Information entropy and its extension, which are important generalizations of entropy, are currently applied to many research domains. In this paper, a novel generalized relative entropy is constructed to avoid some defects of traditional relative entropy. We present the structure of generalized relative entropy after the discussion of defects in relative entropy. Moreover, some properties of the provided generalized relative entropy are presented and proved. The provided generalized relative entropy is proved to have a finite range and is a finite distance metric. Finally, we predict nucleosome positioning of fly and yeast based on generalized relative entropy and relative entropy respectively. The experimental results show that the properties of generalized relative entropy are better than relative entropy.Keywords: relative entropy; generalized relative entropy; upper bound; distance metric; adjusted distance BackgroundThe concept of entropy was proposed by T. Clausius as one of the parameters to reflect the degree of chaos for the object. Later, research found that information was such an abstract concept that was hard to make it clear to obtain its amount. Indeed, it was not until the information entropy was proposed by Shannon that we had a standard measure for the amount of information. Then, some related concepts based on information entropy have been proposed subsequently, such as cross entropy, relative entropy and mutual information, which offered an effective method to solve the complex problems of information processing. Therefore, the study of a novel metric based on information entropy was significant in the research domain of information science.Information entropy was first proposed by Shannon. Assuming an information source I is composed by n different signals I i , H(I), the information entropy of I was shown in Equation (1), where p i = amount of I i signal s amount of I denotes frequency of I i , E() means mathematical expectation, k > 1 denotes the base of logarithm. When k = 2, the unit of H(I) is bit.Information entropy was a metric of the chaos degree for an information source. The bigger the information entropy was, the more chaotic the information source, and vice versa. Afterwards cross entropy was proposed based on information entropy, the definition was shown in Equation (2) where P
Cell reprogramming has played important roles in medical science, such as tissue repair, organ reconstruction, disease treatment, new drug development, and new species breeding. Oct4, a core pluripotency factor, has especially played a key role in somatic cell reprogramming through transcriptional control and affects the expression level of genes by its combination intensity. However, the quantitative relationship between Oct4 combination intensity and target gene expression is still not clear. Therefore, firstly, a generalized linear regression method was constructed to predict gene expression values in promoter regions affected by Oct4 combination intensity. Training data, including Oct4 combination intensity and target gene expression, were from promoter regions of genes with different cell development stages. Additionally, the quantitative relationship between gene expression and Oct4 combination intensity was analyzed with the proposed model. Then, the quantitative relationship between gene expression and Oct4 combination intensity at each stage of cell development was classified into high and low levels. Experimental analysis showed that the combination height of Oct4-inhibited gene expression decremented by a temporal exponential value, whereas the combination width of Oct4-promoted gene expression incremented by a temporal logarithmic value. Experimental results showed that the proposed method can achieve goodness of fit with high confidence.
INTRODUCTION: Evaluation method of network multimedia English teaching quality is studied based on information entropy. OBJECTIVES: A effective method is proposed to monitor and manage network multimedia teaching of English, which can improve the level of English teaching. METHODS: Attribute reduction of conditional information entropy is used to obtain the key evaluation indexes by removing the redundant evaluation indexe, and the evaluation model is constructed to evaluate the quality of network multimedia teaching of English. RESULTS: The results show that in English multimedia classroom teaching, the key knowledge points are explained thoroughly, the ability to analyze and solve practical problems and the ability of innovative thinking have the highest weight, and have the greatest impact on the quality of English network multimedia teaching. In the future network multimedia English teaching, K1, K2 and K3 teachers should properly improve the quality of their network multimedia English courseware; K4, K5 and K6 teachers should pay attention to improving the teaching effect of Multimedia English classroom. CONCLUSION: This method effectively evaluates the quality of English multimedia classroom teaching, can help teachers improve the quality of education, provide development suggestions for teachers, and provide a scientific basis for improving the level of English Teaching in Colleges and universities.
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