Electroencephalography(EEG)is a non-invasive measurement method for brain activity.Due to its safety,high resolution,and hypersensitivity to dynamic changes in brain neural signals,EEG has aroused much interest in sci...Electroencephalography(EEG)is a non-invasive measurement method for brain activity.Due to its safety,high resolution,and hypersensitivity to dynamic changes in brain neural signals,EEG has aroused much interest in scientific research and medical felds.This article reviews the types of EEG signals,multiple EEG signal analysis methods,and the application of relevant methods in the neuroscience feld and for diagnosing neurological diseases.First,3 types of EEG signals,including time-invariant EEG,accurate event-related EEG,and random event-related EEG,are introduced.Second,5 main directions for the methods of EEG analysis,including power spectrum analysis,time-frequency analysis,connectivity analysis,source localization methods,and machine learning methods,are described in the main section,along with diferent sub-methods and effect evaluations for solving the same problem.Finally,the application scenarios of different EEG analysis methods are emphasized,and the advantages and disadvantages of similar methods are distinguished.This article is expected to assist researchers in selecting suitable EEG analysis methods based on their research objectives,provide references for subsequent research,and summarize current issues and prospects for the future.展开更多
Recently,Jia proposed a formalism to apply the variational principle to a coherent-pair condensate for a two-body Hamiltonian.The present study extends this formalism by including three-body forces.The result is the s...Recently,Jia proposed a formalism to apply the variational principle to a coherent-pair condensate for a two-body Hamiltonian.The present study extends this formalism by including three-body forces.The result is the same as the so-called variation after particle-number projection in the BCS case,but now,the particle number is always conserved,and the time-consuming projection is avoided.Specifically,analytical formulas of the average energy are derived along with its gradient for a three-body Hamiltonian in terms of the coherent-pair structure.Gradient vanishment is required to obtain analytical expressions for the pair structure at the energy minimum.The new algorithm iterates on these pair-structure expressions to minimize energy for a three-body Hamiltonian.The new code is numerically demonstrated when applied to realistic two-body forces and random three-body forces in large model spaces.The average energy can be minimized to practically any arbitrary precision.展开更多
基金supported by the STI2030 Major Projects(2021ZD0204300)the National Natural Science Foundation of China(61803003,62003228).
文摘Electroencephalography(EEG)is a non-invasive measurement method for brain activity.Due to its safety,high resolution,and hypersensitivity to dynamic changes in brain neural signals,EEG has aroused much interest in scientific research and medical felds.This article reviews the types of EEG signals,multiple EEG signal analysis methods,and the application of relevant methods in the neuroscience feld and for diagnosing neurological diseases.First,3 types of EEG signals,including time-invariant EEG,accurate event-related EEG,and random event-related EEG,are introduced.Second,5 main directions for the methods of EEG analysis,including power spectrum analysis,time-frequency analysis,connectivity analysis,source localization methods,and machine learning methods,are described in the main section,along with diferent sub-methods and effect evaluations for solving the same problem.Finally,the application scenarios of different EEG analysis methods are emphasized,and the advantages and disadvantages of similar methods are distinguished.This article is expected to assist researchers in selecting suitable EEG analysis methods based on their research objectives,provide references for subsequent research,and summarize current issues and prospects for the future.
基金Supported by the National Natural Science Foundation of China(11405109)。
文摘Recently,Jia proposed a formalism to apply the variational principle to a coherent-pair condensate for a two-body Hamiltonian.The present study extends this formalism by including three-body forces.The result is the same as the so-called variation after particle-number projection in the BCS case,but now,the particle number is always conserved,and the time-consuming projection is avoided.Specifically,analytical formulas of the average energy are derived along with its gradient for a three-body Hamiltonian in terms of the coherent-pair structure.Gradient vanishment is required to obtain analytical expressions for the pair structure at the energy minimum.The new algorithm iterates on these pair-structure expressions to minimize energy for a three-body Hamiltonian.The new code is numerically demonstrated when applied to realistic two-body forces and random three-body forces in large model spaces.The average energy can be minimized to practically any arbitrary precision.
