The hydrodynamics of active liquid crystal models has attracted much attention in recent years due to many applications of these models.In this paper,we study the weak-strong uniqueness for the Leray-Hopf type weak so...The hydrodynamics of active liquid crystal models has attracted much attention in recent years due to many applications of these models.In this paper,we study the weak-strong uniqueness for the Leray-Hopf type weak solutions to the incompressible active liquid crystals in R^(3).Our results yield that if there exists a strong solution,then it is unique among the Leray-Hopf type weak solutions associated with the same initial data.展开更多
We consider the Navier-Stokes equations with a pressure function satisfying a hard-sphere law.That means the pressure,as a function of the density,becomes infinite when the density approaches a finite critical value.U...We consider the Navier-Stokes equations with a pressure function satisfying a hard-sphere law.That means the pressure,as a function of the density,becomes infinite when the density approaches a finite critical value.Under some structural constraints imposed on the pressure law,we show a weak-strong uniqueness principle in periodic spatial domains.The method is based on a modified relative entropy inequality for the system.The main difficulty is that the pressure potential associated with the internal energy of the system is largely dominated by the pressure itself in the area close to the critical density.As a result,several terms appearing in the relative energy inequality cannot be controlled by the total energy.展开更多
在图像语义分割领域,无监督领域自适应技术的发展有效降低了模型对标注数据的依赖,提升了自动驾驶等智能系统的效率和广泛适用性。针对无监督领域自适应技术在新场景泛化能力有限及在稀有类别中分割效果差的问题,文章提出了一种基于强...在图像语义分割领域,无监督领域自适应技术的发展有效降低了模型对标注数据的依赖,提升了自动驾驶等智能系统的效率和广泛适用性。针对无监督领域自适应技术在新场景泛化能力有限及在稀有类别中分割效果差的问题,文章提出了一种基于强弱一致性的无监督领域自适应语义分割算法。算法首先通过增加特征级别的增强,拓展图像增强空间的维度,改善了只利用图像级增强局限性。其次,采用基于能量分数的伪标签筛选方法,筛选出足够接近当前训练数据的样本赋予伪标签,避免了使用Softmax置信度方法在稀有类别中存在局限性,使模型更新更加稳健。最后,构建结合图像级别增强和特征级别增强的双重一致性框架,更充分的利用一致性训练,进一步提高模型的泛化能力。实验结果证明,提出的方法在GTA5-to-Cityscapes公开数据集中平均交并比指标(mean Intersection over Union,mIoU)可提升至52.6%,较PixMatch算法,性能提升了4.3%。展开更多
基金partially supported by NSFC(11831003,12031012)the Institute of Modern Analysis-A Frontier Research Center of Shanghai。
文摘The hydrodynamics of active liquid crystal models has attracted much attention in recent years due to many applications of these models.In this paper,we study the weak-strong uniqueness for the Leray-Hopf type weak solutions to the incompressible active liquid crystals in R^(3).Our results yield that if there exists a strong solution,then it is unique among the Leray-Hopf type weak solutions associated with the same initial data.
基金the European Research Council under the European Union’s Seventh Framework Programme (Grant No. FP7/2007-2013)European Research Council (ERC) Grant Agreement (Grant No. 320078)The Institute of Mathematics of the Academy of Sciences of the Czech Republic was supported by Rozvoj Vyzkumn Organizace (RVO) (Grant No. 67985840)
文摘We consider the Navier-Stokes equations with a pressure function satisfying a hard-sphere law.That means the pressure,as a function of the density,becomes infinite when the density approaches a finite critical value.Under some structural constraints imposed on the pressure law,we show a weak-strong uniqueness principle in periodic spatial domains.The method is based on a modified relative entropy inequality for the system.The main difficulty is that the pressure potential associated with the internal energy of the system is largely dominated by the pressure itself in the area close to the critical density.As a result,several terms appearing in the relative energy inequality cannot be controlled by the total energy.
文摘在图像语义分割领域,无监督领域自适应技术的发展有效降低了模型对标注数据的依赖,提升了自动驾驶等智能系统的效率和广泛适用性。针对无监督领域自适应技术在新场景泛化能力有限及在稀有类别中分割效果差的问题,文章提出了一种基于强弱一致性的无监督领域自适应语义分割算法。算法首先通过增加特征级别的增强,拓展图像增强空间的维度,改善了只利用图像级增强局限性。其次,采用基于能量分数的伪标签筛选方法,筛选出足够接近当前训练数据的样本赋予伪标签,避免了使用Softmax置信度方法在稀有类别中存在局限性,使模型更新更加稳健。最后,构建结合图像级别增强和特征级别增强的双重一致性框架,更充分的利用一致性训练,进一步提高模型的泛化能力。实验结果证明,提出的方法在GTA5-to-Cityscapes公开数据集中平均交并比指标(mean Intersection over Union,mIoU)可提升至52.6%,较PixMatch算法,性能提升了4.3%。
