Yen- Chang

On the Mass-Period Distributions and Correlations of Extrasolar Planets

In addition to fitting the data of 233 extra-solar planets with power laws, we construct a correlated mass-period distribution function of extrasolar planets, as the first time in this field. The algorithm to generate a pair of positively correlated beta-distributed random variables is introduced and used for the construction of correlated distribution functions. We investigate the mass-period correlations of extrasolar planets both in the linear and logarithm spaces, determine the confidence intervals of the correlation coefficients, and confirm that there is a positive mass-period correlation for the extrasolar planets. In addition to the paucity of massive close-in planets, which makes the main contribution on this correlation, there are other fine structures for the data in the mass-period plane.

ON THE FUNDAMENTAL MASS-PERIOD FUNCTIONS OF EXTRASOLAR PLANETS

Employing a catalog of 175 extrasolar planets (exoplanets) detected by the Doppler-shift method, we constructed the independent and coupled mass-period functions. It is the first time in this field that the selection effect is considered in the coupled mass-period functions. Our results are consistent with those of Tabachnik and Tremaine in 2002, with the major difference that we obtain a flatter mass function but a steeper period function. Moreover, our coupled mass-period functions show that about 2.5% of stars would have a planet with mass between Earth Mass and Neptune Mass, and about 3% of stars would have a planet with mass between Neptune Mass and Jupiter Mass.

CONSTRUCTION OF COUPLED PERIOD-MASS FUNCTIONS IN EXTRASOLAR PLANETS THROUGH A NONPARAMETRIC APPROACH

Using the period and mass data of 279 extrasolar planets, we have constructed a coupled period-mass function through a nonparametric approach. This analytic expression of the coupled period-mass function has been obtained for the first time in this field. Moreover, due to a moderate period-mass correlation, the shapes of mass/period functions vary as a function of period/mass. These results of mass and period functions give way to two important implications: (1) the deficit of massive close-in planets is confirmed, and (2) the more massive planets have larger ranges of possible semimajor axes. These interesting statistical results will provide important clues to the theories of planetary formation.

Weight selection in W-K-means algorithm with an application in color image segmentation

In this paper, a weight selection procedure in the W-k-means algorithm is proposed based on the statistical variation viewpoint. This approach can solve the W-k-means algorithms problem that the clustering quality is greatly affected by the initial value of weight. After the statistics of data, the weights of data are designed to provide more information for the character of W-k-means algorithm so as to improve the precision. Furthermore, the corresponding computational complexity is analyzed as well. We compare the clustering results of the W-k-means algorithm with the different initialization methods. Results from color image segmentation illustrate that the proposed procedure produces better segmentation than the random initialization according to Liu and Yangs (1994) evaluation function.

Fuzzy classification maximum likelihood algorithms for mixed-Weibull distributions

In this paper we propose an efficient algorithm based on Yang’s (Fuzzy Sets Syst 57:365–337, 1993) concept, namely the fuzzy classification maximum likelihood (FCML) algorithm, to estimate the mixed-Weibull parameters. Compared with EM and Jiang and Murthy (IEEE Trans Reliab 44:477–488, 1995) methods, the proposed FCML algorithm presents better accuracy. Thus, we recommend FCML as another acceptable method for estimating the mixed-Weibull parameters.

A modified fuzzy c-means algorithm for differentiation in MRI of ophthalmology

In this paper we propose an algorithm, called the modified suppressed fuzzy c-means (MS-FCM), that simultaneously performs clustering and parameter selection for the suppressed FCM (S-FCM) proposed by Fan et al. [2]. Numerical examples illustrate the effectiveness of the proposed MS-FCM algorithm. Finally, the S-FCM and MS-FCM algorithms are applied in the segmentation of the magnetic resonance image (MRI) of an ophthalmic patient. In our comparisons of S-FCM, MS-FCM and alternative FCM (AFCM) proposed by Wu and Yang [14] for these MRI segmentation results, we find that the MS-FCM provides better detection of abnormal tissue than S-FCM and AFCM when based on a window selection. Overall, the MS-FCM clustering algorithm is more efficient and is strongly recommended as an MRI segmentation technique.

Optimization of process parameters using weighted convex loss functions

Setting the optimal process parameters under certain criterion is among the most important factor to determine a products profit. In this study, we generalize Taguchi quality model to more general process scenario, which consider multiple input and output quality variables simultaneously. Using the weighted convex loss function, we discuss the optimization of process parameters for Taguchi quality model and a trade-off problem as well. The working requirements for optimization are presented and the examples to illustrate our result are demonstrated.

Software release policies on a shot-noise process model

An important software reliability application model involves determining the software release time. In this paper, we treat the optimal release time as an open-loop-feedback-optimal (OLFO) control problem. The underlying model is based on a shot-noise process model. A cost model for removing software system errors and the cost risk due to software failure is used.

A Reliability-Constrained Software Release Policy Using A Non-Gaussian Kalman Filter Model

Software reliability is one of important characteristics of software quality, and software release time is an important application of the software reliability model. In this article we consider a software release policy based on a Gamma-Gamma-type Kalman filter as well as the risk cost due to software failures and the cost for debugging in software systems. Under this model, the optimal release time that minimizes the expected cost in every test-debugging stage subject to a reliability constraint is discussed. An example to illustrate the framework of our model is given.

Comparison between method of moments and entropy regularization algorithm applied to parameter estimation for mixed-Weibull distribution

Mixed-Weibull distribution has been used to model a wide range of failure data sets, and in many practical situations the number of components in a mixture model is unknown. Thus, the parameter estimation of a mixed-Weibull distribution is considered and the important issue of how to determine the number of components is discussed. Two approaches are proposed to solve this problem. One is the method of moments and the other is a regularization type of fuzzy clustering algorithm. Finally, numerical examples and two real data sets are given to illustrate the features of the proposed approaches.