By the generalized variational principle of two kinds of variables in general me-chanics,it was demonstrated that two Lagrangian classical relationships can be applied to both holonomic systems and nonholonomic system...By the generalized variational principle of two kinds of variables in general me-chanics,it was demonstrated that two Lagrangian classical relationships can be applied to both holonomic systems and nonholonomic systems. And the restriction that two Lagrangian classical relationships cannot be applied to nonholonomic systems for a long time was overcome. Then,one important formula of similar La-grangian classical relationship called the popularized Lagrangian classical rela-tionship was derived. From Vakonomic model,by two Lagrangian classical rela-tionships and the popularized Lagrangian classical relationship,the result is the same with Chetaev's model,and thus Chetaev's model and Vakonomic model were unified. Simultaneously,the Lagrangian theoretical framework of dynamics of nonholonomic system was established. By some representative examples,it was validated that the Lagrangian theoretical framework of dynamics of nonholonomic systems is right.展开更多
Self-rated health (SRH)—a person’s subjective evaluation of his general health—is a more valid and powerful predictor of morbidity and mortality than any other combination of objective and self-reported measures. H...Self-rated health (SRH)—a person’s subjective evaluation of his general health—is a more valid and powerful predictor of morbidity and mortality than any other combination of objective and self-reported measures. However, current theoretical frameworks fail to explain this association. Here, we sought to investigate SRH in relation to health outcomes from a transdisciplinary perspective. Using a selective review of epidemiological, clinical and qualitative SRH literature, we analyzed the relationships between this global subjective self-perception of health (the whole) and its directly measurable constituents (the parts). Although SRH often predicts major health outcomes, its underpinnings vary from person to person. Factors influencing individual’s health interact in complex ways evade reductionist methods assessing the parts, and may be best captured by global self-perceptions of health. The study of SRH from a transdisciplinary perspective exemplifies the notion that the whole is greater than the sum of its parts. Insight into individual’s experience of “health”, their association with physiological processes, and impact on the health/disease continuum may contribute to the development of individualized strategies for health care and promotion with aging. In particular, this should be most valuable for addressing non-communicable health conditions where cross-talk between health domains (biological, psychological, social, behavioral, spiritual) may significantly contribute to pathophysiology.展开更多
The Golden Ratio Theorem, deeply rooted in fractal mathematics, presents a pioneering perspective on deciphering complex systems. It draws a profound connection between the principles of interchangeability, self-simil...The Golden Ratio Theorem, deeply rooted in fractal mathematics, presents a pioneering perspective on deciphering complex systems. It draws a profound connection between the principles of interchangeability, self-similarity, and the mathematical elegance of the Golden Ratio. This research unravels a unique methodological paradigm, emphasizing the omnipresence of the Golden Ratio in shaping system dynamics. The novelty of this study stems from its detailed exposition of self-similarity and interchangeability, transforming them from mere abstract notions into actionable, concrete insights. By highlighting the fractal nature of the Golden Ratio, the implications of these revelations become far-reaching, heralding new avenues for both theoretical advancements and pragmatic applications across a spectrum of scientific disciplines.展开更多
Theory allows studying why Evolution might select core genetic commitment circuit topologies over alternatives. The nonlinear dynamics of the underlying gene regulation together with the unescapable subtle interplay o...Theory allows studying why Evolution might select core genetic commitment circuit topologies over alternatives. The nonlinear dynamics of the underlying gene regulation together with the unescapable subtle interplay of intrinsic biochemical noise impact the range of possible evolutionary choices. The question of why certain genetic regulation circuits might present robustness to phenotype-delivery breaking over others, is therefore of high interest. Here, the behavior of systematically more complex commitment circuits is studied, in the presence of intrinsic noise, with a focus on two aspects relevant to biology： parameter asymmetry and time-scale separation. We show that phenotype delivery is broken in simple two- and three-gene circuits. In the two-gene circuit, we show how stochastic potential wells of different depths break commitment. In the three-gene circuit, we show that the onset of oscillations breaks the commitment phenotype in a systematic way. Finally, we also show that higher dimensional circuits （four-gene and five-gene circuits） may be intrinsically more robust.展开更多
Stochastic dynamics pervades gene regulation. Despite being random, the dynamics displays a kind of innate structure. In fact, two stochastic forces combine driving efforts： one force originates from the gradient of ...Stochastic dynamics pervades gene regulation. Despite being random, the dynamics displays a kind of innate structure. In fact, two stochastic forces combine driving efforts： one force originates from the gradient of the underlying stochastic potential, and the other originates from the mathematical curl of the probability flux. The curl force gives rise to rotation. The gradient force gives rise to drift. Together they give rise to helical behavior. Here, it is shown that around and about the vicinity of attractive fixed points, the gradient force naturally wanes but the curl force is found to remain high. This leads to a locally noticeably different type of stochastic track near and about attractive fixed points, compared to tracks in regions where drift dominates. The consistency of this observation with the experimental fact that, in biology, fate commitment appears to not be a-priory locked-in, but rather necessitating active maintenance, is discussed. Hence attractive fixed-points are not only fuzzy, but may effectively be, locally, ＂more free＂.展开更多
基金Supported by the National Natural Science Foundation of China (Grant No. 10272034)the Research Fund for the Doctoral Program of Higher Education of Chinathe Basic Research Foundation of Harbin Engineering University (Grant No. 20060217020)
文摘By the generalized variational principle of two kinds of variables in general me-chanics,it was demonstrated that two Lagrangian classical relationships can be applied to both holonomic systems and nonholonomic systems. And the restriction that two Lagrangian classical relationships cannot be applied to nonholonomic systems for a long time was overcome. Then,one important formula of similar La-grangian classical relationship called the popularized Lagrangian classical rela-tionship was derived. From Vakonomic model,by two Lagrangian classical rela-tionships and the popularized Lagrangian classical relationship,the result is the same with Chetaev's model,and thus Chetaev's model and Vakonomic model were unified. Simultaneously,the Lagrangian theoretical framework of dynamics of nonholonomic system was established. By some representative examples,it was validated that the Lagrangian theoretical framework of dynamics of nonholonomic systems is right.
文摘Self-rated health (SRH)—a person’s subjective evaluation of his general health—is a more valid and powerful predictor of morbidity and mortality than any other combination of objective and self-reported measures. However, current theoretical frameworks fail to explain this association. Here, we sought to investigate SRH in relation to health outcomes from a transdisciplinary perspective. Using a selective review of epidemiological, clinical and qualitative SRH literature, we analyzed the relationships between this global subjective self-perception of health (the whole) and its directly measurable constituents (the parts). Although SRH often predicts major health outcomes, its underpinnings vary from person to person. Factors influencing individual’s health interact in complex ways evade reductionist methods assessing the parts, and may be best captured by global self-perceptions of health. The study of SRH from a transdisciplinary perspective exemplifies the notion that the whole is greater than the sum of its parts. Insight into individual’s experience of “health”, their association with physiological processes, and impact on the health/disease continuum may contribute to the development of individualized strategies for health care and promotion with aging. In particular, this should be most valuable for addressing non-communicable health conditions where cross-talk between health domains (biological, psychological, social, behavioral, spiritual) may significantly contribute to pathophysiology.
文摘The Golden Ratio Theorem, deeply rooted in fractal mathematics, presents a pioneering perspective on deciphering complex systems. It draws a profound connection between the principles of interchangeability, self-similarity, and the mathematical elegance of the Golden Ratio. This research unravels a unique methodological paradigm, emphasizing the omnipresence of the Golden Ratio in shaping system dynamics. The novelty of this study stems from its detailed exposition of self-similarity and interchangeability, transforming them from mere abstract notions into actionable, concrete insights. By highlighting the fractal nature of the Golden Ratio, the implications of these revelations become far-reaching, heralding new avenues for both theoretical advancements and pragmatic applications across a spectrum of scientific disciplines.
文摘Theory allows studying why Evolution might select core genetic commitment circuit topologies over alternatives. The nonlinear dynamics of the underlying gene regulation together with the unescapable subtle interplay of intrinsic biochemical noise impact the range of possible evolutionary choices. The question of why certain genetic regulation circuits might present robustness to phenotype-delivery breaking over others, is therefore of high interest. Here, the behavior of systematically more complex commitment circuits is studied, in the presence of intrinsic noise, with a focus on two aspects relevant to biology： parameter asymmetry and time-scale separation. We show that phenotype delivery is broken in simple two- and three-gene circuits. In the two-gene circuit, we show how stochastic potential wells of different depths break commitment. In the three-gene circuit, we show that the onset of oscillations breaks the commitment phenotype in a systematic way. Finally, we also show that higher dimensional circuits （four-gene and five-gene circuits） may be intrinsically more robust.
文摘Stochastic dynamics pervades gene regulation. Despite being random, the dynamics displays a kind of innate structure. In fact, two stochastic forces combine driving efforts： one force originates from the gradient of the underlying stochastic potential, and the other originates from the mathematical curl of the probability flux. The curl force gives rise to rotation. The gradient force gives rise to drift. Together they give rise to helical behavior. Here, it is shown that around and about the vicinity of attractive fixed points, the gradient force naturally wanes but the curl force is found to remain high. This leads to a locally noticeably different type of stochastic track near and about attractive fixed points, compared to tracks in regions where drift dominates. The consistency of this observation with the experimental fact that, in biology, fate commitment appears to not be a-priory locked-in, but rather necessitating active maintenance, is discussed. Hence attractive fixed-points are not only fuzzy, but may effectively be, locally, ＂more free＂.
