arXiv subjects

Rui Chen

Publications and source records attributed to Rui Chen.

At least 37 records · Page 2Linked to original sources

arXiv2026

MotionPersona: Real-Time Locomotion Control across Personas, Bodies, and Styles

We present MotionPersona, a generative framework for character-aware locomotion control, in which the motion for a command depends on the captured persona, the body shape, and the character's style. Unlike style, which one performer can vary at will, persona and body shape are coupled in capture: each performer is observed in only one body. The captured data therefore cannot uniquely determine which motion characteristics should follow the persona and which should change with the body, leaving unseen persona-body combinations unconstrained. We capture 48 performers, aged 5 to 68, under the same nine styles and seven commands, 44 of them with persona annotation. From this repeated-measures design, we identify two robust associations between body shape and gait. These measurements guide a cross-body specification of which characteristics should change and which should be preserved. We implement this specification through a physically informed retargeting pipeline, producing cross-body training data while penalizing penetration and foot skating. On this data we train a single generative controller. A shape-aware VAE compresses each motion block into a few latent tokens and renders them on a conditioned target body under explicit geometric supervision; over these tokens, a latent flow-matching prior generates persona- and style-conditioned motion in two sampling steps. The controller covers all captured personas, a wide family of SMPL-X target bodies, and nine styles in one model, and runs at 27 ms per block on two threads of a laptop CPU. We verify the framework at every stage, following the same gait descriptors from captured to retargeted to generated motion and sweeping each axis in isolation. To our knowledge, this is the first real-time locomotion controller that carries part of a captured persona's performer-specific variation across independently selected body shapes and styles.

cs.GR↗

arXiv2026

The Logarithmic Laplacian on Complete Riemannian Manifolds

We introduce, for the first time, a Bochner representation of the logarithmic Laplacian on general complete Riemannian manifolds via spectral calculus and the heat semigroup. More precisely, letting $P_0=E(\{0\})$ denote the orthogonal projection onto $\ker(-Δ)$ and $Q=I-P_0$, and defining the logarithmic operator to vanish on $\ker(-Δ)$, we prove \[ \log(-Δ)f = \int_0^\infty \frac{e^{-t}Qf-e^{tΔ}Qf}{t}\,dt, \] where the integral converges in the strong improper sense in $L^2$. This representation recovers the classical pointwise logarithmic Laplacian on $\mathbb R^n$. Under a lower Ricci curvature bound and an explicit large-time heat-kernel integrability condition, we derive a pointwise integral representation on complete noncompact manifolds. We also compare the spectral and heat-kernel definitions and identify their difference explicitly in terms of the loss of heat mass. On $\mathbb H^n$, $n\ge2$, we compute the fractional and logarithmic kernels, determine their asymptotics at zero and infinity, and derive absolute convergence, continuity, and $L^p$ integrability under Dini and weighted integrability assumptions.

math.AP↗

arXiv2026

The Fractional-Logarithmic Laplacian: Fundamental Properties and Eigenvalues

In this paper, we introduce the fractional--logarithmic Laplacian $ (-Δ)^{s+\log} $, defined as the derivative of the fractional Laplacian $ (-Δ)^t $ at $t=s$. It is a singular integral operator with Fourier symbol $ |ξ|^{2s}\log|ξ|^2 $. We derive its pointwise integral representation \[ (-Δ)^{s+\log}u(x) = c_{n,s}\,\operatorname{PV}\int_{\mathbb{R}^n} \frac{u(x)-u(y)}{|x-y|^{n+2s}} \bigl(-2\log|x-y|\bigr)\,dy + b_{n,s}(-Δ)^s u(x), \] where $c_{n,s}$ is the normalization constant of the fractional Laplacian and $b_{n,s}:=\frac{d}{ds}\log c_{n,s}$. We also establish equivalent formulations of $ (-Δ)^{s+\log} $, including a definition via spectral calculus and a characterization through an extension problem. We develop the functional-analytic setting for $ (-Δ)^{s+\log} $ both on $\mathbb{R}^n$ and on bounded domains with continuous boundary. We introduce the associated energy spaces and prove Sobolev and Poincaré inequalities. In particular, we obtain a compact embedding at the critical exponent $2_s^*=\frac{2n}{n-2s}$, in contrast with the classical and fractional Sobolev embeddings. We further study the Poisson problem and prove existence and $L^\infty$-regularity results. We then investigate the Dirichlet eigenvalue problem and establish qualitative spectral properties. Finally, we derive Weyl-type asymptotics for the eigenvalue counting function and for the $k$-th Dirichlet eigenvalue. These asymptotics combine the fractional Weyl power law with an additional logarithmic factor, consistently connecting the high-frequency growth of the fractional Laplacian with that of the logarithmic Laplacian.

math.AP↗

arXiv2026

Existence and Convergence of Least-Energy Solutions Involving the Logarithmic Schrödinger Operator

In this paper, we study critical semilinear nonlocal elliptic equations involving the logarithmic Schrödinger operator and its fractional pseudo-relativistic counterpart, both arising in quantum models with nonlocal and relativistic effects. We first establish the existence, uniqueness, and regularity of weak solutions to equations involving the logarithmic operator $(I - Δ)^{\ln}$ with subcritical logarithmic nonlinearities. We then investigate a Brezis--Nirenberg-type problem involving the fractional pseudo-relativistic Schrödinger operator $(I - Δ)^s$, and prove the existence of least-energy solutions under both subcritical and critical nonlinearities. In particular, we show that these least-energy solutions converge, up to a subsequence, to a nontrivial least-energy solution of the limiting problem as $s \to 0^+$. Our approach relies on variational methods, including the geometry of the Nehari manifold, uniform positive lower bounds, mountain-pass structure, the Palais--Smale condition, and delicate asymptotic analysis.

math.AP↗

arXiv2026

M2Note: Continual Evolution of Vision Language Models via Mistake Notebook Learning

Vision Language Models (VLMs) have demonstrated remarkable capabilities in multimodal reasoning tasks, yet they still suffer from recurring failures, such as skipping key visual checks, misapplying domain rules, and hallucinating unsupported concepts. Most existing solutions rely on supervised fine-tuning (SFT) and reinforcement learning (RL), which are expensive to iterate and can be brittle under distribution shift. To this end, we propose Multimodal Mistake Notebook Learning (M2Note), a training-free continual evolution framework that externalizes learning into an editable memory. M2Note transforms failed trajectories into compact subject-guidance notes: the subject summarizes the underlying domain and concept, while the guidance provides actionable verification steps that can be reused in future inference. At test time, M2Note retrieves relevant notes via multimodal retrieval-augmented generation (RAG) and appends them to the model context, steering reasoning away from previously observed pitfalls. To stabilize continual evolution, we adopt batch-level post-verification with rollback, which commits notebook edits only if they improve performance on the same batch, reducing noisy updates and preventing regressions. M2Note supports both self-evolving, where the same VLM acts as solver and supervisor, and cross-model evolving, where a stronger supervisor guides a weaker solver, enabling capability transfer without weight updates. Experiments on six multimodal reasoning benchmarks show consistent improvements across domains and backbones, while achieving strong cost and sample efficiency and remaining complementary to Chain-of-Thought (CoT) prompting.

cs.MA↗

arXiv2026

Fundamental Gaps for the Dirichlet p-Laplacian on Convex Domains

We study the fundamental gap of the Dirichlet $p$-Laplacian on bounded convex domains. We first prove the sharp one-dimensional estimate $Γ_p(I_D,V)\ge (p-1)(2^p-1)(π_p/D)^p$, $I_D=(-D/2,D/2)$, for all $1 2$, $G_{p,N}>0$ and the infimum is attained. We obtain explicit dimension-dependent bounds and $G_{p,N}\asymp_p N^{p-2}$ as $N\to\infty$, while for fixed $N$, $\lim_{p\downarrow2}G_{p,N}=3π^2$ and $\lim_{p\to\infty}G_{p,N}^{1/p}=4$. We also characterize the collapse as $p\downarrow2$: minimizing domains degenerate, and every limiting normalized ground-state measure is supported on a unit segment and, up to rigid motions, equals $2\cos^2(πt)\,dt$ on $(-1/2,1/2)$. The proof establishes log-concavity of the first $p$-eigenfunction with convex potential, a degenerate weighted Poincaré inequality for the ground-state measure, and a lower gap bound in terms of the first eigenvalue and the associated weighted Poincaré constant. These estimates also give the compactness and equality analysis for the collapsing minimizers.

math.AP↗

arXiv2026

ActiveArena: Benchmarking and Understanding Active Perception in Robotic Manipulation

Active perception and manipulation are crucial for robots to interact with complex scenes. Existing benchmarks struggle to evaluate how robots effectively acquire and maintain information in memory in an active manner. To this end, we introduce ActiveArena-Sim, an active-perception simulator with controllable viewpoints and large-scale workspaces as the foundation. Built on this, we propose ActiveArena-Bench, which comprises 35 tasks across 5 fine-grained categories, covering visual exploration and interactive information acquisition. Each task is difficult to solve from passive observations alone, requiring multi-round evidence acquisition and memory-based reasoning. The benchmark provides rich memory annotations, standardized training data, and ID/OOD protocols featuring disjoint scenes, unseen distractor configurations, and novel backgrounds. Moreover, we present ActiveArena-VLA, a modular suite of 13 vision-language-action configurations for controlled studies of memory writing, memory capacity, proprioceptive state, subtask supervision, and high-level planning in active perception. Benchmark results reveal a substantial ID-OOD gap: uniform memory sampling, increased memory capacity under reliable write policies, proprioceptive inputs, and subtask supervision improve OOD generalization, while planner-guided memory management and decision-making achieve performance close to the best-performing configuration using only sparse memory. ActiveArena thus provides a unified testbed to develop and diagnose models for active perception and manipulation.

cs.RO↗

arXiv2026

The Right Future for Action: Learning Action-Relevant Predictive States in World Action Models

Generation-free world action models (WAMs) retain future-video prediction during training but act from internal video features at inference, leaving unclear what these features should preserve for control. Our representation diagnostics show that representations with more predictable future changes need not make linear action decoding easier. Observed future changes provide additional action information beyond the present, and linearly readable action information is spatially concentrated. These findings motivate Action-Relevant Predictive States (ARPS), a compact predictive interface between the video and action experts. ARPS uses a horizon-conditioned state predictor to aggregate intermediate video features into a compact state that supplies all visual context to the action expert. Future-representation supervision trains different parts of this state to predict visual representations at different future times, together with their changes relative to the present. At inference, the supervision branch is removed, and the action expert only uses the learned predictive state computed from current observations. Controlled ablations show that future supervision substantially improves generalization under distribution shift. ARPS achieves 99.2% success on LIBERO and transfers to LIBERO-Plus without adaptation, reaching 87.3% and exceeding Fast-WAM by 39.2 percentage points.

cs.CV↗

arXiv2026

The Coulhon--Duong conjecture for the Riesz transform on complete Riemannian manifolds

Let $M$ be a complete, non-compact Riemannian manifold. We prove that its Riesz transform is of weak type $(1,1)$, with constant $2$ for real-valued functions. Consequently, it is bounded on $L^p(M)$ for $1<p\leq2$, with constants depending only on $p$, which proves the Coulhon--Duong conjecture. The proof uses an obstacle decomposition for positive self-adjoint operators with sub-Markovian semigroups. Applying this decomposition to the shifted square-root Laplacian and using locality of the Sobolev differential yields the endpoint estimate without geometric or heat kernel assumptions. We also obtain the corresponding result for Dirichlet spaces admitting a local Hilbertian differential calculus.

math.CA↗

arXiv2026

$D^{(*)}Δ$ interactions and the molecular interpretation of $Σ_c(3200)^0$

Inspired by the recent observation of the $Σ_c(3200)^0$ baryon in the $Λ_c^+π^-$ invariant mass spectrum by the LHCb Collaboration, we perform a comprehensive investigation of the $D^{(*)}Δ$ interactions within the one-boson-exchange framework. Our results show that the $D^*Δ$ molecule with $I(J^P)=1(1/2^-)$ can be regarded as the most natural candidate for the $Σ_c(3200)$, and predict the existence of several $D^*Δ$ molecular partners with $I(J^P)=1(3/2^-, 5/2^-)$ and $2(1/2^{\pm}, 3/2^{\pm}, 5/2^-)$. After including the coupled channel effects between $DΔ$ and $D^*Δ$, several shallowly bound $DΔ$-dominated molecular candidates also emerge, especially for the $I(J^P)=1,2(3/2^-)$ and the $2(1/2^+,3/2^+)$ systems. These results provide a unified molecular interpretation of the newly observed $Σ_c(3200)^0$ and useful guidance for future experimental searches for exotic charmed-baryon states. We expect the high-statistics data from the LHCb Upgrade and Belle~II runs will directly test these predictions.

hep-ph↗

arXiv2026

4DStreamCtrl: Interactive Video Generation with Online 4D Control

Generative video models now synthesize footage nearly indistinguishable from reality. Their promise as interactive tools hinges on fine-grained control of how objects and the camera move over time, yet each existing approach captures only part of this: camera-parameter methods steer the viewpoint but cannot move objects, 2D-trajectory methods act in the image plane and ignore depth and occlusion, and recent 3D methods add geometry but run only offline at a fixed length. In particular, none combines 3D-consistent control of both camera and objects with real-time, streaming generation. Here we show that camera motion, object trajectories, and depth can be unified into a single 3D point-track representation, from which one model performs joint camera and object control, depth editing, and motion transfer in a single forward pass. To learn this interface at scale, we mine in-the-wild video for 3D motion supervision, yielding OpenVidHD-Motion3D, and encode it with a lightweight Geometric Motion Head that plugs into a pretrained video diffusion model. Because this encoder is temporally separable, we distill the model into a causal streaming student that generates arbitrarily long video in four denoising steps at memory independent of length. This unified design surpasses prior camera-only, 2D, and offline-3D methods in motion-control precision while covering modalities they address only in isolation. 4DStreamCtrl runs at 20 FPS on a single high-end GPU for 480p video and stays temporally coherent over hundreds of frames, enabling, to our knowledge, interactive 4D-controllable streaming generation for the first time. More broadly, grounding generation in explicit 3D geometry with efficient causal inference points toward interactive world models with closed-loop spatiotemporal control, from controllable simulators to real-time visual imagination for embodied agents.

cs.CV↗

arXiv2026

On Faber-Krahn inequality for Dirichlet Fractional-Logarithmic Laplacian

We study the Faber--Krahn problem for the fractional--logarithmic Laplacian $(-Δ)^{s+\ln}$, $0<s<1$, with Fourier symbol $|ξ|^{2s}\ln|ξ|^2$. We prove a small-volume and large-volume dichotomy. For sufficiently small volume, balls minimize the first Dirichlet eigenvalue, with rigidity up to translation.

math.AP↗

arXiv2026

Doppler-Robust Vortex Wavefront Design for Integrated Sensing and Communication

Integrated sensing and communication (ISAC) is a promising paradigm for future wireless systems due to spectrum reuse, hardware sharing, and joint waveform design. In dynamic scenes, Doppler shifts degrade both sensing and communication, which is particularly critical for beam-sensitive orbital angular momentum (OAM) wavefronts. To address this, we propose a Doppler-robust ISAC framework, which first senses and then communicates. Specifically, in the sensing phase, multiple vortex modes are simultaneously transmitted via code-division mode-multiplexing (CDMM). To solve Doppler-induced inter-mode interference, we propose a velocity-consistency matching (VCM)-expectation maximization (EM) algorithm that jointly decodes the sensing matrix and estimates range, azimuth, elevation, and velocity for multiple moving targets. In the communication phase, the joint transmitter (Tx) beamforming and receiver (Rx) beam steering are configured from the estimated channel state information (CSI). We further quantify the sensing-communication allocation trade-off by evaluating how pilot length affects estimation accuracy, beam alignment, and spectral efficiency (SE). Simulation results show that the proposed VCM-EM and ISAC designs achieve higher sensing accuracy and communication SE than baseline schemes in dynamic scenarios.

eess.SP↗

arXiv2026

Fully Coupled Nonlinear Forward-Backward Stochastic Difference Equations: Spectral Contraction and Infinite-Horizon Maximum Principle

This paper develops an explicit spectral-contraction approach to studying fully coupled nonlinear forward--backward stochastic difference equations on infinite horizon and their applications to stochastic control. The estimates for this fully coupled system are assembled into an explicit two-dimensional nonnegative matrix. Its spectral radius yields an explicit sufficient discount threshold, and a corresponding equivalent weighted product norm is constructed to establish the contraction property. Moreover, for an infinite-horizon control problem with convex control constraints and an accumulated discounted running cost, we derive a Pontryagin-type stochastic maximum principle, its equivalent pointwise normal-cone formulation, and a verification theorem. Finally, a recursive risk-adjusted portfolio example is given to demonstrate the applications of our theoretical results, and a projection-type sufficient optimality condition for this example is derived.

math.OC↗

arXiv2026

Two-point estimates for the logarithmic p-flux of the first Dirichlet p-eigenfunction

Let $u>0$ be the first Dirichlet $p$-eigenfunction on a bounded convex domain $Ω\subset\mathbb R^N$, and set \[ X_Ω:=|\nabla\log u|^{p-2}\nabla\log u. \] We study whether the sharp one-dimensional two-point modulus for $X_Ω$, which for $p=2$ reduces to the logarithmic-gradient estimate of Andrews and Clutterbuck, persists for $p\neq2$. We prove sharp estimates on intervals and balls for every $p>1$, with the radial modulus on balls strictly larger than the one-dimensional one. In dimensions $N\ge2$, however, the one-dimensional modulus fails on general convex domains for every $p\neq2$. For $1 2$, on thin domains $Ω_\varepsilon=D\times(-\varepsilon,\varepsilon)$, with $D\subset\mathbb R^{N-1}$ bounded and convex, the normalized first eigenfunctions satisfy \[ u_\varepsilon(x,\varepsilon z)\longrightarrow \frac{ϕ(z)}{ϕ(0)} \left(\frac{G_D(x)}{G_D(x_0)}\right)^{2/p} \] locally uniformly in $D\times(-1,1)$, where $ϕ$ and $G_D$ are the first Dirichlet eigenfunctions of the $p$-Laplacian on $(-1,1)$ and of the Laplacian on $D$, respectively. This yields the failure for $p>2$. Finally, for arbitrary $C^2$ functions, positivity of the symmetric differential of the $p$-gradient implies convexity, and the converse holds universally if and only if $p=2$.

math.AP↗

arXiv2026

Editable Visual Design

While diffusion base models such as GPT-Image-2 and Nano-Banana exhibit remarkable visual expressiveness, their end-to-end generation inherently yields flattened bitmaps with error-prone text, precluding layer-wise post-editing. Conversely, code-based visual generation via Coding Agents provides precise layout control and decoupled layers, yet remains constrained by a lack of global aesthetic intuition and the difficulty of coding complex visual assets. To address this, we propose Editable Visual Design, a new paradigm driven by a Coding Agent. We designate the VLM as the ``creative brain'' for requirement comprehension, task planning, and aesthetic judgment, while utilizing the image generation model as an on-demand ``visual world simulator'' to synthesize standalone visual assets. Operating under an ``imagine first, then act'' closed-loop workflow, the agent generates isolated assets, writes native HTML/CSS, and iteratively refines the design against visual rendering feedback. Furthermore, Agent Design Replay faithfully reproduces the creative and reasoning trajectory akin to that of professional human designers. Ultimately, the system delivers editable artifacts with decoupled layers and real text, enabling users to perform intuitive mouse dragging and layout adjustments on a graphical user interface. Validations on posters, infographics, and other scenarios show that this paradigm successfully achieves both refined aesthetics and production-grade editability.

cs.CV↗

arXiv2026

Learning 3D Editing without Paired Supervision via Generative Prior Distillation

Instruction-guided 3D editing is essential for interactive content creation, yet it faces a significant bottleneck: the severe scarcity of high-quality paired training data. Existing approaches attempt to bypass this by either relying on slow test-time optimization or training on pseudo-pairs constructed via complex pipelines, which often introduce structural drift and geometric artifacts. In this paper, we propose a novel framework that learns feed-forward 3D editing without paired 3D supervision via Generative Prior Distillation. Instead of relying on ground-truth 3D pairs, our core idea is to distill visual, semantic, and geometric knowledge from powerful foundation models directly into a 3D editing model. Specifically, through a differentiable rendering pipeline, we supervise the 3D representation using two complementary signals: a 2D visual prior from an image editing model at the main editing view, and a semantic prior from a Vision-Language Model at novel views to ensure strict instruction following and source identity preservation. Crucially, to address the geometric collapse and multi-view inconsistencies inherent in 2D projection supervision, we introduce a 3D-aware Distribution Matching regularization. Acting as a geometric prior, this term operates in the 3D latent space, constraining the edited output to remain within the manifold of realistic 3D assets defined by a pretrained image to 3D teacher model. Extensive experiments demonstrate that our method achieves superior instruction fidelity and cross-view consistency, significantly outperforming state-of-the-art baselines. Our project is available at: https://github.com/thiamine128/PriorEdit3D.

cs.CV↗

arXiv2026

Analysis of Electromagnetic Scattering from Semiconductor Nanostructures by Solving Coupled Volume Integral and Two-fluid Hydrodynamic Equations

Semiconductor-based plasmonic nanostructures support localized surface plasmon modes in the infrared region. Unlike metallic nanostructures, they support both free electrons and holes, requiring a two-fluid hydrodynamic Drude equation (HDE) to accurately capture spatial dispersion effects and low-frequency acoustic plasmon modes that cannot be described by single-fluid models. In this work, a volume integral equation (VIE)-based solver is proposed for the analysis of electromagnetic scattering from semiconductor nanostructures. The proposed approach couples the VIE, formulated in terms of the electric flux density and the free-electron and hole polarization currents, with the two-fluid HDE. The coupled system is discretized using a tetrahedral mesh and solved efficiently using a two-level iterative solver. In contrast to finite-element-based methods, the proposed VIE-based approach does not require domain-wide meshing and inherently satisfies the radiation condition, thereby eliminating artificial absorbing boundaries. Numerical results for InSb-type semiconductor nanostructures demonstrate the accuracy and efficiency of the proposed VIE-based solver and its ability to capture unique optical phenomena, such as acoustic plasmon resonances and the blueshift of localized surface plasmon resonances, that cannot be described by the single-fluid HDE or classical Drude-based models.

physics.optics↗