-JEPA Policy, a simple framework that builds a WAM on the latent space of a frozen V-JEPA 2.1 encoder. An instruction-conditioned future-latent predictor and a flow-matching action expert are jointly learned from scratch in a single downstream stage, with the predictor's future-informed context key–value states conditioning action generation. With 0.9B total parameters, of which 0.6B are trainable, V-JEPA Policy achieves competitive performance with representative WAM and vision-language-action baselines across LIBERO, LIBERO-Plus, and RoboCasa-GR1. Comparing visual foundations under the same downstream framework and training budget identifies V-JEPA latents as more effective than the discriminative, reconstructive, and video-understanding-oriented alternatives, particularly under distribution shifts. Beyond task-specific learning, pretraining the predictor on DROID video–instruction pairs without action labels and adapting it into a WAM yields substantial gains in downstream control and out-of-distribution generalization. Together, these findings establish predictive visual latents as a foundation for effective WAM learning from task-specific demonstrations and for transferring future-modeling knowledge acquired from broader in-the-wild videos. Project page: https://breez3young.github.io/vjepa-policy/

This paper shows that an almost-isometric Sobolev map from a Lipschitz subset of an oriented manifold $M$ into another oriented manifold $N$ can be approximated by a map of class $C^{1,\alpha}$, with a universal bound on the $W^{2,m}$ norm, for any $m\in(1,\infty)$. This, in turn, implies a universal bound on the $C^{1,\alpha}$ seminorm. The $W^{1,p}$ distance of the approximation from the original map is controlled in terms of the $L^p$-deviation from being an isometry, with the optimal scaling. The manifolds $M$ and $N$ are assumed to be compact, oriented and have equal dimension; $M$ may have a boundary.

Long-duration gravitational-wave (GW) inference inevitably encounters data gaps, which are often accompanied by abrupt, non-stationary changes in the detector noise power spectral density (PSD). Conventional practice typically analyzes the pre-gap and post-gap data separately, causing avoidable information loss and potentially degrading parameter inference. We build on Bayesian gap augmentation in the Wilson–Daubechies–Meyer (WDM) time–frequency domain and focus on a practically important failure mode: short gaps with large PSD amplitude jumps. In this regime, the local diagonal (Whittle-like) approximation that underpins the WDM likelihood can no longer be relied upon in the time direction near the gap edges, which may lead to biased and/or less robust inference unless the local diagonal validity is restored without resorting to full segmentation. We propose a two-stage, validity-driven remedy. First, frequency-domain prior-predictive prewhitening (PW) incorporates endpoint-informed noise information to mitigate the dominant mismatch responsible for poor diagonal behavior, enabling a more favorable WDM representation while retaining computational tractability. Second, when a time-direction smoothness criterion still fails, we apply adaptive gap expanding (AGE), selectively enlarging only the minimal neighborhood around the gap boundaries needed to restore local diagonal validity. Toy-model simulations with chimeric PSD transitions show that WDM+PW+AGE yields substantially tighter and more accurate posteriors than single-sided pre-gap/post-gap analyses, while maintaining computational efficiency suitable for next-generation missions.

Permanent air-quality networks are expensive to install and maintain, yet many decisions depend on one future regional exposure rather than the complete pollution field. We introduce Target-Aware Permanent Sampling (TAPS), a graph-diffusion framework for selecting permanent locations observed repeatedly over time, that can reduce unnecessary sensor installations, maintenance, and cost while preserving the information needed for future air-quality decisions, subject to validation with the estimator that will use the network. We formulate the permanent space-time sampling problem and show that, in the noiseless model, recovery of one prescribed target can require less information than full-state identification, for which we give an explicit lower bound on the permanent-location count. We also derive a greedy rule whose marginal gain factors into raw target response and a finite-update correction. We evaluate TAPS on regulatory air-quality networks in California, Canada, and England. In each case the prescribed regional target becomes numerically recoverable at permanent-location budgets well below those required to identify the retained state, and TAPS attains lower regularized target risk than target-weight, geometric, and design-based placements. A blind prospective study further shows that the criterion can be applied before candidate sites have any ground-monitor history, using exogenous environmental covariates alone.