Papers

Real-world robot learning is constrained by the cost of collecting experience and evaluating candidate behaviors. Video generation models offer a scalable foundation for visual simulators that predict action outcomes before physical execution. Yet they often favor visual plausibility over accurate action following and coherent robot–object dynamics, while action-conditioned simulators depend on scarce, embodiment-specific data that are difficult to share across incompatible control spaces. We introduce WorldLine, an action-driven visual simulator that decouples transferable dynamics learning from heterogeneous action grounding. WorldLine learns manipulation dynamics from more than 10,000 hours of action-free robot videos and grounds them using over 2,000 hours of action trajectories across more than ten embodiments. An image-space action representation provides a shared control interface across embodiments, while multi-view and failure-enriched training with relational regularization improves interaction-sensitive prediction. Robot-focused few-step distillation enables efficient causal rollout while preserving action-critical motion. Across held-out and out-of-domain settings, WorldLine maintains strong visual quality and robot-motion agreement; on failed trajectories, it improves robot-mask IoU by 0.1626 over the strongest baseline. It predicts trajectory success with 74% mean accuracy across RoboTwin and AgiBot, one percentage point above the strongest baseline. Without RoboTwin training or adaptation, its rollouts improve task success by up to 21.4 percentage points over direct policy execution. Together, these capabilities make WorldLine a scalable and efficient visual simulator for policy evaluation and embodied planning. More results are available at \href{https://zhengsh123.github.io/WorldLine/}{project page}.

Time Series Foundation Models (TSFMs) currently provide state-of-the-art results in forecasting tasks. They are available out-of-the-box and rely on in-context learning to make their predictions, which makes the quality of their performance highly sensitive to the user-selected lookback, covariates, horizon and training data distributions. In practise, the quality of the forecasts are variable but complementary, which highlights the need for a principled ensembling approach, rather than selecting the best context. This paper introduces Latent Inference-Time Guidance for TSFMs, which adaptively combines a pool of TSFM forecasts through a time-dependent latent space with independent components. The framework comes equipped with identifiability and reconstruction guarantees, whilst maintaining the off-the-shelf aspect of foundation models. We provide experiments on datasets at various frequencies and from multiple domains: these show that the approach is competitive with traditional ensembling approaches.

Improving robot policies on new tasks without collecting additional expert demonstrations remains a central challenge in robot learning. World action models (WAMs) use broad video priors to jointly predict future videos and actions, offering a potential source of supervision for adapting to new tasks. However, generated videos may fail to depict task completion, and even visually successful videos may be paired with inconsistent actions that lead to execution failure. We propose EVO-WAM, a framework that adapts WAMs to unseen tasks by learning from their own generated video-action trajectories, without executing candidate actions in an external environment. First, we augment WAM training with state prediction and anchored multi-frame context to enable complete autoregressive rollouts without external execution feedback. Second, we identify reliable training experience by selecting task-completing prefixes with a vision-language model and verifying their video-action consistency with an inverse dynamics model. Third, we iteratively train the WAM on verified prefixes and generate new rollouts with the updated model. On seven unseen RoboTwin 2.0 tasks, EVO-WAM increases average success rates from 26.9% to 68.0% for Cosmos3 and from 28.5% to 46.4% for DreamZero, reaching approximately $2.5\times$ and $1.6\times$ their initial success rates. On three unseen long-horizon composite tasks in the real world, it improves Cosmos3's average success rate from 20.0% to 76.7%, a gain of 56.7 percentage points. Project Page: https://evo-wam.github.io/.

The liquidity providers of most typical automated market makers (AMMs) are passive and known to suffer from adverse selection. AMMs traditionally rely on trades executed on them to sync the price with external markets (and a notion of fair value thereof). As a result, when an external fair value moves, arbitrageurs trade on AMMs to pick off their stale quotes. A recent approach termed proprietary automated market makers (propAMMs) emerged as a response in 2024: these on-chain programs instead have their singular operator quote from its own inventory, repricing without a trade via efficiently provided price updates. By 2026, propAMMs accounted for more than half of SOL/USDC volume on Solana. We present the first year-long longitudinal measurement of propAMMs on Solana, Base and Monad, and decode the on-chain logic of the dominant propAMM on Base. We find that two seconds after a fill, propAMMs earn 0.37 bps on Solana and 1.19 bps on Base, while AMMs lose 0.22 and 0.62 bps. We empirically quantify and classify their edge as stemming from four factors: propAMMs continuously reprice rather than waiting for a trade, they charge for the source-dependent risk each counterparty might bring, they avoid cross-venue arbitrage from other on-chain markets (such as other AMMs), and they spoof by filling trades at a worse price than they quote. Finally, we show that on our proxy for retail flow (i.e., fills that arrive when the reference price is not moving) propAMMs collect 0.26 bps on Solana where AMMs collect 2.59 bps, indicating that they offer better prices for short-term uninformed flow.

We investigate neutron stars admixed with repulsively self-interacting bosonic dark matter (DM) using current multi-messenger observations. The dark component is modeled as a complex scalar field coupled to baryonic matter only through gravity, allowing dark-core and dark-halo configurations. To quantify baryonic equation-of-state (EOS) uncertainties, we combine a three-dimensional scan over $(m_\chi,\lambda,F_\chi)$ with 27 DDME2-based covariant density-functional EOSs spanning $L_{\rm sym}=30,50,70$ MeV and $-600\le Q_{\rm sat}\le 1000$ MeV. The models are confronted in a Bayesian framework with NICER mass–radius measurements from the Amsterdam and Maryland/Illinois analyses and the GW170817 tidal-deformability constraint. After Bayesian evidence weighting over the EOS ensemble, the EOS-relevant dark-sector scale $\mu_\chi\equiv m_\chi/\lambda^{1/4}$ is localized around 250 MeV for both NICER data sets. In the $(m_\chi,\lambda)$ parameterization, the marginalized boson-mass posterior peaks at $m_\chi\simeq300$–$330$ MeV, while $\lambda$ remains broadly distributed. Since the bosonic EOS depends on $m_\chi$ and $\lambda$ only through $\mu_\chi$, their separate marginals are conditional on the adopted independent priors. The inferred DM fraction is more data-set dependent, with posterior modes near 4% for Maryland/Illinois and 12% for Amsterdam. Bosonic DM also shifts the inferred $Q_{\rm sat}$ from negative toward intermediate and positive values, whereas the response of $L_{\rm sym}$ is weaker. This indicates a model-dependent trade-off between DM-induced compactification and the high-density stiffness of baryonic matter. These constraints remain conditional on the selected EOS family and the assumption of a common effective $F_\chi$ for all sources.

We present Pow3R-SLAM, a real-time RGB-D simultaneous localization and mapping (SLAM) system that uses Pow3R for tracking and mapping. Inspired by MASt3R-SLAM, a recent work on monocular SLAM using two-view 3D reconstruction priors, we extend the work to incorporate depth as a prior on the network's prediction, rather than as geometry to fuse. Where traditional RGB-D SLAM systems struggle with sparsity in the depth images, Pow3R utilizes the available depth to give a better-conditioned pointmap, while inferring the depths in empty regions from the two-view photometric, depth, and intrinsic data. Evaluated against MASt3R-SLAM following its protocol on 24 sequences from TUM, 7-Scenes, and Replica, Pow3R-SLAM runs 1.6x faster in wall time, has 15% lower mean trajectory error, a 3.1x lower unscaled error, and produces denser maps, with a 30% lower Chamfer distance. We also introduce a hybrid variant that runs 2.1x faster than MASt3R-SLAM at 25.3 frames per second (FPS), while maintaining improved tracking and mapping accuracy. Against ORB-SLAM3 in RGB-D mode, Pow3R-SLAM is more accurate on TUM, 7-Scenes, and ETH3D-SLAM, and completes every TUM sequence. While Pow3R-SLAM can struggle on a small set of self-similar scenes, its overall performance shows that adding depth as a prior for two-view 3D reconstruction SLAM can be beneficial. A project webpage is available at: https://ChrisKolios.github.io/Pow3R-SLAM , and code will be made open-source upon acceptance.

Approximate filtered vector search (FVS), a core operation in many data management tasks that combine structured data with vector embeddings, exhibits increased complexity due to the characteristics of filtering predicates. Each predicate is defined by selectivity (i.e., the fraction of vectors that satisfy the predicate) and correlation (i.e., the relationship between the filter and the vector space), which can significantly affect search difficulty even for the same query vector. This poses a key challenge for users aiming to integrate vector search with structured data, as efficient execution often requires extensive manual tuning of algorithm parameters. In this paper, we present VADER, the first approach that eliminates hyperparameter tuning by introducing declarative recall for approximate filtered vector search. With declarative recall, users specify a desired recall target, and VADER executes FVS queries to meet this target without requiring manual configuration. VADER achieves this by employing a filter-aware recall predictor that generalizes across varying selectivities and correlations without explicit tuning, and by performing early termination once the predicted recall reaches the user-defined target. Through extensive experimental evaluation, we show that VADER achieves near-optimal early termination, while providing significant speedups of up to 53% faster and improved result quality of 28% compared to the best-performing baseline.

We study the inflationary no-boundary wavefunction in a “linear-roll limit,” in which $G_N \to 0$ while the Hubble scale $H$ and the slope of the inflaton potential are held fixed. Although bulk graviton fluctuations are suppressed in this limit, quantum inflaton fluctuations remain finite. Because reheating occurs on a surface of fixed inflaton value, these fluctuations become fluctuations of the conformal factor of the reheating metric. The probability measure for these fluctuations simplifies drastically and becomes Gaussian, even for large fluctuations. The resulting log-correlated theory at superhorizon scales is a $d$-dimensional analog of Liouville gravity without the exponential potential, which we call Logarithmic Gravity. The quadratic and linear terms are determined by conformally covariant scattering data; in even dimensions we relate them to the critical GJMS operator and Branson $Q$-curvature. From bulk unitarity, we argue that one-loop effects do not generate additional conformal-factor dependence in the physical probability measure, and we verify the cancellation explicitly in $2 + 1$ dimensions. For the no-boundary norm with a rolling inflaton, we show that the noncompact residual conformal symmetries can be gauge fixed with a finite Faddeev-Popov determinant, so they do not force the sphere contribution to vanish. In addition, conditioning on the absence of vacuum decay by bubble nucleation generates the Liouville exponential potential in the probability measure.

We study generalized learning dynamics in multi-agent systems whose joint state evolves on a manifold and whose agents act through state-dependent, potentially nonholonomic vector fields. Under a bundle-splitting condition, we show that these dynamics admit an intrinsic representation as projected Riemannian gradients, giving rise to a class of nonholonomic gradient play dynamics. We characterize the local stability of its equilibria through an intrinsic linearization that explicitly captures the effects of the Riemannian connection and the nonholonomy of the actuation frame. The framework recovers classical gradient play on Euclidean spaces and manifolds as special cases while accommodating nonholonomic actuation. We then develop a geometric theory of deception under asymmetric information, whereby an agent exploits privileged knowledge of other agents' learning rules to manipulate the emerging equilibrium. We show that deception effectively tilts the Riemannian geometry perceived by the oblivious agents, distorting their projected gradient directions. We establish persistence of exponentially stable equilibria over an open set of deception parameters and derive an explicit first-order characterization of the resulting equilibrium displacement. Analytical and numerical examples illustrate the framework and its implications for equilibrium manipulation in games.

We investigate self-interacting dark matter in an $O(N)$-symmetric real scalar multiplet model with Higgs-portal interactions involving the Standard Model Higgs and a real singlet scalar. After spontaneous breaking of the singlet $\mathbb{Z}_2$ symmetry, the singlet scalar mixes with the SM Higgs boson. We focus on the regime where the resulting light scalar serves as a mediator, leading to sizable and velocity-dependent self-interactions. We impose constraints from Higgs measurements, rare $B$-meson decays, the dark matter relic abundance, spin-independent direct-detection searches, and scalar coupling perturbativity. We find viable parameter regions in which destructive interference between scalar-mediated scattering amplitudes suppresses the direct-detection cross section while allowing self-interactions relevant to dwarf-galaxy scales. Among these viable parameter regions, a subset also satisfies electroweak vacuum stability up to the Planck scale. Finally, we show that future long-lived-particle searches can probe part of the viable parameter space, providing complementary tests of Higgs-portal self-interacting dark matter with a light scalar mediator.

Generative models for function-valued data, such as time series and solutions of partial differential equations, must learn distributions over infinite-dimensional spaces. Functional Flow Matching (FFM) extends Flow Matching to this setting, learning a velocity field whose flow transports a Gaussian prior to the data distribution, but it inherits the independent endpoint pairing of standard Flow Matching: in each batch, prior and data samples are matched arbitrarily, so the conditional bridge must traverse both the shared global structure of the dataset and instance-specific residuals. In function space this is harder to fix than in finite dimensions, since optimal transport (OT) on function spaces is delicate to formulate and a flat Euclidean surrogate ignores the geometry that distinguishes function-valued data. We propose kernel Functional Flow Matching (kFFM), which replaces the independent pairing by entropic OT under a kernel-induced cost, the coupling underlying the Hilbert Sinkhorn Divergence (HSD), leaving the FFM neural-operator architecture unchanged. We prove that the kernel cost and the HSD objective are uniformly bounded and well-posed on Banach ambient spaces, derive an error decomposition against quadratic-cost OT on compact metric spaces that isolates an irreducible kernel-cost mismatch term, and prove a discretization-invariance bound whose rate is governed by Sobolev regularity. Empirically, kFFM improves distributional matching over FFM, diffusion, adversarial, and finite-dimensional OT baselines on time-series and PDE benchmarks, with significant paired-seed gains over FFM and improvements that persist under non-kernel and physics-based diagnostics, including a turbulent Navier-Stokes benchmark. Bounded kernel costs already outperform raw $L^2$ Sinkhorn, and function-space-aware kernels (signature, Sobolev RBF) give further gains on rough or path-valued data.

We propose a QCQP-representable IMU pre-integration factor that enables certifiable estimation with pre-integrated inertial measurements. To the best of our knowledge, this is the first work to directly incorporate IMU pre-integration into certifiable estimation. Inertial sensing is a common and reliable modality in robotics, and incorporating it broadens the practical scope of certifiable estimation. The main challenges are obtaining the required algebraic structure and a sufficiently tight convex relaxation. Standard IMU pre-integration relies on the exponential map, which does not admit an exact polynomial representation. Moreover, obtaining a QCQP formulation requires auxiliary lifting variables, for which the standard semidefinite programming (SDP) relaxation can be loose. We address these issues by deriving an IMU pre-integration factor based on the Cayley map and an explicit set of redundant constraints that tighten the resulting relaxation. To validate the proposed factor, we apply it to certifiable GNSS-IMU smoothing and evaluate it on synthetic and real-world data. The results show that the proposed formulation yields tight relaxations and solves the resulting estimation problems to verified global optimality.

Beke, Csáji, Csikvári, and Pituk showed that the Merino–Welsh quotient $\Phi(M)=T_M(1,1)^2/(T_M(2,0)T_M(0,2))$ can be arbitrarily large, so the multiplicative Merino-Welsh inequality fails for matroids in general. We show that $\Phi$ is uniformly bounded on the class of matroids whose cyclic-flat lattice avoids any fixed finite poset $P$ as an induced subposet. We further prove $\Phi(M)\leq1$ for matroids of cyclic width at most $7$, cyclic height at most $6$, and for loop- and coloop-free $4$-paving or $4$-copaving matroids.

Egocentric human demonstrations offer an accessible source of task experience, but differences in body scale and controller response, together with missing robot states, limit their value as humanoid training supervision. We present EgoAlign, a data-construction framework that converts these demonstrations into action and state supervision compatible with a general-purpose, continuous whole-body controller, without collecting physical-robot demonstrations. Using the target-robot model and simulator, EgoAlign guides demonstration collection through execution feedback. It preserves locomotion references for visually guided periodic stepping while adapting upper-body interaction geometry through scale alignment and controller-in-the-loop refinement. A final causal replay reconstructs the corresponding robot states and motion-token labels for training with the human observations. We assess the resulting supervision by fine-tuning a vision–language–action model solely on adapted human demonstrations and deploying it zero-shot on a physical humanoid. The resulting policies perform long-range object relocation, navigation to unseen goal positions, and independently evaluated foot interaction. Refinement improves simulated hand alignment and physical pickup success over kinematic alignment alone, while human collection reduces on-site acquisition time relative to teleoperation. https://lambdahumanoid.github.io/EgoAlign/

Atomic bilayers of transition metal dichalcogenides (TMDs) host quantum phases governed by the layer degree of freedom, including bilayer Wigner crystals, fractional Chern insulators, and exciton condensates. These phases are probed primarily through exciton spectroscopy, yet it remains poorly understood how excitons and carriers interact to form Fermi polarons in bilayers, where both the impurity and the Fermi sea carry a layer pseudospin. Progress has been limited because most TMD bilayers have momentum-indirect optical bandgaps, in which non-radiative decay and inhomogeneous broadening obscure the intrinsic spectra. Here, we show that bilayer MoTe$_2$, unlike most TMD bilayers, retains a direct optical bandgap, providing a clean platform for studying bilayer Fermi-polaron physics. In a dual-gated device, an out-of-plane electric field continuously tunes the hybridization between intralayer and interlayer excitons, forming layer-coherent excitons. Upon electrostatic doping, the excitonic spectrum evolves into multiple polaron branches, controlled by both carrier doping and the out-of-plane electric field. Among these, we identify a polaron with no analog in monolayers, in which a layer-coherent exciton is dressed by carriers in the opposite layer, and is quantitatively captured by our field-theoretic model. Our results establish that pseudospin structure in both the impurity and the bath reshapes polaron formation, opening new avenues to many-body states such as Bose-Einstein condensates with interlayer coherence.

We reveal an unexpected connection between two interacting particle systems: Kac's walk and the Kipnis-Marchioro-Presutti (KMP) process. We first establish a mixing-time analogue of Aldous's conjecture for the KMP process on general graphs: the mixing time of the $t$-particle process on any connected $d$-vertex graph is at most $O(\log d)$ times the corresponding single-particle mixing time, uniformly in $t$. As an application, we improve the mixing-time bound for coordinate hit-and-run on the $n$-dimensional standard simplex from $\widetilde{O}(n^3)$ [KV26] to $O(n\log n)$, while removing the dependence on the initial distribution. We then show that the twirling channel induced by the parallel Kac's walk on the symmetric subspace can be exactly encoded by a Markov chain on partitions, which naturally lifts to a parallel KMP chain on the complete graph. We prove that $O(\log d+\log(1/\varepsilon))$ repetitions of the parallel Kac's walk suffice to approximate Haar twirling on the symmetric subspace of $(\mathbb{C}^d)^{\otimes t}$ to error $\varepsilon$, uniformly in all $t$. Our main technical contribution is a new structural property of KMP-type dynamics: conditional product structure, which holds for both the standard KMP processes on general graphs and the parallel KMP processes on complete graphs. Conditioned on suitable auxiliary randomness, the evolution of the labeled KMP process factorizes into independent single-particle updates. Combining this structure with an exact coupling, we remove the dependence on the number of particles from the mixing bounds for both unlabeled KMP models. This bypasses the $\log(\pi_{\min}^{-1})$ dependency from spectral-gap arguments, which is often prohibitively large for many-particle systems. Using this framework, we prove mixing bounds that are sharp up to logarithmic factors for both unlabeled KMP models.

Interactive agent benchmarks and multi-turn reinforcement learning increasingly place a second language model in the role of the user. This simulated user controls what information the agent receives and when, yet current benchmarks score only the agent and do not directly measure whether the user correctly executed its assigned role. We introduce UserProxyBench, an evaluation layer over the tau-bench family, and the User Fidelity Score (UFS), which measures adherence to the benchmark's private user instructions using task-grounded rubric criteria scored independently of agent success. Holding the agent fixed at GPT-5.5 and varying only the user proxy across 375 enterprise tasks changes mean task reward by 15.2 points, while 24.4% of successful episodes contain a user-specification violation. The dominant failure is premature disclosure: users provide information before it is requested. This behavior has little effect on task reward, yet among successful episodes it causes the agent to make 1.06 fewer tool calls on average, changing the interaction being evaluated while preserving the reward. Finally, across seven proxies we identify an empirical cost-fidelity frontier, enabling practitioners to select the least expensive simulator that satisfies a required fidelity level.

Cold atomic hydrogen plays a crucial role in the life cycle of interstellar gas. It serves as the intermediary phase in the condensation and cooling processes that bridge the warm diffuse gas in and around galaxies, and the cold molecular gas that drives star formation. HI self-absorption in the 21-cm emission line is the most direct observational tracer of cold HI gas that does not require a continuum background source, yet its systematic extraction remains a long-standing challenge. Existing methods of self-absorption identification rely on subjective by-eye inspection or modelling of the underlying emission, making repeatable, thorough, and large-scale applications difficult. We present a lightweight convolutional neural network designed to detect self-absorption features and infer their velocities via a post-hoc process, without assumptions about the underlying emission or the use of ancillary data. Trained on synthetic emission spectra, the neural network achieves 96.5 per cent accuracy, 96.0 per cent precision, and 97.0 per cent recall on held-out synthetic data. Applied to observed 21-cm emission data from the Riegel–Crutcher cloud and giant molecular filament regions towards the Galactic Plane, the network recovers the spatial distributions and velocities of known self-absorption structures when compared to previous analyses and ancillary 13CO emission data. Crucially, the neural network is computationally efficient, processing detections for ~15,000 spectra per second on a single consumer laptop GPU, enabling real-time cold HI detection at the data rates anticipated by next-generation facilities such as the Square Kilometre Array.

We prove a sharp Santaló-type inequality for the product of $V(\varphi)$ and $V$ of the Legendre transform of $\varphi$, where $\varphi$ is an even geometric convex function on $\mathbb{R}^n$ and $V(\varphi)=\int(1+\varphi)^{-(n+1)}$. For this size functional, the Legendre transform and functional polarity give the same volume, so the same inequality holds for both dualities. Through a projective correspondence, the problem is equivalent to a new Santaló-type inequality with respect to standard volume and standard polarity, on a class of not necessarily centered convex bodies. This class consists of convex bodies $K\subset\mathbb R^n\times[-1,1]$ containing $\{0\}\times[-1,1]$, for which every horizontal section is centrally symmetric about the distinguished vertical axis. We determine the sharp upper bound for $\operatorname{vol}_{n+1}(K)\operatorname{vol}_{n+1}(K^\circ)$ in this class and classify all equality cases. When $n=1$, the extremizers are the disk and its horizontal linear images. When $n\ge 2$, the ball is no longer a maximizer, and the extremizer is unique up to horizontal linear transformations and the reflection $t\mapsto -t$. The symmetric Santaló inequality applied to horizontal sections, together with monotone transport, reduces the problem to a maximization problem for increasing curves in the square $[-1,1]^2$. We solve this problem using a global potential when $n=1$ and two Hamilton-Jacobi branches when $n\ge 2$. Finally, in dimension one we provide a sharp family of functional Santaló inequalities for the Legendre duality, interpolating between the volume $V$ and the exponential volume $\int \exp(-\varphi)$, with centered quadratics as the only equality cases.

For real codimension two smooth foliations, we study the transversely complex structures, transversely complex projective structures and transverse opers associated to the foliation. We prove a uniqueness theorem for the transversely holomorphic ${\mathbb C}{\mathbb P}^1$–bundle naturally associated with a transversely complex projective structures. A similar uniqueness theorem is proved for the transversely holomorphic filtered ${\mathbb C}{\mathbb P}^{r-1}$–bundle naturally associated to a transverse ${\rm PGL}(r,{\mathbb C})$–oper.

Aims. We aim to illuminate how the pulsars' integrated pulse profiles and single-pulse modulation evolve with radio frequency, while separating intrinsic and propagation effects. Methods. We present integrated pulse profiles and phase-resolved modulation indices for 12 radio pulsars at up to five frequency bands. Our wideband dataset was systematically acquired with the Nancay Radio Observatory telescopes and the uGMRT, covering the frequency range 10 MHz to 2.8 GHz, including NenuFAR, LOFAR FR606, uGMRT, and NRT observations. We carefully measured the pulse widths and scattering times using multi-component profile fitting. We employed a profile width scaling model to separate the profile evolution into scattering and intrinsic contributions. We quantified the pulsars' single-pulse variability across frequency. Results. We describe the pulse profile evolution. Two pulsars have scattering indices compatible with Kolmogorov turbulence, while the majority have flatter scattering indices. This suggests complex scattering environments, dominated by localised turbulence. Complex scattering behaviour is seen in some pulsars, and most profiles are scattering-dominated below 200 MHz. The measured intrinsic power law indices are small, with absolute values between 0 and 0.3. Five pulsars exhibit decreasing intrinsic widths, two or three pulsars show flat behaviour, and four pulsars have increasing profile widths with frequency. Accounting for biases, most pulsar modulation parameters decrease with frequency, while three pulsars show flat behaviour. Conclusions. The pulse width evolution is explained by intrinsic radio beam narrowing, the emergence of profile components, and the balance between the two. Our modulation analysis indicates that the single-pulse emission from most of our pulsars becomes more erratic towards lower radio frequencies, consistent with increasing amplitude modulation.

Entanglement distillation from noisy bipartite states and reliable quantum communication over noisy channels are fundamental tasks in quantum information theory. Yet existing coding schemes typically require prior knowledge of the underlying state or channel, or assume independent or weakly correlated quantum information sources. Here, using Schur-Weyl duality, we establish a universal quantum error-correction principle that overcomes these limitations. We show that the irreducible permutation spaces arising from the local Schur-Weyl decomposition of multiple copies of an unknown bipartite mixed state form maximally entangled quantum code spaces whose error structure is governed entirely by representation theory. Correcting these symmetry-resolved errors yields protocols for entanglement distillation and quantum communication that achieve coherent-information rates with exponentially vanishing error and optimal second-order corrections, even in the case of almost i.i.d. resources. Our approach also provides sharp finite-copy guarantees that are worst-case optimal at every finite block length, including in the sample-efficient regime, where the number of copies scales only polynomially with the number of qubits. Together, these results establish Schur-Weyl duality as a general mechanism for universal, robust, and optimal quantum coding, unifying entanglement distillation, quantum error correction, and quantum communication within a common representation-theoretic framework.

Emergence, features of a whole that no part shows alone, is central to complex systems but rarely measured so as to locate its source. Viewing a system structurally, as a network of interacting parts, we evaluate emergence as what observing the coupled whole reveals beyond, or erases from, the combined observations of the parts. For observations that build what they see route by route, we show that every emergent feature is produced by its own route across the interface between parts, a route that traces it to the components and interactions responsible. We show the number of all such boundary-crossing paths bounds the total emergence discrepancy, and equals the emergence of measures that count routes. The bound is computed locally around the interface, validated through network examples, and in a nervous system the routes show that interneurons relay most of the emergence. Our work associates emergence with path structure in the network system that can be anticipated, attributed, and engineered.

Understanding gender biases in large language models (LLMs) is increasingly important as these systems become embedded in decision-support tools with real consequences. Prior research has focused only on a small set of models, leaving open the extent to which gender biases are common and heterogeneous across LLMs. We address this gap across ten models released between April 2025 and June 2026, spanning nine vendors, using two paradigms: gender attribution to stereotyped phrases (Study 1) and moral judgment of abuse or torture against a woman or a man to prevent a catastrophic outcome (Study 2). In Study 1, two of ten models attributed masculine-stereotyped phrases to female writers more often than the reverse, while three models showed the opposite pattern. In Study 2, several models converged on a male-disadvantaging asymmetry that was directionally consistent with a documented human tendency to protect female targets from harm, though the specific conditions under which this asymmetry emerged varied by model; three other models, by contrast, showed no variation across conditions. These results indicate that gender-related biases are common in LLMs. Their direction and magnitude, however, are highly heterogeneous, to the point that some models behave in diametrically opposite ways to others. Bias auditing should therefore be treated as an ongoing, multi-vendor process, rather than a one-time assessment.

We give an explicit solution to the five expert prediction with expert advice partial differential equation (PDE) in the finite-time horizon setting. The solution formula establishes that the adversary's rank strategy $(1,0,1,0,0)$ is globally optimal, and the COMB strategy $(1,0,1,0,1)$ is optimal exactly on the set where $x_1=x_2$ and $x_3=x_4$. The formula is derived from the solution of the geometric-stopping problem given in our companion paper through the transform principle of Bayraktar, Ekren and Zhang, which links the two problems by a Laplace transform. Inverting the transform term by term expresses the solution through a series of Gaussian and complementary error function kernels. The optimality of $(1,0,1,0,0)$ is reduced to the signs of $41$ one-variable Gaussian series, which are certified with computer assistance by Poisson summation, first-mode domination and interval arithmetic on $1616$ rational cells. The proofs of our main theorems, certificates included, are also formalized in the Lean proof assistant.

We study fair and strategy-proof allocation of multiple divisible resources with Leontief utilities, motivated by cloud computing. The canonical mechanism, Dominant Resource Fairness (DRF), satisfies sharing incentive (SI), envy-freeness (EF), strategy-proofness (SP), and Pareto optimality (PO), but can be highly inefficient in terms of utilitarian social welfare. Under the classical approximation benchmark, no mechanism satisfying even one of SI, EF, and SP can improve on the trivial worst-case guarantee. We therefore adopt the recently introduced fair-ratio benchmark, which compares a mechanism only with the welfare-maximizing allocation that itself satisfies SI and EF. For two resources, we first introduce Adaptive-Speed Fairness (ASF), a unified parametric framework that captures previous mechanisms as special or boundary cases. Every ASF mechanism satisfies SI, EF, and PO, and we derive a general sufficient condition that guarantees SP. Optimizing within this framework yields a strategy-proof mechanism with asymptotic fair-ratio $2/(2\sqrt{2}-1)\approx 1.094$, substantially improving the previous best guarantee $3-\sqrt{3}\approx1.268$. We complement this upper bound with a lower bound of $1.0789$ for all ASF mechanisms. To overcome this limitation, we introduce Corrected Resource Balancing (CRB), which uses the full resource-load structure together with a one-agent incentive correction. CRB satisfies SI, EF, SP, and PO and achieves fair-ratio at most $1+1/n$. Together with a general $1+\Omega(1/n)$ lower bound, this establishes the optimal asymptotic order $1+\Theta(1/n)$ for two resources. Finally, for every $m\ge3$, any deterministic mechanism satisfying SI and SP has fair-ratio exactly $m$. The same lower bound holds for randomized mechanisms satisfying ex-post SI and truthfulness in expectation.

Interlayer excitons in transition metal dichalcogenide (TMD) heterostructures exhibit long lifetimes and long-range transport, making them promising for excitonic devices and quantum many-body phases, such as Bose-Einstein condensates. Achieving these goals requires a precise understanding of spin-allowed bright and nominally spin-forbidden dark excitons, because the lowest-energy exciton species governs population, transport, and condensation. Despite substantial progress, unambiguously distinguishing singlet and triplet interlayer excitons has been challenging, as moiré excitons in these heterostructures can mimic their optical signatures. Here, we report the direct spectroscopic identification of bright (singlet) and dark (triplet) interlayer excitons in high-quality, dual-gated WSe$_2$/hBN/WSe$_2$ homobilayers. Electric-field-dependent photoluminescence and reflectance reveal two momentum-direct interlayer transitions with distinct spin configurations. The interlayer dark excitons obey selection rules that differ from those of bright excitons. Strikingly, interlayer dark excitons retain strong valley polarization, even with their ultralong lifetime exceeding microseconds. Finally, we demonstrate twist-angle control, wherein twist-induced electron-hole momentum mismatch modulates interlayer exciton emission. These results provide critical insights into the electronic and excitonic structure of TMD heterostructures, opening new avenues for excitonic many-body physics and optoelectronic devices.

We prove a conjecture proposed by the first-named author in 1998. Let $f\colon\mathbb{C}\to\mathbb{P}^n$ be a transcendental linearly non-degenerate holomorphic curve of finite lower order. If the counting function $N_1(r,f)$ of its Wronskian zeros satisfies $N_1(r,f)=o(T(r,f))$, then its order and lower order coincide and belong to $\{1+k/q:k\in\mathbb{Z}_{\geq 0},\ 2\le q\le n+1\}$, and its characteristic is regularly varying. Every order in this set occurs. We also prove the sharp inequality $\limsup_{r\to\infty}N_1(r,f)/T(r,f)\geq 1$ for transcendental linearly non-degenerate curves of order zero.

We prove weak solvability for a two dimensional nonlinear Boussinesq type groundwaterflow problem motivated by the Moche CHAVIMOCHIC aquifer in northern Peru. The model couples state dependent storage and transmissivity with a boundary decomposition into Dirichlet, Neumann, and nonlinear Robin parts dictated by the hydrogeological geometry. In contrast with much of the groundwater Boussinesq literature, which is devoted to exact, similarity, perturbative, semi-analytical, or linearized solutions for special geometries and boundary data, our objective is a variational existence result for a genuinely two-dimensional mixed-boundary problem. Because the physical transmissivity is proportional to the saturated thickness, the equation degenerates at local depletion. We therefore isolate a physically admissible saturated range and construct uniformly positive extensions of the constitutive laws. For the resulting uniformly parabolic problem, existence of a weak solution is obtained through an implicit Euler Rothe scheme, a nonlinear energy adapted to the storage law, uniform estimates for the discrete derivative of the storage potential, discrete compactness, and strong convergence of boundary traces. We then give a precise consistency statement showing when the abstract solution solves the original Moche model and identify the fully depleted regime as a distinct porous medium type problem.

We investigate the recently introduced polygonal hypergeometric functions [arXiv:2502.12127, arXiv:2507.01904], which are conjectured to evaluate multipoint parametric one-loop conformal integrals in arbitrary dimensions. These functions can be systematically constructed using a diagrammatic algorithm that operates in terms of simple planar shapes. Given an $n$-point polygonal power series, we formulate the corresponding GKZ hypergeometric system, which admits an explicit diagrammatic interpretation. In particular, the transianic matrix, which encodes all the relevant diagrammatic data, determines the corresponding toric matrix along with a basis of the lattice of relations, thereby singling out a finite subsystem of $n(n-3)/2$ toric equations. This finite subsystem consists of second- and third-order equations, whereas the full toric family also includes higher-order ones. We illustrate the general procedure with several prominent examples of polygonal functions, including the fourth Appell and the Srivastava–Daoust functions.