What kind of judiciary do we want?: the access to justice in Brazil

The goal of this paper is to discuss a key issue in the Democratic Rule of Law State: what are the role and main functions of the Judiciary in Brazil? Is the Judiciary mainly a public service provider, adjudicating disputes and guaranteeing individual rights? Or also as a state power, it should mainly control and guide the moral values of the society, changing the status quo and reducing social conflicts? In this sense, what are the conflicts that must be examined by the Judiciary? We will seek to answer these questions based on a discussion subsidized by courts official statistics and the results of surveys conducted with the Brazilian general population. The surveys measured how do citizens feel about their judicial system and what are the circumstances and the facts that determine the judicialization of conflicts. We work with the perceptions and attitudes of citizens relating to the Judiciary as it is today and discuss the Judiciary they want. Then, we compare how attitudes and perceptions relate to actual behavior and use of courts.

Global stabilizing feedback law for a problem of biological control of mosquito-borne diseases

The control of the spread of dengue fever by introduction of the intracellular parasitic bacterium Wolbachia in populations of the vector Aedes aegypti, is presently one of the most promising tools for eliminating dengue, in the absence of an efficient vaccine. The success of this operation requires locally careful planning to determine the adequate number of mosquitoes carrying the Wolbachia parasite that need to be introduced into the natural population. The latter are expected to eventually replace the Wolbachia-free population and guarantee permanent protection against the transmission of dengue to human. In this paper, we propose and analyze a model describing the fundamental aspects of the competition between mosquitoes carrying Wolbachia and mosquitoes free of the parasite. We then introduce a simple feedback control law to synthesize an introduction protocol, and prove that the population is guaranteed to converge to a stable equilibrium where the totality of mosquitoes carry Wolbachia. The techniques are based on the theory of monotone control systems, as developed after Angeli and Sontag. Due to bistability, the considered input-output system has multivalued static characteristics, but the existing results are unable to prove almost-global stabilization, and ad hoc analysis has to be conducted.