The biological diversity, which depends on the genetic material DNA, is the foundation for a species to survive and evolve. The entropy is the best measurement of biological diversity. Based on the sin-gle-parameter a...The biological diversity, which depends on the genetic material DNA, is the foundation for a species to survive and evolve. The entropy is the best measurement of biological diversity. Based on the sin-gle-parameter and the two-parameter models, here we established some differential equations about the point mutation of a DNA sequence with finite length, as well as some functions describing the processes of the variation in quantities of 4 kinds of bases (A, T, G and C) in the DNA sequence. At the molecular level, we discussed the entropy characteristics of point mutation. The results proved that a species maintained its entropy and evolved in the direction of the increasing biological diversity. In order to testify the theoretical results, we did a series of computer simulations of random point muta- tion in Matlab environment. The results were well consistent with the theoretical researches.展开更多
The Shannon information entropy for the Schrodinger equation with a nonuniform solitonic mass is evaluated for a hyperbolic-type potential. The number of nodes of the wave functions in the transformed space z are brok...The Shannon information entropy for the Schrodinger equation with a nonuniform solitonic mass is evaluated for a hyperbolic-type potential. The number of nodes of the wave functions in the transformed space z are broken when recovered to original space x. The position Sx and momentum S p information entropies for six low-lying states are calculated. We notice that the Sx decreases with the increasing mass barrier width a and becomes negative beyond a particular width a,while the Sp first increases with a and then decreases with it. The negative Sx exists for the probability densities that are highly localized. We find that the probability density ρ（x） for n = 1, 3, 5 are greater than 1 at position x = 0. Some interesting features of the information entropy densities ρs（x） and ρs（p） are demonstrated. The Bialynicki-Birula-Mycielski（BBM）inequality is also tested for these states and found to hold.展开更多
文摘The biological diversity, which depends on the genetic material DNA, is the foundation for a species to survive and evolve. The entropy is the best measurement of biological diversity. Based on the sin-gle-parameter and the two-parameter models, here we established some differential equations about the point mutation of a DNA sequence with finite length, as well as some functions describing the processes of the variation in quantities of 4 kinds of bases (A, T, G and C) in the DNA sequence. At the molecular level, we discussed the entropy characteristics of point mutation. The results proved that a species maintained its entropy and evolved in the direction of the increasing biological diversity. In order to testify the theoretical results, we did a series of computer simulations of random point muta- tion in Matlab environment. The results were well consistent with the theoretical researches.
基金supported partially by project 20150964SIP-IPN, COFAA-IPN, Mexico
文摘The Shannon information entropy for the Schrodinger equation with a nonuniform solitonic mass is evaluated for a hyperbolic-type potential. The number of nodes of the wave functions in the transformed space z are broken when recovered to original space x. The position Sx and momentum S p information entropies for six low-lying states are calculated. We notice that the Sx decreases with the increasing mass barrier width a and becomes negative beyond a particular width a,while the Sp first increases with a and then decreases with it. The negative Sx exists for the probability densities that are highly localized. We find that the probability density ρ（x） for n = 1, 3, 5 are greater than 1 at position x = 0. Some interesting features of the information entropy densities ρs（x） and ρs（p） are demonstrated. The Bialynicki-Birula-Mycielski（BBM）inequality is also tested for these states and found to hold.
