The Owen’s T function is presented in four new ways, one of them as a series similar to the Euler’s arctangent series divided by 2π, which is its majorant series. All possibilities enable numerically stable ...The Owen’s T function is presented in four new ways, one of them as a series similar to the Euler’s arctangent series divided by 2π, which is its majorant series. All possibilities enable numerically stable and fast convergent computation of the bivariate normal integral with simple recursion. When tested computation on a random sample of one million parameter triplets with uniformly distributed components and using double precision arithmetic, the maximum absolute error was 3.45 × 10<sup>-</sup><sup>16</sup>. In additional testing, focusing on cases with correlation coefficients close to one in absolute value, when the computation may be very sensitive to small rounding errors, the accuracy was retained. In rare potentially critical cases, a simple adjustment to the computation procedure was performed—one potentially critical computation was replaced with two equivalent non-critical ones. All new series are suitable for vector and high-precision computation, assuming they are supplemented with appropriate efficient and accurate computation of the arctangent and standard normal cumulative distribution functions. They are implemented by the R package Phi2rho, available on CRAN. Its functions allow vector arguments and are ready to work with the Rmpfr package, which enables the use of arbitrary precision instead of double precision numbers. A special test with up to 1024-bit precision computation is also presented.展开更多
Large cities suffer from traffic congestion,particularly at intersections,due to a large number of vehicles,which leads to the loss of time by increasing carbon emissions,including fuel consumption.Therefore,the need ...Large cities suffer from traffic congestion,particularly at intersections,due to a large number of vehicles,which leads to the loss of time by increasing carbon emissions,including fuel consumption.Therefore,the need for optimising the flow of vehicles at different intersections and reducing the waiting time is a critical challenge.Conventional traffic lights have been used to control traffic flow at different intersections and have been improved to become more efficient by using different algorithms,sensors and cameras.However,they also face some challenges,such as high-cost installation,operation,and maintenance issues.This paper develops a new system based on the Virtual Traffic Light(VTL)technology to improve traffic flow at different intersections and reduce the encountered loss of time and vehicles’travel time.Additionally,it reduces the costs of installation,maintenance and operation over various conventional traffic light systems.Consequently,the system proposes algorithms for traffic scheduling and lane identification by using vehicle ID,priority and time of arrival.To evaluate the system,four scenarios were presented where each scenario uses a different number of vehicles consisting of three types(emergency vehicles,public buses and private vehicles),each given a different priority.The proposed system is evaluated by integrating two simulators,namely,(OMNeT++)and(SUMO),and two frameworks,namely,(VEINS)and(INET)to prepare an appropriate working environment.the results prove that an improvement in the average travel time for several vehicles reaches 44.43%–49.76%compared with conventional traffic lights.Further,it is proven from the obtained results that the average waiting time for emergency vehicles is enhanced by 96.63%–97.63%,while the average waiting time for public buses is improved by 94.81%–97.23%.On the other hand,the waiting time for private vehicles‘improved by 87.14%to 89.71%’.展开更多
The Shapiro-Wilk test (SWT) for normality is well known for its competitive power against numerous one-dimensional alternatives. Several extensions of the SWT to multi-dimensions have also been proposed. This paper in...The Shapiro-Wilk test (SWT) for normality is well known for its competitive power against numerous one-dimensional alternatives. Several extensions of the SWT to multi-dimensions have also been proposed. This paper investigates the relative strength and rotational robustness of some SWT-based normality tests. In particular, the Royston’s H-test and the SWT-based test proposed by Villase?or-Alva and González-Estrada have R packages available for testing multivariate normality;thus they are user friendly but lack of rotational robustness compared to the test proposed by Fattorini. Numerical power comparison is provided for illustration along with some practical guidelines on the choice of these SWT-type tests in practice.展开更多
In this paper, we study the gravitational quasi-normal modes（QNMs） for a static R^2 black hole（BH） in Anti-de Sitter（AdS） spacetime. The corresponding master equation of odd parity is derived and the QNMs are ev...In this paper, we study the gravitational quasi-normal modes（QNMs） for a static R^2 black hole（BH） in Anti-de Sitter（AdS） spacetime. The corresponding master equation of odd parity is derived and the QNMs are evaluated by the Horowitz and Hubeny method. Meanwhile the stability of such BH is also discussed through the temporal evolution of the perturbation field. Here we mainly consider the coefficient λ, which is related to the radius of AdS black hole, on the QNMs of the R^2 AdS BH. The results show that the Re（ω） and ｜Im（ω）｜ of the QNMs increase together as ｜λ｜ increases for a given angular momentum number l. That indicates with a larger value of ｜λ｜ the corresponding R^2 AdS BH returns to stable much more quickly. The dynamic evolution of the perturbation field is consistent with the results derived by the Horowitz and Hubeny method. Since in the conformal field theory the QNMs can reflect its approach to equilibrium, so our related results could be referential to studies of the AdS/CFT conjecture. The relationship between λ and the properties of the static R^2 BH might be helpful for the development of R^2 gravitational theory.展开更多
文摘The Owen’s T function is presented in four new ways, one of them as a series similar to the Euler’s arctangent series divided by 2π, which is its majorant series. All possibilities enable numerically stable and fast convergent computation of the bivariate normal integral with simple recursion. When tested computation on a random sample of one million parameter triplets with uniformly distributed components and using double precision arithmetic, the maximum absolute error was 3.45 × 10<sup>-</sup><sup>16</sup>. In additional testing, focusing on cases with correlation coefficients close to one in absolute value, when the computation may be very sensitive to small rounding errors, the accuracy was retained. In rare potentially critical cases, a simple adjustment to the computation procedure was performed—one potentially critical computation was replaced with two equivalent non-critical ones. All new series are suitable for vector and high-precision computation, assuming they are supplemented with appropriate efficient and accurate computation of the arctangent and standard normal cumulative distribution functions. They are implemented by the R package Phi2rho, available on CRAN. Its functions allow vector arguments and are ready to work with the Rmpfr package, which enables the use of arbitrary precision instead of double precision numbers. A special test with up to 1024-bit precision computation is also presented.
文摘Large cities suffer from traffic congestion,particularly at intersections,due to a large number of vehicles,which leads to the loss of time by increasing carbon emissions,including fuel consumption.Therefore,the need for optimising the flow of vehicles at different intersections and reducing the waiting time is a critical challenge.Conventional traffic lights have been used to control traffic flow at different intersections and have been improved to become more efficient by using different algorithms,sensors and cameras.However,they also face some challenges,such as high-cost installation,operation,and maintenance issues.This paper develops a new system based on the Virtual Traffic Light(VTL)technology to improve traffic flow at different intersections and reduce the encountered loss of time and vehicles’travel time.Additionally,it reduces the costs of installation,maintenance and operation over various conventional traffic light systems.Consequently,the system proposes algorithms for traffic scheduling and lane identification by using vehicle ID,priority and time of arrival.To evaluate the system,four scenarios were presented where each scenario uses a different number of vehicles consisting of three types(emergency vehicles,public buses and private vehicles),each given a different priority.The proposed system is evaluated by integrating two simulators,namely,(OMNeT++)and(SUMO),and two frameworks,namely,(VEINS)and(INET)to prepare an appropriate working environment.the results prove that an improvement in the average travel time for several vehicles reaches 44.43%–49.76%compared with conventional traffic lights.Further,it is proven from the obtained results that the average waiting time for emergency vehicles is enhanced by 96.63%–97.63%,while the average waiting time for public buses is improved by 94.81%–97.23%.On the other hand,the waiting time for private vehicles‘improved by 87.14%to 89.71%’.
文摘The Shapiro-Wilk test (SWT) for normality is well known for its competitive power against numerous one-dimensional alternatives. Several extensions of the SWT to multi-dimensions have also been proposed. This paper investigates the relative strength and rotational robustness of some SWT-based normality tests. In particular, the Royston’s H-test and the SWT-based test proposed by Villase?or-Alva and González-Estrada have R packages available for testing multivariate normality;thus they are user friendly but lack of rotational robustness compared to the test proposed by Fattorini. Numerical power comparison is provided for illustration along with some practical guidelines on the choice of these SWT-type tests in practice.
基金supported by the National Natural Science Foundation of China(Grant Nos.11205254,11178018,11375279,and 11605015)the Fundamental Research Funds for the Central Universities,China(Grant Nos.106112016CDJXY300002 and CDJRC10300003)+1 种基金the Chinese State Scholarship Fund,FAPESP(Grant No.2012/08934-0)the Natural Science Foundation Project of CQ CSTC(Grant No.2011BB0052)
文摘In this paper, we study the gravitational quasi-normal modes（QNMs） for a static R^2 black hole（BH） in Anti-de Sitter（AdS） spacetime. The corresponding master equation of odd parity is derived and the QNMs are evaluated by the Horowitz and Hubeny method. Meanwhile the stability of such BH is also discussed through the temporal evolution of the perturbation field. Here we mainly consider the coefficient λ, which is related to the radius of AdS black hole, on the QNMs of the R^2 AdS BH. The results show that the Re（ω） and ｜Im（ω）｜ of the QNMs increase together as ｜λ｜ increases for a given angular momentum number l. That indicates with a larger value of ｜λ｜ the corresponding R^2 AdS BH returns to stable much more quickly. The dynamic evolution of the perturbation field is consistent with the results derived by the Horowitz and Hubeny method. Since in the conformal field theory the QNMs can reflect its approach to equilibrium, so our related results could be referential to studies of the AdS/CFT conjecture. The relationship between λ and the properties of the static R^2 BH might be helpful for the development of R^2 gravitational theory.
