Papers

Many emerging applications, from computational biology to digital twins and urban planning, rely heavily on three-dimensional spatial joins over polyhedral meshes. These joins comprise computationally-intensive triangle–triangle intersection tests that pairwise compare the faces of polyhedral meshes. Since each mesh may contain thousands of faces, the resulting cost challenges the responsiveness of spatial data management techniques. Existing techniques follow the filter-and-refine paradigm, accelerating either the filtering step through indexing or the refinement step through progressive mesh compression combined with GPU parallelization of triangle–triangle tests. However, the former neglects the high cost of intra-geometry refinements, whereas the latter lowers this cost but still relies on the same pairwise triangle–triangle tests. In this paper, we introduce Pierce, an approach that reformulates three-dimensional spatial joins over complex polyhedral meshes as ray-tracing operations and leverages the hardware ray-tracing units (RT cores) of modern GPUs to accelerate query execution. Our approach casts rays along the edges of one mesh against a spatial hierarchy built over the other, performing ray–node tests at the internal levels to prune distant geometries and ray–triangle tests at the leaves to identify intersecting meshes, both of which RT cores accelerate in hardware. We evaluated Pierce on real and synthetic data against multiple baselines, demonstrating more than two orders of magnitude speedup on digital pathology data compared to the state-of-the-art approach.

Let $G$ be a group and $k$ be a commutative ring. The Gorenstein homological dimension $\text{Ghd}_k G$ and the Gorenstein cohomological dimension $\text{Gcd}_k G$ of $G$ over $k$ are defined as the Gorenstein flat and the Gorenstein projective dimension, respectively, of the trivial $kG$-module $k$. We prove that the Gorenstein cohomological dimension of a countable group $G$ is at most one more than its Gorenstein homological dimension and, more generally, that $\text{Gcd}_k G\le\text{Ghd}_k G+m+1$ for every $m\ge0$ and every group $G$ of cardinality at most $\aleph_m$. When the supremum sfli$k$ of the flat dimensions of the injective $k$-modules is finite, this gives $\text{Ghd}_k G\le\text{Gcd}_k G\le\text{Ghd}_k G+1$ for every countable group $G$, so that the two dimensions are finite simultaneously. These results are Gorenstein analogues of Bieri's inequality for the homological and the cohomological dimension of countable groups. They rest on a module-theoretic theorem of independent interest, which is a Gorenstein version of results of Jensen and Osofsky on the projective dimension of flat modules: over an arbitrary ring, every $\aleph_m$-presented Gorenstein flat module has projectively coresolved Gorenstein flat dimension at most $m+1$. An appendix characterizes the modules of PGF-dimension at most $n$ as the direct summands of the strongly $n$-PGF modules.

Contact-rich precision insertion is a key manipulation skill in robotic assembly. Tight clearances make insertion more sensitive to alignment errors and prone to collisions and jamming, while variations in geometry and clearance across parts further complicate policy reuse. We present a reinforcement learning framework that trains insertion policies entirely in simulation for direct deployment without real-world demonstrations or policy fine-tuning. By combining target poses with compact three-dimensional fingertip force feedback, the policy learns to search for alignment and correct its motion despite errors in the estimated hole position. A decoupled gated reward coordinates alignment and insertion. Force-signal smoothing and state-independent standard deviations stabilize the learning process. The resulting policies perform real-world insertion across multiple hole geometries with a minimum nominal clearance of 0.02 mm and improve success while reducing peak contact forces under hole-position errors. Cross-clearance and cross-geometry evaluations further confirm policy generalization. The system achieved the first perfect score of 20/20 on ManipulationNet's peg-in-hole benchmark under its Human-in-the-Loop protocol, with fully autonomous insertion motions. A single policy trained only on a simulated hexagonal insertion task achieved an overall success rate of 95.0% across eight unseen real-world insertion tasks. These results show that learning entirely in simulation can yield precision insertion skills that can be deployed directly and reused across real-world tasks. The project website (https://mzhsoul.github.io/InsertAnything/) provides open-source simulation and real-robot experiment scripts, assets, and trained checkpoints.

Recent advances in vision foundation models (VFMs) have shown remarkable capabilities across diverse unimodal visual tasks. However, adapting VFMs to referring image segmentation (RIS) typically necessitates precise vision-language alignment via full fine-tuning, incurring substantial computational overhead and risking catastrophic forgetting. While existing parameter-efficient fine-tuning (PEFT) methods enable safe knowledge transfer with minimal training costs, they predominantly operate independently within individual modalities or focus exclusively on unidirectional guidance from language to vision, overlooking progressive cross-modal interaction and visual feedback for textual refinement. To address these limitations, we propose $\textbf{B}$idirectional $\textbf{R}$eciprocal $\textbf{L}$earning ($\textbf{BRL}$), a novel adapter-based PEFT framework that facilitates hierarchical, bidirectional information flow within both token-mixing and channel-mixing layers of frozen foundation models. Specifically, BRL introduces two complementary lightweight modules. The Reciprocal Attention Adapter (RAA) performs cross-modal query-key exchanges at the token level, enabling visual and linguistic tokens to mutually attend to each other for fine-grained spatial grounding. The Reciprocal Gate Adapter (RGA) generates cross-modal gating signals at the channel level, allowing global semantic context from one modality to adaptively recalibrate channel activations of the other. Extensive experiments on RefCOCO, RefCOCO+, and RefCOCOg benchmarks demonstrate the superiority of BRL over prior RIS methods, achieving state-of-the-art performance while requiring less than 0.5% backbone parameter updates. Code and models will be released at https://github.com/xiaoqiang-lu/BRL.

CUR approximation is a popular approach for constructing an interpretable low-rank approximation of a matrix. There are many approaches for constructing the CUR approximation, many of which are based on the SVD. Results in the literature bounding the quality of the approximation usually rely on the assumption that all or part of the SVD is computed exactly. In this work, we relax this assumption and show how the quality of the approximation is affected by an inexact SVD. Moreover, we analyze the effect of finite precision arithmetic on the DEIM-CUR method. Our analysis suggests guidelines for selecting the working precisions for the SVD and the DEIM index selection algorithm. In particular, it suggests that in many cases one can use very low precisions for these computations without significantly impacting the approximation quality. A set of numerical experiments is presented to demonstrate the theoretical results.

We investigate multipartite entanglement in a particular family of pure $n$-qubit hypergraph states through a statistical-mechanics framework, where the average bipartite purity maps onto an effective Hamiltonian of $2^n$ classical binary spins. In this correspondence, each hypergraph state uniquely corresponds to a classical spin configuration, while temperature serves as a control parameter that continuously interpolates between a uniform ensemble of random hypergraph states at high temperature and maximally multipartite entangled states (MMES) at zero temperature. Remarkably, the exponential of the zero-temperature entropy directly gives the number of MMES within the set of hypergraph states. For small system sizes ($n \leq 5$), we perform an exact enumeration, fully characterizing the energy landscape and associated thermodynamic observables, and validating known MMES counts. For larger systems ($n = 6$ and $7$), where exact methods become computationally infeasible, we employ simulated annealing and parallel tempering algorithms to efficiently sample the exponentially large state space. Our analysis yields quantitative predictions of the number of MMES and reveals how entanglement is statistically distributed across the sets of hypergraph states. These results establish hypergraph states as an ideal platform for investigating multipartite entanglement through thermodynamic methods, offering both computational advances and physical insights into the structure of quantum entanglement in restricted families of quantum states.

Visuomotor policies trained from a few demonstrations may reproduce demonstrated trajectories without reliably following changes in object position. Existing approaches with explicit attention typically obtain spatial priors from human annotation or visual models. We introduce TACIT (tactile contact informs attention), which uses measured tactile contacts from teleoperated demonstrations to supervise spatial attention without additional point annotation. Gaussian targets over preceding camera point clouds supervise an attention head whose pooled output conditions a visuotactile diffusion policy. Targets are used only during training; tactile observations remain inputs at inference. In the primary real-robot benchmark, with ten demonstrations per task and five demonstrated placement regions, TACIT achieves 66.7% success on ball placement and 73.3% on peg insertion, compared with 10.0% and 20.0% for input-matched 3D visuotactile fusion and 20.0% and 43.3% for vision-only DP3. TACIT enters the 150 mm palm-to-object approach region within 12 seconds in all 30 trials per task; all remaining failures occur after arrival. Across three training seeds on real ball and simulated peg, TACIT outperforms input-matched fusion and an architecture-matched control without explicit attention supervision, supporting the contribution of supervision beyond branch capacity. Pre-contact and contact-time supervision show no consistent ordering. These results demonstrate that measured tactile contact provides effective spatial supervision for approach behavior from few demonstrations within the evaluated workspace.

In environmental feedback systems, self-interested behaviors of rational agents often undermine cooperation and environmental sustainability. Although punitive incentive mechanisms are widely recognized as effective in addressing such social dilemmas, the timing of their implementation under different environmental conditions remains insufficiently understood. In this paper, we develop a multi-agent environmental feedback game framework with coupled incentive intensities across resource states. We investigate how system dynamics vary with incentive intensity under both resource-abundant and resource-scarce conditions. Theoretical analysis shows that imposing penalties in resource-abundant states can transform the system from a tragedy of the commons into a bistable regime that supports full cooperation. In contrast, imposing penalties in resource-scarce states leads to complex dynamical behaviors, including interior stability, heteroclinic cycles, and Hopf bifurcations, which hinder the emergence of stable cooperation. These results highlight the importance of timing in incentive regulation. Proactive intervention under favorable environmental conditions is more effective in sustaining cooperation than delayed enforcement after environmental degradation.

Model merging combines separately fine-tuned checkpoints by arithmetic on their weights, and is now a routine way to assemble capabilities cheaply. We ask what it does to emergent capabilities: behaviors that arise from fine-tuning but were never an explicit training target. Studying two independent testbeds (activation oracles and emergent-misaligned models) across three model families, we find that the answer is threefold. First, merging preserves an emergent capability that both parents carry: merging two misaligned checkpoints retains most of their broad misalignment across the whole mixing range. Second, merging cannot create an emergent capability that is superadditive in its parents: no weighted merge of two single-task oracles reaches the jointly-trained oracle's auditing ability. Third, when only one parent carries the capability, merging dilutes it faster than the trained capability that accompanies it: the gap is significant in most settings.

Puncturable signatures, proposed by Bellare et al. (EUROCRYPT 2016), allow a signing key to be punctured (updated) so that it loses the ability to sign particular messages while retaining the ability to sign all others. Halevi et al. (ASIACRYPT 2017) introduced prefix puncturable signatures, in which the signing key can be punctured with respect to a target prefix so that it cannot sign messages whose prefixes match the target prefix. So far, several generic constructions of prefix puncturable signature schemes have been proposed, including constructions based on identity-based signatures (IBS) (ESORICS 2022) and delegated constrained signatures (IEEE Trans. Inf. Forensics Secure. 2024). However, these constructions suffer from drawbacks in terms of key size. When the prefix space is the set of all l-bit strings, the former construction requires a signing key consisting of 2^{l} IBS signing keys. The latter construction, when instantiated with a lattice-based delegated constrained signature scheme, yields a punctured signing key whose size grows quadratically with the number of puncturing operations Q^{Punc}. In this paper, we present a generic construction of prefix puncturable signatures from hierarchical identity-based signature (HIBS) schemes. When the prefix space is {0,1}^{l} and our construction is instantiated with the lattice-based HIBS scheme HIBS^{GPV} by Ruckert (PQC 2010), our construction achieves a punctured signing key size bounded by O(lQ^{Punc}).

Carrier-induced helical magnetism can arise in interacting one-dimensional systems coupled to localized moments. Here, we investigate the coupled-wire sliding-Luttinger-liquid counterparts with and without valley degrees of freedom, using isolated Tomonaga-Luttinger liquids as reference limits. The carrier spin susceptibility mediates a Ruderman-Kittel-Kasuya-Yosida interaction that selects the helical ordering wave vector, while interchannel correlations lock the relative helix phases and stabilize a collective quasi-two-dimensional texture. Using a variational treatment, we estimate the helix-induced partial gap and analyze the reconstruction of the remaining gapless carrier modes. To probe the spatial texture through transport, we incorporate the helix into an anisotropic superconductor-normal-metal-superconductor Josephson junction motivated by the coupled-channel structure of twisted bilayer WTe$_2$. We exploit flux focusing near the junction interfaces to make an applied in-plane field a controlled probe of the spin helix. Relative to junctions without the helix, the helical exchange field modifies the central-lobe width and relative lobe weights. In the transverse-channel geometry, it also produces field-dependent side-lobe asymmetry and central-peak displacement, which remain negligible in the matched references for the parameters considered. The reconstructed carrier sector also exhibits modified local-density-of-states exponents, spin-relaxation behavior, and competing correlations, with distinct signatures in isolated and coupled-wire systems. Our results connect collective helical order in coupled-wire systems to carrier-sector reconstruction and identify field-tunable Josephson interferometry as a complementary transport probe of the spatial spin texture.

Tensor completion has attracted significant attention in both applications and theoretical research. Under standard uniform sampling, existing polynomial-time guarantees generally require more observations than the number of degree of freedom, motivating the study of a possible statistical-to-computational gap in highly missing regimes. Fortunately, in many practical scenarios, side information is available, which can provide valuable insights to mitigate these challenges. In this paper, we introduce an algorithm called Tensor Completion using Subspace Information (TCSI) that incorporates side information through an estimated subspace. Our approach first extracts the subspace from the available side information and then reformulates tensor completion as a matrix regression problem. We provide a theoretical analysis showing that, when accurate subspace information is available, the required sample complexity is reduced to nearly linear order in the uncoupled ambient dimensions, removing the coupled-mode dimension from the leading term. Leveraging the estimated subspace information, we obtain a less stringent sufficient signal-to-noise ratio requirement than those in several existing passive-uniform-sampling guarantees. Under additional mild conditions, we obtain a sharper statistical error bound. Our theoretical findings are supported by numerical simulations. We apply TCSI to the reconstruction of global Total Electron Content (TEC) maps and observe lower reconstruction errors than the compared methods in our experiments.

Two-point correlation functions are a standard summary statistic in cosmic shear and large-scale-structure analyses. Their values are, however, constrained: non-negativity of the underlying power spectrum restricts any admissible sequence of correlation coefficients $(r_1,\ldots,r_N)$ to a bounded convex region, described in the one-dimensional case by the recursive interval geometry of Schneider & Hartlap (2009). Their formalism introduces an affine variable $x_n$ that maps the admissible interval for $r_n$, given $r_1,\ldots,r_{n-1}$, to $[-1,+1]$. We identify $x_n$ with the partial autocorrelation coefficient $\alpha_n$ of the associated positive Toeplitz correlation matrix, a classical quantity in time-series analysis. The partial autocorrelations thus provide natural coordinates on the admissible region, each $\alpha_n$ varying independently in $[-1,+1]$. This identification makes the standard partial-autocorrelation toolbox directly applicable. The admissible intervals for $r_n$, cumbersome to obtain at higher order in the original determinant-based formalism, now follow from an $\mathcal{O}(N^2)$ recursion at arbitrary order. The inverse hyperbolic tangent used in the quasi-Gaussian likelihood construction of Wilking & Schneider (2013) becomes Fisher's $z$-transformation of partial autocorrelations, providing a classical statistical interpretation of its empirical Gaussianising effect. Numerical experiments illustrate the practical use of these natural coordinates in the tested one-dimensional settings. Higher-dimensional isotropic constraints require additional geometric input and lie outside the direct scope of this identification.

Pneumatic proprioceptive actuators integrate actuation and sensing for soft robots that attract interest due to functional potential. Existing approaches often suffer from assembly errors or stress concentrations caused by heterogeneous materials. In this work, we propose the Monolithic Force-Proprioception Soft (MFPS) design and fabrication method that integrates an Asymmetric Origami Bending (AOB) chamber and a Force-Proprioception Soft (FPS) sensor with single material through one-step Fused Deposition Modeling (FDM) fabrication. Based on the resistance response to strain of conductive thermoplastic polyurethane (TPU), we design and analyze the structure of the FPS sensor, and conduct parametric analysis on the sensing characteristics. The FDM fabrication parameters of the MFPS actuator are analyzed, followed by actuator fabrication and characterization of the actuation and proprioception performance. Experimental results show that the MFPS actuator achieves a bending angle of 40{\deg}, an output force of 12.5 N, and a resistance change of 26.9% as the applied external force increased from 0 to 45 N. A two-finger force-proprioception gripper is developed based on the MFPS actuator. The grasping and force-proprioception capabilities are experimentally validated, proving that the MFPS design method provides a new approach for the development of self-sensing actuators.

Space-based Very Long Baseline Interferometry (VLBI) can improve both the angular and temporal resolution of images over terrestrial VLBI techniques. Future space VLBI (sVLBI) missions are targeting higher observation frequencies than modern, terrestrial VLBI, and therefore these missions will require higher stability frequency references than standard hydrogen masers. While existing frequency references for space-based applications have concentrated on long-term stability, in this effort, we present a frequency reference with high short-term stability intended for sVLBI missions. This reference leverages developments in cavity-stabilized lasers from the Laser Interferometer Space Antenna (LISA) mission and commercial efforts towards a robust, space-qualifiable optical frequency comb. We describe the implementation and experimental results of this system with a path to spaceflight, which demonstrates an Allan deviation of $3.26 \times 10^{-14}$ at 1 second, $6.00 \times 10^{-15}$ at 10 seconds, and $6.73 \times 10^{-15}$ at 30 seconds for the 100 MHz frequency reference signal, and show that this performance meets the needs of future sVLBI missions.

Real-time motion planning remains challenging in large and high-dimensional environments. Prior acceleration of RRT* follows tree-centric state organization, which reduces per-query cost but preserves superlinear end-to-end complexity and limits parallelism through structural dependencies. This paper presents ScaleMPA, a motion-planning accelerator that rethinks RRT* with a grid-native representation. By replacing hierarchical traversal with direct grid-based access, ScaleMPA reduces the planner critical path and exposes fine-grained parallelism. To make this reformulation practical under sparse high-dimensional planning, ScaleMPA further proposes a multi-resolution grid search engine and a hash-grid memory system. Implemented in 28 nm CMOS, ScaleMPA achieves millisecond-level planning latency and delivers 4.7$\times$–44.4$\times$ speedup over state-of-the-art motion-planning accelerators.

Safety-critical decision systems often require a downstream optimizer to choose from an unknown feasible set determined by an unobserved label $Y$. Given a context $X$, the goal is to construct a safe subset $D(X)$ contained in the oracle feasible set $A(X,Y)$ with probability at least $1-\alpha$. Existing conformal approaches typically construct a prediction set of the unobserved label $Y$ and retain decisions that are safe for every value in this set. Although valid, this requires a stronger intermediate event than set inclusion. We propose Directed Inclusion Safety Calibration (DISC), a conformal framework that directly controls the probability of this inclusion event by reducing its verification to a scalar critical-inclusion score. Given a pretrained nested family of candidate feasible sets, DISC assigns each labeled observation the smallest nestedness level at which the corresponding subset is contained in $A(X,Y)$, and constructs the safe feasible set using an empirical quantile at test-time. With data exchangeability, this yields a finite-sample, distribution-free inclusion guarantee. Under two practical set families, we show that DISC produces a safe feasible set containing that obtained by the corresponding calibration baseline. We further develop optimization-based score computation and decision-aware procedures for learning subset families. Experiments across continuous and structured decision problems show that DISC achieves the target inclusion guarantee while producing larger feasible regions.

Coronal streamer kink waves excited by an impact of coronal mass ejections (CMEs) are routinely used to estimate the coronal Alfvén speed. These estimates generally assume wave propagation parallel to the equilibrium magnetic field directed radially outward to the Sun, in the plane of the sky. However, the geometry of CME impacts naturally allows for oblique propagation. We investigate the properties of obliquely propagating kink waves guided by a plasma slab with a central current sheet representing a coronal streamer stalk. We consider both cold and warm streamer plasmas and analyse influence of propagation obliquity on wave dispersion, eigenfunctions, and seismological diagnostics. We find that increasing the propagation obliquity reduces the phase speed owing to both projection effects and the intrinsic dependence of the phase speed on the propagation angle. The wave structure also undergoes a gradual transition from a body mode to a surface mode, leading to stronger perturbations at the slab boundaries and enhanced wave localization. Consequently, for a given energy deposited by a CME impact, oblique kink waves are expected to produce larger observable amplitudes than field-aligned waves. Applying the developed theory to streamer waves reported previously, we infer Alfvén speeds in the range of 50-500 km/s. We show that neglecting wave propagation obliquity may underestimate the Alfvén speed by up to a factor of 1.5. These results demonstrate that wave propagation obliquity should be taken into account in coronal seismology of streamer waves and that stereoscopic observations will be required to constrain the true propagation direction.

Accurate monocular depth estimation serves as a core enabler for single camera scene understanding. However, existing self-supervised monocular depth estimation methods generally suffer from the bottleneck of inefficient cross-scale information interaction and difficulty in balancing local and global spatial modeling. In this paper, we propose CMambaDepth, a self-supervised framework that achieves efficient multi-scale feature fusion and fine-grained contextual modeling via channel-wise selective state propagation. Specifically, Bidirectional Channel Mamba (Bi-CMamba) aligns encoder features across scales and enables bidirectional information exchange among ordered scale groups. Unidirectional Channel Mamba (Uni-CMamba) progressively aggregates decoder features and retains fine-grained scale groups through a group selection mechanism for subsequent fusion. Furthermore, a Hybrid Attention Module (HAM) is introduced to combine large-kernel local context and Manhattan self-attention for complementary spatial modeling. Experimental results demonstrate that our method achieves highly competitive performance. Specifically, our model achieves an AbsRel of 0.094 and an RMSE of 4.156 on KITTI, and an AbsRel of 0.140 on DDAD. In the zero-shot cross-dataset generalization test on NYUv2, it attains an AbsRel of 0.232, outperforming the baseline RA-Depth by 7.2%.

Trust develops through learning, while collective behavior can alter the environment in which later decisions are made. Reinforcement-learning models describe adaptation, and eco-evolutionary models describe behavior-environment feedback, but how an endogenous environment changes trust through material incentives and perceived states remains unclear. We couple a fixed-role, two-population hierarchical trust game populated by heterogeneous tabular $Q$-learning agents to a centered endogenous environment. For the main feedback comparisons, we initialize the fixed-payoff baseline and feedback branches from the same learned state to control for prior learning. We then compare responses when payoff parameters or the observed environmental tier vary. As the payoff multiplication factor increased, successful trust in the fixed-payoff game crossed from a low to a higher finite-horizon level, led by risk-seeking investors. Environmental feedback promoted trust near perception-tier boundaries and reinforced its decline at the high-return operating point. At the high-return operating point, payoff feedback reinforced the learning-driven decline in trust. Stronger drive and longer horizons deepened this negative effect. Compared with a fixed-payoff trust game, environmental feedback carries past collective outcomes into future payoffs and observed states.

Long-shot windsurfing video combines small targets, large camera pans, prolonged overlaps, and rapidly changing backgrounds. The desired output is not a generic MOT trace but a separate, stable rider-relative video for each surfer; one false identity merge can invalidate an otherwise useful result. We present an offline analysis system that detects surfers, forms conservative local tracklets, links them globally with camera-compensated motion and a foreground-masked sail-color descriptor, and uses two pose keypoints on the rig to drive a rider-relative virtual camera. The tracking stage is evaluated on 21 manually reconstructed development videos containing 41,004 retained observations. On this fixed-observation protocol, the production system achieves 0.957 pairwise precision, 0.918 recall, and 0.937 F1, compared with 0.792 F1 for OC-SORT and 0.828 for BoT-SORT. Compared with OC-SORT, it reduces fragmentation excess from 845 to 42, but nine of its 95 output tracks mix rider identities and these errors affect seven of the 21 videos.

2-step ideals are ideals $I$ of the polynomial ring that satisfy $\mathfrak{m}^{k+2}\subsetneq I\subsetneq \mathfrak{m}^k$ where $\mathfrak{m}$ is the maximal ideal generated by variables. This class of ideals was recently introduced in [F. Giovenzana, L. Giovenzana, M. Graffeo, P. Lella: New components of Hilbert schemes of points and 2-step ideals, 2025, arxiv: 2507.02789] with the aim to obtain new irreducible components of $\mathrm{Hilb}^d(\mathbb{A}^n)$ and in particular to obtain new loci in $\mathrm{Hilb}^d(\mathbb{A}^3)$ of large dimension. In this paper we use the correspondence between Hilbert schemes and varieties of commuting matrices to define loci of commuting matrices that correspond to 2-step ideals. Then we estimate the dimensions of the obtained loci to get new proofs for the estimates of dimensions of loci of 2-step ideals in the case $n=3$. In this case we are also able to omit some assumptions in the dimension estimates in the above mentioned paper.

A two-component Bose–Einstein condensate can host a pseudospin Hopf texture coupled to the viscous normal flow of its thermal cloud. Motivated by OpenAI's reported finite-time Navier–Stokes singular solution, we evolve such a texture in a smooth flow reproducing the geometry and similarity scaling of the collapsing axisymmetric core. The evolution creates and annihilates preimage pairs while preserving the Hopf charge. The first one-to-three transition exhibits the square-root opening characteristic of a Thom $A_2$ fold. A subsequent three-to-five transition precedes a burst-like regime of recurrent fold catastrophes and near-caustic activity.

Offline reinforcement learning (RL) typically trains a critic by minimizing a regression loss against bootstrapped value targets stabilized by target networks with exponential moving average (EMA) updates. Multi-step targets incorporate behavior-policy actions and therefore require off-policy correction. We instead impose in-sample Bellman optimality on the critic through inequality constraints. We formulate the Lifted Bellman Linear Program (LBLP), which lifts the linear programming characterization of Bellman optimality to the joint $(Q,V)$ space so that every constraint involves only state-action pairs in the dataset. Its unique minimizer is the in-sample optimal pair, and constraints along $K$-step segments of dataset trajectories leave this minimizer unchanged for any rollout policy and horizon. Under deterministic dynamics, this minimizer lies between the best dataset return and the optimal value. Relaxing the constraints into hinge penalties recovers the same solution above a finite penalty coefficient in the tabular case. Approximate Lifted Bellman Unconstrained Minimization (ALBUM) implements this relaxation with neural networks and detaches the $K$-step rollout targets by stop gradient. Its objective contains no squared regression onto bootstrapped targets, so it can be trained without target networks or EMA updates. Under deterministic dynamics, the LBLP solution is a stationary point of the detached update under a coefficient condition independent of $\gamma$ and $K$, and the inequality constraints allow discounted returns along dataset trajectories to serve as lower bounds without off-policy correction or action chunking. On OGBench, ALBUM uses a single critic with a Gaussian policy, matches the average performance of FQL, and is comparable to recent action-chunking methods, while using the fewest parameters and the least peak GPU memory among all compared methods.

We prove sharp two-eigenvalue isoperimetric inequalities for Neumann and Aharonov–Bohm Neumann spectra on surfaces. If $\Omega\subset\mathbb S^2$ is smooth, simply connected and proper, then the harmonic mean of $\mu_2(\Omega)$ and $\mu_3(\Omega)$ is bounded above by the first positive Neumann eigenvalue of the equal-area geodesic disk, with equality only for disks. For simply connected surfaces with Gaussian curvature bounded above, we obtain the magnetic analogue for the first two Aharonov–Bohm eigenvalues. The proof combines a two-dimensional reciprocal Rayleigh–Ritz principle with Green-level comparison. A key additional ingredient is a spectral ordering theorem for magnetic spherical caps: for $0<\nu<1/2$, the first two eigenvalues lie in the angular sectors of effective orders $\nu$ and $1-\nu$. We prove this by the factorization $L_0=T^*T$, $L_1=TT^*$ and an exact Neumann–Dirichlet spectral shift. We also obtain sharp full-sphere and closed-surface bounds, and an annular inequality in terms of conformal modulus and flux.

In this work, we present a method for shape reconstruction and tracking from video via agentic analysis-by-synthesis. Unlike prior methods which first estimate dense pixel correspondences and then recover object motion from them, our method infers a structured 3D object model, including its geometry and kinematic structure, and uses this model to optimise object track estimates over time. In our optimisation loop, a Vision-Language Model (VLM) agent iteratively refines shape or generalised pose through a render-and-compare loop, combining coarse visual reasoning with numerical pose optimisation for precise state estimation. This structured formulation enables our method to track through large motion, articulation, and severe occlusion without relying on pixel-matching objectives. Quantitatively, on ARCTIC, our method substantially outperforms state-of-the-art 3D point-tracking baselines for articulated objects, and on HOT3D it outperforms all evaluated rigid-object tracking baselines.

Let K be any field and E any directed graph. We investigate the existence of divisible non-injective left modules over the Leavitt path algebra L_K(E) for a broad class of graphs. Our main tool is a general criterion for divisibility that is particularly well suited to our setting.

Visual token pruning is a promising approach to reducing the inference cost of large vision-language models (LVLMs), yet aggressive token reduction often causes substantial performance degradation. We identify three key factors behind this degradation: text-guided selection bias, information loss from discarded tokens, and positional distortion caused by sequence compaction. Based on these observations, we propose VPRune, a training-free pre-LLM pruning framework consisting of visual-only diversity selection, similarity-guided token recycling, and position-preserving restoration. Experiments on FastVLM-1.5B across multiple vision-language benchmarks demonstrate that VPRune achieves a favorable accuracy–compression trade-off, with particularly pronounced advantages under aggressive compression. Furthermore, evaluations on edge-device show that VPRune effectively reduces end-to-end inference latency while maintaining superior task performance, demonstrating its practicality for resource-constrained LVLM deployment.

Let \(X\) be a smooth open manifold of even dimension, \(T\) be a topological space, and \(\{J_t\}_{t\in T}\) be a continuous family of smooth integrable Stein structures on \(X\). The family is said to be tame if the \(J_t\)-convex hulls of any compact set in \(X\) are upper semicontinuous with respect to \(t\in T\). It was recently shown that tame Stein families have good function-theoretic properties; in particular, they satisfy the Oka principle for families of holomorphic maps to any Oka manifold. We analyse some constructions and operations on Stein manifolds that preserve tameness of families and we exhibit several conceptually new examples of tame Stein families.

We study finite-$N$ coherent-state overlap kernels in multi-matrix BPS sectors of $\mathcal N=4$ super Yang–Mills theory. For commuting coherent-state parameters, the kernel is a Laplace transform of the Haar-pushforward measure on the unistochastic set. After quotienting row- and column-shift redundancies, the nontrivial source is an $(N-1)\times(N-1)$ matrix $D$. On the physical $m$-matrix locus, $D$ is a Gram matrix with $\operatorname{rank}D\leq m$, and the ordinary HCIZ sector is precisely the rank-at-most-one stratum. For $N=3$ we obtain an exact Bessel-integral representation of the first genuinely rank-two kernel. Along the rank-one ray $D=rE_{11}$, $F_N={}_1F_1(1;N;r)$ for arbitrary finite $N$. Using $K_N=\log F_N$ as the reduced Kähler potential, we study a controlled two-matrix embedding of the HCIZ sector and determine its transverse metric, second fundamental form, and Gauss–Codazzi geometry. The embedding is non-totally-geodesic at finite $N$. In the scaling $r=N\rho$, we find \begin{equation} Nh_N\to\min(\rho,1), \qquad \|B\|^2\to2(1-\rho)_+. \end{equation}