大连理工大学数学科学学院
通知与公告

2021年应用拓扑讲习班(线上、线下)通知

2021年06月03日 08:22  点击:[]

为推进国内应用拓扑交叉研究的发展,促进相关领域的交流与合作研究,给国内有志于做应用拓扑交叉研究的青年学者和研究生搭建一个学习和交流的平台,兹定于202166-11日在大连举办“应用拓扑讲习班”,按线下、线上同步模式进行。讲习班将开设短期课程三门:

课程1:代数拓扑在数据科学的应用(河北师范大学吴杰教授主讲,48学时);

课程2:计算拓扑与几何算法(大连理工大学雷娜教授主讲,48学时);

课程3:三维流形中的一些基本算法问题(大连理工大学雷逢春教授主讲,36学时)。

讲习班同时邀请活跃在一线的国内外一些知名专家和青年学者做前沿研究报告。本次讲习班活动由国家自然科学基金委基金部分资助,由大连理工大学数学科学学院和辽宁师范大学数学学院共同承办。

会议学术委员会

 任:方复全(南方科技大学)

委员:Andrey Vesnin 教授(俄罗斯托木斯克大学)

段海豹(中国科学院)

吴杰(河北师范大学)

雷逢春(大连理工大学)

刘西民(大连理工大学)

韩友发(辽宁师范大学)

 

会议日程安排

线下会议地点:大连理工大学国际会议中心3楼第二会议室

 202166日(周日)

会议号

腾讯会议 ID487 2905 7712或者点击链接入会

https://meeting.tencent.com/s/EaGfk4ZnraMC

报告时间

报告人与报告题目

8:20-8:30

开幕式

8:30-10:00

代数拓扑在数据科学的应用I

(河北师范大学吴杰教授)

10:00-10:20

 

10:20-11:20

超图的概率边界:拓扑视角?

刘兴武教授(大连理工大学)

11:20-14:00

午休

14:00-15:30

三维流形中的一些基本算法问题I

雷逢春教授(大连理工大学)

15:30-15:50

 

15:50-16:50

Hyper-simplicial sets and hypergraphs

刘健博士(河北师范大学)

16:50-17:00

 

17:00-17:30

Inverse problem and optimization with TDA

何宇楠博士(重庆理工大学)

17:30-18:00

Fuzzy Fundamental Groupoid

李泽龙(河北师范大学)

202167日(周一)

会议号

腾讯会议 ID487 2905 7712或者点击链接入会

https://meeting.tencent.com/s/EaGfk4ZnraMC

报告时间

报告人与报告题目

8:30-10:00

三维流形中的一些基本算法问题II

雷逢春教授(大连理工大学)

10:00-10:20

 

10:20-11:20

Spatial topological analysis of sympathetic neurovascular characteristic of acupoints in Ren meridian using advanced tissue-clearing and near infrared II 3 imaging

冯异教授(复旦大学)

11:20-14:00

午休

14:00-15:30

代数拓扑在数据科学的应用II

吴杰教授(河北师范大学)

15:30-15:50

 歇 (合影)

15:50-16:50

莫尔斯理论(Morse Theory)简介

段海豹研究员(中科院数学所)

16:50-17:00

 

17:00-18:00

Stochastic Symplectic Methods of Stochastic Hamiltonian Systems

洪佳林研究员(中科院计算所)

202168日(周二)

会议号

腾讯会议 ID487 2905 7712或者点击链接入会

https://meeting.tencent.com/s/EaGfk4ZnraMC

报告时间

报告人与报告题目

8:30-10:00

计算拓扑与几何算法I

雷娜教授(大连理工大学)

10:00-10:20

 

10:20-11:50

三维流形中的一些基本算法问题III

雷逢春教授(大连理工大学)

11:50-14:00

午休

14:00-15:00

关于DNA拓扑结构的一些思考

李天虎教授(新加坡南洋理工大学)

15:00-15:20

 

15:20-16:20

Topological data analysis (TDA) based machine learning models for drug design

夏克林教授(新加坡南洋理工大学)

16:20-16:30

 

16:30-17:00

Topological data analysis and its applications

赵彦(河北师范大学)

17:00-17:30

Neighborhood complex based machine learning models for drug design

刘祥(河北师范大学与南开大学)

17:30-18:00

Persistent homology analysis on stabilities of C60 isomers

高亚茹(大连理工大学)

202169日(周三)上午

会议号

腾讯会议 ID487 2905 7712或者点击链接入会

https://meeting.tencent.com/s/EaGfk4ZnraMC

报告时间

报告人与报告题目

8:30-10:00

计算拓扑与几何算法II

雷娜教授(大连理工大学)

10:00-10:20

 

10:20-11:50

代数拓扑在数据科学的应用III

吴杰教授(河北师范大学)

下午

休息

2021610日(周四)

会议号

腾讯会议 ID487 2905 7712或者点击链接入会

https://meeting.tencent.com/s/EaGfk4ZnraMC

报告时间

报告人与报告题目

8:30-10:00

代数拓扑在数据科学的应用IV

吴杰教授(河北师范大学)

10:00-10:20

 

10:20-11:20

Equivariant cohomology and self-dual binary codes

吕志教授(复旦大学)

11:20-14:00

午休

14:00-15:30

计算拓扑与几何算法III

雷娜教授(大连理工大学)

15:30-15:50

 

15:50-16:50

三角剖分数的估计

赵学志教授(首都师范大学)

16:50-17:00

 

17:00-17:30

Homological scaffolds of Brain Functional Connectivity Networks

赵琦(复旦大学)

17:30-18:00

Towards the topological characterization of models in asynchronous distributed system

岳云光博士(大连理工大学)

2021611日(周五)上午

会议号

腾讯会议 ID487 2905 7712或者点击链接入会

https://meeting.tencent.com/s/EaGfk4ZnraMC

报告时间

报告人与报告题目

8:30-10:00

计算拓扑与几何算法IV

雷娜教授(大连理工大学)

10:00-10:20

 

10:20-11:20

Superconnections and an intrinsic Gauss-Bonnet-Chern formula for Finsler manifolds

冯惠涛教授(南开大学)

 

会议结束

 

 

报告题目与摘要

 

报告人:吴杰教授(河北师范大学)

课程1代数拓扑在数据科学的应用。

内容简介:本课程讨论代数拓扑在数据科学中的应用及其最新进展。主要内容包括:

1)数据科学及拓扑数据分析简介。

2)复习代数拓扑的一些基本概念,如单纯复形,Δ-复形,Δ-集,单纯集以及单纯群等。

3)超图及双超图的同调理论,以及超持续同调理论。

Course 1: Algebraic Topology in Data Science

Abstract: In this minicourse, we will discuss the applications of algebraic topology in data science, which mainly contains the following contents: (1) An overview of data science and topological data analysis. (2) Review of some basic notions in algebraic topology such as simplicial complexes, Δ-complexes, Δ-sets, simplicial sets and simplicial groups. (2) homology theory of hypergraphs and super-hypergraphs, and super-persistent homology.

 

报告人:雷娜教授(大连理工大学国际信息与软件学院)

课程2: 计算拓扑与几何算法

内容简介:本课程将简要介绍基本的拓扑与几何算法,例如代数拓扑中的同伦群、同调群、上同调群,微分拓扑中的De-Ram上同调、Hodge分解、叶状结构,以及拓扑大数据分析中的核心算法持续同调等的相关理论与计算方法。

 

报告人:雷逢春教授(大连理工大学)

课程3三维流形中的一些基本算法问题

内容简介:本课程将简要介绍三维流形组合拓扑中的正则曲面理论及其在几个算法问题(决定问题)上的应用,包括:(1) 判定一个剖分的三维流形中是否是可约的(即它是否包含一个不界定实心球的2-球面)(2) 判定一个剖分的三维流形中是否为Haken流形(包含双侧不可压缩曲面的不可约三维流形)(3) 判定中的一个纽结是否为平凡纽结。 

 

报告人:刘兴武教授(大连理工大学)

Title: 超图的概率边界:拓扑视角?

Abstract: 乘积概率空间中一组事件的相关性可以通过超图来刻画,而超图的概率边界,指的满足其约束且能覆盖全空间的一组事件的最小概率向量。超图的概率边界对于算法设计与分析很重要,但是定界却极具挑战性。超图的拓扑模型能否提供一条可由之路?

 

报告人:刘健博士(河北师范大学)

Title: Hyper-simplicial sets and hypergraphs

AbstractThe hyper-simplicial set is a generalization of simplicial set. In this report, we develop a theory of hyper-simplicial sets, which can be used to explain the homology of hypergraphs and digraphs. Moreover, we introduce a new geometry which can decode the geometry of hyper-simplicial sets.

 

报告人:何宇楠博士(重庆理工大学)

Title: Inverse problem and optimization with TDA

AbstractPersistence diagrams are usually computed on point clouds and its inverse problem is to tweak the point cloud so that the corresponding persistence diagram satisfies some properties. For example, we want to maximize the total persistence and figure out how does the point cloud look. In this talk, we try to solve this inverse problem by defining a loss function that rewards total persistence, so the problem is converted to an optimization problem. This method can be applied to a wide variety of situations in topological data analysis where it is necessary to solve an inverse problem, from persistence diagrams to point cloud data.

 

报告人:李泽龙(河北师范大学)

Title: Fuzzy Fundamental Groupoid

AbstractDeveloped by Leland McInnes et al. in 2018, UMAP (Uniform Manifold Approximation and Projection) is a novel and competitive manifold learning technique for dimension reduction. The mathematics behind this algorithm boils down to a fuzzy setting on simplicial sets. On the other hand, a recovery of the homotopy type for any compact Riemannian manifold via Vietoris-Rips complex is widely discussed by algebraic topologists for various application purposes. In this talk, we will briefly survey the results and introduce a fuzzy fundamental groupoid to study edge-paths.

 

报告人:冯异教授(复旦大学)

Title: Spatial topological analysis of sympathetic neurovascular characteristic of acupoints in Ren meridian using advanced tissue-clearing and near infrared II 3 imaging

AbstractAcupuncture has been used for treating various medical conditions in traditional Chinese medicine. Both manual and electro-acupuncture stimulate specific acupoints to obtain local and systemic biological effects, but the underlying mechanisms remain unclear. Here, we used three-dimensional tissue-clearing technology to study acupoints on the Ren meridian of mice to reveal the distribution, density, branching, and relationships between blood vessels and nerves. Using topological Mapper methods, we found that sympathetic neurovascular networks were denser in the CV 4 acupoint compared with surrounding non-acupoints. Furthermore, high resolution in vivo real-time vascular imaging using the near infrared-II probe LZ-1105 demonstrated increased blood flow in the CV 4 acupoint compared with neighboring non-acupoints after manual or electro-acupuncture. Consistent with earlier findings, our research indicated that acupuncture could enhance local blood flow, and our high-resolution 3D images show for the first time the important role of sympathetic neurovascular networks in the CV 4 acupoint.

 

报告人:段海豹研究员(中科院数学所)

Title: 莫尔斯理论(Morse Theory)简介

Abstract: 本报告将简要介绍莫尔斯理论(Morse Theory)的相关内容及研究进展。

 

报告人:洪佳林研究员(中科院计算所)

Title: Stochastic Symplectic Methods of Stochastic Hamiltonian Systems

Abstract: Plenty of numerical experiments show that stochastic symplectic methods are superior to non-symplectic ones especially in long-time computation, when applied to stochastic Hamiltonian systems. In this talk we first review some basic results on stochastic symplectic methods of stochastic Hamiltonian systems, such as the theory of stochastic generating functions, variational integrators, pseudo-symplectic methods, etc. Then we present the probabilistic superiority of stochastic symplectic methods of stochastic Hamiltonian systems via large deviations principle. (In collaboration with Dr. Chuchu Chen, Dr. Diancong Jin and Dr. Liying Sun)

 

报告人:Prof. Tianhu Li (李天虎,  新加坡南洋理工大学化学与生物化学系 (until October 2021),中国西北工业大学化学制造研究院 (since April 2020))

Title:  关于DNA拓扑结构的一些思考

Abstract: DNA(脱氧核糖核酸)是线形的大分子。在真核细胞中,这种大分子呈现多种不同的拓扑结构状态:

(1) 双螺旋结构 (double helices)

(2) 三螺旋 (triple helices)

(3) 四聚体 (G-quadruplex and i-motif)

(4) 十字 (DNA Cruciform)

(5) 超螺旋 supercoiling

在上面提到的DNA拓扑结构中, 又可以发现有不同的拓扑同分异构体存在。在本次汇报中,本人围绕着下面提及的几个内容和大家表达一下个人的理解和想法:

1)上面提到的DNA拓扑形态存在的结构基础和结构特点

2)为什么只有DNA能支撑上面提到的拓扑形态, 而这些结构在其它生物大分子(蛋白质和聚糖)上不出现

3)上面提到的DNA拓扑结构的存在的生物意义

4)在DNA超螺旋结构里,超螺旋密度(super-helical density)和能量的关系

 

报告人:Prof. Kelin Xia新加坡南洋理工大学

Title: Topological data analysis (TDA) based machine learning models for drug design

Abstract: Effective molecular representation is key to the success of machine learning models for drug design. In this talk, we will discuss a series of TDA-related models, including persistent homology, persistent spectral models, and persistent Ricci curvature and their combination with machine learning models. Unlike traditional graph/network or geometric models, these filtration-induced persistent models can characterize the multiscale intrinsic information, thus significantly reduces molecular data complexity and dimensionality.  Feature vectors are obtained from various persistent attributes and inputted into machine learning models, in particular, random forest, gradient boosting tree and convolutional neural network. Our persistent representations based molecular fingerprints can significantly boost the performance of learning models in drug design.

 

报告人:赵彦(河北师范大学)

Title:  Topological data analysis and its applications

AbstractTopological data analysis (TDA) is an emerging area that bridges computational methods with the mathematical theory of topology. Persistent homology is a powerful method for measuring topological features of a space. It converts the data into simplicial complexes and describes the topological structure of a space at different spatial resolutions (scales). In this lecture, we discuss the applications of TDA in biomolecules.

 

报告人:刘祥(河北师范大学,南开大学)

Title: Neighborhood complex based machine learning models for drug design

AbstractThe importance of drug design cannot be overemphasized. Recently, artificial intelligence (AI) based drug design has demonstrated great potential to fundamentally change the pharmaceutical industries. However, a main issue for AI-based learning models is still finding efficient molecular descriptors or fingerprints. In this talk, i will introduce our recently proposed neighborhood complex based learning models for drug design. More specifically, after giving the neighborhood complex based molecular structure and interaction characterization, we consider the persistent spectral model and use the persistent attributes to construct the learning descriptors. To test our model, we consider the protein-ligand binding affinity prediction, one of the most important issues in drug design. Our model is tested on three most commonly used databases, including PDBbind-2007, PDBbind-2013 and PDBbind-2016. It has been found that our model can outperform all the existing machine learning models with traditional learning descriptors.

 

报告人:高亚茹(大连理工大学)

Title: Persistent homology analysis on stabilities of C60 isomers

AbstractThe structures of fullerene isomers are determined by their 1-skeleton. Though only very few of fullerene isomers are actually synthesized, their physical and chemical properties can be predicted theoretically. Many topological indices of fullerene graphs are known to have strong correlation with formation energies of fullerenes. We investigate topological descriptors of the 3D structure. More precisely, we try to make connections between coordinates of atoms of 1812 C60 isomers and their relative stabilities via persistent homology.

 

报告人:吕志教授(复旦大学)

Title: Equivariant cohomology and self-dual binary codes

 

报告人:赵学志教授(首都师范大学)

Title: 三角剖分数的估计

 

报告人:赵琦(复旦大学)

Title: Homological scaffolds of Brain Functional Connectivity Networks

AbstractWe understand the brain as a collection of regions that structurally connect but also organize into large functional modules in order to support a range of behaviors..Here, we study the characteristics of functional connectivity networks at the mesoscopic level from a novel perspective that highlights the role of inhomogeneities in the fabric of functional connections. This can be done by focusing on the features of a set of topological objects—homological cycles—associated with the weighted functional network. We leverage the detected topological information to define the homological scaffolds, a new set of objects designed to represent compactly the homological features of the correlation network and simultaneously make their homological properties amenable to networks theoretical methods. Moreover, we study the correlation between these objects and traditional complex network indicators, e.g. node degree distribution and node centrality.

 

报告人:岳云光博士 (大连理工大学)

Title: Towards the topological characterization of models in asynchronous distributed system

Abstract: In this talk, we first investigate topological characterization of the solvability of arbitrary solo model and the complexity of general resilient-fault model in asynchronous distributed system, and then present some applications of them.

 

报告人:冯惠涛教授(南开大学)

Title: Superconnections and an intrinsic Gauss-Bonnet-Chern formula for Finsler manifolds

Abstract: In this talk, we establish an intrinsic Gauss-Bonnet-Chern formula for Finsler manifolds by using Mathai-Quillens superconnection formalism, in which no extra vector field is involved. Furthermore, we prove a more general Lichnerowich formula in this direction through a geometric localization procedure.

 

 

                                                                                            

会议组委会

大连理工大学 数学科学学院

辽宁师范大学数学学院

2021-6-2

 

 

 

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