Estudo da transição de fase da percolação através da entropia da informação

Various physical systems have dynamics that can be modeled by percolation processes. Percolation is used to study issues ranging from fluid diffusion through disordered media to fragmentation of a computer network caused by hacker attacks. A common feature of all of these systems is the presence of two non-coexistent regimes associated to certain properties of the system. For example: the disordered media can allow or not allow the flow of the fluid depending on its porosity. The change from one regime to another characterizes the percolation phase transition. The standard way of analyzing this transition uses the order parameter, a variable related to some characteristic of the system that exhibits zero value in one of the regimes and a nonzero value in the other. The proposal introduced in this thesis is that this phase transition can be investigated without the explicit use of the order parameter, but rather through the Shannon entropy. This entropy is a measure of the uncertainty degree in the information content of a probability distribution. The proposal is evaluated in the context of cluster formation in random graphs, and we apply the method to both classical percolation (Erd¨os- R´enyi) and explosive percolation. It is based in the computation of the entropy contained in the cluster size probability distribution and the results show that the transition critical point relates to the derivatives of the entropy. Furthermore, the difference between the smooth and abrupt aspects of the classical and explosive percolation transitions, respectively, is reinforced by the observation that the entropy has a maximum value in the classical transition critical point, while that correspondence does not occurs during the explosive percolation.

Transição demográfica e a questão educacional: uma abordagem para o ensino médio do Rio Grande do Norte

Due to demographic transition process, the educational public sector politics formers encounter a highly specific demographic situation because, nowadays, despite the demographic transition, population is still growing because of the demographic inertia; however, due to steady decline in fertility, young population tends to decrease in next years. In this way, aiming to make high school widely accessible in the country, the issue of education quality is highlighted as well the importance of the physical structure of schools and their teaching equipments to confirm a favorable or not environment for developing educational processes. In this way, this work aims to relate the enrollment of students as school types with the demand of young people who will be able to attend high school on the Rio Grande do Norte state by the year of 2020, emphasizing teaching unities structural aspects, from a school profiling to the design of three prospective alternatives. So, from INEP's Scholar Census data and IBGE population's projections, this work is composed by four stages: i) literature review about research related subjects; ii) database design and build; iii) school profiling; and, iv) prospective alternatives creation. As results, three alternatives relate potential demand and enrollment using the built profiles and they are: i) “Alternative A” attends PEE's requirements related to demands but do not provide improvements in the school structural aspects; ii) “Alternative B” points into an increase of enrollment offering to the detriment of school's structural conditions which are offered to these students; iii) “Alternative C” propitiates a quantitative enrollment increasing combined with improvements on school's physical structure. These alternatives help to support decision making related to goals and realization of universal access with physical conditions which are necessary to a favorable environment to educational activity development.

Áreas de transição rural e urbana em São Gonçalo do Amarante : elementos para delimitação no planejamento territorial

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior