Papers

Hypergraphs model interactions involving groups of entities, and finding highly connected groups is a fundamental task in analyzing these data. When interactions arrive and expire, maintaining a dense group can require frequent and expensive changes to the underlying representation. We propose CAP, a scalable algorithm that explicitly maintains a $(1+\epsilon)$-approximate densest subhypergraph under hyperedge insertions and deletions. The algorithm keeps a solution candidate together with an endpoint allocation that bounds the optimum density. The candidate's density guides maintenance: an update triggers repair only when this bound is too large to establish the required approximation. Local searches redistribute load or find a denser candidate, allowing CAP to retain useful solutions across many updates. We give an analysis that relates maintenance work to the size of the regions searched and the density lost by the maintained solution. It identifies conditions under which local repair remains inexpensive and provides a theoretical explanation for the observed efficiency. Experiments on real-world hypergraphs show speedups of up to nearly four orders of magnitude over the evaluated dynamic baselines, while supporting frequent queries and high accuracy. CAP also remains competitive with specialized dynamic graph methods on ordinary graphs, with speedups of up to approximately $64\times$ on the tested workloads.

LLM-based multi-agent systems coordinate specialized reasoning through aggregation, interaction, and adaptive control, yet their potential for graph learning remains unexplored. Graph learning is a natural setting for such systems because useful evidence may arise from heterogeneous local, long-range, global structural, and semantic perspectives whose relevance varies across instances. Existing LLM-based graph learning approaches primarily rely on single-agent reasoning, while multi-agent coordination has been studied mainly in general reasoning settings. Consequently, it remains unclear whether multiple specialized agents can improve graph learning and how coordination strategies should be designed and evaluated. To address this gap, we introduce GraphMAS, a systematic benchmark of multi-agent coordination for graph learning. GraphMAS builds a shared pool of graph reasoning specialists and organizes coordination along two dimensions, inter-agent interaction and runtime adaptivity, yielding four paradigms and seven representative coordination methods. Under a unified protocol, we evaluate these methods across seven text-attributed graphs, three domains, and two graph learning tasks. We find that heterogeneous graph perspectives are complementary, and that coordinating specialists improves over individual specialists and single-agent graph reasoning, with gains from decomposing reasoning across specialists rather than from broader evidence access alone. However, richer inter-agent interaction does not reliably help, whereas instance-adaptive specialist selection yields the strongest accuracy-efficiency trade-off. We further show that coordination can be learned over a fixed specialist pool and transfers to held-out graphs. GraphMAS therefore provides a controlled evaluation framework and empirical principles for understanding when and how multi-agent coordination benefits graph learning.

With the rapid development of the low-altitude economy, low-altitude operations are booming, where complex missions require collaborative efforts among multiple heterogeneous low-altitude aircrafts (LAAs). Specifically, different LAAs assume distinct roles: some for sensing, some for communication, some for computing, and others for mission execution, together forming a sensing-communication-computing-control (SC3) closed loop, akin to a reflex arc. To enable efficient coordination in such multi-LAA swarms, we introduce the concept of operational-capability entropy (OCE) to quantify the effective work capability of operational LAAs. Accordingly, by jointly considering heterogeneous OCE and channel conditions among LAAs, we formulate the power allocation problem with the goal of minimizing the linear quadratic regulator (LQR) cost, which serves as a metric for mission efficiency. The resulting complex optimization problem is decomposed into two convex subproblems that are solved iteratively, with closed-form solutions derived for each. Simulation results demonstrate that the proposed mission-oriented adaptive power allocation scheme significantly outperforms traditional ones.

Ultralight axions can be gravitationally captured by massive bodies such as the Sun, producing solar-bound gravitational atom states that amplify the local dark matter density through Bose-enhanced capture. For axion masses in the range $10^{-14}\text{eV}\lesssim m_a \lesssim 10^{-13}\text{eV}$, this mechanism becomes exponentially efficient. We show that, for a representative decay constant $f_a\sim 3.5\times10^7$ GeV, the local axion dark matter density at Earth can grow to more than ten times the standard Galactic value of $\rho_0 = 0.4 \text{ GeV/cm}^{3}$. Incorporating this overdensity, we derive updated limits on the axion-photon coupling from existing satellite and terrestrial measurements and present improved projections for upcoming experiments.

Prior studies on quantum money from knots, and the invariant money framework that generalizes it, anchor their security on the hardness of path-finding. However, we show that the hardness of path-finding is proven to be necessary for security under certain conditions. In other conditions, this assumption is not a direct anchoring hardness problem such that breaking it allows an adversary to forge a banknote directly. In particular, for quantum money from knots, even when the path-finding assumption does not hold, an adversary still cannot directly forge a banknote. The adversary needs to additionally prepare the uniform superposition over the paths it finds, which we show is as hard as the original problem. Existing security proofs supplement path-finding hardness with knowledge-of-path assumptions. While this combination is sufficient, it may not be necessary. We identify an assumption pair, preparation assumption and transfer assumption, that is both necessary and sufficient for the security of every invariant money scheme. Breaking either assumption directly enables a forgery. The preparation assumption says that no efficient algorithm, given the serial number of a banknote and one object measured from it, prepares a state that verification accepts. While quantum money security gives a forger one quantum state and asks for two that pass, our assumption concerns a problem that takes only classical inputs and asks for one quantum state that passes. This assumption is equivalent to security against forgers that measure their banknote first. Given that its inputs are classical, it is falsifiable and can be attacked and bounded like other computational problems. The transfer assumption covers forgers that keep the banknote coherent, stating that every such forger only has an advantage over the measure-first adversary by at most a polynomial factor.

Crystal structure governs material properties, making crystal structure prediction (CSP) a fundamental problem in materials science. Generative models are a promising approach for solving this problem, but the prevalence of polymorphism, coupled with large unit cells and complex packing geometry, makes the molecular CSP task challenging for existing models. To address this, we introduce Coarse-Grained Open Materials Generation (CG-OMatG), an equivariant Riemannian flow-based generative model. CG-OMatG predicts molecular crystal structures via a coarse-grained, hierarchical representation. CG-OMatG treats molecules as rigid bodies—performing both inter- and intra-molecular message passing to construct a geometric representation for molecular packings—and learns to reconstruct molecule centroid positions, orientations, and lattice parameters, conditioned on chemical species and conformer geometry. We train the model on subsets of the Open Molecular Crystals (OMC25) and Cambridge Structural Database (CSD) datasets. Further, we fine-tune the model via policy gradient reinforcement learning to steer the model towards generating low-energy candidate structures. We validate the generated structures on the CSP blind test benchmark, assessing agreement with experimentally determined crystals using COMPACK packing-similarity analysis. CG-OMatG exhibits strong performance for generative molecular crystal structure prediction, paving the way for accelerated polymorph screening and organic solid-state materials discovery.

Membrane curvature has been shown to bias the location of lipid or protein domains, but the roles of bending rigidity, spontaneous curvature, Gaussian bending modulus, and line tension are difficult to separate in general. We develop a small-domain description for a membrane whose shape is held fixed, e.g. by strong adhesion to a curved substrate. Combining a local Helfrich energy with the small-area isoperimetric expansion gives a position-dependent energy determined by the local mean and Gaussian curvatures. We identify four generic regimes of curvature preference whose boundaries depend on only two dimensionless parameters. On specific membrane shapes with complex curvature, we show that this curvature preference determines the energy landscapes experienced by small domains, which are strongly dependent on the size of the domain through the line tension contribution. For example, on an oblate-shaped membrane, very small domains tend to localize at the poles, whereas larger domains prefer to localize at the equator. Whether this transition is continuous or discontinuous is found to strongly depend on the spontaneous curvature of the domain. This ordering suggests a mechanism by which small domains can collect and coalesce at one location before relocating as they grow.

When $G$ is a complex reductive algebraic group, MV polytopes are in bijection with the non-negative tropical points of the unipotent group of $G$. In this paper, we prove a similar theorem for certain subclasses of rank 2 affine MV polytopes. For the Kac-Moody group $\widehat{SL_2}$, an affine MV polytopes splits into three subpolytopes: a lower, a middle and an upper polytope. The lower polytopes are natural generalizations of finite-type polytopes with highest vertex labelled by an arbitrary Weyl element. We extend the known results from this subclass of finite-type MV polytopes to the case of lower affine MV polytopes of rank 2. We prove that for an element $w$ of the affine Weyl group, the class of lower affine MV polytopes with highest vertex $w$ are in bijection with the non-negative tropical points of the reduced double Bruhat cell labelled by $w^{-1}$. To do this, we describe the BZ data of a rank 2 affine MV polytope and show that certain generalized minor functions satisfy the conditions of a lower polytope. As any upper polytope is a reflection of some lower polytope, a analogous result will hold for the class of upper affine MV polytopes of rank 2.

We study the reversible reaction $1+2\rightleftarrows3+4$ in a dilute gas described by a Boltzmann system. We prove that the outgoing flux of one product species determines the forward collision kernel throughout the domain on a prescribed admissible set of relative velocities and outgoing directions. The elastic collision laws are known, and the reverse kernel is fixed by a prescribed reciprocity relation. The measurements use two synchronized incoming packets with fixed relative velocity and a common velocity tending to infinity. Under bounded angularly integrated collision rates, the short transit time allows us to isolate the contribution of one forward reaction, with estimates uniform as the packets concentrate. Suitable tests of the product flux yield the spatial line integrals of the kernel and a Fourier reconstruction, without differentiating the nonlinear boundary map. We also estimate the effects of finite beam speed, packet width, detector resolution, and measurement noise on the recovered line integrals.

With the assistance of AI (Artificial Intelligence) tools, we revisit some mathematically well-formulated problems from our previous studies of BMN (Berenstein-Maldacena-Nastase) strings on type IIB string theory pp-wave background. These mathematical problems have important physical implications, relating to the computations of higher-genus critical superstring amplitudes, possible estimate of the cosmological constant. We make significant progress on some problems, while others remain unresolved.

Certifying a deployed neural network raises decision problems that the verification literature has not classified: whether the model carries a backdoor planted in its training data, whether a fault in its stored parameters can drive it into an unsafe state, whether its output leaks a private part of its input. We formalise eight such problems and classify what we can. The organising observation is a logical one. The function computed by a piecewise linear network, together with all its node values, is definable by a quantifier-free formula of real addition of size linear in the network, so a property of the network is a quantifier-alternation sentence, which Sontag's 1985 theorem places in the polynomial hierarchy at the level of its prefix. Membership results are thus corollaries, and the argument makes plain what they need: that the quantified objects are inputs rather than the network's own parameters. Non-interference, monotonicity and counterfactual fairness have exactly the complexity of network equivalence and of interval verification, all co-NP- complete over ReLU. Detection of backdoor triggers from a quantised alphabet is Sigma_2^P-complete, one level above robustness certification, so it does not reduce to polynomially many robustness queries unless the hierarchy collapses. Inversion resistance is co-NP-complete for every l_p metric, p a fixed positive integer. Quantifying over parameters instead of inputs - the fault model of bit-flip attacks, radiation upsets and analog accelerators - makes verification exists-R-complete already for networks of identity nodes, for which every previously studied problem is in P, and it stays so when each parameter is confined to a box of inverse-polynomial width; the corresponding safety question is forall-R-complete for ReLU.

The scale and expense of pre-training language models make efficient hyperparameter tuning essential, yet a principled guidance is still missing. In this work, we analyze language model pre-training dynamics from a local landscape geometry perspective. Our study reveals two distinct phases. In Phase I, sharpness of the local landscape is initially high, leading to instability and loss plateaus under large learning rates (LRs). The landscape shifts from sharp to flatter regions early in training. This dynamic explains the necessity of LR warmup and further suggests that larger peak LRs require proportionally longer warmup periods. In Phase II, the local landscape is governed by the gradient noise scale. Our theory identifies a depth flatness trade-off: high noise from smaller batches widens the loss basin, whereas reduced noise from larger batches deepens it. This theory motivates a dynamic batch-size (BS) scheduler that begins with a small BS and increases it late in training. Together, we provide a unified view of loss landscape evolution, which translates into actionable tuning strategies for large-scale pre-training.

We introduce notions of non-commutative Fano varieties and non-commutative minifolds, and study the latter in dimension three. We prove that the Euler matrices of full exceptional collections generating geometric helices on these minifolds form five mutation classes, distinguished by their Euler degrees \(22,40,54,64,72.\) The first four classes are realized by (commutative) Fano threefolds \(X_{22},V_5,Q^3,\mathbb P^3,\) respectively. The fifth is realized by the non-commutative family \(M_{72}\) and cannot be realized by a full exceptional collection on a smooth projective threefold.

Agent memory faces heterogeneous access needs: a single-hop question may require one piece of evidence, whereas a multi-hop question must combine evidence from multiple sources. Predefined memory workflows cannot adapt to these varying needs. Recent adaptive methods search or learn over memory components and their compositions, but the design space itself remains predefined. We introduce MemCodex, a self-evolving hierarchical memory system that organizes experience into executable memory programs for summaries, relational knowledge, reusable skills, and latent memory. Open-ended program evolution searches the open design space of layer programs by rewriting how each layer is constructed, indexed, retrieved, and routed, thereby adapting both within-layer implementations and cross-layer composition. At query time, reads traverse the hierarchy from coarse to fine and stop once sufficient evidence is found, descending to the original history when needed. We further develop MemArena, a unified runtime that places heterogeneous data and memory systems behind a common interface. MemCodex improves average task success by 10.1% relative to the strongest adaptive-memory baseline, while using 3.4x fewer context tokens and achieving 2.1x faster inference.

Measurements and feedforward enhance the power of shallow quantum circuits, enabling the deterministic implementation of global unitary operations and the preparation of long-range entangled states. We establish a general correspondence between all such protocols and quantum error-correcting codes: the circuit preceding the measurements acts as an encoder, and unitary feedforward can eliminate post-selection if and only if the measurement projectors are detectable errors on the codespace. This correspondence provides a common framework for state preparation and implementation of global unitaries with measurements and feedforward, turning both into a code-design problem. For stabilizer codes with Pauli measurements, although the resulting operation can be non-Clifford, we show that its nonstabilizerness originates entirely from the encoder. We overcome this restriction using non-Pauli measurements or non-additive codes, constructing protocols that generate long-range nonstabilizerness while requiring only single-qubit unitary corrections.

Pretrained video foundation models encode rich semantic and spatiotemporal priors for embodied navigation, yet converting these priors into UAV motion typically requires expensive future-video synthesis and geometric reconstruction. We investigate whether the motion implicit in future visual prediction can instead be recovered directly from the predictive representations of a frozen video model. To this end, we present DiffWAM, a geometry-conditioned navigation world-action model that directly transforms multi-level predictive features into continuous camera trajectories. Its Grid-Motion module preserves spatial-temporal motion associations, while Latent2Pose grounds them with first-frame geometry to recover metrically meaningful 3D motion. Complete video rollouts and geometric reconstruction are required only for offline supervision, eliminating future-video decoding and multi-frame reconstruction during deployment. We further introduce FastDreamer, which overlaps predictive and geometric computation with ongoing flight and performs timestamp-aware asynchronous trajectory handoff for continuous UAV execution. DiffWAM achieves a trajectory RMSE of 0.3492 m and an endpoint success rate of 74.40% on the 1,000-sample DiffWAM-1000 benchmark, while representative real-world experiments demonstrate complex behaviors including constrained traversal, orbiting, S-shaped flight, and multi-stage navigation. An onboard DiffWAM-Flash implementation further reaches 1.08 s model-pipeline latency on NVIDIA Jetson AGX Thor. These results demonstrate that predictive video representations can be efficiently grounded into continuous 3D motion, providing a direct alternative to generate-then-reconstruct navigation pipelines. Project page: https://zzmmzzm.github.io/diffwam.github.io/.

Both the uniform Roe algebras and the quasi-local algebras encode the large scale geometry of metric spaces. Whether these algebras coincide is a question which goes back to Roe and has only been recently solved by Ozawa. We propose a dynamical point of view on this problem. Given a set $X$, every map $h\colon X\to\mathbb{R}$ induces a one-parameter group $\sigma_h$ of automorphisms of $\mathcal{B}(\ell_2(X))$, given by conjugation by the diagonal unitaries $e^{ith}$, and we show that the operators which are continuity points of $\sigma_h$ are precisely the uniform Roe algebra of the pseudo-metric induced by $h$. If we moreover assume that $X$ is a uniformly locally finite metric space and $h$ is allowed to range over all coarse maps, this gives dynamical characterizations of both algebras: $\mathrm{C}^*_{ql}(X)$ consists exactly of the operators which are continuous for all such flows, while $\mathrm{C}^*_u(X)$ consists exactly of norm limits of those which are analytic. The regularity conditions lying between continuity and analyticity then give rise to $\mathrm{C}^*$-algebras between $\mathrm{C}^*_u(X)$ and $\mathrm{C}^*_{ql}(X)$ which are invariant under bijective coarse equivalence, and we show that this scale is not degenerate: if $X$ is a coarse disjoint union of expander graphs, the algebra generated by operators which are analytic on a strip for every diagonal flow sits strictly between $\mathrm{C}^*_u(X)$ and $\mathrm{C}^*_{ql}(X)$.

In this paper, we investigate weakly persistent centers for several classes of planar cubic differential systems, including systems with a nondegenerate linear center and systems with a nilpotent center. Necessary parameter relations are obtained by computing singular point quantities or quasi-Lyapunov constants, while their sufficiency is established by suitable analytic constructions. For the general complex cubic system, we obtain necessary and sufficient conditions for the origin to be a weakly persistent center, and the corresponding result for the associated general real cubic system follows by imposing the conjugacy relations between the complex coefficients. We further characterize the weakly persistent isochronous centers of the general complex cubic system by combining the weakly persistent center conditions with the vanishing of the linearization quantities and constructing time-preserving analytic linearizations.

We study superfluid vortices in two-color QCD and more general pseudoreal gauge theories with even flavor number $N_f=2m$ at finite baryon density. The antisymmetric diquark condensate admits fractional minimal vortices with baryon-phase winding $\nu=1/m$, corresponding to $1/m$ of the conventional circulation quantum, each localizing an $Sp(2)\simeq SU(2)$ core sector. For vortices embedded in mutually orthogonal flavor planes, the leading-order chiral action factorizes exactly. Off-diagonal flavor zero modes are non-normalizable at finite separation but become localized at coincidence, enhancing the normalizable sector from $[Sp(2)]^m$ to $Sp(2m)$. For fundamental fermions of an $Sp(2N)$ gauge theory, the bulk Wess–Zumino–Witten (WZW) term descends compatibly: a cluster of $n$ coincident minimal vortices carries an $Sp(2n)_N$ WZW theory, while a flavor-symmetric vortex with positive integer baryon-phase winding $\nu$ carries $Sp(2m)_{N\nu}$. At unit winding this yields the vortex map to $Sp(2m)_N$, with central charge $c=Nm(2m+1)/(N+m+1)$ at the WZW fixed point, and suggests a broader nonsupersymmetric four-dimensional/two-dimensional correspondence.

Motivated by the discovery of a meteor with velocity more than 300~km/s (Afanasiev et al. 2007) we study how dust grains formed in the supernova (SN) ejecta at its free-expansion phase can keep their high velocity obtained from the gas, where these grains were born. Using a one-dimensional spherically symmetric Lagrangian approach we follow the dynamics of grains during the interaction of a SN ejecta with the ambient interstellar gas. We found that grains larger $\sim 0.3~\mu$m can cross the SN forward shock front and reach the ambient interstellar medium. They are destroyed inefficiently, thus, their sizes remain close to the initial ones. In a diffuse interstellar gas of density $\lesssim 1$ cm$^{-3}$ grains larger as $\gtrsim 1~\mu$m move with velocity around $1-2$ thousand km/s and spread over distances exceeding $\sim 40-90$ pc from the SN origin within tens of kiloyears. In dense environment the propagation of grains is significantly suppressed: even large grains do not spread over distances greater than 50% of the current SN remnant size. Grains born close to the edge of the SN ejecta core in less-massive ejecta reach greater distances. Thus, high-velocity grains are expected to be formed in this part of the ejecta with mass lower than $\sim 3~M_\odot$ of the SN remnant evolving in a diffuse gas with density $\lesssim 1$ cm$^{-3}$. We discuss possible consequences for dust transport out from galactic disks.

We present a unified algebraic theory of Clifford spacetime quantum fault tolerance, which underpins universal fault-tolerant quantum computation. We construct a spacetime chain complex from a tensor network representation of a circuit that encodes fault propagation, detector syndromes, and logical actions through the associated gauge and stabilizer structure. We show that this theory (1) unifies various formulations of quantum fault tolerance including spacetime codes, Gottesman's gadget framework, fault complexes, and ZX calculus; (2) connects spacetime distances to the gadget-level correctness properties in Gottesman's formalism; (3) naturally accommodates a range of fault models, in particular phenomenological and circuit-level models, bringing these often separately formulated descriptions into a common algebraic framework through different tensor decompositions and fault assignments; and (4) recovers many known fault tolerance constructions and results as special cases, including repeated syndrome extraction, correlated detectors for transversal and fold-transversal gates, Steane- and Knill-type syndrome extraction gadgets, and single-shot error correction.

Black-box distillation is a practical route for transferring capabilities from API-accessible large language models that expose only text outputs into smaller student models. Recent on-policy adversarial methods such as GAD improve over SeqKD by forming an adversarial loop between a critic and a student, where the critic provides rewards for GRPO-based student policy optimization over the student's sampled responses. However, GRPO computes advantages from the within-group relative rewards of student samples for the same prompt, whereas the critic is trained primarily to distinguish teacher responses from student responses. This objective mismatch can produce reward groups with collapsed scale or fragile margins, leading to brittle grouped optimization signals. We propose Groupwise Reward Geometry Conditioning (GRGC), a two-stage framework that improves advantage construction by shaping student-side reward groups during both critic training and policy optimization. To improve critic-side conditioning, Gaussian groupwise Optimal Transport calibration regularizes the critic during training to produce reward groups with non-collapsed spread and smooth rank-wise gaps by matching sorted prompt-wise rewards to group-centered Gaussian quantiles. Building on this conditioned reward geometry, policy-side group power modulation reshapes the prompt-wise reward groups before they are converted into advantages, preserving the critic-induced ordering while increasing optimization-relevant margin separability. Extensive experiments across diverse teachers, student model families and scales, and training datasets demonstrate the effectiveness of GRGC on both in-distribution and out-of-distribution evaluations, while introducing negligible overhead over GAD. The code is available at https://github.com/2018cx/GRGC.

This article introduces an algorithm that uses a U-Net architecture to determine vertical ground surface displacements from unmanned aerial vehicle (UAV)-photogrammetry point clouds, offering an alternative to traditional ground filtering methods. Unlike con-ventional ground filters that rely on point cloud classification, the proposed approach em-ploys heteroscedastic regression. The U-Net model predicts the conditional expected val-ues of the elevation corrections, aiming to reduce the impact of vegetation on determined ground surface elevations. Concurrently, it estimates the logarithm of the elevation cor-rection variance, allowing for direct quantification of the uncertainty associated with each elevation correction value. The algorithm was evaluated using three metrics: the root mean square error (RMSE) of vertical displacements, the percentage of nodes with deter-mined displacement values, and the percentage of outliers among those values. Perfor-mance was assessed using the technique for order of preference by similarity to ideal so-lution (TOPSIS) method and compared against several ground-filter-based algorithms across four datasets, each including at least two time intervals. In most cases, the U-Net-based approach demonstrated a slight performance advantage over traditional ground filtering techniques. For example, for the U-Net-based algorithm, for one of the test da-tasets, the RMSE of the determined subsidences was 6.1 cm, the percentage of nodes with determined subsidences was 80.5%, and the percentage of outliers was 0.2%. For the same case, the algorithm based on the next best model (SMRF) allowed an RMSE of 7.7 cm to be obtained; for 77.3% of nodes, the subsidences were determined; and the percentage of outliers was 0.3%.

Safe and efficient quadruped navigation over unfamiliar terrain requires predicting terrain-robot interaction before contact: geometry and visual appearance alone cannot reveal how the robot will slip, load its feet, or expend energy. This paper presents a continual learning pipeline that uses locomotion experience to learn these interaction outcomes from pre-contact images and continually updates the predictions as new contacts are observed. Pre-contact descriptors, produced by a DINOv3 backbone model frozen during training, are mapped to five proprioceptive indicators weighted according to measurement reliability: planar foot slip, mean normal ground-reaction force, traction index, cost of transport, and touchdown loading rate. A compact evidential regressor allows us to predict these indicators together with aleatoric and epistemic uncertainty from the visual descriptors. Continual adaptation combines bounded experience replay with a validation gate: candidate models replace the deployed predictor only when they improve performance on recent held-out data while keeping degradation on historical held-out data within a prescribed tolerance. Predictions and epistemic uncertainty are projected into a local multilayer map and combined into a conservative traversability score map whose property weights can be adjusted without retraining. The resulting map is used for downstream navigation tests. The ROS2 implementation supports evaluation on a Unitree Go2 in simulation and on hardware, with models trained separately in each domain. On a sequential hardware stream over three previously unseen terrains, gated replay reduces final anchor negative log-likelihood (NLL) degradation by 23.1% relative to replay without the gate while attaining similar new-terrain adaptation.

Robot foundation policies predict action chunks, but how many actions to execute before replanning depends on the current task phase. We introduce ChunkTrust, which treats the execution horizon as a latent variable inferred from action-expert evidence rather than a fixed hyperparameter. Its training-free Action-aware Horizon Selector (AHS) combines intra-chunk spectral stability of generation traces with inter-chunk continuity between executed history and predicted actions. An online Beta posterior with kernel forgetting tracks horizon preferences across replans. A lightweight Query-based Horizon Adapter (QHA) optionally learns a context-conditioned dense prior from complementary evidence, fused with current evidence and episode-local Beta memory while the base policy remains frozen. Across RoboTwin2.0 and RoboCasa GR1 Tabletop, AHS improves overall task-averaged success for each evaluated base-policy configuration, including gains of +6.80 percentage points on $\pi_{0.5}$ over all 50 RoboTwin2.0 tasks and +9.67 percentage points on Qwen3GR00T in RoboCasa. AHS+QHA raises the gain over Base to +9.44 percentage points on the eight-task $\pi_{0.5}$ evaluation. On four real-world household tasks, AHS improves the equal-task mean normalized process score from 50.4% to 57.5%. Ablations examine the contributions of both evidence terms, temporal memory, and the learned prior. Project page is https://hf618.github.io/ChunkTrust.github.io/

The structure of $^{22}$C remains unsettled more than a decade after the 2010 reaction-cross-section measurement. The nucleus sits at $N=16$, where the spherical closure of $^{24}$O competes with the deformation of $^{20}$C. We develop a multi-reference density functional approach that restores particle number and angular momentum and mixes quadrupole shapes while retaining the continuum. The calculation gives a deformed two-neutron halo with matter radius of 3.29 fm, closer to the carbon-target extraction, and a long $s$-wave tail. The ground state $0_{1}^{+}$ is dominated by oblate configurations, with $B(E2)$ values comparable to those of $^{20}$C. The valence neutrons occupy mixed $sd$ orbits; the $N=16$ closure established in $^{24}$O is substantially weakened in $^{22}$C.

High-altitude platform stations (HAPSs) are expected to coexist with terrestrial networks (TNs) to provide seamless wide-area wireless connectivity in future sixth-generation (6G) systems. However, the strong line-of-sight (LoS) propagation of HAPS links introduces severe cross-tier interference under spectrum sharing. This paper proposes a reverse time division duplexing (RTDD)-based transmission framework for integrated HAPS–TN systems, where the HAPS and terrestrial base station (BS) operate in opposite transmission directions to mitigate cross-tier interference while preserving TDD channel reciprocity. Standardized 3GPP channel models are adopted for both HAPS and terrestrial links. To enable tractable performance analysis, an analytical Kronecker channel model is developed to approximate the empirical 3GPP terrestrial BS channel, based on which a random matrix theory (RMT)-based large-system analysis is established to derive deterministic approximations for the uplink and downlink signal-to-interference-plus-noise ratios (SINRs). Numerical results demonstrate an excellent agreement between the proposed analysis and Monte Carlo simulations. Moreover, the proposed RTDD framework effectively suppresses cross-tier interference, achieves near interference-free performance.

Planning with learned world models combines online trajectory optimization with learned value and policy functions for high-dimensional control. Because the planner determines the experience used for learning, while the learned critic and actor in turn score and propose future plans, planning and learning form a closed feedback loop. TD-MPC is a prominent instance of this design. Recent policy-constrained variants strengthen one part of the loop by aligning the learned policy with planner behavior. We introduce PL-MPC (Planning-Learning MPC), which additionally modifies critic supervision and planner terminal-value estimation. Hybrid multi-step TD targets expose critic updates to more realized rewards before bootstrapping; disagreement-aware terminal estimates reduce the influence of uncertain critic values during MPPI planning; and return-weighted actor distillation emphasizes planner-executed actions from high-return episodes. The world-model architecture and MPPI optimizer are otherwise unchanged. On HumanoidBench, the largest gains occur on balance-hard, where Total Average Return (TAR) increases from $98\pm18$ to $387\pm255$, and hurdle, from $199\pm13$ to $466\pm200$; performance across the broader benchmark remains task dependent, and PL-MPC remains competitive on DMControl. Controlled ablations show different component interactions across the two tasks. We further demonstrate zero-shot sim-to-real transfer on wrench-nut alignment with a 7-DoF KUKA IIWA14, obtaining higher observed success than TD-M(PC)^2 on the training object size and two unseen sizes. Code and data will be available at: https://pl-mpc-humanoid.github.io.

Gamified points are widely used to represent learner participation, but cumulative point totals provide limited information about how participation changes over time. This limitation matters in continuously enrolling programmes, where learners have different opportunities to accumulate points. This study examines how gamified participation data can be interpreted as indicators of behavioural engagement in a large-scale, continuously enrolling remote internship. Using an anonymised operational dataset, 3,607 distinct started learners were first classified by participation status, separating dormant learners from those with observable participation. The 1,871 active learners were then grouped using K-means clustering on normalised longitudinal and opportunity-aware participation features. Four participation patterns emerged: Thriving Core, Tapering, Fast Starters, and Occasional Participants. Their trajectories differed in both level and direction. A perception survey of 597 respondents provided complementary learner-reported evidence, integrated with the behavioural strand through a joint display by segment. Perceptions differed across segments, while individual-level correlations between perceptions and behaviour were small, and learners with low recorded participation could report positive perceptions of the points system alongside external barriers. Segments assigned from the first four weeks were then checked against eleven weeks of later platform records: 94% of the Thriving Core attended at least ten further sessions and 22% completed the internship, against under 7% and under 1% in the low-engagement segments. The findings suggest that gamified participation data are more informative when interpreted as longitudinal, opportunity-aware behavioural indicators rather than cumulative scores alone.

Routing and switch placement are fundamental combinatorial optimization problems in chip design, requiring the joint optimization of routing topology and physical placement under strict structural, geometric and logical constraints. Existing approaches typically rely on carefully engineered heuristics that incorporate strong problem-specific biases to navigate the enormous space of possible designs. In this work, we introduce a hierarchical reinforcement learning framework for joint routing and switch placement at the level of logical communication routes. Starting from a minimal routing graph, our method progressively constructs increasingly expressive solutions through three coupled operations: switch expansion, switch placement, and route refinement. These operations preserve routing validity by construction, restricting exploration to feasible configurations where every communicating initiator-target pair has one assigned loop-free route. We explore the induced solution space using Gumbel Monte Carlo Tree Search, showing that neural-guided search substantially improves solution quality over non-learning optimization methods. Furthermore, pretraining across floorplans provides a strong initialization for fine-tuning on unseen instances.