Robust Reconstruction of Complex Networks from Sparse Data

Reconstructing complex networks from measurable data is a fundamental problem for understanding and controlling collective dynamics of complex networked systems. However, a significant challenge arises when we attempt to decode structural information hidden in limited amounts of data accompanied by noise and in the presence of inaccessible nodes. Here, we develop a general framework for robust reconstruction of complex networks from sparse and noisy data. Specifically, we decompose the task of reconstructing the whole network into recovering local structures centered at each node. Thus, the natural sparsity of complex networks ensures a conversion from the local structure reconstruction into a sparse signal reconstruction problem that can be addressed by using the lasso, a convex optimization method. We apply our method to evolutionary games, transportation and communication processes taking place in a variety of model and real complex networks, finding that universal high reconstruction accuracy can be achieved from sparse data in spite of noise in time series and missing data of partial nodes. Our approach opens new routes to the network reconstruction problem and has potential applications in a wide range of fields.

Reconstructing propagation networks with natural diversity and identifying hidden sources

Our ability to uncover complex network structure and dynamics from data is fundamental to understanding and controlling collective dynamics in complex systems. Despite recent progress in this area, reconstructing networks with stochastic dynamical processes from limited time series remains to be an outstanding problem. Here we develop a framework based on compressed sensing to reconstruct complex networks on which stochastic spreading dynamics take place. We apply the methodology to a large number of model and real networks, finding that a full reconstruction of inhomogeneous interactions can be achieved from small amounts of polarized (binary) data, a virtue of compressed sensing. Further, we demonstrate that a hidden source that triggers the spreading process but is externally inaccessible can be ascertained and located with high confidence in the absence of direct routes of propagation from it. Our approach thus establishes a paradigm for tracing and controlling epidemic invasion and information diffusion in complex networked systems.

Alignment of the photoelectron spectroscopy beamline at NSRL

The photoelectron spectroscopy beamline at National Synchrotron Radiation Laboratory (NSRL) is equipped with a spherical grating monochromator with the included angle of 174 deg. Three gratings with line density of 200, 700 and 1200 lines/mm are used to cover the energy region from 60 eV to 1000 eV. After several years operation, the spectral resolution and flux throughput were deteriorated, realignment is necessary to improve the performance. First, the wavelength scanning mechanism, the optical components position and the exit slit guide direction are aligned according to the design value. Second, the gratings are checked by Atomic Force Microscopy (AFM). And then the gas absorption spectrum is measured to optimize the focusing condition of the monochromator. The spectral resolving power is recovered to the designed value of 1000@244eV. The flux at the end station for the 200 lines/mm grating is about 10^10 photons/sec/200mA, which is in accordance with the design. The photon flux for the 700 lines/mm grating is about 5 X 10^8 photons/sec/200mA, which is lower than expected. This poor flux throughput may be caused by carbon contamination on the optical components. The 1200 lines/mm grating has roughness much higher than expected so the diffraction efficiency is too low to detect any signal. A new grating would be ordered. After the alignment, the beamline has significant performance improvements in both the resolving power and the flux throughput for 200 and 700 lines/mm gratings and is provided to users.

Topological insulator and the Dirac equation

We present a general description of topological insulators from the point of view of Dirac equations. The Z_{2} index for the Dirac equation is always zero, and thus the Dirac equation is topologically trivial. After the quadratic B term in momentum is introduced to correct the mass term m or the band gap of the Dirac equation, the Z_{2} index is modified as 1 for mB>0 and 0 for mB<0. For a fixed B there exists a topological quantum phase transition from a topologically trivial system to a non-trivial one system when the sign of mass m changes. A series of solutions near the boundary in the modified Dirac equation are obtained, which is characteristic of topological insulator. From the solutions of the bound states and the Z_{2} index we establish a relation between the Dirac equation and topological insulators.