Realistic human reconstruction embraces an extensive range of applications as depth sensors advance.However,current stateof-the-art methods with RGB-D input still suffer from artefacts,such as noisy surfaces,non-human...Realistic human reconstruction embraces an extensive range of applications as depth sensors advance.However,current stateof-the-art methods with RGB-D input still suffer from artefacts,such as noisy surfaces,non-human shapes,and depth ambiguity,especially for the invisible parts.The authors observe the main issue is the lack of geometric semantics without using depth input priors fully.This paper focuses on improving the representation ability of implicit function,exploring an effective method to utilise depth-related semantics effectively and efficiently.The proposed geometry-enhanced implicit function enhances the geometric semantics with the extra voxel-aligned features from point clouds,promoting the completion of missing parts for unseen regions while preserving the local details on the input.For incorporating multi-scale pixel-aligned and voxelaligned features,the authors use the Squeeze-and-Excitation attention to capture and fully use channel interdependencies.For the multi-view reconstruction,the proposed depth-enhanced attention explicitly excites the network to“sense”the geometric structure for a more reasonable feature aggregation.Experiments and results show that our method outperforms current RGB and depth-based SOTA methods on the challenging data from Twindom and Thuman3.0,and achieves a detailed and completed human reconstruction,balancing performance and efficiency well.展开更多
The filled function method is an approach for finding a global minimum of multi-dimensional functions. With more and more relevant research, it becomes a promising way used in unconstrained global optimization. Some f...The filled function method is an approach for finding a global minimum of multi-dimensional functions. With more and more relevant research, it becomes a promising way used in unconstrained global optimization. Some filled functions with one or two parameters have already been suggested. However, there is no certain criterion to choose a parameter appropriately. In this paper, a parameter-free filled function was proposed. The definition of the original filled function and assumptions of the objective function given by Ge were improved according to the presented parameter-free filled function. The algorithm and numerical results of test functions were reported. Conclusions were drawn in the end. Key words global optimization - filled function method - local minimizer MSC 2000 90C30展开更多
In this paper, a new filled function with only one parameter is proposed. The main advantages of the new filled function are that it not only can be analyzed easily, but also can be approximated uniformly by a continu...In this paper, a new filled function with only one parameter is proposed. The main advantages of the new filled function are that it not only can be analyzed easily, but also can be approximated uniformly by a continuously differentiable function. Thus, a minimizer of the proposed filled function can be obtained easily by using a local optimization algorithm. The obtained minimizer is taken as the initial point to minimize the objective function and a better minimizer will be found. By repeating the above processes, we will find a global minimizer at last. The results of numerical experiments show that the new proposed filled function method is effective.展开更多
Quantification of right ventricular(RV)volume and function remains a challenge because of RV complex geometry by conventional echocardiography.The purpose of this study was to assess RV global longitudinal function in...Quantification of right ventricular(RV)volume and function remains a challenge because of RV complex geometry by conventional echocardiography.The purpose of this study was to assess RV global longitudinal function in patients with tetralogy of Fallot(TOF)by 2-dimensional ultrasound speckle tracking imaging(STI).Thirty-eight patients with TOF were enrolled in this study and divided into child group(n=25)and adult group(n=13)according to age.Thirty-eight age-and sex-matched normal subjects were selected as c...展开更多
In this paper, we considered a homogeneous reaction-diffusion predator-prey system with Holling type II functional response subject to Neumann boundary conditions. Some new sufficient conditions were analytically esta...In this paper, we considered a homogeneous reaction-diffusion predator-prey system with Holling type II functional response subject to Neumann boundary conditions. Some new sufficient conditions were analytically established to ensure that this system has globally asymptotically stable equilibria and Hopf bifurcation surrounding interior equilibrium. In the analysis of Hopf bifurcation, based on the phenomenon of Turing instability and well-done conditions, the system undergoes a Hopf bifurcation and an example incorporating with numerical simulations to support the existence of Hopf bifurcation is presented. We also derived a useful algorithm for determining direction of Hopf bifurcation and stability of bifurcating periodic solutions correspond to j ≠0 and j = 0, respectively. Finally, all these theoretical results are expected to be useful in the future study of dynamical complexity of ecological environment.展开更多
The paper is concerned with the filled functions for global optimization of a continuous function of several variables.More general forms of filled functions are presented for smooth and nonsmooth optimizations.These ...The paper is concerned with the filled functions for global optimization of a continuous function of several variables.More general forms of filled functions are presented for smooth and nonsmooth optimizations.These functions have either two adjustable parameters or one adjustable parameter.Conditions on functions and on the values of parameters are given so that the constructed functions are desired filled functions.展开更多
This paper deals with the questio n of global stability of the positive locally asymptotically stable equilibrium in a class of predator\|prey system of Gause\|typ e with Holling Ⅲ functional response. The Dulac'...This paper deals with the questio n of global stability of the positive locally asymptotically stable equilibrium in a class of predator\|prey system of Gause\|typ e with Holling Ⅲ functional response. The Dulac's criterion is applied and lia punov functions are constructed to establish the global stability.展开更多
To solve the global optimization problems which have several local minimizers,a new F-C function is proposes by combining a lled function and a cross function.The properties of the F-C function are discussed and the c...To solve the global optimization problems which have several local minimizers,a new F-C function is proposes by combining a lled function and a cross function.The properties of the F-C function are discussed and the corresponding algorithm is given in this paper.F-C function has the same local minimizers with the objective function.Therefore,the F-C function method only needs to minimize the objective function once in the rst iteration.Numerical experiments are performed and the results show that the proposed method is very effective.展开更多
A class of discontinuous penalty functions was proposed to solve constrained minimization problems with the integral approach to global optimization, m-mean value and v-variance optimality conditions of a constrained ...A class of discontinuous penalty functions was proposed to solve constrained minimization problems with the integral approach to global optimization, m-mean value and v-variance optimality conditions of a constrained and penalized minimization problem were investigated. A nonsequential algorithm was proposed. Numerical examples were given to illustrate the effectiveness of the algorithm.展开更多
A filled function with adjustable parameters is suggested in this paper for finding a global minimum point of a general class of nonlinear programming problems with a bounded and closed domain. This function has two a...A filled function with adjustable parameters is suggested in this paper for finding a global minimum point of a general class of nonlinear programming problems with a bounded and closed domain. This function has two adjustable parameters. We will discuss the properties of the proposed filled function. Conditions on this function and on the values of parameters are given so that the constructed function has the desired properties of traditional filled function.展开更多
In this paper, auxiliary function method for global optimization with box constraints is considered. First, a new non-parameter filled function which has the same local minimizers of the objective function is proposed...In this paper, auxiliary function method for global optimization with box constraints is considered. First, a new non-parameter filled function which has the same local minimizers of the objective function is proposed. By the character that having same local minimizers, and these minimizers are all better than the current minimizer of the objective function, it does not need to minimize the objective function except for thefirst iteration in the filled function method. It changes the frame of conventional filled function methods that objective function and filled function are minimized alternately,and can effectively reduce the iterations of the algorithm and accelerate the speed of global optimization. And then the theoretical properties of the filled function are discussed and the corresponding algorithm is established. Finally, numerical experiments are made and comparisons on several test problems are shown which exhibit the feasibility and effectiveness of the algorithm.展开更多
In the paper,to solve the global optimization problems,we propose a novel parameter-free filled function.Based on the non-parameter filled function,a new filled function algorithm is designed.In the algorithm,the sele...In the paper,to solve the global optimization problems,we propose a novel parameter-free filled function.Based on the non-parameter filled function,a new filled function algorithm is designed.In the algorithm,the selection and adjustment of parameters can be ignored by the characteristic that the filled function is parameter-free.In addition,in the region lower than the current local minimizer of the objective function,the filled function is continuously differentiable which enables any gradient descent method to be used as a local search method in the algorithm.Through numerical experiments by solving two test problems,the effectiveness of the algorithm is verified.展开更多
In this paper,we present an approach for smooth surface reconstructions interpolating triangular meshes with ar- bitrary topology and geometry.The approach is based on the well-known radial basis functions (RBFs) and ...In this paper,we present an approach for smooth surface reconstructions interpolating triangular meshes with ar- bitrary topology and geometry.The approach is based on the well-known radial basis functions (RBFs) and the constructed surfaces are generalized thin-plate spline surfaces.Our algorithm first defines a pair of offset points for each vertex of a given mesh to en- hance the controUability of local geometry and to assure stability of the construction.A linear system is then solved by LU decomposi- tion and the implicit governing equation of interpolating surface is obtained.The constructed surfaces finally are visualized by a Marching Cubes based polygonizer.The approach provides a robust and efficient solution for smooth surface reconstruction from various 3 D meshes.展开更多
In order to measure the correlation propeties of two Boolean functions,the global avalanche characteristics of Boolean functions constructed by concatenation are discussed,i.e.,f_1‖f_2and f_1‖f_2‖f_3‖f_4.Firstly,f...In order to measure the correlation propeties of two Boolean functions,the global avalanche characteristics of Boolean functions constructed by concatenation are discussed,i.e.,f_1‖f_2and f_1‖f_2‖f_3‖f_4.Firstly,for the function f = f_1‖f_2,the cross-correlation function of f_1,f_2 in the special condition are studied.In this case,f,f_1,f_2 must be in desired form.By computing their sum-of-squares indicators,the crosscorrelation function between f_1,f_2 is obtained.Secondly,for the function g = f_1‖f_2‖f_3‖f_4,by analyzing the relation among their auto-correlation functions,their sum-of-squares indicators are investigated.Based on them,the sum-of-squares indicators of functions obtained by Canteaut et al.are investigated.The results show that the correlation property of g is good when the correlation properties of Boolean functions f_1,f_2,f_3,f_4 are good.展开更多
Global minimization algorithm is indispensable for solving protein folding problems based on thermodynamic hypothesis. A contact difference （CD） based on pseudo potential function, for simulating empirical contact p...Global minimization algorithm is indispensable for solving protein folding problems based on thermodynamic hypothesis. A contact difference （CD） based on pseudo potential function, for simulating empirical contact potential functions and testing global minimization algorithm was proposed. The present article describes a conformational sampiing and global minimization algorithm, which is called WL, based on Monte Carlo simulation and simulated annealing. It can be used to locate CD＇s globe minimum and refold extended protein structures, as small as 0. 03 nm, from the native structures, back to ones with root mean square distance（RMSD）. These results demonstrate that the global minimization problems for empirical contact potential functions may be solvable.展开更多
Global minimization algorithm is indispensable to solving the protein folding problem based upon thermodynamic hypothesis. Here we propose a pseudo potential function, contact difference(CD), for simulating empirical ...Global minimization algorithm is indispensable to solving the protein folding problem based upon thermodynamic hypothesis. Here we propose a pseudo potential function, contact difference(CD), for simulating empirical contact potential functions and testing global minimization algorithm. The present paper covers conformational sampling and global minimization algorithm called BML03, based upon Monte Carlo and simulated annealing, which is able to locate CD′s global minimum and refold extended protein structures into ones with root mean square distance(RMSD) as small as 0.03 nm from the native structures. For empirical contact potential functions, these results demonstrate that their global minimization problems may be solvable.展开更多
The stability of a periodic oscillation and the global exponential class of recurrent neural networks with non-monotone activation functions and time-varying delays are analyzed. For two sets of activation functions, ...The stability of a periodic oscillation and the global exponential class of recurrent neural networks with non-monotone activation functions and time-varying delays are analyzed. For two sets of activation functions, some algebraic criteria for ascertaining global exponential periodicity and global exponential stability of the class of recurrent neural networks are derived by using the comparison principle and the theory of monotone operator. These conditions are easy to check in terms of system parameters. In addition, we provide a new and efficacious method for the qualitative analysis of various neural networks.展开更多
The reconstruction problem for elliptic voids located in the regular (equilateral) triangle is studied. A known point source is applied to the boundary of the domain, and it is assumed that the input data is obtained ...The reconstruction problem for elliptic voids located in the regular (equilateral) triangle is studied. A known point source is applied to the boundary of the domain, and it is assumed that the input data is obtained from the free-surface input data over a certain finite-length interval of the outer boundary. In the case when the boundary contour of the internal object is unknown, we propose a new algorithm to reconstruct its position and size on the basis of the input data. The key specific character of the proposed method is the construction of a special explicit-form Green's function satisfying the boundary condition over the outer boundary of the triangular domain. Some numerical examples demonstrate good stability of the proposed algorithm.展开更多
Surface-based geometric modeling has many advantages in terms of visualization and traditional subtractive manufacturing using computer-numerical-control cutting-machine tools.However,it is not an ideal solution for a...Surface-based geometric modeling has many advantages in terms of visualization and traditional subtractive manufacturing using computer-numerical-control cutting-machine tools.However,it is not an ideal solution for additive manufacturing because to digitally print a surface-represented geometric object using a certain additive manufacturing technology,the object has to be converted into a solid representation.However,converting a known surface-based geometric representation into a printable representation is essentially a redesign process,and this is especially the case,when its interior material structure needs to be considered.To specify a 3D geometric object that is ready to be digitally manufactured,its representation has to be in a certain volumetric form.In this research,we show how some of the difficulties experienced in additive manufacturing can be easily solved by using implicitly represented geometric objects.Like surface-based geometric representation is subtractive manufacturing-friendly,implicitly described geometric objects are additive manufacturing-friendly:implicit shapes are 3D printing ready.The implicit geometric representation allows to combine a geometric shape,material colors,an interior material structure,and other required attributes in one single description as a set of implicit functions,and no conversion is needed.In addition,as implicit objects are typically specified procedurally,very little data is used in their specifications,which makes them particularly useful for design and visualization with modern cloud-based mobile devices,which usually do not have very big storage spaces.Finally,implicit modeling is a design procedure that is parallel computing-friendly,as the design of a complex geometric object can be divided into a set of simple shape-designing tasks,owing to the availability of shape-preserving implicit blending operations.展开更多
In this paper,the forecasting equations of a 2nd-order space-time differential remainder are deduced from the Navier-Stokes primitive equations and Eulerian operator by Taylor-series expansion.Here we introduce a cubi...In this paper,the forecasting equations of a 2nd-order space-time differential remainder are deduced from the Navier-Stokes primitive equations and Eulerian operator by Taylor-series expansion.Here we introduce a cubic spline numerical model(Spline Model for short),which is with a quasi-Lagrangian time-split integration scheme of fitting cubic spline/bicubic surface to all physical variable fields in the atmospheric equations on spherical discrete latitude-longitude mesh.A new algorithm of"fitting cubic spline—time step integration—fitting cubic spline—……"is developed to determine their first-and2nd-order derivatives and their upstream points for time discrete integral to the governing equations in Spline Model.And the cubic spline function and its mathematical polarities are also discussed to understand the Spline Model’s mathematical foundation of numerical analysis.It is pointed out that the Spline Model has mathematical laws of"convergence"of the cubic spline functions contracting to the original functions as well as its 1st-order and 2nd-order derivatives.The"optimality"of the 2nd-order derivative of the cubic spline functions is optimal approximation to that of the original functions.In addition,a Hermite bicubic patch is equivalent to operate on a grid for a 2nd-order derivative variable field.Besides,the slopes and curvatures of a central difference are identified respectively,with a smoothing coefficient of 1/3,three-point smoothing of that of a cubic spline.Then the slopes and curvatures of a central difference are calculated from the smoothing coefficient 1/3 and three-point smoothing of that of a cubic spline,respectively.Furthermore,a global simulation case of adiabatic,non-frictional and"incompressible"model atmosphere is shown with the quasi-Lagrangian time integration by using a global Spline Model,whose initial condition comes from the NCEP reanalysis data,along with quasi-uniform latitude-longitude grids and the so-called"shallow atmosphere"Navier-Stokes primitive equations in the spherical coordinates.The Spline Model,which adopted the Navier-Stokes primitive equations and quasi-Lagrangian time-split integration scheme,provides an initial ideal case of global atmospheric circulation.In addition,considering the essentially non-linear atmospheric motions,the Spline Model could judge reasonably well simple points of any smoothed variable field according to its fitting spline curvatures that must conform to its physical interpretation.展开更多
基金supported by the National Key R&D Programme of China(2022YFF0902200).
文摘Realistic human reconstruction embraces an extensive range of applications as depth sensors advance.However,current stateof-the-art methods with RGB-D input still suffer from artefacts,such as noisy surfaces,non-human shapes,and depth ambiguity,especially for the invisible parts.The authors observe the main issue is the lack of geometric semantics without using depth input priors fully.This paper focuses on improving the representation ability of implicit function,exploring an effective method to utilise depth-related semantics effectively and efficiently.The proposed geometry-enhanced implicit function enhances the geometric semantics with the extra voxel-aligned features from point clouds,promoting the completion of missing parts for unseen regions while preserving the local details on the input.For incorporating multi-scale pixel-aligned and voxelaligned features,the authors use the Squeeze-and-Excitation attention to capture and fully use channel interdependencies.For the multi-view reconstruction,the proposed depth-enhanced attention explicitly excites the network to“sense”the geometric structure for a more reasonable feature aggregation.Experiments and results show that our method outperforms current RGB and depth-based SOTA methods on the challenging data from Twindom and Thuman3.0,and achieves a detailed and completed human reconstruction,balancing performance and efficiency well.
文摘The filled function method is an approach for finding a global minimum of multi-dimensional functions. With more and more relevant research, it becomes a promising way used in unconstrained global optimization. Some filled functions with one or two parameters have already been suggested. However, there is no certain criterion to choose a parameter appropriately. In this paper, a parameter-free filled function was proposed. The definition of the original filled function and assumptions of the objective function given by Ge were improved according to the presented parameter-free filled function. The algorithm and numerical results of test functions were reported. Conclusions were drawn in the end. Key words global optimization - filled function method - local minimizer MSC 2000 90C30
文摘In this paper, a new filled function with only one parameter is proposed. The main advantages of the new filled function are that it not only can be analyzed easily, but also can be approximated uniformly by a continuously differentiable function. Thus, a minimizer of the proposed filled function can be obtained easily by using a local optimization algorithm. The obtained minimizer is taken as the initial point to minimize the objective function and a better minimizer will be found. By repeating the above processes, we will find a global minimizer at last. The results of numerical experiments show that the new proposed filled function method is effective.
文摘Quantification of right ventricular(RV)volume and function remains a challenge because of RV complex geometry by conventional echocardiography.The purpose of this study was to assess RV global longitudinal function in patients with tetralogy of Fallot(TOF)by 2-dimensional ultrasound speckle tracking imaging(STI).Thirty-eight patients with TOF were enrolled in this study and divided into child group(n=25)and adult group(n=13)according to age.Thirty-eight age-and sex-matched normal subjects were selected as c...
文摘In this paper, we considered a homogeneous reaction-diffusion predator-prey system with Holling type II functional response subject to Neumann boundary conditions. Some new sufficient conditions were analytically established to ensure that this system has globally asymptotically stable equilibria and Hopf bifurcation surrounding interior equilibrium. In the analysis of Hopf bifurcation, based on the phenomenon of Turing instability and well-done conditions, the system undergoes a Hopf bifurcation and an example incorporating with numerical simulations to support the existence of Hopf bifurcation is presented. We also derived a useful algorithm for determining direction of Hopf bifurcation and stability of bifurcating periodic solutions correspond to j ≠0 and j = 0, respectively. Finally, all these theoretical results are expected to be useful in the future study of dynamical complexity of ecological environment.
文摘The paper is concerned with the filled functions for global optimization of a continuous function of several variables.More general forms of filled functions are presented for smooth and nonsmooth optimizations.These functions have either two adjustable parameters or one adjustable parameter.Conditions on functions and on the values of parameters are given so that the constructed functions are desired filled functions.
基金Supported by the National Natural Science Foundation of China(195 310 70 )
文摘This paper deals with the questio n of global stability of the positive locally asymptotically stable equilibrium in a class of predator\|prey system of Gause\|typ e with Holling Ⅲ functional response. The Dulac's criterion is applied and lia punov functions are constructed to establish the global stability.
基金Supported by National Natural Science Foundation of China(No.11471102)Basic research projects for key scientific research projects in Henan Province(No.20ZX001)。
文摘To solve the global optimization problems which have several local minimizers,a new F-C function is proposes by combining a lled function and a cross function.The properties of the F-C function are discussed and the corresponding algorithm is given in this paper.F-C function has the same local minimizers with the objective function.Therefore,the F-C function method only needs to minimize the objective function once in the rst iteration.Numerical experiments are performed and the results show that the proposed method is very effective.
文摘A class of discontinuous penalty functions was proposed to solve constrained minimization problems with the integral approach to global optimization, m-mean value and v-variance optimality conditions of a constrained and penalized minimization problem were investigated. A nonsequential algorithm was proposed. Numerical examples were given to illustrate the effectiveness of the algorithm.
基金Supported by the National Science Foundation of China(10171118)Supported by the Science Foundation of University of Science and Technology of Henan(2003ZY06)
文摘A filled function with adjustable parameters is suggested in this paper for finding a global minimum point of a general class of nonlinear programming problems with a bounded and closed domain. This function has two adjustable parameters. We will discuss the properties of the proposed filled function. Conditions on this function and on the values of parameters are given so that the constructed function has the desired properties of traditional filled function.
基金Supported by National Natural Science Foundation of China (Grant No. 11471102, 11701150,12071112)Basic research projects for key scientific research projects in Henan Province (Grant No. 20ZX001)。
文摘In this paper, auxiliary function method for global optimization with box constraints is considered. First, a new non-parameter filled function which has the same local minimizers of the objective function is proposed. By the character that having same local minimizers, and these minimizers are all better than the current minimizer of the objective function, it does not need to minimize the objective function except for thefirst iteration in the filled function method. It changes the frame of conventional filled function methods that objective function and filled function are minimized alternately,and can effectively reduce the iterations of the algorithm and accelerate the speed of global optimization. And then the theoretical properties of the filled function are discussed and the corresponding algorithm is established. Finally, numerical experiments are made and comparisons on several test problems are shown which exhibit the feasibility and effectiveness of the algorithm.
文摘In the paper,to solve the global optimization problems,we propose a novel parameter-free filled function.Based on the non-parameter filled function,a new filled function algorithm is designed.In the algorithm,the selection and adjustment of parameters can be ignored by the characteristic that the filled function is parameter-free.In addition,in the region lower than the current local minimizer of the objective function,the filled function is continuously differentiable which enables any gradient descent method to be used as a local search method in the algorithm.Through numerical experiments by solving two test problems,the effectiveness of the algorithm is verified.
文摘In this paper,we present an approach for smooth surface reconstructions interpolating triangular meshes with ar- bitrary topology and geometry.The approach is based on the well-known radial basis functions (RBFs) and the constructed surfaces are generalized thin-plate spline surfaces.Our algorithm first defines a pair of offset points for each vertex of a given mesh to en- hance the controUability of local geometry and to assure stability of the construction.A linear system is then solved by LU decomposi- tion and the implicit governing equation of interpolating surface is obtained.The constructed surfaces finally are visualized by a Marching Cubes based polygonizer.The approach provides a robust and efficient solution for smooth surface reconstruction from various 3 D meshes.
基金Sponsored by the National Natural Science Foundations of Anhui Higher Education Institutions of China(Grant No.KJ2014A220,KJ2014A231)the Anhui Provincial Natural Science Foundation(Grant No.1608085MF143)the Key Program in the Youth Elite Support Plan in Universities of Anhui Province(Grant No.gxyq ZD2016112)
文摘In order to measure the correlation propeties of two Boolean functions,the global avalanche characteristics of Boolean functions constructed by concatenation are discussed,i.e.,f_1‖f_2and f_1‖f_2‖f_3‖f_4.Firstly,for the function f = f_1‖f_2,the cross-correlation function of f_1,f_2 in the special condition are studied.In this case,f,f_1,f_2 must be in desired form.By computing their sum-of-squares indicators,the crosscorrelation function between f_1,f_2 is obtained.Secondly,for the function g = f_1‖f_2‖f_3‖f_4,by analyzing the relation among their auto-correlation functions,their sum-of-squares indicators are investigated.Based on them,the sum-of-squares indicators of functions obtained by Canteaut et al.are investigated.The results show that the correlation property of g is good when the correlation properties of Boolean functions f_1,f_2,f_3,f_4 are good.
文摘Global minimization algorithm is indispensable for solving protein folding problems based on thermodynamic hypothesis. A contact difference （CD） based on pseudo potential function, for simulating empirical contact potential functions and testing global minimization algorithm was proposed. The present article describes a conformational sampiing and global minimization algorithm, which is called WL, based on Monte Carlo simulation and simulated annealing. It can be used to locate CD＇s globe minimum and refold extended protein structures, as small as 0. 03 nm, from the native structures, back to ones with root mean square distance（RMSD）. These results demonstrate that the global minimization problems for empirical contact potential functions may be solvable.
基金Supported by the National Natural Science Foundation of China(No.30 2 4 0 0 16)
文摘Global minimization algorithm is indispensable to solving the protein folding problem based upon thermodynamic hypothesis. Here we propose a pseudo potential function, contact difference(CD), for simulating empirical contact potential functions and testing global minimization algorithm. The present paper covers conformational sampling and global minimization algorithm called BML03, based upon Monte Carlo and simulated annealing, which is able to locate CD′s global minimum and refold extended protein structures into ones with root mean square distance(RMSD) as small as 0.03 nm from the native structures. For empirical contact potential functions, these results demonstrate that their global minimization problems may be solvable.
基金Supported by the Natural Science Foundation of Hubei Province (2007ABA124)the Youth Project Foundation of Hubei Province Education Department (Q200722001)the Major Foundation of Hubei Province Education Department (D200722002)
文摘The stability of a periodic oscillation and the global exponential class of recurrent neural networks with non-monotone activation functions and time-varying delays are analyzed. For two sets of activation functions, some algebraic criteria for ascertaining global exponential periodicity and global exponential stability of the class of recurrent neural networks are derived by using the comparison principle and the theory of monotone operator. These conditions are easy to check in terms of system parameters. In addition, we provide a new and efficacious method for the qualitative analysis of various neural networks.
文摘The reconstruction problem for elliptic voids located in the regular (equilateral) triangle is studied. A known point source is applied to the boundary of the domain, and it is assumed that the input data is obtained from the free-surface input data over a certain finite-length interval of the outer boundary. In the case when the boundary contour of the internal object is unknown, we propose a new algorithm to reconstruct its position and size on the basis of the input data. The key specific character of the proposed method is the construction of a special explicit-form Green's function satisfying the boundary condition over the outer boundary of the triangular domain. Some numerical examples demonstrate good stability of the proposed algorithm.
基金supported by the National Natural Science Foundation of China(Grant No.61502402 and 61379080)the Natural Science Foundation of Fujian Province of China(Grant No.2015J05129).
文摘Surface-based geometric modeling has many advantages in terms of visualization and traditional subtractive manufacturing using computer-numerical-control cutting-machine tools.However,it is not an ideal solution for additive manufacturing because to digitally print a surface-represented geometric object using a certain additive manufacturing technology,the object has to be converted into a solid representation.However,converting a known surface-based geometric representation into a printable representation is essentially a redesign process,and this is especially the case,when its interior material structure needs to be considered.To specify a 3D geometric object that is ready to be digitally manufactured,its representation has to be in a certain volumetric form.In this research,we show how some of the difficulties experienced in additive manufacturing can be easily solved by using implicitly represented geometric objects.Like surface-based geometric representation is subtractive manufacturing-friendly,implicitly described geometric objects are additive manufacturing-friendly:implicit shapes are 3D printing ready.The implicit geometric representation allows to combine a geometric shape,material colors,an interior material structure,and other required attributes in one single description as a set of implicit functions,and no conversion is needed.In addition,as implicit objects are typically specified procedurally,very little data is used in their specifications,which makes them particularly useful for design and visualization with modern cloud-based mobile devices,which usually do not have very big storage spaces.Finally,implicit modeling is a design procedure that is parallel computing-friendly,as the design of a complex geometric object can be divided into a set of simple shape-designing tasks,owing to the availability of shape-preserving implicit blending operations.
文摘In this paper,the forecasting equations of a 2nd-order space-time differential remainder are deduced from the Navier-Stokes primitive equations and Eulerian operator by Taylor-series expansion.Here we introduce a cubic spline numerical model(Spline Model for short),which is with a quasi-Lagrangian time-split integration scheme of fitting cubic spline/bicubic surface to all physical variable fields in the atmospheric equations on spherical discrete latitude-longitude mesh.A new algorithm of"fitting cubic spline—time step integration—fitting cubic spline—……"is developed to determine their first-and2nd-order derivatives and their upstream points for time discrete integral to the governing equations in Spline Model.And the cubic spline function and its mathematical polarities are also discussed to understand the Spline Model’s mathematical foundation of numerical analysis.It is pointed out that the Spline Model has mathematical laws of"convergence"of the cubic spline functions contracting to the original functions as well as its 1st-order and 2nd-order derivatives.The"optimality"of the 2nd-order derivative of the cubic spline functions is optimal approximation to that of the original functions.In addition,a Hermite bicubic patch is equivalent to operate on a grid for a 2nd-order derivative variable field.Besides,the slopes and curvatures of a central difference are identified respectively,with a smoothing coefficient of 1/3,three-point smoothing of that of a cubic spline.Then the slopes and curvatures of a central difference are calculated from the smoothing coefficient 1/3 and three-point smoothing of that of a cubic spline,respectively.Furthermore,a global simulation case of adiabatic,non-frictional and"incompressible"model atmosphere is shown with the quasi-Lagrangian time integration by using a global Spline Model,whose initial condition comes from the NCEP reanalysis data,along with quasi-uniform latitude-longitude grids and the so-called"shallow atmosphere"Navier-Stokes primitive equations in the spherical coordinates.The Spline Model,which adopted the Navier-Stokes primitive equations and quasi-Lagrangian time-split integration scheme,provides an initial ideal case of global atmospheric circulation.In addition,considering the essentially non-linear atmospheric motions,the Spline Model could judge reasonably well simple points of any smoothed variable field according to its fitting spline curvatures that must conform to its physical interpretation.
