Community Detection from Location-Tagged Networks

Many real world systems or web services can be represented as a network such as social networks and transportation networks. In the past decade, many algorithms have been developed to detect the communities in a network using connections between nodes. However in many real world networks, the locations of nodes have great influence on the community structure. For example, in a social network, more connections are established between geographically proximate users. The impact of locations on community has not been fully investigated by the research literature. In this paper, we propose a community detection method which takes locations of nodes into consideration. The goal is to detect communities with both geographic proximity and network closeness. We analyze the distribution of the distances between connected and unconnected nodes to measure the influence of location on the network structure on two real location-tagged social networks. We propose a method to determine if a location-based community detection method is suitable for a given network. We propose a new community detection algorithm that pushes the location information into the community detection. We test our proposed method on both synthetic data and real world network datasets. The results show that the communities detected by our method distribute in a smaller area compared with the traditional methods and have the similar or higher tightness on network connections

Gauge choices and Entanglement Entropy of two dimensional lattice gauge fields

In this paper, we explore the question of how different gauge choices in a gauge theory affect the tensor product structure of the Hilbert space in configuration space. In particular, we study the Coulomb gauge and observe that the naive gauge potential degrees of freedom cease to be local operators as soon as we impose the Dirac brackets. We construct new local set of operators and compute the entanglement entropy according to this algebra in $2+1$ dimensions. We find that our proposal would lead to an entanglement entropy that behave very similar to a single scalar degree of freedom if we do not include further centers, but approaches that of a gauge field if we include non-trivial centers. We explore also the situation where the gauge field is Higgsed, and construct a local operator algebra that again requires some deformation. This should give us some insight into interpreting the entanglement entropy in generic gauge theories and perhaps also in gravitational theories.Comment: 38 pages,25 figure

Masses and decay constants of the heavy tensor mesons with QCD sum rules

In this article, we calculate the contributions of the vacuum condensates up to dimension-6 in the operator product expansion, study the masses and decay constants of the heavy tensor mesons $D_2^*(2460)$, $D_{s2}^*(2573)$, $B_2^*(5747)$, $B_{s2}^*(5840)$ using the QCD sum rules. The predicted masses are in excellent agreement with the experimental data, while the ratios of the decay constants $\frac{f_{D_{s2}^*}}{f_{D_{2}^*}}\approx\frac{f_{B_{s2}^*}}{f_{B_{2}^*}}\approx\frac{f_{D_{s}}}{f_{D}}\mid_{\rm exp}$, where the exp denotes the experimental value.Comment: 13 pages, 13 figure

Analysis of the scalar, axialvector, vector, tensor doubly charmed tetraquark states with QCD sum rules

In this article, we construct the axialvector-diquark-axialvector-antidiquark type currents to interpolate the scalar, axialvector, vector, tensor doubly charmed tetraquark states, and study them with QCD sum rules systematically by carrying out the operator product expansion up to the vacuum condensates of dimension 10 in a consistent way, the predicted masses can be confronted to the experimental data in the future. We can search for those doubly charmed tetraquark states in the Okubo-Zweig-Iizuka super-allowed strong decays to the charmed meson pairs.Comment: 23 pages, 29 figures. arXiv admin note: substantial text overlap with arXiv:1708.0454

Analysis of the DDˉ∗KD\bar{D}^*K system with QCD sum rules

In this article, we construct the color singlet-singlet-singlet interpolating current with $I\left(J^P\right)=\frac{3}{2}\left(1^-\right)$ to study the $D\bar{D}^*K$ system through QCD sum rules approach. In calculations, we consider the contributions of the vacuum condensates up to dimension-16 and employ the formula $\mu=\sqrt{M_{X/Y/Z}^{2}-\left(2{\mathbb{M}}_{c}\right)^{2}}$ to choose the optimal energy scale of the QCD spectral density. The numerical result $M_Z=4.71_{-0.11}^{+0.19}\,\rm{GeV}$ indicates that there exists a resonance state $Z$ lying above the $D\bar{D}^*K$ threshold to saturate the QCD sum rules. This resonance state $Z$ may be found by focusing on the channel $J/\psi \pi K$ of the decay $B\longrightarrow J/\psi \pi \pi K$ in the future.Comment: 9 pages, 4 figure