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Yupeng Wang

Publications and source records attributed to Yupeng Wang.

At least 19 recordsLinked to original sources
arXiv2026

Explicit Boundary-Entropy Deficits in the XX Spin Chain with arbitrary boundary fields

The exact thermodynamics of the XX spin-1/2 chain with arbitrary Hermitian boundary fields is constructed via fusion techniques. The rigorous result shows that (1) each end with a nonzero transverse field contributes $+\frac12T\ln2$ to the low-temperature free energy, whereas strictly diagonal and free ends contribute no such linear term; (2) each nondiagonal end has a characteristic temperature $T_B$, which scales as $T_B\propto h_\perp^2/J$ in the weak-field regime. For $T\ll\min\{J,T_B\}$, the boundary entropy approaches a deficit of $\frac12\ln2$ relative to a diagonal end. As the transverse field tends to zero, the boundary crossover scale vanishes and the low-temperature expansion becomes nonuniform. The present result provides a clear benchmark not only for the boundary thermodynamics of open boundary quantum integrable systems, but also for dot defects in quantum critical systems.

math-ph↗
arXiv2026

An elliptic generalization of the $D^{(2)}_{2}$ Spin chain

An integrable elliptic generalization of the closed $D^{(2)}_2$ quantum spin chain is constructed. Taking the trigonometric limit, we have shown that the corresponding R-matrix reduces to that of the $D^{(2)}_2$ one, up to a similarity transformation. Basing on the very fact of the factorization for the R-matrix and the corresponding transfer matrix which indeed ensures the integrability of the model, we give the exact solution of the model which can be expressed in terms of a homogeneous T-Q relation.

math-ph↗
arXiv2026

A $p$-adic Riemann--Hilbert correspondence over Robba rings

We construct overconvergent period sheaves $\mathcal{O}\widetilde{\mathbb{C}}^{I,\dagger}$ and $\mathcal{O}\mathbb{B}_{\mathrm{dR}}^{\dagger,+}$ on the $v$-site of a liftable semi-stable formal scheme $\mathfrak{X}_Z$. By establishing a decompletion theorem for small representations, we prove a $p$-adic Riemann-Hilbert correspondence relating small $\widetilde{\mathbb{C}}^I$-local systems (resp. $\mathbb{B}_{\mathrm{dR}}^+$-local systems) on the generic fiber $X_Z$ to small flat connections on the associated period ringed spaces. We further analyze the local Frobenius action and show that this correspondence is compatible with the Frobenius structure. As an application, we prove a comparison theorem between the cohomology of these period sheaves and the rigid cohomology of the special fiber, refining results of Le Bras and Colmez--Nizioł.

math.AG↗
arXiv2026

TacHair: Tactile Contact-Distribution Guided Online Correction for Robotic Hair Stroking and Perception

Hair stroking is common in daily grooming and personal care, and is also widely used in hair-product evaluation, motivating robots with similar physical interaction capabilities. Existing robotic hair-care and surface-following methods mainly rely on trajectory planning, compliance, force regulation, or tactile-conditioned policies, but deformable hair can remain in contact while gradually drifting across the end-effector, making local interaction difficult to regulate. We propose TacHair, a tactile contact-distribution guided online correction framework that represents high-resolution tactile observations as a spatial hair-contact distribution. A visuotactile imitation policy generates the nominal stroking motion, while a separately trained residual module corrects local contact deviations, separating task progression from contact recovery. We evaluate TacHair in 525 real-robot trials across five head geometries and three hair conditions. A successful stroke requires both sufficient task progression and contact maintenance; our method improves success from 42.9% to 62.3% and contact maintenance from 59.4% to 88.0% over the same visuotactile policy without correction. These results demonstrate spatial tactile contact distributions as an effective feedback representation for contact-preserving interaction with deformable and visually occluded surfaces. Demos, code, and datasets are available at https://tachair.github.io.

cs.RO↗
arXiv2026

Sharp embeddings between quasi-Banach Besov spaces and shallow ReLU variation spaces

Let $\mathbb{D}$ be the ridge dictionary generated by $\operatorname{ReLU}^k$ on a bounded Lipschitz domain $Ω\subset\mathbb{R}^d$. We establish sharp embeddings between Besov spaces and the associated variation space $\mathcal L_1(\mathbb{D})$ in the quasi-Banach range $0 k+d/p$ for $1<q\le\infty$. A rescaled-bump construction shows that this smoothness threshold is sharp. Conversely, for $0<p<1$, \[ \mathcal L_1(\mathbb{D})\hookrightarrow B^{k+1}_{p,2}(Ω), \] and both the smoothness $k+1$ and the fine index $2$ are optimal. The forward embedding converts Besov regularity of functions and solutions of partial differential equations into quantitative finite-width approximation bounds and greedy-algorithm convergence guarantees for shallow $\operatorname{ReLU}^k$ networks. The proofs use Littlewood-Paley localization, Fourier-Radon representations, measure-valued derivatives, and vector-valued singular integrals.

math.FA↗
arXiv2026

An explicit basis for the extended Catalan arrangement of type Dl

Motivated by Kawanoue's construction with the finite-sum formulas, we construct an explicit homogeneous basis for the derivation module of the cone of the extended Catalan arrangement of type Dl. We further show that the restriction of this basis at infinity coincides, up to a nonzero constant, with the integral basis constructed by Feigin-Wang-Yoshinaga. This identifies the geometric motivation behind the parameter choices.

math.CO↗
arXiv2026

A stacky $p$-adic Riemann--Hilbert correspondence on Hitchin-small locus

Let $C$ be an algebraically closed perfectoid field over $\mathbb{Q}_p$ with the ring of integer $\mathcal{O}_C$ and the infinitesimal thickening $\Ainf$. Let $\mathfrak X$ be a semi-stable formal scheme over $\mathcal{O}_C$ with a fixed flat lifting $\widetilde{\mathfrak X}$ over $\Ainf$. Let $X$ be the generic fiber of $\mathfrak{X}$ and $\widetilde X$ be its lifting over $\BdRp$ induced by $\widetilde{\mathfrak X}$. Let $\MIC_r(\widetilde X)^{{\rm H}\text{-small}}$ and $\rL\rS_r(X,\BBdRp)^{{\rm H}\text{-small}}$ be the $v$-stacks of rank-$r$ Hitchin-small integrable connections on $X_{\et}$ and $\BBdRp$-local systems on $X_{v}$, respectively. In this paper, we establish an equivalence between these two stacks by introducing a new period sheaf with connection $(\calO\bB_{\dR,\pd}^+,\rd)$ on $X_{v}$.

math.AG↗
arXiv2026

Touvigation: Embodied Adaptive Object Acquisition for Blind and Low-Vision Users in Unfamiliar Indoor Environments

Blind and low-vision users often face challenges when locating and physically acquiring objects in unfamiliar indoor environments. Existing vision-language-model-based assistants can provide semantic descriptions but may introduce latency, hallucinations, and guidance that is poorly aligned with embodied action. We present Touvigation, a hands-free object acquisition system that combines vision-language understanding with persistent local spatial modeling to provide low-latency, body-relative guidance. Drawing on formative interviews with eight blind and low-vision participants, we design a multi-stage guidance framework that adapts spatial references as users transition from orienting, to walking, to reaching and tactile verification. We evaluated Touvigation with 12 blind and low-vision participants against a multimodal large-language-model assistant and unassisted search. Touvigation achieved 100% task success, compared with 58% for the multimodal assistant and 85% for unassisted search, while reducing completion time and cognitive workload. Our findings demonstrate how persistent spatial grounding and adaptive embodied guidance can improve object acquisition for blind and low-vision users.

cs.HC↗
arXiv2026

Chronological stability for nonstationary matrix refinement

A matrix cascade is an iterative refinement process in which vector-valued data are repeatedly filtered by matrix-valued masks across successively finer scales. Such cascades arise in multichannel subdivision, Hermite refinement, multiresolution synthesis, and exponential-spline constructions, and in nonstationary schemes the masks may vary with scale. We develop a chronological stability framework for this setting, allowing both the transition operators and the associated matching spaces to change from level to level. If the chronological radius satisfies $ρ_{\rm ch}<1$ and the matching defects are summable, then the cascade converges uniformly and, for every $q\in(ρ_{\rm ch},1)$, \[ \|F_n-Φ\|_\infty \lesssim q^n+\sum_{j=1}^nδ_j q^{\,n-j} +\sum_{j>n}δ_j . \] The time-weighted defect term records the level at which each perturbation is inserted, and the matching spaces need not converge; they may even alternate indefinitely. For compact piecewise-linear seeds, every finite ordered matrix cascade admits an exact fixed-width ReLU realization with $O(n)$ depth and parameters, and this linear depth order is worst-case optimal at fixed width. Consequently, exponentially decaying defects yield certified approximants of size $O(\log\varepsilon^{-1})$. We further construct stable two-channel classes in which the chronological radius and the leading metric-entropy coefficient are independent invariants, showing that stability does not determine finite-accuracy description complexity. The framework therefore provides tolerance-controlled finite representations for nonstationary multiresolution and exponential-spline refinement.

math.NA↗
arXiv2026

Sharp approximation rates for shallow ReLU neuralnetworks on critical Besov classes

Let $\mathbb D$ be the normalized ridge dictionary generated by $\operatorname{ReLU}^k$ on a bounded Lipschitz domain $Ω\subset\mathbb R^d$. We determine the sharp algebraic rate of finite $n$-term approximation from $\mathbb D$ when the outer $\ell^1$ coefficient budget is independent of $n$. More precisely, let $d\ge3$, $k\in\mathbb N_+$, $0\le m\le k$, $0<p<1$, and $0<q\le1$. For the unit ball of the critical Besov space $B_{p,q}^{k+d/p}(Ω)$, measured in $H^m(Ω)$, the optimal algebraic exponent is \[ \min\left\{\frac{k-m+d/2}{d-1}, \frac{k-m+d/2+1/p-1/2}{d}\right\}. \] We prove two-sided estimates in the three regimes determined by the two branches of this minimum and give the corresponding logarithmic factors at and beyond the transition. The estimates coincide without logarithmic loss in the strict angular regime and at the transition when $q\le[1/2+(k-m+d/2)/(d-1)]^{-1}$. The upper estimate combines critical wavelet sparsity, localized Fourier--Radon representations, and a stable allocation of directions and biases. The lower estimates arise from two distinct obstructions, namely radial ridge approximation on the direction sphere and Gevrey localization in the joint direction--bias space. The critical smoothness is exactly the endpoint at which Besov regularity provides a uniform shallow-network variation bound without additional scale decay. The resulting representation exponent is strictly larger than the degree-limited exponent for fixed-degree isotropic finite elements under a parameter-count comparison. This last statement concerns best approximation, not training or computational complexity.

math.NA↗
arXiv2026

Quantum fluctuations in a quartet superfluid of two-dimensional Fermi mixture

We study quantum fluctuations in a quartet superfluid (QSF) of two-dimensional (2D) fermion mixtures with mass imbalance. Here QSF is a high-order superfluid that corresponds to the condensation of ($1+3$) clusters, each consisting of a light fermion and three heavy ones. By incorporating the Gaussian fluctuations respecting dominant four-body correlations in this system, our theory successfully recovers the leading universal logarithmic contribution to the 2D equation of state in the deep binding regime, thereby offering a correct physical picture of quartet clusters behaving as composite bosons. By extending the Gaussian fluctuation theory from pairing to quartet superfluids, our results shed light on quantum fluctuations in general fermion superfluids with arbitrarily high-order correlations.

cond-mat.quant-gas↗
arXiv2026

Self-calibrated multiparameter measurement of three-dimensional microwave fields

Rydberg atoms are promising for microwave (MW) sensing and control, but full local MW characterization remains difficult. Existing methods generally do not provide self-calibrated reconstruction of the three-dimensional vector field, which is valuable for both atom-based sensing and in-situ field characterization in complex electromagnetic environments. We propose and implement multi-level, Zeeman-resolved Rydberg electromagnetically induced transparency (EIT) spectroscopy in a laser-cooled atomic ensemble. We extract the three polarization amplitudes from a single spectrum and show that the MW polarization components give rise to closed interferometric loops within the atoms' internal Hilbert space, enabling extraction of their relative phases. Moreover, it is self-calibrated and requires no external reference MW fields, with MW parameters largely separable from one another and from other experimental parameters. These features make it broadly applicable to dedicated sensing platforms as well as quantum optics and quantum information experiments.

physics.atom-ph↗
arXiv2026

Galois representations over convergent de Rham period ring

Let $\mathbf{B}_{\mathrm{dR}}^{+, \dagger} \subset \mathbf{B}_{\mathrm{dR}}^{+}$ be the ``convergent" de Rham period ring which is the (un-completed) stalk at the de Rham point of the Fargues--Fontaine curve. We develop a Tate--Sen formalism to relate Galois representations over $\mathbf{B}_{\mathrm{dR}}^{+, \dagger}$ to regular connections over convergent functions. As a consequence, when the Sen weights (of the mod $t$ reduction) satisfy a $p$-adic non-Liouville condition, Galois cohomology of a $\mathbf{B}_{\mathrm{dR}}^{+, \dagger}$-representation compares to that of its $\mathbf{B}_{\mathrm{dR}}^{+}$-base change, and hence is finite. In addition, restricted to objects whose Sen weights are algebraic numbers, the categories of $\mathbf{B}_{\mathrm{dR}}^{+, \dagger}$-representations and $\mathbf{B}_{\mathrm{dR}}^{+}$-representations are equivalent.

math.NT↗
arXiv2026

ViTac-Tracing: Visual-Tactile Imitation Learning of Deformable Object Tracing

Deformable objects often appear in unstructured configurations. Tracing deformable objects helps bringing them into extended states and facilitating the downstream manipulation tasks. Due to the requirements for object-specific modeling or sim-to-real transfer, existing tracing methods either lack generalizability across different categories of deformable objects or struggle to complete tasks reliably in the real world. To address this, we propose a novel visual-tactile imitation learning method to achieve one-dimensional (1D) and two-dimensional (2D) deformable object tracing with a unified model. Our method is designed from both local and global perspectives based on visual and tactile sensing. Locally, we introduce a weighted loss that emphasizes actions maintaining contact near the center of the tactile image, improving fine-grained adjustment. Globally, we propose a tracing task loss that helps the policy to regulate task progression. On the hardware side, to compensate for the limited features extracted from visual information, we integrate tactile sensing into a low-cost teleoperation system considering both the teleoperator and the robot. Extensive ablation and comparative experiments on diverse 1D and 2D deformable objects demonstrate the effectiveness of our approach, achieving an average success rate of 80% on seen objects and 65% on unseen objects.

cs.RO↗
arXiv2026

TMR-VLA:Vision-Language-Action Model for Magnetic Motion Control of Tri-leg Silicone-based Soft Robot

In-vivo environments, magnetically actuated soft robots offer advantages such as wireless operation and precise control, showing promising potential for painless detection and therapeutic procedures. We developed a trileg magnetically driven soft robot (TMR) whose multi-legged design enables more flexible gaits and diverse motion patterns. For the silicone made of reconfigurable soft robots, its navigation ability can be separated into sequential motions, namely squatting, rotation, lifting a leg, walking and so on. Its motion and behavior depend on its bending shapes. To bridge motion type description and specific low-level voltage control, we introduced TMR-VLA, an end-to-end multi-modal system for a trileg magnetic soft robot capable of performing hybrid motion types, which is promising for developing a navigation ability by adapting its shape to language-constrained motion types. The TMR-VLA deploys embodied endoluminal localization ability from EndoVLA, and fuses sequential frames and natural language commands as input. Low-level voltage output is generated based on the current observation state and specific motion type description. The result shows the TMR-VLA can predict how the voltage applied to TMR will change the dynamics of a silicon-made soft robot. The TMR-VLA reached a 74% average success rate.

cs.RO↗
arXiv2026

Nonlinear optical spectra from Rydberg-mediated photon-photon interactions

While Rydberg-Rydberg interactions are essential for quantum nonlinear optics and quantum information processing, their role in microwave and radio-frequency sensing remains poorly understood. Here we experimentally investigate Rydberg interaction-induced nonlinearity in cold-atom Rydberg electromagnetically induced transparency (EIT). In a three-level EIT system, increasing photon-photon interactions produces nonlinear spectral broadening accompanied by resonance shifts, while a microwave-dressed four-level system exhibits pronounced nonlinear broadening without detectable spectral shifts. Our three-level data can be explained by a conditional superatom model, whereas our four-level observations are surprisingly captured by a simple dephasing model. Comparisons with three representative models provide key insights to the role of many-body interactions in Rydberg EIT spectroscopy. Furthermore, our results clarify the conditions under which microwave field characterization can be performed in the nonlinear regime without introducing systematic bias. Our study advances both fundamental understanding of many-body physics and practical development of atomic sensors.

physics.atom-ph↗
arXiv2026

Integrable Stochastic Processes Associated with the $D_2$ Algebra

We introduce an integrable stochastic process associated with the $D_2$ quantum group, which can be decomposed into two symmetric simple exclusion processes. We establish the integrability of the model under three types of boundary conditions (periodic, twisted, and open boundaries), and present its exact solution, including the spectrum, eigenstates, and some observables. This integrable model can be generalized to the asymmetric case, decomposing into two asymmetric simple exclusion processes, and its exact solutions are also studied.

math-ph↗
arXiv2025

Prismatic crystals for smooth schemes in characteristic $p$ with Frobenius lifting mod $p^2$

Let $(A,(p))$ be a crystalline prism with $A_n = A/p^{n+1}A$ for all $n\geq 0$. Let $\frakX_0$ be a smooth scheme over $A_0$. Suppose that $\frakX_0$ admits a lifting $\frakX_n$ over $A_n$ and the absolute Frobenius $\rF_{\frakX_0}:\frakX_0\to \frakX_0$ admits a lifting over $A_1$. Then we show that there is an equivalence between the category of the prismatic crystals of truncation $n$ on $(\frakX_0/A)_{\Prism}$ and the category of $p$-connections over $\frakX_n$, which is compatible with cohomologies. This generalises a previous work of Ogus. We also give some remarks on trivializing the Hodge--Tate gerbe $π_{\frakX_0}^{\rm HT}:\frakX_0^{\rm HT}\to\frakX_0$ introduced by Bhatt--Lurie.

math.AG↗