This paper focuses on studying the Poisson theory and the integration method of a Birkhoffian system in the event space. The Birkhoff＇s equations in the event space are given. The Poisson theory of the Birkhoffian sy...This paper focuses on studying the Poisson theory and the integration method of a Birkhoffian system in the event space. The Birkhoff＇s equations in the event space are given. The Poisson theory of the Birkhoffian system in the event space is established. The definition of the Jacobi last multiplier of the system is given, and the relation between the Jacobi last multiplier and the first integrals of the system is discussed. The researches show that for a Birkhoffian system in the event space, whose configuration is determined by （2n ＋ 1） Birkhoff＇s variables, the solution of the system can be found by the Jacobi last multiplier if 2n first integrals are known. An example is given to illustrate the application of the results.展开更多
A discrete event system is a dynamical system whose state evolves in time by the occurrence of events at possibly irregular time intervals. Timed Petri nets are a graphical and mathematical modeling tool applicable to...A discrete event system is a dynamical system whose state evolves in time by the occurrence of events at possibly irregular time intervals. Timed Petri nets are a graphical and mathematical modeling tool applicable to discrete event systems in order to represent its states evolution where the timing at which the state changes is taken into consideration. One of the most important performance issues to be considered in a discrete event system is its stability. Lyapunov theory provides the required tools needed to aboard the stability and stabilization problems for discrete event systems modeled with timed Petri nets whose mathematical model is given in terms of difference equations. By proving stability one guarantees a bound on the discrete event systems state dynamics. When the system is unstable, a sufficient condition to stabilize the system is given. It is shown that it is possible to restrict the discrete event systems state space in such a way that boundedness is achieved. However, the restriction is not numerically precisely known. This inconvenience is overcome by considering a specific recurrence equation, in the max-plus algebra, which is assigned to the timed Petri net graphical model.展开更多
In this paper,the parametric equations with multipliers of nonholonomic nonconservative sys- tems in the event space are established,their properties are studied,and their explicit formulation is obtained. And then th...In this paper,the parametric equations with multipliers of nonholonomic nonconservative sys- tems in the event space are established,their properties are studied,and their explicit formulation is obtained. And then the field method for integrating these equations is given.Finally,an example illustrating the appli- cation of the integration method is given.展开更多
The relative amplitude method （RAM） is more suitable for source inversion of low magnitude earthquakes because it avoids the modeling of short-period waveforms. We introduced an improved relative amplitude method （...The relative amplitude method （RAM） is more suitable for source inversion of low magnitude earthquakes because it avoids the modeling of short-period waveforms. We introduced an improved relative amplitude method （IRAM） which is more robust in practical cases. The IRAM uses a certain function to quantify the fitness between the observed and the predicted relative amplitudes among direct P wave, surface reflected pP and sP waves for a given focal mechanism. Using the IRAM, we got the fault-plane solutions of two earthquakes of mb4.9 and mb3.8, occurred in Issyk-Kul lake, Kyrgyzstan. For the larger event, its fault-plane solutions are consistent with the Harvard＇s CMT solutions. As to the smaller one, the strikes of the solution are consistent with those of the main faults near the epicenter. The synthetic long period waveforms and the predicted P wave first motions of the solutions are consistent with observations at some of regional stations. Finally, we demonstrated that fault-solutions cannot interpret the characteristics of teleseismic P waveforms of the underground nuclear explosion detonated in Democratic People＇s Republic of Korea （DPRK） on October 9, 2006.展开更多
There is a growing interest in the diagnosis and treatment of patients with dementia and cognitive impairment at an early stage. Recent imaging studies have explored neural mechanisms underlying cognitive dysfunction ...There is a growing interest in the diagnosis and treatment of patients with dementia and cognitive impairment at an early stage. Recent imaging studies have explored neural mechanisms underlying cognitive dysfunction based on brain network architecture and functioning. The dorsal anterior cingulate cortex (dACC) is thought to regulate large-scale intrinsic brain networks, and plays a primary role in cognitive processing with the anterior insular cortex (aIC), thus providing salience functions. Although neural mechanisms have been elucidated at the connectivity level by imaging studies, their understanding at the activity level still remains unclear because of limited time-based resolution of conventional imaging techniques. In this study, we investigated temporal activity of the dACC during word (verb) generation tasks based on our newly developed event-related deep brain activity (ER-DBA) method using occipital electroencephalogram (EEG) alpha-2 powers with a time resolution of a few hundred milliseconds. The dACC exhibited dip-like temporal waveforms indicating deactivation in an initial stage of each trial when appropriate verbs were successfully generated. By contrast, monotonous increase was observed for incorrect responses and a decrease was detected for no responses. The dip depth was correlated with the percentage of success. Additionally, the dip depth linearly increased with increasing slow component of the DBA index at rest across all subjects. These findings suggest that dACC deactivation is essential for cognitive processing, whereas its activation is required for goal-oriented behavioral outputs, such as cued speech. Such dACC functioning, represented by the dip depth, is supported by the activity of the upper brainstem region including monoaminergic neural systems.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.10972151)
文摘This paper focuses on studying the Poisson theory and the integration method of a Birkhoffian system in the event space. The Birkhoff＇s equations in the event space are given. The Poisson theory of the Birkhoffian system in the event space is established. The definition of the Jacobi last multiplier of the system is given, and the relation between the Jacobi last multiplier and the first integrals of the system is discussed. The researches show that for a Birkhoffian system in the event space, whose configuration is determined by （2n ＋ 1） Birkhoff＇s variables, the solution of the system can be found by the Jacobi last multiplier if 2n first integrals are known. An example is given to illustrate the application of the results.
文摘A discrete event system is a dynamical system whose state evolves in time by the occurrence of events at possibly irregular time intervals. Timed Petri nets are a graphical and mathematical modeling tool applicable to discrete event systems in order to represent its states evolution where the timing at which the state changes is taken into consideration. One of the most important performance issues to be considered in a discrete event system is its stability. Lyapunov theory provides the required tools needed to aboard the stability and stabilization problems for discrete event systems modeled with timed Petri nets whose mathematical model is given in terms of difference equations. By proving stability one guarantees a bound on the discrete event systems state dynamics. When the system is unstable, a sufficient condition to stabilize the system is given. It is shown that it is possible to restrict the discrete event systems state space in such a way that boundedness is achieved. However, the restriction is not numerically precisely known. This inconvenience is overcome by considering a specific recurrence equation, in the max-plus algebra, which is assigned to the timed Petri net graphical model.
基金The Project is supported by the National Natural Science Foundation of China
文摘In this paper,the parametric equations with multipliers of nonholonomic nonconservative sys- tems in the event space are established,their properties are studied,and their explicit formulation is obtained. And then the field method for integrating these equations is given.Finally,an example illustrating the appli- cation of the integration method is given.
基金supported by Foundation of Verification Researches for Army Control Technology (513310101)
文摘The relative amplitude method （RAM） is more suitable for source inversion of low magnitude earthquakes because it avoids the modeling of short-period waveforms. We introduced an improved relative amplitude method （IRAM） which is more robust in practical cases. The IRAM uses a certain function to quantify the fitness between the observed and the predicted relative amplitudes among direct P wave, surface reflected pP and sP waves for a given focal mechanism. Using the IRAM, we got the fault-plane solutions of two earthquakes of mb4.9 and mb3.8, occurred in Issyk-Kul lake, Kyrgyzstan. For the larger event, its fault-plane solutions are consistent with the Harvard＇s CMT solutions. As to the smaller one, the strikes of the solution are consistent with those of the main faults near the epicenter. The synthetic long period waveforms and the predicted P wave first motions of the solutions are consistent with observations at some of regional stations. Finally, we demonstrated that fault-solutions cannot interpret the characteristics of teleseismic P waveforms of the underground nuclear explosion detonated in Democratic People＇s Republic of Korea （DPRK） on October 9, 2006.
文摘There is a growing interest in the diagnosis and treatment of patients with dementia and cognitive impairment at an early stage. Recent imaging studies have explored neural mechanisms underlying cognitive dysfunction based on brain network architecture and functioning. The dorsal anterior cingulate cortex (dACC) is thought to regulate large-scale intrinsic brain networks, and plays a primary role in cognitive processing with the anterior insular cortex (aIC), thus providing salience functions. Although neural mechanisms have been elucidated at the connectivity level by imaging studies, their understanding at the activity level still remains unclear because of limited time-based resolution of conventional imaging techniques. In this study, we investigated temporal activity of the dACC during word (verb) generation tasks based on our newly developed event-related deep brain activity (ER-DBA) method using occipital electroencephalogram (EEG) alpha-2 powers with a time resolution of a few hundred milliseconds. The dACC exhibited dip-like temporal waveforms indicating deactivation in an initial stage of each trial when appropriate verbs were successfully generated. By contrast, monotonous increase was observed for incorrect responses and a decrease was detected for no responses. The dip depth was correlated with the percentage of success. Additionally, the dip depth linearly increased with increasing slow component of the DBA index at rest across all subjects. These findings suggest that dACC deactivation is essential for cognitive processing, whereas its activation is required for goal-oriented behavioral outputs, such as cued speech. Such dACC functioning, represented by the dip depth, is supported by the activity of the upper brainstem region including monoaminergic neural systems.
