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Chengcheng Wu

Publications and source records attributed to Chengcheng Wu.

9 recordsLinked to original sources
arXiv2026

Compactness of positive radial Solution Sets and corresponding $L^2$-Mass sets for "Zero Mass" Quasi-linear Schr\"odinger Equations

We study the compactness of two sets of positive radial solutions to ``zero mass'' quasi-linear Schr\"odinger equation \[ -\Delta u-u\Delta(|u|^2)=g(u) \quad\text{in }\mathbb R^N,\quad N\ge5. \] For nonlinearities that are either strictly subcritical or asymptotically critical at infinity, we prove that the set of least energy positive radial solutions is nonempty and compact in the natural space. Moreover, in the strictly subcritical case and under additional assumptions, we show that the set of all finite $L^2$-mass positive radial solutions is compact in \(L^2(\mathbb R^N)\). The proof relies on uniform decay estimates for the corresponding positive radial solutions of the transformed semilinear equation, which yield the required uniform \(L^2\)-tail control.

math.AP↗
arXiv2026

Extremizers for a trilinear Stein-Weiss inequality with nonnegative weights

We study extremizers for a trilinear Stein-Weiss inequality on $\mathbb{R}^n$. Within the known boundedness region, we prove attainment under two additional assumptions: all six weight exponents are nonnegative, and at least one pair of Lebesgue exponents is admissible. The proof combines symmetric decreasing rearrangement with a logarithmic radial reduction to a translation-invariant bilinear operator on $\mathbb{R}$ whose kernel belongs to $L^1\left(\mathbb{R}^2\right)$. A common-scale compactness argument rules out relative separation of the two arguments and yields norm attainment. We then derive the Euler-Lagrange system. In the fully symmetric case, every normalized nonnegative extremizing triple is diagonal. Finally, we establish the origin-centered Kelvin invariance of the resulting scalar equation at the scaling exponent and record the unweighted conformal example.

math.AP↗
arXiv2026

GLM-5V-Turbo: Toward a Native Foundation Model for Multimodal Agents

We present GLM-5V-Turbo, a step toward native foundation models for multimodal agents. As foundation models are increasingly deployed in real environments, agentic capability depends not only on language reasoning, but also on the ability to perceive, interpret, and act over heterogeneous contexts such as images, videos, webpages, documents, GUIs. GLM-5V-Turbo is built around this objective: multimodal perception is integrated as a core component of reasoning, planning, tool use, and execution, rather than as an auxiliary interface to a language model. This report summarizes the main improvements behind GLM-5V-Turbo across model design, multimodal training, reinforcement learning, toolchain expansion, and integration with agent frameworks. These developments lead to strong performance in multimodal coding, visual tool use, and framework-based agentic tasks, while preserving competitive text-only coding capability. More importantly, our development process offers practical insights for building multimodal agents, highlighting the central role of multimodal perception, hierarchical optimization, and reliable end-to-end verification.

cs.CV↗
arXiv2025

UniVector: Unified Vector Extraction via Instance-Geometry Interaction

Vector extraction retrieves structured vector geometry from raster images, offering high-fidelity representation and broad applicability. Existing methods, however, are usually tailored to a single vector type (e.g., polygons, polylines, line segments), requiring separate models for different structures. This stems from treating instance attributes (category, structure) and geometric attributes (point coordinates, connections) independently, limiting the ability to capture complex structures. Inspired by the human brain's simultaneous use of semantic and spatial interactions in visual perception, we propose UniVector, a unified VE framework that leverages instance-geometry interaction to extract multiple vector types within a single model. UniVector encodes vectors as structured queries containing both instance- and geometry-level information, and iteratively updates them through an interaction module for cross-level context exchange. A dynamic shape constraint further refines global structures and key points. To benchmark multi-structure scenarios, we introduce the Multi-Vector dataset with diverse polygons, polylines, and line segments. Experiments show UniVector sets a new state of the art on both single- and multi-structure VE tasks. Code and dataset will be released at https://github.com/yyyyll0ss/UniVector.

cs.CV↗
arXiv2024

Theta and/or alpha? Neural oscillational substrates for dynamic inter-brain synchrony during mother-child cooperation

Mother-child interaction is a highly dynamic process neurally characterized by inter-brain synchrony (IBS) at {\theta} and/or {\alpha} rhythms. However, their establishment, dynamic changes, and roles in mother-child interactions remain unknown. Through dynamic analysis of dual-EEG from 40 mother-child dyads during turn-taking cooperation, we uncover that {\theta}-IBS and {\alpha}-IBS alternated with interactive behaviors, with EEG frequency-shift as a prerequisite for IBS transitions. When mothers attempt to track their children's attention and/or predict their intentions, they will adjust their EEG frequencies to align with their children's {\theta} oscillations, leading to a higher occurrence of the {\theta}-IBS state. Conversely, the {\alpha}-IBS state, accompanied by the EEG frequency-shift to the {\alpha} range, is more prominent during mother-led interactions. Further exploratory analysis reveals greater presence and stability of the {\theta}-IBS state during cooperative than non-cooperative conditions, particularly in dyads with stronger emotional attachments and more frequent interactions in their daily lives. Our findings shed light on the neural oscillational substrates underlying the IBS dynamics during mother-child interactions.

q-bio.NC↗
arXiv2024

Normalized grounded states for a coupled nonlinear schr\"{o}dinger system on $\mathbb{R}^3$

We investigate the existence of normalized ground states to the system of coupled Schr\"odinger equations: \begin{equation}\label{eq:0.1} \begin{cases} -\Delta u_1 + \lambda_1 u_1 = \mu_1 |u_1|^{p_1-2}u_1 + \beta r_1|u_1|^{r_1-2}u_1|u_2|^{r_2} & \text{ in } \mathbb{R}^{3}, -\Delta u_2 + \lambda_2 u_2 = \mu_2|u_2|^{p_2-2}u_2 + \beta r_2|u_1|^{r_1}|u_2|^{r_2-2}u_2 & \text{ in } \mathbb{R}^3, \end{cases} \end{equation} subject to the constraints $\mathcal{S}_{a_1} \times \mathcal{S}_{a_2} = \{(u_1 \in H^1(\mathbb{R}^3))|\int_{\mathbb{R}^3} u_1^2 dx = a_1^2\} \times \{(u_2 \in H^1(\mathbb{R}^3))|\int_{\mathbb{R}^3} u_2^2 dx = a_2^2\}$, where $\mu_1, \mu_2 > 0$, $r_1, r_2 > 1$, and $\beta \geq 0$. Our focus is on the coupled mass super-critical case, specifically, $$\frac{10}{3} < p_1, p_2, r_1 + r_2 < 2^* = 6.$$ We demonstrate that there exists a $\tilde{\beta} \geq 0$ such that equation (\ref{eq:0.1}) admits positive, radially symmetric, normalized ground state solutions when $\beta > \tilde{\beta}$. Furthermore, this result can be generalized to systems with an arbitrary number of components, and the corresponding standing wave is orbitally unstable.

math.AP↗
arXiv2023

On existence, uniqueness and radiality of normalized solutions to Schr\"{o}dinger-Poisson equations with non-autonomous nonlinearity

We investigate the existence, uniqueness, and radial symmetry of normalized solutions to the Schr\"{o}dinger Poisson equation with non-autonomous nonlinearity $f(x,u)$: \begin{equation} -\triangle u+(|x|^{-1}*|u|^2)u=f(x,u)+\lambda u, \nonumber \end{equation} subject to the constraint $\mathcal{S}_c=\{u\in H^1(\mathbb{R}^3)|\int_{\mathbb{R}^3}u^2=c>0 \}$. We consider three cases based on the behavior of $f(x,u)$: the $L^2$ supercritical case, the $L^2$ subcritical case with growth speed less than three power times, and the $L^2$ subcritical case with growth speed more than three power times. We establish the existence of solutions using three different methods depending on $f(x,u)$. Furthermore, we demonstrate the uniqueness and radial symmetry of normalized solutions using an implicit function framework when $c$ is small.

math.AP↗
arXiv2022

Design of Automatic Driving Safety Level and Positioning Accuracy

Autonomous driving is a hot research topic in the frontier of science and technology. Technology companies and traditional car companies are developing and designing autonomous driving technology from two different directions. Based on the automatic driving classification standard and ISO safety level, combined with the number of traffic accidents and death data in China, and referring to the risk allocation method of the automated driving virtual drive system in the United States, the risk allocation of China's virtual drive system will be carried out. In addition, combined with the vehicle "positioning box" model, the theoretical calculation of the alarm limit of positioning accuracy in China will be carried out and the positioning accuracy requirements of related vehicles will be designed.

eess.SY↗