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Background: To investigate the application effect of artificial intelligence (AI)-based fundus screening system in real-world clinical environment. Methods: A total of 637 color fundus images were included in the analysis of the application of the AI-based fundus screening system in the clinical environment and 20,355 images were analyzed in the population screening. Results: The AI-based fundus screening system demonstrated superior diagnostic effectiveness for diabetic retinopathy (DR), retinal vein occlusion (RVO) and pathological myopia (PM) according to gold standard referral. The sensitivity, specificity, accuracy, positive predictive value (PPV) and negative predictive value (NPV) of three fundus abnormalities were greater (all > 80%) than those for age-related macular degeneration (ARMD), referable glaucoma and other abnormalities. The percentages of different diagnostic conditions were similar in both the clinical environment and the population screening. Conclusions: In a real-world setting, our AI-based fundus screening system could detect 7 conditions, with better performance for DR, RVO and PM. Testing in the clinical environment and through population screening demonstrated the clinical utility of our AI-based fundus screening system in the early detection of ocular fundus abnormalities and the prevention of blindness. [ABSTRACT FROM AUTHOR]

In this paper we propose a stable finite difference method to solve the fractional reaction–diffusion systems in a two-dimensional domain. The space discretization is implemented by the weighted shifted Grünwald difference (WSGD) which results in a stiff system of nonlinear ordinary differential equations (ODEs). This system of ordinary differential equations is solved by an efficient compact implicit integration factor (cIIF) method. The stability of the second order cIIF scheme is proved in the discrete L 2 -norm. We also prove the second-order convergence of the proposed scheme. Numerical examples are given to demonstrate the accuracy, efficiency, and robustness of the method. [ABSTRACT FROM AUTHOR]

In this paper, we study the ground and first excited states of the fractional Bose–Einstein condensates (BEC) which is modeled by fractional Gross–Pitaevskii (GP) equation. We first introduce the normalized gradient flow method and prove its energy diminishing property. Then the weighted shifted Grünwald–Letnikov difference (WSGD) method is used to discretize the Gross–Pitaevskii equation. The corresponding normalization and energy diminishing property for the semi-discrete scheme are proved. For the time discretization, we use the implicit integration factor (IIF) method which decouples the diffusion and nonlinear terms separately. Finally the numerical methods are applied to compute the ground and first excited states of fractional BEC with harmonic oscillator, harmonic-plus-optical lattice and box potential. Our numerical results show that the ground and excited states in fractional GP equation differ from those of the standard (non-fractional) GP equation. [ABSTRACT FROM AUTHOR]

Selective catalytic reduction (SCR) systems for marine low-speed diesel engine can be categorized into two types—the after-turbine low-pressure SCR (LP-SCR) system and the pre-turbine high-pressure SCR (HP-SCR) system. The exhaust pressure in the HP-SCR system is higher, which requires a more compact structural arrangement. According to the exhaust conditions of marine low-speed diesel engine, the vaporizer/mixer, the bend pipe, and the sudden-changed pipe of HP-SCR system were optimized in this paper. Based on a 3D-CFD model coupled with reaction kinetics, the flow fields of a HP-SCR system with various flow-guiding devices were calculated, as well as the impact of the structural shapes and sizes of the flow-guiding devices on the exhaust flow being comprehensively analyzed. From the perspectives of the flow field, the concentration field, and the pressure loss, both the disturbance and mixing effects on the two kinds of the structural flow-guiding devices with vaporizer/mixer were evaluated. Likewise, the axial pressure distribution along the exhaust flow direction in the vaporizer/mixer was also obtained. Moreover, from the perspectives of velocity uniformity and pressure loss, diversion effects on 10 kinds of flow-guiding devices with a bent pipe and a sudden-changed pipe were evaluated—thereby even obtaining the optimization design of the HP-SCR system. By installing the flow-guiding devices in the vaporizer/mixer, the bend pipe, and the sudden-changed pipe of the HP-SCR system, the upwind velocity uniformity in front of the SCR catalyst was enhanced. In the optimization design for the HP-SCR system, the total pressure loss was 4491.3 Pa, and the standard deviation of the upwind velocity in front of the SCR catalyst was 10.17%, which can meet with the design requirement of the velocity uniformity for the marine diesel engine HP-SCR system. [ABSTRACT FROM AUTHOR]

The working process of high-pressure SCR (HP-SCR) system is a kind of catalytic reaction process in the high-pressure exhaust flow, which involves urea decomposition reaction, catalytic reduction reaction of NOx and oxidizing reaction of NH3. Based on existing exhaust conditions of marine low-speed diesel engines, computational fluid dynamics (CFD) coupled with the chemical reaction kinetics, the catalytic process, and the working performance of the HP-SCR system were correspondingly studied in this paper. With the optimized scheme of the HP-SCR system, concentration uniformity, linear velocity, and total pressure loss were determined. Likewise, the concentration distribution of NH3, NO, and NO2 were obtained, and the catalytic kinetics of the NOx reduction reaction was analyzed. For the optimized scheme, the concentration of NH3 and the flow uniformity of the catalyst upwind section was met with the design requirements of the HP-SCR system, and the pressure loss of the SCR catalyst layer occupied about 40% of the total pressure loss. With NO, NO2, and NH3 existing together in the exhaust, both the standard SCR reaction and fast SCR reaction are competitive, and they mostly react along the first layer of catalyst. Finally, the weighted average value of the NOx emission behind the HP-SCR system was determined using the ISO8717 test cycle E3, and the value was 2.67 g/kWh, which met with the NOx limited requirement of the IMO Tier III. [ABSTRACT FROM AUTHOR]

In this study, we present a conservative Fourier spectral collocation (FSC) method to solve the two-dimensional nonlinear Schrödinger (NLS) equation. We prove that the proposed method preserves the mass and energy conservation laws in semi-discrete formulations. Using the spectral differentiation matrices, the NLS equation is reduced to a system of nonlinear ordinary differential equations (ODEs). The compact implicit integration factor (cIIF) method is later developed for the nonlinear ODEs. In this approach, the storage and CPU cost are significantly reduced such that the use of cIIF method becomes attractive for two-dimensional NLS equation. Numerical results are presented to demonstrate the conservation, accuracy, and efficiency of the method. [ABSTRACT FROM AUTHOR]

The advection–diffusion–reaction (ADR) systems are often used to describe the chemotaxis models arising in biology. In general, the stiffness from the reaction and diffusion terms often requires very restricted time step size, and the advection term depending on the concentration gradients of another component (the chemoattractant) may lead to sharp peaks in localized spatial regions. It is challenging to design numerical methods that can efficiently handle both difficulties. In this paper, we apply the operator splitting approach to solve the advection–diffusion–reaction systems. In particular, for advection term, we use the positivity-preserving DG method with strong stability preserving (SSP) high order time discretizations. For reaction–diffusion term, direct discontinuous Galerkin (DDG) method is used in spatial discretization and Krylov IIF method is applied in time discretization. Numerical examples are shown to demonstrate the accuracy, efficiency and robustness of the method. [ABSTRACT FROM AUTHOR]

Numerical computations of ground and excited states of Bose–Einstein condensates (BECs) require high spatial resolution due to the presence of the multiscale structures and boundary layers and interior layers in the solution. In this paper, a new discontinuous Galerkin (DG) method is presented for the computation of ground and excited states of BECs. For the spatial discretization, the direct discontinuous Galerkin (DDG) method is applied by using the normalized gradient flow. For the time discretization, we integrate the ordinary differential equations (ODEs) which is obtained by linearizing the interaction term. To evaluate the matrix exponential operator efficiently, we apply the Krylov subspace approximations to the matrix exponential operator. Numerical examples with different potentials are reported to demonstrate the validity and effectiveness of the semi-implicit DG method. [ABSTRACT FROM AUTHOR]

To get the stationary patterns in the approximation of reaction diffusion systems, the computation of evolution equations on large intervals of time is required. In this paper, a new nonlinear Galerkin method based on finite element discretization is presented for the approximation of reaction diffusion equations on large intervals. The new scheme is based on two different finite element spaces defined respectively on one subspace of lower-degree shape function and one of higher-degree shape function. Nonlinearity and time dependence are both treated on the lower-degree space and only a fixed stationary equation needs to be solved on the higher-degree space at each time level. The proof of the stability and convergence of the method is presented in one dimension. Numerical solutions of some well-studied reaction–diffusion systems are presented to demonstrate the effectiveness of the nonlinear Galerkin method. [ABSTRACT FROM AUTHOR]

Abstract: Nonlinear reaction–diffusion systems are often employed in mathematical modeling for pattern formation. Most of the work to date has been concerned within one-dimensional or rectangular domains. However, it is recognised that in most applications multidimensional complex geometrical domains are typically more important. In this paper we solve reaction–diffusion systems by combining direct discontinuous Galerkin (DDG) finite element methods with implicit integration factor (IIF) time integration method, on triangular meshes. This allows us solve the nonlinear algebraic systems on an element-by-element bases with significant gains in computational time. Numerical solutions of two reaction–diffusion systems, the well-studied Schnakenberg model and chloride–iodide–malonic acid (CIMA) reactive model, are presented to demonstrate effects of various domain geometries on the resulting biological patterns. Our numerical results are in good agreement with other numerical and analytical results, and with experimental results. [Copyright &y& Elsevier]

In this article, we present local discontinuous Galerkin (LDG) method for solving a model of energy exchanges in an N -carrier system with Neumann boundary conditions. This model extends the concept of the well-known parabolic two-step model for microheat transfer to the energy exchanges in a generalized N -carrier system with heat sources. The energy norm stability and error estimate of the LDG method is proved for solving N -carrier system. Some numerical examples are given. The numerical results when compared with the exact solution and other numerical results indicate that the present method is seen to be a very good alternative to some existing techniques for realistic problems. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2011 [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a numerical solution for the generalized Burger’s–Huxley equation and the generalized Burger’s–Fisher equation are presented by using the local discontinuous Galerkin method. Firstly we rewrite the two kinds of equations into first order systems, then apply the discontinuous Galerkin method to the systems. Secondly, the systems for ordinary differential equations yielded are solved by the third-order Runge–Kutta time integration method. The numerical results obtained by this way are compared with exact solution to demonstrate accuracy and capability of the method. [Copyright &y& Elsevier]

This paper introduces a novel approach employing the fast cosine transform to tackle the 2-D and 3-D fractional nonlinear Schrödinger equation (fNLSE). The fractional Laplace operator under homogeneous Neumann boundary conditions is first defined through spectral decomposition. The difference matrix Laplace operator is developed by the second-order central finite difference method. Then, we diagonalize the difference matrix based on the properties of Kronecker products. The time discretization employs the Crank–Nicolson method. The conservation of mass and energy is proved for the fully discrete scheme. The advantage of this method is the implementation of the Fast Discrete Cosine Transform (FDCT), which significantly improves computational efficiency. Finally, the accuracy and effectiveness of the method are verified through two-dimensional and three-dimensional numerical experiments, solitons in different dimensions are simulated, and the influence of fractional order on soliton evolution is obtained; that is, the smaller the alpha, the lower the soliton evolution. [ABSTRACT FROM AUTHOR]

In the publication of this article [1], there is an error in one of the authors’ name. This has now been included in this correction. [ABSTRACT FROM AUTHOR]

This paper proposes and analyzes an efficient compact finite difference scheme for reaction-diffusion equation in high spatial dimensions. The scheme is based on a compact finite difference method (cFDM) for the spatial discretization. We prove that the proposed method is asymptotically stable for the linear case. By introducing the differentiation matrices, the semi-discrete reaction-diffusion equation can be rewritten as a system of nonlinear ordinary differential equations (ODEs) in matrices formulations. For the time discretization, we apply the compact implicit integration factor (cIIF) method which demands much less computational effort. This method combines the advantages of cFDM and cIIF methods to improve the accuracy without increasing the computational cost and reducing the stability range. Numerical examples are shown to demonstrate the accuracy, efficiency, and robustness of the method. [ABSTRACT FROM AUTHOR]

A new combined method is constructed for solving incompressible miscible displacement in porous media. In this procedure, a hybrid mixed element method is constructed for the pressure and velocity equation, while a symmetric discontinuous Galerkin finite element method is proposed for the concentration equation. The introduction of these two numerical methods not only makes the coefficient matrixes symmetric positive definite, but also conserves the local mass balance. The stability and consistency of the method are analyzed and the optimal error estimate in L ∞ ( L 2 ) for velocity and concentration and the super convergence in L ∞ ( H 1 ) for pressure are derived. Finally, some numerical results are presented. [ABSTRACT FROM AUTHOR]

Chemotaxis models are described by a system of coupled nonlinear partial differential equations: a convection–diffusion type cell density equation and a parabolic or reaction–diffusion type chemical concentration equation. This paper is focused on development of a new numerical method for these models. In this method, a splitting mixed element technique is used to solve the chemical concentration equation, where the LBB condition is not necessary and the flux equation is separated from the chemical concentration equation. Moreover a mass-conservative characteristic finite element method is used to solve the cell density equation, avoiding nonphysically oscillations and keeping mass balance globally. The coefficient matrices of the discrete system are symmetric and positive definite. The convergence of this method is analyzed and the corresponding error estimates are derived for pre-blow-up time since we assume boundedness of the exact solution. Numerical simulations are performed to verify that our method can obtain accurate, nonnegative, oscillation-free solutions and has the ability to recover blowing-up solutions. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, the system of two-dimensional Burgers’ equations are solved by local discontinuous Galerkin (LDG) finite element method. The new method is based on the two-dimensional Hopf–Cole transformations, which transform the system of two-dimensional Burgers’ equations into a linear heat equation. Then the linear heat equation is solved by the LDG finite element method. The numerical solution of the heat equation is used to derive the numerical solutions of Burgers’ equations directly. Such a LDG method can also be used to find the numerical solution of the two-dimensional Burgers’ equation by rewriting Burgers’ equation as a system of the two-dimensional Burgers’ equations. Three numerical examples are used to demonstrate the efficiency and accuracy of the method. [Copyright &y& Elsevier]

Abstract: In general, it is difficult to use the Newton–Krylov methods to solve the large-scale multi-variable nonequilibrium reaction–diffusion systems. In this paper, by employing two new semi-implicit discretization schemes to construct the preconditioners, the preconditioned Newton–Krylov methods are presented to solve the multidimensional problems. These methods cannot only improve the number of iterations, but also speed up the convergence of solutions. Numerical results are given to illustrate the effectiveness. [Copyright &y& Elsevier]

Abstract: Jacobian-free Newton–Krylov (JFNK) method is an effective algorithm for solving large scale nonlinear equations. One of the most important advantages of JFNK method is that there is no necessity to form and store the Jacobian matrix of the nonlinear system when JFNK method is employed. However, an approximation of the Jacobian is needed for the purpose of preconditioning. In this paper, JFNK method is employed to solve a class of non-equilibrium radiation diffusion coupled to material thermal conduction equations, and two preconditioners are designed by linearizing the equations in two methods. Numerical results show that the two preconditioning methods can improve the convergence behavior and efficiency of JFNK method. [Copyright &y& Elsevier]