arXiv subjects

Ji Li

Publications and source records attributed to Ji Li.

At least 19 recordsLinked to original sources

arXiv2026

Fefferman--Stein type inequalities via area and maximal functions for Schr\"odinger operators with applications

In this paper, we establish a Fefferman--Stein inequality in terms of area function and non-tangential maximal function associated with the Schr\"odinger operator $\mathcal{L} = -\Delta + V$ on stratified Lie groups $\mathcal G$, where $\Delta$ denotes the sub-Laplacian on $\mathcal G$ and $V$ is a nonnegative locally integrable function. As an application, we extend this inequality to the tensor product $\mathcal G_1 \times \mathcal G_2$ of two stratified Lie groups and develop atomic decompositions associated with the Schr\"odinger operator for functions in the Orlicz space $L\log^{+}L(\mathcal G_1 \times \mathcal G_2).$ Using these atomic decompositions, we further prove weak-type endpoint estimates for the area integral operator and the Riesz transforms associated with the Schr\"odinger operator on $L\log^{+}L(\mathcal G_1 \times \mathcal G_2),$ thereby extending the celebrated result of R.\,Fefferman and E.M.\,Stein \cite{FSt1982} to the setting of singular integrals with non-smooth kernels.

math.AP↗

arXiv2026

ReDeck: Step-Level Render-Grounded Refinement for Document-to-Slide Generation

Document-to-slide generation is challenging because slides are dense editable artifacts that require both faithful content selection and precise spatial layout. Recent slide agents adopt iterative reflection, but typically follow a monolithic "one version, one feedback" loop: a slide or deck is rewritten, rendered afterward, and critiqued only at the turn boundary. This delayed feedback makes local failures such as overflow, overlap, clipping, and off-canvas placement difficult to attribute and repair. We propose ReDeck, a step-level render-grounded refinement framework that decomposes slide revision into atomic edit actions and returns renderer-derived observations after each step, turning refinement into "one edit, one observation." To balance local repair with global quality, ReDeck uses multi-granular feedback: step-level render feedback for spatial errors, a turn-level adaptive critic for semantic and design guidance, and a submission-level gate for hard layout validation. We further introduce DeckQuiz, a benchmark that decouples content fidelity, spatial correctness, and design quality. Across GPT-5.4, Claude-4.6, and Gemini-3.1, ReDeck consistently outperforms existing slide-generation agents, and ablations confirm that feedback timing and granularity are critical for reliable slide refinement.

cs.AI↗

arXiv2026

BMO Classification for Two-Dimensional Dunkl Newton and Green Kernels

Using Gaussian heat-kernel estimates, we classify planar Dunkl Newton kernels in weighted Euclidean BMO and obtain the corresponding local classification for unit-ball Green kernels. For atomic Newton potentials supported on a regular reflection orbit, orbit BMO detects exactly whether the coefficients are constant along the orbit. We also prove an intrinsic Dunkl--CLMS theorem in the heat-semigroup Hardy space and derive intrinsic and Euclidean-source Newton--Wente estimates, extending the BMO--Hardy-space method of Chanillo and Li to the Dunkl setting. Further consequences include sharp local atomic estimates, same-domain criteria, a localized $L^1$-to-BMO bound, and a Brezis--Merle-type estimate.

math.AP↗

arXiv2026

A Fefferman--Stein inequality for the Dunkl Poisson semigroup and its chamber-lifted formulation

We prove a Fefferman--Stein good-$\lambda$ inequality for the Dunkl Poisson semigroup associated with a finite reflection group and a non-negative multiplicity function. For arbitrary complex-valued $f\in C_c^\infty(\mathbb R^N)$, with no $G$-invariance assumption, it compares the orbit-conical non-tangential maximal function $\mathcal N_P^\beta f$ with the area function $\mathcal S_Pf$ formed from the full space-time Dunkl carr\'e du champ, including its reflection-difference energy. The main obstruction is that a general cut-off creates wall differences not controlled by the local Euclidean-gradient product identity. The good set $E=\{x:\mathcal N_P^\beta f(x)\le\lambda\}$ is $G$-invariant; by the equivariance of the Poisson semigroup, so is $a=\varphi(P_t \mathbf 1_E)$, and hence all reflection differences of the cut-off vanish. Poisson maximal and tail estimates, together with the $L^2$ Littlewood--Paley estimate for $P_t \mathbf 1_{E^c}$, then yield the desired distribution inequality. Its integrated form gives maximal-to-area estimates for every $0<p<2$ and endpoint $H^1$-to-$L^1$ bounds for the orbit-conical and Euclidean-conical intrinsic area functions. For chamber lifts of globally smooth data, the inequality has an equivalent formulation on a fundamental chamber, where orbit cones become Euclidean cones and the reflection energy becomes a finite wall coupling. Combined with the known semigroup square-function characterization, these bounds characterize the Dunkl Poisson maximal Hardy space among $L^1(d\omega)$ data.

math.CA↗

arXiv2026

Two-weight commutators for the Bessel Riesz transform with Andersen--Kerman weights

Let $\alpha>-1/2$, $\alpha\ne0$, and let $$ \Delta_\alpha=-\frac{d^2}{dx^2}-\frac{2\alpha}{x}\frac{d}{dx} $$ be the Bessel operator on $\mathbb R_+=(0,\infty)$. We characterize boundedness and compactness of commutators of $R_\alpha=\frac{d}{dx}\Delta_\alpha^{-1/2}$ on the Andersen--Kerman two-weight setting. For $1<p<\infty$ and $\mu,\lambda\in A_{p,\alpha}$, put $ \nu=\left(\frac{\mu}{\lambda}\right)^{1/p}, \ d\rho_\alpha(x)=x^{2\alpha+1}\,dx. $ For real-valued symbols, $$ \|[b,R_\alpha]\|_{L^p(\mu\,dx)\to L^p(\lambda\,dx)} \simeq \|b\|_{\rm{BMO}_{\nu,\alpha}}, $$ where the Bloom oscillation is computed with respect to $d\rho_\alpha$. Moreover $$ [b,R_\alpha]:L^p(\mu\,dx)\to L^p(\lambda\,dx) \text{ is compact} \quad\Longleftrightarrow\quad b\in\rm{VMO}_{\nu,\alpha}. $$ The proof uses the exact conjugation $ U_w(x)=x^{p-2\alpha-1}w(x), \ [U_w]_{A_p(\rho_\alpha)}=[w]_{A_{p,\alpha}}, $ which transfers the problem to the quotient Bessel kernel on $(\mathbb R_+,|x-y|,\rho_\alpha)$. We isolate the required Calder\'on--Zygmund estimates and one-sided non-degeneracy in this quotient normalization. The measure $d\rho_\alpha$ is distinct from the usual Bessel measure $dm_\alpha=x^{2\alpha}\,dx$. It is the Bloom base measure selected by the Andersen--Kerman conjugation and is used throughout the two-weight theory below.

math.CA↗

arXiv2026

On the endpoint estimate for discrete spherical average over sparse sequences

Let $d\geq5$. For a strictly increasing sequence $(\mu_k)$ of positive integers, set $\lambda_k=\mu_k!$ and consider the lacunary discrete spherical maximal operator $A_\star f:=\sup_k |A_{\lambda_k}f|$ associated with the discrete spherical averages \[ A_\lambda f(x):=\frac1{s_\lambda}\sum_{\substack{n\in\mathbb Z^d,\ |n|^2=\lambda}} f(x-n), \] where $s_\lambda:=\#\{n\in\mathbb Z^d:|n|^2=\lambda\}$. Kesler, Lacey and Mena proved that $A_\star$ is bounded on $\ell^p(\mathbb Z^d)$ for every $p>1$ if $\log\mu_k/\log k\longrightarrow\infty$, and asked about its endpoint behavior at $\ell\log\ell$. We resolve this endpoint question by characterizing all factorial sequences for which the $\ell\log\ell$ estimate holds. Define \[ C_{\log}=\sup_{N\geq2}\frac{\#\left\{k\geq 1:\mu_k\leq N\right\}}{1+\log N}. \] We prove that the $\ell\log\ell$ endpoint estimate holds if and only if $C_{\log}<\infty$. More precisely, if $C_{\log}<\infty$, then for every $\alpha>0$ and every finitely supported $f:\mathbb Z^d\to\mathbb C$, \begin{align*} \#\{x\in\mathbb Z^d:A_\star f(x)>\alpha\} \leq C_d(1+C_{\log})\sum_x \frac{|f(x)|}{\alpha} \left(1+\log^+\frac{|f(x)|}{\alpha}\right), \end{align*} where $C_d$ depends only on $d$. Conversely, if the above inequality holds with a finite constant $C_0$ in place of $C_d(1+C_{\log})$, then $C_{\log}\leq C_d(1+C_0)$. Thus their growth condition alone is insufficient at this endpoint. In particular, the estimate holds for $\lambda_k=(2^k)!$ and fails for $\lambda_k=(k+\lceil\exp(\sqrt{k})\rceil)!$.

math.CA↗

arXiv2026

Single-atom sensor for low-frequency electric field

Precision measurement of low-frequency electric field (LFEF) signals with frequency from 30 kHz to 300 kHz is crucial for advancing both fundamental science and practical applications, owing to their unique frequency regime. For conventional electromagnetic antennas, the long wavelength (i.e., several kilometers) of the LFEF leads to a severe size constraint that efficient radiation becomes challenging to achieve when the antenna size is much smaller than the long wavelength of the LFEF signals, which in turn results in a reduction of measurement sensitivity and compromises antenna's performance. By exploiting the high intrinsic sensitivity of cold trapped ions to weak alternating electric signals via Coulomb interaction, we demonstrate a single-ion phonon laser sensor acted by an injection-locked 40Ca+ ion confined in a surface-electrode trap. Combining the beat frequency technique with the injection-locked phonon laser oscillation, we demonstrate a practical and efficient approach for simultaneous extraction of the frequency, phase, and amplitude from a single measurement, without the need for sideband cooling. This approach achieves precision detection for LFEF signals with the sensitivity of 404 uV/(m * Hz1/2) and the detection limit of 61.5 uV/m. Besides, this approach also shows remarkable robustness against noise. Our study helps realizing practical single-atom sensors in the low-frequency regime, opening avenues for applications in subsurface communication, precision metrology, mass spectrometry, and biomedical monitoring.

quant-ph↗

arXiv2026

Beam-excited resonant modes in RF cavities

Beam-excited resonant modes in RF cavities are important sources of beam-coupling impedance and coupled-bunch instabilities in high-current storage rings. We develop a unified framework for longitudinal and transverse resonant impedances based on Maxwell's equations and generalized cavity-voltage definitions, and derive analytical expressions for impedances obtained from finite-length truncated wakefields. The formulation enables the resonant frequencies, normalized longitudinal and transverse shunt impedances, and, when sufficiently constrained, the quality factors to be extracted from practical wakefield simulations without requiring fully converged long-range wakes. The method is validated with an axisymmetric pillbox cavity through comparison with analytical results and eigenmode calculations. It is then applied to the RF cavity of the Storage-Ring-based Coherent Light Source (SRCLS), where the extracted HOM parameters are used to reconstruct total impedance spectra, evaluate coupled-bunch instability thresholds, and guide cavity-geometry optimization. The results demonstrate an efficient connection between wakefield analysis, eigenmode characterization, and beam-stability evaluation for practical RF-cavity designs.

physics.acc-ph↗

arXiv2026

RESOURCE2SKILL: Distilling Executable Agent Skills from Human-Created Multimodal Resources

Skills are a useful abstraction for software agents, turning human and agent experience into reusable procedural knowledge. Yet existing skill libraries are mostly hand-written, text-centric, or derived from agent traces, leaving tutorial videos and other multimodal human resources largely underused. We present RESOURCE2SKILL, a framework that distills multimodal resources, including tutorial videos, repositories, articles, and reference artifacts, into executable skills for software agents. RESOURCE2SKILL organizes these skills as a hierarchical multimodal Skill Wiki, where each entry combines structured text, code, visual examples, metadata, and provenance. This design preserves complementary signals from different resources: videos capture temporal operations and visual effects, code captures executable tool patterns, and articles or artifacts provide conceptual and stylistic grounding. At inference time, agents retrieve and compose relevant skills from the wiki; when coverage is insufficient, the same construction operator can acquire new skills online. Across seven practical authoring domains, RESOURCE2SKILL improves average overall score by +11.9 percentage points over no-skill agents and outperforms strong harness baselines in 26 of 28 main-aggregate model-domain cells. Ablations confirm the value of multimodal skill format, hierarchical organization, source diversity, selection strategy, and online acquisition.

cs.SE↗

arXiv2026

Finite-Time Electrometry with a Quantum-Regime Single-Ion Phonon Laser

The phonon laser realized in a trapped ion, i.e., a self-sustained mechanical oscillator, has demonstrated the unique characteristics in practically detecting externally applied electric signals without the prerequisite of sideband cooling. Entering the quantum regime via sideband cooling is expected to further improve its sensing performance. Here we report the first experimental realization of a quantum-regime single-ion phonon laser ($\bar{n}<10$) using a trapped $^{40}\mathrm{Ca}^+$ ion and demonstrate electrometry based on its phase-space symmetry-breaking response to weak resonant electric fields. By tuning the phonon-laser parameters, we reveal that the sensing performance is fundamentally governed by the finite-time relaxation dynamics of the underlying open quantum system. We find that a slow Liouvillian relaxation, correlated with the finite experimental interaction window, effectively enhances the dynamic susceptibility while maintaining the structural robustness of the limit cycle. This regime, when applied to the detection of electric fields, produces a shot-noise-limited peak sensitivity of $14.15 \pm 0.77~\mu\mathrm{V/m}/\sqrt{\mathrm{Hz}}$ and a minimum detectable field variation of $\delta E_{\mathrm{min}} \approx 1.83~\mu\mathrm{V/m}$. Our results establish quantum phonon lasers as a practical platform for advanced sensing and highlight the central role of Liouvillian dynamics in non-equilibrium electrometry.

quant-ph↗

arXiv2026

Spectral stability in the modified Camassa-Holm equation

We investigate the spectral stability of small-amplitude, periodic, traveling-wave solutions of the modified Camassa-Holm equation with cubic nonlinearities. More precisely, we analyze the $L^2(\mr)$-spectrum of the associated linearized operator in a neighborhood of the origin in the spectral plane. Inspired by a recently novel method based on Kato's perturbation theory [Berti et al, Full description of Benjamin-Feir instability of Stokes waves in deep water, \textit{Invent. Math.}, 230 (2022), 651-711.], we provide a complete description of the spectrum near the origin of the linearized operator--an integro-differential operator with periodic coefficients--and thus prove that such waves are not subject to modulational instability. Moreover, a spectral analysis reveals a remarkable threshold phenomenon: such waves with wave number $k^2\leq 3$ exhibit spectral stability, while instability emerges when $k^2>3$.

math.AP↗

arXiv2026

A Distributed Multi-UGV Exploration Framework With Loop-Aware Planning and Descriptor-Aided Localization in Resource-Limited Environments

Robust and efficient cooperative exploration with multiple unmanned ground vehicles (UGVs) in unknown, GPSdenied, and bandwidth-limited environments without prior maps remains challenging, as localization drift degrades map consistency and induces redundant coverage. This paper presents a fully distributed exploration framework that couples descriptoraided inter-UGV loop closure with loop-aware hierarchical planning while enabling autonomous localization and exploration. We develop a lightweight LiDAR global descriptor with range-image prealignment to enable robust cross-UGV place recognition under large yaw and lateral variations, and use verified loop closures to maintain globally consistent trajectories and a sparse topological representation. We further introduce an uncertainty-aware crossUGV loop-closure selection module that scores candidate loop closures under pose uncertainty and retains high-utility loop closures as planning anchors for global task allocation and local route refinement. Simulations and real-UGV experiments show that the loop-closure module achieves AR@1/AR@1% of 89.9%/95.5%, distributed optimization reduces absolute trajectory error, the system substantially reduces two-way communication volume, and the overall framework reduces exploration time and travel distance by 15% and 14%, respectively, compared with an mTSP baseline.

cs.RO↗

arXiv2026

Chamber lifting and non-radial Dunkl multipliers

We study non-radial Dunkl multipliers via chamber lifting. For an arbitrary finite reflection group $G$, the chamber lifting records all reflected values of a function and conjugates a multiplier into a finite matrix-valued operator on the chamber. If the dyadic matrix entries admit off-diagonal kernels satisfying the chamber $L^2$ H\"ormander condition $\operatorname{CH}^2_{s,\eta}$ with $s>N_\kappa/2$, then the original multiplier is bounded on $L^p(\mathbb R^N,d\omega)$ for every $1 N_\kappa/2$ therefore imply $L^p$ boundedness, for all $1<p<\infty$, for a genuinely non-radial class of symbols. The order $N_\kappa/2$ is forced already by the rank-one Bessel transform. The same chamber theorem also applies to non-product examples once the matrix kernel condition is known, including the dihedral groups $I_2(q)$ and hence $A_2\simeq I_2(3)$ and $B_2\simeq I_2(4)$. The scalar Walsh--Sobolev verification is specific to $A_1^N$. In non-product groups such as $A_2$, $A_{N-1}$, and $B_N$, the product parity calculus is absent, so a scalar theorem of the same form would require additional transform estimates.

math.CA↗

arXiv2026

Two-weight inequalities for the Dunkl--Poisson integrals

We prove an $L^2$ two-weight testing theorem for the Dunkl--Poisson semigroup. The difficulty is geometric. The Dunkl orbit distance has several reflected diagonals, so a single orbit-box test may mix different chamber components. We avoid this by working on one Weyl chamber and keeping the chamber indices. Under the wall-null assumption the full operator becomes a finite matrix of scalar positive Poisson-type operators. In each entry the orbit diagonal is just the ordinary diagonal in the chamber variables. The scalar proof is then a principal-cube stopping-time argument, with two Dunkl kernel comparisons as the only new estimates. The resulting forward and backward tests are necessary and sufficient for the original Dunkl--Poisson inequality.

math.CA↗

arXiv2026

Calderon-type commutators and chamber lifting in the Dunkl setting

Let $G$ be a finite reflection group, and let $T_j$, $\Delta_\kappa$, and $d\omega$ denote its Dunkl operators, Laplacian, and measure, respectively. Write $\mathcal R_j=-T_j(-\Delta_\kappa)^{-1/2}$ for the $j$th Dunkl Riesz transform. We study the Calder\'on-type commutator $[M_b,T_i\mathcal R_j]$ on the full space $L^p(\R^N,d\omega)$, without assuming $G$-invariance of the functions. For $b\in\Lipd$, a full-space Dunkl $T1$ argument for $[M_b,(-\Delta_\kappa)^{1/2}]$, combined with the exact factorization $$ [M_b,T_i\mathcal R_j] =-M_{\partial_i b}\mathcal R_j-\mathcal R_iM_{\partial_jb} +\mathcal R_i[M_b,(-\Delta_\kappa)^{1/2}]\mathcal R_j, $$ implies boundedness on $L^p(d\omega)$ for every $1<p<\infty$. We also prove that the prescribed heat truncations are uniformly bounded on $L^2(d\omega)$ and converge jointly to this operator. To control these truncations, we lift all reflected values of an arbitrary function to separate coordinates on a fixed Weyl chamber. This chamber lifting retains all non-$G$-invariant information and places every possible orbit singularity on the ordinary chamber diagonal of a finite matrix operator. Wall-layer estimates and scalar $T1$ bounds for the integrated entries are uniform in both heat endpoints. A dense-core argument then proves joint, path-independent weak-operator convergence to the factorized commutator. The lifted limit is associated, in the separated-support sense, with a finite matrix of scalar Calder\'on--Zygmund kernels on the chamber.

math.CA↗

arXiv2026

Lens: Rethinking Training Efficiency for Foundational Text-to-Image Models

We introduce Lens, a 3.8B-parameter T2I model that achieves performance competitive with, and in several cases surpassing, state-of-the-art models with more than 6B parameters across various benchmarks, while requiring significantly less training compute. For example, Lens requires only about 19.3% of the training compute used by Z-Image. The training efficiency of Lens stems from two key strategies beyond its compact model size. First, we maximize data information density per training batch by (i) training on Lens-800M, a dataset of 800M densely captioned image-text pairs whose captions are generated by GPT-4.1 and contain approximately 109 words on average, providing richer semantic supervision than conventional short captions, and (ii) constructing each batch from images with multiple resolutions and diverse aspect ratios, thereby enlarging the effective visual coverage of each optimization step. Second, we improve convergence speed through careful architectural choices, including adopting a semantic VAE that provides better latent representations and employing a strong language encoder that accelerates optimization while enabling multilingual generalization from English-only training data. After pre-training, we apply RL with taxonomy-driven prompts (Lens-RL-8K) and structured reward rubrics to suppress artifacts and improve visual quality, a reasoner module with training-free system prompt search to better align user requests with the model, and distillation-based acceleration for 4-step inference. Through efficient training and systematic optimization, Lens generalizes to arbitrary aspect ratios from 1:2 to 2:1 and resolutions up to 1440^2, and supports prompts in several commonly used languages. Thanks to its compact size, Lens generates a 1024^2 image in 3.15 seconds on a single NVIDIA H100 GPU, while its distilled turbo version performs 4-step generation in 0.84 seconds.

cs.CV↗

arXiv2026

Enhanced detection of electric field signals via squeezing-induced stochastic resonance

Stochastic resonance (SR) could amplify weak electric-field signals in nonlinear systems by means of the externally injected noises. Here we propose and experimentally demonstrate a modified SR method, termed squeezing-induced SR, implemented in the system involving a trapped ion behaving as a Duffing oscillator. We find that squeezing the phase noise of the oscillator results in amplified fluctuation of the corresponding amplitude, which helps achieve the SR. Since no auxiliary noise source is needed, the squeezing-induced SR may enhance the signal-to-noise ratio by 4.28 $\pm$ 0.39 dB compared to the conventional noise-induced SR under identical conditions of the electric-field detection. This technique offers a promising approach for developing atomic ion sensors for detecting weak electric-field signals.

physics.atom-ph↗

arXiv2026

InsightTok: Improving Text and Face Fidelity in Discrete Tokenization for Autoregressive Image Generation

Text and faces are among the most perceptually salient and practically important patterns in visual generation, yet they remain challenging for autoregressive generators built on discrete tokenization. A central bottleneck is the tokenizer: aggressive downsampling and quantization often discard the fine-grained structures needed to preserve readable glyphs and distinctive facial features. We attribute this gap to standard discrete-tokenizer objectives being weakly aligned with text legibility and facial fidelity, as these objectives typically optimize generic reconstruction while compressing diverse content uniformly. To address this, we propose InsightTok, a simple yet effective discrete visual tokenization framework that enhances text and face fidelity through localized, content-aware perceptual losses. With a compact 16k codebook and a 16x downsampling rate, InsightTok significantly outperforms prior tokenizers in text and face reconstruction without compromising general reconstruction quality. These gains consistently transfer to autoregressive image generation in InsightAR, producing images with clearer text and more faithful facial details. Overall, our results highlight the potential of specialized supervision in tokenizer training for advancing discrete image generation.

cs.CV↗