Mathematical models describing the effects of different tax evasion behaviors

Microscopic models describing a whole of economic interactions in a closed society are considered. The presence of a tax system combined with a redistribution process is taken into account, as well as the occurrence of tax evasion. In particular, the existence is postulated, in relation to the level of evasion, of different individual taxpayer behaviors. The effects of the mentioned different behaviors on shape and features of the emerging income distribution profile are investigated qualitatively and quantitatively. Numerical solutions show that the Gini inequality index of the total population increases when the evasion level is higher, but does not depend significantly on the evasion spread. For fixed spread, the relative difference between the average incomes of the worst evaders and honest taxpayers increases approximately as a quadratic function of the evasion level.Comment: To appear in J. of Economic Interaction and Coordinatio

Network rewiring in the rr-KK plane

We generate correlated scale-free networks in the configuration model through a new rewiring algorithm which allows to tune the Newman assortativity coefficient $r$ and the average degree of the nearest neighbors $K$ (in the range $-1\le r \le 1$, $K\ge \langle k \rangle$). At each attempted rewiring step, local variations $\Delta r$ and $\Delta K$ are computed and then the step is accepted according to a standard Metropolis probability $\exp(\pm\Delta r/T)$, where $T$ is a variable temperature. We prove a general relation between $\Delta r$ and $\Delta K$, thus finding a connection between two variables which have very different definitions and topological meaning. We describe rewiring trajectories in the $r$-$K$ plane and explore the limits of maximally assortative and disassortative networks, including the case of small minimum degree ($k_{min} \ge 1$) which has previously not been considered. The size of the giant component and the entropy of the network are monitored in the rewiring. The average number of second neighbours in the branching approximation $\bar{z}_{2,B}$ is proven to be constant in the rewiring, and independent from the correlations for Markovian networks. As a function of the degree, however, the number of second neighbors gives useful information on the network connectivity and is also monitored.Comment: 21 pages, 7 figure

The Bass diffusion model on finite Barabasi-Albert networks

Using a mean-field network formulation of the Bass innovation diffusion model and exact results by Fotouhi and Rabbat on the degree correlations of Barabasi-Albert networks, we compute the times of the diffusion peak and compare them with those on scale-free networks which have the same scale-free exponent but different assortativity properties. We compare our results with those obtained by Caldarelli et al. for the SIS epidemic model with the spectral method applied to adjacency matrices. It turns out that diffusion times on finite Barabasi-Albert networks are at a minimum. This may be due to a little-known property of these networks: although the value of the assortativity coefficient is close to zero, they look disassortative if one considers only a bounded range of degrees, including the smallest ones, and slightly assortative on the range of the higher degrees. We also find that if the trickle-down character of the diffusion process is enhanced by a larger initial stimulus on the hubs (via a inhomogeneous linear term in the Bass model), the relative difference between the diffusion times for BA networks and uncorrelated networks is even larger, reaching for instance the 34% in a typical case on a network with $10^4$ nodes.Comment: 19 pages, 8 figures. Misspelling in citations correcte

Dynamic hysteresis from zigzag domain walls

We investigate dynamic hysteresis in ferromagnetic thin films with zigzag domain walls. We introduce a discrete model describing the motion of a wall in a disordered ferromagnet with in-plane magnetization, driven by an external magnetic field, considering the effects of dipolar interactions and anisotropy. We analyze the effects of external field frequency and temperature on the coercive field by Monte Carlo simulations, and find a good agreement with the experimental data reported in literature for Fe/GaAs films. This implies that dynamic hysteresis in this case can be explained by a single propagating domain wall model without invoking domain nucleation.Comment: 10 pages, 13 figures; minor modifications and two figures adde

Spin-wave instabilities in spin-transfer-driven magnetization dynamics

We study the stability of magnetization precessions induced in spin-transfer devices by the injection of spin-polarized electric currents. Instability conditions are derived by introducing a generalized, far-from-equilibrium interpretation of spin-waves. It is shown that instabilities are generated by distinct groups of magnetostatically coupled spin-waves. Stability diagrams are constructed as a function of external magnetic field and injected spin-polarized current. These diagrams show that applying larger fields and currents has a stabilizing effect on magnetization precessions. Analytical results are compared with numerical simulations of spin-transfer-driven magnetization dynamics.Comment: 4 pages, 2 figure

The effect of the motion of the Sun on the light-time in interplanetary relativistic experiments

In 2002 a measurement of the effect of solar gravity upon the phase of coherent microwave beams passing near the Sun has been carried out with the Cassini mission, allowing a very accurate measurement of the PPN parameter $\gamma$. The data have been analyzed with NASA's Orbit Determination Program (ODP) in the Barycentric Celestial Reference System, in which the Sun moves around the centre of mass of the solar system with a velocity $v_\odot$ of about 10 m/sec; the question arises, what correction this implies for the predicted phase shift. After a review of the way the ODP works, we set the problem in the framework of Lorentz (and Galilean) transformations and evaluate the correction; it is several orders of magnitude below our experimental accuracy. We also discuss a recent paper \cite{kopeikin07}, which claims wrong and much larger corrections, and clarify the reasons for the discrepancy.Comment: Final version accepted by Classical and Quantum Gravity (8 Jan. 2008