Black-Scholes Model (B-SM) simulates the dynamics of financial market and contains instruments such as options and puts which are major indices requiring solution. B-SM is known to estimate the correct prices of Europ...Black-Scholes Model (B-SM) simulates the dynamics of financial market and contains instruments such as options and puts which are major indices requiring solution. B-SM is known to estimate the correct prices of European Stock options and establish the theoretical foundation for Option pricing. Therefore, this paper evaluates the Black-Schole model in simulating the European call in a cash flow in the dependent drift and focuses on obtaining analytic and then approximate solution for the model. The work also examines Fokker Planck Equation (FPE) and extracts the link between FPE and B-SM for non equilibrium systems. The B-SM is then solved via the Elzaki transform method (ETM). The computational procedures were obtained using MAPLE 18 with the solution provided in the form of convergent series.展开更多
Micro-expressions are spontaneous, unconscious movements that reveal true emotions.Accurate facial movement information and network training learning methods are crucial for micro-expression recognition.However, most ...Micro-expressions are spontaneous, unconscious movements that reveal true emotions.Accurate facial movement information and network training learning methods are crucial for micro-expression recognition.However, most existing micro-expression recognition technologies so far focus on modeling the single category of micro-expression images and neural network structure.Aiming at the problems of low recognition rate and weak model generalization ability in micro-expression recognition, a micro-expression recognition algorithm is proposed based on graph convolution network(GCN) and Transformer model.Firstly, action unit(AU) feature detection is extracted and facial muscle nodes in the neighborhood are divided into three subsets for recognition.Then, graph convolution layer is used to find the layout of dependencies between AU nodes of micro-expression classification.Finally, multiple attentional features of each facial action are enriched with Transformer model to include more sequence information before calculating the overall correlation of each region.The proposed method is validated in CASME II and CAS(ME)^2 datasets, and the recognition rate reached 69.85%.展开更多
文摘Black-Scholes Model (B-SM) simulates the dynamics of financial market and contains instruments such as options and puts which are major indices requiring solution. B-SM is known to estimate the correct prices of European Stock options and establish the theoretical foundation for Option pricing. Therefore, this paper evaluates the Black-Schole model in simulating the European call in a cash flow in the dependent drift and focuses on obtaining analytic and then approximate solution for the model. The work also examines Fokker Planck Equation (FPE) and extracts the link between FPE and B-SM for non equilibrium systems. The B-SM is then solved via the Elzaki transform method (ETM). The computational procedures were obtained using MAPLE 18 with the solution provided in the form of convergent series.
基金Supported by Shaanxi Province Key Research and Development Project (2021GY-280)the National Natural Science Foundation of China (No.61834005,61772417,61802304)。
文摘Micro-expressions are spontaneous, unconscious movements that reveal true emotions.Accurate facial movement information and network training learning methods are crucial for micro-expression recognition.However, most existing micro-expression recognition technologies so far focus on modeling the single category of micro-expression images and neural network structure.Aiming at the problems of low recognition rate and weak model generalization ability in micro-expression recognition, a micro-expression recognition algorithm is proposed based on graph convolution network(GCN) and Transformer model.Firstly, action unit(AU) feature detection is extracted and facial muscle nodes in the neighborhood are divided into three subsets for recognition.Then, graph convolution layer is used to find the layout of dependencies between AU nodes of micro-expression classification.Finally, multiple attentional features of each facial action are enriched with Transformer model to include more sequence information before calculating the overall correlation of each region.The proposed method is validated in CASME II and CAS(ME)^2 datasets, and the recognition rate reached 69.85%.