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.Comment: to be published in AJ, tentatively in December 200

A robust clustering procedure for fuzzy data

AbstractIn this paper we propose a robust clustering method for handling LR-type fuzzy numbers. The proposed method based on similarity measures is not necessary to specify the cluster number and initials. Several numerical examples demonstrate the effectiveness of the proposed robust clustering method, especially robust to outliers, different cluster shapes and initial guess. We then apply this algorithm to three real data sets. These are Taiwanese tea, student data and patient blood pressure data sets. Because tea evaluation comes under an expert subjective judgment for Taiwanese tea, the quality levels are ambiguity and imprecision inherent to human perception. Thus, LR-type fuzzy numbers are used to describe these quality levels. The proposed robust clustering method successfully establishes a performance evaluation system to help consumers better understand and choose Taiwanese tea. Similarly, LR-type fuzzy numbers are also used to describe data types for student and patient blood pressure data. The proposed method actually presents good clustering results for these real data sets

Topological Entropy for Shifts of Finite Type Over Z\mathbb{Z} and Tree

We study the topological entropy of hom tree-shifts and show that, although the topological entropy is not conjugacy invariant for tree-shifts in general, it remains invariant for hom tree higher block shifts. In doi:10.1016/j.tcs.2018.05.034 and doi:10.3934/dcds.2020186, Petersen and Salama demonstrated the existence of topological entropy for tree-shifts and $h(\mathcal{T}_X) \geq h(X)$, where $\mathcal{T}_X$ is the hom tree-shift derived from $X$. We characterize a necessary and sufficient condition when the equality holds for the case where $X$ is a shift of finite type. In addition, two novel phenomena have been revealed for tree-shifts. There is a gap in the set of topological entropy of hom tree-shifts of finite type, which makes such a set not dense. Last but not least, the topological entropy of a reducible hom tree-shift of finite type is equal to or larger than that of its maximal irreducible component

Image Tamper Detection and Recovery by Intersecting Signatures

In this paper, we propose an exact image authentication scheme that can, in the best case, detect image tampering with the accuracy of one pixel. This method is based on constructing blocks in the image in such a manner that they intersect with one another in different directions. Such a technique is very useful to identify whether an individual image pixel has been tampered with. Moreover, the tampered region can be well recovered with the embedded recover data