Computational & Applied Mathematics (CAM) Seminar
Student No.:40
Time:Wed 15:20-16:55
Instructor:Shi Zuoqiang  [Tsinghua University]
Place:Conference Room 1, Jin Chun Yuan West Bldg.
Starting Date:2018-3-8
Ending Date:2018-6-13



Speaker: Qin Li [University of Wisconsin at Madison]


Title: Boundary layers in kinetic-fluid coupling


Abstract: Many kinetic equations have the corresponding fluid limit. In the zero limit of the Knudsen number, one derives the Euler equation out of the Boltzmann equation and the heat equation out of the radiative transfer equation. While there are good numerical solvers for both kinetic and fluid equations, it is not quite well-understood when the two regimes co-exist. In this talk, we model the layer between the fluid and the kinetic using a half-space equation, study the well-posedness, design a numerical solver, and utilize it to couple the two sets of equations that govern separate domains.




Speaker: 高跃 [清华大学软件学院]


Title: 超图结构学习


Abstract: 本报告主要介绍超图结构学习的理论及应用。超图是一种广义的图结构,因其具有较强的数据样本间非线性高阶关联的刻画和挖掘能力而被广泛应用于数据分类、检索等任务中。针对这一技术及其在多领域中的应用,本报告首先介绍基于超图结构的多种建模方法,特别是基于单模态和多模态环境下的数据关联建模机制。进一步,围绕超图上的关联学习介绍从传统的学习方法到超图结构学习的系列算法。针对实际应用中存在的数据样本不平衡、分类代价敏感、数据关联建模复杂等挑战,介绍了基于代价敏感信息的超图学习及动态超图结构学习方法。最后,介绍了超图结构学习在软件缺陷检测、列车节能自动驾驶、遥感数据分类等领域的应用。


高跃,清华大学软件学院副教授、博士生导师。2012年毕业于清华大学获得博士学位。2012年至2016年分别于新加坡国立大学和北卡罗来纳大学教堂山分校从事计算机及医学领域研究工作。2016年入选国家千人计划青年项目。近年来作为项目负责人承担国家重点研发计划重点专项、自然科学基金-广东联合基金重点项目等多项课题,主要研究领域为计算机视觉、机器学习及医学图像处理,在IEEE、TIP、TCSVT、TMM、TNNLS、HBM及MICCAI、CVPR、AAAI、IJCAI等国际期刊及会议发表论文100余篇,由Elsevier出版视觉计算英文专著两部,相关成果被引用4500余次(Google Scholar)。担任Journal of Visual Communication and Image Representation、Neurocomputing等多个国际期刊编委。





Speaker: Hongwei Li [Capital Normal University]


Title: An Image Reconstruction Model Regularized by Edge-preserving Diffusion and Smoothing for Limited-angle Computed Tomography


Abstract: Limited-angle computed tomography is a very challenging problem in applications. Due to high degree of ill-posedness, conventional reconstruction algorithms will introduce blurring along the directions perpendicular to the missing X-Rays as well as streaking artifacts when applied on limited-angle data. we propose a reconstruction model which incorporates two regularization terms that play the role of edge-preserving diffusion and smoothing, along the $x$-direction and $y$-direction respectively. Our model is based on the observation that, for the reconstructed images by the Algebraic Reconstruction Technique (ART) or Simultaneous Algebraic Reconstruction Technique (SART), while the singularities (edges) along $y$-direction are lost due to blurring, the singularities (edges) along the $x$-direction, however, could be rather accurately recovered. Experiments on both simulated data and real data show that the proposed model and its solution algorithm could produce promising results and outperform state-of-the-art algorithms for limited-angle tomography.





Speaker: 李沛尧  [解放军总医院]


Title: 临床大数据的分析与思考


Abstract: 随着医疗技术的进步,临床环境与实践产生了大量的数据,这些数据来源众多且形式各异,如电子健康档案(EHR)、医学影像、基因测序以及可穿戴设备等,基于“大数据”的新型临床决策辅助系统为改进临床诊疗实践提供了新的机会。但是目前的临床数据领域还面临着诸如数据结构不统一、“数据孤岛”、“数据荒漠”等挑战。如何在这种“机会与挑战”并存的“临床大数据”时代,利用数据,发现新的知识是我们需要深入思考的问题。在本次讨论中,我们将以重症监护领域风险模型的最新进展为例深入探讨,诸如深度学习在临床环境下的机会。同时我们还将分享我们团队在临床数据建设方面的进展和心得。




Speaker: Bao Chenglong [YMSC, Tsinghua University]


Title: Spare representations in image processing: algorithms, models and beyond


Abstract: In recent years, the concept of sparse representation has been widely used in many applications. Among extensive works in this direction, K-SVD is a typical method in the dictionary learning. However, the convergence of K-SVD is not clear. In this talk, I will introduce an efficient numerical algorithm for solving L0-norm related problems with convergence guarantee. Additionaly, some variants of dictionary learning models are proposed for dynamic texture classification and cerebellar functional parcellation. At last, the approximation analysis for the dictionary learning models is discussed.




Speaker: Songting Li [Courant Institute, NYU]


Title: Mathematical Modeling and Analysis of Single-Neuron Computation


Abstract: A neuron with dendrites is believed to be the fundamental computational unit in the brain. To understand information processing in the brain, mathematical modeling of single-neuron dynamics has proven to be an effective approach. Among all the neuron models, multi-compartment (PDEs) models and single-compartment (ODE) models are two popular frameworks that describe a neuron at different levels. In general, multi-compartment models incorporating dendritic features are biologically detailed but mathematically intractable and computationally inefficient, while single-compartment models only characterizing the cell body are mathematically tractable and computationally efficient but biologically oversimplified. A neuron model with both simple mathematical structure and rich biological detail is thus still lacking. In this talk, by using asymptotic analysis, I will derive a class of single-compartment neuron models, consisting of one ordinary differential equation, from the corresponding multi-compartment models consisting of hundreds of partial differential equations, and further verify the derived model in realistic neuron simulations and biological experiments. In contrast to the existing single-compartment models, our derived model is capable of performing detailed dendritic computations such as feature selectivity and sound localization, and can greatly reduce the computational cost in large-scale neuronal network simulations without the loss of dendritic functions.