Reduce the rank calculation of a high-dimensional sparse matrix based on network controllability theory

Numerical computing of the rank of a matrix is a fundamental problem in scientific computation. The datasets generated by the internet often correspond to the analysis of high-dimensional sparse matrices. Notwithstanding recent advances in the promotion of traditional singular value decomposition (SVD), an efficient estimation algorithm for the rank of a high-dimensional sparse matrix is still lacking. Inspired by the controllability theory of complex networks, we converted the rank of a matrix into maximum matching computing. Then, we established a fast rank estimation algorithm by using the cavity method, a powerful approximate technique for computing the maximum matching, to estimate the rank of a sparse matrix. In the merit of the natural low complexity of the cavity method, we showed that the rank of a high-dimensional sparse matrix can be estimated in a much faster way than SVD with high accuracy. Our method offers an efficient pathway to quickly estimate the rank of the high-dimensional sparse matrix when the time cost of computing the rank by SVD is unacceptable.Comment: 10 pages, 4 figure

Exact controllability of multiplex networks

Date of Acceptance: 11/09/2014Peer reviewedPublisher PD

Glass transitions in native silk fibres studied by dynamic mechanical thermal analysis

Silks are a family of semi-crystalline structural materials, spun naturally by insects, spiders and even crustaceans. Compared to the characteristic β-sheet crystalline structure in silks, the non-crystalline structure and its composition deserves more attention as it is equally critical to the filaments' high toughness and strength. Here we further unravel the structure-property relationship in silks using Dynamic Mechanical Thermal Analysis (DMTA). This technique allows us to examine the most important structural relaxation event of the disordered structure the disordered structure, the glass transition (GT), in native silk fibres of the lepidopteran Bombyx mori and Antheraea pernyi and the spider Nephila edulis. The measured glass transition temperature Tg, loss tangent tan δ and dynamic storage modulus are quantitatively modelled based on Group Interaction Modelling (GIM). The "variability" issue in native silks can be conveniently explained by the different degrees of structural disorder as revealed by DMTA. The new insights will facilitate a more comprehensive understanding of the structure-property relations for a wide range of biopolymers

Global Synchronization in Complex Networks with Adaptive Coupling

Global synchronization in adaptive coupling networks is studied in this paper. A new simple adaptive controller is proposed based on a concept of asymptotically stable led by partial state variables. Under the proposed adaptive update law, the network can achieve global synchronization without calculating the eigenvalues of the outer coupling matrix. The update law is only dependent on partial state variables of individual oscillators. Numerical simulations are given to show the effectiveness of the proposed method, in which the unified chaotic system is chosen as the nodes of the network with different topologies