Papers

In Taiwanese Hokkien automatic speech recognition (ASR), prior studies often treat tone sandhi as a major challenge under the assumption that models fail to process implicit phonological variations. However, our experiments on Taiwanese Hokkien reveal that speech foundation models actually handle tone sandhi variations effectively, and the real performance bottleneck stems from a localized confusion between these variations and retained citation tones. To address this, we propose T-SANDHI to explicitly decouple surface acoustics from underlying lexical intent on top of a frozen Whisper backbone. Using a lexicon-guided multi-task learning structure driven by text-derived pseudo labels, our lightweight hybrid injection module integrates independent citation and sandhi phonetic streams via dynamic gating. Extensive evaluation on the TAT-MOE corpus and two blind test sets demonstrates that this explicit disentanglement effectively resolves tonal mapping confusion, outperforming baselines with strict parameter efficiency.

World models can anticipate the consequences of navigation actions, but predicted action sequences may become invalid during execution, especially when wheel-legged robots encounter dynamic obstacles or change locomotion modes. We propose WAVE-Go, an image-goal navigation framework that separates world-action prediction from interruptible command execution. Its executor adaptively selects an action prefix and cancels pending commands when updated observations invalidate execution. A conditional-risk formulation specifies prefix selection under an estimated cumulative failure budget, while posture and locomotion-mode transitions require clearance, stability, and task-evidence checks. In the reported navigation evaluation, WAVE-Go achieves 74.1% in-distribution success and 63.3% dynamic out-of-distribution success, exceeding the strongest baseline by 4.7 and 7.7 percentage points, respectively, while reducing collisions from 4.4 to 2.9 per 100 m. Compared with interruptible fixed four-command execution, WAVE-Go raises success by 4.0 percentage points while reducing replanning frequency by 51.2% and collision rate by 6.5%. Execution ablations also show that runtime interruption improves success, collision rate, and reaction latency at the cost of additional replanning. These results support adaptive, interruptible execution as a means of balancing navigation performance and planning overhead. Code is available at https://github.com/vigorlee/wave-go.

We present RadioAstron observations of the M87 jet obtained on 2014 February 4-5 at 4.8 GHz ($\lambda=6.2$ cm). The correlated signals between the 10-m space antenna and ground-based radio telescopes were detected up to projected baselines of $\thicksim3$\,Earth diameters (0.65~G$\lambda$). The orientation of the jet downstream of the core shifts northward, consistent with the long-term oscillating trend reported in other studies. An elliptical body mode of the Kelvin-Helmholtz instability can create the observed helical shape of the jet. The estimated wavelength of this instability mode suggests that its origin may be related to some processes in the accretion disc. We present 1.7 - 4.8 GHz and 4.8 - 15.4 GHz spectral index maps showing flattening of the spectrum along the outer streamlines and along the jet spine. Simulations and analysis show that this spectral flattening is partially artificial and is a common systematic effect of the CLEAN procedure of VLBI imaging. The spectral index of the M87 jet is consistent with the optically thin emission, while its steepening can be produced by the propagation of the instability modes causing higher pressure regions near the jet boundary and in its interior.

Agile quadrotor avoidance of fast-moving obstacles requires anticipating collisions and selecting feasible maneuvers within short reaction windows. Reliable predictive avoidance remains challenging because sparse range observations do not directly reveal obstacle motion, while online trajectory optimizers either scale poorly with obstacle count or remain efficient at the expense of reliability in dense, high-speed encounters. We present OmniRisk, an omnidirectional planning framework that learns trajectory-level risk offline for efficient onboard evasion. A fixed-dimensional tensor combines LiDAR range panoramas, dynamic masks, and Cartesian surface velocities to represent geometry and motion jointly. We formulate an asymmetric risk field aligned with obstacle velocity that emphasizes approaching interactions and attenuates receding ones. Accumulating this risk along predicted relative trajectories provides dense supervision and discourages unnecessary hesitation after obstacles pass. A dual-branch circular convolutional network predicts terminal boundary states and dynamic risks for candidate primitives over an omnidirectional anchor lattice in a single forward pass, followed by selection and closed-form reconstruction of the selected candidate primitive. This formulation removes online risk accumulation along trajectories and makes risk-inference cost independent of obstacle count. OmniRisk enables efficient onboard avoidance, with real-world flights demonstrating consecutive evasive maneuvers at relative encounter speeds up to 15 m/s without fine-tuning. Code is available at https://github.com/VANdexj/OmniRisk.

How neural representations preserve the structure of input changes connects representation analysis with internal intervention. We study operable representational content through compatible actions of reference transformations on neural features. We characterise when a transformation descends through an encoder, and give a linear setting in which the defect is governed by the transformation's demand for discarded information, measured in the metric the representation induces. On a rectifier the failure to realise a transformation has two distinguishable sources — what the source region has already made unrecoverable, and what it costs to satisfy every region the transformation visits with one operator — and for a measured harmonic carrier the same question has a closed answer: a linear realisation exists exactly when the retained harmonic blocks are invariant under the action. Using colour as the in-depth instance, we find that hue orbits in frozen visual features concentrate 84–88% of their energy in the first two harmonics with rotation planes shared across shapes, that this organisation is substantially inherited from input and architecture and is reshaped by training and depth, and that the measured structure supports prediction, transport from new starting states, and composition — with global and local realisations differing sharply in which they achieve. Guided by the measurements, we construct a compact interface whose rotation action is fixed by the structure and never fitted: it reads hue zero-shot at 3.4$^\circ$ median error on unseen shapes. Theory, structural measurement, and construction together establish transformation laws as a concrete object connecting the understanding of neural representations to their design.

Recently, momentum-space nonsymmorphic symmetries have attracted considerable attention. However, their realizations typically rely on fine-tuning hopping phases to satisfy the required projective symmetry algebras. Here, we show that such symmetry algebras arise naturally on bipartite lattices through the interplay of crystalline and sublattice symmetries. Unlike previously studied cases, these symmetry operators can anticommute with the Hamiltonian and are therefore referred to as momentum-space nonsymmorphic chiral symmetries. Although the free actions of these symmetries reduce the Brillouin torus to more elementary manifolds, the resulting manifolds are twisted in the Atiyah–Segal formalism. In particular, chiral glide reflection (screw rotation) gives rise to a twisted Klein bottle (dicosm) in two (three) dimensions, and this twisting dramatically alters the topological classification. Unlike the untwisted Klein bottle, whose nonorientability forces the Chern number to vanish, the twisted Klein bottle can host nonzero Chern numbers, corresponding to even Chern numbers on the torus. At open boundaries, the corresponding topological invariant manifests itself through chiral edge states exhibiting a glide-reflection structure in energy–momentum space. Our results establish momentum-space nonsymmorphic chiral symmetry as a new organizing principle for discovering and engineering topological phases beyond conventional crystalline classifications.

AI-assisted sourcing streamlines candidate review, reducing the administrative burden of manual screening for recruiters. However, deploying language models as production rankers remains challenging. Zero-shot Large Language Models (LLMs) may produce unstable, non-deterministic scores and rank less accurately, while conventional deep neural rankers require millions of logged interactions that a low-traffic, niche sourcing platform does not produce. What is available instead is a few hundred thousand ordinal relevance labels – small by ranker-training standards, but sufficient when a pretrained language model already encodes the general world knowledge the task depends on. We present single-token expected-value scoring, a ranking primitive that casts candidate-job relevance as an ordinal classification over the grade tokens {1, ..., 5} and reads the relevance score as the expectation of the first-token probability distribution. Because the score comes from a single decoding step rather than open-ended generation, it is a deterministic function of the model's logits, requires no output parsing, and serves at low latency. To learn the non-linear interdependencies of heterogeneous hiring criteria from this supervision alone, we fine-tune a Small Language Model (SLM) with a hybrid ordinal regression loss combining a Mean Squared Error term, which preserves ordinal distance, with a categorical Cross-Entropy term, which sharpens class boundaries. We evaluate along two dimensions – Jobseeker Relevance and Employer Relevance – using NDCG@10 and low relevance rate. Offline, our fine-tuned model outperforms a heuristic baseline and zero-shot LLMs. An end-to-end simulation shows the same direction at larger magnitude (+54.2% Jobseeker NDCG@10, -46.7% low relevance rate), and a live online experiment reduces employer low-relevance by 27.3% and raises employer keep rate by 7.07%.

We consider $n\times n$ covariance matrices $M=\frac{1}{n}XX^*$ where $X=(x_{i,j})$ is a matrix whose entries are independent complex random variables with $\mathbb{E}(x_{i,j})=0$ and $\mathbb{E}(|x_{i,j}|^2)=1$. We derive a $\frac{1}{n}$ expansion of the mixed moments, $\frac{1}{n}\mathbb{E}(\Tr(M^{(r_1)}\cdots M^{(r_q)}))$, of the form $a_0+a_1\frac{1}{n}+O(\frac{1}{n^2})$. This permits us to find explicit formulas for the moments and infinitesimal moments of several covariance matrices where we allow repetition. As an application of our formulas, we derive asymptotic freeness and infinitesimal freeness of independent covariance matrices under a fourth-moment condition. This generalizes previous results for the Wishart ensemble in which $x_{i,j}$ is complex Gaussian.

In recent years, large language model-based AI companion and role play chatbots have grown increasingly popular. People turn to these chatbots for emotional support and to engage in romantic and erotic role play. Although prior research suggests that digital role play can help people explore their gender and sexuality, LLM based technologies are also replete with gender and sexuality biases. In this study, we examine one way that AI chatbots can harm users: misgendering. In order to study chatbot misgendering we qualitatively analyzed 326 posts mentioning misgendering that were shared in AI companion or role play subreddits. We document how chatbot misgendering takes place and how, in response, users engage in ongoing work to curate their gender presentation to prevent and repair misgendering. We discuss how researchers and designers can mitigate chatbot misgendering and consider the implications of using AI chatbots for identity exploration.

We establish three weak averaging principles for distribution-dependent stochastic Navier–Stokes equations with rapidly oscillating coefficients on the torus $\T^2$. First, solution laws are relatively compact on finite time intervals, and every limit point as $\var\to0$ is the path law of a variational martingale solution of the averaged equation. Under a dissipative condition, we can choose bounded complete variational solution laws of the original and averaged equations so that every sequence with $\var\to0$ has a subsequence converging weakly to a bounded complete variational solution law of the averaged equation. At the level of probability laws, the original nonautonomous equation admits a family of weak pullback attractors, while the averaged equation has a weak global attractor. The weak pullback attractors converge upper semicontinuously to the weak global attractor of the averaged equation, uniformly with respect to the coefficient hull.

This paper investigates generalized conformal modules over the Virasoro conformal algebra $Vir$, a notion originally defined by V.~Kac but largely unexplored in the literature. First, we present a twisted construction that produces new generalized conformal modules over any Lie conformal algebra from existing conformal modules. Then we give a complete classification of non-trivial generalized conformal modules over $Vir$ that are free of rank one over $\mathbb C[\partial]$, which in turn yields a classification of modules over the Lie algebra \(W_1=\bigoplus_{i\geq -1}\C L_i\) of vector fields on a line that are free of rank one over $\mathbb C[L_{-1}]$ with explicit actions expressed in terms of Bell polynomials. For arbitrary finite rank $n$, we construct a class of generalized conformal modules $V_{a,b,C(\partial)}$ and establish a complete irreducibility criterion in terms of the differential operator $\mathcal L=\frac{d}{d\partial}+C(\partial)$ acting on $\mathbb{C}(\partial)^n$. In the case of $n=2$, this criterion reduces to the absence of rational solutions of a Riccati equation. Then we prove the existence of irreducible generalized conformal modules of arbitrary finite rank, revealing a striking contrast with the conformal setting. We also construct and classify a family of infinite torsion generalized conformal modules over $Vir$, which are non-trivial and irreducible under suitable conditions.

The properties of water under high pressure and high temperature (HP-HT) are critical in multiple geochemical processes in deep Earth. Ab initio molecular dynamics (AIMD) is a promising approach to study water under extreme conditions without any empirical parameters. However, the accuracy of AIMD simulations is determined by the exchange-correlation (XC) functional including the dispersion correction used in density functional theory calculations. While van der Waals (vdW) interactions are well known to be critically important for water under ambient conditions, the influence of the dispersion correction on the properties of HP-HT water as found in Earth's mantle remains largely unexplored. To address this, we carried out AIMD simulations for supercritical water at 1, 5, and 10 GPa, and 1000 K. We compared PBE, PBE-D3, RPBE-D3, and SCAN functionals, where D3 means Grimme's D3 dispersion correction. We compared the structural, diffusion, and vibrational properties of water as computed with these XC functionals. Overall, the discrepancies between the functionals are reduced under extreme P-T conditions relative to ambient conditions. PBE and PBE-D3 exhibit higher proton-transfer rates than RPBE-D3 and SCAN, suggesting that while vdW interactions do not significantly affect the water structure under extreme conditions, the oxygen-hydrogen bond strength does influence proton transfer. Our results provide molecular-level insight into water in Earth's mantle and offer valuable guidance for selecting appropriate XC functionals in AIMD simulations of aqueous solutions under extreme conditions.

Real-world agents fundamentally require persistent non-parametric knowledge for dynamic reasoning, i.e., long-term memory and retrieval-augmented generation. While graphs have shown reliable advantages in providing structured evidence, the sparse graph representations naturally restrict machine readability and semantic density required for complex agentic workflows. Driven by this limitation, the entire industry is witnessing a paradigm shift from traditional sparse graphs to LLM Wiki, an agent-native knowledge representation that couples dense document contexts with markdown files containing multi-layered topological linkages. However, parameterizing such rich semantics is challenging to encode dense textual contexts using traditional sparse graph embeddings. Moreover, learning LLM Wiki with existing graph encoders could overwhelm distributed system overheads that hinder deployment in large-scale commercial scenarios. To this end, we propose a novel paradigm Wiki Foundation Model, i.e., WFM, tailored for scalable, agent-native representation and retrieval. Specifically, (i) we formalize a Wiki Graph schema that seamlessly bridges fine-grained structures with dense contexts, maintaining explicit topologies alongside continuous semantics; (ii) A query-conditioned attentive aggregation is tailored for rich wiki message passing and explicit attention variance regularization; (iii) We engineer an infrastructural NCCL boundary exchange protocol that hoists static partition indices and leverages fixed-shape GPU-to-GPU collectives, bypassing CPU serialization and memory copy overheads. Extensive evaluations across five long-term agent memory and multi-hop reasoning benchmarks demonstrate the remarkable performance of WFM, while achieving a 10.5 times training acceleration on distributed clusters.

Replication studies revisit previous experimental findings for multiple purposes, including assessing reliability, exploring generalisability, and evaluating research methods. Such studies entail design decisions that a single replication label cannot fully capture, making their designs difficult to describe and compare. We present REPVIS2, a validated design space that describes how a replication study relates to a reference study across eight practical dimensions, each coded as identical, similar, or different. We refined our initial design space, REPVIS1, by applying it to a corpus of replication studies and validated REPVIS2 against a separate corpus. We then characterised 86 replication studies from 51 papers in visualisation through paired reading of the replication and reference reports. Studies often retained the task while changing the procedure, interface, environment, participant population, evidence, or analysis. Additions beyond the replication core were also common. REPVIS2 makes replication design explicit for characterisation, reporting, and planning. An interactive visualisation and supplementary materials are available at https://replication-study.github.io/.

We present a GPU-accelerated, PyTorch tensor-based simulation framework designed to generate high-fidelity galaxy-galaxy strong lensing images. By integrating synthetic Spectral Energy Distribution (SEDs), the pipeline accurately models the redshift-dependent photometric properties of lens and source galaxies, ensuring physical consistency across multi-band observations. The framework incorporates key observational parameters, including Point Spread Functions (PSF), magnitude limits, and zero points, to replicate specific survey conditions, thereby enabling robust cross-survey joint analyses. As an application, we simulate multi-band images for KiDS, LSST, and Euclid using identical lens model parameters, and employ a deep learning network to evaluate image deblending performance. In particular, the simulation leverages PyTorch to ensure full auto-differentiability and GPU acceleration, making it a highly efficient tool for advanced deep learning algorithms that require gradient-based optimization beyond standard model training. Our framework achieves a speedup of approximately $\mathcal{O}(10^3)$ over traditional CPU-based pipelines, demonstrating the potential feasibility of joint gradient-based lens modeling across next-generation surveys.

Let $f_n$ be the $n$-th Fibonacci number with $f_1=f_2=1$. Recently exact formulas for the integer parts of the tails of inverse reciprocal Fibonacci numbers have been obtained in several cases. However, the cubic case ($s=3$) is much more complicated because of highly oscillating error terms. Thus it is difficult to construct a precise continuous approximation and algebraic estimates simultaneously. In this paper, we give a complete and unified algebraic method to solve this difficulty. More precisely we construct an explicit closed form of sequence $g_n$, preserving the principal part $f_n^3-f_{n-1}^3$, such that $\ds \lim_{n\rightarrow\infty}\left\{ \left( \sum^\infty_{k=n}\frac{1}{f_k^3} \right)^{-1}-g_n \right\}=0. $ By decomposing the error terms and investigating the algebraic identities, we establish the lower and upper bounds $ \ds g_n<\left( \sum^\infty_{k=n}\frac{1}{f_k^3} \right)^{-1}<g_n+2/f_n $ for sufficiently large $n$. As an application of the explicit form of the sequence $g_n$ and these estimates, we completely determine the exact value of the floor function for $s=3$.

Distributed model training at scale is frequently interrupted by transient network failures, conventionally forcing cluster managers to abort all processes and roll back to the latest checkpoint. While periodic checkpointing provides durability, frequent snapshotting introduces severe storage backpressure: our measurements on a 1.216B-parameter decoder reveal that per-update asynchronous checkpointing incurs up to a +656.7% latency overhead, consumes 32.5 GiB of host memory, and generates 3.39 TB/hour of storage traffic. To eliminate this overhead, we present AccelPact, a parallel runtime enabling zero-I/O in-memory fault recovery for sharded distributed training. When communication fails at a committed optimizer step, device memory remains quiescent and uncorrupted, yet continuation fails because frameworks like PyTorch FSDP cache internal communication handles across module wrappers and parameter hierarchies. AccelPact resolves this dependency invalidation via a non-invasive reference-rebinding mechanism coordinated by an out-of-band Gloo consensus protocol. On 16 NVIDIA RTX 5880 GPUs training full-parameter Mistral-7B, AccelPact eliminates checkpoint replay, yielding a 1.197x whole-run goodput improvement over cold restart and 1.194x over NVRx checkpoint restoration at checkpoint age 5, rising to 1.698x at age 18. Across ten successive fault injections, all 16 ranks maintain bit-identical parameter state with zero numerical drift. Across 4-to-16 GPU cluster topologies, reference rebinding executes in constant time (0.493-0.518 ms). Operating directly on native communicator instances, AccelPact requires zero application-code modifications and avoids compiler graph breaks under torch.compile, providing an efficient foundation for resilient deep learning.

In this paper, a lattice Boltzmann method with an adaptive relaxation parameter and a Lax–Friedrichs-type equilibrium is proposed for hyperbolic systems with source terms. The equilibrium distribution recovers the conservative variables and physical fluxes while incorporating dissipation determined by characteristic-speed bounds. To balance accuracy and robustness, the relaxation parameter is selected from a local smoothness indicator based on characteristic projections. In smooth regions, the parameter approaches the low-dissipation limit, retaining second-order accuracy; near discontinuities, it is automatically reduced to introduce localized dissipation and suppress nonphysical oscillations. The stabilization acts directly through the local collision step and preserves the standard collide-and-stream structure, without a posteriori recomputation or interface-based limiting. Maxwell iteration establishes second-order consistency in smooth regions, and a weighted $L^2$-stability estimate is proved for linear hyperbolic systems with periodic boundary conditions under a standard CFL condition. Numerical experiments for scalar advection, Euler, shallow-water, and reactive Euler equations demonstrate the expected accuracy for smooth solutions and robust resolution of challenging one- and two-dimensional discontinuous problems, including wet–dry fronts and reactive discontinuities. A large-scale simulation of a 2D cellular detonation further demonstrates the capability of the method to resolve long-time multidimensional shock–reaction interactions.

Mixture-of-Experts (MoE) architectures decouple model capacity from computational cost, yet incur high memory footprints as parameters grow linearly with the number of experts. Recurrent Transformers achieve parameter efficiency by reusing layer weights, but typically lack the capacity for competitive language modeling. We propose Mixture of Reused Experts (MoRE), a hybrid that shares expert pools across groups of adjacent layers. Each layer retains its own router but selects from a larger shared pool, expanding the diversity of routing combinations without additional parameters. To enable shared experts to distinguish between layers, we introduce lightweight learnable depth embeddings that condition each layer's input before routing. Experiments across three model scales (114M-1.15B parameters) show that MoRE consistently achieves lower perplexity and stronger downstream performance than standard MoEs and state-of-the-art weight-sharing architectures at matched compute and parameter budgets, with only minimal modifications to existing MoE implementations.

Let $f(k)$ denote the smallest integer such that every oriented graph $D$ with chromatic number at least $f(k)$ contains every oriented tree on $k$ vertices. Burr (1980) showed that $f(k)\le (k-1)^2$ and conjectured that $f(k)=2k-2$. Bessy, Gonçalves and Reinald (2025) proved that $f(k)=O(k^{3/2})$. In this paper, by using an absorbing set method, we show that $f(k)\le \lfloor 31\log (k!)\rfloor=O(k\log k)$.

Dexterous in-hand manipulation requires policies that coordinate high-DoF hand joints through intermittent, contact-rich interaction. Beyond target-orientation tracking, such policies must discover finger gaits that preserve object stability while adapting to geometry, anisotropy, pose, contact, and sensing changes. We propose \method, a tactile-conditioned behavior prior model for dexterous reorientation. \method distills multi-scale sphere specialists into a latent controller and lets downstream policies reuse the fixed tactile prior through residual latent actions, reducing renewed exploration from raw joint commands. The prior conditions on tactile-proprioceptive history so latent behavior reflects the current hand-object interaction. We evaluate arbitrary-pose transfer across anisotropic objects, commanded-axis rotation, and an arm-hand Grasp-to-AnyPose task in which the robot must grasp, lift, transport, and reach goal poses for novel tool geometries and generalized placements. Extensive experiments demonstrate that the proposed method accelerates training and enables stable policies where matched raw-action PPO remains near failure, with successful sim-to-real transfer in in-hand and arm-hand tasks.

Vehicle tracking is fundamental to applications ranging from urban mobility and public safety to security and defense. Conventional tracking relies on direct access to sensors that provide strong observations such as vehicle identity and location. In practice, however, factors such as ownership, privacy, cost, and operational constraints may limit directly accessible sensors, leaving sparse observations and long tracking gaps. Meanwhile, many additional third-party sensing assets may be present across the environment but remain inaccessible at the raw-data level, preventing their direct integration into the tracking system. In this work, we investigate whether weak, indirect observations with uncertain spatial and temporal cues can complement sparse direct sensing for vehicle tracking. Specifically, we propose GrayTrack, which fuses weak anonymous events with sparse direct observations using a road-constrained particle filter. We build a CARLA-Mininet-WiFi pipeline to evaluate the system under controlled conditions, generating direct observations from accessible cameras and indirect observations from third-party cameras. Our learning-based detector achieves an F1 score of 0.989 for anonymous vehicle passages. Further, incorporating indirect third-party observations reduces trajectory RMSE by 60.1% and catastrophic track loss from 35.8% to 0.3%. These results demonstrate that GrayTrack can effectively exploit weak indirect observations to extend tracking capabilities.

Applied instrumental variables (IV) practice reports a first-stage F, now often the conditional F of Sanderson and Windmeijer (2016), and reads a large value as license to interpret the second stage. We show that no first-stage diagnostic can provide it. With a scalar instrument, a scalar treatment, and covariates entered linearly, the 2SLS estimand splits into a signal that a saturated specification would target and a contamination, the covariance between curvature in the instrument propensity and a covariate level function. The same nuisance sits in both terms, so it biases the estimand and inflates the reported strength at once. When the instrument is nearly collinear with the covariates the signal vanishes and the strength is manufactured. When the strength is honest the curvature still biases the estimand through the outcome, where no first-stage number reaches it. We prove that no functional of the joint distribution of instrument, treatment, and covariates can detect this second bias, and we give a directed test built from reduced-form regressions, a corrected estimator, and a reportable contamination share. Two applications show the modes. A husband's insurance instrument (Olson, 1998) has a conditional F above 36,000, yet correcting a linear income control more than doubles the estimate. The instrument of Nunn and Wantchekon (2011) loses most of its first stage once geography enters flexibly.

We develop an \(m\)-Hessian approach to the construction of finite-Monge–Ampère weights on complete noncompact Kähler manifolds. Let \((M^n,g)\) be a complete noncompact Kähler manifold of complex dimension \(n\ge3\) with positive holomorphic bisectional curvature. The main new ingredient is a quantitative capacity mechanism based on lower-order complex Hessian operators. More precisely, we obtain decay estimates for suitable relative \(m\)-Hessian capacities on dyadic annuli and show that these estimates imply the summability of the top-degree Monge–Ampère masses of a uniformly Lipschitz plurisubharmonic exhaustion. Consequently, we construct a proper function $$ u\in PSH(M)\cap C^{0,1}(M) $$ such that $$ \int_M(dd^c u)^n<+\infty. $$ The key point is the passage from lower-order \(m\)-Hessian capacity decay to finite Monge–Ampère mass, which is not a formal consequence of \(m<n\) Hessian mass estimates. We then explain how this finite-Monge–Ampère weight fits into the weighted holomorphic-function and analytic Bezout framework for uniformization. In particular, the construction provides a higher-dimensional pluripotential-theoretic mechanism that complements recent surface results and opens a route toward uniformization under positive curvature in complex dimensions \(n\ge3\).

We obtain exact solutions of the nonlinear Dirac equation in $1+1$ dimensions of the form $\psi(x,t) = e^{-i\omega t} \psi(x)$ for scalar-scalar (SS) plus vector-vector (VV) interaction with interaction Lagrangian given by $$L_{I} = \frac{g^2}{\kappa+1}[(\bar{\psi} \psi)^{\kappa+1} +\frac{1}{p} (\bar{\psi} \gamma_\mu \psi \bar{\psi} \gamma^{\mu} \psi)^{\kappa+1}]$$ where $p > 0$ but arbitrary otherwise. We look for solutions with $0 < \omega < m$ where $\omega, m$ are frequency and mass, respectively. We find solutions for all values of $\omega$ in this range. We compute the charge $Q$ and the energy $E$ for each of the solitary wave solutions and explore the region in the ($p, \kappa$) parameter space in which solitary wave bound states exist (i.e., for which $E/Q < m$). We show that for all the cases while both $E$ and $Q$ depend on the coupling constant $g$, their ratio $E/Q$ is independent of $g$. We further find that in case $p\kappa \le 1$, the charge density for all the solitary waves have only single hump while for $p \kappa > 1$ there is a transition from double to single hump and we determine it as a function of $\omega/m$. We notice that for all $p$ there is a transition at $\kappa=2$ in the behavior of $E/Q$ as a function of $\omega$ which we speculate is related to the onset of instability of the solutions at $\kappa=2$. We obtain the nonrelativistic reduction of the two-parameter family to a non-relativistic modified nonlinear Schrödinger equation (NLSE) and discuss the stability of the single hump olitary waves in the domain of validity of the modified NLSE.

Self-motion manifold (SMM) characterizes the geometric structure of the infinite inverse kinematic solutions set of a redundant manipulator at a fixed end-effector pose, and its efficient recovery underpins feasible and global optimal motion planning. Existing methods such as null-space continuation and learning-based methods are formulated around the assumption that an SMM is a curve, and do not extend to higher redundancy orders. We instead adopt a probabilistic view: SMMs are the support of the conditional posterior over configurations given a target pose, so that recovering it reduces to sampling from a learned distribution and separating its disjoint components by clustering. The formulation is independent of the manifold dimension and requires no architectural change as the redundancy order grows. In this work, we demonstrate that our method can approximate 1-D SMMs with performance comparable to the latest null-space continuation and learning-based approach, and that it is the first method capable of approximating highly redundant 4-D SMMs in a 7R manipulator for position tasks. Project website: \href{https://github.com/accuracy-maker/high-dimenstional-self-motion-manifold-approximation}{https://github.com/accuracy-maker/high-dimenstional-self-motion-manifold-approximation}

The Higgs vacuum expectation value (VEV) alters both the electroweak and strong interaction rates. We study both effects on big bang nucleosynthesis (BBN) and seek concordance between observed primordial abundances of light elements and cosmological constraints from CMB fluctuations and anisotropies. We find a strong negative correlation between primordial 4He abundance and the Higgs VEV. Consequently, using a 1.58% uplift of the Higgs VEV during BBN from the current value, an agreement can be achieved among the new primordial 4He abundance, observed by the EMPRESS group, Deuterium abundance determined from absorption lines in the Lyman-alpha forest along the line-of-sight of high-redshift quasars, and the lithium abundance on the Spite plateau. This agreement requires a baryon-to-photon ratio different from the CMB determination, indicating the need for nonstandard cosmological evolution between BBN and recombination epochs. We also demonstrate that a 0.2% uplift in the Higgs VEV can partially alleviate the "cosmic Li problem," keeping consistency with the CMB with remaining discrepancy potentially accounted for by stellar depletion mechanisms.

Adapting to changes in robot dynamics requires learning from new data without discarding experience that may still be useful. In continual model-based reinforcement learning (RL), replay collected before a dynamics change can slow adaptation, while removing it unnecessarily reduces available training data and can be especially costly if earlier dynamics return. We study when recent transitions are preferable to the full replay history. Two quantities characterize this trade-off: change magnitude and age-staleness area under the curve (AUC), measuring how well transition age separates stale from fresh data. Forgetting stale data helps after large permanent shifts but hurts when dynamics recur and older data becomes useful again. Choosing a replay strategy therefore depends on predicting when older data will help or hurt. We test these effects across two locomotion morphologies, two model-based RL algorithms, and Real-World RL benchmark perturbations. Because ground-truth staleness labels are unavailable on deployed robots, we evaluate whether an estimator built from interaction data can still provide the quantities needed to choose a replay strategy after permanent changes. Our results show that replay retention depends on change magnitude and on how the dynamics evolve.

We study the challenging problem of learning depth-three circuits in the mistake-bound model of (realizable) online learning, which is a more difficult model than distribution-free PAC learning. Prior algorithms for this problem, due to Servedio and Tan [ST17], could only learn polynomial-size depth-three circuits of poly$(n)$ size over $\{0,1\}^n$ with a running time of $2^{n - \Omega(n/\log n)}$, and hence they ran in time $N^{1-o(1)}$ where $N=2^n$ is the running time of a naive memorization-based approach. In this work we substantially improve on the [ST17] result: for any constant $\gamma\geq1$, we give an algorithm that learns depth-three circuits of size $n^\gamma$ with running time \[ 2^{n-c_\gamma n}, \] where $c_\gamma>0$ depends only on $\gamma$ and not on $n$. Hence we achieve a polynomial savings over the naive approach for learning any polynomial-size depth-three circuit. The main driving force behind our improvement is an improved bound on the approximate degree of width-$k$ CNFs. Inspired by Szegedy [Sze04] and Magniez et al. [MNRS11], the rough idea of our construction is to use a Chebyshev polynomial to efficiently amplify the spectral gap of a carefully designed random walk. This is combined with a random-restriction-like approach to separately learn different subfunctions corresponding to different assignments to a randomly chosen set of variables, using the Perceptron algorithm over a specially designed feature space. A simplified warmup instantiation of our approach achieves $c_\gamma = \exp(-O(\gamma))$; by augmenting this warmup with further ingredients we obtain the sharp form of our result, which achieves $c_\gamma=\Omega(1)/\gamma$.

A low-impedance robot finger reports through joint torque how strongly it is loaded, but the same torque can arise from a small force near the fingertip or a large force near the joint. Resolving the force therefore requires knowing where along the finger contact occurred. LUMO makes that location externally observable. Embedded LEDs illuminate a compliant silicone pad, and contact deforms the pad so that light emerging from the finger's side changes in a pattern set by where the load acts. Because the same structure also carries the contact load, we optimize its cross-section, including the pad profile, rigid carrier, and lateral void, for two behaviors at once. Mechanically, the pad conforms under low preload while the carrier increasingly restricts further deformation as load rises. Optically, different contact locations produce separated responses on the finger's side. The search uses rigid–soft contact simulation, ray tracing, and multi-objective Bayesian optimization. Across two silicones, six contact locations, and 10- and 30-mm spherical indenters, the optimized morphologies improve neighboring-location separation relative to variation from re-establishing contact by \(15\)–\(59\%\). Estimating contact location from the optical response using the known LED spacing and combining it with joint torque gives \(1.44~\mathrm{N}\) normal-force MAE over 931 samples. In a two-finger hand, localized side responses appear on several links simultaneously during grasps.