Although there were many ancient Chinese mathematicians contributed a lot on geometry, Geometric morphometrics （GM） in modern concept was not firstly proposed by Chinese. The super capability of geometric morphometr...Although there were many ancient Chinese mathematicians contributed a lot on geometry, Geometric morphometrics （GM） in modern concept was not firstly proposed by Chinese. The super capability of geometric morphometries in scientific computing and problem solving has gained a lot of attentions in the world. Until early of 21 centuries, geometric morphometries was introduced into China. Since then, GM was rapidly applied in many research fields. However, it is a pity that GM is still not well-known in China as many works are published out of China. Thus, the special issue ＂Geometric morphometrics： Current shape and future directions＂ is organized. The present issue presents a series of contributions in this scientific field. In future, there will be many considerable new developing fields on GM needed to pay more attentions, for instances, 3D geometric morphometrics, 4D analysis, visualization of amber, new machine developing, new software developing, automatic identification system, etc. Once these technical bottle-necks on 3D data collecting and merging geometric morphometric data from multiple characters could be solved, the automatic identification system and other fields based on Big Data would come true.展开更多
Geometric morphometrics （GM） is an important method of shape analysis and increasingly used in a wide range of scientific disciplines. Presently, a single character comparison system of geometric morphometric data i...Geometric morphometrics （GM） is an important method of shape analysis and increasingly used in a wide range of scientific disciplines. Presently, a single character comparison system of geometric morphometric data is used in almost all empirical studies, and this approach is sufficient for many scientific problems. However, the estimation of overall similarity among taxa or objects based on multiple characters is crucial in a variety of contexts （e.g. （semi-）automated identification, phenetic relationships, tracing of character evolution, phylogenetic reconstruction）. Here we propose a new web-based tool for merging several geometric morphometrics data files from multiple characters into a single data file. Using this approach information from multiple characters can be compared in combination and an overall similarity estimate can be obtained in a convenient and geometrically rigorous manner. To illustrate our method, we provide an example analysis of 25 dung beetle species with seven Procrustes superimposed landmark data files representing the morphological variation of body features： the epipharynx, right mandible, pronotum, elytra, hindwing, and the metendosternite in dorsal and lateral view. All seven files were merged into a single one containing information on 649 landmark locations. The possible applications of such merged data files in different fields of science are discussed.展开更多
In this paper it is proved that sum from N=N+1 to N+H x（n）ψ（n）（?）<sub>ε</sub> H<sup>1-（1/r）</sup>q<sup>(</sup>（1/4（r-）1）+ε, where r=4,q is a prime power,χ and ψ are...In this paper it is proved that sum from N=N+1 to N+H x（n）ψ（n）（?）<sub>ε</sub> H<sup>1-（1/r）</sup>q<sup>(</sup>（1/4（r-）1）+ε, where r=4,q is a prime power,χ and ψ are multiplicative and additive characters modulo q respectively,with χ nontrivial.展开更多
基金supported by the National Natural Science Foundation of China(31672345)Research Equipment Development Project of Chinese Academy of Sciences(YZ201509)
文摘Although there were many ancient Chinese mathematicians contributed a lot on geometry, Geometric morphometrics （GM） in modern concept was not firstly proposed by Chinese. The super capability of geometric morphometries in scientific computing and problem solving has gained a lot of attentions in the world. Until early of 21 centuries, geometric morphometries was introduced into China. Since then, GM was rapidly applied in many research fields. However, it is a pity that GM is still not well-known in China as many works are published out of China. Thus, the special issue ＂Geometric morphometrics： Current shape and future directions＂ is organized. The present issue presents a series of contributions in this scientific field. In future, there will be many considerable new developing fields on GM needed to pay more attentions, for instances, 3D geometric morphometrics, 4D analysis, visualization of amber, new machine developing, new software developing, automatic identification system, etc. Once these technical bottle-necks on 3D data collecting and merging geometric morphometric data from multiple characters could be solved, the automatic identification system and other fields based on Big Data would come true.
基金supported by the National Natural Science Foundation of China(31672345,51305057,61379087)the Research Equipment Development Project of Chinese Academy of Sciences(YZ201509)a Humboldt Fellowship(M.B.) from Alexander von Humboldt Foundation
文摘Geometric morphometrics （GM） is an important method of shape analysis and increasingly used in a wide range of scientific disciplines. Presently, a single character comparison system of geometric morphometric data is used in almost all empirical studies, and this approach is sufficient for many scientific problems. However, the estimation of overall similarity among taxa or objects based on multiple characters is crucial in a variety of contexts （e.g. （semi-）automated identification, phenetic relationships, tracing of character evolution, phylogenetic reconstruction）. Here we propose a new web-based tool for merging several geometric morphometrics data files from multiple characters into a single data file. Using this approach information from multiple characters can be compared in combination and an overall similarity estimate can be obtained in a convenient and geometrically rigorous manner. To illustrate our method, we provide an example analysis of 25 dung beetle species with seven Procrustes superimposed landmark data files representing the morphological variation of body features： the epipharynx, right mandible, pronotum, elytra, hindwing, and the metendosternite in dorsal and lateral view. All seven files were merged into a single one containing information on 649 landmark locations. The possible applications of such merged data files in different fields of science are discussed.
基金Supported by the Natural Science Foundation of China.
文摘In this paper it is proved that sum from N=N+1 to N+H x（n）ψ（n）（?）<sub>ε</sub> H<sup>1-（1/r）</sup>q<sup>(</sup>（1/4（r-）1）+ε, where r=4,q is a prime power,χ and ψ are multiplicative and additive characters modulo q respectively,with χ nontrivial.
