A modified epidemiological model for computer viruses

Since the computer viruses pose a serious problem to individual and corporative computer systems, a lot of effort has been dedicated to study how to avoid their deleterious actions, trying to create anti-virus programs acting as vaccines in personal computers or in strategic network nodes. Another way to combat viruses propagation is to establish preventive policies based on the whole operation of a system that can be modeled with population models, similar to those that are used in epidemiological studies. Here, a modified version of the SIR (Susceptible-Infected-Removed) model is presented and how its parameters are related to network characteristics is explained. Then, disease-free and endemic equilibrium points are calculated, stability and bifurcation conditions are derived and some numerical simulations are shown. The relations among the model parameters in the several bifurcation conditions allow a network design minimizing viruses risks. (C) 2009 Elsevier Inc. All rights reserved.

On state representations of time-varying nonlinear systems

This work considers a nonlinear time-varying system described by a state representation, with input u and state x. A given set of functions v, which is not necessarily the original input u of the system, is the (new) input candidate. The main result provides necessary and sufficient conditions for the existence of a local classical state space representation with input v. These conditions rely on integrability tests that are based on a derived flag. As a byproduct, one obtains a sufficient condition of differential flatness of nonlinear systems. (C) 2009 Elsevier Ltd. All rights reserved.

Underground systems of Asteraceae species from the Brazilian Cerrado

Underground systems of Asteraceac species from the Brazilian Cerrado. The aim or this study was to describe the underground systems structure, the origin of the shoot buds, and to identify the storage reserve of seven Asteraceae species in order to understand the adaptive strategies of these species in burned Cerrado areas and their higher frequency in the floristic Surveys for herbaceous and undershrub layers of this biome. The subterranean systems types-diffuse underground system, rhizophore, tuberous roots, and xylopodium-varied among the studied species, but all of them have high shoot bud-forming potential. Fructans of the inulin type were detected as storage substances. The presence of these characteristics on the underground systems Could explain the frequency of these species in the floristic surveys from the Brazilian Cerrado, in which Fire and seasonal drought are frequent. It is possible that the belowground bud banks in the Cerrado biome are as important as demonstrated in North American prairies where fire is also frequent. However, in the Cerrado, as demonstrated here, there are types of underground systems other than rhizomes that are usually described in the prairie. Understanding the anatomical features of these plants is one of the steps to appropriate conservation management of these species in the Cerrado.