In this paper, the authors present a modelling activity developed from a thematic project in the models and mathematical modelling class of the professional master＇s degree program in mathematics education at the Fed...In this paper, the authors present a modelling activity developed from a thematic project in the models and mathematical modelling class of the professional master＇s degree program in mathematics education at the Federal University of Ouro Preto. The students enrolled in the class chose to study the theme Brazilian Public Politics. After several debates regarding the theme, the students were separated into three groups and each group chose a subtheme to study. The themes were IDH （index of human development）, minimum wage and social security. As an example, a description of the thematic project about the minimum wage in Brazil is presented. The principal results obtained in the study of this theme include a discussion about the potentialities of the theme as a classroom activity in different levels of schooling. As an educational activity, the thematic project demonstrated itself to be greatly relevant, since not only did it provide the learning possibility of mathematics related to the issues studied, but also promoted various discussions regarding the theme, which, in our conception, contributes to the social-critical development of the students. Finally, from the point of view of applied mathematics and mathematics education, the development of a modelling activity from thematic projects showed itself to be a good source of researches.展开更多
This paper deals with the statistical modeling of latent topic hierarchies in text corpora. The height of the topic tree is assumed as fixed, while the number of topics on each level as unknown a priori and to be infe...This paper deals with the statistical modeling of latent topic hierarchies in text corpora. The height of the topic tree is assumed as fixed, while the number of topics on each level as unknown a priori and to be inferred from data. Taking a nonpara-metric Bayesian approach to this problem, we propose a new probabilistic generative model based on the nested hierarchical Dirichlet process (nHDP) and present a Markov chain Monte Carlo sampling algorithm for the inference of the topic tree structure as well as the word distribution of each topic and topic distribution of each document. Our theoretical analysis and experiment results show that this model can produce a more compact hierarchical topic structure and captures more fine-grained topic rela-tionships compared to the hierarchical latent Dirichlet allocation model.展开更多
文摘In this paper, the authors present a modelling activity developed from a thematic project in the models and mathematical modelling class of the professional master＇s degree program in mathematics education at the Federal University of Ouro Preto. The students enrolled in the class chose to study the theme Brazilian Public Politics. After several debates regarding the theme, the students were separated into three groups and each group chose a subtheme to study. The themes were IDH （index of human development）, minimum wage and social security. As an example, a description of the thematic project about the minimum wage in Brazil is presented. The principal results obtained in the study of this theme include a discussion about the potentialities of the theme as a classroom activity in different levels of schooling. As an educational activity, the thematic project demonstrated itself to be greatly relevant, since not only did it provide the learning possibility of mathematics related to the issues studied, but also promoted various discussions regarding the theme, which, in our conception, contributes to the social-critical development of the students. Finally, from the point of view of applied mathematics and mathematics education, the development of a modelling activity from thematic projects showed itself to be a good source of researches.
基金Project (No. 60773180) supported by the National Natural Science Foundation of China
文摘This paper deals with the statistical modeling of latent topic hierarchies in text corpora. The height of the topic tree is assumed as fixed, while the number of topics on each level as unknown a priori and to be inferred from data. Taking a nonpara-metric Bayesian approach to this problem, we propose a new probabilistic generative model based on the nested hierarchical Dirichlet process (nHDP) and present a Markov chain Monte Carlo sampling algorithm for the inference of the topic tree structure as well as the word distribution of each topic and topic distribution of each document. Our theoretical analysis and experiment results show that this model can produce a more compact hierarchical topic structure and captures more fine-grained topic rela-tionships compared to the hierarchical latent Dirichlet allocation model.
