We study tolerance and topology of random scale-free networks under attack and defense strategies that depend on the degree k of the nodes. This situation occurs, for example, when the robustness of a node depends on its degree or in an intentional attack with insufficient knowledge of the network. We determine, for all strategies, the critical fraction p(c) of nodes that must be removed for disintegrating the network. We find that, for an intentional attack, little knowledge of the well-connected sites is sufficient to strongly reduce p(c). At criticality, the topology of the network depends on the removal strategy, implying that different strategies may lead to different kinds of percolation transitions.

The present paper deals with the photophysical properties of columnar liquid crystals formed by hexakis-(alky1oxy)triphenylenes. Absorption and fluorescence spectra of solutions are analyzed on the basis of quantum chemical calculations performed by the CS-INDO-CI (conformations spectra-intermediate neglect of differential overlap-configuration interaction) m e t h d . the absorption maximum is due to the SO -Sq transition while fluorescence originates from the weak SO -S1 transition. In columnar aggregates, the former transition corresponds to delocalized excited states while the latter corresponds to localized ones; calculation of intermolecular interactions shows that, at the temperature domain of the mesophases, all the molecules have the same excitation energy and, therefore, no spectral diffusion of the fluorescence is expected, in agreement with the time-resolved emission spectra. Excitation transfer is investigated by studying the fluorescence decays of mesophases doped with energy traps. Their analysis is made by means of Monte Carlo simulations considering both intracolumnar and intercolumnar jumps and using four different models for the distance dependence of the hopping probability. The best description is obtained with a model based on the extended dipole approximation and taking into account molecular orientation.

We model the spreading of a crisis by constructing a global economic network and applying the Susceptible-Infected-Recovered (SIR) epidemic model with a variable probability of infection. The probability of infection depends on the strength of economic relations between the pair of countries, and the strength of the target country.It is expected that a crisis which originates in a large country, such as the USA, has the potential to spread globally, like the recent crisis. Surprisingly we show that also countries with much lower GDP, such as Belgium, are able to initiate a global crisis. Using the k-shell decomposition method to quantify the spreading power (of a node), we obtain a measure of "centrality" as a spreader of each country in the economic network. We thus rank the different countries according to the shell they belong to, and find the 12 most central countries. These countries are the most likely to spread a crisis globally. Of these 12 only six are large economies, while the other six are medium/small ones, a result that could not have been otherwise anticipated.Furthermore, we use our model to predict the crisis spreading potential of countries belonging to different shells according to the crisis magnitude.

We introduce an immunization method where the percentage of required vaccinations for immunity are close to the optimal value of a targeted immunization scheme of highest degree nodes. Our strategy retains the advantage of being purely local, without the need for knowledge on the global network structure or identification of the highest degree nodes. The method consists of selecting a random node and asking for a neighbor that has more links than himself or more than a given threshold and immunizing him. We compare this method to other efficient strategies on three real social networks and on a scale-free network model and find it to be significantly more effective.

We have re-examined the random release of particles from fractal polymer matrices using Monte Carlo simulations, a problem originally studied by Bunde et al. [J. Chem. Phys. 83, 5909 (1985)]. A certain population of particles diffuses on a fractal structure, and as particles reach the boundaries of the structure they are removed from the system. We find that the number of particles that escape from the matrix as a function of time can be approximated by a Weibull (stretched exponential) function, similar to the case of release from Euclidean matrices. The earlier result that fractal release rates are described by power laws is correct only at the initial stage of the release, but it has to be modified if one is to describe in one picture the entire process for a finite system. These results pertain to the release of drugs, chemicals, agrochemicals, etc., from delivery systems.