Studies on drug combinations are becoming more and more popular in the past few decades, with the development of computer and algorithms. One of the most common methods in optimizing drug combinations is regression of...Studies on drug combinations are becoming more and more popular in the past few decades, with the development of computer and algorithms. One of the most common methods in optimizing drug combinations is regression of a polynomial model based on certain number of experimental observations. In this paper, we study how to determine the degree of polynomials in different circumstances of drug combination optimization. Using cross-validation, we have found that in most cases, a high degree results in failures of accurate prediction, named overfitting. An anti-noise test has also revealed that polynomial model with high degree tends to be less resistant to random errors in the observations.展开更多
This paper revisits the Space-Time Gradient(STG) method which was developed for efficient analysis of unsteady flows due to rotor–stator interaction and presents the method from an alternative time-clocking perspecti...This paper revisits the Space-Time Gradient(STG) method which was developed for efficient analysis of unsteady flows due to rotor–stator interaction and presents the method from an alternative time-clocking perspective. The STG method requires reordering of blade passages according to their relative clocking positions with respect to blades of an adjacent blade row. As the space-clocking is linked to an equivalent time-clocking, the passage reordering can be performed according to the alternative time-clocking. With the time-clocking perspective, unsteady flow solutions from different passages of the same blade row are mapped to flow solutions of the same passage at different time instants or phase angles. Accordingly, the time derivative of the unsteady flow equation is discretized in time directly, which is more natural than transforming the time derivative to a spatial one as with the original STG method. To improve the solution accuracy, a ninth order difference scheme has been investigated for discretizing the time derivative. To achieve a stable solution for the high order scheme, the implicit solution method of Lower-Upper Symmetric GaussSeidel/Gauss-Seidel(LU-SGS/GS) has been employed. The NASA Stage 35 and its blade-countreduced variant are used to demonstrate the validity of the time-clocking based passage reordering and the advantages of the high order difference scheme for the STG method. Results from an existing harmonic balance flow solver are also provided to contrast the two methods in terms of solution stability and computational cost.展开更多
文摘Studies on drug combinations are becoming more and more popular in the past few decades, with the development of computer and algorithms. One of the most common methods in optimizing drug combinations is regression of a polynomial model based on certain number of experimental observations. In this paper, we study how to determine the degree of polynomials in different circumstances of drug combination optimization. Using cross-validation, we have found that in most cases, a high degree results in failures of accurate prediction, named overfitting. An anti-noise test has also revealed that polynomial model with high degree tends to be less resistant to random errors in the observations.
基金co-supported by the National Natural Science Foundation of China(No.51976172)the National Science and Technology Major Project of China(No.2017-Ⅱ-0009-0023)。
文摘This paper revisits the Space-Time Gradient(STG) method which was developed for efficient analysis of unsteady flows due to rotor–stator interaction and presents the method from an alternative time-clocking perspective. The STG method requires reordering of blade passages according to their relative clocking positions with respect to blades of an adjacent blade row. As the space-clocking is linked to an equivalent time-clocking, the passage reordering can be performed according to the alternative time-clocking. With the time-clocking perspective, unsteady flow solutions from different passages of the same blade row are mapped to flow solutions of the same passage at different time instants or phase angles. Accordingly, the time derivative of the unsteady flow equation is discretized in time directly, which is more natural than transforming the time derivative to a spatial one as with the original STG method. To improve the solution accuracy, a ninth order difference scheme has been investigated for discretizing the time derivative. To achieve a stable solution for the high order scheme, the implicit solution method of Lower-Upper Symmetric GaussSeidel/Gauss-Seidel(LU-SGS/GS) has been employed. The NASA Stage 35 and its blade-countreduced variant are used to demonstrate the validity of the time-clocking based passage reordering and the advantages of the high order difference scheme for the STG method. Results from an existing harmonic balance flow solver are also provided to contrast the two methods in terms of solution stability and computational cost.
