The authors study the tractability and strong tractability of a multivariate integration problem in the worst case setting for weighted 1-periodic continuous functions spaces of d coordinates with absolutely convergen...The authors study the tractability and strong tractability of a multivariate integration problem in the worst case setting for weighted 1-periodic continuous functions spaces of d coordinates with absolutely convergent Fourier series. The authors reduce the initial error by a factor ε for functions from the unit ball of the weighted periodic continuous functions spaces. Tractability is the minimal number of function samples required to solve the problem in polynomial in ε^-1 and d, and the strong tractability is the presence of only a polynomial dependence in ε^-1. This problem has been recently studied for quasi-Monte Carlo quadrature rules, quadrature rules with non-negative coefficients, and rules for which all quadrature weights are arbitrary for weighted Korobov spaces of smooth periodic functions of d variables. The authors show that the tractability and strong tractability of a multivariate integration problem in worst case setting hold for the weighted periodic continuous functions spaces with absolutely convergent Fourier series under the same assumptions as in Ref,[14] on the weights of the Korobov space for quasi-Monte Carlo rules and rules for which all quadrature weights are non-negative. The arguments are not constructive.展开更多
In order to classify the minimal hepatic encephalopathy （MHE） patients from healthy controls, the independent component analysis （ICA） is used to generate the default mode network （DMN） from resting-state functi...In order to classify the minimal hepatic encephalopathy （MHE） patients from healthy controls, the independent component analysis （ICA） is used to generate the default mode network （DMN） from resting-state functional magnetic resonance imaging （fMRI）. Then a Bayesian voxel- wised method, graphical-model-based multivariate analysis （GAMMA）, is used to explore the associations between abnormal functional integration within DMN and clinical variable. Without any prior knowledge, five machine learning methods, namely, support vector machines （SVMs）, classification and regression trees （ CART ）, logistic regression, the Bayesian network, and C4.5, are applied to the classification. The functional integration patterns were alternative within DMN, which have the power to predict MHE with an accuracy of 98%. The GAMMA method generating functional integration patterns within DMN can become a simple, objective, and common imaging biomarker for detecting MIIE and can serve as a supplement to the existing diagnostic methods.展开更多
基金Project supported by the National Natural Science Foundation of China(10671019)Research Fund for the Doctoral Program Higher Education(20050027007)Beijing Educational Committee(2002Kj112)
文摘The authors study the tractability and strong tractability of a multivariate integration problem in the worst case setting for weighted 1-periodic continuous functions spaces of d coordinates with absolutely convergent Fourier series. The authors reduce the initial error by a factor ε for functions from the unit ball of the weighted periodic continuous functions spaces. Tractability is the minimal number of function samples required to solve the problem in polynomial in ε^-1 and d, and the strong tractability is the presence of only a polynomial dependence in ε^-1. This problem has been recently studied for quasi-Monte Carlo quadrature rules, quadrature rules with non-negative coefficients, and rules for which all quadrature weights are arbitrary for weighted Korobov spaces of smooth periodic functions of d variables. The authors show that the tractability and strong tractability of a multivariate integration problem in worst case setting hold for the weighted periodic continuous functions spaces with absolutely convergent Fourier series under the same assumptions as in Ref,[14] on the weights of the Korobov space for quasi-Monte Carlo rules and rules for which all quadrature weights are non-negative. The arguments are not constructive.
基金The National Natural Science Foundation of China(No.8123003481271739+2 种基金81501453)the Special Program of Medical Science of Jiangsu Province(No.BL2013029)the Natural Science Foundation of Jiangsu Province(No.BK20141342)
文摘In order to classify the minimal hepatic encephalopathy （MHE） patients from healthy controls, the independent component analysis （ICA） is used to generate the default mode network （DMN） from resting-state functional magnetic resonance imaging （fMRI）. Then a Bayesian voxel- wised method, graphical-model-based multivariate analysis （GAMMA）, is used to explore the associations between abnormal functional integration within DMN and clinical variable. Without any prior knowledge, five machine learning methods, namely, support vector machines （SVMs）, classification and regression trees （ CART ）, logistic regression, the Bayesian network, and C4.5, are applied to the classification. The functional integration patterns were alternative within DMN, which have the power to predict MHE with an accuracy of 98%. The GAMMA method generating functional integration patterns within DMN can become a simple, objective, and common imaging biomarker for detecting MIIE and can serve as a supplement to the existing diagnostic methods.
