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Lang Wang

Publications and source records attributed to Lang Wang.

At least 19 recordsLinked to original sources
arXiv2026

Small exponent Schatten class Toeplitz operators on convex domains of finite type

In this paper, we study the characterizations of Schatten \(p\)-class Toeplitz operators on smoothly bounded convex domains of finite type in \(\C^n\). On one hand, by using discrete Kobayashi lattice, we characterize the Schatten \(p\)-class Toeplitz operators by employing a probabilistic selection method for \(0 \frac{n}{n+1}\). On the other hand, as an application, the criterion gives a geometric characterization for Schatten \(p\)-class weighted composition operators for \(0 \frac{2n}{n+1}\). Our main results give an answer to the question that find a geometric or analytic characterization of the Schatten \(p\)-class weighted composition operators whenever \(0<p<2\) raised by Xiao-Yang-Yuan \cite{Xiao2026}.

math.FA↗
arXiv2026

Geometry of bounded generic domains with piecewise smooth boundary

In this paper, we study the geometry of bounded domains with piecewise smooth boundary. Specifically, we obtain the relationship between the squeezing function corresponding to polydisk and Levi flatness on bounded generic convex domains. As an application, we prove that a two dimensional bounded generic convex domain with piecewise $C^2$-smooth boundary that admits a finite volume quotient is biholomorphic to bidisk. Moreover, we show that any Teichm$\ddot{\operatorname{u}}$ller space $\mathcal{T}_g$ with $g\geq2$ can not be biholomorphic to a bounded generic domain with piecewise $C^2$-smooth boundary.

math.CV↗
arXiv2025

A note for Carleson measure on bounded $\mathbb{C}$-convex domains

Let \(0<q<p<\infty\), \(Ω\) be a bounded \(\bbC\)-convex domains in \(\bbC^n\). We establish several equivalent characterizations for the boundedness of Carleson embedding \(J_μ:A_α^p\hookrightarrow L^q(μ)\) on \(Ω\) with sharp \(\cB\) condition. Furthermore, we prove that the boundedness of \(J_μ\) is equivalent to its compactness.

math.CV↗
arXiv2025

The growth rate on the volume of $\mathcal{M}_g^{<L(g)}$

Let $\mathcal{M}_g$ be the moduli space of hyperbolic surfaces of genus g endowed with the Weil-Petersson metric. In this paper, we introduce a function $L(g)$ of genus $g$ and call the geodesics whose length less than $L(g)$ short geodesics. We compute the growth rate on the volume of the subset of hyperbolic surfaces with short geodesics. In particular, when $g$ approaches infinity, if $L(g)$ also approaches infinity, then the volume of surfaces characterized by short geodesics is equal to $V_g$ almost surely.

math.GT↗
arXiv2025

K$\ddot{\operatorname{a}}$hlerity of invariant metrics on pseudoconvex domain of dimension two

For a two dimensional bounded pseudoconvex domain of finite type, we prove uniformization theorems via K$\ddot{\operatorname{a}}$hler-Kobayashi metric or K$\ddot{\operatorname{a}}$hler-Carath$\acute{\operatorname{e}}$odory metric with quasi-finite geometry of order three. In particular, a pseudoconvex Reinhardt domain of finite type is the unit ball if and only if the Bergman metric is a scalar multiple of the Kobayashi metric or Carath$\acute{\operatorname{e}}$odory metric. Moreover, we establish a rigidity theorem concerning holomorphic sectional curvature of Bergman metric and Lu constant.

math.CV↗
arXiv2024

Loss-driven miniaturized bound state in continuum biosensing system

Optical metasurface has brought a revolution in label-free molecular sensing, attracting extensive attention. Currently, such sensing approaches are being designed to respond to peak wavelengths with a higher Q factor in the visible and near-infrared regions.Nevertheless, a higher Q factor that enhances light confinement will inevitably deteriorate the wavelength sensitivity and complicate the sensing system. We propose a Q-switched sensing mechanism, which enables the real part of the refractive index to effectively perturbate the damping loss of the oscillator, resulting in a boost of peak intensity.Consequently, a higher Q factor in Q-switched sensor can further enhance the peak sensitivity while remaining compatible with broadband light sources, simultaneously meeting the requirements of high performance and a compact system.This is achieved in a unique 3D bound-state-in-continuum (BIC) metasurface which can be mass-produced by wafer-scale aluminum-nanoimprinting technology and provides a peak intensity sensitivity up to 928 %/RIU.Therefore, a miniaturized BIC biosensing system is realized, with a limit of detection to 10E-5 refractive index units and 129 aM extracellular vesicles in clinical lung cancer diagnosis, both of which are magnitudes lower than those of current state-of-the-art biosensors. It further demonstrates significant potential for home cancer self-testing equipment for post-operative follow-up. This Q-switched sensing mechanism offers a new perspective for the commercialization of advanced and practical BIC optical biosensing systems in real-setting scenarios.

physics.optics↗
arXiv2024

CAMEL2: Enhancing weakly supervised learning for histopathology images by incorporating the significance ratio

Histopathology image analysis plays a crucial role in cancer diagnosis. However, training a clinically applicable segmentation algorithm requires pathologists to engage in labour-intensive labelling. In contrast, weakly supervised learning methods, which only require coarse-grained labels at the image level, can significantly reduce the labeling efforts. Unfortunately, while these methods perform reasonably well in slide-level prediction, their ability to locate cancerous regions, which is essential for many clinical applications, remains unsatisfactory. Previously, we proposed CAMEL, which achieves comparable results to those of fully supervised baselines in pixel-level segmentation. However, CAMEL requires 1,280x1,280 image-level binary annotations for positive WSIs. Here, we present CAMEL2, by introducing a threshold of the cancerous ratio for positive bags, it allows us to better utilize the information, consequently enabling us to scale up the image-level setting from 1,280x1,280 to 5,120x5,120 while maintaining the accuracy. Our results with various datasets, demonstrate that CAMEL2, with the help of 5,120x5,120 image-level binary annotations, which are easy to annotate, achieves comparable performance to that of a fully supervised baseline in both instance- and slide-level classifications.

cs.CV↗
arXiv2024

Statistical estimation theory detection limits for label-free imaging

The emergence of label-free microscopy techniques has significantly improved our ability to precisely characterize biochemical targets, enabling non-invasive visualization of cellular organelles and tissue organization. Each label-free method has specific benefits, drawbacks, and varied varied sensitivity under measurement conditions across different types of specimens. To link all these disparate label-free optical interactions together and to compare detection sensitivity of these modalities, we investigate their sensitivity within the framework of statistical estimation theory. This paper introduces a comprehensive unified framework for evaluating the bounds for signal detection with label-free microscopy methods, including second harmonic generation (SHG), third harmonic generation (THG), coherent anti-Stokes Raman scattering (CARS), coherent Stokes Raman scattering (CSRS), stimulated Raman loss (SRL), stimulated Raman gain (SRG), stimulated emission (SE), impulsive stimulated Raman scattering (ISRS), transient absorption (TA), and photothermal effect (PTE). A general model for signal generation induced by optical scattering is developed. Based on this model, the information obtained is quantitatively analyzed using Fisher information, and the fundamental constraints on estimation precision are evaluated through the Cramér-Rao Lower Bound (CRLB).

physics.optics↗
arXiv2024

Synthetic aperture holographic third harmonic generation microscopy

Third harmonic generation (THG) provides a valuable, label-free approach to imaging biological systems. To date, THG microscopy has been performed using point scanning methods that rely on intensity measurements lacking phase information of the complex field. We report the first demonstration of THG holographic microscopy and the reconstruction of the complex THG signal field with spatial synthetic aperture imaging. Phase distortions arising from measurement-to-measurement fluctuations and imaging components cause optical aberrations in the reconstructed THG field. We have developed an aberration-correction algorithm that estimates and corrects for these phase distortions to reconstruct the spatial synthetic aperture THG field without optical aberrations.

physics.optics↗
arXiv2023

Robust and Tuning-Free Sparse Linear Regression via Square-Root Slope

We consider the high-dimensional linear regression model and assume that a fraction of the measurements are altered by an adversary with complete knowledge of the data and the underlying distribution. We are interested in a scenario where dense additive noise is heavy-tailed while the measurement vectors follow a sub-Gaussian distribution. Within this framework, we establish minimax lower bounds for the performance of an arbitrary estimator that depend on the the fraction of corrupted observations as well as the tail behavior of the additive noise. Moreover, we design a modification of the so-called Square-Root Slope estimator with several desirable features: (a) it is provably robust to adversarial contamination, and satisfies performance guarantees in the form of sub-Gaussian deviation inequalities that match the lower error bounds, up to logarithmic factors; (b) it is fully adaptive with respect to the unknown sparsity level and the variance of the additive noise, and (c) it is computationally tractable as a solution of a convex optimization problem. To analyze performance of the proposed estimator, we prove several properties of matrices with sub-Gaussian rows that may be of independent interest.

math.ST↗
arXiv2023

Clausius-Mossotti Relation Revisited: Media with Electric and Magnetic Response

A reexamination of the Clausius-Mossotti relation in which material with both electric and magnetic responses yields surprising results. Materials with indices near zero and with real parts less than zero, that is the real part of both the permeability and permittivity are negative, are found to emerge from the interaction of electric and magnetic responses in a self-consistent theory. The new results point the way to artificial and natural materials with exotic responses. A simulation with 10^10 particles shows good agreement with the analytical results.

physics.optics↗
arXiv2023

Aberration free synthetic aperture second harmonic generation holography

Second harmonic generation (SHG) microscopy is a valuable tool for optical microscopy. SHG microscopy is normally performed as a point scanning imaging method, which lacks phase information and is limited in spatial resolution by the spatial frequency support of the illumination optics. In addition, aberrations in the illumination are difficult to remove. We propose and demonstrate SHG holographic synthetic aperture holographic imaging in both the forward (transmission) and backward (epi) imaging geometries. By taking a set of holograms with varying incident angle plane wave illumination, the spatial frequency support is increased and the input and output pupil phase aberrations are estimated and corrected -- producing diffraction limited SHG imaging that combines the spatial frequency support of the input and output optics. The phase correction algorithm is computationally efficient and robust and can be applied to any set of measured field imaging data.

physics.optics↗
arXiv2022

Deeply Supervised Layer Selective Attention Network: Towards Label-Efficient Learning for Medical Image Classification

Labeling medical images depends on professional knowledge, making it difficult to acquire large amount of annotated medical images with high quality in a short time. Thus, making good use of limited labeled samples in a small dataset to build a high-performance model is the key to medical image classification problem. In this paper, we propose a deeply supervised Layer Selective Attention Network (LSANet), which comprehensively uses label information in feature-level and prediction-level supervision. For feature-level supervision, in order to better fuse the low-level features and high-level features, we propose a novel visual attention module, Layer Selective Attention (LSA), to focus on the feature selection of different layers. LSA introduces a weight allocation scheme which can dynamically adjust the weighting factor of each auxiliary branch during the whole training process to further enhance deeply supervised learning and ensure its generalization. For prediction-level supervision, we adopt the knowledge synergy strategy to promote hierarchical information interactions among all supervision branches via pairwise knowledge matching. Using the public dataset, MedMNIST, which is a large-scale benchmark for biomedical image classification covering diverse medical specialties, we evaluate LSANet on multiple mainstream CNN architectures and various visual attention modules. The experimental results show the substantial improvements of our proposed method over its corresponding counterparts, demonstrating that LSANet can provide a promising solution for label-efficient learning in the field of medical image classification.

cs.CV↗
arXiv2022

Automated Scoring System of HER2 in Pathological Images under the Microscope

Breast cancer is the most common cancer among women worldwide. The human epidermal growth factor receptor 2 (HER2) with immunohistochemical (IHC) is widely used for pathological evaluation to provide the appropriate therapy for patients with breast cancer. However, the deficiency of pathologists and subjective and susceptible to inter-observer variation of visual diagnosis are the main challenges. Recently, with the rapid development of artificial intelligence (AI) in disease diagnosis, several automated HER2 scoring methods using traditional computer vision or machine learning methods indicate the improvement of the HER2 diagnostic accuracy, but the unreasonable interpretation in pathology, as well as the expensive and ethical issues for annotation, make these methods still have a long way to deploy in hospitals to ease pathologists' burden in real. In this paper, we propose a HER2 automated scoring system that strictly follows the HER2 scoring guidelines simulating the real workflow of HER2 scores diagnosis by pathologists. Unlike the previous work, our method considers the positive control of HER2 to make sure the assay performance for each slide, eliminating work for repeated comparison between the current field of view (FOV) and positive control FOV, especially for the borderline cases. Besides, for each selected FOV under the microscope, our system provides real-time HER2 scores analysis and visualizations of the membrane staining intensity and completeness corresponding with the cell classifications. Our rigorous workflow along with the flexible interactive adjustion in demand substantially assists pathologists to finish the HER2 diagnosis faster and improves the robustness and accuracy. The proposed system will be embedded in our Thorough Eye platform for deployment in hospitals.

q-bio.QM↗
arXiv2022

Robust Estimation of Covariance Matrices: Adversarial Contamination and Beyond

We consider the problem of estimating the covariance structure of a random vector $Y\in \mathbb R^d$ from a sample $Y_1,\ldots,Y_n$. We are interested in the situation when $d$ is large compared to $n$ but the covariance matrix $Σ$ of interest has (exactly or approximately) low rank. We assume that the given sample is (a) $ε$-adversarially corrupted, meaning that $ε$ fraction of the observations could have been replaced by arbitrary vectors, or that (b) the sample is i.i.d. but the underlying distribution is heavy-tailed, meaning that the norm of $Y$ possesses only finite fourth moments. We propose an estimator that is adaptive to the potential low-rank structure of the covariance matrix as well as to the proportion of contaminated data, and admits tight deviation guarantees despite rather weak assumptions on the underlying distribution. Finally, we discuss the algorithms that allow to approximate the proposed estimator in a numerically efficient way.

math.ST↗
arXiv2021

Clustering Diffused-Particle Method for Scattering from Large Ensembles of Electromagnetically Polarizable Particles

The Foldy-Lax equation is generalized for a medium which consists of particles with both electric and magnetic responses. The result is used to compute fields scattered from ensembles of particles. The computational complexity is reduced by hierarchical clustering techniques to enable simulations with on the order of 10^10 particles. With so many particles we are able to see the transition to bulk media behavior of the fields. For non-magnetic materials, the observable index, permittivity, and permeability of the effective bulk medium are in good agreement with the Clausius-Mossotti relation. The fields simulated for particles with both electric and magnetic responses are in good agreement with new analytical results for a generalized effective medium theory.

physics.optics↗