abstract

In earlier rumor spreading models of the real world complex networks, nodes contact all of their neighbors at each time step. In more realistic scenario, a node may contact only some of its neighbors to spread the rumor. The rumor spreading rate may also depend on the degree of the spreader and ignorant nodes. We have given a new modified rumor spreading model to accommodate these facts. This new model has been studied for rumor spreading in scale free networks model of real world complex networks. Nonlinear rumor spread exponent \(\alpha \) and degree dependent tie strength exponent \(\beta \) of nodes affect the rumor threshold. By using the given two exponents, rumor threshold has some finite value. This was not observed in the earlier models for scale free networks. The rumor threshold becomes independent of network size when \(\alpha \) and \(\beta \) parameters are tuned to appropriate value. In any social network, rumors can spread and may have undesirable effect. One of the possible solutions to control rumor spread is to inoculate a certain fraction of nodes against rumors. We have used modified rumor spreading model over scale free networks to investigate the efficacy of random and targeted inoculation schemes. It has been observed that rumor threshold in targeted inoculation scheme is higher than in the random inoculation. Therefore, it is hard to spread rumors using modified rumor spreading model in scale free networks using targeted inoculation scheme. The proposed hypothesis is also verified by the simulation results.

abstract

Iqbal and Toor in Phys. Rev.  A65, 022306 (2002) and Commun. Theor. Phys. 42, 335 (2004) generalized the Marinatto–Weber quantum scheme for \(2 \times 2\) games in order to study bimatrix games of \(3 \times 3\) dimension, in particular the Rock–Paper–Scissors game. In our paper, we show that Iqbal and Toor’s generalization exhibits certain undesirable property that can considerably influence the game result. To support our argumentation, in the further part of the paper we construct the protocol corresponding to the MW concept for any finite bimatrix game that is free from the fault.

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We study dynamics of two coupled periodically driven oscillators. The internal motion is separated off exactly to yield a nonlinear fourth-order equation describing inner dynamics. Periodic steady-state solutions of the fourth-order equation are determined within the Krylov–Bogoliubov–Mitropolsky approach and we compute the corresponding amplitude profiles. In the present paper, we explore rich variety of singular points of the amplitude profiles. Metamorphoses of these curves induced by changes of control parameters and the corresponding changes of dynamics are studied.

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In this paper, we present results of high precision computations for the ground energy of weakly coupled double well potential in quantum mechanics. We give a numerical evidence for cancelation of imaginary contributions to energy coming from Borel resummation and multi-instanton terms. We also estimate several higher coefficients of the multi-instanton expansion which are not given in the literature.

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We derive the Landau energy levels for twisted \(N\)-enlarged Newton–Hooke space-time, i.e. we find the time-dependent energy spectrum and the corresponding eigenstates for an electron moving in uniform magnetic as well as in uniform electric external fields.

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The canonical quantum Hamiltonian eigenvalue problem for an anharmonic oscillator with a Lagrangian \(L = \dot \phi ^2/2 - m^2 \phi ^2/2 - g m^3 \phi ^4\) is numerically solved in two ways. One of the ways uses a plain cutoff on the number of basis states and the other employs a renormalization group procedure. The latter yields superior results to the former because it allows one to calculate the effective Hamiltonians. Matrices of effective Hamiltonians are quite small in comparison to the initial cutoff but nevertheless yield accurate eigenvalues thanks to the fact that just eight of their highest-energy matrix elements are proper functions of the small effective cutoff. We explain how these cutoff-dependent matrix elements emerge from the structure of the Hamiltonian and the renormalization group recursion, and we show that such small number of cutoff-dependent terms is sufficient to renormalize any band-diagonal Hamiltonian.

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Spontaneous supersymmetry (SUSY) breaking is revealed in all phenomena in which vacuum condensates are physically relevant. The dynamical breakdown of SUSY is generated by the condensates themselves, which lift the zero point energy. Evidence is presented in the case of the Wess–Zumino model, and the flavor mixing case is treated in detail.

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Bifurcation analysis of a two-dimensional binary mixture of hard needles, which due to the second order of the transition character gives directly the density of the transitions, thus the phase diagram, has been performed for a complete set of the compositions and the needles lengths ratios within the framework of the Onsager approach. A limit of a mixture of needles and dot-like particles has been given. The possible changes in the phase diagrams caused by modification of the interaction strength of the different type particles are discussed. Prognosis of applications for the surfacial adsorption of the rod-type molecules like fibrinogen has been suggested.

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We investigate accreting disk systems with polytropic gas in Keplerian motion. Numerical data and partial analytic results show that the self-gravitation of the disk speeds up its rotation — its rotational frequency is larger than that given by the well known strictly Keplerian formula that takes into account the central mass only. Thus determination of central mass in systems with massive disks requires great care — the strictly Keplerian formula yields only an upper bound. The effect of self-gravity depends on geometric aspects of disk configurations. Disk systems with a small (circa \(10^{-4}\)) ratio of the innermost radius to the outermost disk radius have the central mass close to the upper limit, but if this ratio is of the order of unity then the central mass can be smaller by many orders of magnitude from this bound.