arXiv subjects

Chao Ji

Publications and source records attributed to Chao Ji.

At least 19 recordsLinked to original sources

arXiv2026

Normalized solutions of $L^2$-supercritical NLS equations with periodic potentials and localized nonlinearities

In this paper, we study the existence of normalized solutions to the following $L^2$-supercritical nonlinear Schr\"{o}dinger equation with a periodic potential \[ \begin{dcases} -\Delta u +V (x)u + \lambda u=\chi_{{\Omega}}(x)f(u)\quad \text{in }\mathbb{R}^N, u>0 \quad \text{in} \ \mathbb{R}^N, \int_{\mathbb{R}^N}\abs{u}^2\, dx =\mu, \end{dcases} \] where $N \geq 1$, $\mu>0$ is prescribed, $\lambda \in \mathbb{R}$ is a Lagrange multiplier, $V\in C(\mathbb{R}^N)$ is $1$-periodic in $x_1,...,x_N$, $f \in C^1(\mathbb{R})$ exhibits a general mass supercritical growth at infinity, $\Omega\subset \mathbb{R}^N$ is a (nonempty) bounded open set with smooth boundary $\partial \Omega$ and $\chi_{{\Omega}}$ is the characteristic function of ${\Omega}$. We prove the existence of normalized solutions for all $\mu>0$ sufficiently small. Moreover, if $f$ further has a mass-supercritical growth near the origin, then the existence result extends to every $\mu>0$. The result is obtained through a combination of the monotonicity trick, minimax principle with Morse index information for constrained functionals and blow-up analysis.

math.AP↗

arXiv2026

A partial answer to Brezis' Open Problem 2.1

In this paper, we give a partial answer to Brezis' Open Problem~2.1, which concerns the uniqueness of solutions to the Ginzburg--Landau equation in the unit disc with the degree-one boundary condition. Let $\lambda_1$ be the first Dirichlet eigenvalue of $-\Delta$ in the unit disc and set $\varepsilon_*:=\lambda_1^{-1/2}$. We prove that there exists $\delta>0$ such that the radial solution is the unique weak solution for every $\varepsilon\in(\varepsilon_*-\delta,\infty)$. More generally, we establish the analogous uniqueness result for the Ginzburg--Landau system on bounded connected $C^{1,1}$ domains in $\mathbb R^N$, $2\leq N\leq4$, with nontrivial boundary data. In particular, uniqueness persists slightly below the convexity threshold $\varepsilon_*$, where the strict convexity argument is no longer available. The proof combines strict convexity for $\varepsilon\geq\varepsilon_*$ with a compactness argument, nondegeneracy of the solution at $\varepsilon=\varepsilon_*$ and the implicit function theorem.

math.AP↗

arXiv2026

VR3D: View-Robust 3D Representation Learning for Aerial-Ground Person Re-Identification

Aerial-ground person re-identification is a challenging task due to cross-platform viewpoint variations, which cause severe occlusion and geometric deformation. Existing methods attempt to learn view-invariant representations exclusively within the 2D image space, where drastic viewpoint variations cause the learned features to remain coupled with viewpoint bias. To address this, we propose VR3D, a View-Robust 3D Representation Learning framework that maps images into a unified 3D coordinate space to achieve view-independent feature interaction. Specifically, we introduce View-Robust 3D Representation Interaction, which leverages 3D priors extracted from single 2D observations to lift 2D appearance features into a canonical 3D space. VR3I employs 3D Geometry-Semantic Attention to establish interactions between 2D patches and 3D voxels from corresponding body parts based on their 3D spatial locations, effectively grounding 2D semantics within a 3D framework. In addition, as the reliability of these representations varies across samples due to viewpoint changes and 3D reconstruction errors, we introduce Reliability-Aware Fusion, which estimates sample-specific reliability and adaptively aggregates the multi-source representations. Extensive experiments on three benchmark datasets (CARGO, AG-ReID.v1, and AG-ReID.v2) demonstrate that VR3D outperforms recent methods. For example, it achieves a 5.63% improvement in Rank-1 on CARGO. Our code will be released.

cs.CV↗

arXiv2026

iFLYTEK-Embodied-Omni Technical Report

General-purpose embodied agents must understand multimodal instructions, anticipate how their environment will evolve, and produce precise control actions over extended horizons. Existing approaches typically specialize in visual-language reasoning, video-based world modeling, or action generation, while cascaded pipelines that first synthesize future observations and then infer actions can introduce interface bottlenecks and compound prediction errors. We present iFLYTEK-Embodied-Omni, a unified multimodal foundation model that jointly models vision(videos and images), language, and action within a single Omni framework. Its modality-specific visual-language, video-generation, and action-generation components communicate through shared multimodal self-attention. This design establishes brain-cerebellum collaboration: the vision-language modeland video generation model form a high-level brain for instruction understanding, task planning, progress tracking, and future visual-state prediction, whereas the action generation modelserves as a low-level cerebellum that directly converts planned subgoals and shared multimodal context into executable action chunks. To develop these capabilities, we combine action-annotated and action-free embodied videos from human demonstrations and robot interactions with embodied reasoning, embodied perception, and general-purpose image-text data to construct a comprehensive dataset. We further adopt a four-stage strategy that progressively trains the VLM, VGM, and AGM before jointly fine-tuning the complete model.

cs.AI↗

arXiv2026

Singular limit of lattice graphs and its application to critical Lane--Emden equations on lattice graphs

In this paper, we establish new connections between lattice graphs and metric grids, providing a unified framework for the study of singular limit problems and Gagliardo--Nirenberg type inequalities on lattice graphs. The main technical ingredients are restriction and extension estimates, which enable us to compare variational problems posed on lattice graphs, metric grids and $\mathbb R^d$. As applications, we first prove that extensions of action ($2 2^*$), the singular limit of energy ground states in the mass-supercritical regime ($p>2+\frac{4}{d}$) on lattice graphs, and the optimal constants in Gagliardo-Nirenberg type inequalities in the Sobolev critical case $d \geq 3$ and $p=2^*$ on lattice graphs. Notably, we settle an open problem posed by Dovetta [Adv. Math. 444 (2024), 109633] by establishing a new Gagliardo-Nirenberg type inequality.

math.AP↗

arXiv2025

Normalized solutions of nonlinear magnetic Schr\"odinger equations on metric graphs

In this paper we first establish the theory of a magnetic Sobolev space $H^1_A(\mathcal{G},\mathbb{C})$ on metric graphs $\mathcal{G}$ and we prove the self-adjointness of its corresponding magnetic Schr\"odinger operator. Then, in this setting, we investigate the existence and multiplicity of normalized solutions to nonlinear magnetic Schr\"odinger equations on compact metric graphs and on noncompact metric graphs with localized nonlinearities or nonlinearities acting on whole metric graphs, covering the mass-subcritical, mass-critical, and mass-supercritical cases.

math.AP↗

arXiv2025

Bridging Scale Discrepancies in Robotic Control via Language-Based Action Representations

Recent end-to-end robotic manipulation research increasingly adopts architectures inspired by large language models to enable robust manipulation. However, a critical challenge arises from severe distribution shifts between robotic action data, primarily due to substantial numerical variations in action commands across diverse robotic platforms and tasks, hindering the effective transfer of pretrained knowledge. To address this limitation, we propose a semantically grounded linguistic representation to normalize actions for efficient pretraining. Unlike conventional discretized action representations that are sensitive to numerical scales, the motion representation specifically disregards numeric scale effects, emphasizing directionality instead. This abstraction mitigates distribution shifts, yielding a more generalizable pretraining representation. Moreover, using the motion representation narrows the feature distance between action tokens and standard vocabulary tokens, mitigating modality gaps. Multi-task experiments on two benchmarks demonstrate that the proposed method significantly improves generalization performance and transferability in robotic manipulation tasks.

cs.RO↗

arXiv2025

Normalized solutions for $L^2$-supercritical Schr\"odinger equations with nonlinear point defects on noncompact metric graphs

In this paper, we study the existence and multiplicity of normalized solutions for the following $L^2$-supercritical Schr\"odinger equation with nonlinear point defects on a noncompact metric graph $\G=(\V,\E)$ \begin{equation*} \begin{cases} u'' = \lambda u & \text{on every } \e \in \E, \\ \int_\G \abs{u}^2\, dx = \mu & \\ \displaystyle \sum_{\e \succ \vv} u'_\e(\vv) = -|u(\vv)|^{p-2}u(\vv) & \text{at every } \vv \in \V_0, \\ \displaystyle \sum_{\e \succ \vv} u'_\e(\vv) = 0 & \text{at every } \vv \in \V \setminus \V_0, \end{cases} \end{equation*} where $p>4$, $\G$ has finitely many edges and no self-loops, $\V_0 \subset \V$ is nonempty, $\mu>0$ is a given constant, $\lambda$ is an unknown Lagrange multiplier, $\e \succ \vv$ means that the edge $\e$ is incident at $\vv$, and the notation $u'_\e(\vv)$ stands for $u'_\e(0)$ or $-u'_\e(\ell_\e)$, according to whether the vertex $\vv$ is identified with $0$ or $\ell_\e$. We first prove the existence of a positive normalized solution for every prescribed mass and every nonempty set of defect vertices. We then establish a multiplicity result for normalized solutions when the prescribed mass is sufficiently small and sufficiently many half-lines are attached to the defect vertices.

math.AP↗

arXiv2025

iFlyBot-VLM Technical Report

We introduce iFlyBot-VLM, a general-purpose Vision-Language Model (VLM) used to improve the domain of Embodied Intelligence. The central objective of iFlyBot-VLM is to bridge the cross-modal semantic gap between high-dimensional environmental perception and low-level robotic motion control. To this end, the model abstracts complex visual and spatial information into a body-agnostic and transferable Operational Language, thereby enabling seamless perception-action closed-loop coordination across diverse robotic platforms. The architecture of iFlyBot-VLM is systematically designed to realize four key functional capabilities essential for embodied intelligence: 1) Spatial Understanding and Metric Reasoning; 2) Interactive Target Grounding; 3) Action Abstraction and Control Parameter Generation; 4) Task Planning and Skill Sequencing. We envision iFlyBot-VLM as a scalable and generalizable foundation model for embodied AI, facilitating the progression from specialized task-oriented systems toward generalist, cognitively capable agents. We conducted evaluations on 10 current mainstream embodied intelligence-related VLM benchmark datasets, such as Blink and Where2Place, and achieved optimal performance while preserving the model's general capabilities. We will publicly release both the training data and model weights to foster further research and development in the field of Embodied Intelligence.

cs.RO↗

arXiv2025

iFlyBot-VLA Technical Report

We introduce iFlyBot-VLA, a large-scale Vision-Language-Action (VLA) model trained under a novel framework. The main contributions are listed as follows: (1) a latent action model thoroughly trained on large-scale human and robotic manipulation videos; (2) a dual-level action representation framework that jointly supervises both the Vision-Language Model (VLM) and the action expert during training; (3) a mixed training strategy that combines robot trajectory data with general QA and spatial QA datasets, effectively enhancing the 3D perceptual and reasoning capabilities of the VLM backbone. Specifically, the VLM is trained to predict two complementary forms of actions: latent actions, derived from our latent action model pretrained on cross-embodiment manipulation data, which capture implicit high-level intentions; and structured discrete action tokens, obtained through frequency-domain transformations of continuous control signals, which encode explicit low-level dynamics. This dual supervision aligns the representation spaces of language, vision, and action, enabling the VLM to directly contribute to action generation. Experimental results on the LIBERO Franka benchmark demonstrate the superiority of our frame-work, while real-world evaluations further show that iFlyBot-VLA achieves competitive success rates across diverse and challenging manipulation tasks. Furthermore, we plan to open-source a portion of our self-constructed dataset to support future research in the community

cs.CV↗

arXiv2025

Nonrelativistic limit of normalized solutions of nonlinear Dirac equations on noncompact metric graphs with localized nonlinearities

In this paper, we study the nonrelativistic limit of normalized solutions for the following nonlinear Dirac equation (NLDE) on noncompact metric graph $\G$ with finitely many edges and a non-empty compact core $\K$ \begin{equation*} \D u - \omega u= \chi_\K\abs{u}^{p-2}u, \end{equation*} under the constraint $\int_\G\abs{u}^2\,dx = 1$, where $\D$ is the Dirac operator on $\G$, $u: \G \to \mathbb{C}^2$, the frequency $\omega \in \mathbb{R}$ is part of the unknowns which arises as a Lagrange multiplier, $\chi_\K$ is the characteristic function of the compact core $\K$, and $2<p<6$. To the best of our knowledge, this is the first study to investigate the nonrelativistic limit of normalized solutions to (NLDE) on metric graphs.

math.AP↗

arXiv2025

Transferable Class Statistics and Multi-scale Feature Approximation for 3D Object Detection

This paper investigates multi-scale feature approximation and transferable features for object detection from point clouds. Multi-scale features are critical for object detection from point clouds. However, multi-scale feature learning usually involves multiple neighborhood searches and scale-aware layers, which can hinder efforts to achieve lightweight models and may not be conducive to research constrained by limited computational resources. This paper approximates point-based multi-scale features from a single neighborhood based on knowledge distillation. To compensate for the loss of constructive diversity in a single neighborhood, this paper designs a transferable feature embedding mechanism. Specifically, class-aware statistics are employed as transferable features given the small computational cost. In addition, this paper introduces the central weighted intersection over union for localization to alleviate the misalignment brought by the center offset in optimization. Note that the method presented in this paper saves computational costs. Extensive experiments on public datasets demonstrate the effectiveness of the proposed method.

cs.CV↗

arXiv2025

Existence and multiplicity of normalized solutions to a large class of elliptic equations on bounded domains with general boundary conditions

In this paper, by adapting the perturbation method, we study the existence and multiplicity of normalized solutions for the following nonlinear Schr\"odinger equation $$ \left\{ \begin{array}{ll} -\Delta u = \lambda u + f(u)\quad & \text{in } \Omega, \mathcal{B}_{\alpha,\zeta,\gamma}u = 0 & \text{on } \partial \Omega, \int_{\Omega} |u|^2\,dx = \mu, \end{array} \right. \leqno{(P)^\mu_{\alpha,\zeta,\gamma}} $$ where $\Omega \subset \mathbb{R}^N$ ($N \geq 1$) is a smooth bounded domain, $\mu>0$ is prescribed, $\lambda \in \mathbb{R}$ is a part of the unknown which appears as a Lagrange multiplier, $f,g:\mathbb{R} \to \mathbb{R}$ are continuous functions satisfying some technical conditions. The boundary operator $\mathcal{B}_{\alpha,\zeta,\gamma}$ is defined by $$ \mathcal{B}_{\alpha,\zeta,\gamma}u=\alpha u+\zeta \frac{\partial u}{\partial \eta }-\gamma g(u), $$ where $\alpha,\zeta,\gamma \in \{0,1\}$ and $\eta$ denotes the outward unit normal on $\partial\Omega$. Moreover, we highlight several further applications of our approach, including the nonlinear Schr\"{o}dinger equations with critical exponential growth in $\mathbb{R}^{2}$, the nonlinear Schr\"{o}dinger equations with magnetic fields, the biharmonic equations, and the Choquard equations, among others.

math.AP↗

arXiv2025

Existence of normalized solutions to nonlinear Schr\"odinger equations on lattice graphs

In this paper, using a discrete Schwarz rearrangement on lattice graphs developed in \cite{DSR}, we study the existence of global minimizers for the following functional $I:H^1\left(\mathbb{Z}^N\right)\to \R$, $$I(u)=\frac{1}{2} \int_{\mathbb{Z}^N}|\nabla u|^2 \,d\mu-\int_{\mathbb{Z}^N} F(u)\, d\mu,$$ constrained on $S_m:=\left\{u \in H^1\left(\mathbb{Z}^N\right) \mid\|u\|_{\ell^2\left(\mathbb{Z}^N\right)}^2=m\right\}$, where $N \geq 2$, $m>0$ is prescribed, $f \in C(\mathbb{R}, \mathbb{R})$ satisfying some technical assumptions and $F(t):=\int_0^t f(\tau) \,d\tau$. We prove the following minimization problem $$ \inf_{u \in S_m} I(u) $$ has an excitation threshold $m^*\in [0,+\infty]$ such that \begin{equation*} \inf_{u \in S_m} I(u)<0 \quad \text{if and only if } m>m^*. \end{equation*} Based primarily on $m^* \in (0,+\infty)$ or $m^*=0$, we classify the problem into three different cases: $L^2$-subcritical, $L^2$-critical and $L^2$-supercritical. Moreover, for all three cases, under assumptions that we believe to be nearly optimal, we show that $m^*$ also separates the existence and nonexistence of global minimizers for $I(u)$ constrained on $S_{m}$.

math.AP↗

arXiv2025

Existence and multiplicity of normalized solutions for the generalized Kadomtsev-Petviashvili equation in $\mathbb{R}^2$

In this paper, we study the existence and {multiplicity} of nontrivial solitary waves for the generalized Kadomtsev-Petviashvili equation with prescribed {$L^2$-norm} \begin{equation*}\label{Equation1} \left\{\begin{array}{l} \left(-u_{x x}+D_x^{-2} u_{y y}+\lambda u-f(u)\right)_x=0,{\quad x \in \mathbb{R}^2, } \\[10pt] \displaystyle \int_{\mathbb{R}^2}u^2 d x=a^2, \end{array}\right.%\tag{$\mathscr E_\lambda$} \end{equation*} where $a>0$ and $\lambda \in \mathbb{R}$ is an unknown parameter that appears as a Lagrange multiplier. For the case $f(t)=|t|^{q-2}t$, with $2 0$, we prove the existence of normalized ground state solutions which corresponds to a local minimum of the associated energy functional. In this case, we further show that there exists a sequence $(a_n) \subset (0,a_0)$ with $a_n \to 0$ as $n \to+\infty$, such that for each $a=a_n$, the problem admits a second solution with positive energy. To the best of our knowledge, this is the first work that studies the existence of solutions for the generalized Kadomtsev-Petviashvili equations under the $L^2$-constraint, which we refer to them as the normalized solutions.

math.AP↗

arXiv2025

Normalized solutions of nonlinear Dirac equations on noncompact metric graphs with localized nonlinearities

In this paper, we study the following nonlinear Dirac equations (NLDE) on noncompact metric graph $\mathcal{G}$ with localized nonlinearities \begin{equation} \mathcal{D} u - \omega u= a\chi_{\mathcal{K}}|u|^{p-2}u, \end{equation} where $\mathcal{D}$ is the Dirac operator on $\mathcal{G}$, $u: \mathcal{G} \to \mathbb{C}^2$, $\omega\in \mathbb{R}$, $a > 0$, $\chi_{\mathcal{K}}$ is the characteristic function of the compact core $\mathcal{K}$, and $p>2$. First, for $2 2$, prove the existence of normalized solutions to (NLDE) when $\lambda = -mc^2$ is an eigenvalue of the operator $\mathcal{D}$. In the Appendix, we study the influence of the parameters $m, c > 0$ on the existence of normalized solutions to (NLDE). To the best of our knowledge, this is the first study to investigate the normalized solutions to (NLDE) on metric graphs.

math.AP↗

arXiv2025

High-Precision Transformer-Based Visual Servoing for Humanoid Robots in Aligning Tiny Objects

High-precision tiny object alignment remains a common and critical challenge for humanoid robots in real-world. To address this problem, this paper proposes a vision-based framework for precisely estimating and controlling the relative position between a handheld tool and a target object for humanoid robots, e.g., a screwdriver tip and a screw head slot. By fusing images from the head and torso cameras on a robot with its head joint angles, the proposed Transformer-based visual servoing method can correct the handheld tool's positional errors effectively, especially at a close distance. Experiments on M4-M8 screws demonstrate an average convergence error of 0.8-1.3 mm and a success rate of 93\%-100\%. Through comparative analysis, the results validate that this capability of high-precision tiny object alignment is enabled by the Distance Estimation Transformer architecture and the Multi-Perception-Head mechanism proposed in this paper.

cs.CV↗

arXiv2024

Existence and multiplicity of normalized solutions for $(2,q)$-Laplacian equations with generic double-behaviour nonlinearities

In this paper, we study {existence and multiplicity} of normalized solutions for the following $(2, q)$-Laplacian equation \begin{equation*}\label{Eq-Equation1} \left\{\begin{array}{l} -\Delta u-\Delta_q u+\lambda u=f(u) \quad x \in \mathbb{R}^N , \int_{\mathbb{R}^N}u^2 d x=c^2, \end{array}\right. \end{equation*} where $1 0$ is a constant. The nonlinearity $f:\mathbb{R}\rightarrow \mathbb{R}$ is continuous, with mass-subcritical growth at the origin, mass-supercritical growth at infinity, and is more general than the sum of two powers. Under different assumptions, we prove the existence of a locally least-energy solution and the existence of a second solution with higher energy.

math.AP↗