Community detection is one of the most important problems in the field of complex networks in recent years. The majority of present algorithms only find disjoint communities, however, community often overlap to some extent in many real-world networks. In this paper, an improved multi-objective quantum-behaved particle swarm optimization (IMOQPSO) based on spectral-clustering is proposed to detect the overlapping community structure in complex networks. Firstly, the line graph of the graph modeling the network is formed, and a spectral method is employed to extract the spectral information of the line graph. Secondly, IMOQPSO is employed to solve the multi-objective optimization problem so as to resolve the separated community structure in the line graph which corresponding to the overlapping community structure in the graph presenting the network. Finally, a fine-tuning strategy is adopted to improve the accuracy of community detection. The experiments on both synthetic and real-world networks demonstrate our method achieves cover results which fit the real situation in an even better fashion.

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The human brain automatically extracts regularities embedded in environmental auditory events. This study investigated the extraction of abstract patterns by measuring mismatch negativity (MMN). Participants watched a silent subtitled movie and ignored a sequence of auditory events comprising frequent standards and rare deviants presented in the background. Tone triplets with varying pitch (first-order property) served as the auditory events. The pitch intervals (interval 1 and interval 2) between the tones in a triplet and the ratio of interval 1 and 2 were considered second- and third-order properties, respectively. Both second- and third-order properties of the standards were kept constant in the mixed patterns block, while only the third-order property was kept constant in the ratio pattern block. Four sets of tone triplets violating the interval and ratio patterns with different deviance levels were presented as deviants in both blocks, and subtracted with physically identical stimuli in a control block to isolate the MMNs. Interval and ratio pattern deviants elicited MMNs in the mixed patterns block while only ratio pattern deviants elicited MMNs in the ratio pattern block. Larger MMNs were elicited by large deviants as compared to small deviants. These results suggest that the change detection system is sensitive to the violation of both second- and third-order abstract patterns. In addition to regularities in the abstract properties of auditory events, regularities in the relationships between abstract properties can also be extracted. This ability plays an important role in music and language perception.

Current theories of automatic or preattentive change detection suggest a regularity or prediction violation mechanism involving functional connectivity between the inferior frontal cortex (IFC) and the superior temporal cortex (STC). By disrupting the IFC function with transcranial magnetic stimulation (TMS) and recording the later STC mismatch response with event‐related optical signal (EROS), previous study demonstrated a causal IFC‐to‐STC functional connection in detecting a pitch or physical change. However, physical change detection can be achieved by memory comparison of the physical features and may not necessarily involve regularity/rule extraction and prediction. The current study investigated the IFC–STC functional connectivity in detecting rule violation (i.e., an abstract change). Frequent standard tone pairs with a constant relative pitch difference, but varying pitches, were presented to establish a pitch interval rule. This abstract rule was violated by deviants with reduced relative pitch intervals. The EROS STC mismatch response to the deviants was abolished by the TMS applied at the IFC 80 ms after deviance onset, but preserved in the spatial (TMS on vertex), auditory (TMS sound), and temporal (200 ms after deviance onset) control conditions. These results demonstrate the IFC–STC connection in preattentive abstract change detection and support the regularity or prediction violation account.