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
The computation of the multivariate normal integral over a Complex Subspace is a challenge, especially when the inte-gration region is of a complex nature. Such integrals are met with, for example, in the generalized ...The computation of the multivariate normal integral over a Complex Subspace is a challenge, especially when the inte-gration region is of a complex nature. Such integrals are met with, for example, in the generalized Neyman-Pearson criterion, conditional Bayesian problems of testing many hypotheses and so on. The Monte-Carlo methods could be used for their computation, but at increasing dimensionality of the integral the computation time increases unjustifiedly. Therefore a method of computation of such integrals by series after reduction of dimensionality to one without information loss is offered below. The calculation results are given.展开更多
BACKGROUND Peripherally inserted central catheter(PICC)is the preferred intravenous route for chemotherapy in patients with cancer,but its complications,especially deep vein thrombosis(DVT),are becoming increasingly p...BACKGROUND Peripherally inserted central catheter(PICC)is the preferred intravenous route for chemotherapy in patients with cancer,but its complications,especially deep vein thrombosis(DVT),are becoming increasingly prevalent.Medical staff proficient in intubation and maintenance techniques can reduce complications.The multivariate integration teaching model applies the integration of“teaching learning application”to medical training,which helps shift the prevention of complications from“passive management of complications”to“active construction of risk immunity”,thereby ensuring foundational competency for PICC in patients with cancer.AIM To investigate the efficacy of the multivariate integration teaching model in patients with gastric cancer and concurrent DVT after PICC intubation and analyze its effect on patients’quality of life index(QLI)and satisfaction.METHODS A retrospective analysis of medical records of 100 patients with gastric cancer and PICC treated at Zhejiang Provincial People’s Hospital from May 2019 to November 2020 was conducted.According to the different treatment methods and teaching modes received by medical staff,they were divided into a control group and an experimental group,with 50 cases in each group.The routine clinical teaching model and the multivariate integration teaching model were administered to the medical staff for the control group and the experimental group,respectively,to compare the incidence rates of DVT and other adverse reactions,QLI scores,Karnofsky Performance Scale scores,Mental Status Scale in Non-Psychiatric Settings scores,patient satisfaction,medical staff’s test marks,and satisfaction evaluation of the teaching model.RESULTS Compared with the control group,the experimental group exhibited significantly lower incidence rates of DVT and other adverse reactions and MSSNS scores but significantly higher QLI scores,KPS scores,patient satisfaction,medical staff’s test marks,and their satisfaction evaluations of the teaching model(P<0.05).CONCLUSION In a single-center practice,performing the multivariate integration teaching model for medical staff may effectively improve the patients’QLI and satisfaction and may have certain application value in preventing DVT in patients with gastric cancer and PICC.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.
文摘The computation of the multivariate normal integral over a Complex Subspace is a challenge, especially when the inte-gration region is of a complex nature. Such integrals are met with, for example, in the generalized Neyman-Pearson criterion, conditional Bayesian problems of testing many hypotheses and so on. The Monte-Carlo methods could be used for their computation, but at increasing dimensionality of the integral the computation time increases unjustifiedly. Therefore a method of computation of such integrals by series after reduction of dimensionality to one without information loss is offered below. The calculation results are given.
文摘BACKGROUND Peripherally inserted central catheter(PICC)is the preferred intravenous route for chemotherapy in patients with cancer,but its complications,especially deep vein thrombosis(DVT),are becoming increasingly prevalent.Medical staff proficient in intubation and maintenance techniques can reduce complications.The multivariate integration teaching model applies the integration of“teaching learning application”to medical training,which helps shift the prevention of complications from“passive management of complications”to“active construction of risk immunity”,thereby ensuring foundational competency for PICC in patients with cancer.AIM To investigate the efficacy of the multivariate integration teaching model in patients with gastric cancer and concurrent DVT after PICC intubation and analyze its effect on patients’quality of life index(QLI)and satisfaction.METHODS A retrospective analysis of medical records of 100 patients with gastric cancer and PICC treated at Zhejiang Provincial People’s Hospital from May 2019 to November 2020 was conducted.According to the different treatment methods and teaching modes received by medical staff,they were divided into a control group and an experimental group,with 50 cases in each group.The routine clinical teaching model and the multivariate integration teaching model were administered to the medical staff for the control group and the experimental group,respectively,to compare the incidence rates of DVT and other adverse reactions,QLI scores,Karnofsky Performance Scale scores,Mental Status Scale in Non-Psychiatric Settings scores,patient satisfaction,medical staff’s test marks,and satisfaction evaluation of the teaching model.RESULTS Compared with the control group,the experimental group exhibited significantly lower incidence rates of DVT and other adverse reactions and MSSNS scores but significantly higher QLI scores,KPS scores,patient satisfaction,medical staff’s test marks,and their satisfaction evaluations of the teaching model(P<0.05).CONCLUSION In a single-center practice,performing the multivariate integration teaching model for medical staff may effectively improve the patients’QLI and satisfaction and may have certain application value in preventing DVT in patients with gastric cancer and PICC.
