Papers

We prove the hyperkähler SYZ conjecture: the sections of some power of a non-trivial nef isotropic line bundle define a Lagrangian fibration.

Legged robots are promising candidates for future lunar surface missions because they can traverse steep, loose, and obstacle-rich terrain that challenges conventional wheeled rovers. However, readiness for lunar deployment is limited by uncertainties in foot-regolith interaction, dust generation, illumination-driven perception degradation, and operational constraints. This paper reports lessons from the 2025 LUNA analogue campaign, where ANYmal-D and Magnecko traversed loose regolith simulant and crater-like terrain and collected long-horizon navigation and visual-inertial data under challenging lighting. We show that quadrupedal robots can traverse regolith simulant, but performance is affected by sinkage and slip, dust-generating contacts, and perception failures caused by overexposure, shadows, and low-texture regions. These results motivate tighter integration of regolith-aware locomotion policies, illumination-robust perception, repeatable analogue testing, and mission-level operational validation for future lunar legged robots.

Since 2001, we have used the TEXES high resolution mid-infrared spectrograph at NASA's Infrared Telescope Facility to study the density of Io's SO$_{2}$-dominated atmosphere. The spectra cover several SO$_{2}$ absorption lines near 530 cm$^{-1}$ and are used to retrieve the equatorial SO$_{2}$ column density. In addition to covering a long time period, our 191 independent observations also cover the full range of Io central longitudes, allowing us to study the longitudinal variability of Io's dayside atmosphere in more depth than has previously been possible. By improving our modeling of longitudinal variability and using a seasonal model to apply a temporal normalization to the retrieved SO$_{2}$ densities, we produce two complete longitudinal distributions of Io's equatorial SO$_{2}$ column abundances, one representing perihelion and one representing aphelion. Both show the same hemispheric asymmetry that has been observed in previous studies, with the highest densities near 200W and the lowest densities near 305W. We find that the contrast between the maximum and minimum densities is a factor of ~27 at aphelion and a factor of ~16 at perihelion. Both longitudinal distributions are asymmetric, with a sharper drop-off on Io's trailing hemisphere than on the leading. We compare these longitudinal distributions to the distributions expected if the spatial variability were primarily driven by volcanic activity, SO$_{2}$-ice inhomogeneity or the effects of eclipses. We conclude that the effect of eclipses is important, but insufficient to explain the shape of the observed longitudinal variability, and frost distribution is likely to also be important.

Text-to-SQL models are commonly trained to map questions directly to static queries, whereas real-world database agents operate through stateful, multi-turn interaction with live databases – inspecting schemas, executing probe queries, diagnosing errors, and revising hypotheses. This creates a critical train-deploy mismatch, as the execution harness that mediates this interaction is introduced only at inference time. To bridge this gap, we propose HarnessSQL, a harness-native post-training framework that preserves the full interaction structure throughout both supervised fine-tuning and reinforcement learning. HarnessSQL builds isolated, executable database environments paired with hidden execution oracles, rolls out teachers directly inside the target SQL harness, and retains only verified trajectories for full-sequence SFT, followed by execution-reward RL. Across Spider 2.0-SQLite, HarnessSQL dramatically boosts the execution accuracy of compact models, raising Qwen3-8B from 15.5% to 45.2% and Qwen3-14B from 22.2% to 54.8%, while transferring effectively to out-of-distribution interactive benchmarks such as BIRD-Interact and LiveSQLBench. Our findings demonstrate that training database agents directly within their execution harness is essential for mastering complex, long-horizon database workflows.

Motion artifacts in three-dimensional photoacoustic tomography (PAT), caused by extended mechanical scanning of sparse arrays, degrade image quality. Since sparse sampling results in low-quality sub-reconstructions, tracking motion directly is challenging. While final image quality could in principle guide artifact correction, conventional regularizers do not accurately reflect photoacoustic image quality. Here, we introduce deep preferential evolution (DPE), a derivative-free optimization framework where a learned image comparator guides evolutionary search over reconstruction parameters. By learning relative quality differences between same-target image pairs rather than absolute quality scores, the comparator generalized more robustly from simulation to in-vivo images (after unlabeled domain calibration) than an absolute scorer. Comparator-based DPE successfully corrected synthetic motion across diverse anatomies and backgrounds, and it mitigated artifacts from natural, unconstrained motion in human palm images. These results demonstrate that pairwise learned comparison can provide a transferable optimization objective for high-dimensional image restoration when labeled experimental training data are scarce.

This paper investigates the feasibility of deploying quadruped walking robots for the automation of work in roof environments. While quadrupeds have demonstrated versatility across various domains, their large-scale deployment remains limited, partly due to lack of application-specific designs. Roof environments represent a novel and unexplored use case, combining high safety risks for human workers with repetitive, strenuous tasks that could benefit from robotic assistance. A dedicated test rig of a roof's surface was designed to evaluate the baseline performance of a commercial quadruped, the Unitree Go2, in this new environment. Experiments revealed that standard ball feet are inherently inadequate for locomotion on sloped roofs: slippage increased quadratically with incline angle, get-up and lie-down sequences were only possible on small inclines, and critical failures already occurred regularly on moderate inclines of 25{\deg}. This work provides the first systematic assessment of quadruped locomotion in roof environments, highlighting both the potential and the current limitations of this application and establishes a baseline for future research. Effective solutions will require a combination of task-oriented foot designs, advanced contact mechanics and environment-specific control strategies, such as reinforcement learning for roof-adapted gaits.

The entanglement structure of a bipartite pure state is characterized by its entanglement spectrum, or equivalently, by the family of Rényi-$k$ entanglement entropies with integer $k$. Taking the difference of two such entropies defines a quantity known as an entanglement spread, that is monotonous under local operations, and that vanishes if and only if the entanglement spectrum of the state is flat. We introduce a multipartite generalization of this notion which, for a fixed number $D\geq 3$ of parties, results in a collection of maps indexed by pairs of $D$-edge-colored graphs (obeying some condition). Each member of this collection takes the form of a difference of two multipartite Rényi entanglement entropies, each associated to a local unitary polynomial invariant (known in this context as a trace-invariant), and is shown to be monotonous under local operations. We then argue that a previously introduced family of so-called hypergraph-tensor (HT) states can be understood as a multipartite counterpart to the family of flat bipartite states. Indeed, we first prove that, when $D=3$, a tripartite pure state is HT if and only if it minimizes a particular (infinite) family of entanglement spreads. Second, we embed the set of HT states into the much larger family of spectral hypergraph-tensor (SHT) states, defined by a new Ansatz we introduce. We then prove that HT states can be uniquely characterized as the minimizers of some fixed entanglement spread among SHT states, for arbitrary $D\geq 3$. We also investigate SHT states in their own right: in particular, we characterize their orbits under local unitary transformations. Finally, along the way, the asymptotic large-$N$ expectation values of a number of entanglement spreads are computed in the Haar-random state of local dimension $N$.

The development of multimodal sensing capabilities is crucial for realizing immersive communications and enabling rich, natural remote interactions in future sixth-generation~(6G) communications. However, transmitting high-dimensional sensory streams places substantial pressure on wireless resources and leaves a fundamental question unresolved: what information about the underlying physical process should be preserved across wireless delivery? To address this issue, we establish an event-native immersive-communication framework in which a service-relevant physical event defines the communication object, while event beliefs represent the information available to transceiver agents before and after wireless delivery. Based on this event-native framework, we further propose event-belief deficiency (EBD) to evaluate quality of experience (QoE) in immersive communications, which differs from the conventional normalized mean-squared error (NMSE), as NMSE can be insensitive to physically distinct procedures whose stream distortions lie in a similar range. For Gaussian event beliefs with mode-separable delivery over Rayleigh fading, we derive the log-det EBD, its induced received signal-to-noise ratio (SNR) threshold, the exact outage probability, and the required transmit SNR. Simulation results with a physics-driven source show that stream NMSE can remain nearly unchanged across physically distinct event procedures, whereas log-det EBD reliably reflects their event-level uncertainty. Relative to a mean-squared-error (MSE)-oriented interface, event-native delivery reduces normalized log-det EBD by up to $63.6\%$ and lowers the required average received SNR by $3.47$~dB under the evaluated outage constraint, substantiating the effectiveness of the proposed framework.

Runtime monitors are increasingly used to improve the reliability of LLM-based coding agents by inspecting execution trajectories and delivering corrective guidance upon detecting misbehavior. However, their effectiveness remains limited by static guidance triggering schemes. Existing monitors rely either on fixed inspection intervals, missing timely guidance during severe misbehaviors while incurring unnecessary overhead during healthy execution, or on rigid heuristic rules, failing to detect complex reasoning errors. To address these limitations, we propose Cadence, a dynamic monitoring framework that adaptively schedules inspections and delivers guidance according to the agent's real-time execution health. Cadence consists of two core modules: a two-tier intervention module and an inspection scheduler. The intervention module delivers advisory-level guidance for normal executions and minor lapses, while providing replacement-level guidance for severe misbehaviors. Driven by the intervention level, the scheduler adjusts the inspection frequency by tightening supervision after replacement-level guidance and relaxing it after advisory-level guidance. Evaluated on 300 SWE-bench Lite tasks across two distinct agents, mini-swe-agent and Moatless, Cadence achieves the highest resolve rate among all evaluated monitors. Specifically, Cadence outperforms vanilla agents by 25.33% (+76 resolved tasks) on mini-swe-agent and 15.67% (+47 resolved tasks) on Moatless, while maintaining competitive token efficiency compared to state-of-the-art baselines.

Let $G$ be a locally compact group, let $\Gamma$ be a lattice in $G$, and let $\eta$ be a spread-out probability measure on $G$. A Furstenberg discretization of $\eta$ to $\Gamma$ is a probability measure $\mu$ on $\Gamma$ such that every $(G,\eta)$-stationary space is also $(\Gamma,\mu)$-stationary. For cocompact lattices $\Gamma$ and under mild regularity conditions on $\eta$, we construct Furstenberg discretizations satisfying finite moment conditions of arbitrary order with respect to arbitrary prescribed subadditive functions. Our approach relies on a rather general study of differential entropy and Lyapunov exponents in the setting of locally compact groups. We relate Lyapunov exponents to spectral radii in weighted $L^{1}$-algebras and prove vanishing results for weights coming from length functions. Additionally, we prove that if $G$ has the property of rapid decay or the Kunze–Stein property, this yields entropy formulas for stationary actions whose Koopman representation is weakly contained in the left-regular representation. As consequences, we obtain preservation results for Poisson boundaries under discretization and characterize Zimmer amenability of stationary actions in terms of weak containment and maximal Furstenberg entropy.

Climate multistability and tipping points are fundamental properties of planetary climates that depend sensitively on climate feedbacks. We introduce the Geneva Energy Balance Model (Gen-EBM), a new 1-D latitudinal EBM for rapid exploration of terrestrial planet climates, and use it to investigate how planetary rotation, eccentricity, and thermal inertia shape climate attractors and multistability. Gen-EBM is implemented in Rust and builds on previous exoplanet EBMs by incorporating a temperature-dependent outgoing longwave radiation prescription spanning Earth-like, runaway-onset, and post-runaway greenhouse regimes. We construct bifurcation diagrams from ensembles of simulations and explore the effects of rotation rate, orbital eccentricity under the mean-flux approximation, and surface thermal inertia. Including post-runaway greenhouse states substantially enlarges the parameter space over which multiple climate states coexist. Within our model framework, slow rotators approach the spatially homogeneous limit and maintain broader temperate stability ranges, whereas fast rotators develop strong equator-to-pole temperature gradients that narrow the temperate branch. Under the mean-flux approximation, increasing eccentricity enhances climate variability and can alter the attractor structure itself. The critical eccentricity at which temperate climates disappear depends strongly on thermal inertia, with ocean-rich planets remaining stable to larger eccentricities than land-dominated planets. Gen-EBM therefore broadens rapid parameter-space exploration to climates spanning temperate, runaway-onset, and post-runaway regimes. Its computational efficiency and flexibility make it a valuable bridge between simple climate models and 3-D general circulation models.

Multimodal large language models have made remarkable progress in bridging vision and language, facilitating various perception tasks essential for human-machine interaction, robotics, and autonomous driving. However, existing MLLM-based perception methods predominantly rely on text-based coordinate representation, which suffers from excessive token overhead, or fixed-range quantization, which suffers from range and precision constraints, especially for 3D domains with unbounded spatial range and high localization accuracy requirements. To address these challenges, we propose a dynamic vector decoding method named DVD, which unifies the representation of 2D and 3D perception tasks. Specifically, we first transform diverse perceptual representation (i.e., 2D bounding boxes, 2D masks, and 3D bounding boxes) into 1D vector sequences, which are then mapped to compact discrete tokens in the high-dimensional space. Then, a lightweight de-tokenizer enables seamless integration with MLLMs by decoding output tokens back to original 2D and 3D perceptual representations. Extensive experiments on 2D and 3D perception benchmarks including RefCOCO series, SUN-RGBD, KITTI, Hypersim, nuScenes demonstrate that DVD achieves superior performance in 2D and 3D tasks and reduces significantly the token overhead and inference latency. DVD provides an efficient and general framework for integrating perception capabilities into MLLMs, overcoming the inherent limitations of existing methods.

Accurate workload forecasting is critical for elastic resource provisioning in web-scale cloud services, where distribution shifts driven by viral content, product launches, and user behavior degrade offline-trained models rapidly. Naive online learning recovers accuracy but incurs prohibitive per-step compute cost. We propose AdaptLSTM, an adaptive online framework that detects drift via validation-calibrated thresholds and applies selective, targeted updates. On the Alibaba Machine Trace, AdaptLSTM recovers 54% of Naive Online's improvement at 20% cost ($2.7\times$ efficiency, $p=0.002$ over 10 seeds). On the more volatile Container Trace, it achieves 96% at 20% cost ($4.8\times$ efficiency, $+75\%$ MAE reduction over Static). Unlike classical drift detectors (ADWIN, DDM, Page-Hinkley) which fail to trigger on regression-scale error streams, AdaptLSTM fires 42 times over 301 steps and outperforms matched-budget baselines. Wall-clock profiling shows $1.33\times$ throughput gain and 45% update-time reduction. The framework is model-agnostic: identical Pareto patterns hold for LSTM, GRU, and Transformer backbones.

We propose and experimentally demonstrate an asymmetric key-generation scheme in which public and private keys are derived from a six-qubit photonic entangled state. A six-qubit entangled state is generated from two photons, each carrying one polarization and two path qubits. The state is prepared in an equal superposition of eight of the sixty-four six-qubit basis states, in which each photon's three qubits form a codeword of the classical [3,2,2] even-parity code, and are distributed between the two parties, Alice and Bob. This ensures, each triple is a uniformly random codeword and the two codewords are locked together through the correlation. The parity constraint is a local stabilizer, so each party verifies it on its own data every round, and eliminates the bit flip errors arising from imperfections, detector dark counts and multiple occupancy before it enters the raw key. A single publicly announced bit, chosen at random from either of the path qubits, allows each party to reconstruct the other's full triple while leaking no information to third party. We realize the desired six-qubit state using a Sagnac-based type-II SPDC source, reporting a Bell-CHSH parameter S = 2.798 +/- 0.008, by implementing gate operation on polarization and path degree's of freedom. This approach provides a physics-based alternative to public-key cryptosystems built on computational hardness assumptions. A t-bit string generated from multiple rounds for encryption will be intrinsically random. Without the private key, one needs at least O(2^t) runs on an t-qubit quantum system to find the matching bit to decrypt.

We revisit the relation between the Kontsevich commutative graph complex and the homology of $\GL(n,\Z)$ found by Brown–Chan–Galatius–Payne using the sharbly complex of Ash–Miller–Patzt.

We demonstrate how horizon symmetries of AdS black holes are realised in the hydrodynamic actions for the dynamics of the dual stress tensor. A recent approach for obtaining such actions involves a choice of horizon boundary conditions, and we show that diffeomorphisms that preserve these give rise to symmetries of the corresponding hydrodynamic action. We obtain explicit hydrodynamic actions for small amplitude perturbations of black holes in JT and AdS$_3$ gravity using this approach and demonstrate explicitly the existence of these symmetries. For a natural choice of boundary conditions, the resulting actions manifestly realise gauge symmetries previously proposed for effective theories of maximal chaos.

We discuss the recently introduced concept of hyperquivers, due to Muller, Nanda, and Seigal, from the point of view of Kähler and hyperkähler quotients. In particular, we show that the Kähler hyperquiver variety ${\mathcal M}$, corresponding to a hyperquiver with a single hyperedge, is a projective variety isomorphic to the geometric quotient of the space of tensors with maximal multilinear rank. Moreover, the hyperkähler hyperquiver variety corresponding to doubling of this hyperquiver can be identified with the linear scheme corresponding to the sheaf of reflexive $1$-forms on ${\mathcal M}$.

We investigate the best constants associated with several types of Moser–Trudinger inequalities within the framework of the Finsler metric in $\mathbb{R}^n$. By employing a convex-symmetrization-free approach, we first establish both the critical and subcritical anisotropic singular Moser–Trudinger inequalities. We further study anisotropic Moser–Trudinger inequalities in both singular and nonsingular cases under the exact growth condition, highlighting the optimality of the best constant as well as the sharp exponent appearing in the denominator. To further enrich the theory, we introduce quasi-conformal-type transformations adapted to the Finsler metric setting to derive several new variants of such inequalities. We also characterize the attainability and nonattainability of maximizers for a generalized version of anisotropic Moser–Trudinger inequalities with the exact growth and explicitly determine the corresponding supremum values. As an application of these inequalities, we analyze the existence and nonexistence of positive ground state solutions to a class of $n$-Finsler-Laplace equations involving constant potential in $\mathbb{R}^n$, where the nonlinearity exhibits a critical exponential growth at infinity.

We present the `Bias of Overdensities in Large-scale Tracers on the Sphere' (BOLTS) model, a novel analytic galaxy bias model for projected fields on the sphere that incorporates stochasticity and non-locality already at linear order while enforcing physicality and statistical isotropy. Rather than as a deterministic transfer function, we model galaxy bias as a statistically isotropic random field, allowing stochasticity to enter through fluctuations in the bias itself. The construction yields an explicit decomposition into a linear, non-local stochastic and deterministic components in harmonic space. We fit the model parameters to the projected power spectra measured in large-volume hydrodynamical simulations (FLAMINGO), enabling sampling of galaxy populations from simulated matter fields while conditioning on galaxy properties such as halo mass or redshift. By construction, the model reproduces the two-point statistics down to the simulation resolution, and without being calibrated on it, BOLTS recovers the equilateral bispectrum within the sample variance of the simulation down to comoving scales of $\mathcal{O}(10 \, \mathrm{Mpc})$ for halo masses $ M_{\rm{h}} > 10^{11.5}\,\rm{M}_{\odot} $ over redshifts $0 < z < 3$. Relative to local bias prescriptions, it more accurately captures amplitude-phase correlations and mode coupling in the measured wavelet phase harmonics wherever the stochasticity of the tracers exceeds their discreteness, including low redshifts and lower halo masses $M_{\rm{h}} = 10^{11.5}\,\rm{M}_{\odot}$ where non-linearities become important. This model enables efficient field-level forward modelling for simulation-based inference and model comparison with large datasets from forthcoming galaxy surveys including Euclid, Rubin LSST, and Roman, while improving the accuracy of galaxy bias modelling with respect to standard linear deterministic models.

We study a class of expanding Markov maps on the unit interval, which includes sofic \(\beta\)-transformations, Gauss maps, tent maps and cookie-cutter maps. We investigate the quantitative recurrence property for points that are dynamically badly approximable, namely, points whose orbits eventually remain a positive distance from a given point. We show that the Hausdorff dimension of the intersection of a recurrence set and a badly approximable set is determined by the same pressure function as that of the corresponding recurrence set. We further obtain the Hausdorff dimensions of two related intersections: recurrence sets with non-recurrent sets, and shrinking target sets with badly approximable sets.

The vanadium-based kagome superconductor CsV$_3$Sb$_5$ exhibits an intricate interplay between charge density wave (CDW) and superconductivity (SC). Substituting Ta for V will suppress the CDW order and enhance superconductivity. Here, we report a high-pressure study up to 48 GPa on Ta-doped Cs(V$_{0.86}$Ta$_{0.14}$)$_3$Sb$_5$ with enhanced $T_\mathrm{c}$ around 5.29 K and without CDW order. At low pressures, unlike the characteristic $``$M-shaped" temperature-pressure phase diagram of the pristine CsV$_3$Sb$_5$, the Ta-doped compound exhibits a distinct non-monotonic evolution. Initially, $T_\mathrm{c}$ drops slightly from 5.29 K at ambient pressure to 4.90 K at 0.33 GPa, before increasing to a maximum of 5.70 K at 0.61 GPa. Upon further compression, $T_\mathrm{c}$ decreases continuously to 0.98 K at 12.3 GPa. At higher pressures, $T_\mathrm{c}$ rises again, reaching 4.46 K at 47.7 GPa. This evolution of $T_\mathrm{c}$ establishes two superconducting domes under pressure, which are similar to those in CsV$_3$Sb$_5$. Our results demonstrate that pressure-induced double-dome superconductivity is intrinsic to these V-based kagome superconductors, even in the absence of long-range CDW order.

Omnimodal embeddings naturally involve both shared representations and modality-specific features across heterogeneous inputs. However, existing omnimodal embedding methods often rely on a single shared parameter space over mixed-modality data, limiting structural separation between universal and modality-specific representations. To address this, we propose Syn-Omni, a unified framework for structured omnimodal adaptation with modality specialization and controlled cross-modal collaboration. Specifically, we introduce Orthogonal Modality-Expert LoRA (OME-LoRA), which decomposes adaptation into a shared LoRA path for universal semantics and modality-expert LoRA paths for modality-aware specialization. Furthermore, Progressive Synergy Routing (PSR) enables experts to first establish modality-specific priors, then gradually interact with other modality-experts for cross-modal synergy. Evaluated across 81 diverse tasks spanning image, video, audio, and audiovisual modalities, Syn-Omni consistently outperforms omnimodal baselines, demonstrating the effectiveness of structured specialization and cross-modal progressive collaboration.

Let $A$ and $X$ be connected based CW complexes with $H_1(A;\mathbb Q)\neq 0$, and let $m\geq 1$ be the least degree with $\widetilde H_m(X;\mathbb Q)\neq0$. We prove that the Bousfield–Kan rational completion map of $A\vee X$ induces a map on $H_{2m}(-;\mathbb Q)$ whose cokernel has dimension at least $2^{\aleph_0}$. In particular, $A\vee X$ is $\mathbb Q$-bad.

Let $\Gamma<\operatorname{PSL}_2(\mathbb R)$ be a torsion-free, non-elementary, finitely generated Fuchsian group with parabolic elements, and let $\rho:\Gamma\to G$ be a type-preserving, Zariski dense, positive representation into a connected split semisimple real algebraic group. We prove quantitative local mixing for Bowen–Margulis–Sullivan measures on $\rho(\Gamma)\backslash G/M$, where $M$ is the centralizer of a maximal split torus in a compatible maximal compact subgroup. For every $u$ in the interior of the limit cone of $\rho(\Gamma)$, correlations of smooth compactly supported functions along $\exp(tu)$, normalized by $t^{(\operatorname{rank}_{\mathbb R}G-1)/2}$, admit a complete asymptotic expansion in integer powers of $t^{-1}$. We also obtain a uniform Gaussian asymptotic for transverse displacements, with an integrable remainder. We deduce asymptotics for matrix coefficients of the quasi-regular representation on $L^2(\rho(\Gamma)\backslash G)$ and for orbital counting in Riemannian balls. More generally, these conclusions hold for Zariski dense, relatively Borel Anosov representations of $\Gamma$ satisfying a peripheral root-balance condition. This includes relatively Borel Anosov representations into split simple groups of rank at most three and self-joinings of type-preserving geometrically finite real hyperbolic representations. To prove these results, we develop an intrinsic cusp geometry on the limit set of $\rho(\Gamma)$ in the Furstenberg boundary and use it to construct a countable Markov coding. We establish exponential moment bounds and uniform distortion estimates for the unbounded vector-valued return cocycle. Using peripheral Cartan growth and Zariski density, we establish the quantitative non-integrability needed for the spectral analysis.

We study global regularity and the infinite Prandtl number limit for temperature patches of the two-dimensional nondiffusive Boussinesq system on $\mathbb R^2$, with velocity dissipation $\Lambda^{2\alpha}$, $\frac12<\alpha\leq1$. We establish global well-posedness for $\theta_0\in L^1\cap L^\infty$ and divergence-free $u_0\in W^{1,p}$, $2\leq p<\infty$. Under suitable profile and striated regularity assumptions, we prove global persistence of $C^{1,\gamma}$ and $C^{2,\gamma}$ patch boundaries for every $0<\gamma\leq1$, allowing nonconstant profiles and including the Lipschitz endpoints $W^{2,\infty}$ and $W^{3,\infty}$. The velocity gradient and boundary regularity estimates are uniform in $\mathrm{Pr}\in[1,\infty)$ on each finite time interval. Uniform global $L^r$ velocity bounds hold for suitable finite $r$ when $\alpha<1$, and at $\alpha=1$ for zero-mean initial temperatures with finite first absolute moment. Such bounds fail at $\alpha=1$ for compactly supported nonzero-mean data. For temperature patches, we justify the infinite Prandtl number limit in the original frame when $\alpha<1$ or the initial temperature has zero mean, and in a moving frame otherwise. The limit is the unique normalized global weak solution of the (fractional) Stokes-transport system and, importantly, preserves the patch structure and boundary regularity.

We study the positive Helson form $h_0[a,b]=\sum_{m,n\ge1}\alpha(mn)a_n\overline{b_m}$ on the finitely supported sequences $c_{00}\subset\ell^2(\mathbb{N})$, where $\alpha(n)=\int_{\mathbb{R}}n^{-s}d\mu(s)<\infty$ for a finite positive Borel measure $\mu$. Under the Carleman condition $\sum_{k\ge1}\alpha(4^k)^{-1/(2k)}=\infty$, closability of $h_0$ is equivalent to $\sqrt{n}\alpha(n)\to0$, and hence to $\mu((-\infty,1/2])=0$. For measures concentrated on $(1/2,\infty)$, we identify the closure of the operator $N_0a=\sum_{n\ge1}a_nn^{-s}$, defined on $c_{00}$, with its maximal realization from $\ell^2(\mathbb{N})$ to $L^2(\mu)$. We further prove that the sequences $a\in c_{00}$ satisfying $\sum_{n\ge1}a_n/\sqrt{n}=0$ form an operator core for the positive self-adjoint operator associated with the closure of $h_0$.

A fixed network of McCulloch-Pitts threshold units with weights in {-1,0,1} can hold other threshold networks in its state and run them: the state is a ring of banks of records, each record a unit of a stored network, and each step evaluates one record. We use such a network to carry out von Neumann's universal construction and self-reproduction exactly. As a cellular automaton keeps its rule, the fixed network keeps its weights, and what reproduces is a stored network. A constructor of 143 records reads the description of a network from its tape, builds that network in the next bank, copies the description onto the next tape and hands control to what it built; started on its own description, it rebuilds itself, weights included, in every generation. The scheme scales to a universal computer. A SUBLEQ computer of 17,598 ternary units, stored as 36,080 records and running a program of 27 instructions, builds any network that fits a bank and reproduces itself in the same way, at every word width from eight bits on; run directly, it emits the serialization of its own weights, memory and tape. Integer pre-activations give every orbit a margin of 1/2, and replicating each unit r times multiplies it by r. That suffices against noise of any size on the pre-activations, but against von Neumann's output flips only below a threshold inversely proportional to the fan-in. These results are proved in Rocq.

Pretrained audio encoders are reused for downstream tasks that are often unknown when the encoder is trained, so their usefulness depends partly on which signal properties survive the pretext objective. We study this retained information through paired source reconstruction. Using a shared Stable Audio Open latent diffusion decoder, we reconstruct five-second, 44.1-kHz stereo music from frozen representations produced by supervised classifiers (VGGish, ConvNeXt), an audio-text contrastive model (CLAP), and a waveform-reconstruction model (EnCodec). These objectives impose different pressures to preserve source detail, while their exposed interfaces vary substantially in temporal and spectral resolution. Evaluating on the Million Song Dataset (MSD), we find clear differences in reconstructability across encoder families, while within encoder comparisons show improved recovery when finer temporal or spectral structure is exposed. Even compressed task oriented embeddings support reconstructions that preserve measurable source specificity and high level musical content.

We study real-time motion planning in dynamic hazard fields through a controlled comparison between classical planning and learning-based methods. Rather than introducing a new planner, we construct a unified benchmark in which representative classical and learning-based methods face the same environments, motion constraints, information assumptions, and evaluation metrics. The test environment consists of planar domains populated with rotating sprinkler-like hazards that generate time-varying forbidden regions via sweeping angular sectors. Our results show a clear regime shift. In deterministic environments, classical planners achieve near-perfect success and higher-quality paths, though sometimes at the cost of substantial planning or replanning time. Under stochastic obstacle dynamics, however, online search becomes strongly budget-sensitive: low budgets lead to frequent failure, while high budgets improve success at the cost of latency and longer trajectories. PPO-based policies, trained under the same scenario distribution, consistently outperform in latency, success rate, and path quality in these stochastic regimes. Overall, the results indicate that uncertainty in obstacle evolution, more than partial observability, is the dominant factor determining which planning paradigm is practically effective for the problem at hand.

Wearable augmented reality (AR) assistants are moving toward continuous real-world interaction, where they perceive the user's activity through first-person video and audio and provide timely spoken guidance without being explicitly asked. While proactive video assistants, spoken dialog systems, and egocentric task understanding have each advanced rapidly, existing systems do not address the joint problem of deciding when to speak and what to say from continuous first-person streams. We introduce EgoVoice, a framework for training and evaluating proactive egocentric spoken assistants. From HoloAssist video recordings of real human instructors, we construct clean audio streams through source separation and speech resynthesis, and convert each video session into a format where the model must decide at each moment whether to remain silent or provide spoken guidance. We fine-tune an omni-modal LLM with our data, and further improve its proactive intervention behavior with direct preference optimization. Experiments across closed and open-source models show that existing systems rarely produce well-timed, meaningful proactive interventions, while EgoVoice yields clear improvements in intervention timing, content relevance, and human preference over the zero-shot backbone.