arXiv subjects

Ji Li

Publications and source records attributed to Ji Li.

At least 37 records · Page 2Linked to original sources

arXiv2026

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

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

math.CA↗

arXiv2026

Maximal Averages on the Affine Group $G_n$ and applications

Let $G_n=\mathbb R^n\rtimes\mathbb R_+$ be equipped with the left Haar measure $ dμ(x,y)=\frac{dx\,dy}{y^{n+1}}. $ We study maximal averages associated with three basic motions on $G_n$: horizontal translations, vertical dilations, and fixed hyperbolic geodesics in the upper half-space model. The translation maximal operator is the Euclidean Hardy--Littlewood maximal operator on each horizontal slice. The Haar-compatible dilation maximal operator is of weak type $(1,1)$ and bounded on $L^p(G_n)$ for $1<p\le\infty$, but it is not strongly bounded on $L^1(G_n)$. By contrast, the unweighted Lebesgue dilation average is unbounded on every finite $L^p(G_n)$ and is not of weak type $(1,1)$. For fixed hyperbolic geodesic averages, the large-time part is strongly bounded on $L^1(G_n)$ because of modular exponential decay. The small-time part is a finite-type parabolic maximal problem. Using the corresponding local finite-type $L\log\log L$ endpoint estimate for the geodesic slice, we prove $ \mathcal M_{γ_ω}:L\log\log L(G_n) \longrightarrow L^{1,\infty}(G_n) $ in weak Orlicz form, together with the strong $L^p(G_n)$ bounds for $1<p\le\infty$. We also show that the strong $L^1$ endpoint fails. Finally, we record a discrete random-walk maximal inequality whose sufficient condition is expressed through the modular drift $$ ρ_p(σ)=\int_{G_n}y(h)^{n/p}\,dσ(h), $$ where $σ$ is the probability measure defining the right random walk.

math.CA↗

arXiv2026

D$_4$CNN$\times$AnaCal: Physics-Informed Machine Learning for Accurate and Precise Weak Lensing Shear Estimation

Traditional weak gravitational lensing shear estimators are carefully calibrated but struggle to fully capture realistic galaxy morphologies, point-spread-function (PSF) effects, blending, and noise in deep surveys, while blindly trained machine learning (ML) models can introduce significant calibration biases. Here we construct a fully D$_4$-equivariant deep neural network for galaxy shape measurement whose architecture enforces symmetry under 90$^{\circ}$ rotations and mirror transformations, and adopt the Analytical Calibration framework (AnaCal) to calibrate the model using its backpropagated gradients. For isolated galaxies in LSST-like single-band simulations, we demonstrate that our approach achieves $\sim$10% lower shape noise than the traditional moment-based Fourier Power Function Shapelets estimator in the high-noise regime, equivalent to a $\sim$20% gain in effective galaxy number density, while simultaneously achieving multiplicative biases consistent with zero across a wide range of noise levels, PSF sizes and ellipticities, and magnitude selection cuts, with all measurements satisfying $|m| {<} 2 \times 10^{-3}$ (i.e., within the 0.2% LSST requirement) and most at the ${\sim}10^{-4}$ level. We demonstrate this framework on isolated single-band galaxy images with Gaussian noise and known PSF, establishing a rigorous, physics-informed foundation for future extensions of ML-based shear estimation to blended sources and multi-band observations in Stage-IV surveys. All codes and data products will be made publicly available upon acceptance.

astro-ph.IM↗

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

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

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

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 $14.15 \pm 0.77~μ\mathrm{V/m}/\sqrt{\mathrm{Hz}}$ and a minimum detectable field variation of $δE_{\mathrm{min}} \approx 1.83~μ\mathrm{V/m}$. 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 $L^2$ Hörmander condition $\operatorname{CH}^2_{s,η}$ with $s>N_κ/2$, then the original multiplier is bounded on $L^p(\mathbb R^N,dω)$ for every $1 N_κ/2$ therefore imply $L^p$ boundedness, for all $1<p<\infty$, for a genuinely non-radial class of symbols. The order $N_κ/2$ 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

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↗

arXiv2026

Covering Human Action Space for Computer Use: Data Synthesis and Benchmark

Computer-use agents (CUAs) automate on-screen work, as illustrated by GPT-5.4 and Claude. Yet their reliability on complex, low-frequency interactions is still poor, limiting user trust. Our analysis of failure cases from advanced models suggests a long-tail pattern in GUI operations, where a relatively small fraction of complex and diverse interactions accounts for a disproportionate share of task failures. We hypothesize that this issue largely stems from the scarcity of data for complex interactions. To address this problem, we propose a new benchmark CUActSpot for evaluating models' capabilities on complex interactions across five modalities: GUI, text, table, canvas, and natural image, as well as a variety of actions (click, drag, draw, etc.), covering a broader range of interaction types than prior click-centric benchmarks that focus mainly on GUI widgets. We also design a renderer-based data-synthesis pipeline: scenes are automatically generated for each modality, screenshots and element coordinates are recorded, and an LLM produces matching instructions and action traces. After training on this corpus, our Phi-Ground-Any-4B outperforms open-source models with fewer than 32B parameters. We will release our benchmark, data, code, and models at https://github.com/microsoft/Phi-Ground.git

cs.CV↗

arXiv2026

MM-WebAgent: A Hierarchical Multimodal Web Agent for Webpage Generation

The rapid progress of Artificial Intelligence Generated Content (AIGC) tools enables images, videos, and visualizations to be created on demand for webpage design, offering a flexible and increasingly adopted paradigm for modern UI/UX. However, directly integrating such tools into automated webpage generation often leads to style inconsistency and poor global coherence, as elements are generated in isolation. We propose MM-WebAgent, a hierarchical agentic framework for multimodal webpage generation that coordinates AIGC-based element generation through hierarchical planning and iterative self-reflection. MM-WebAgent jointly optimizes global layout, local multimodal content, and their integration, producing coherent and visually consistent webpages. We further introduce a benchmark for multimodal webpage generation and a multi-level evaluation protocol for systematic assessment. Experiments demonstrate that MM-WebAgent outperforms code-generation and agent-based baselines, especially on multimodal element generation and integration. Code & Data: https://aka.ms/mm-webagent.

cs.CV↗

arXiv2026

Haar bases for multi-parameter twisted structures

Motivated by the Cauchy--Szegő projections on a broad class of Siegel domains and the geometric quotient structures of nilpotent Lie groups observed by Nagel, Ricci, and Stein, we develop a martingale and Haar wavelet framework for twisted multi-parameter geometries. We introduce twisted dyadic filtrations and construct adapted Haar bases on Euclidean spaces $\mathbb{R}^{2m}$. Each of the resulting dyadic systems forms a complete orthonormal basis of $L^2(\mathbb R^{2m})$, and their union yields a tight frame with frame bound $3$. We establish $L^p$-equivalences for the associated discrete twisted Littlewood--Paley square functions. Furthermore, we extend this discrete real-variable theory to the non-abelian setting of a nilpotent Lie group of step two, $\mathscr{N}$, which serves as the Shilov boundary of certain fundamental Siegel domains. By projecting product fractal tiles from a lifting group of Heisenberg products, we define twisted dyadic shards and construct twisted nilpotent Haar frames. More precisely, we first introduce raw projected shards that reflect the quotient geometry, and then pass to analytic dyadic shards which are exactly rectifiable and remain uniformly comparable to the raw quotient structure in the relevant scale regimes. This yields a discrete framework adapted to twisted quotient geometries in both the Euclidean and nilpotent settings, providing a basic dyadic infrastructure for further developments in twisted real-variable theory.

math.CA↗

arXiv2026

Maximal functions with twisted structures, distribution inequality and applications

Motivated by the geometric reduction of Cauchy--Szegő projections on quadratic surfaces of higher codimension (Nagel--Ricci--Stein, 2001) and recent developments on the real-variable theory adapted to twisted multiparameter structures (arXiv:2603.26119), we establish the Fefferman--Stein type distribution inequality relating the twisted area function and the twisted non-tangential maximal function over $\mathbb{R}^{2m}$. By deploying a recursive integration-by-parts argument involving the twisted gradient and Laplacian, and constructing smooth, compactly supported weight functions to absorb cross-derivative errors, we obtain the required estimate. As an application, we prove the uniform $L^1$ boundedness of the twisted maximal function on the twisted atoms and complete the maximal function characterization of the twisted Hardy space.

math.CA↗