We introduce a force decomposition to construct a potential function in deterministic dynamics described by ordinary differential equations in the context of dissipative gyroscopic systems.Such a potential function serves as the corresponding Lyapunov function for the dynamics,hence it gives both quantitative and qualitative descriptions for stability of motion.As an example we apply our force decomposition to a four-dimensional dissipative gyroscopic system.We explicitly obtain the potential function for all parameter regimes in the linear limit,including those regimes where the Lyapunov function was previously believed not to exist.
For a physical system, regardless of time reversal symmetry, a potential function serves also as a Lyapunov function, providing convergence and stability information. In this paper, the converse is constructively proved that any dynamics with a Lyapunov function has a corresponding physical realization： a friction force, a Lorentz force, and a potential function. Such construction establishes a set of equations with physical meaning for Lyapunov function and suggests new approaches on the significant unsolved problem namely to construct Lyapunov functions for general nonlinear systems. In addition, a connection is found that the Lyapunov equation is a reduced form of a generalized Einstein relation for linear systems, revealing further insights of the construction.
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 develop
Hang SuGaowei WangRuoshi YuanJunqiang WangYing TangPing AoXiaomei Zhu
Animal models are increasingly gaining values by cross-comparisons of response or resistance to clinical agents used for patients.However,many disease mechanisms and drug effects generated from animal models are not transferable to human.To address these issues,we developed SysFinder（http：//lifecenter.sgst.cn/SysFinder）,a platform for scientists to find appropriate animal models for translational research.SysFinder offers a ＂topic-centered＂ approach for systematic comparisons of human genes,whose functions are involved in a specific scientific topic,to the corresponding homologous genes of animal models.Scientific topic can be a certain disease,drug,gene function or biological pathway.SysFinder calculates multi-level similarity indexes to evaluate the similarities between human and animal models in specified scientific topics.Meanwhile,SysFinder offers species-specific information to investigate the differences in molecular mechanisms between humans and animal models.Furthermore,SysFinder provides a userfriendly platform for determination of short guide RNAs（sgRNAs） and homology arms to design a new animal model.Case studies illustrate the ability of SysFinder in helping experimental scientists.SysFinder is a useful platform for experimental scientists to carry out their research in the human molecular mechanisms.
Shuang YangGuoqing ZhangWan LiuZhen WangJifeng ZhangDongshan YangY.Eugene ChenHong SunYixue Li
