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Xiaoshan Li

Publications and source records attributed to Xiaoshan Li.

At least 19 recordsLinked to original sources
arXiv2026

A note on csc Bergman metric

In this note, we show that if the Bergman metric of a pseudoconvex domain in $\mathbb C^n$($n\geq 3$) has constant scalar curvature, then every strongly pseudoconvex boundary point of the domain is spherical.

math.CV↗
arXiv2026

Localization of Bergman Kernels and the Cheng-Yau Conjecture on Real Analytic Pseudoconvex Domains

In this paper, we establish the localization of Bergman kernels for unbounded pseudoconvex domains near boundary points of finite D'Angelo type. This result was proved by Engli\v{s} more than twenty years ago for bounded pseudoconvex domains and had remained as an open question in the unbounded setting. Related foundational work was carried out by Fefferman, Kerzman, Boutet de Monvel--Sj\"ostrand, Boas, Bell, and others. Combining our localization theorem with an extension theorem of Mir--Zaitsev, we prove that the Bergman metric of a bounded pseudoconvex domain with real-analytic boundary is Einstein if and only if the domain is biholomorphic to the unit ball. This result advances a longstanding conjecture of Cheng and Yau. A key step is to show that the Bergman metric of a smooth, possibly unbounded, pseudoconvex domain cannot be K\"ahler--Einstein if its boundary contains a non-strongly pseudoconvex \(h\)-extendible point. We further prove that a bounded weakly pseudoconvex real-analytic domain with a K\"ahler--Einstein Bergman metric must possess a weakly pseudoconvex \(h\)-extendible boundary point, thereby reducing the problem to the \(h\)-extendible setting. This paper draws deeply on, and reveals essential connections among many subfields of microlocal analysis, several complex variables, and complex geometry.

math.CV↗
arXiv2025

Contraction property on complex hyperbolic ball

We prove an isoperimetric inequalitie on the complex hyperbolic ball with Assumption \ref{assumption}}. As an application, we prove a contraction property for the holomorphic functions in Hardy and weighted Bergman spaces on the complex hyperbolic ball with this assumption. The results can be seen as partial generalization of Kulikov's result on the complex hyperbolic plane.

math.CV↗
arXiv2024

VCEMO: Multi-Modal Emotion Recognition for Chinese Voiceprints

Emotion recognition can enhance humanized machine responses to user commands, while voiceprint-based perception systems can be easily integrated into commonly used devices like smartphones and stereos. Despite having the largest number of speakers, there is a noticeable absence of high-quality corpus datasets for emotion recognition using Chinese voiceprints. Hence, this paper introduces the VCEMO dataset to address this deficiency. The proposed dataset is constructed from everyday conversations and comprises over 100 users and 7,747 textual samples. Furthermore, this paper proposes a multimodal-based model as a benchmark, which effectively fuses speech, text, and external knowledge using a co-attention structure. The system employs contrastive learning-based regulation for the uneven distribution of the dataset and the diversity of emotional expressions. The experiments demonstrate the significant improvement of the proposed model over SOTA on the VCEMO and IEMOCAP datasets. Code and dataset will be released for research.

cs.MM↗
arXiv2023

Semi-classical asymptotics of partial Bergman kernels on $\mathbb{R}$-symmetric complex manifolds with boundary

Let $M$ be a relatively compact connected open subset with smooth connected boundary of a complex manifold $M'$. Let $(L,h^L)\rightarrow M'$ be a positive line bundle over $M'$. Suppose that $M'$ admits a holomorphic $\mathbb{R}$-action which preserves the boundary of $M$ and lifts to $L$. We establish the asymptotic expansion of a partial Bergman kernel associated to a package of Fourier modes of high frequency with respect to the $\mathbb{R}$-action in the high powers of $L$. As an application, we establish an $\mathbb{R}$-equivariant analogue of Fefferman's and Bell-Ligocka's result about smooth extension up to the boundary of biholomorphic maps between weakly pseudoconvex domains in $\mathbb{C}^n$. Another application concerns the embedding of pseudoconcave manifolds.

math.CV↗
arXiv2023

$G$-invariant Bergman kernel and geometric quantization on complex manifolds with boundary

Let $M$ be a complex manifold with boundary $X$, which admits a holomorphic Lie group $G$-action preserving $X$. We establish a full asymptotic expansion for the $G$-invariant Bergman kernel under certain assumptions. As an application, we get $G$-invariant version of Fefferman's result about regularity of biholomorphic maps on strongly pseudoconvex domains of $\mathbb C^n$. Moreover, we show that the Guillemin-Sternberg map on a complex manifold with boundary is Fredholm by developing reduction to boundary technique, which establish ``quantization commutes with reduction" in this case.

math.CV↗
arXiv2022

On Bergman kernel functions and weak Morse inequalities

We give simple and unified proofs of weak holomorhpic Morse inequalities on complete manifolds, $q$-convex manifolds, pseudoconvex domains, weakly $1$-complete manifolds and covering manifolds. This paper is essentially based on the asymptotic Bergman kernel functions and the Bochner-Kodaira-Nakano formulas.

math.CV↗
arXiv2021

Performance, Successes and Limitations of Deep Learning Semantic Segmentation of Multiple Defects in Transmission Electron Micrographs

In this work, we perform semantic segmentation of multiple defect types in electron microscopy images of irradiated FeCrAl alloys using a deep learning Mask Regional Convolutional Neural Network (Mask R-CNN) model. We conduct an in-depth analysis of key model performance statistics, with a focus on quantities such as predicted distributions of defect shapes, defect sizes, and defect areal densities relevant to informing modeling and understanding of irradiated Fe-based materials properties. To better understand the performance and present limitations of the model, we provide examples of useful evaluation tests which include a suite of random splits, and dataset size-dependent and domain-targeted cross validation tests. Overall, we find that the current model is a fast, effective tool for automatically characterizing and quantifying multiple defect types in microscopy images, with a level of accuracy on par with human domain expert labelers. More specifically, the model can achieve average defect identification F1 scores as high as 0.8, and, based on random cross validation, have low overall average (+/- standard deviation) defect size and density percentage errors of 7.3 (+/- 3.8)% and 12.7 (+/- 5.3)%, respectively. Further, our model predicts the expected material hardening to within 10-20 MPa (about 10% of total hardening), which is about the same error level as experiments. Our targeted evaluation tests also suggest the best path toward improving future models is not expanding existing databases with more labeled images but instead data additions that target weak points of the model domain, such as images from different microscopes, imaging conditions, irradiation environments, and alloy types. Finally, we discuss the first phase of an effort to provide an easy-to-use, open-source object detection tool to the broader community for identifying defects in new images.

cs.CV↗
arXiv2020

$S^1$-equivariant Index theorems and Morse inequalities on complex manifolds with boundary

Let $M$ be a complex manifold of dimension $n$ with smooth connected boundary $X$. Assume that $\overline M$ admits a holomorphic $S^1$-action preserving the boundary $X$ and the $S^1$-action is transversal on $X$. We show that the $\overline\partial$-Neumann Laplacian on $M$ is transversally elliptic and as a consequence, the $m$-th Fourier component of the $q$-th Dolbeault cohomology group $H^q_m(\overline M)$ is finite dimensional, for every $m\in\mathbb Z$ and every $q=0,1,\ldots,n$. This enables us to define $\sum^{n}_{j=0}(-1)^j{\rm dim\,}H^q_m(\overline M)$ the $m$-th Fourier component of the Euler characteristic on $M$ and to study large $m$-behavior of $H^q_m(\overline M)$. In this paper, we establish an index formula for $\sum^{n}_{j=0}(-1)^j{\rm dim\,}H^q_m(\overline M)$ and Morse inequalities for $H^q_m(\overline M)$.

math.CV↗
arXiv2020

Szegő kernels and equivariant embedding theorems for CR manifolds

We consider a compact connected CR manifold with a transversal CR locally free $\mathbb R$-action endowed with a rigid positive CR line bundle. We prove that a certain weighted Fourier-Szegő kernel of the CR sections in the high tensor powers admits a full asymptotic expansion and we establish $\mathbb R$-equivariant Kodaira embedding theorem for CR manifolds. Using similar methods we also establish an analytic proof of an $\mathbb R$-equivariant Boutet de Monvel embedding theorem for strongly pseudoconvex CR manifolds. In particular, we obtain equivariant embedding theorems for irregular Sasakian manifolds. As applications of our results, we obtain Torus equivariant Kodaira and Boutet de Monvel embedding theorems for CR manifolds and Torus equivariant Kodaira embedding theorem for complex manifolds.

math.CV↗
arXiv2018

An Integrated Transfer Learning and Multitask Learning Approach for Pharmacokinetic Parameter Prediction

Background: Pharmacokinetic evaluation is one of the key processes in drug discovery and development. However, current absorption, distribution, metabolism, excretion prediction models still have limited accuracy. Aim: This study aims to construct an integrated transfer learning and multitask learning approach for developing quantitative structure-activity relationship models to predict four human pharmacokinetic parameters. Methods: A pharmacokinetic dataset included 1104 U.S. FDA approved small molecule drugs. The dataset included four human pharmacokinetic parameter subsets (oral bioavailability, plasma protein binding rate, apparent volume of distribution at steady-state and elimination half-life). The pre-trained model was trained on over 30 million bioactivity data. An integrated transfer learning and multitask learning approach was established to enhance the model generalization. Results: The pharmacokinetic dataset was split into three parts (60:20:20) for training, validation and test by the improved Maximum Dissimilarity algorithm with the representative initial set selection algorithm and the weighted distance function. The multitask learning techniques enhanced the model predictive ability. The integrated transfer learning and multitask learning model demonstrated the best accuracies, because deep neural networks have the general feature extraction ability, transfer learning and multitask learning improved the model generalization. Conclusions: The integrated transfer learning and multitask learning approach with the improved dataset splitting algorithm was firstly introduced to predict the pharmacokinetic parameters. This method can be further employed in drug discovery and development.

cs.LG↗
arXiv2018

Deep learning for in vitro prediction of pharmaceutical formulations

Current pharmaceutical formulation development still strongly relies on the traditional trial-and-error approach by individual experiences of pharmaceutical scientists, which is laborious, time-consuming and costly. Recently, deep learning has been widely applied in many challenging domains because of its important capability of automatic feature extraction. The aim of this research is to use deep learning to predict pharmaceutical formulations. In this paper, two different types of dosage forms were chosen as model systems. Evaluation criteria suitable for pharmaceutics were applied to assessing the performance of the models. Moreover, an automatic dataset selection algorithm was developed for selecting the representative data as validation and test datasets. Six machine learning methods were compared with deep learning. The result shows the accuracies of both two deep neural networks were above 80% and higher than other machine learning models, which showed good prediction in pharmaceutical formulations. In summary, deep learning with the automatic data splitting algorithm and the evaluation criteria suitable for pharmaceutical formulation data was firstly developed for the prediction of pharmaceutical formulations. The cross-disciplinary integration of pharmaceutics and artificial intelligence may shift the paradigm of pharmaceutical researches from experience-dependent studies to data-driven methodologies.

cs.LG↗
arXiv2018

Automated Prototype Generation from Formal Requirements Model

Prototyping is an effective and efficient way of requirement validation to avoid introducing errors in the early stage of software development. However, manually developing a prototype of a software system requires additional efforts, which would increase the overall cost of software development. In this paper, we present an approach with a developed tool to automatic generation of prototypes from formal requirements models. A requirements model consists of a use case diagram, a conceptual class diagram, use case definitions specified by system sequence diagrams and the contracts of their system operations. We propose a method to decompose a contract into executable parts and non-executable parts. A set of transformation rules is given to decompose the executable part into pre-implemented primitive operations. A non-executable part is usually realized by significant algorithms such as sorting a list, finding the shortest path or domain-specific computation. It can be implemented manually or by using existing code. A CASE tool is developed that provides an interface for developers to develop a program for each non-executable part of a contract, and automatically transforms the executables into sequences of pre-implemented primitive operations. We have conducted four cases studies with over 50 use cases. The experimental result shows that the 93.65% of requirement specifications are executable, and only 6.35% are non-executable such as sorting and event-call, which can be implemented by developers manually or invoking the APIs of advanced algorithms in Java library. The one second generated the prototype of a case study requires approximate nine hours manual implementation by a skilled programmer. Overall, the result is satisfiable, and the proposed approach with the developed CASE tool can be applied to the software industry for requirements engineering.

cs.SE↗
arXiv2018

Szegö kernel asymptotics and Morse inequalities on CR manifolds with $S^1$ action

Let $X$ be a compact connected CR manifold of dimension $2n-1, n\geq 2$. We assume that there is a transversal CR locally free $S^1$ action on $X$. Let $L^k$ be the $k$-th power of a rigid CR line bundle $L$ over $X$. Without any assumption on the Levi-form of $X$, we obtain a scaling upper-bound for the partial Szegő kernel on $(0,q)$-forms with values in $L^k$. After integration, this gives the weak Morse inequalities. By a refined spectral analysis, we also obtain the strong Morse inequalities in CR setting. We apply the strong Morse inequalities to show that the Grauert-Riemenschneider criterion is also true in the CR setting.

math.CV↗