Searcharxiv⌕ Search

arXiv subjects

Jianjun Zhang

Publications and source records attributed to Jianjun Zhang.

At least 19 recordsLinked to original sources
arXiv2026

Liouville theorems and symmetry of positive solutions for partially confined nonlinear Schr\"odinger equations

We study positive solutions of the partially confined stationary nonlinear Schr\"odinger equation $$-\Delta u+|y|^2u+\lambda u=g(u),\quad (y,z)\in\mathbb{R}^d\times\mathbb{R}^{m},\quad 1\leq d -d$, we establish the existence of positive solutions under some standard assumptions. Furthermore, every positive solution decaying at infinity is radially symmetric and strictly decreasing in the confined variables and, up to one common translation, radially symmetric and strictly decreasing in the free variables. \vskip 0.2in Dedicated to our supervisor Prof. Wenming Zou on the occasion of his 60th birthday.

math.AP↗
arXiv2026

Photonic-chip-based generation of sub-100-femtosecond optical frequency combs

Sub-100-fs optical pulses and frequency comb sources have been revolutionizing a wide range of applications, from ultrafast optical science to optical frequency standard and measurement. To date, the leading techniques for generating such pulses in practical systems rely on tabletop mode-locked lasers, which inherently suffer from high system complexity, limited long-term reliability, and pronounced environmental sensitivity. Meanwhile, driven by advances in photonic integration, chip-scale approaches have sought to realize miniaturized pulse sources. However, simultaneously achieving sub-100-fs duration, ideal pulse shape, and a broadband flat-topped spectrum remains a significant challenge. Here, we address these challenges by combining two key photonic chip technologies: TFLN EO modulators for picosecond seed pulse generation, and highly nonlinear optical loop mirrors (NOLM) based on AlGaAsOI nanowaveguides for efficient temporal pulse cleaning and spectral broadening. In theoretical simulation and experiment, we show that for an input seed pulse centred at ~1550nm, a single-stage AlGaAs NOLM with a loop length of 1cm can produce flat-topped, nearly tenfold spectral broadening and over tenfold compression of pulse width, and more than 10dB suppression of pulse pedestals. Using initial EO comb pulses with ps-level durations at repetition rates of 10-20GHz, we demonstrate photonic-chip-enabled pulses with an unprecedented duration of 55fs and a flat-topped comb spectrum whose 10dB optical bandwidth exceeds 90nm. Our results highlight the remarkable potential of photonic chip technologies to realize high-repetition-rate, miniaturized sub-100-fs optical pulse generators with the prospect of superior stability and operability. The demonstrated photonic-chip-based sub-100-fs optical frequency comb sources may establish a new paradigm for both scientific research and practical applications.

physics.optics↗
arXiv2026

DSWAM: A Dual-System World Action Foundation Model for Fine-Grained Robot Manipulation

World Action Models (WAMs) provide a promising alternative to Vision-Language-Action (VLA) policies by using video-based world modeling as dense supervision for robot action learning. Existing WAMs excel at physically grounded execution, but typically lack the explicit language-level planning interface in VLM-based VLAs for decomposing coarse instructions. Such decomposition becomes important when household tasks involve complex multi-step goals, where coarse user commands need to be converted into sequences of fine-grained executable subtasks. Meanwhile, the field still lacks a fair real-robot comparison between VLA and WAM execution capabilities, since existing systems often differ in data, robot embodiments, and task protocols. To address both the decomposition gap and the need for a controlled WAM-VLA comparison, we introduce DSWAM, a Dual-System World Action Foundation Model for fine-grained robot manipulation. DSWAM keeps a System 1 WAM executor as the default control path and optionally activates a System 2 vision-language subtask planner only when task decomposition is useful. The planner predicts executable subtasks from short-term visual history and a global task prompt, while the WAM executor performs world-aware action generation for each instruction or subtask. The executor is trained with action prediction and video co-training, but inference directly predicts action chunks without explicit future video generation. To make this execution path practical on real robots, we further integrate TensorRT acceleration, asynchronous execution, and real-time chunking (RTC) so that policy queries do not block robot control. To provide a fair real-robot comparison with VLA policies, we build and evaluate DSWAM under the DeMaVLA real-world deformable manipulation setting with matched robot platform, pretraining data, post-training data, and evaluation criteria.

cs.RO↗
arXiv2026

Learning 4D Geometric Priors for Inference-Efficient World Action Models

World Action Models (WAMs) have shown strong potential for robotic manipulation by jointly modeling visual future dynamics and executable action sequences. However, existing video-action co-training methods primarily optimize appearance-oriented video latents, which may insufficiently capture the temporally evolving geometry required for precise manipulation. We propose MECo-WAM, a Multi-Expert Co-Training World Action Model that injects action-relevant 4D geometric priors into video-action representations while preserving the original lightweight inference graph. During training, MECo-WAM combines video and action experts with a lightweight 4D expert supervised by relational targets from a frozen VGGT encoder. Asymmetric expert visibility prevents non-causal shortcuts from auxiliary geometry to action generation. To transfer geometric knowledge into the deployed video-action pathway, we introduce decayed 4D read-mask attention, which provides restricted current-frame geometric guidance early in training and progressively removes this dependency. We further propose action-aware temporal geometric distillation, which aligns within-frame geometric relations and their temporal evolution while emphasizing visual regions most relevant to robot actions. At deployment, all auxiliary 4D components are removed. Experiments on LIBERO (98.2%), RoboTwin 2.0 (92.6%), and challenging real-world manipulation tasks show that MECo-WAM improves manipulation performance without increasing inference cost.

cs.RO↗
arXiv2026

PiL-World: A Chunk-Wise World Model for VLA Policy-in-the-Loop Evaluation

Vision-language-action (VLA) policies operate in a closed loop in real-world robot tasks: a robot observes the scene, executes an action chunk, and conditions its next decision on the resulting observation. However, most existing world models for robot action evaluation are limited to open-loop prediction along pre-collected action trajectories. This prevents them from supporting closed-loop VLA evaluation, where each action chunk must be conditioned on the observation generated by the previous execution. To address this gap, we propose PiL-World, a chunk-wise world model designed for policy-in-the-loop VLA evaluation. Given the current observation and the action trajectory rolled out by a VLA policy, PiL-World generates multi-view future observations that are consistent with the VLA rollout and match the image inputs required by the policy. By alternating between VLA inference and world-model prediction, PiL-World enables closed-loop evaluation without real robot execution at every step. To improve rollout fidelity, PiL-World conditions video generation on action-derived visual control from head-view robot motion and latent histories that encode task execution context, while jointly predicting complementary multi-view observations. Beyond successful teleoperated demonstrations, it also learns from failed execution trajectories, helping the imagined rollouts better match the distribution of real policy executions. We evaluate PiL-World on three real dual-arm manipulation tasks. PiL-World generates imagined rollouts that are highly consistent with real robot executions. More importantly, compared with the baseline, it reduces the error between VLA success rates measured in real-world rollouts and those estimated through closed-loop world-model evaluation from 63.2% to 12.0%.

cs.RO↗
arXiv2026

DeMaVLA: A Vision-Language-Action Foundation Model for Generalizable Deformable Manipulation

Real-world household robots require Vision-Language-Action (VLA) foundation models that can acquire reusable manipulation skills across diverse objects, task conditions, and household environments. Deformable-object folding is a representative challenge, requiring robots to handle clothing items from random initial states across varying categories, geometries, materials, and scenes. However, existing VLA systems commonly train separate policies for different object categories, while naively mixed multi-task training often suffers from task interference and degraded performance. To move beyond category-specific folding policies, we introduce DeMaVLA, a VLA foundation model for generalizable Deformable Manipulation. DeMaVLA adopts a VLM backbone with an action expert and formulates continuous action generation using flow matching. To improve efficiency, the action expert is constructed by pruning every other transformer layer while preserving layer-wise alignment with the VLM backbone, reducing training and inference cost. DeMaVLA is first pre-trained on approximately 5,000 hours of selected real-world dual-arm demonstrations to acquire general manipulation priors. It is then post-trained on mixed folding data that aggregates self-collected demonstrations and corrective trajectories from real-robot failures across multiple folding tasks through a human-in-the-loop Data Aggregation~(DAgger) pipeline. Experiments show that DeMaVLA achieves competitive performance on RoboTwin 2.0 and strong real-world results on our household folding benchmark. These results highlight the value of scalable real-world data, efficient action generation, and corrective learning for general-purpose VLA policies in deformable-object manipulation.

cs.RO↗
arXiv2026

Sharp Stability for the Affine Fractional Sobolev Inequality

In this paper, we prove a sharp quantitative stability result for the affine fractional \(L^2\)-Sobolev inequality in \(\dot H^s(\mathbb R^n)\), \(0<s<1\), introduced by Haddad--Ludwig (\emph{Math. Ann.} \textbf{388} (2024), 1091--1115). In particular, we identify the kernel of the affine Hessian, determine the sharp local spectral gap, and show that the optimal global stability constant is strictly smaller than the corresponding local spectral value.

math.AP↗
arXiv2025

Uniqueness of radial solutions for $m$-Laplacian equations in low dimensions

This paper extends the uniqueness results of Serrin and Tang [\textit{Indiana Univ. Math. J.}, 49 (2000), pp. 897--923] to the low-dimensional case $1\leq N\leq m$ with $m>1$. We consider radial solutions of the overdetermined problem \[ \begin{cases} -\Delta_m u = f(u), \quad u>0 & \text{in } B_R,\\[4pt] u = \partial_\nu u = 0 & \text{on } \partial B_R, \text{ if } R<\infty,\\[4pt] \displaystyle\lim_{|x|\to\infty} u(x)=0, & \text{if } R=\infty, \end{cases} \] where $B_R$ is the open ball in $\mathbb{R}^N$ centered at the origin with radius $R>0$ (the case $R=\infty$ corresponds to the whole space, for studying positive ground states). Under suitable assumptions on the nonlinearity $f$, we establish the uniqueness of such solutions, whenever they exist. Our analysis is motivated by connections to sharp forms of the Gagliardo--Nirenberg and Nash inequalities. Although the overall framework follows that of Serrin and Tang, the details of our proofs differ substantially in the low-dimensional setting. In particular, Serrin and Tang explicitly noted that their techniques rely heavily on the condition $N>m$ and do not readily extend to $N\leq m$ (see Subsection~6.2 of their work). The present paper closes this gap, thereby providing a complete uniqueness theory for all dimensions. As a concrete example, for the canonical nonlinearity $f(u) = -u^p + u^q$ with $p m$ and $m^* = \infty$ for $N\leq m$. Consequently, our work also completely resolves an open problem posed by Pucci and Serrin [\textit{Indiana Univ. Math. J.}, 47 (1998), pp. 501--528], which had been settled for $N>m$ in the earlier work of Serrin and Tang.

math.AP↗
arXiv2025

Towards High-Consistency Embodied World Model with Multi-View Trajectory Videos

Embodied world models aim to predict and interact with the physical world through visual observations and actions. However, existing models struggle to accurately translate low-level actions (e.g., joint positions) into precise robotic movements in predicted frames, leading to inconsistencies with real-world physical interactions. To address these limitations, we propose MTV-World, an embodied world model that introduces Multi-view Trajectory-Video control for precise visuomotor prediction. Specifically, instead of directly using low-level actions for control, we employ trajectory videos obtained through camera intrinsic and extrinsic parameters and Cartesian-space transformation as control signals. However, projecting 3D raw actions onto 2D images inevitably causes a loss of spatial information, making a single view insufficient for accurate interaction modeling. To overcome this, we introduce a multi-view framework that compensates for spatial information loss and ensures high-consistency with physical world. MTV-World forecasts future frames based on multi-view trajectory videos as input and conditioning on an initial frame per view. Furthermore, to systematically evaluate both robotic motion precision and object interaction accuracy, we develop an auto-evaluation pipeline leveraging multimodal large models and referring video object segmentation models. To measure spatial consistency, we formulate it as an object location matching problem and adopt the Jaccard Index as the evaluation metric. Extensive experiments demonstrate that MTV-World achieves precise control execution and accurate physical interaction modeling in complex dual-arm scenarios.

cs.RO↗
arXiv2025

The Next Layer: Augmenting Foundation Models with Structure-Preserving and Attention-Guided Learning for Local Patches to Global Context Awareness in Computational Pathology

Foundation models have recently emerged as powerful feature extractors in computational pathology, yet they typically omit mechanisms for leveraging the global spatial structure of tissues and the local contextual relationships among diagnostically relevant regions - key elements for understanding the tumor microenvironment. Multiple instance learning (MIL) remains an essential next step following foundation model, designing a framework to aggregate patch-level features into slide-level predictions. We present EAGLE-Net, a structure-preserving, attention-guided MIL architecture designed to augment prediction and interpretability. EAGLE-Net integrates multi-scale absolute spatial encoding to capture global tissue architecture, a top-K neighborhood-aware loss to focus attention on local microenvironments, and background suppression loss to minimize false positives. We benchmarked EAGLE-Net on large pan-cancer datasets, including three cancer types for classification (10,260 slides) and seven cancer types for survival prediction (4,172 slides), using three distinct histology foundation backbones (REMEDIES, Uni-V1, Uni2-h). Across tasks, EAGLE-Net achieved up to 3% higher classification accuracy and the top concordance indices in 6 of 7 cancer types, producing smooth, biologically coherent attention maps that aligned with expert annotations and highlighted invasive fronts, necrosis, and immune infiltration. These results position EAGLE-Net as a generalizable, interpretable framework that complements foundation models, enabling improved biomarker discovery, prognostic modeling, and clinical decision support

q-bio.QM↗
arXiv2025

On the existence of normalized solutions to a class of fractional Choquard equation with potentials

This paper investigates the existence of normalized solutions to the nonlinear fractional Choquard equation: $$ (-\Delta)^s u+V(x) u=\lambda u+f(x)\left(I_\alpha *\left(f|u|^q\right)\right)|u|^{q-2} u+g(x)\left(I_\alpha *\left(g|u|^p\right)\right)|u|^{p-2} u, \quad x \in \mathbb{R}^N $$ subject to the mass constraint $$ \int_{\mathbb{R}^N}|u|^2 d x=a>0, $$ where $N>2 s, s \in(0,1), \alpha \in(0, N)$, and $\frac{N+\alpha}{N} \leq q<p \leq \frac{N+\alpha+2 s}{N}$. Here, the parameter $\lambda \in \mathbb{R}$ appears as an unknown Lagrange multiplier associated with the normalization condition. By employing variational methods under appropriate assumptions on the potentials $V(x), f(x)$, and $g(x)$, we establish several existence results for normalized solutions.

math.AP↗
arXiv2025

From Classical Machine Learning to Emerging Foundation Models: Review on Multimodal Data Integration for Cancer Research

Cancer research is increasingly driven by the integration of diverse data modalities, spanning from genomics and proteomics to imaging and clinical factors. However, extracting actionable insights from these vast and heterogeneous datasets remains a key challenge. The rise of foundation models (FMs) -- large deep-learning models pretrained on extensive amounts of data serving as a backbone for a wide range of downstream tasks -- offers new avenues for discovering biomarkers, improving diagnosis, and personalizing treatment. This paper presents a comprehensive review of widely adopted integration strategies of multimodal data to assist advance the computational approaches for data-driven discoveries in oncology. We examine emerging trends in machine learning (ML) and deep learning (DL), including methodological frameworks, validation protocols, and open-source resources targeting cancer subtype classification, biomarker discovery, treatment guidance, and outcome prediction. This study also comprehensively covers the shift from traditional ML to FMs for multimodal integration. We present a holistic view of recent FMs advancements and challenges faced during the integration of multi-omics with advanced imaging data. We identify the state-of-the-art FMs, publicly available multi-modal repositories, and advanced tools and methods for data integration. We argue that current state-of-the-art integrative methods provide the essential groundwork for developing the next generation of large-scale, pre-trained models poised to further revolutionize oncology. To the best of our knowledge, this is the first review to systematically map the transition from conventional ML to advanced FM for multimodal data integration in oncology, while also framing these developments as foundational for the forthcoming era of large-scale AI models in cancer research.

q-bio.QM↗
arXiv2025

Deep learning based infrared small object segmentation: Challenges and future directions

Infrared sensing is a core method for supporting unmanned systems, such as autonomous vehicles and drones. Recently, infrared sensors have been widely deployed on mobile and stationary platforms for detection and classification of objects from long distances and in wide field of views. Given its success in the vision image analysis domain, deep learning has also been applied for object recognition in infrared images. However, techniques that have proven successful in visible light perception face new challenges in the infrared domain. These challenges include extremely low signal-to-noise ratios in infrared images, very small and blurred objects of interest, and limited availability of labeled/unlabeled training data due to the specialized nature of infrared sensors. Numerous methods have been proposed in the literature for the detection and classification of small objects in infrared images achieving varied levels of success. There is a need for a survey paper that critically analyzes existing techniques in this domain, identifies unsolved challenges and provides future research directions. This paper fills the gap and offers a concise and insightful review of deep learning-based methods. It also identifies the challenges faced by existing infrared object segmentation methods and provides a structured review of existing infrared perception methods from the perspective of these challenges and highlights the motivations behind the various approaches. Finally, this review suggests promising future directions based on recent advancements within this domain.

cs.CV↗
arXiv2025

A Mathematics Framework of Artificial Shifted Population Risk and Its Further Understanding Related to Consistency Regularization

Data augmentation is an important technique in training deep neural networks as it enhances their ability to generalize and remain robust. While data augmentation is commonly used to expand the sample size and act as a consistency regularization term, there is a lack of research on the relationship between them. To address this gap, this paper introduces a more comprehensive mathematical framework for data augmentation. Through this framework, we establish that the expected risk of the shifted population is the sum of the original population risk and a gap term, which can be interpreted as a consistency regularization term. The paper also provides a theoretical understanding of this gap, highlighting its negative effects on the early stages of training. We also propose a method to mitigate these effects. To validate our approach, we conducted experiments using same data augmentation techniques and computing resources under several scenarios, including standard training, out-of-distribution, and imbalanced classification. The results demonstrate that our methods surpass compared methods under all scenarios in terms of generalization ability and convergence stability. We provide our code implementation at the following link: https://github.com/ydlsfhll/ASPR.

cs.LG↗
arXiv2025

Broadband bright biphotons from periodically poled triple-resonance metasurface

Biphotons from spontaneous parametric down conversion with broad bandwidth are highly wanted in many quantum technologies. However, achieving broad bandwidth in both frequency and momentum while keeping a high rate remains a challenge for both conventional nonlinear crystals and recently emerging nonlinear metasurfaces. Here, we address this challenge by introducing a periodically poled triple-resonance metasurface (PPTM) incorporating a nano-grating atop a periodically poled LiNbO$_3$ thin film. PPTM supports high-Q guided mode resonances at pump, signal, and idler wavelengths meanwhile enabling quasi-phase matching between three guided modes in a broad frequency/momentum range. The predicted biphoton rate is over 100 MHz/mW with a frequency bandwidth of 165 nm around 1550 nm and a momentum bandwidth of $13^\circ \times 6^\circ$, improving the state-of-the-art by over three orders of magnitude in rate and one order of magnitude in bandwidths. This ultrathin broadband bright biphoton source could stimulate system-level miniaturization of various free-space quantum photonic technologies.

physics.optics↗
arXiv2025

On nodal solutions with a prescribed number of nodes for a Kirchhoff-type problem

We are concerned with the existence and asymptotic behavior of multiple radial sign-changing solutions with the nodal characterization for a Kirchhoff-type problem involving the nonlinearity $|u|^{p-2}u(2<p<4)$ in $\mathbb{R}^3$. By developing some useful analysis techniques and introducing a novel definition of the Nehari manifold for the auxiliary system of the equations, we show that, for any positive integer $k$, the problem has a sign-changing solution $u_k^b$ changing signs exactly $k$ times. Furthermore, the energy of $u_k^b$ is strictly increasing in $k$, as well as some asymptotic behaviors of $u_k^b$ are obtained. Our result is a complement of [Deng Y, Peng S, Shuai W, {\it J. Funct. Anal.}, {\bf269}(2015), 3500-3527], where the case $2<p<4$ is left open.

math.AP↗
arXiv2025

Beyond the band edge: Unveiling high-mobility hot carriers in a two-dimensional conjugated coordination polymer

Hot carriers, inheriting excess kinetic energy from high-energy photons, underpin numerous optoelectronic applications involving non-equilibrium transport processes. Current research on hot carriers has predominantly focused on inorganic materials, with little attention paid to organic-based systems due to their ultrafast energy relaxation and inefficient charge transport. Here, we overturn this paradigm by demonstrating highly mobile hot carriers in solution-processable, highly crystalline two-dimensional conjugated coordination polymer (2D c-CP) Cu3BHT (BHT = benzenehexathiol) films. Leveraging a suite of ultrafast spectroscopic and imaging techniques, we unravel the microscopic charge transport landscape in Cu3BHT films following non-equilibrium photoexcitation across temporal, spatial, and frequency domains, revealing two distinct high-mobility transport regimes. In the non-equilibrium transport regime, hot carriers achieve ultrahigh mobility of ~2,000 cm2 V-1 s-1, traversing grain boundaries up to 300 nm within a picosecond. In the quasi-equilibrium transport regime, free carriers exhibit Drude-type band-like transport with a remarkable mobility of ~400 cm2 V-1 s-1 and an intrinsic diffusion length exceeding 1 micrometer. These findings establish 2D c-CPs as versatile platforms for exploring high-mobility non-equilibrium transport, unlocking new opportunities for organic-based hot carrier applications.

cond-mat.mtrl-sci↗