Mobile geolocation data is a valuable asset in the assessment of movement patterns of a population. Once a highly contagious disease takes place in a location the movement patterns aid in predicting the potential spatial spreading of the disease, hence mobile data becomes a crucial tool to epidemic models. In this work, based on millions of anonymized mobile visits data in Brazil, we investigate the most probable spreading patterns of the COVID-19 within states of Brazil. The study is intended to help public administrators in action plans and resources allocation, whilst studying how mobile geolocation data may be employed as a measure of population mobility during an epidemic. This study focuses on the states of São Paulo and Rio de Janeiro during the period of March 2020, when the disease first started to spread in these states. Metapopulation models for the disease spread were simulated in order to evaluate the risk of infection of each city within the states, by ranking them according to the time the disease will take to infect each city. We observed that, although the high-risk regions are those closer to the capital cities, where the outbreak has started, there are also cities in the countryside with great risk. The mathematical framework developed in this paper is quite general and may be applied to locations around the world to evaluate the risk of infection by diseases, in special the COVID-19, when geolocation data is available.

We prove that the position of the condensate of reversible, critical zero-range processes on a finite set S evolves, in a suitable time scale, as a continuous-time Markov chain on S whose jump rates are proportional to the capacities of the underlying random walk which describes the jumps of particles in the zero-range dynamics.

Mobile geolocation data is a valuable asset in the assessment of movement patterns of a population. Once a highly contagious disease takes place in a location the movement patterns aid in predicting the potential spatial spreading of the disease, hence mobile data becomes a crucial tool to epidemic models. In this work, based on millions of anonymized mobile visits data in Brazil, we investigate the most probable spreading patterns of the COVID-19 within states of Brazil. The study is intended to help public administrators in action plans and resources allocation, whilst studying how mobile geolocation data may be employed as a measure of population mobility during an epidemic. The first part of the study focus on the states of São Paulo and Rio de Janeiro during the period of March 2020, when the disease first started to spread in these states. Metapopulation models for the disease spread were simulated in order to evaluate the risk of infection of each city within the states, by ranking them according to the time the disease will take to infect each city. We observed that, although the high risk regions are those closer to the capital cities, where the outbreak has started, there are also cities in the countryside with great risk.

We provide a necessary and sufficient condition for the metastability of a Markov chain, expressed in terms of a property of the solutions of the resolvent equation. As an application of this result, we prove the metastability of reversible, critical zero-range processes starting from a configuration.

This paper uses a classical approach to feature selection: minimization of a cost function applied on estimated joint distributions. However, in this new formulation, the optimization search space is extended. The original search space is the Boolean lattice of features sets (BLFS), while the extended one is a collection of Boolean lattices of ordered pairs (CBLOP), that is (features, associated value), indexed by the elements of the BLFS. In this approach, we may not only select the features that are most related to a variable Y, but also select the values of the features that most influence the variable or that are most prone to have a specific value of Y. A local formulation of Shannon's mutual information, which generalizes Shannon's original definition, is applied on a CBLOP to generate a multiple resolution scale for characterizing variable dependence, the Local Lift Dependence Scale (LLDS). The main contribution of this paper is to define and apply the LLDS to analyse local properties of joint distributions that are neglected by the classical Shannon's global measure in order to select features. This approach is applied to select features based on the dependence between: i-the performance of students on university entrance exams and on courses of their first semester in the university; ii-the congress representative party and his vote on different matters; iii-the cover type of terrains and several terrain properties.