We in this paper give a decomposition concerning the general matrix triplet over an arbitrary divisionring F with the same row or column numbers. We also design a practical algorithm for the decomposition of thematrix...We in this paper give a decomposition concerning the general matrix triplet over an arbitrary divisionring F with the same row or column numbers. We also design a practical algorithm for the decomposition of thematrix triplet. As applications, we present necessary and suficient conditions for the existence of the generalsolutions to the system of matrix equations DXA = C1, EXB = C2, F XC = C3 and the matrix equation AXD + BY E + CZF = Gover F. We give the expressions of the general solutions to the system and the matrix equation when thesolvability conditions are satisfied. Moreover, we present numerical examples to illustrate the results of thispaper. We also mention the other applications of the equivalence canonical form, for instance, for the compressionof color images.展开更多
As complex traits evolve, each component of the trait may be under different selection pressures and could respond independently to distinct evolutionary forces. We used comparative methods to examine patterns of evol...As complex traits evolve, each component of the trait may be under different selection pressures and could respond independently to distinct evolutionary forces. We used comparative methods to examine patterns of evolution in multiple components of a complex courtship signal in darters, specifically addressing the question of how nuptial coloration evolves across different areas of the body. Using spectral reflectance, we defined 4 broad color classes present on the body and fins of 17 species of freshwater fishes （genus Etheostoma） and quantified differences in hue within each color class. Ancestral state reconstruction suggests that most color traits were expressed in the most recent common ancestor of sampled species and that differences among species are mostly due to losses in coloration. The evolutionary lability of coloration varied across body regions; we found sig- nificant phylogenetic signal for orange color on the body but not for most colors on fins. Finally, patterns of color evolution and hue Of the colors were correlated among the two dorsal fins and between the anterior dorsal and anal fins, but not between any of the fins and the body. The observed patterns support the hypothesis that different components of complex signals may be subject to distinct evolutionary pressures, and suggests that the combination of behavioral displays and morphology in communication may have a strong influence on patterns of signal evolution .展开更多
基金supported by National Natural Science Foundation of China (GrantNo. 60672160)the Ph.D. Programs Foundation of Ministry of Education of China (Grant No. 20093108110001)+3 种基金the Scientific Research Innovation Foundation of Shanghai Municipal Education Commission (Grant No. 09YZ13)the Netherlands Organization for Scientific Research (NWO)Singapore MoE Tier 1 Research Grant RG60/07Shanghai Leading Academic Discipline Project (Grant No. J50101)
文摘We in this paper give a decomposition concerning the general matrix triplet over an arbitrary divisionring F with the same row or column numbers. We also design a practical algorithm for the decomposition of thematrix triplet. As applications, we present necessary and suficient conditions for the existence of the generalsolutions to the system of matrix equations DXA = C1, EXB = C2, F XC = C3 and the matrix equation AXD + BY E + CZF = Gover F. We give the expressions of the general solutions to the system and the matrix equation when thesolvability conditions are satisfied. Moreover, we present numerical examples to illustrate the results of thispaper. We also mention the other applications of the equivalence canonical form, for instance, for the compressionof color images.
基金Acknowledgements We thank Michael Martin, Tory Williams, and Alex Nahm for assistance in collecting fishes and the Mendelson lab for assistance in fish maintenance. We thank Chioma Ihekweazu for assistance with spectral analysis. We also thank Karen Carleton for use of the software to calculate spectral location. Tom Cronin, Kevin Omland, Megan Porter, Kate Feller, Nick Friedman and Brian Dalton provided helpful discussions throughout the course of this work. We thank two anonymous reviewers and the editor for their helpful comments on previous versions of this manuscript. We especially thank Eileen Hebets for the invitation to submit to this special issue. This work was funded through a National Science Foundation grant to TCM （#DEB 0718987）. Additional support for this work came from the NSF, NCEAS and NESCENT funded ＂Comparative Phylogenetics in R＂ workshop attended by JMG.
文摘As complex traits evolve, each component of the trait may be under different selection pressures and could respond independently to distinct evolutionary forces. We used comparative methods to examine patterns of evolution in multiple components of a complex courtship signal in darters, specifically addressing the question of how nuptial coloration evolves across different areas of the body. Using spectral reflectance, we defined 4 broad color classes present on the body and fins of 17 species of freshwater fishes （genus Etheostoma） and quantified differences in hue within each color class. Ancestral state reconstruction suggests that most color traits were expressed in the most recent common ancestor of sampled species and that differences among species are mostly due to losses in coloration. The evolutionary lability of coloration varied across body regions; we found sig- nificant phylogenetic signal for orange color on the body but not for most colors on fins. Finally, patterns of color evolution and hue Of the colors were correlated among the two dorsal fins and between the anterior dorsal and anal fins, but not between any of the fins and the body. The observed patterns support the hypothesis that different components of complex signals may be subject to distinct evolutionary pressures, and suggests that the combination of behavioral displays and morphology in communication may have a strong influence on patterns of signal evolution .
