In this paper, the global controllability for a class of high dimensional polynomial systems has been investigated and a constructive algebraic criterion algorithm for their global controllability has been obtained. B...In this paper, the global controllability for a class of high dimensional polynomial systems has been investigated and a constructive algebraic criterion algorithm for their global controllability has been obtained. By the criterion algorithm, the global controllability can be determined in finite steps of arithmetic operations. The algorithm is imposed on the coefficients of the polynomials only and the analysis technique is based on Sturm Theorem in real algebraic geometry and its modern progress. Finally, the authors will give some examples to show the application of our results.展开更多
基金supported by the Natural Science Foundation of China under Grant Nos.60804008,61174048and 11071263the Fundamental Research Funds for the Central Universities and Guangdong Province Key Laboratory of Computational Science at Sun Yat-Sen University
文摘In this paper, the global controllability for a class of high dimensional polynomial systems has been investigated and a constructive algebraic criterion algorithm for their global controllability has been obtained. By the criterion algorithm, the global controllability can be determined in finite steps of arithmetic operations. The algorithm is imposed on the coefficients of the polynomials only and the analysis technique is based on Sturm Theorem in real algebraic geometry and its modern progress. Finally, the authors will give some examples to show the application of our results.
文摘现有的基于双向长短时记忆(BiLSTM)网络的命名实体识别(NER)模型难以全面理解文本的整体语义以及捕捉复杂的实体关系。因此,提出一种基于全域信息融合和多维关系感知的NER模型。首先,通过BERT(Bidirectional Encoder Representations from Transformers)获取输入序列的向量表示,并结合BiLSTM进一步学习输入序列的上下文信息。其次,提出由梯度稳定层和特征融合模块组成的全域信息融合机制:前者使模型保持稳定的梯度传播并更新优化输入序列的表示,后者则融合BiLSTM的前后向表示获取更全面的特征表示。接着,构建多维关系感知结构学习不同子空间单词的关联性,以捕获文档中复杂的实体关系。此外,使用自适应焦点损失函数动态调整不同类别实体的权重,提高模型对少数类实体的识别性能。最后,在7个公开数据集上将所提模型和11个基线模型进行对比,实验结果表明所提模型的F1值均优于对比模型,可见该模型的综合性较优。
