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Xiaoshan Li

Publications and source records attributed to Xiaoshan Li.

35 records · Page 2Linked to original sources
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↗
arXiv2018

Szegő kernel asymptotic expansion on CR manifolds with $S^1$ action

Let $X$ be a compact connected strongly pseudoconvex CR manifold of dimension $2n+1, n \ge 1$ with a transversal CR $S^1$ action on $X$. We establish an asymptotic expansion for the $m$-th Fourier component of the Szegő kernel function as $m\rightarrow\infty$, where the expansion involves a contribution in terms of a distance function from lower dimensional strata of the $S^1$ action. We also obtain explicit formulas for the first three coefficients of the expansion.

math.CV↗
arXiv2018

Szegő kernel expansion and equivariant embedding of CR manifolds with circle action

Let $X$ be a compact strongly pseudoconvex CR manifold with a transversal CR $S^1$-action. In this paper, we establish the asymptotic expansion of Szegő kernels of positive Fourier components and by using the asymptotics, we show that $X$ can be equivariant CR embedded into some $\mathbb C^N$ equipped with a simple $S^1$-action. An equivariant embedding of quasi-regular Sasakian manifold is also derived.

math.CV↗
arXiv2018

MicroShare: Privacy-Preserved Medical Resource Sharing through MicroService Architecture

This paper takes up the problem of medical resource sharing through MicroService architecture without compromising patient privacy. To achieve this goal, we suggest refactoring the legacy EHR systems into autonomous MicroServices communicating by the unified techniques such as RESTFul web service. This lets us handle clinical data queries directly and far more efficiently for both internal and external queries. The novelty of the proposed approach lies in avoiding the data de-identification process often used as a means of preserving patient privacy. The implemented toolkit combines software engineering technologies such as Java EE, RESTful web services, JSON Web Tokens to allow exchanging medical data in an unidentifiable XML and JSON format as well as restricting users to the need-to-know principle. Our technique also inhibits retrospective processing of data such as attacks by an adversary on a medical dataset using advanced computational methods to reveal Protected Health Information (PHI). The approach is validated on an endoscopic reporting application based on openEHR and MST standards. From the usability perspective, the approach can be used to query datasets by clinical researchers, governmental or non-governmental organizations in monitoring health care and medical record services to improve quality of care and treatment.

cs.SE↗
arXiv2018

Predicting Oral Disintegrating Tablet Formulations by Neural Network Techniques

Oral Disintegrating Tablets (ODTs) is a novel dosage form that can be dissolved on the tongue within 3min or less especially for geriatric and pediatric patients. Current ODT formulation studies usually rely on the personal experience of pharmaceutical experts and trial-and-error in the laboratory, which is inefficient and time-consuming. The aim of current research was to establish the prediction model of ODT formulations with direct compression process by Artificial Neural Network (ANN) and Deep Neural Network (DNN) techniques. 145 formulation data were extracted from Web of Science. All data sets were divided into three parts: training set (105 data), validation set (20) and testing set (20). ANN and DNN were compared for the prediction of the disintegrating time. The accuracy of the ANN model has reached 85.60%, 80.00% and 75.00% on the training set, validation set and testing set respectively, whereas that of the DNN model was 85.60%, 85.00% and 80.00%, respectively. Compared with the ANN, DNN showed the better prediction for ODT formulations. It is the first time that deep neural network with the improved dataset selection algorithm is applied to formulation prediction on small data. The proposed predictive approach could evaluate the critical parameters about quality control of formulation, and guide research and process development. The implementation of this prediction model could effectively reduce drug product development timeline and material usage, and proactively facilitate the development of a robust drug product.

stat.ML↗
arXiv2018

MedShare: Medical Resource Sharing among Autonomous Healthcare Providers

Legacy Electronic Health Records (EHRs) systems were not developed with the level of connectivity expected from them nowadays. Therefore, interoperability weakness inherent in the legacy systems can result in poor patient care and waste of financial resources. Large hospitals are less likely to share their data with external hospitals due to economic and political reasons. Motivated by these facts, we aim to provide a set of software implementation guidelines, i.e., MedShare to deal with interoperability issues among disconnected healthcare systems. The proposed integrated architecture includes: 1) a data extractor to fetch legacy medical data from a hemodialysis center, 2) converting it to a common data model, 3) indexing patient information using the HashMap technique, and 4) a set of services and tools that can be installed as a coherent environment on top of stand-alone EHRs systems. Our work enabled three cooperating but autonomous hospitals to mutually exchange medical data and helped them develop a common reference architecture. It lets stakeholders retain control over their patient data, winning the trust and confidence much needed towards a successful deployment of MedShare. Security concerns were effectively addressed that also included patient consent in the data exchange process. Thereby, the implemented toolset offered a collaborative environment to share EHRs by the healthcare providers.

cs.SE↗
arXiv2018

Integrating UML with Service Refinement for Requirements Modeling and Analysis

Unified Modeling Language (UML) is the de facto standard for requirements modeling and system design. UML as a visual language can tremendously help customers, project managers, and developers to specify the requirements of a target system. However, UML lacks the ability to specify the requirements precisely such as the contracts of the system operation, and verify the consistency and refinement of the requirements. These disadvantages result in that the potential faults of software are hard to be discovered in the early stage of software development process, and then requiring more efforts in software testing to find the bugs. Service refinement is a formal method, which could be a supplement to enhance the UML. In this paper, we show how to integrate UML with service refinement to specify requirements, and verify the consistency and refinements of the requirements through a case study of online shopping system. Particularly, requirements are modeled through UML diagrams, which includes a) use case diagram, b) system sequence diagrams and c) conceptual class diagram. Service refinement enhances the requirements model by introducing the contracts. Furthermore, the consistency and refinements of requirement model can be verified through service refinement. Our approach demonstrates integrating UML with service refinement can require fewer efforts to achieve the consistency requirements than only using UML for requirement modeling.

cs.SE↗
arXiv2018

Real-time System Modeling and Verification through Labeled Transition System Analyser (LTSA)

With the advancement of software engineering in recent years, the model checking techniques are widely applied in various areas to do the verification for the system model. However, it is difficult to apply the model checking to verify requirements due to lacking the details of the design. Unlike other model checking tools, LTSA provides the structure diagram, which can bridge the gap between the requirements and the design. In this paper, we demonstrate the abilities of LTSA shipped with the classic case study of the steam boiler system. The structure diagram of LTSA can specify the interactions between the controller and the steam boiler, which can be derived from UML requirements model such as system sequence diagram of the steam boiler system. The start-up design model of LTSA can be generated from the structure diagram. Furthermore, we provide a variation law of the steam rate to avoid the issue of state space explosion and show how explicitly and implicitly model the time that reflects the difference between system modeling and the physical world. Finally, the derived model is verified against the required properties. Our work demonstrates the potential power of integrating UML with model checking tools in requirement elicitation, system design, and verification.

cs.SE↗
arXiv2017

Equivariant Kodaira embedding of CR manifolds with circle action

We consider a compact CR manifold with a transversal CR locally free circle 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. As a consequence, we establish an equivariant Kodaira embedding theorem.

math.CV↗
arXiv2016

Morse inequalities for Fourier components of Kohn-Rossi cohomology of CR manifolds with $S^1$-action

Let $X$ be a compact connected CR manifold of dimension $2n-1, n\geq 2$ with a transversal CR $S^1$-action on $X$. We study the Fourier components of the Kohn-Rossi cohomology with respect to the $S^1$-action. By studying the Szegö kernel of the Fourier components we establish the Morse inequalities on $X$. Using the Morse inequalities we have established on $X$ we prove that there are abundant CR functions on $X$ when $X$ is weakly pseudoconvex and strongly pseudoconvex at a point.

math.CV↗
arXiv2014

Non-embeddability into a fixed sphere for a family of compact real algebraic hypersurfaces

We study the holomorphic embedding problem from a compact strongly pseudoconvex real algebraic hypersurface into a sphere of higher dimension. We construct a family of compact strongly pseudoconvex hypersurfaces $M_ε$ in $\mathbb{C}^2,$ and prove that for any integer $N$, there is a number $ε(N)$ with $0<ε(N)<1$ such that for any $ε$ with $0<ε<ε(N)$, $M_ε$ can not be locally holomorphically embedded into the unit sphere $\mathbb{S}^{2N-1}$ in $\mathbb{C}^N.$

math.CV↗
arXiv2013

Tucker Tensor Regression and Neuroimaging Analysis

Large-scale neuroimaging studies have been collecting brain images of study individuals, which take the form of two-dimensional, three-dimensional, or higher dimensional arrays, also known as tensors. Addressing scientific questions arising from such data demands new regression models that take multidimensional arrays as covariates. Simply turning an image array into a long vector causes extremely high dimensionality that compromises classical regression methods, and, more seriously, destroys the inherent spatial structure of array data that possesses wealth of information. In this article, we propose a family of generalized linear tensor regression models based upon the Tucker decomposition of regression coefficient arrays. Effectively exploiting the low rank structure of tensor covariates brings the ultrahigh dimensionality to a manageable level that leads to efficient estimation. We demonstrate, both numerically that the new model could provide a sound recovery of even high rank signals, and asymptotically that the model is consistently estimating the best Tucker structure approximation to the full array model in the sense of Kullback-Liebler distance. The new model is also compared to a recently proposed tensor regression model that relies upon an alternative CANDECOMP/PARAFAC (CP) decomposition.

stat.ME↗
arXiv2011

Saying HelloWorld with QVTR-XSLT - A Solution to the TTC 2011 Instructive Case

In this short paper we present our solution for the Hello World case study of the Transformation Tool Contest (TTC) 2011 using the QVTR-XSLT tool. The tool supports editing and execution of the graphical notation of QVT Relations language. The case study consists of a set of simple transformation tasks which covers the basic functions required for a transformation language, such as creating, reading/querying, updating and deleting of model elements. We design a transformation for each of the tasks.

cs.SE↗
arXiv2011

Solving the TTC 2011 Compiler Optimization Case with QVTR-XSLT

In this short paper we present our solution for the Compiler Optimization case study of the Transformation Tool Contest (TTC) 2011 using the QVTR-XSLT tool. The tool supports editing and execution of the graphical notation of QVT Relations language

cs.SE↗