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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Inverse Problems and Their Applications
逆问题 系统辨识 正问题
2023/5/12
反问题和正问题是成对出现的。通常，学术界将已知原因（输入）、过程（模型）而探求结果（输出）的一类问题称为正问题。与此相对应，就有了两种反问题：已知模型、输出求未知输入的“溯源”问题和已知输入、输出来反求模型（或模型参数）的系统辨识问题。在现实社会和人类生活中，反问题无处不在；在关系国家命脉的经济生产和国防军事领域中反问题更是随处可见。例如，与人类健康福祉密切相关的无痛无损伤、在体表进行测量的医学诊...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Hausdorff dimension, singular vectors and divergent trajectories
豪斯多夫维数 奇异向量 发散轨迹
2023/5/12
In this talk, I will give a survey of results related to the problem of computing Hausdorff dimension of various dynamically defined sets, such as singular vectors. The aim is to try to describe the l...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：超导量子退火技术
超导 量子退火 量子隧穿效应
2023/5/12
基于量子隧穿效应的量子退火技术是利用量子隧穿现象来优化问题解的一种方法。在量子退火中，通过调控量子系统的能量和耦合强度，利用量子隧穿效应来探索解空间，并寻找最优解。这种技术可以在优化问题中快速搜索全局最小值，相较于传统算法具有潜在的加速优势。本报告重点介绍一下基于超导电路实现超导量子退火技术，Ising模型、二次无约束二值优化QUBO 模型是指（Quadratic Unconstrained Bi...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The complexity of computing Markov perfect equilibrium in general-sum stochastic games
一般 随机博弈 马尔可夫完美均衡 计算复杂性
2023/5/12
Similar to the role of Markov decision processes in reinforcement learning, Markov games (also known as stochastic games) form the basis for the study of multi-agent reinforcement learning and sequenc...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Coupling by change of measures for dimension-free Harnack inequality
无维 哈纳克不等式 测度 耦合
2023/5/12
简要介绍概率论中的耦合方法及其在基础数学中的应用。引入新的变测度耦合，以简单的随机微分方程为例，将其应用于建立无穷维Harnack不等式、Bisnut导数公式和分布积分公式。
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：离散型数学在信息科学中的一些应用
离散 数学 信息科学
2023/5/12
上世纪六十年代以来，随着数字通信技术的快速发展，离散型数学（组合设计和图论，数论，代数以及有限域上代数几何）逐渐成为通信许多应用领域的重要数学工具。本报告沿着六十年来历史发展的足迹，通俗介绍在代数纠错码和信息安全方面一些重要发展和数学问题，以实际例子说明数学所起的作用。
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars： Derivation of the Vlasov equation from quantum many-body Fermionic systems with singular interaction
奇异相互作用 量子多体 费米子系统 弗拉索夫方程
2023/5/12
We consider the combined mean-field and semiclassical limit for a system of the N fermions interacting through singular potentials. We prove the uniformly in the Planck constant h propagation of quant...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Stability of degree-2 Rossby-Haurwitz waves
2度 罗斯比-豪维茨波 稳定性
2023/5/12
Rossby-Haurwitz waves are an important class of explicit solutions to the incompressible Euler equation on a rotating 2-sphere. We will introduce our recent work on the nonlinear stability of degree-2...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Solitons and Breathers in the modulus KdV equations
模量 KdV方程 孤子 呼吸器
2023/5/12
Compared to the soliton solutions, the breathers, which are constructed in the mKdV or Gardner equation via integrability methods, are less studied. In our numerical study, we show the interactions be...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：中国式现代化与积极应对人口老龄化战略
中国式现代化 积极应对 人口老龄化
2023/5/10
人口快速老龄化、超大规模老年人口是中国式现代化面临的重要国情。当下，中国正面临人口老龄化加速发展期与实现中国式现代化过程叠加的发展新阶段，创造有利于经济高质量发展的人口条件，以及形成适应人口老龄化的经济发展新模式，是中国社会主义现代化发展的必由之路。因此，要以积极的态度看待人口老龄化带来的风险和挑战，挖掘老龄社会中存在的机遇，并主动应对人口老龄化问题，从根本上解决造成人口老龄化不断加速的难点、痛点...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：含任意未知输入下的状态估计与参数辨识
任意未知输入 状态估计 参数辨识
2023/5/10
现存的含未知输入系统的卡尔曼滤波方法假设噪声协方差矩阵已知而且要求系统强可观。针对实际中广泛存在的不精确知道噪声协方差矩阵或系统非强可观的情况，如何在工程应用如机器人定位中实现卡尔曼滤波是一个重要且亟需解决的难题。本报告中，报告人将探讨含未知输入滤波领域的研究现状，并以基于相关性的方法为典型，讨论含未知输入下噪声协方差矩阵的可辨识性问题。如果时间允许，报告人也将探讨其在机器人智能感知与决策方面的一...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Harmonic analysis meets wave equation
谐波分析 符合 波动方程
2023/5/10
In this talk I plan to survey some progress on Hardy and BMO spaces, Riesz transforms, Bochner-Riesz means and spherical means by using the method of wave equation,and show interesting connections and...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Introduction to Allard’s regularity theorem（I）
阿拉德 正则性 定理 导论
2023/5/10
In this short seminar, we will discuss the proof of the Allard regularity theorem, which is an $\epsilon$-regularity theorem for the mean curvature equation in the Geometric Measure Theory(GMT) settin...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Singular integral and geometry
奇异积分 几何 谐波分析
2023/5/8
The geometric considerations enter in a decisive way in many questions of harmonic analysis. For example, the estimation of the Fourier transform of surface-carried measure, which played a key role in...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Numerical PDEs for Fluid-Structure Interaction (FSI) Problems
流固耦合 数值 偏微分方程
2023/5/8
The interaction of a flexible structure with a flowing fluid in which it is submersed or by which it is surrounded gives rise to a rich variety of physical phenomena with applications in many fields o...