Analysis of hidden-bottom bb\bar{b}\bar{b} states

Motivated by the searching for $bb\bar{b}\bar{b}$ states at LHC recently, we calculate the ground-state energies of $bb\bar{b}\bar{b}$ states with quantum numbers $IJ^P=00^+,01^+,02^+$ in a nonrelativistic chiral quark model using the Gaussian expansion method. In our calculations, two structures, meson-meson and diquark-antidiquark, and their coupling, along with all possible color configurations are considered. It is expected that the studies shall be helpful for the experimental searching of fully-heavy exotic tetraquark states.Comment: 7 pages, 1 figur

Is the exotic X(5568)X(5568) a bound state?

Stimulated by the recent observation of the exotic $X(5568)$ state by D0 Collaboration, we study the four-quark system $us\bar{b}\bar{d}$ with quantum numbers $J^P=0^+$ in the framework of chiral quark model. Two structures, diquark-antidiquark and meson-meson, with all possible color configurations are investigated by using Gaussian expansion method. The results show that energies of the tetraquark states with diquark-antiquark structure are too high to the candidate of $X(5568)$, and no molecular structure can be formed in our calculations. The calculation is also extended to the four-quark system $us\bar{c}\bar{d}$ and the same results as that of $us\bar{b}\bar{d}$ are obtained.Comment: 5 pages, 1 figur

Star-factors of tournaments

Let S_m denote the m-vertex simple digraph formed by m-1 edges with a common tail. Let f(m) denote the minimum n such that every n-vertex tournament has a spanning subgraph consisting of n/m disjoint copies of S_m. We prove that m lg m - m lg lg m <= f(m) <= 4m^2 - 6m for sufficiently large m.Comment: 5 pages, 1 figur

MST-Based Semi-Supervised Clustering Using M-Labeled Objects

Most of the existing semi-supervised clustering algorithms depend on pairwise constraints, and they usually use lots of priori knowledge to improve their accuracies. In this paper, we use another semi-supervised method called label propagation to help detect clusters. We propose two new semi-supervised algorithms named K-SSMST and M-SSMST. Both of them aim to discover clusters of diverse density and arbitrary shape. Based on Minimum Spanning Tree's algorithm variant, K-SSMST can automatically find natural clusters in a dataset by using K labeled data objects where K is the number of clusters. M-SSMST can detect new clusters with insufficient semi-supervised information. Our algorithms have been tested on various artificial and UCI datasets. The results demonstrate that the algorithm's accuracy is better than other supervised and semi-supervised approaches