Critical transitions and tipping phenomena between two meta-stable states in stochastic dynamical systems are a scientific issue.In this work,we expand the methodology of identifying the most probable transition pathw...Critical transitions and tipping phenomena between two meta-stable states in stochastic dynamical systems are a scientific issue.In this work,we expand the methodology of identifying the most probable transition pathway between two meta-stable states with Onsager±Machlup action functional,to investigate the evolutionary transition dynamics between two meta-stable invariant sets with Schrödinger bridge.In contrast to existing methodologies such as statistical analysis,bifurcation theory,information theory,statistical physics,topology,and graph theory for early warning indicators,we introduce a novel framework on Early Warning Signals (EWS) within the realm of probability measures that align with the entropy production rate.To validate our framework,we apply it to the Morris±Lecar model and investigate the transition dynamics between a meta-stable state and a stable invariant set (the limit cycle or homoclinic orbit) under various conditions.Additionally,we analyze real Alzheimer’s data from the Alzheimer’s Disease Neuroimaging Initiative database to explore EWS indicating the transition from healthy to pre-AD states.This framework not only expands the transition pathway to encompass measures between two specified densities on invariant sets,but also demonstrates the potential of our early warning indicators for complex diseases.展开更多
Dietary restriction（DR） can delay senescence, prolong lifespan of mammals and improve their learning-memory activity. The purpose of the study was to explore the effects of DR on hypolipidemic action and liver funct...Dietary restriction（DR） can delay senescence, prolong lifespan of mammals and improve their learning-memory activity. The purpose of the study was to explore the effects of DR on hypolipidemic action and liver function of mice with hyperlipidemia. To investigate these effects, hyperlipidemia mouse models were established with high-fat diet（HFD）（34% of energy）, then randomly divided into HFD group, DR30% group and DR50% group. Mice in DR30% and DR50% group were respectively supplied with HFD as much as about 70% and 50% of the consumption of HFD in the mice of HFD group. Rats in control group were fed routinely. After DR for 5 weeks, the average body weight, liver weight, liver index, serum lipids and glucose levels in both DR groups decreased significantly as compared with the HFD group（P〈0.05 or P〈0.01）, so did alanine aminotransferase（ALT）, aspartate aminotransferase（AST）, lactate dehydrogenase（LDH） levels and the ratio of LDL-C/HDL-C in the DR50% group（P〈0.05 or P〈0.01）. Histopathology examination of liver tissues further proved ameliorative effect of DR on liver function. Western blotting showed that DR significantly increased the expression of silent mating type information regulation 2 homolog 1（SIRT1） in liver and adipose, while notably decreased the expression of peroxisome proliferators-activated receptors-gamma（PPARγ） in adipose（P〈0.05 or P〈0.01）. The increase of SIRT1 and decrease of PPARγ may be a mechanism by which DR reduces blood lipids and ameliorates liver function.展开更多
The effects of stochastic perturbations and periodic excitations on the eutrophicated lake ecosystem are explored.Unlike the existing work in detecting early warning signals,this paper presents the most probable trans...The effects of stochastic perturbations and periodic excitations on the eutrophicated lake ecosystem are explored.Unlike the existing work in detecting early warning signals,this paper presents the most probable transition paths to characterize the regime shifts.The most probable transition paths are obtained by minimizing the Freidlin-Wentzell(FW)action functional and Onsager-Machlup(OM)action functional,respectively.The most probable path shows the movement trend of the lake eutrophication system under noise excitation,and describes the global transition behavior of the system.Under the excitation of Gaussian noise,the results show that the stability of the eutrophic state and the oligotrophic state has different results from two perspectives of potential well and the most probable transition paths.Under the excitation of Gaussian white noise and periodic force,we find that the transition occurs near the nearest distance between the stable periodic solution and the unstable periodic solution.展开更多
In this paper, we prove that the homographic solutions to the rhombus four body prob- lem are the variational minimizers of the Lagrangian action restricted on a holonomically constrained rhombus loop space.
基金National Key Research and Development Program of China,Grant/Award Number:2021ZD0201300National Natural Science Foundation of China,Grant/Award Numbers:12401233,12141107+2 种基金Guangdong Provincial Key Laboratory of Mathematical and Neural Dynamical Systems,Grant/Award Number:2024B1212010004Cross Disciplinary Research Team on Data Science and Intelligent Medicine,Grant/Award Number:2023KCXTD054Guangdong-Dongguan Joint Research,Grant/Award Number:2023A1515140016。
文摘Critical transitions and tipping phenomena between two meta-stable states in stochastic dynamical systems are a scientific issue.In this work,we expand the methodology of identifying the most probable transition pathway between two meta-stable states with Onsager±Machlup action functional,to investigate the evolutionary transition dynamics between two meta-stable invariant sets with Schrödinger bridge.In contrast to existing methodologies such as statistical analysis,bifurcation theory,information theory,statistical physics,topology,and graph theory for early warning indicators,we introduce a novel framework on Early Warning Signals (EWS) within the realm of probability measures that align with the entropy production rate.To validate our framework,we apply it to the Morris±Lecar model and investigate the transition dynamics between a meta-stable state and a stable invariant set (the limit cycle or homoclinic orbit) under various conditions.Additionally,we analyze real Alzheimer’s data from the Alzheimer’s Disease Neuroimaging Initiative database to explore EWS indicating the transition from healthy to pre-AD states.This framework not only expands the transition pathway to encompass measures between two specified densities on invariant sets,but also demonstrates the potential of our early warning indicators for complex diseases.
基金supported by a grant from the Social Development Research Program of Science and Technology Agency of Jiangsu Province(No.BE2015646)
文摘Dietary restriction（DR） can delay senescence, prolong lifespan of mammals and improve their learning-memory activity. The purpose of the study was to explore the effects of DR on hypolipidemic action and liver function of mice with hyperlipidemia. To investigate these effects, hyperlipidemia mouse models were established with high-fat diet（HFD）（34% of energy）, then randomly divided into HFD group, DR30% group and DR50% group. Mice in DR30% and DR50% group were respectively supplied with HFD as much as about 70% and 50% of the consumption of HFD in the mice of HFD group. Rats in control group were fed routinely. After DR for 5 weeks, the average body weight, liver weight, liver index, serum lipids and glucose levels in both DR groups decreased significantly as compared with the HFD group（P〈0.05 or P〈0.01）, so did alanine aminotransferase（ALT）, aspartate aminotransferase（AST）, lactate dehydrogenase（LDH） levels and the ratio of LDL-C/HDL-C in the DR50% group（P〈0.05 or P〈0.01）. Histopathology examination of liver tissues further proved ameliorative effect of DR on liver function. Western blotting showed that DR significantly increased the expression of silent mating type information regulation 2 homolog 1（SIRT1） in liver and adipose, while notably decreased the expression of peroxisome proliferators-activated receptors-gamma（PPARγ） in adipose（P〈0.05 or P〈0.01）. The increase of SIRT1 and decrease of PPARγ may be a mechanism by which DR reduces blood lipids and ameliorates liver function.
基金supported by the National Natural Science Foundation of China(Grant Nos.12072261 and 11872305)。
文摘The effects of stochastic perturbations and periodic excitations on the eutrophicated lake ecosystem are explored.Unlike the existing work in detecting early warning signals,this paper presents the most probable transition paths to characterize the regime shifts.The most probable transition paths are obtained by minimizing the Freidlin-Wentzell(FW)action functional and Onsager-Machlup(OM)action functional,respectively.The most probable path shows the movement trend of the lake eutrophication system under noise excitation,and describes the global transition behavior of the system.Under the excitation of Gaussian noise,the results show that the stability of the eutrophic state and the oligotrophic state has different results from two perspectives of potential well and the most probable transition paths.Under the excitation of Gaussian white noise and periodic force,we find that the transition occurs near the nearest distance between the stable periodic solution and the unstable periodic solution.
基金supported by Libyan Higer Education Fundsupported by Discovery Grant,Natural Sciences and Engineering Research Council of Canada
文摘In this paper, we prove that the homographic solutions to the rhombus four body prob- lem are the variational minimizers of the Lagrangian action restricted on a holonomically constrained rhombus loop space.
