Antithetic Power Transformed Random Variables in Computer Simulations: An Error Correction Mechanism

A traditional method of Monte Carlo computer simulation is to obtain uniformly distributed random numbers on the interval from zero to one from a linear congruential generator (LCG) or other methods. Random variates can then be obtained by the inverse transformation technique applied to random numbers. The random variates can then be used as input to a computer simulation. A response variable is obtained from the simulation results. The response variable may be biased for various reasons. One reason may be the presence of small traces of serial correlation in the random numbers. The purpose of this paper is to introduce an alternative method of response variable acquisition by a power transformation applied to the response variable. The power transformation produces a new variable that is negatively correlated with the response variable. The response variable is then regressed on its power transformation to convert the units of the power transformed variable back to those of the original response variable. A weighted combination of these two variables gives the final estimate. The combined estimate is shown to have negligible bias. The correlations of various antithetic variates obtained from the power transformation are derived and illustrated to provide insights for this research and for future research into this method.

A Study on the Principle of Chinese Antithetical Couplet Translation

As the quintessence of Chinese culture,Chinese antithetical couplets enjoy a long history and have unique styles.Due to the linguistic and cultural elements,it is difficult to translate Chinese antithetical couplet.This paper discusses the literal and free translation principle in Chinese antithetical couplet translation.

Reservoir controlling differences between consequent faults and antithetic faults in slope area outside of source: A case study of the south-central Wenan slope of Jizhong Depression, Bohai Bay Basin, East China

The control effects of different occurrence faults on oil and gas accumulation and distribution in the outer slope area of oil and gas reservoirs were studied taking the south-central Wen’an slope of the Jizhong depression in the Bohai Bay Basin as an example.Based on 3D seismic data and the distribution of oil and water,the controlling differences between consequent fault and antithetic fault were analyzed and compared from the formation and evolution rule of faults and the formation mechanism of fault traps,including development positions of the consequent fault traps and antithetic fault traps,oil and gas distribution horizon adjusted by fault and formation period of fault traps.The differences between consequent faults and antithetic faults in controlling reservoirs have three main aspects:(1)Consequent fault traps and antithetic fault traps are in different positions,the consequent fault traps are at the segmented growing point in the hanging wall of"hard-linkage"faults,while the antithetic fault traps are developed in the position with the largest throw in the footwall because of tilting action;(2)The two kinds of faults result in different oil and gas distribution vertically,oil and gas adjusted by consequent faults is distributed in a single layer or multi-layers,while oil and gas adjusted by antithetic faults occur in single layers;(3)The two kinds of fault traps are formed in different periods,the consequent fault traps are formed at the time when the related faults enter the stage of"hard-linkage",while the antithetic fault traps are formed at the beginning of the fault active period.

Destruction or Survival: Antithetical Characters in The Bluest Eye and Sula

In Toni Morrison’s novel The Bluest Eye and Sula, there are two pairs of antithetical characters, one is Pecola and Claudia, the other is Sula and Nel. Due to the lack of redeeming intelligence, family emotional support and community help, the protagonists Pecola and Sula gradually sink into destruction. In contrast, the less important characters Claudia and Nel manage to survive and gain some spiritual growth.

General Theory of Antithetic Time Series

A generalized antithetic time series theory for exponentially derived antithetic random variables is developed. The correlation function between a generalized gamma distributed random variable and its pth exponent is derived. We prove that the correlation approaches minus one as the exponent approaches zero from the left and the shape parameter approaches infinity.