We present universal construction for the Calogero-Moser system with two types spins interaction of trigonometric potential based on the root system of semi-simple Lie algebra. In this formalism, we successfully build...We present universal construction for the Calogero-Moser system with two types spins interaction of trigonometric potential based on the root system of semi-simple Lie algebra. In this formalism, we successfully build up the correct Lax pair as well as the R-matrix for this generalized Calogero-Moser models. Moreover using the property of root system, we make a concise explanation that in the quantized model, the R-matrix takes the same form as the classical one, which is the main new result of this paper.展开更多
Plant root development is strongly affected by nutrient availability. Despite the importance of structure and function of roots in nutrient acquisition,statistical modeling approaches to evaluate dynamic and temporal ...Plant root development is strongly affected by nutrient availability. Despite the importance of structure and function of roots in nutrient acquisition,statistical modeling approaches to evaluate dynamic and temporal modulations of root system architecture in response to nutrient availability have remained as widely open and exploratory areas in root biology. In this study,we developed a statistical modeling approach to investigate modulations of root system architecture in response to nitrogen availability. Mathematical models were designed for quantitative assessment of root growth and root branching phenotypes and their dynamic relationships based on hierarchical con figuration of primary and lateral roots formulating the fishbone-shaped root system architecture in Arabidopsis thaliana. Time-series datasets reporting dynamic changes in root developmental traits on different nitrate or ammonium concentrations were generated for statistical analyses. Regression analyses unraveled key parameters associated with：（i） inhibition of primary root growth under nitrogen limitation or on ammonium;（ii） rapid progression of lateral root emergence in response to ammonium; and（iii） inhibition of lateral root elongation in the presence of excess nitrate or ammonium. This study provides a statistical framework for interpreting dynamic modulation of root system architecture,supported by metaanalysis of datasets displaying morphological responses of roots to diverse nitrogen supplies.展开更多
文摘We present universal construction for the Calogero-Moser system with two types spins interaction of trigonometric potential based on the root system of semi-simple Lie algebra. In this formalism, we successfully build up the correct Lax pair as well as the R-matrix for this generalized Calogero-Moser models. Moreover using the property of root system, we make a concise explanation that in the quantized model, the R-matrix takes the same form as the classical one, which is the main new result of this paper.
基金supported in part by the National Science Foundation(IOS-1444549 to H.T.)the Deutsche Forschungsgemeinschaft(WI1728/13-1 to N.v.W.)Grants-in-aid for Scientific Research from the Ministry of Education,Culture,Sports,Science,and Technology of Japan(T.K.)
文摘Plant root development is strongly affected by nutrient availability. Despite the importance of structure and function of roots in nutrient acquisition,statistical modeling approaches to evaluate dynamic and temporal modulations of root system architecture in response to nutrient availability have remained as widely open and exploratory areas in root biology. In this study,we developed a statistical modeling approach to investigate modulations of root system architecture in response to nitrogen availability. Mathematical models were designed for quantitative assessment of root growth and root branching phenotypes and their dynamic relationships based on hierarchical con figuration of primary and lateral roots formulating the fishbone-shaped root system architecture in Arabidopsis thaliana. Time-series datasets reporting dynamic changes in root developmental traits on different nitrate or ammonium concentrations were generated for statistical analyses. Regression analyses unraveled key parameters associated with：（i） inhibition of primary root growth under nitrogen limitation or on ammonium;（ii） rapid progression of lateral root emergence in response to ammonium; and（iii） inhibition of lateral root elongation in the presence of excess nitrate or ammonium. This study provides a statistical framework for interpreting dynamic modulation of root system architecture,supported by metaanalysis of datasets displaying morphological responses of roots to diverse nitrogen supplies.
