The polystyrene (PS) materials tend to yellow over time. The yellowing phenomenon is an indicator of the material’s reduced performance and structural integrity. In the natural environment, sunlight is a major contri...The polystyrene (PS) materials tend to yellow over time. The yellowing phenomenon is an indicator of the material’s reduced performance and structural integrity. In the natural environment, sunlight is a major contributor to the yellowing, and elevated temperatures can accelerate the chemical reactions that lead to yellowing. The natural environmental factors are difficult to control, making it challenging to predict the yellowing process accurately. In this paper, we established a model to quantify the relationship between the yellowing index and key factors, solar radiation and temperature, from outdoor monitored climatic data. The model is trained and tested by the datasets collected from atmospheric exposure test stations located in Guangzhou and Qionghai. Same kinds of PS materials were exposed to external natural environments at the stations for one year. The parameters were estimated by least squares method. The results indicated that the model fits training and testing datasets well with R2 of 0.980 and 0.985, respectively.展开更多
In this paper, the global controllability for a class of high dimensional polynomial systems has been investigated and a constructive algebraic criterion algorithm for their global controllability has been obtained. B...In this paper, the global controllability for a class of high dimensional polynomial systems has been investigated and a constructive algebraic criterion algorithm for their global controllability has been obtained. By the criterion algorithm, the global controllability can be determined in finite steps of arithmetic operations. The algorithm is imposed on the coefficients of the polynomials only and the analysis technique is based on Sturm Theorem in real algebraic geometry and its modern progress. Finally, the authors will give some examples to show the application of our results.展开更多
Transmission disequilibrium tests (TDT) is a well-known case-parents family-based method to detect the association between genetic polymorphisms and a disease phenotype. Various extensions of the TDT have been develop...Transmission disequilibrium tests (TDT) is a well-known case-parents family-based method to detect the association between genetic polymorphisms and a disease phenotype. Various extensions of the TDT have been developed and widely applied in medical research. In this article, we introduced a simple simulation algorithm based on a transition model to generate general nuclear families rather than trios to simulate multiple tightly linked markers. The simulations show that the empirical distributions of the test statistics coincide with the expected distribution under the null hypothesis.展开更多
The aim of this paper is to investigate the numerical solution of the hypersingular integral equation reduced by the harmonic equation. First, we transform the hypersingular integral equation into 2π-periodic hypersi...The aim of this paper is to investigate the numerical solution of the hypersingular integral equation reduced by the harmonic equation. First, we transform the hypersingular integral equation into 2π-periodic hypersingular integral equation with the map x=cot（θ/2）. Second, we initiate the study of the multiscale Galerkin method for the 2π-periodic hypersingular integral equation. The trigonometric wavelets are used as trial functions. Consequently, the 2j＋1 × 2j＋1 stiffness matrix Kj can be partitioned j×j block matrices. Furthermore, these block matrices are zeros except main diagonal block matrices. These main diagonal block matrices are symmetrical and circulant matrices, and hence the solution of the associated linear algebraic system can be solved with the fast Fourier transform and the inverse fast Fourier transform instead of the inverse matrix. Finally, we provide several numerical examples to demonstrate our method has good accuracy even though the exact solutions are multi-peak and almost singular.展开更多
There are several difficulties in generalized/extended finite element methods(GFEM/XFEM)for moving interface problems.First,the GFEM/XFEM may be unstable in a sense that condition numbers of system matrices could be m...There are several difficulties in generalized/extended finite element methods(GFEM/XFEM)for moving interface problems.First,the GFEM/XFEM may be unstable in a sense that condition numbers of system matrices could be much bigger than those of standard FEM.Second,they may not be robust in that the condition numbers increase rapidly as interface curves approach edges of meshes.Furthermore,time stepping schemes need carrying out carefully since both enrichment functions and enriched nodes in the GFEM/XFEM vary in time.This paper is devoted to proposing the stable and robust GFEM/XFEM with efficient time stepping schemes for the parabolic interface problems with moving interfaces.A so-called stable GFEM(SGFEM)developed for elliptical interface problems is extended to the parabolic interface problems for spatial discretizations;while backward difference formulae(BDF)are used for the time stepping.Numerical studies demonstrate that the SGFEM with the first and second order BDF(also known as backward Euler method and BDF2)is stable,robust,and achieves optimal convergence rates.Comparisons of the proposed SGFEM with various commonly-used GFEM/XFEM are made,which show advantages of the SGFEM over the other GFEM/XFEM in aspects of stability,robustness,and convergence.展开更多
For case-parents data, the information from offspring can be used to reduce the uncertainty of parents’ haplotype. In this article we develop likelihood ratio test to compare haplotype frequencies in transmitted and ...For case-parents data, the information from offspring can be used to reduce the uncertainty of parents’ haplotype. In this article we develop likelihood ratio test to compare haplotype frequencies in transmitted and non-transmitted group. The maximum likelihood estimate of the haplotype frequencies for the family data is obtained via expectation-maximization (EM) algorithm. Our proposed method can handle the uncertainty of haplotypes and missing data. The simulations show that the method is more powerful to test association between haplotype and traits than TRANSMIT. We also demonstrated the method to detect the association between Megsin gene and immunoglobulin A nephropathy.展开更多
Transmission disequilibrium test (TDT) is a popular family based genetic association method. Under multiplicative assumption, a conditional logistic regression for matched pair, affected offspring with allele transmit...Transmission disequilibrium test (TDT) is a popular family based genetic association method. Under multiplicative assumption, a conditional logistic regression for matched pair, affected offspring with allele transmitted from parents and pseudo-offspring (control) with allele non-transmitted from parents, was built to detect the <span style="font-family:Verdana;">main </span><span style="font-family:Verdana;">effects of genes and gene-covariate interaction</span><span style="font-family:Verdana;">s</span><span style="font-family:;" "=""><span style="font-family:Verdana;">. When there exist genotype uncertainties, expectation-maximization (EM) algorithm was adopted to estimate the coefficients. The transmission model was applied to detect the association between M235T polymorphism in AGT gene and essential hypertension (ESH). Most of parents are not available in the 126 families from HongKong Chinese population. The results </span><span style="font-family:Verdana;">showed M235T is associat</span></span><span style="font-family:Verdana;">ed</span><span style="font-family:Verdana;"> with hypertension and there is interaction between M235T and the case’s sex. The allele T is higher risk for male than female</span><span style="font-family:Verdana;">.</span>展开更多
In this paper,we analyze two classes of spectral volume(SV)methods for one-dimensional hyperbolic equations with degenerate variable coefficients.Two classes of SV methods are constructed by letting a piecewise k-th o...In this paper,we analyze two classes of spectral volume(SV)methods for one-dimensional hyperbolic equations with degenerate variable coefficients.Two classes of SV methods are constructed by letting a piecewise k-th order(k≥1 is an integer)polynomial to satisfy the conservation law in each control volume,which is obtained by refining spectral volumes(SV)of the underlying mesh with k Gauss-Legendre points(LSV)or Radaus points(RSV)in each SV.The L^(2)-norm stability and optimal order convergence properties for both methods are rigorously proved for general non-uniform meshes.Surprisingly,we discover some very interesting superconvergence phenomena:At some special points,the SV flux function approximates the exact flux with(k+2)-th order and the SV solution itself approximates the exact solution with(k+3/2)-th order,some superconvergence behaviors for element averages errors have been also discovered.Moreover,these superconvergence phenomena are rigorously proved by using the so-called correction function method.Our theoretical findings are verified by several numerical experiments.展开更多
Background and aims:Hepatocellular carcinoma(HCC),which is prevalent worldwide and has a high mortality rate,needs to be effectively diagnosed.We aimed to evaluate the significance of plasma microRNA-15a/16-1(miR-15a/...Background and aims:Hepatocellular carcinoma(HCC),which is prevalent worldwide and has a high mortality rate,needs to be effectively diagnosed.We aimed to evaluate the significance of plasma microRNA-15a/16-1(miR-15a/16)as a biomarker of hepatitis B virus-related HCC(HBV-HCC)using the machine learning model.This study was the first large-scale investigation of these two miRNAs in HCC plasma samples.Methods:Using quantitative polymerase chain reaction,we measured the plasma miR-15a/16 levels in a total of 766 participants,including 74 healthy controls,335 with chronic hepatitis B(CHB),47 with compensated liver cirrhosis,and 310 with HBV-HCC.The diagnostic performance of miR-15a/16 was examined using a machine learning model and compared with that of alpha-fetoprotein(AFP).Lastly,to validate the diagnostic efficiency of miR-15a/16,we performed pseudotemporal sorting of the samples to simulate progression from CHB to HCC.Results:Plasma miR-15a/16 was significantly decreased in HCC than in all control groups(P<0.05 for all).In the training cohort,the area under the receiver operating characteristic curve(AUC),sensitivity,and average precision(AP)for the detection of HCC were higher for miR-15a(AUC=0.80,67.3%,AP=0.80)and miR-16(AUC=0.83,79.0%,AP=0.83)than for AFP(AUC=0.74,61.7%,AP=0.72).Combining miR-15a/16 with AFP increased the AUC to 0.86(sensitivity 85.9%)and the AP to 0.85 and was significantly superior to the other markers in this study(P<0.05 for all),as further demonstrated by the detection error tradeoff curves.Moreover,miR-15a/16 impressively showed potent diagnostic power in early-stage,small-tumor,and AFP-negative HCC.A validation cohort confirmed these results.Lastly,the simulated follow-up of patients further validated the diagnostic efficiency of miR-15a/16.Conclusions:We developed and validated a plasma miR-15a/16-based machine learning model,which exhibited better diagnostic performance for the early diagnosis of HCC compared to that of AFP.展开更多
The V-system is a complete orthogonal system of functions defined on the interval [0, 1], generated by finite Legendre polynomials and the dilation and translation of a function generator, which consists of a finite n...The V-system is a complete orthogonal system of functions defined on the interval [0, 1], generated by finite Legendre polynomials and the dilation and translation of a function generator, which consists of a finite number of continuous and discontinuous functions. The V-system has interesting properties, such as orthogonality, symmetry, completeness and short compact support. It is shown in this paper that the V-system is essentially a special multi-wavelet basis. As a result, some basic properties of the V-system are established through the well-developed theory of multi-wavelets. From this point of view, more other V-systems are constructed.展开更多
In this paper,we mainly study an inverse source problem of time fractional diffusion equation in a bounded domain with an over-specified terminal condition at a fixed time.A novel regularization method,which we call t...In this paper,we mainly study an inverse source problem of time fractional diffusion equation in a bounded domain with an over-specified terminal condition at a fixed time.A novel regularization method,which we call the exponential Tikhonov regularization method with a parameter γ,is proposed to solve the inverse source problem,and the corresponding convergence analysis is given under a-priori and a-posteriori regularization parameter choice rules.Whenγis less than or equal to zero,the optimal convergence rate can be achieved and it is independent of the value of γ.However,when γ is greater than zero,the optimal convergence rate depends on the value of γ which is related to the regularity of the unknown source.Finally,numerical experiments are conducted for showing the effectiveness of the proposed exponential regularization method.展开更多
Regulatory molecules present on the core promoter of a gene interact often in a dynamic,highly combinatorial and possibly energy-dependent manner, leading to complex promoter structure and even complex global dynamics...Regulatory molecules present on the core promoter of a gene interact often in a dynamic,highly combinatorial and possibly energy-dependent manner, leading to complex promoter structure and even complex global dynamics. The authors analyze dynamics of an arbitrarily complex promoter from the view of thermodynamics combined with statistic physics. First, the authors formulize transcription factors-mediated promoter kinetics in terms of energy. Then, the authors analyze energetic cost in several representative cases of promoter structure, deriving useful analytical results. Third, the authors derive analytical expressions for mean dwell times of the promoter activity states, experimentally measurable quantities related to the energy cost of promoter dynamics. The overall framework lays a theoretical foundation for analysis of complex promoter kinetics and gene expression dynamics.展开更多
The classical eigenvalue problem of the second-order elliptic operator is approxlmateo with hi-quadratic finite element in this paper. We construct a new superconvergent function recovery operator, from which the O（...The classical eigenvalue problem of the second-order elliptic operator is approxlmateo with hi-quadratic finite element in this paper. We construct a new superconvergent function recovery operator, from which the O（h^8｜ in h｜^2） ultraconvergence of eigenvalue approximation is obtained. Numerical experiments verify the theoretical results.展开更多
This paper concerns the construction and regularity of a transition （probability） function of a nonhomogeneous continuous-time Maxkov process with given transition rates and a general state space. Motivating from a ...This paper concerns the construction and regularity of a transition （probability） function of a nonhomogeneous continuous-time Maxkov process with given transition rates and a general state space. Motivating from a lot of restriction in applications of a transition function with continuous （in t ≥0） and consewative transition rates q（t, x, A）, we consider the case that q（t, x, A） axe only required to satisfy a mild measurability （in t ≥ O） condition, which is a generalization of the continuity condition. Under the measurability condition we construct a transition function with the given transition rates, provide a necessary and sufficient condition for it to be regular, and further obtain some interesting additional results.展开更多
Recently,there has been emerging interest in constructing reproducing kernel Banach spaces(RKBS)for applied and theoretical purposes such as machine learning,sampling reconstruction,sparse approximation and functional...Recently,there has been emerging interest in constructing reproducing kernel Banach spaces(RKBS)for applied and theoretical purposes such as machine learning,sampling reconstruction,sparse approximation and functional analysis.Existing constructions include the reflexive RKBS via a bilinear form,the semi-inner-product RKBS,the RKBS with?~1 norm,the p-norm RKBS via generalized Mercer kernels,etc.The definitions of RKBS and the associated reproducing kernel in those references are dependent on the construction.Moreover,relations among those constructions are unclear.We explore a generic definition of RKBS and the reproducing kernel for RKBS that is independent of construction.Furthermore,we propose a framework of constructing RKBSs that leads to new RKBSs based on Orlicz spaces and unifies existing constructions mentioned above via a continuous bilinear form and a pair of feature maps.Finally,we develop representer theorems for machine learning in RKBSs constructed in our framework,which also unifies representer theorems in existing RKBSs.展开更多
Abstract.In this paper,a novel implementation of immersed interface method combined with Stokes solver on a MAC staggered grid for solving the steady two-fluid Stokes equations with interfaces.The velocity components ...Abstract.In this paper,a novel implementation of immersed interface method combined with Stokes solver on a MAC staggered grid for solving the steady two-fluid Stokes equations with interfaces.The velocity components along the interface are introduced as two augmented variables and the resulting augmented equation is then solved by the GMRES method.The augmented variables and/or the forces are related to the jumps in pressure and the jumps in the derivatives of both pressure and velocity,and are interpolated using cubic splines and are then applied to the fluid through the jump conditions.The Stokes equations are discretized on a staggered Cartesian grid via a second order finite difference method and solved by the conjugate gradient Uzawa-typemethod.The numerical results show that the overall scheme is second order accurate.The major advantages of the present IIM-Stokes solver are the efficiency and flexibility in terms of types of fluid flow and different boundary conditions.The proposed method avoids solution of the pressure Poisson equation,and comparisons are made to show the advantages of time savings by the present method.The generalized two-phase Stokes solver with correction terms has also been applied to incompressible two-phase Navier-Stokes flow.展开更多
Proposition 5.5.6(ii)in the book Markov Chains and Stochastic Stability(2nd ed,Cambridge Univ.Press,2009)has been used in the proof of a theorem about ergodicity of Markov chains.Unfortunately,an example in this paper...Proposition 5.5.6(ii)in the book Markov Chains and Stochastic Stability(2nd ed,Cambridge Univ.Press,2009)has been used in the proof of a theorem about ergodicity of Markov chains.Unfortunately,an example in this paper shows that this proposition is not always true.Thus,a correction of this proposition is provided.展开更多
In this paper, a necessary and sufficient condition of the global controllability for a class of low dimensional polynomial affine nonlinear systems with special structure is obtained. The condition is imposed on the ...In this paper, a necessary and sufficient condition of the global controllability for a class of low dimensional polynomial affine nonlinear systems with special structure is obtained. The condition is imposed on the coefficients of the system only and the methods are based on Green＇s formula and the trajectory analysis of planar linear system. Furthermore, I point out that the global controllability does not hold for the corresponding high dimensional polynomial system.展开更多
Background:Oral cavity(OC),oropharyngeal(OP),hypopharyngeal(HP),and laryngeal(LA)squamous cell carcinoma(SCC)have a high incidence of regional lymph node metastasis(LNM).Elective irradiation for clinically node-negati...Background:Oral cavity(OC),oropharyngeal(OP),hypopharyngeal(HP),and laryngeal(LA)squamous cell carcinoma(SCC)have a high incidence of regional lymph node metastasis(LNM).Elective irradiation for clinically node-negative neck is routinely administered to treat lymph nodes harboring occult metastasis.However,the optimal elective irradiation schemes are still inconclusive.In this study,we aimed to establish individualized elective irradiation schemes for the ipsilateral and contralateral node-negative neck of these four types of cancer.Methods:From July 2005 to December 2018,793 patients with OC-SCC,464 with OP-SCC,413 with HP-SCC,and 645 with LA-SCC were recruited retrospectively.Based on the actual incidence of LNM and the tumor characteristics,risk factors for contralateral LNM,as well as node level coverage schemes for elective irradiation,were determined using logistic regression analysis.Additionally,we developed a publicly available online tool to facilitate the widespread clinical use of these schemes.Results:For the ipsilateral node-negative neck,elective irradiation at levels Ⅰ-Ⅲ for OC-SCC and levels Ⅱ-Ⅳa for OP-,HP-and LA-SCC are generally recommended.In addition,level Ⅶa should be included in patients with OPSCC.Multivariate analyses revealed that posterior hypopharyngeal wall and post-cricoid region involvement were independently associated with level Ⅶa metastasis in HP-SCC(all P<0.05).For the contralateral node-negative neck,multivariate analyses revealed that ipsilateral N2b2-N3,tumors with body midline involvement,and degree of tumor invasion were the independent factors for contralateral LNM(all P<0.05).In patients who require contralateral neck irradiation,levels Ⅰ-Ⅱ are recommended for OC-SCC,and additional level Ⅲ is recommended for patients with ipsilateral N3 disease.Levels Ⅱ-Ⅲ are recommended for OP-,HP-,and LA-SCC,and additional level Ⅳa is recommended for patients with advanced T or ipsilateralNclassifications.Furthermore,additional level Ⅶa is recommended only for OP-SCC with T4 and ipsilateral N3 disease.Conclusion:Based on our findings,we suggest that individualized and computer-aided elective irradiation schemes could reduce irradiation volumes in OC-,OP-and HP-SCC patients,as compared to current guidelines,and could thus positively impact the patients’quality of life after radiotherapy.展开更多
In this paper,we present a Hessian recovery based linear finite element method to simulate the molecular beam epitaxy growth model with slope selection.For the time discretization,we apply a first-order convex splitti...In this paper,we present a Hessian recovery based linear finite element method to simulate the molecular beam epitaxy growth model with slope selection.For the time discretization,we apply a first-order convex splitting method and secondorder Crank-Nicolson scheme.For the space discretization,we utilize the Hessian recovery operator to approximate second-order derivatives of a C^(0)linear finite element function and hence the weak formulation of the fourth-order differential operator can be discretized in the linear finite element space.The energy-decay property of our proposed fully discrete schemes is rigorously proved.The robustness and the optimal-order convergence of the proposed algorithm are numerically verified.In a large spatial domain for a long period,we simulate coarsening dynamics,where 1/3-power-law is observed.展开更多
文摘The polystyrene (PS) materials tend to yellow over time. The yellowing phenomenon is an indicator of the material’s reduced performance and structural integrity. In the natural environment, sunlight is a major contributor to the yellowing, and elevated temperatures can accelerate the chemical reactions that lead to yellowing. The natural environmental factors are difficult to control, making it challenging to predict the yellowing process accurately. In this paper, we established a model to quantify the relationship between the yellowing index and key factors, solar radiation and temperature, from outdoor monitored climatic data. The model is trained and tested by the datasets collected from atmospheric exposure test stations located in Guangzhou and Qionghai. Same kinds of PS materials were exposed to external natural environments at the stations for one year. The parameters were estimated by least squares method. The results indicated that the model fits training and testing datasets well with R2 of 0.980 and 0.985, respectively.
基金supported by the Natural Science Foundation of China under Grant Nos.60804008,61174048and 11071263the Fundamental Research Funds for the Central Universities and Guangdong Province Key Laboratory of Computational Science at Sun Yat-Sen University
文摘In this paper, the global controllability for a class of high dimensional polynomial systems has been investigated and a constructive algebraic criterion algorithm for their global controllability has been obtained. By the criterion algorithm, the global controllability can be determined in finite steps of arithmetic operations. The algorithm is imposed on the coefficients of the polynomials only and the analysis technique is based on Sturm Theorem in real algebraic geometry and its modern progress. Finally, the authors will give some examples to show the application of our results.
文摘Transmission disequilibrium tests (TDT) is a well-known case-parents family-based method to detect the association between genetic polymorphisms and a disease phenotype. Various extensions of the TDT have been developed and widely applied in medical research. In this article, we introduced a simple simulation algorithm based on a transition model to generate general nuclear families rather than trios to simulate multiple tightly linked markers. The simulations show that the empirical distributions of the test statistics coincide with the expected distribution under the null hypothesis.
文摘The aim of this paper is to investigate the numerical solution of the hypersingular integral equation reduced by the harmonic equation. First, we transform the hypersingular integral equation into 2π-periodic hypersingular integral equation with the map x=cot（θ/2）. Second, we initiate the study of the multiscale Galerkin method for the 2π-periodic hypersingular integral equation. The trigonometric wavelets are used as trial functions. Consequently, the 2j＋1 × 2j＋1 stiffness matrix Kj can be partitioned j×j block matrices. Furthermore, these block matrices are zeros except main diagonal block matrices. These main diagonal block matrices are symmetrical and circulant matrices, and hence the solution of the associated linear algebraic system can be solved with the fast Fourier transform and the inverse fast Fourier transform instead of the inverse matrix. Finally, we provide several numerical examples to demonstrate our method has good accuracy even though the exact solutions are multi-peak and almost singular.
基金supported by the Natural Science Foundation of China under grants 11471343,11628104,and Guangdong Provincial Natural Science Foundation of China under grant 2015A030306016.
文摘There are several difficulties in generalized/extended finite element methods(GFEM/XFEM)for moving interface problems.First,the GFEM/XFEM may be unstable in a sense that condition numbers of system matrices could be much bigger than those of standard FEM.Second,they may not be robust in that the condition numbers increase rapidly as interface curves approach edges of meshes.Furthermore,time stepping schemes need carrying out carefully since both enrichment functions and enriched nodes in the GFEM/XFEM vary in time.This paper is devoted to proposing the stable and robust GFEM/XFEM with efficient time stepping schemes for the parabolic interface problems with moving interfaces.A so-called stable GFEM(SGFEM)developed for elliptical interface problems is extended to the parabolic interface problems for spatial discretizations;while backward difference formulae(BDF)are used for the time stepping.Numerical studies demonstrate that the SGFEM with the first and second order BDF(also known as backward Euler method and BDF2)is stable,robust,and achieves optimal convergence rates.Comparisons of the proposed SGFEM with various commonly-used GFEM/XFEM are made,which show advantages of the SGFEM over the other GFEM/XFEM in aspects of stability,robustness,and convergence.
文摘For case-parents data, the information from offspring can be used to reduce the uncertainty of parents’ haplotype. In this article we develop likelihood ratio test to compare haplotype frequencies in transmitted and non-transmitted group. The maximum likelihood estimate of the haplotype frequencies for the family data is obtained via expectation-maximization (EM) algorithm. Our proposed method can handle the uncertainty of haplotypes and missing data. The simulations show that the method is more powerful to test association between haplotype and traits than TRANSMIT. We also demonstrated the method to detect the association between Megsin gene and immunoglobulin A nephropathy.
文摘Transmission disequilibrium test (TDT) is a popular family based genetic association method. Under multiplicative assumption, a conditional logistic regression for matched pair, affected offspring with allele transmitted from parents and pseudo-offspring (control) with allele non-transmitted from parents, was built to detect the <span style="font-family:Verdana;">main </span><span style="font-family:Verdana;">effects of genes and gene-covariate interaction</span><span style="font-family:Verdana;">s</span><span style="font-family:;" "=""><span style="font-family:Verdana;">. When there exist genotype uncertainties, expectation-maximization (EM) algorithm was adopted to estimate the coefficients. The transmission model was applied to detect the association between M235T polymorphism in AGT gene and essential hypertension (ESH). Most of parents are not available in the 126 families from HongKong Chinese population. The results </span><span style="font-family:Verdana;">showed M235T is associat</span></span><span style="font-family:Verdana;">ed</span><span style="font-family:Verdana;"> with hypertension and there is interaction between M235T and the case’s sex. The allele T is higher risk for male than female</span><span style="font-family:Verdana;">.</span>
基金supported by the NSFC(Grants 92370113,12071496,12271482)Moreover,the first author was also supported by the Zhejiang Provincial NSF(Grant LZ23A010006)+1 种基金by the Key Research Project of Zhejiang Lab(Grant 2022PE0AC01)the fourth author was also supported by the Guangdong Provincial NSF(Grant 2023A1515012097).
文摘In this paper,we analyze two classes of spectral volume(SV)methods for one-dimensional hyperbolic equations with degenerate variable coefficients.Two classes of SV methods are constructed by letting a piecewise k-th order(k≥1 is an integer)polynomial to satisfy the conservation law in each control volume,which is obtained by refining spectral volumes(SV)of the underlying mesh with k Gauss-Legendre points(LSV)or Radaus points(RSV)in each SV.The L^(2)-norm stability and optimal order convergence properties for both methods are rigorously proved for general non-uniform meshes.Surprisingly,we discover some very interesting superconvergence phenomena:At some special points,the SV flux function approximates the exact flux with(k+2)-th order and the SV solution itself approximates the exact solution with(k+3/2)-th order,some superconvergence behaviors for element averages errors have been also discovered.Moreover,these superconvergence phenomena are rigorously proved by using the so-called correction function method.Our theoretical findings are verified by several numerical experiments.
基金supported by Research and Development Planned Project in Key Areas of Guangdong Province(No.2019B110233002)National Natural Science Foundation of China(No.12171494 and 11931019)+3 种基金Natural Science Foundation of Guangdong Province,China(No.2022A1515011540)Guangdong Province Key Laboratory of Computational Science at the Sun Yat-sen University(No.2020B1212060032)Joint Key Projects of City and Hospital of Guangzhou Science and Technology(No.202201020422)General Planned Project of Guangzhou Science and Technology(No.202201010950).
文摘Background and aims:Hepatocellular carcinoma(HCC),which is prevalent worldwide and has a high mortality rate,needs to be effectively diagnosed.We aimed to evaluate the significance of plasma microRNA-15a/16-1(miR-15a/16)as a biomarker of hepatitis B virus-related HCC(HBV-HCC)using the machine learning model.This study was the first large-scale investigation of these two miRNAs in HCC plasma samples.Methods:Using quantitative polymerase chain reaction,we measured the plasma miR-15a/16 levels in a total of 766 participants,including 74 healthy controls,335 with chronic hepatitis B(CHB),47 with compensated liver cirrhosis,and 310 with HBV-HCC.The diagnostic performance of miR-15a/16 was examined using a machine learning model and compared with that of alpha-fetoprotein(AFP).Lastly,to validate the diagnostic efficiency of miR-15a/16,we performed pseudotemporal sorting of the samples to simulate progression from CHB to HCC.Results:Plasma miR-15a/16 was significantly decreased in HCC than in all control groups(P<0.05 for all).In the training cohort,the area under the receiver operating characteristic curve(AUC),sensitivity,and average precision(AP)for the detection of HCC were higher for miR-15a(AUC=0.80,67.3%,AP=0.80)and miR-16(AUC=0.83,79.0%,AP=0.83)than for AFP(AUC=0.74,61.7%,AP=0.72).Combining miR-15a/16 with AFP increased the AUC to 0.86(sensitivity 85.9%)and the AP to 0.85 and was significantly superior to the other markers in this study(P<0.05 for all),as further demonstrated by the detection error tradeoff curves.Moreover,miR-15a/16 impressively showed potent diagnostic power in early-stage,small-tumor,and AFP-negative HCC.A validation cohort confirmed these results.Lastly,the simulated follow-up of patients further validated the diagnostic efficiency of miR-15a/16.Conclusions:We developed and validated a plasma miR-15a/16-based machine learning model,which exhibited better diagnostic performance for the early diagnosis of HCC compared to that of AFP.
基金Supported by National Natural Science Foundation of China (Grant Nos.11071261,60873088 and 10911120394)
文摘The V-system is a complete orthogonal system of functions defined on the interval [0, 1], generated by finite Legendre polynomials and the dilation and translation of a function generator, which consists of a finite number of continuous and discontinuous functions. The V-system has interesting properties, such as orthogonality, symmetry, completeness and short compact support. It is shown in this paper that the V-system is essentially a special multi-wavelet basis. As a result, some basic properties of the V-system are established through the well-developed theory of multi-wavelets. From this point of view, more other V-systems are constructed.
基金supported by National Natural Science Foundation of China(11961002,11761007,11861007)Key Project of the Natural Science Foundation of Jiangxi Province(20212ACB201001).
文摘In this paper,we mainly study an inverse source problem of time fractional diffusion equation in a bounded domain with an over-specified terminal condition at a fixed time.A novel regularization method,which we call the exponential Tikhonov regularization method with a parameter γ,is proposed to solve the inverse source problem,and the corresponding convergence analysis is given under a-priori and a-posteriori regularization parameter choice rules.Whenγis less than or equal to zero,the optimal convergence rate can be achieved and it is independent of the value of γ.However,when γ is greater than zero,the optimal convergence rate depends on the value of γ which is related to the regularity of the unknown source.Finally,numerical experiments are conducted for showing the effectiveness of the proposed exponential regularization method.
基金supported by Science and Technology Department under Grant No.2014CB964703the Natural Science Foundation under Grant Nos.91530320 and 11761025
文摘Regulatory molecules present on the core promoter of a gene interact often in a dynamic,highly combinatorial and possibly energy-dependent manner, leading to complex promoter structure and even complex global dynamics. The authors analyze dynamics of an arbitrarily complex promoter from the view of thermodynamics combined with statistic physics. First, the authors formulize transcription factors-mediated promoter kinetics in terms of energy. Then, the authors analyze energetic cost in several representative cases of promoter structure, deriving useful analytical results. Third, the authors derive analytical expressions for mean dwell times of the promoter activity states, experimentally measurable quantities related to the energy cost of promoter dynamics. The overall framework lays a theoretical foundation for analysis of complex promoter kinetics and gene expression dynamics.
文摘The classical eigenvalue problem of the second-order elliptic operator is approxlmateo with hi-quadratic finite element in this paper. We construct a new superconvergent function recovery operator, from which the O（h^8｜ in h｜^2） ultraconvergence of eigenvalue approximation is obtained. Numerical experiments verify the theoretical results.
基金Supported by the National Natural Science Foundation of China (No.10925107)Guangdong Province Universities and Colleges Pearl River Scholar Funded Schemethe Fundamental Research Funds for the Central Universities (No.11612314)
文摘This paper concerns the construction and regularity of a transition （probability） function of a nonhomogeneous continuous-time Maxkov process with given transition rates and a general state space. Motivating from a lot of restriction in applications of a transition function with continuous （in t ≥0） and consewative transition rates q（t, x, A）, we consider the case that q（t, x, A） axe only required to satisfy a mild measurability （in t ≥ O） condition, which is a generalization of the continuity condition. Under the measurability condition we construct a transition function with the given transition rates, provide a necessary and sufficient condition for it to be regular, and further obtain some interesting additional results.
基金Supported by Natural Science Foundation of China(Grant Nos.11971490,11901595)Natural Science Foundation of Guangdong Province(Grant No.2018A030313841)+1 种基金Guangdong Province Key Laboratory of Computational Science at the Sun Yat-sen University(Grant No.2020B1212060032)AFOSR(Grant No.FA9550-19-1-0213)through a subcontract from University of California,Los Angeles。
文摘Recently,there has been emerging interest in constructing reproducing kernel Banach spaces(RKBS)for applied and theoretical purposes such as machine learning,sampling reconstruction,sparse approximation and functional analysis.Existing constructions include the reflexive RKBS via a bilinear form,the semi-inner-product RKBS,the RKBS with?~1 norm,the p-norm RKBS via generalized Mercer kernels,etc.The definitions of RKBS and the associated reproducing kernel in those references are dependent on the construction.Moreover,relations among those constructions are unclear.We explore a generic definition of RKBS and the reproducing kernel for RKBS that is independent of construction.Furthermore,we propose a framework of constructing RKBSs that leads to new RKBSs based on Orlicz spaces and unifies existing constructions mentioned above via a continuous bilinear form and a pair of feature maps.Finally,we develop representer theorems for machine learning in RKBSs constructed in our framework,which also unifies representer theorems in existing RKBSs.
基金supported by Guangdong Provincial Government of China through the“Computational Science Innovative Research Team”program and the Sun Yat-sen University“Hundred Talents Program”(34000-3181201)and the National Natural Science Foundation of China(No.11101446).
文摘Abstract.In this paper,a novel implementation of immersed interface method combined with Stokes solver on a MAC staggered grid for solving the steady two-fluid Stokes equations with interfaces.The velocity components along the interface are introduced as two augmented variables and the resulting augmented equation is then solved by the GMRES method.The augmented variables and/or the forces are related to the jumps in pressure and the jumps in the derivatives of both pressure and velocity,and are interpolated using cubic splines and are then applied to the fluid through the jump conditions.The Stokes equations are discretized on a staggered Cartesian grid via a second order finite difference method and solved by the conjugate gradient Uzawa-typemethod.The numerical results show that the overall scheme is second order accurate.The major advantages of the present IIM-Stokes solver are the efficiency and flexibility in terms of types of fluid flow and different boundary conditions.The proposed method avoids solution of the pressure Poisson equation,and comparisons are made to show the advantages of time savings by the present method.The generalized two-phase Stokes solver with correction terms has also been applied to incompressible two-phase Navier-Stokes flow.
基金This work was supported in part by the National Natural Science Foundation of China(Grant Nos.11931018,61773411)the National Natural Science Foundation of Guangdong Province,China(Grant No.2021A1515010057)and Guangdong Province Key Laboratory of Computational Science at the Sun Yat-sen University,China(2020B1212060032).
文摘Proposition 5.5.6(ii)in the book Markov Chains and Stochastic Stability(2nd ed,Cambridge Univ.Press,2009)has been used in the proof of a theorem about ergodicity of Markov chains.Unfortunately,an example in this paper shows that this proposition is not always true.Thus,a correction of this proposition is provided.
基金supported by the Natural Science Foundation of China(No.60804008)the Ph.D.Programs Foundation of Ministry of Education of Chinathe Fundamental Research Funds for the Central Universities
文摘In this paper, a necessary and sufficient condition of the global controllability for a class of low dimensional polynomial affine nonlinear systems with special structure is obtained. The condition is imposed on the coefficients of the system only and the methods are based on Green＇s formula and the trajectory analysis of planar linear system. Furthermore, I point out that the global controllability does not hold for the corresponding high dimensional polynomial system.
基金supported by the National Natural Science Foundation of China[grant number 81872463 and 81930072]Special Support Program of Sun Yat-sen University Cancer Center[grant number 16zxtzlc06]+5 种基金Key-Area Research and Development Program of Guangdong Province[grant number 2019A1515012045 and 2019B020230002]Health&Medical Collaborative Innovation Project of Guangzhou City,China[grant number 201803040003]Science and Technology Program of Guangzhou,China,[grant number 201607010199]Innovation Team Development Plan of the Ministry of Education(No.IRT_17R110)Overseas Expertise Introduction Project for Discipline Innovation(111 Project,B14035)Natural Science Foundation of Guang Dong Province(No.2017A030312003).
文摘Background:Oral cavity(OC),oropharyngeal(OP),hypopharyngeal(HP),and laryngeal(LA)squamous cell carcinoma(SCC)have a high incidence of regional lymph node metastasis(LNM).Elective irradiation for clinically node-negative neck is routinely administered to treat lymph nodes harboring occult metastasis.However,the optimal elective irradiation schemes are still inconclusive.In this study,we aimed to establish individualized elective irradiation schemes for the ipsilateral and contralateral node-negative neck of these four types of cancer.Methods:From July 2005 to December 2018,793 patients with OC-SCC,464 with OP-SCC,413 with HP-SCC,and 645 with LA-SCC were recruited retrospectively.Based on the actual incidence of LNM and the tumor characteristics,risk factors for contralateral LNM,as well as node level coverage schemes for elective irradiation,were determined using logistic regression analysis.Additionally,we developed a publicly available online tool to facilitate the widespread clinical use of these schemes.Results:For the ipsilateral node-negative neck,elective irradiation at levels Ⅰ-Ⅲ for OC-SCC and levels Ⅱ-Ⅳa for OP-,HP-and LA-SCC are generally recommended.In addition,level Ⅶa should be included in patients with OPSCC.Multivariate analyses revealed that posterior hypopharyngeal wall and post-cricoid region involvement were independently associated with level Ⅶa metastasis in HP-SCC(all P<0.05).For the contralateral node-negative neck,multivariate analyses revealed that ipsilateral N2b2-N3,tumors with body midline involvement,and degree of tumor invasion were the independent factors for contralateral LNM(all P<0.05).In patients who require contralateral neck irradiation,levels Ⅰ-Ⅱ are recommended for OC-SCC,and additional level Ⅲ is recommended for patients with ipsilateral N3 disease.Levels Ⅱ-Ⅲ are recommended for OP-,HP-,and LA-SCC,and additional level Ⅳa is recommended for patients with advanced T or ipsilateralNclassifications.Furthermore,additional level Ⅶa is recommended only for OP-SCC with T4 and ipsilateral N3 disease.Conclusion:Based on our findings,we suggest that individualized and computer-aided elective irradiation schemes could reduce irradiation volumes in OC-,OP-and HP-SCC patients,as compared to current guidelines,and could thus positively impact the patients’quality of life after radiotherapy.
基金supported by General Scientific Research Projects of Zhejiang Education Department(No.Y202147013)the Opening Project of Guangdong Province Key Laboratory of Computational Science at the Sun Yat-Sen University(No.2021008)+1 种基金supported in part by NSFC Grant(No.12071496)Guangdong Province Key Laboratory of Computational Science at the Sun Yat-sen University(No.2020B1212060032)。
文摘In this paper,we present a Hessian recovery based linear finite element method to simulate the molecular beam epitaxy growth model with slope selection.For the time discretization,we apply a first-order convex splitting method and secondorder Crank-Nicolson scheme.For the space discretization,we utilize the Hessian recovery operator to approximate second-order derivatives of a C^(0)linear finite element function and hence the weak formulation of the fourth-order differential operator can be discretized in the linear finite element space.The energy-decay property of our proposed fully discrete schemes is rigorously proved.The robustness and the optimal-order convergence of the proposed algorithm are numerically verified.In a large spatial domain for a long period,we simulate coarsening dynamics,where 1/3-power-law is observed.
