The scattered-energy spectra of monochronized synchrotron-radiation photons toward 90 by C, Al, Fe, Cu, Au, and Pb samples were measured using high-purity Ge detectors to obtain incoherent scattering function (S) in the 1.14 & x & 2.28-A region. The multiple-scattering intensity was evaluated by a Monte Carlo calculation while considering the Doppler broadening of the Comptonscattered photons and the photon linear polarization. The measured S of C, Al, Fe, and Cu agreed with that based on the Wailer-Hartree theory (S), as well as that based on a relativistic impulse approximation (S) within the experiment error (2.5' %%uo). The measured S of high-Z atoms (Au and Pb) agrees with S aud is smaller than S by 3-6'%%uo.
We study the level spacing distribution p(s) in the spectrum of random networks. According to our numerical results, the shape of p(s) in the Erdős-Rényi (E-R) random graph is determined by the average degree k and p(s) undergoes a dramatic change when k is varied around the critical point of the percolation transition, k = 1. When k 1, the p(s) is described by the statistics of the Gaussian orthogonal ensemble (GOE), one of the major statistical ensembles in Random Matrix Theory, whereas at k = 1 it follows the Poisson level spacing distribution. Closely above the critical point, p(s) can be described in terms of an intermediate distribution between Poisson and the GOE, the Brodydistribution. Furthermore, below the critical point p(s) can be given with the help of the regularized Gamma-function. Motivated by these results, we analyse the behaviour of p(s) in real networks such as the internet, a word association network and a protein-protein interaction network as well. When the giant component of these networks is destroyed in a node deletion process simulating the networks subjected to intentional attack, their level spacing distribution undergoes a similar transition to that of the E-R graph.
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