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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Quantum Algorithms for High-Dimensional Sampling Problems
高维采样 量子算法 高维抽样问题
2023/4/14
High-dimensional sampling problems are ubiquitous in statistics, operations research, machine learning, etc. In this talk, I will introduce quantum algorithms for two important problems in high-dimens...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：量子直接通信：原理与进展
量子直接通信 量子通信技术 中继量子网络
2023/4/14
量子直接通信是一种不同于量子密钥分发的量子通信技术。2000年由龙桂鲁等原创提出，具有感知和阻止窃听的能力，实现噪声和窃听信道中的安全可靠通信。20多年来，实用化技术取得突破，成功研制样机，可实现100公里光纤kbps量级的通信，并在金融等场景开展试应用。美国新美国安全中心的报告称，量子直接通信能继续提高量子通信整体的安全性和价值定位。6G研究白皮书指出，量子直接通信在6G有巨大潜力。建设基于量子...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Efficient algorithms for the anisotropic dendritic crystal models
各向异性 树枝状晶体 有效算法
2023/4/14
We consider numerical approximations of the anisotropic phase-field dendritic crystal growth model. This is a highly complex coupled nonlinear system consisting of the anisotropic Allen-Cahn equation,...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Deep neural network approximation to inverse conductivity problems for elliptic equations
椭圆方程 反电导率 深度神经网络
2023/4/14
The focus of this talk is on the numerical methods used to identify parameters in partial differential equations. Typically, an optimization approach is used to solve this class of inverse problems, w...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：计算机图形学：从描点法到内容生成
计算机图形学 描点法 内容生成
2023/4/17
计算机图形学是用计算机表示生成处理三维图形的一门学科。半个多世纪以来，计算机图形学经历了连续曲线曲面表示，数字几何处理，数据驱动及内容生成几个阶段。报告简述了图形学的历史变化，并对未来发展趋势进行了展望。
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Well/ill-posedness bifurcation for the Boltzmann equation
玻尔兹曼方程 好/非适定 分岔
2023/4/17
We study the well/ill-posedness of the Boltzmann equation with dispersive methods. We take the constant collision kernel case as the 1st example. We construct a family of special solutions, which are ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：基于自监督表征学习的图像聚类算法研究
自监督表征学习 图像聚类算法 语义伪标签
2023/4/17
自监督学习可以为图像聚类算法提供良好的表征，但是当表征和聚类同步学习时会存在一些问题。具体来说，基于对比的自监督学习方法通常需要大量的负样本来使得所有样本的表征分离，但是负样本会带来类别冲突，进而影响下游的聚类性能；反之，基于非对比的自监督学习方法虽然避免了类别冲突问题，但是由于缺少负样本，与聚类任务联合优化时容易造成聚类崩溃。本报告将围绕这两个问题，分别介绍基于语义伪标签和原型对比的图像聚类算法...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Maximal $L^1$-regularity and application to a free boundary problem of Navier-Stokes equations near half-space in critical space (I)
临界空间 近半空间 纳维-斯托克斯方程 最大$L^1$-正则性 自由边界问题
2023/4/17
In this talk, time-dependent free surface problem for the incompressible Navier-Stokes equations which describes the motion of viscous incompressible fluid nearly half-space are considered. We will di...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Boltzmann方程的适定性和流体动力学极限
Boltzmann方程 适定性 流体动力学 极限
2023/4/17
Boltzmann 方程是统计力学中的基本方程，被用来描述稀疏气体的运动，其解的整体适定性和大时间渐近行为是偏微分方程领域的重要问题。另一方面，Hilbert 于1912 年提出了Boltzmann 方程的Hilbert 展开，从形式上说明了Boltzmann 方程的一阶近似是可压缩Euler 方程。此后，从数学上严格证明Boltzmann 方程到可压Euler 方程的流体动力学极限一直是很多数学...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：不可压缩理想磁流体方程的自由边界问题
不可压缩 理想磁流体方程 自由边界问题
2023/4/17
针对不可压缩理想磁流体方程自由边界问题的适定性，对有界初始区域的情形做较详细的阐述，并对相关的背景、研究进展和存在的问题作简要的介绍。
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Qualitative study of two types of kinetic equations
动力学方程 定性研究 弗拉索夫方程
2023/4/18
In recent years, the study of kinetic equations has attracted much attention because it involves many important scientific phenomena and fields of science, such as nuclear reactor diffusion phenomena,...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Graph Refinement via Simultaneously Low-rank and Sparse Approximation
低秩 稀疏近似 图细化
2023/4/18
Graphs play an important role in many fields of machine learning such as clustering. Many graph-based machine learning approaches assume that the graphs have hidden group structures. However, the grou...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Global existence and decay of solutions to compressible Prandtl system with small analytic data
少量分析数据 可压缩 Prandtl系统解 全局存在 衰减
2023/4/18
In this talk, we shall prove the global existence and the large time decay estimate of solutions to compressible Prandtl system with small initial data, which is analytical in the tangential variable....
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Solution Landscapes of Nematic Liquid Crystal Systems
向列液晶系统 解决方案 各向异性材料
2023/4/18
Nematic liquid crystals (NLCs) are anisotropic material intermediate that combine the fluidity of liquids with the orientational order of solids. NLCs are best known for their applications in the thri...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Optimal decay rates on compressible Navier-Stokes equations with degenerate viscosity and vacuum
简并粘度 真空 可压缩 NS方程 最佳衰减率
2023/4/18
In this talk, we consider the large time behavior of the weak solution to the free boundary problem for one-dimensional isentropic compressible Navier-Stokes equations with degenerate viscosity and va...