为了更全面地对睡眠脑电进行特征提取,提出一种基于多视图与注意力机制的睡眠脑电分期方法。首先针对原始睡眠脑电信号构造时域和时频域两类视图数据;然后设计融合注意力机制的混合神经网络对多视图数据进行表征学习;接着通过双向长短...为了更全面地对睡眠脑电进行特征提取,提出一种基于多视图与注意力机制的睡眠脑电分期方法。首先针对原始睡眠脑电信号构造时域和时频域两类视图数据;然后设计融合注意力机制的混合神经网络对多视图数据进行表征学习;接着通过双向长短时记忆(bi-directional long short-term memory,BiLSTM)网络进一步学习睡眠阶段之间的转换规则;最后使用Softmax函数进行睡眠分期,并利用类别加权损失函数解决睡眠数据类别不均衡的问题。实验使用Sleep-EDF数据库中前20名受试者的单通道脑电信号并采用20折交叉验证对模型进行性能评估,睡眠分期准确率达到83.7%,宏平均F_(1)值达到79.0%,Cohen′s Kappa系数达到0.78。与现有方法相比,算法性能提升明显,证明了所提方法的有效性。展开更多
This manuscript addresses Muckenhoupt Ap weight theory in connection to Mor- rey and BMO spaces. It is proved that a; belongs to Muckenhoupt Ap class, if and only if Hardy-Littlewood maximal function M is bounded from...This manuscript addresses Muckenhoupt Ap weight theory in connection to Mor- rey and BMO spaces. It is proved that a; belongs to Muckenhoupt Ap class, if and only if Hardy-Littlewood maximal function M is bounded from weighted Lebesgue spaces LP（w） to weighted Morrey spaces Mpq（ω） for 1 〈 q 〈 p 〈 ∞. As a corollary, if M is （weak） bounded on Mpq（ω）, then ω∈Ap. The Ap condition also characterizes the boundedness of the Riesz transform Rj and convolution operators Tε on weighted Morrey spaces. Finally, we show that ω∈Ap if and only if ω∈BMOp＇ （ω） for 1 ≤ p 〈 ∞ and 1/p ＋ 1/p＇ = 1.展开更多
In this work we prove the weighted Gevrey regularity of solutions to the incompressible Euler equation with initial data decaying polynomially at infinity. This is motivated by the well-posedness problem of vertical b...In this work we prove the weighted Gevrey regularity of solutions to the incompressible Euler equation with initial data decaying polynomially at infinity. This is motivated by the well-posedness problem of vertical boundary layer equation for fast rotating fluid. The method presented here is based on the basic weighted L;-estimate, and the main difficulty arises from the estimate on the pressure term due to the appearance of weight function.展开更多
文摘为了更全面地对睡眠脑电进行特征提取,提出一种基于多视图与注意力机制的睡眠脑电分期方法。首先针对原始睡眠脑电信号构造时域和时频域两类视图数据;然后设计融合注意力机制的混合神经网络对多视图数据进行表征学习;接着通过双向长短时记忆(bi-directional long short-term memory,BiLSTM)网络进一步学习睡眠阶段之间的转换规则;最后使用Softmax函数进行睡眠分期,并利用类别加权损失函数解决睡眠数据类别不均衡的问题。实验使用Sleep-EDF数据库中前20名受试者的单通道脑电信号并采用20折交叉验证对模型进行性能评估,睡眠分期准确率达到83.7%,宏平均F_(1)值达到79.0%,Cohen′s Kappa系数达到0.78。与现有方法相比,算法性能提升明显,证明了所提方法的有效性。
基金supported by National Natural Science Foundation of China(Grant No.11661075)
文摘This manuscript addresses Muckenhoupt Ap weight theory in connection to Mor- rey and BMO spaces. It is proved that a; belongs to Muckenhoupt Ap class, if and only if Hardy-Littlewood maximal function M is bounded from weighted Lebesgue spaces LP（w） to weighted Morrey spaces Mpq（ω） for 1 〈 q 〈 p 〈 ∞. As a corollary, if M is （weak） bounded on Mpq（ω）, then ω∈Ap. The Ap condition also characterizes the boundedness of the Riesz transform Rj and convolution operators Tε on weighted Morrey spaces. Finally, we show that ω∈Ap if and only if ω∈BMOp＇ （ω） for 1 ≤ p 〈 ∞ and 1/p ＋ 1/p＇ = 1.
基金supported by NSF of China(11422106)the NSF of China(11171261)+1 种基金Fok Ying Tung Education Foundation(151001)supported by“Fundamental Research Funds for the Central Universities”
文摘In this work we prove the weighted Gevrey regularity of solutions to the incompressible Euler equation with initial data decaying polynomially at infinity. This is motivated by the well-posedness problem of vertical boundary layer equation for fast rotating fluid. The method presented here is based on the basic weighted L;-estimate, and the main difficulty arises from the estimate on the pressure term due to the appearance of weight function.
文摘深度学习近年来在故障诊断领域受到广泛应用,但基于深度学习的故障诊断模型缺乏工程上的物理解释性,难以保证其故障诊断结果的稳定性。以轴承为例,建立了以小波时频图像为故障诊断依据的卷积神经网络模型(convolutional neural network,CNN),提出了一种基于梯度加权类激活热力图(gradient-weighted class activation map,Grad-CAM)的网络模型鲁棒性分析方法,并利用美国凯斯西储大学(Case Western Reserve University,CWRU)轴承数据集进行验证。首先,将故障直径轴承数据以不同方式混合并训练大、小多个模型。其次,利用Grad-CAM方法,建立时频区域与故障模式之间的联系。最后,利用其他工况下的轴承故障数据,以及含噪数据进行测试,并根据结果结合模型最注重的时频区域进行分析。结果表明,基于深度学习的轴承故障诊断模型在参数较少时更加注重低频区域,并能使其具有更好的鲁棒性。
