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Yujiao Jiang

Publications and source records attributed to Yujiao Jiang.

11 recordsLinked to original sources
arXiv2026

Efficient broadband second-harmonic generation in a multi-pass cell

Second-harmonic generation (SHG) is a widely used nonlinear optical process that has been optimized for high frequency conversion efficiency, broad bandwidths, and optimum spatial and temporal quality of the generated light. However, limitations of the generation efficiency arise due to temporal dispersion and pulse walk-off effects introduced by the nonlinear crystal. To circumvent these limitations, quasi-waveguide schemes, in particular multi-pass cells (MPCs), can be employed, providing flexible phase-tuning capabilities. In this work, we demonstrate for the first time broadband and efficient SHG in an MPC. SHG efficiencies of 72% (for 63 fs, 50 uJ pulses) and 47% (for 15 fs, 20 uJ pulses) are obtained by simultaneously matching the relative phase and group delay between the fundamental and second-harmonic fields over multiple passes through the MPC. Our work sets a new record for efficient Gaussian-beam, ultrashort-pulse SHG and provides a general route to address efficiency-bandwidth limitations of nonlinear optical processes.

physics.optics↗
arXiv2026

The second moment of derivatives of quadratic twists of modular $L$-functions

We prove an asymptotic formula for the second moment of the first derivative of quadratic twists of modular $L$-functions with three leading order main terms. It improves the previous result of Kumar et al. with the first main term. The proof is based on the large sieve type inequality established by Li, with a key input that we convert the problem into computing an asymptotic formula for the completed twisted modular $L$-functions with large shifts.

math.NT↗
arXiv2026

SmoothSync: Dual-Stream Diffusion Transformers for Jitter-Robust Beat-Synchronized Gesture Generation from Quantized Audio

Co-speech gesture generation is a critical area of research aimed at synthesizing speech-synchronized human-like gestures. Existing methods often suffer from issues such as rhythmic inconsistency, motion jitter, foot sliding and limited multi-sampling diversity. In this paper, we present SmoothSync, a novel framework that leverages quantized audio tokens in a novel dual-stream Diffusion Transformer (DiT) architecture to synthesis holistic gestures and enhance sampling variation. Specifically, we (1) fuse audio-motion features via complementary transformer streams to achieve superior synchronization, (2) introduce a jitter-suppression loss to improve temporal smoothness, (3) implement probabilistic audio quantization to generate distinct gesture sequences from identical inputs. To reliably evaluate beat synchronization under jitter, we introduce Smooth-BC, a robust variant of the beat consistency metric less sensitive to motion noise. Comprehensive experiments on the BEAT2 and SHOW datasets demonstrate SmoothSync's superiority, outperforming state-of-the-art methods by -30.6% FGD, 10.3% Smooth-BC, and 8.4% Diversity on BEAT2, while reducing jitter and foot sliding by -62.9% and -17.1% respectively. The code will be released to facilitate future research.

cs.SD↗
arXiv2025

On Hypothesis H of Rudnick and Sarnak

We prove Hypothesis H in full generality for ${\rm GL}_n$ over any number field. This result is a consequence of our stronger effective bound on Euler products involving Rankin--Selberg coefficients at prime ideal powers. The proof rests on a new analytic method, which employs a power sieve over number fields and an iterative argument to bypass the functoriality barrier that had restricted prior results to $n\leq 4$. As applications, we unconditionally establish the GUE statistics for automorphic $L$-function zeros, provide the first effective polynomial bound for the strong multiplicity one problem for coefficients, and resolve the Selberg orthogonality conjecture with stronger error terms.

math.NT↗
arXiv2025

OccGaussian: 3D Gaussian Splatting for Occluded Human Rendering

Rendering dynamic 3D human from monocular videos is crucial for various applications such as virtual reality and digital entertainment. Most methods assume the people is in an unobstructed scene, while various objects may cause the occlusion of body parts in real-life scenarios. Previous method utilizing NeRF for surface rendering to recover the occluded areas, but it requiring more than one day to train and several seconds to render, failing to meet the requirements of real-time interactive applications. To address these issues, we propose OccGaussian based on 3D Gaussian Splatting, which can be trained within 6 minutes and produces high-quality human renderings up to 160 FPS with occluded input. OccGaussian initializes 3D Gaussian distributions in the canonical space, and we perform occlusion feature query at occluded regions, the aggregated pixel-align feature is extracted to compensate for the missing information. Then we use Gaussian Feature MLP to further process the feature along with the occlusion-aware loss functions to better perceive the occluded area. Extensive experiments both in simulated and real-world occlusions, demonstrate that our method achieves comparable or even superior performance compared to the state-of-the-art method. And we improving training and inference speeds by 250x and 800x, respectively. Our code will be available for research purposes.

cs.CV↗
arXiv2024

SMPLX-Lite: A Realistic and Drivable Avatar Benchmark with Rich Geometry and Texture Annotations

Recovering photorealistic and drivable full-body avatars is crucial for numerous applications, including virtual reality, 3D games, and tele-presence. Most methods, whether reconstruction or generation, require large numbers of human motion sequences and corresponding textured meshes. To easily learn a drivable avatar, a reasonable parametric body model with unified topology is paramount. However, existing human body datasets either have images or textured models and lack parametric models which fit clothes well. We propose a new parametric model SMPLX-Lite-D, which can fit detailed geometry of the scanned mesh while maintaining stable geometry in the face, hand and foot regions. We present SMPLX-Lite dataset, the most comprehensive clothing avatar dataset with multi-view RGB sequences, keypoints annotations, textured scanned meshes, and textured SMPLX-Lite-D models. With the SMPLX-Lite dataset, we train a conditional variational autoencoder model that takes human pose and facial keypoints as input, and generates a photorealistic drivable human avatar.

cs.CV↗
arXiv2024

UV Gaussians: Joint Learning of Mesh Deformation and Gaussian Textures for Human Avatar Modeling

Reconstructing photo-realistic drivable human avatars from multi-view image sequences has been a popular and challenging topic in the field of computer vision and graphics. While existing NeRF-based methods can achieve high-quality novel view rendering of human models, both training and inference processes are time-consuming. Recent approaches have utilized 3D Gaussians to represent the human body, enabling faster training and rendering. However, they undermine the importance of the mesh guidance and directly predict Gaussians in 3D space with coarse mesh guidance. This hinders the learning procedure of the Gaussians and tends to produce blurry textures. Therefore, we propose UV Gaussians, which models the 3D human body by jointly learning mesh deformations and 2D UV-space Gaussian textures. We utilize the embedding of UV map to learn Gaussian textures in 2D space, leveraging the capabilities of powerful 2D networks to extract features. Additionally, through an independent Mesh network, we optimize pose-dependent geometric deformations, thereby guiding Gaussian rendering and significantly enhancing rendering quality. We collect and process a new dataset of human motion, which includes multi-view images, scanned models, parametric model registration, and corresponding texture maps. Experimental results demonstrate that our method achieves state-of-the-art synthesis of novel view and novel pose. The code and data will be made available on the homepage https://alex-jyj.github.io/UV-Gaussians/ once the paper is accepted.

cs.CV↗
arXiv2022

Correlations of multiplicative functions with automorphic L-functions

Let $λ_ϕ(n)$ be the Fourier coefficients of a Hecke holomorphic or Hecke--Maass cusp form on ${\rm SL}_2(\mathbb Z)$, and $f$ be any multiplicative function that satisfies two mild hypotheses. We establish a non-trivial upper bound for the correlation $\sum_{n \leq X}f(n)λ_ϕ(n+h)$ uniformly in $0<|h|\ll X$. As applications, we consider some special cases, including $λ_π(n), \,μ(n)λ_π(n)$ and any divisor-bounded multiplicative function. Here $λ_π(n)$ denotes the $n$-th Dirichlet coefficient of $\text{GL}_m$ automorphic $L$-function $L(s,π)$ for an automorphic irreducible cuspidal representation $π$, and $μ(n)$ denotes the Möbius function. In particular, some savings are achieved for shifted convolution problems on ${\rm GL}_m\times {\rm GL}_2\, (m\geq 4)$ and Hypothesis C for the first time.

math.NT↗
arXiv2022

Additive divisor problem for multiplicative functions

Let $τ$ denote the divisor function, and $f$ be any multiplicative function that satisfies some mild hypotheses. We establish the asymptotic formula or non-trivial upper bound for the shifted convolution sum $\sum_{n \leq X}f(n)τ(n-1)$. We also derive several applications to multiplicative functions in the automorphic context, including the functions $λ_π(n), \,μ(n)λ_π(n)$ and $λ_ϕ(n)^l$. Here $λ_π(n)$ denotes the $n$-th Dirichlet coefficient of $\text{GL}_m$ automorphic $L$-function $L(s,π)$ for an automorphic irreducible cuspidal representation $π$, $λ_ϕ(n)$ denotes the $n$-th Fourier coefficient of a holomorphic or Maass cusp form $ϕ$ on ${\rm SL}_2(\mathbb Z)$, and $μ(n)$ denotes the Möbius function. We present two different arguments. The first one mainly relies on the uniform estimates for the binary additive divisor problem, while the second is based on the recent estimates of Bettin--Chandee for trilinear forms in Kloosterman fractions. In addition, the Bourgain-Kátai-Sarnak-Ziegler criterion and Linnik's dispersion method are both employed in these two arguments.

math.NT↗
arXiv2021

A Bombieri-Vinogradov theorem for higher rank groups

We establish a result of Bombieri-Vinogradov type for the Dirichlet coefficients at prime ideals of the standard $L$-function associated to a self-dual cuspidal automorphic representation $π$ of $\mathrm{GL}_n$ over a number field $F$ which is not a quadratic twist of itself. Our result does not rely on any unproven progress towards the generalized Ramanujan conjecture or the nonexistence of Landau-Siegel zeros. In particular, when $π$ is fixed and not equal to a quadratic twist of itself, we prove the first unconditional Siegel-type lower bound for the twisted $L$-values $|L(1,π\otimesχ)|$ in the $χ$-aspect, where $χ$ is a primitive quadratic Hecke character over $F$. Our result improves the levels of distribution in other works that relied on these unproven hypotheses. As applications, when $n=2,3,4$, we prove a $\mathrm{GL}_n$ analogue of the Titchmarsh divisor problem and a nontrivial bound for a certain $\mathrm{GL}_n\times\mathrm{GL}_2$ shifted convolution sum.

math.NT↗