Short-Time Critical Dynamics of Damage Spreading in the Two-Dimensional Ising Model

The short-time critical dynamics of propagation of damage in the Ising ferromagnet in two dimensions is studied by means of Monte Carlo simulations. Starting with equilibrium configurations at $T= \infty$ and magnetization $M=0$, an initial damage is created by flipping a small amount of spins in one of the two replicas studied. In this way, the initial damage is proportional to the initial magnetization $M_0$ in one of the configurations upon quenching the system at $T_C$, the Onsager critical temperature of the ferromagnetic-paramagnetic transition. It is found that, at short times, the damage increases with an exponent $\theta_D=1.915(3)$, which is much larger than the exponent $\theta=0.197$ characteristic of the initial increase of the magnetization $M(t)$. Also, an epidemic study was performed. It is found that the average distance from the origin of the epidemic ($\langle R^2(t)\rangle$) grows with an exponent $z^* \approx \eta \approx 1.9$, which is the same, within error bars, as the exponent $\theta_D$. However, the survival probability of the epidemics reaches a plateau so that $\delta=0$. On the other hand, by quenching the system to lower temperatures one observes the critical spreading of the damage at $T_{D}\simeq 0.51 T_C$, where all the measured observables exhibit power laws with exponents $\theta_D = 1.026(3)$, $\delta = 0.133(1)$, and $z^*=1.74(3)$.Comment: 11 pages, 9 figures (included). Phys. Rev. E (2010), in press

The capital gains from trade are not enough: Evidence from the environmental accounts of Venezuela and Mexico

In principle, a country can not endure negative genuine savings for long periods of time without experiencing declining consumption. Nevertheless, theoreticians envisage two alternatives to explain how an exporter of non-renewable natural resources could experience permanent negative genuine savings and still ensure sustainability. The first one alleges that the capital gains arising from the expected improvement in the terms of trade would suffice to compensate for the negative savings of the resource exporter. The second alternative points at technological change as a way to avoid economic collapse. This paper uses the data of Venezuela and Mexico to empirically test the first of these two hypotheses. The results presented here prove that the terms of trade do not suffice to compensate the depletion of oil reserves in these two open economies.Exhaustive resources, environmental accounts, net national product, genuine savings, foreign trade

A Simple Approach to Maximum Intractable Likelihood Estimation

Approximate Bayesian Computation (ABC) can be viewed as an analytic approximation of an intractable likelihood coupled with an elementary simulation step. Such a view, combined with a suitable instrumental prior distribution permits maximum-likelihood (or maximum-a-posteriori) inference to be conducted, approximately, using essentially the same techniques. An elementary approach to this problem which simply obtains a nonparametric approximation of the likelihood surface which is then used as a smooth proxy for the likelihood in a subsequent maximisation step is developed here and the convergence of this class of algorithms is characterised theoretically. The use of non-sufficient summary statistics in this context is considered. Applying the proposed method to four problems demonstrates good performance. The proposed approach provides an alternative for approximating the maximum likelihood estimator (MLE) in complex scenarios

Development and implementation of an adaptive digital beamforming network for satellite communication systems

The use of adaptive digital beamforming techniques has, until recently, been largely restricted to high performance military radar systems. Recent advances in digital technology, however, have enabled the design of single chip digital beamforming networks. This, coupled with advances in digital signal processor technology, enables complete beamforming systems to be constructed at a lower cost, thus making the application of these techniques to commercial communications systems attractive. The design and development of such an adaptative digital beamforming network are described. The system is being developed as a proof of concept laboratory based demonstrator to enable the feasibility of adaptive digital beamforming techniques for communication systems to be determined. Ultimately, digital beamforming could be used in conjunction with large array antennas for communication satellite systems. This will enable the simultaneous steering of high gain antenna beams in the direction of gr...Peer ReviewedPostprint (published version