Background: In this article, we seek to break the paradigm of traditional estimates (deterministically) to estimate the probability of transition from poverty and diet change in Mexico through a stochastic model while...Background: In this article, we seek to break the paradigm of traditional estimates (deterministically) to estimate the probability of transition from poverty and diet change in Mexico through a stochastic model while providing a comparative study in the time between the diet change and poverty. Methods: A model based on the theory of Markov applied to the different dimensions of poverty and diet type from aggregate data from government agencies was used. Also likely future state changes were estimated and Monte Carlo simulation was used to find a balance between the transition probabilities of the different states. Results: It was shown that there was a high probability of consuming more fat than protein and carbohydrates in Mexico. In the case of poverty, it was found that poverty of patrimony presented the highest probability of change. Estimates for 2030 show as well that the Mexican population will have equal probabilities of state transition to the type of diet and poverty, as long as you consider changing some current values of both consumption and poverty. Conclusions: It was shown that there was indeed a close relationship between poverty of patrimony and an unbalanced diet where the probability of fat intake was high. The stochastic approach had enabled us, in addition to linking poverty and changing diet, to prevent the Mexican population of future scenarios that could be dramatic and, to avoid this situation, alternatives of change of state consumption and poverty had been proposed.展开更多
This paper presents a simple but informative mathematical model to describe the mixing of three dissimilar components of particulate solids that have the tendency to segregate within one another. A nonlinear Markov ch...This paper presents a simple but informative mathematical model to describe the mixing of three dissimilar components of particulate solids that have the tendency to segregate within one another. A nonlinear Markov chain model is proposed to describe the process. At each time step, the exchange of particulate solids between the cells of the chain is divided into two virtual stages. The first is pure stochastic mixing accompanied by downward segregation. Upon the completion of this stage, some of the cells appear to be overfilled with the mixture, while others appear to have a void space. The second stage is related to upward segregation. Components from the overfilled cells fill the upper cells （those with the void space） according to the proposed algorithm. The degree of non-homogeneity in the mixture （the standard deviation） is calculated at each time step, which allows the mixing kinetics to be described. The optimum mixing time is found to provide the maximum homogeneity in the ternary mixture. However, this “common” time differs from the optimum mixing times for individual components. The model is verified using a lab-scale vibration vessel, and a reasonable correlation between the calculated and experimental data is obtained展开更多
文摘Background: In this article, we seek to break the paradigm of traditional estimates (deterministically) to estimate the probability of transition from poverty and diet change in Mexico through a stochastic model while providing a comparative study in the time between the diet change and poverty. Methods: A model based on the theory of Markov applied to the different dimensions of poverty and diet type from aggregate data from government agencies was used. Also likely future state changes were estimated and Monte Carlo simulation was used to find a balance between the transition probabilities of the different states. Results: It was shown that there was a high probability of consuming more fat than protein and carbohydrates in Mexico. In the case of poverty, it was found that poverty of patrimony presented the highest probability of change. Estimates for 2030 show as well that the Mexican population will have equal probabilities of state transition to the type of diet and poverty, as long as you consider changing some current values of both consumption and poverty. Conclusions: It was shown that there was indeed a close relationship between poverty of patrimony and an unbalanced diet where the probability of fat intake was high. The stochastic approach had enabled us, in addition to linking poverty and changing diet, to prevent the Mexican population of future scenarios that could be dramatic and, to avoid this situation, alternatives of change of state consumption and poverty had been proposed.
文摘This paper presents a simple but informative mathematical model to describe the mixing of three dissimilar components of particulate solids that have the tendency to segregate within one another. A nonlinear Markov chain model is proposed to describe the process. At each time step, the exchange of particulate solids between the cells of the chain is divided into two virtual stages. The first is pure stochastic mixing accompanied by downward segregation. Upon the completion of this stage, some of the cells appear to be overfilled with the mixture, while others appear to have a void space. The second stage is related to upward segregation. Components from the overfilled cells fill the upper cells （those with the void space） according to the proposed algorithm. The degree of non-homogeneity in the mixture （the standard deviation） is calculated at each time step, which allows the mixing kinetics to be described. The optimum mixing time is found to provide the maximum homogeneity in the ternary mixture. However, this “common” time differs from the optimum mixing times for individual components. The model is verified using a lab-scale vibration vessel, and a reasonable correlation between the calculated and experimental data is obtained
