In this paper, we developed a new numerical scheme which aimed to solve some initial value problems of ordinary differential equations. The full breakdown of this new numerical scheme derivation is presented. While in...In this paper, we developed a new numerical scheme which aimed to solve some initial value problems of ordinary differential equations. The full breakdown of this new numerical scheme derivation is presented. While in our subsequent research, we shall fully examine the characteristics of the scheme such as consistency, convergence and stability. Also, the implementation of this new numerical scheme shall be worked-on and comparison shall also be made with some existing methods.展开更多
The introduction of 'hydrostatic extraction' scheme, or 'standard stratification approximation', into spectral model gained some advantages compared with commonly used schemes. However, computational i...The introduction of 'hydrostatic extraction' scheme, or 'standard stratification approximation', into spectral model gained some advantages compared with commonly used schemes. However, computational instability may occur for high vertical resolution versions if the stratification parameter C0 taken as a constant. In this paper, the possible cause leading to the instability is discussed and an improved scheme presented where C0 is generalized to be a function of both height and latitudes. Hence the reference atmosphere gets closer to the real atmosphere and the temperature deviation field to be expanded becomes smoother everywhere. Test by real case forecasts shows good computational stability of the new scheme and better prediction performance than-usual schemes of spectral model.展开更多
A decade ago mainstream molecular biologists regarded it impossible or biologically ill-motivated to understand the dynamics of complex biological phenomena, such as cancer genesis and progression, from a network pers...A decade ago mainstream molecular biologists regarded it impossible or biologically ill-motivated to understand the dynamics of complex biological phenomena, such as cancer genesis and progression, from a network perspective. Indeed, there are numerical difficulties even for those who were determined to explore along this direction. Undeterred, seven years ago a group of Chinese scientists started a program aiming to obtain quantitative connections between tumors and network dynamics. Many interesting results have been obtained. In this paper we wish to test such idea from a different angle: the connection between a normal biological process and the network dynamics. We have taken early myelopoiesis as our biological model. A standard roadmap for the cell-fate diversification during hematopoiesis has already been well established experimentally, yet little was known for its underpinning dynamical mechanisms. Compounding this difficulty there were additional experimental challenges, such as the seemingly conflicting hematopoietic roadmaps and the cell-fate inter-conversion events. With early myeloid cell-fate determination in mind, we constructed a core molecular endogenous network from well-documented gene regulation and signal transduction knowledge. Turning the network into a set of dynamical equations, we found computationally several structurally robust states. Those states nicely correspond to known cell phenotypes. We also found the states connecting those stable states.They reveal the developmental routes—how one stable state would most likely turn into another stable state. Such interconnected network among stable states enabled a natural organization of cell-fates into a multi-stable state landscape. Accordingly, both the myeloid cell phenotypes and the standard roadmap were explained mechanistically in a straightforward manner. Furthermore,recent challenging observations were also explained naturally. Moreover, the landscape visually enables a prediction of a pool of additional cell states and developmental routes, including the non-sequential and cross-branch transitions, which are testable by future experiments. In summary, the endogenous network dynamics provide an integrated quantitative framework to understand the heterogeneity and lineage commitment in myeloid progenitors.展开更多
文摘In this paper, we developed a new numerical scheme which aimed to solve some initial value problems of ordinary differential equations. The full breakdown of this new numerical scheme derivation is presented. While in our subsequent research, we shall fully examine the characteristics of the scheme such as consistency, convergence and stability. Also, the implementation of this new numerical scheme shall be worked-on and comparison shall also be made with some existing methods.
基金This work has been carried out under the support of the Medium-range Numerical Weather Forecast research project
文摘The introduction of 'hydrostatic extraction' scheme, or 'standard stratification approximation', into spectral model gained some advantages compared with commonly used schemes. However, computational instability may occur for high vertical resolution versions if the stratification parameter C0 taken as a constant. In this paper, the possible cause leading to the instability is discussed and an improved scheme presented where C0 is generalized to be a function of both height and latitudes. Hence the reference atmosphere gets closer to the real atmosphere and the temperature deviation field to be expanded becomes smoother everywhere. Test by real case forecasts shows good computational stability of the new scheme and better prediction performance than-usual schemes of spectral model.
基金supported by the National Basic Research Program of China(2010CB529200)National Natural Science Foundation of China(91029738)
文摘A decade ago mainstream molecular biologists regarded it impossible or biologically ill-motivated to understand the dynamics of complex biological phenomena, such as cancer genesis and progression, from a network perspective. Indeed, there are numerical difficulties even for those who were determined to explore along this direction. Undeterred, seven years ago a group of Chinese scientists started a program aiming to obtain quantitative connections between tumors and network dynamics. Many interesting results have been obtained. In this paper we wish to test such idea from a different angle: the connection between a normal biological process and the network dynamics. We have taken early myelopoiesis as our biological model. A standard roadmap for the cell-fate diversification during hematopoiesis has already been well established experimentally, yet little was known for its underpinning dynamical mechanisms. Compounding this difficulty there were additional experimental challenges, such as the seemingly conflicting hematopoietic roadmaps and the cell-fate inter-conversion events. With early myeloid cell-fate determination in mind, we constructed a core molecular endogenous network from well-documented gene regulation and signal transduction knowledge. Turning the network into a set of dynamical equations, we found computationally several structurally robust states. Those states nicely correspond to known cell phenotypes. We also found the states connecting those stable states.They reveal the developmental routes—how one stable state would most likely turn into another stable state. Such interconnected network among stable states enabled a natural organization of cell-fates into a multi-stable state landscape. Accordingly, both the myeloid cell phenotypes and the standard roadmap were explained mechanistically in a straightforward manner. Furthermore,recent challenging observations were also explained naturally. Moreover, the landscape visually enables a prediction of a pool of additional cell states and developmental routes, including the non-sequential and cross-branch transitions, which are testable by future experiments. In summary, the endogenous network dynamics provide an integrated quantitative framework to understand the heterogeneity and lineage commitment in myeloid progenitors.
