Assessing Percolation Threshold Based on High-Order Non-Backtracking Matrices

Percolation threshold of a network is the critical value such that when nodes or edges are randomly selected with probability below the value, the network is fragmented but when the probability is above the value, a giant component connecting large portion of the network would emerge. Assessing the percolation threshold of networks has wide applications in network reliability, information spread, epidemic control, etc. The theoretical approach so far to assess the percolation threshold is mainly based on spectral radius of adjacency matrix or non-backtracking matrix, which is limited to dense graphs or locally treelike graphs, and is less effective for sparse networks with non-negligible amount of triangles and loops. In this paper, we study high-order non-backtracking matrices and their application to assessing percolation threshold. We first define high-order non-backtracking matrices and study the properties of their spectral radii. Then we focus on 2nd-order non-backtracking matrix and demonstrate analytically that the reciprocal of its spectral radius gives a tighter lower bound than those of adjacency and standard non-backtracking matrices. We further build a smaller size matrix with the same largest eigenvalue as the 2nd-order non-backtracking matrix to improve computation efficiency. Finally, we use both synthetic networks and 42 real networks to illustrate that the use of 2nd-order non-backtracking matrix does give better lower bound for assessing percolation threshold than adjacency and standard non-backtracking matrices.Comment: to appear in proceedings of the 26th International World Wide Web Conference(WWW2017

Variable selection based on entropic criterion and its application to the debris-flow triggering

We propose a new data analyzing scheme, the method of minimum entropy analysis (MEA), in this paper. New MEA provides a quantitative criterion to select relevant variables for modeling the physical system interested. Such method can be easily extended to various geophysical/geological data analysis, where many relevant or irrelevant available measurements may obscure the understanding of the highly complicated physical system like the triggering of debris-flows. After demonstrating and testing the MEA method, we apply this method to a dataset of debris-flow occurrences in Taiwan and successfully find out three relevant variables, i.e. the hydrological form factor, numbers and areas of landslides, to the triggering of observed debris-flow events due to the 1996 Typhoon Herb.Comment: 9 pages and 4 table

Effects of Ox-LDL on Macrophages NAD(P)H Autofluorescence Changes by Two-photon Microscopy

Ox-LDL uptakes by macrophage play a critical role in the happening of atherosclerosis. Because of its low damage on observed cells and better signal-to- background ratio, two-photon excitation fluorescence microscopy is used to observe NAD(P)H autofluorescence of macrophage under difference cultured conditions- bare cover glass, coated with fibronectin or poly-D-lysine. The results show that the optimal condition is fibronectin coated surface, on which, macrophages profile can be clearly identified on NAD(P)H autofluorescence images collected by two-photon microscopy. Moreover, different morphology and intensities of autofluorescence under different conditions were observed as well. In the future, effects of ox-LDL on macrophages will be investigated by purposed system to research etiology of atherosclerosis.Comment: Submitted on behalf of TIMA Editions (http://irevues.inist.fr/tima-editions