Triggering one dimensional phase transition with defects at the graphene zigzag edge

One well-known argument about one dimensional(1D) system is that 1D phase transition at finite temperature cannot exist, despite this concept depends on conditions such as range of interaction, external fields and periodicity. Therefore 1D systems usually have random fluctuations with intrinsic domain walls arising which naturally bring disorder during transition. Herein we introduce a real 1D system in which artificially created defects can induce a well-defined 1D phase transition. The dynamics of structural reconstructions at graphene zigzag edges are examined by in situ aberration corrected transmission electron microscopy (ACTEM). Combined with an in-depth analysis by ab-initio simulations and quantum chemical molecular dynamics (QM/MD), the complete defect induced 1D phase transition dynamics at graphene zigzag edge is clearly demonstrated and understood on the atomic scale. Further, following this phase transition scheme, graphene nanoribbons (GNR) with different edge symmetries can be fabricated, and according to our electronic structure and quantum transport calculations, a metal-insulator-semiconductor transition for ultrathin GNRs is proposed.Comment: 6 pages, 4 figure

Fast k-means based on KNN Graph

In the era of big data, k-means clustering has been widely adopted as a basic processing tool in various contexts. However, its computational cost could be prohibitively high as the data size and the cluster number are large. It is well known that the processing bottleneck of k-means lies in the operation of seeking closest centroid in each iteration. In this paper, a novel solution towards the scalability issue of k-means is presented. In the proposal, k-means is supported by an approximate k-nearest neighbors graph. In the k-means iteration, each data sample is only compared to clusters that its nearest neighbors reside. Since the number of nearest neighbors we consider is much less than k, the processing cost in this step becomes minor and irrelevant to k. The processing bottleneck is therefore overcome. The most interesting thing is that k-nearest neighbor graph is constructed by iteratively calling the fast $k$-means itself. Comparing with existing fast k-means variants, the proposed algorithm achieves hundreds to thousands times speed-up while maintaining high clustering quality. As it is tested on 10 million 512-dimensional data, it takes only 5.2 hours to produce 1 million clusters. In contrast, to fulfill the same scale of clustering, it would take 3 years for traditional k-means