Detecting Communities in Networks by Merging Cliques

Many algorithms have been proposed for detecting disjoint communities (relatively densely connected subgraphs) in networks. One popular technique is to optimize modularity, a measure of the quality of a partition in terms of the number of intracommunity and intercommunity edges. Greedy approximate algorithms for maximizing modularity can be very fast and effective. We propose a new algorithm that starts by detecting disjoint cliques and then merges these to optimize modularity. We show that this performs better than other similar algorithms in terms of both modularity and execution speed.Comment: 5 pages, 7 figure

Finding missing edges in networks based on their community structure

Many edge prediction methods have been proposed, based on various local or global properties of the structure of an incomplete network. Community structure is another significant feature of networks: Vertices in a community are more densely connected than average. It is often true that vertices in the same community have "similar" properties, which suggests that missing edges are more likely to be found within communities than elsewhere. We use this insight to propose a strategy for edge prediction that combines existing edge prediction methods with community detection. We show that this method gives better prediction accuracy than existing edge prediction methods alone.Comment: 7 pages, 6 figure

Identifying Communities and Key Vertices by Reconstructing Networks from Samples

Sampling techniques such as Respondent-Driven Sampling (RDS) are widely used in epidemiology to sample "hidden" populations, such that properties of the network can be deduced from the sample. We consider how similar techniques can be designed that allow the discovery of the structure, especially the community structure, of networks. Our method involves collecting samples of a network by random walks and reconstructing the network by probabilistically coalescing vertices, using vertex attributes to determine the probabilities. Even though our method can only approximately reconstruct a part of the original network, it can recover its community structure relatively well. Moreover, it can find the key vertices which, when immunized, can effectively reduce the spread of an infection through the original network.Comment: 15 pages, 17 figure

Generalized Kitaev Spin Liquid model and Emergent Twist Defect

The Kitaev spin liquid model on honeycomb lattice offers an intriguing feature that encapsulates both Abelian and non-Abelian anyons. Recent studies suggest that the comprehensive phase diagram of possible generalized Kitaev model largely depends on the specific details of the discrete lattice, which somewhat deviates from the traditional understanding of "topological" phases. In this paper, we propose an adapted version of the Kitaev spin liquid model on arbitrary planar lattices. Our revised model recovers the toric code model under certain parameter selections within the Hamiltonian terms. Our research indicates that changes in parameters can initiate the emergence of holes, domain walls, or twist defects. Notably, the twist defect, which presents as a lattice dislocation defect, exhibits non-Abelian braiding statistics upon tuning the coefficients of the Hamiltonian on a standard translationally invariant lattice. Additionally, we illustrate that the creation, movement, and fusion of these defects can be accomplished through natural time evolution by linearly interpolating the static Hamiltonian. These defects demonstrate the Ising anyon fusion rule as anticipated. Our findings hint at possible implementation in actual physical materials owing to a more realistically achievable two-body interaction

Homologous illegitimate random integration of foreign DNA into the X chromosome of a transgenic mouse line

<p>Abstract</p> <p>Background</p> <p>It is not clear how foreign DNA molecules insert into the host genome. Recently, we have produced transgenic mice to investigate the role of the <it>fad2 </it>gene in the conversion of oleic acid to linoleic acid. Here we describe an integration mechanism of fad2 transgene by homologous illegitimate random integration.</p> <p>Results</p> <p>We confirmed that one <it>fad2 </it>line had a sole integration site on the X chromosome according to the inheritance patterns. Mapping of insertion sequences with thermal asymmetric interlaced and conventional PCR revealed that the foreign DNA was inserted into the XC1 region of the X chromosome by a homologous illegitimate replacement of an entire 45,556-bp endogenous genomic region, including the ovarian granulosa cell tumourigenesis-4 allele. For 5' and 3' junction sequences, there were very short (3-7 bp) common sequences in the AT-rich domains, which may mediate the recognition of the homologous arms between the transgene and the host genome. In addition, analysis of gene transcription indicated that the transgene was expressed in all tested <it>fad2 </it>tissues and that its transcription level in homozygous female tissues was about twice as high as in the heterozygous female (p < 0.05).</p> <p>Conclusions</p> <p>Taken together, the results indicated that the foreign <it>fad2 </it>behaved like an X-linked gene and that foreign DNA molecules were inserted into the eukaryotic genome through a homologous illegitimate random integration.</p