The evolution of electronic states in molecule has two origins: dynamical one produced by Schr¨odinger equation and kinematical one caused by base transformation due to nuclear motion.In current theories,the form...The evolution of electronic states in molecule has two origins: dynamical one produced by Schr¨odinger equation and kinematical one caused by base transformation due to nuclear motion.In current theories,the former gets analytic expression; the latter depends on heavy numerical calculation,which contains uncertainty.By using connection of fiber bundles,this paper establishes an analytic formula for the latter,and the numerical work is simplified.It shows the mathematical structure of molecule is fiber bundle.展开更多
Majority of type 2 diabetes mellitus(T2DM)patients are highly susceptible to several forms of cognitive impairments,particularly dementia.However,the underlying neural mechanism of these cognitive impairments remains ...Majority of type 2 diabetes mellitus(T2DM)patients are highly susceptible to several forms of cognitive impairments,particularly dementia.However,the underlying neural mechanism of these cognitive impairments remains unclear.We aimed to investigate the correlation between whole brain resting state functional connections(RSFCs)and the cognitive status in 95 patients with T2DM.We constructed an elastic net model to estimate the Montreal Cognitive Assessment(MoCA)scores,which served as an index of the cognitive status of the patients,and to select the RSFCs for further prediction.Subsequently,we utilized a machine learning technique to evaluate the discriminative ability of the connectivity pattern associated with the selected RSFCs.The estimated and chronological MoCA scores were significantly correlated with R=0.81 and the mean absolute error(MAE)=1.20.Additionally,cognitive impairments of patients with T2DM can be identified using the RSFC pattern with classification accuracy of 90.54%and the area under the receiver operating characteristic(ROC)curve(AUC)of 0.9737.This connectivity pattern not only included the connections between regions within the default mode network(DMN),but also the functional connectivity between the task-positive networks and the DMN,as well as those within the task-positive networks.The results suggest that an RSFC pattern could be regarded as a potential biomarker to identify the cognitive status of patients with T2DM.展开更多
文摘The evolution of electronic states in molecule has two origins: dynamical one produced by Schr¨odinger equation and kinematical one caused by base transformation due to nuclear motion.In current theories,the former gets analytic expression; the latter depends on heavy numerical calculation,which contains uncertainty.By using connection of fiber bundles,this paper establishes an analytic formula for the latter,and the numerical work is simplified.It shows the mathematical structure of molecule is fiber bundle.
基金supported by the National Natural Science Foundation of China(Grant Nos.81772012,81227901,61673051,81641168,31470047,81271565,81527805,and61231004)the National Key R&D Program of China(Grant No.2017YFA0205200)the Youth Innovation Promotion Association,Chinese Academy of Sciences(Grant No.2019136)
文摘Majority of type 2 diabetes mellitus(T2DM)patients are highly susceptible to several forms of cognitive impairments,particularly dementia.However,the underlying neural mechanism of these cognitive impairments remains unclear.We aimed to investigate the correlation between whole brain resting state functional connections(RSFCs)and the cognitive status in 95 patients with T2DM.We constructed an elastic net model to estimate the Montreal Cognitive Assessment(MoCA)scores,which served as an index of the cognitive status of the patients,and to select the RSFCs for further prediction.Subsequently,we utilized a machine learning technique to evaluate the discriminative ability of the connectivity pattern associated with the selected RSFCs.The estimated and chronological MoCA scores were significantly correlated with R=0.81 and the mean absolute error(MAE)=1.20.Additionally,cognitive impairments of patients with T2DM can be identified using the RSFC pattern with classification accuracy of 90.54%and the area under the receiver operating characteristic(ROC)curve(AUC)of 0.9737.This connectivity pattern not only included the connections between regions within the default mode network(DMN),but also the functional connectivity between the task-positive networks and the DMN,as well as those within the task-positive networks.The results suggest that an RSFC pattern could be regarded as a potential biomarker to identify the cognitive status of patients with T2DM.
