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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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The energy dependence of the cross section of the neutral pion production is measured in the range 600 + 900 MeV. No unambiguous evidences for the existence of broad isovector dibaryon resonances were obtained. The isoscalar cross section of the pion production does not reveal any structure, predicted by the theory with resonances. 13.75.c; 25.40 Up to now, after observation in Argonne of the striking energy dependence in the difference of the total cross sections in pure longitudinal spin states, there are no convincing evidences for the existence of dibaryon resonances [1]. There are many reasons for this, one of which is that the observed phenomena appear in the region where the scattering amplitudes have sharp energy dependence owing to coupling to A Nchannel. So the question whether the effects observed are the consequence of switching on this new channel or not is open till today. Another difficulty is connected with the fact that the elastic widths of the dinucleon resonances under consideration are very small (according to the results of the phase shift analyses) and therefore the dibaryons have little effect on the observables in the elastic channel. PACS:Thus to answer the question one should scrutinize the inelastic channels, in the first place that of the pion production, where the AN-interaction manifests itself in the most prominent way. Our purpose was to measure the cross sections of the pp ~ pprc ~ reaction with the accuracy 3+4% in the energy range 600+900 MeV. There are good experimental data from Dubna [-21 for energies below 660 MeV and from KEK [3] for higher energies with the step 100 MeV. We performed measurements at seven energies with the step 40 + 50 MeV in order to obtain the reliable energy dependence of the cross section.The experiment was carried out at the LNPI synchrocyclotron with the help of 35-cm hydrogen bubble chamber placed in the 14.8 kGs magnetic field. The proton beam after the degrader was formed by three bending magnets and eight quadrupole lenses. Momentum values of the incident beam were checked independently by the kinematics of the elastic events. The accuracy of the mean value of the incident proton momentum was equal to __ 2 MeV/c, the momentum spread being 4+5%. A total of 300000 pictures was obtained, at low energy more than at high energy -inversely proportional to the expected cross section values. All 2-prong events were selected, the efficiency of the double scanning being 99%. According to the kinematics of the single pion production in NN-collisions the final nucleons are emitted forward, the maximum laboratory angle not exceeding 60 ~ . For this reason only those two-prong events were selected, which had the projection of the proton angle on the film plane smaller than 60 ~ . The selected events could belong not only to the neutral pion production process, but also to the elastic one as well as to the charged pion production. All the events selected were measured and geometrically reconstructed. The channel identification was performed with the help of...

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