arXiv subjects

Weihao Zheng

Publications and source records attributed to Weihao Zheng.

12 recordsLinked to original sources

arXiv2026

Nonlinear stability of continuously self-similar naked singularities for the Einstein-scalar field equations II: linearized stability

This is the second part of a series of papers proving the nonlinear stability of a one-parameter family of continuous self-similar $C^{1,α}$ naked singularity solutions, with $0<α\ll1$, to the spherically symmetric Einstein-scalar field equations. These solutions were constructed by Christodoulou and are known to be unstable under sufficiently rough perturbations due to the blue-shift instability mechanism. In complete contrast to the previous instability results, we establish the linearized stability for those naked singularity spacetimes under perturbations of the same regularity as the background, revealing the central role of regularity in determining the strength of the blue-shift instability mechanism, and showing that it is not triggered at the regularity level of the background spacetime. The linear analysis carried out in this paper provides the foundation for the nonlinear stability result established in the companion paper [W. Zheng, Nonlinear stability of the continuous self-similar naked singularities for the Einstein-scalar field equations I: main results]. Together with that companion paper, this yields the nonlinear stability of these continuously self-similar naked singularities.

gr-qc↗

arXiv2026

Nonlinear stability of continuously self-similar naked singularities for the Einstein-scalar field equations I: main results

This is the first part of a series of papers proving the nonlinear stability of a one-parameter family of continuously self-similar $C^{1,α}$ naked singularity solutions, with $0<α\ll1$, to the spherically symmetric Einstein-scalar field equations. The stability holds for initial perturbations lying in a small open neighborhood of the data generating these naked singularity solutions, measured in a localized Hölder topology. These continuously self-similar naked singularity spacetimes were previously constructed by Christodoulou [D. Christodoulou, Examples of naked singularity formation in the gravitational collapse of a scalar field, Ann. of Math. 140 (1994), 607--653], who also proved their instability to black hole formation under sufficiently rough perturbations [D. Christodoulou, The instability of naked singularities in the gravitational collapse of a scalar field, Ann. of Math. 149 (1999), 183--217], thereby verifying weak cosmic censorship within a rough functional framework. In complete contrast, in this paper, we obtain the first nonlinear stability of these naked singularity spacetimes under general perturbations of the same regularity as the background. We rely on the linearized stability result established in the companion paper [J. Singh and W. Zheng, Nonlinear stability of continuously self-similar naked singularities for the Einstein--scalar field equations II: linearized stability]. Our result underscores the decisive role of the functional framework in formulating the Weak Cosmic Censorship conjecture.

gr-qc↗

arXiv2026

SurfAge-Net: A Hierarchical Surface-Based Network for Interpretable Fine-Grained Brain Age Prediction

Brain age prediction serves as a powerful framework for assessing brain status and detecting deviations associated with neurodevelopmental and neurodegenerative disorders. However, most existing approaches emphasize whole-brain age prediction and therefore overlook the pronounced regional heterogeneity of brain maturation that is crucial for detecting localized atypical trajectories. To address this limitation, we propose a novel spherical surface-based brain age prediction network (SurfAge-Net) that leverages multiple morphological metrics to capture region-specific developmental patterns with enhanced robustness and clinical interpretability. SurfAge-Net establishes a new modeling paradigm by incorporating the connectomic principles of cortical organization: it explicitly models both intra- and inter-hemispheric dependencies through a spatial-channel mixing and a lateralization-aware attention mechanism, enabling the network to characterize the coordinate maturation pattern uniquely associated with each target region. Validated on three fetal and neonatal datasets, SurfAge-Net outperforms existing approaches (global MAE = 0.54, regional MAE = 0.45 in gestational/postmenstrual weeks) and demonstrates strong generalizability across external cohorts. Importantly, it provides spatially precise and biologically interpretable maps of cortical maturation, effectively identifying heterogeneous delays and regional-specific abnormalities in atypical developmental populations. These results established fine-grained brain age prediction as a promising paradigm for advancing neurodevelopmental research and supporting early clinical assessment.

q-bio.NC↗

arXiv2025

Gradient estimates for $(p,V)$-harmonic functions on Riemannian manifolds

In this paper, we study $(p,V)$-harmonic functions on complete Riemannian manifolds using the Moser iteration method. A volume comparison theorem and a Sobolev embedding theorem are established under the Bakry-$\acute{E}$mery curvature condition. Moreover, we obtain an explicit global gradient estimate for positive entire $(p,V)$-harmonic functions.

math.DG↗

arXiv2025

General Phase Segregation and Phase Pinning Effects in Ln-doped Lead Halide Perovskite with Dual-wavelength Lasing

Lead halide perovskites (LHPs) exhibit outstanding optoelectronic properties, making them highly promising for applications in various optoelectronics devices. However, rapid ion migration in LHPs not only undermines device stability but also hinders the development of multi-band composite structures, which are crucial to advancing perovskite bandgap engineering and unlocking novel applications. Here, we introduce a novel and general strategy involving both phase segregation and phase pinning by doping Er$^{3+}$ into CsPb(X$_x$Y$_{1-x}$)$_3$ (X, Y = Cl, Br, I) microplates via a simple one-step chemical vapor deposition method. The ion migration is effectively suppressed and a variety of stable multi-band composite structures are demonstrated, with diverse dual-band photoluminescence emissions covering the red, green, and blue spectral bands. The corresponding high-performance dual-wavelength lasers have also been fabricated, confirming the stability and high crystalline quality of these multi-band composite structures. In addition, this strategy is extended to the doping of various lanthanide ion and the incorporation of different mixed halides into LHPs. As a result, a series of multi-band composite structures based on LHPs and corresponding dual-wavelength lasers are developed, thereby validating the generality of this strategy. Theoretical calculations clarify the phase segregation and phase pinning mechanism in these LHPs. Our work not only facilitates the stability design of LHPs but also significantly advances the bandgap engineering, thereby contributing to the expansion of their potential applications in the optoelectronic future.

cond-mat.mtrl-sci↗

arXiv2025

Surface Vision Mamba: Leveraging Bidirectional State Space Model for Efficient Spherical Manifold Representation

Attention-based methods have demonstrated exceptional performance in modelling long-range dependencies on spherical cortical surfaces, surpassing traditional Geometric Deep Learning (GDL) models. However, their extensive inference time and high memory demands pose challenges for application to large datasets with limited computing resources. Inspired by the state space model in computer vision, we introduce the attention-free Vision Mamba (Vim) to spherical surfaces, presenting a domain-agnostic architecture for analyzing data on spherical manifolds. Our method achieves surface patching by representing spherical data as a sequence of triangular patches derived from a subdivided icosphere. The proposed Surface Vision Mamba (SiM) is evaluated on multiple neurodevelopmental phenotype regression tasks using cortical surface metrics from neonatal brains. Experimental results demonstrate that SiM outperforms both attention- and GDL-based methods, delivering 4.8 times faster inference and achieving 91.7% lower memory consumption compared to the Surface Vision Transformer (SiT) under the Ico-4 grid partitioning. Sensitivity analysis further underscores the potential of SiM to identify subtle cognitive developmental patterns. The code is available at https://github.com/Rongzhao-He/surface-vision-mamba.

cs.CV↗

arXiv2024

Asymptotically Anti-de Sitter Spherically Symmetric Hairy Black Holes

We construct one-parameter families of static spherically symmetric asymptotically anti-de Sitter black hole solutions $(\mathcal{M},g_ε,ϕ_ε)$ to the Einstein-Maxwell-(charged) Klein-Gordon equations. Each family bifurcates off a sub-extremal Reissner-Nordström-AdS spacetime $(\mathcal{M},g_{0},ϕ_{0}\equiv0)$. For a co-dimensional one set of black hole parameters, we show that Dirichlet (respectively Neumann) boundary conditions can be imposed for the scalar field. The construction provides a counter-example to a version of the no-hair conjecture in the context of a negative cosmological constant. Our result is based on our companion work [W. Zheng, \emph{Exponentially-growing Mode Instability on the Reissner-Nordström-Anti-de-Sitter black holes}], in which the existence of linear hair and growing mode solutions have been established. In the charged scalar field case, our result provides the first rigorous mathematical construction of the so-called holographic superconductors, which are of particular significance in high-energy physics.

gr-qc↗

arXiv2024

Exponentially-growing Mode Instability on Reissner-Nordström--Anti-de-Sitter black holes

We construct growing mode solutions to the uncharged and charged Klein-Gordon equations on the sub-extremal Reissner-Nordström--anti-de-Sitter (AdS) spacetime under reflecting (Dirichlet or Neumann) boundary conditions. Our result applies to a range of Klein-Gordon masses above the so-called Breitenlohner-Freedman bound, notably including the conformal mass case. The mode instability of the Reissner-Nordström--AdS spacetime for some black hole parameters is in sharp contrast to the Schwarzschild-AdS spacetime, where the solution to the Klein-Gordon equation is known to decay in time. Contrary to other mode instability results on the Kerr and Kerr-AdS spacetimes, our growing mode solutions of the uncharged and weakly charged Klein-Gordon equation exist independently of the occurrence or absence of superradiance. We discover a novel mechanism leading to a growing mode solution, namely, a near-extremal instability for the Klein-Gordon equation. Our result seems to be the first rigorous mathematical realization of this instability.

gr-qc↗

arXiv2024

Are Large Language Models Possible to Conduct Cognitive Behavioral Therapy?

In contemporary society, the issue of psychological health has become increasingly prominent, characterized by the diversification, complexity, and universality of mental disorders. Cognitive Behavioral Therapy (CBT), currently the most influential and clinically effective psychological treatment method with no side effects, has limited coverage and poor quality in most countries. In recent years, researches on the recognition and intervention of emotional disorders using large language models (LLMs) have been validated, providing new possibilities for psychological assistance therapy. However, are LLMs truly possible to conduct cognitive behavioral therapy? Many concerns have been raised by mental health experts regarding the use of LLMs for therapy. Seeking to answer this question, we collected real CBT corpus from online video websites, designed and conducted a targeted automatic evaluation framework involving the evaluation of emotion tendency of generated text, structured dialogue pattern and proactive inquiry ability. For emotion tendency, we calculate the emotion tendency score of the CBT dialogue text generated by each model. For structured dialogue pattern, we use a diverse range of automatic evaluation metrics to compare speaking style, the ability to maintain consistency of topic and the use of technology in CBT between different models . As for inquiring to guide the patient, we utilize PQA (Proactive Questioning Ability) metric. We also evaluated the CBT ability of the LLM after integrating a CBT knowledge base to explore the help of introducing additional knowledge to enhance the model's CBT counseling ability. Four LLM variants with excellent performance on natural language processing are evaluated, and the experimental result shows the great potential of LLMs in psychological counseling realm, especially after combining with other technological means.

cs.CL↗

arXiv2023

Identification of morphological fingerprint in perinatal brains using quasi-conformal mapping and contrastive learning

The morphological fingerprint in the brain is capable of identifying the uniqueness of an individual. However, whether such individual patterns are present in perinatal brains, and which morphological attributes or cortical regions better characterize the individual differences of ne-onates remain unclear. In this study, we proposed a deep learning framework that projected three-dimensional spherical meshes of three morphological features (i.e., cortical thickness, mean curvature, and sulcal depth) onto two-dimensional planes through quasi-conformal mapping, and employed the ResNet18 and contrastive learning for individual identification. We used the cross-sectional structural MRI data of 682 infants, incorporating with data augmentation, to train the model and fine-tuned the parameters based on 60 infants who had longitudinal scans. The model was validated on 30 longitudinal scanned infant data, and remarkable Top1 and Top5 accuracies of 71.37% and 84.10% were achieved, respectively. The sensorimotor and visual cortices were recognized as the most contributive regions in individual identification. Moreover, the folding morphology demonstrated greater discriminative capability than the cortical thickness, which could serve as the morphological fingerprint in perinatal brains. These findings provided evidence for the emergence of morphological fingerprints in the brain at the beginning of the third trimester, which may hold promising implications for understanding the formation of in-dividual uniqueness in the brain during early development.

cs.LG↗

arXiv2022

A microstructure estimation Transformer inspired by sparse representation for diffusion MRI

Diffusion magnetic resonance imaging (dMRI) is an important tool in characterizing tissue microstructure based on biophysical models, which are complex and highly non-linear. Resolving microstructures with optimization techniques is prone to estimation errors and requires dense sampling in the q-space. Deep learning based approaches have been proposed to overcome these limitations. Motivated by the superior performance of the Transformer, in this work, we present a learning-based framework based on Transformer, namely, a Microstructure Estimation Transformer with Sparse Coding (METSC) for dMRI-based microstructure estimation with downsampled q-space data. To take advantage of the Transformer while addressing its limitation in large training data requirements, we explicitly introduce an inductive bias - model bias into the Transformer using a sparse coding technique to facilitate the training process. Thus, the METSC is composed with three stages, an embedding stage, a sparse representation stage, and a mapping stage. The embedding stage is a Transformer-based structure that encodes the signal to ensure the voxel is represented effectively. In the sparse representation stage, a dictionary is constructed by solving a sparse reconstruction problem that unfolds the Iterative Hard Thresholding (IHT) process. The mapping stage is essentially a decoder that computes the microstructural parameters from the output of the second stage, based on the weighted sum of normalized dictionary coefficients where the weights are also learned. We tested our framework on two dMRI models with downsampled q-space data, including the intravoxel incoherent motion (IVIM) model and the neurite orientation dispersion and density imaging (NODDI) model. The proposed method achieved up to 11.25 folds of acceleration in scan time and outperformed the other state-of-the-art learning-based methods.

eess.SP↗

arXiv2021

WenLan: Bridging Vision and Language by Large-Scale Multi-Modal Pre-Training

Multi-modal pre-training models have been intensively explored to bridge vision and language in recent years. However, most of them explicitly model the cross-modal interaction between image-text pairs, by assuming that there exists strong semantic correlation between the text and image modalities. Since this strong assumption is often invalid in real-world scenarios, we choose to implicitly model the cross-modal correlation for large-scale multi-modal pre-training, which is the focus of the Chinese project `WenLan' led by our team. Specifically, with the weak correlation assumption over image-text pairs, we propose a two-tower pre-training model called BriVL within the cross-modal contrastive learning framework. Unlike OpenAI CLIP that adopts a simple contrastive learning method, we devise a more advanced algorithm by adapting the latest method MoCo into the cross-modal scenario. By building a large queue-based dictionary, our BriVL can incorporate more negative samples in limited GPU resources. We further construct a large Chinese multi-source image-text dataset called RUC-CAS-WenLan for pre-training our BriVL model. Extensive experiments demonstrate that the pre-trained BriVL model outperforms both UNITER and OpenAI CLIP on various downstream tasks.

cs.CV↗