This study presents a novel method for optimizing parameters in urban flood models,aiming to address the tedious and complex issues associated with parameter optimization.First,a coupled one-dimensional pipe network r...This study presents a novel method for optimizing parameters in urban flood models,aiming to address the tedious and complex issues associated with parameter optimization.First,a coupled one-dimensional pipe network runoff model and a two-dimensional surface runoff model were integrated to construct an interpretable urban flood model.Next,a principle for dividing urban hydrological response units was introduced,incorporating surface attribute features.The K-means algorithm was used to explore the clustering patterns of the uncertain parameters in the model,and an artificial neural network(ANN)was employed to identify the sensitive parameters.Finally,a genetic algorithm(GA) was used to calibrate the parameter thresholds of the sub-catchment units in different urban land-use zones within the flood model.The results demonstrate that the parameter optimization method based on K-means-ANN-GA achieved an average Nash-Sutcliffe efficiency coefficient(NSE) of 0.81.Compared to the ANN-GA and K-means-deep neural networks(DNN) methods,the proposed method better characterizes the runoff generation and flow processes.This study demonstrates the significant potential of combining machine learning techniques with physical knowledge in parameter optimization research for flood models.展开更多
We construct free Hom-semigroups when its unary operation is multiplicative and is an involution. Our method of construction is by bracketed words. As a consequence , we obtain free Horn-associative algebras generated...We construct free Hom-semigroups when its unary operation is multiplicative and is an involution. Our method of construction is by bracketed words. As a consequence , we obtain free Horn-associative algebras generated by a set under the same conditions for the unary operation.展开更多
Bracketed words are basic structures both in mathematics （such as Rota-Baxter algebras） and mathematical physics （such as rooted trees） where the locations of the substructures are important. In this paper, we giv...Bracketed words are basic structures both in mathematics （such as Rota-Baxter algebras） and mathematical physics （such as rooted trees） where the locations of the substructures are important. In this paper, we give the classification of the relative locations of two bracketed subwords of a bracketed word in an operated semigroup into the separated, nested, and intersecting cases. We achieve this by establishing a correspondence between relative locations of bracketed words and those of words by applying the concept of Motzkin words which are the algebraic forms of Motzkin paths.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos.42271483,42071364)the Postgraduate Research&Practice Innovation Program of Jiangsu Province (Grant No.KYCX23_1696).
文摘This study presents a novel method for optimizing parameters in urban flood models,aiming to address the tedious and complex issues associated with parameter optimization.First,a coupled one-dimensional pipe network runoff model and a two-dimensional surface runoff model were integrated to construct an interpretable urban flood model.Next,a principle for dividing urban hydrological response units was introduced,incorporating surface attribute features.The K-means algorithm was used to explore the clustering patterns of the uncertain parameters in the model,and an artificial neural network(ANN)was employed to identify the sensitive parameters.Finally,a genetic algorithm(GA) was used to calibrate the parameter thresholds of the sub-catchment units in different urban land-use zones within the flood model.The results demonstrate that the parameter optimization method based on K-means-ANN-GA achieved an average Nash-Sutcliffe efficiency coefficient(NSE) of 0.81.Compared to the ANN-GA and K-means-deep neural networks(DNN) methods,the proposed method better characterizes the runoff generation and flow processes.This study demonstrates the significant potential of combining machine learning techniques with physical knowledge in parameter optimization research for flood models.
基金This work was supported by the National Natural Science Foundation of China （Grant No. 11371178） and the National Science Foundation of US （Grant No. DMS 1001855）.
文摘We construct free Hom-semigroups when its unary operation is multiplicative and is an involution. Our method of construction is by bracketed words. As a consequence , we obtain free Horn-associative algebras generated by a set under the same conditions for the unary operation.
基金Acknowledgements The authors thank the Kavli Institute for Theoretical Physics China and the Morningside Center for Mathematics in Beijing for their hospitality and support. This work was supported by the National Natural Science Foundation of China （Grant Nos. 11201201, 11371178）, the Fundamental Research Funds for the Central Universities （lzujbky-2013-8）, and the National Science Foundation of US （Grant No. DMS 1001855）.
文摘Bracketed words are basic structures both in mathematics （such as Rota-Baxter algebras） and mathematical physics （such as rooted trees） where the locations of the substructures are important. In this paper, we give the classification of the relative locations of two bracketed subwords of a bracketed word in an operated semigroup into the separated, nested, and intersecting cases. We achieve this by establishing a correspondence between relative locations of bracketed words and those of words by applying the concept of Motzkin words which are the algebraic forms of Motzkin paths.
