RESUMO
In this paper we solve the inverse problem for the Curie-Weiss model and its multispecies version when multiple thermodynamic states are present as in the low temperature phase where the phase space is clustered. The inverse problem consists of reconstructing the model parameters starting from configuration data generated according to the distribution of the model. We demonstrate that, without taking into account the presence of many states, the application of the inversion procedure produces very poor inference results. To overcome this problem, we use the clustering algorithm. When the system has two symmetric states of positive and negative magnetizations, the parameter reconstruction can also be obtained with smaller computational effort simply by flipping the sign of the magnetizations from positive to negative (or vice versa). The parameter reconstruction fails when the system undergoes a phase transition: In that case we give the correct inversion formulas for the Curie-Weiss model and we show that they can be used to measure how close the system gets to being critical.
RESUMO
Improving the prevention efficacy of health screening campaigns by increasing their attendance rate represents a challenge that calls for new strategies. This paper analyzes the response to a Pap test screening campaign of 155,000 women over the last decade. Using a mathematical model of statistical physics origins we derive a quantitative estimate of the mutual influence between participating groups. Different scenarios and possible actions are studied from the cost-benefit perspective. The performance of alternative strategies to improve participation are forecasted and compared. The results show that the standard strategies with incentives concentrated toward the low participating groups are outperformed by those toward pivotal groups with higher influence power. Our method provides a flexible tool useful to support policy maker decisions while complying with ethical regulations on privacy and confidentiality.
