Continuously differentiable radial basis functions (C<sup>∞</sup>-RBFs), while being theoretically exponentially convergent are considered impractical computationally because the coefficient matrices are ...Continuously differentiable radial basis functions (C<sup>∞</sup>-RBFs), while being theoretically exponentially convergent are considered impractical computationally because the coefficient matrices are full and can become very ill- conditioned. Similarly, the Hilbert and Vandermonde have full matrices and become ill-conditioned. The difference between a coefficient matrix generated by C<sup>∞</sup>-RBFs for partial differential or integral equations and Hilbert and Vandermonde systems is that C<sup>∞</sup>-RBFs are very sensitive to small changes in the adjustable parameters. These parameters affect the condition number and solution accuracy. The error terrain has many local and global maxima and minima. To find stable and accurate numerical solutions for full linear equation systems, this study proposes a hybrid combination of block Gaussian elimination (BGE) combined with arbitrary precision arithmetic (APA) to minimize the accumulation of rounding errors. In the future, this algorithm can execute faster using preconditioners and implemented on massively parallel computers.展开更多
A novel method based on ant colony optimization （ACO）, algorithm for solving the ill-conditioned linear systems of equations is proposed. ACO is a parallelized bionic optimization algorithm which is inspired from th...A novel method based on ant colony optimization （ACO）, algorithm for solving the ill-conditioned linear systems of equations is proposed. ACO is a parallelized bionic optimization algorithm which is inspired from the behavior of real ants. ACO algorithm is first introduced, a kind of positive feedback mechanism is adopted in ACO. Then, the solu- tion problem of linear systems of equations was reformulated as an unconstrained optimization problem for solution by an ACID algorithm. Finally, the ACID with other traditional methods is applied to solve a kind of multi-dimensional Hilbert ill-conditioned linear equations. The numerical results demonstrate that ACO is effective, robust and recommendable in solving ill-conditioned linear systems of equations.展开更多
The method of condition number is commonly used to diagnose a normal matrix N whether it is ill conditioned state or not. For its shortcoming, a method to measure multi collinearity of a matrix was put forward. The me...The method of condition number is commonly used to diagnose a normal matrix N whether it is ill conditioned state or not. For its shortcoming, a method to measure multi collinearity of a matrix was put forward. The method is that implement Gram Schmidt orthogonalizing process to column vectors of a design matrix A (α l ), then calculate the norms of every vector before and after orthogonalization process and their corresponding ratio, and use the minimum ratio among the group of ratios to measure the multi collinearity of A. According to the corresponding relationship between the multi collinearity and the ill conditioned state of a matrix, the method also studies and offers reference indexes weighing the ill conditioned state of a matrix based on the relative norm. The remarkable characteristics of the method are that the measure of multi collinearity has idiographic geometry meaning and clear lower and upper limit, the size of the measure reflects the multi collinearity of column vectors objectively. It is convenient to study the reason that results in the matrix being multi collinearity and to put forward solving plan according to the method which is summarized as the method of minimum norm and abbreviated as F method.展开更多
Linear Least Squares（LLS） problems are particularly difficult to solve because they are frequently ill-conditioned, and involve large quantities of data. Ill-conditioned LLS problems are commonly seen in mathematics...Linear Least Squares（LLS） problems are particularly difficult to solve because they are frequently ill-conditioned, and involve large quantities of data. Ill-conditioned LLS problems are commonly seen in mathematics and geosciences, where regularization algorithms are employed to seek optimal solutions. For many problems, even with the use of regularization algorithms it may be impossible to obtain an accurate solution. Riley and Golub suggested an iterative scheme for solving LLS problems. For the early iteration algorithm, it is difficult to improve the well-conditioned perturbed matrix and accelerate the convergence at the same time. Aiming at this problem, self-adaptive iteration algorithm（SAIA） is proposed in this paper for solving severe ill-conditioned LLS problems. The algorithm is different from other popular algorithms proposed in recent references. It avoids matrix inverse by using Cholesky decomposition, and tunes the perturbation parameter according to the rate of residual error decline in the iterative process. Example shows that the algorithm can greatly reduce iteration times, accelerate the convergence,and also greatly enhance the computation accuracy.展开更多
To mitigate the ill effects and obtain more accurate and stable solution of the observation equations, the so-called truncated singular-value decomposition (TSVD) method is introduced by modifying the small (nonzero) ...To mitigate the ill effects and obtain more accurate and stable solution of the observation equations, the so-called truncated singular-value decomposition (TSVD) method is introduced by modifying the small (nonzero) singular values of the coefficients matrix. The proposed method directly disposed the ill-conditioning observation equations, which differs considerably from the traditional normal equation method. An application explains that TSVD can mitigate the ill conditioning.展开更多
A progressive neurodegenerative disease,Alzheimer’s disease(AD).Studies suggest that highly expressed protein isoaspartate methyltransferase 1(PCMT1)in brain tissue.In the current study,we explored the effects of neu...A progressive neurodegenerative disease,Alzheimer’s disease(AD).Studies suggest that highly expressed protein isoaspartate methyltransferase 1(PCMT1)in brain tissue.In the current study,we explored the effects of neural stem cell-conditioned medium(NSC-CDM)on the PCMT1/MST1 pathway to alleviate Aβ_(25-35)-induced damage in SH-SY5Y cells.Our data suggested that Aβ_(25-35) markedly inhibited cell viability.NSC-CDM or Neural stem cell-complete medium(NSC-CPM)had a suppression effect on toxicity when treatment with Aβ_(25-35),with a greater effect observed with NSC-CDM.Aβ_(25-35)+NSC-CDM group exhibited an increase in PCMT1 expression.sh-PCMT1 markedly decreased cell proliferation and suppressed the protective role of NSC-CDM through the induction of apoptosis and improved p-MST1 expression.Overexpression of PCMT1 reversed the Aβ_(25-35)-induced decrease in cell proliferation and apoptosis.In summary,our findings suggest that NSC-CDM corrects the Aβ_(25-35)-induced damage to cells by improving PCMT1 expressions,which in turn reduces phosphorylation of MST1.展开更多
The objective of this investigation is to examine the correctness and efficiency of the choice of boundary conditions when using assumed mode approach to simulate flexible multi-body systems. The displacement field du...The objective of this investigation is to examine the correctness and efficiency of the choice of boundary conditions when using assumed mode approach to simulate flexible multi-body systems. The displacement field due to deformation is approximated by the Rayleigh-Ritz assumed modes in floating frame of reference （FFR） formulation. The deformations obtained by the absolute nodal coordinate （ANC） formulation which are transformed by two sets of reference coordinates are introduced as a criterion to verify the accuracy of the simulation results by using the FFR formulation. The relationship between the deformations obtained from different boundary conditions is revealed. Nu- merical simulation examples demonstrate that the assumed modes with cantilevered-free, simply-supported and free- free boundary conditions without inclusion of rigid body modes are suitable for simulation of flexible multi-body system with large over all motion, and the same physical deformation can be obtained using those mode functions, differ only by a coordinate transformation. It is also shown that when using mode shapes with statically indeterminate boundary conditions, significant error may occur. Furthermore, the slider crank mechanism with rigid crank is accurate enough for investigating boundary condition problem of flexible multi-body system, which cost significant less simulating time.展开更多
Quadratic 0-1 problems with linear inequality constraints are briefly considered in this paper.Global optimality conditions for these problems,including a necessary condition and some sufficient conditions,are present...Quadratic 0-1 problems with linear inequality constraints are briefly considered in this paper.Global optimality conditions for these problems,including a necessary condition and some sufficient conditions,are presented.The necessary condition is expressed without dual variables.The relations between the global optimal solutions of nonconvex quadratic 0-1 problems and the associated relaxed convex problems are also studied.展开更多
The purpose of this systematic review is to identify evidence of the appropriate dose of telehealth intervention services provided to community dwelling adults experiencing chronic illness or disability related to eff...The purpose of this systematic review is to identify evidence of the appropriate dose of telehealth intervention services provided to community dwelling adults experiencing chronic illness or disability related to effectiveness, quality, safety, and cost. Academic Search Complete, CINAHL, MEDLINE, Cochrane, and JBI were searched using combinations of “telehealth or telemedicine or telemonitoring or telepractice or telenursing or telecare AND chronic illness or chronic disease”. Of the identified 449 articles, 47 articles met the inclusion criteria. Most study designs were quasi-experimental one group pre-test post-test (N = 16) with few Randomized Controlled Trials (N = 12). Twenty-three published articles studied the effect of telehealth for one chronic condition (49.9%) while 24 (51.1%) examined the effectiveness of telehealth for multiple chronic conditions. Measurement of telehealth outcomes varied and included efficacy, healthcare utilization, quality, adherence, cost, and safety. No standard measure of dose could be extrapolated. Length of intervention was measured and reported differently in each study. The dose of telehealth services that improve care effectiveness, quality, safety, and cost is still unknown for community dwelling adults experiencing chronic illness. The findings from this systematic review do indicate that longer duration of telehealth services (51 weeks), regardless of modality, produced positive outcomes as opposed to those with shorter durations (37 - 38 weeks) that produced neutral or mixed results. Collecting and reporting data related to clinical workflow such as dose of intervention specific to disease and type of modality is recommended. Rigorous study design including standard measurement at the RCT and Comparative Effectiveness level is still needed.展开更多
In this paper two theorems with theoretical and practical significance are given in respect to the preconditioned conjugate gradient method (PCCG). The theorems discuss respectively the qualitative property of the ite...In this paper two theorems with theoretical and practical significance are given in respect to the preconditioned conjugate gradient method (PCCG). The theorems discuss respectively the qualitative property of the iterative solution and the construction principle of the iterative matrix. The authors put forward a new incompletely LU factorizing technique for non-M-matrix and the method of constructing the iterative matrix. This improved PCCG is used to calculate the ill-conditioned problems and large-scale three-dimensional finite element problems, and simultaneously contrasted with other methods. The abnormal phenomenon is analyzed when PCCG is used to solve the system of ill-conditioned equations, ft is shown that the method proposed in this paper is quite effective in solving the system of large-scale finite element equations and the system of ill-conditioned equations.展开更多
The Liaoji Proterozoic rift is an inter-intracontinenatl rift developed from Archean granite-greenstone tectonic regime and contains many important mineral deposits of U, B, magnesite, Pb-Zn, Au, Ag, Co and P. These d...The Liaoji Proterozoic rift is an inter-intracontinenatl rift developed from Archean granite-greenstone tectonic regime and contains many important mineral deposits of U, B, magnesite, Pb-Zn, Au, Ag, Co and P. These deposits were formed as the result of late mobilization, transportation and concentfation of the previously enriched ore-forming mate- rials in several ore-bearing formations formed during the rift stage. So the metallogeny of these deposits in the rift shows both inheritance and new generation of the ore-forming materials. In future ore-searching practice, attentions should be paid on the studies of the ore-bearing formations in the rift, on the multiple stages of metallogeny and and on multiple derivations of the ore-forming materials.展开更多
A class of nonlinear problems with real parameters is defined. Generally, in this class of problems, when the parametric values are very large, the problems become ill-posed and numerical difficulties are encountered ...A class of nonlinear problems with real parameters is defined. Generally, in this class of problems, when the parametric values are very large, the problems become ill-posed and numerical difficulties are encountered when trying to solve these problems. In this paper, the nonlinear problems are reformulated to overcome the numerical difficulties associated with large parametric values. A novel iterative algorithm, which is suitable for large scale problems and can be easily parallelized, is proposed to solve the reformulated problems. Numerical tests indicate that the proposed algorithm gives stable solutions. Convergence properties of the proposed algorithm are investigated. In the limiting case, when the corresponding constraint is exactly satisfied, the proposed method is equivalent to the standard augmented Lagrangian method.展开更多
文摘Continuously differentiable radial basis functions (C<sup>∞</sup>-RBFs), while being theoretically exponentially convergent are considered impractical computationally because the coefficient matrices are full and can become very ill- conditioned. Similarly, the Hilbert and Vandermonde have full matrices and become ill-conditioned. The difference between a coefficient matrix generated by C<sup>∞</sup>-RBFs for partial differential or integral equations and Hilbert and Vandermonde systems is that C<sup>∞</sup>-RBFs are very sensitive to small changes in the adjustable parameters. These parameters affect the condition number and solution accuracy. The error terrain has many local and global maxima and minima. To find stable and accurate numerical solutions for full linear equation systems, this study proposes a hybrid combination of block Gaussian elimination (BGE) combined with arbitrary precision arithmetic (APA) to minimize the accumulation of rounding errors. In the future, this algorithm can execute faster using preconditioners and implemented on massively parallel computers.
文摘A novel method based on ant colony optimization （ACO）, algorithm for solving the ill-conditioned linear systems of equations is proposed. ACO is a parallelized bionic optimization algorithm which is inspired from the behavior of real ants. ACO algorithm is first introduced, a kind of positive feedback mechanism is adopted in ACO. Then, the solu- tion problem of linear systems of equations was reformulated as an unconstrained optimization problem for solution by an ACID algorithm. Finally, the ACID with other traditional methods is applied to solve a kind of multi-dimensional Hilbert ill-conditioned linear equations. The numerical results demonstrate that ACO is effective, robust and recommendable in solving ill-conditioned linear systems of equations.
文摘The method of condition number is commonly used to diagnose a normal matrix N whether it is ill conditioned state or not. For its shortcoming, a method to measure multi collinearity of a matrix was put forward. The method is that implement Gram Schmidt orthogonalizing process to column vectors of a design matrix A (α l ), then calculate the norms of every vector before and after orthogonalization process and their corresponding ratio, and use the minimum ratio among the group of ratios to measure the multi collinearity of A. According to the corresponding relationship between the multi collinearity and the ill conditioned state of a matrix, the method also studies and offers reference indexes weighing the ill conditioned state of a matrix based on the relative norm. The remarkable characteristics of the method are that the measure of multi collinearity has idiographic geometry meaning and clear lower and upper limit, the size of the measure reflects the multi collinearity of column vectors objectively. It is convenient to study the reason that results in the matrix being multi collinearity and to put forward solving plan according to the method which is summarized as the method of minimum norm and abbreviated as F method.
基金supported by Open Fund of Engineering Laboratory of Spatial Information Technology of Highway Geological Disaster Early Warning in Hunan Province(Changsha University of Science&Technology,kfj150602)Hunan Province Science and Technology Program Funded Projects,China(2015NK3035)+1 种基金the Land and Resources Department Scientific Research Project of Hunan Province,China(2013-27)the Education Department Scientific Research Project of Hunan Province,China(13C1011)
文摘Linear Least Squares（LLS） problems are particularly difficult to solve because they are frequently ill-conditioned, and involve large quantities of data. Ill-conditioned LLS problems are commonly seen in mathematics and geosciences, where regularization algorithms are employed to seek optimal solutions. For many problems, even with the use of regularization algorithms it may be impossible to obtain an accurate solution. Riley and Golub suggested an iterative scheme for solving LLS problems. For the early iteration algorithm, it is difficult to improve the well-conditioned perturbed matrix and accelerate the convergence at the same time. Aiming at this problem, self-adaptive iteration algorithm（SAIA） is proposed in this paper for solving severe ill-conditioned LLS problems. The algorithm is different from other popular algorithms proposed in recent references. It avoids matrix inverse by using Cholesky decomposition, and tunes the perturbation parameter according to the rate of residual error decline in the iterative process. Example shows that the algorithm can greatly reduce iteration times, accelerate the convergence,and also greatly enhance the computation accuracy.
基金Project Supported by the National Natural Science Foundation of China for Distinguished Yound Scholars of China (40125013) NationalNatural Science Foundation of China (40074006 , 40274001) Natural Science Foundation of Henan Province , China (004051300 ,0211051100)
文摘To mitigate the ill effects and obtain more accurate and stable solution of the observation equations, the so-called truncated singular-value decomposition (TSVD) method is introduced by modifying the small (nonzero) singular values of the coefficients matrix. The proposed method directly disposed the ill-conditioning observation equations, which differs considerably from the traditional normal equation method. An application explains that TSVD can mitigate the ill conditioning.
文摘A progressive neurodegenerative disease,Alzheimer’s disease(AD).Studies suggest that highly expressed protein isoaspartate methyltransferase 1(PCMT1)in brain tissue.In the current study,we explored the effects of neural stem cell-conditioned medium(NSC-CDM)on the PCMT1/MST1 pathway to alleviate Aβ_(25-35)-induced damage in SH-SY5Y cells.Our data suggested that Aβ_(25-35) markedly inhibited cell viability.NSC-CDM or Neural stem cell-complete medium(NSC-CPM)had a suppression effect on toxicity when treatment with Aβ_(25-35),with a greater effect observed with NSC-CDM.Aβ_(25-35)+NSC-CDM group exhibited an increase in PCMT1 expression.sh-PCMT1 markedly decreased cell proliferation and suppressed the protective role of NSC-CDM through the induction of apoptosis and improved p-MST1 expression.Overexpression of PCMT1 reversed the Aβ_(25-35)-induced decrease in cell proliferation and apoptosis.In summary,our findings suggest that NSC-CDM corrects the Aβ_(25-35)-induced damage to cells by improving PCMT1 expressions,which in turn reduces phosphorylation of MST1.
基金supported by the National Natural Science Foundation of China (10872126)the Research Fund of the Doctoral Program of Higher Education of China (20100073110007)
文摘The objective of this investigation is to examine the correctness and efficiency of the choice of boundary conditions when using assumed mode approach to simulate flexible multi-body systems. The displacement field due to deformation is approximated by the Rayleigh-Ritz assumed modes in floating frame of reference （FFR） formulation. The deformations obtained by the absolute nodal coordinate （ANC） formulation which are transformed by two sets of reference coordinates are introduced as a criterion to verify the accuracy of the simulation results by using the FFR formulation. The relationship between the deformations obtained from different boundary conditions is revealed. Nu- merical simulation examples demonstrate that the assumed modes with cantilevered-free, simply-supported and free- free boundary conditions without inclusion of rigid body modes are suitable for simulation of flexible multi-body system with large over all motion, and the same physical deformation can be obtained using those mode functions, differ only by a coordinate transformation. It is also shown that when using mode shapes with statically indeterminate boundary conditions, significant error may occur. Furthermore, the slider crank mechanism with rigid crank is accurate enough for investigating boundary condition problem of flexible multi-body system, which cost significant less simulating time.
文摘Quadratic 0-1 problems with linear inequality constraints are briefly considered in this paper.Global optimality conditions for these problems,including a necessary condition and some sufficient conditions,are presented.The necessary condition is expressed without dual variables.The relations between the global optimal solutions of nonconvex quadratic 0-1 problems and the associated relaxed convex problems are also studied.
文摘The purpose of this systematic review is to identify evidence of the appropriate dose of telehealth intervention services provided to community dwelling adults experiencing chronic illness or disability related to effectiveness, quality, safety, and cost. Academic Search Complete, CINAHL, MEDLINE, Cochrane, and JBI were searched using combinations of “telehealth or telemedicine or telemonitoring or telepractice or telenursing or telecare AND chronic illness or chronic disease”. Of the identified 449 articles, 47 articles met the inclusion criteria. Most study designs were quasi-experimental one group pre-test post-test (N = 16) with few Randomized Controlled Trials (N = 12). Twenty-three published articles studied the effect of telehealth for one chronic condition (49.9%) while 24 (51.1%) examined the effectiveness of telehealth for multiple chronic conditions. Measurement of telehealth outcomes varied and included efficacy, healthcare utilization, quality, adherence, cost, and safety. No standard measure of dose could be extrapolated. Length of intervention was measured and reported differently in each study. The dose of telehealth services that improve care effectiveness, quality, safety, and cost is still unknown for community dwelling adults experiencing chronic illness. The findings from this systematic review do indicate that longer duration of telehealth services (51 weeks), regardless of modality, produced positive outcomes as opposed to those with shorter durations (37 - 38 weeks) that produced neutral or mixed results. Collecting and reporting data related to clinical workflow such as dose of intervention specific to disease and type of modality is recommended. Rigorous study design including standard measurement at the RCT and Comparative Effectiveness level is still needed.
文摘In this paper two theorems with theoretical and practical significance are given in respect to the preconditioned conjugate gradient method (PCCG). The theorems discuss respectively the qualitative property of the iterative solution and the construction principle of the iterative matrix. The authors put forward a new incompletely LU factorizing technique for non-M-matrix and the method of constructing the iterative matrix. This improved PCCG is used to calculate the ill-conditioned problems and large-scale three-dimensional finite element problems, and simultaneously contrasted with other methods. The abnormal phenomenon is analyzed when PCCG is used to solve the system of ill-conditioned equations, ft is shown that the method proposed in this paper is quite effective in solving the system of large-scale finite element equations and the system of ill-conditioned equations.
文摘The Liaoji Proterozoic rift is an inter-intracontinenatl rift developed from Archean granite-greenstone tectonic regime and contains many important mineral deposits of U, B, magnesite, Pb-Zn, Au, Ag, Co and P. These deposits were formed as the result of late mobilization, transportation and concentfation of the previously enriched ore-forming mate- rials in several ore-bearing formations formed during the rift stage. So the metallogeny of these deposits in the rift shows both inheritance and new generation of the ore-forming materials. In future ore-searching practice, attentions should be paid on the studies of the ore-bearing formations in the rift, on the multiple stages of metallogeny and and on multiple derivations of the ore-forming materials.
文摘A class of nonlinear problems with real parameters is defined. Generally, in this class of problems, when the parametric values are very large, the problems become ill-posed and numerical difficulties are encountered when trying to solve these problems. In this paper, the nonlinear problems are reformulated to overcome the numerical difficulties associated with large parametric values. A novel iterative algorithm, which is suitable for large scale problems and can be easily parallelized, is proposed to solve the reformulated problems. Numerical tests indicate that the proposed algorithm gives stable solutions. Convergence properties of the proposed algorithm are investigated. In the limiting case, when the corresponding constraint is exactly satisfied, the proposed method is equivalent to the standard augmented Lagrangian method.
