Neural firing patterns are investigated by using symbolic dynamics. Bifurcation behaviour of the Hindmarsh-Rose （HR） neuronal model is simulated with the external stimuli gradually decreasing, and various firing act...Neural firing patterns are investigated by using symbolic dynamics. Bifurcation behaviour of the Hindmarsh-Rose （HR） neuronal model is simulated with the external stimuli gradually decreasing, and various firing activities with different topological structures are orderly numbered. Through constructing first-return maps of interspike intervals, all firing patterns are described and identified by symbolic expressions. On the basis of ordering rules of symbolic sequences, the corresponding relation between parameters and firing patterns is established, which will be helpful for encoding neural information. Moreover, using the operation rule of ＊ product, generation mechanisms and intrinsic configurations of periodic patterns can be distinguished in detail. Results show that the symbolic approach is a powerful tool to study neural firing activities. In particular, such a coarse-grained way can be generalized in neural electropt/ysiological experiments to extract much valuable information from complicated experimental data.展开更多
In this paper, we propose a flexible knowledge representation framework which utilizes Symbolic Regression to learn and mathematical expressions to represent the knowledge to be captured from data. In this approach, l...In this paper, we propose a flexible knowledge representation framework which utilizes Symbolic Regression to learn and mathematical expressions to represent the knowledge to be captured from data. In this approach, learning algorithms are used to generate new insights which can be added to domain knowledge bases supporting again symbolic regression. This is used for the generalization of the well-known regression analysis to fulfill supervised classification. The approach aims to produce a learning model which best separates the class members of a labeled training set. The class boundaries are given by a separation surface which is represented by the level set of a model function. The separation boundary is defined by the respective equation. In our symbolic approach, the learned knowledge model is represented by mathematical formulas and it is composed of an optimum set of expressions of a given superset. We show that this property gives human experts options to gain additional insights into the application domain. Furthermore, the representation in terms of mathematical formulas (e.g., the analytical model and its first and second derivative) adds additional value to the classifier and enables to answer questions, which sub-symbolic classifier approaches cannot. The symbolic representation of the models enables an interpretation by human experts. Existing and previously known expert knowledge can be added to the developed knowledge representation framework or it can be used as constraints. Additionally, the knowledge acquisition framework can be repeated several times. In each step, new insights from the search process can be added to the knowledge base to improve the overall performance of the proposed learning algorithms.展开更多
文摘Neural firing patterns are investigated by using symbolic dynamics. Bifurcation behaviour of the Hindmarsh-Rose （HR） neuronal model is simulated with the external stimuli gradually decreasing, and various firing activities with different topological structures are orderly numbered. Through constructing first-return maps of interspike intervals, all firing patterns are described and identified by symbolic expressions. On the basis of ordering rules of symbolic sequences, the corresponding relation between parameters and firing patterns is established, which will be helpful for encoding neural information. Moreover, using the operation rule of ＊ product, generation mechanisms and intrinsic configurations of periodic patterns can be distinguished in detail. Results show that the symbolic approach is a powerful tool to study neural firing activities. In particular, such a coarse-grained way can be generalized in neural electropt/ysiological experiments to extract much valuable information from complicated experimental data.
文摘In this paper, we propose a flexible knowledge representation framework which utilizes Symbolic Regression to learn and mathematical expressions to represent the knowledge to be captured from data. In this approach, learning algorithms are used to generate new insights which can be added to domain knowledge bases supporting again symbolic regression. This is used for the generalization of the well-known regression analysis to fulfill supervised classification. The approach aims to produce a learning model which best separates the class members of a labeled training set. The class boundaries are given by a separation surface which is represented by the level set of a model function. The separation boundary is defined by the respective equation. In our symbolic approach, the learned knowledge model is represented by mathematical formulas and it is composed of an optimum set of expressions of a given superset. We show that this property gives human experts options to gain additional insights into the application domain. Furthermore, the representation in terms of mathematical formulas (e.g., the analytical model and its first and second derivative) adds additional value to the classifier and enables to answer questions, which sub-symbolic classifier approaches cannot. The symbolic representation of the models enables an interpretation by human experts. Existing and previously known expert knowledge can be added to the developed knowledge representation framework or it can be used as constraints. Additionally, the knowledge acquisition framework can be repeated several times. In each step, new insights from the search process can be added to the knowledge base to improve the overall performance of the proposed learning algorithms.
