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Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore最新文献

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Modeling and Simulation for Collective Dynamics 集体动力学建模与仿真
Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore Pub Date : 2022-08-14 DOI: 10.1142/13136
W. Bao, P. Markowich, B. Perthame, E. Tadmor
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引用次数: 1
Models and Methods for Quantum Condensation and Fluids 量子凝聚和流体的模型和方法
Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore Pub Date : 2022-08-09 DOI: 10.1142/13134
W. Bao, Yongyong Cai, I. Danaila, P. Markowich
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引用次数: 1
Heat Kernel Smoothing in Irregular Domains 不规则域的热核平滑
Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore Pub Date : 2019-11-25 DOI: 10.1142/9789811200137_0008
M. Chung, Yanli Wang
{"title":"Heat Kernel Smoothing in Irregular Domains","authors":"M. Chung, Yanli Wang","doi":"10.1142/9789811200137_0008","DOIUrl":"https://doi.org/10.1142/9789811200137_0008","url":null,"abstract":"We review the heat kernel smoothing techniques for denoising and regressing data in irregularly shaped domains embedded in Euclidean spaces. This is a problem often encountered in functional data analysis and medical imaging. In this chapter, we present a unified mathematical framework based on the eigenfunctions of the Laplace-Beltrami operators defined on irregular domains. Numerical implementation issues will be addressed as well. Various examples will be presented. We also present a few new theoretical results on the properties of heat kernel smoothing.","PeriodicalId":367095,"journal":{"name":"Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128441513","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
FRONT MATTER 前页
Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore Pub Date : 2019-11-25 DOI: 10.1142/9789811200137_fmatter
S. Kushnarev, Anqi Qiu, L. Younes
{"title":"FRONT MATTER","authors":"S. Kushnarev, Anqi Qiu, L. Younes","doi":"10.1142/9789811200137_fmatter","DOIUrl":"https://doi.org/10.1142/9789811200137_fmatter","url":null,"abstract":"","PeriodicalId":367095,"journal":{"name":"Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131237382","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Mathematics of Shapes and Applications 形状与应用数学
Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore Pub Date : 2019-11-01 DOI: 10.1142/11272
S. Kushnarev, Anqi Qiu, L. Younes
{"title":"Mathematics of Shapes and Applications","authors":"S. Kushnarev, Anqi Qiu, L. Younes","doi":"10.1142/11272","DOIUrl":"https://doi.org/10.1142/11272","url":null,"abstract":"","PeriodicalId":367095,"journal":{"name":"Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126682442","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Riemannian Geometry for Shape Analysis and Computational Anatomy 用于形状分析和计算解剖的黎曼几何
Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore Pub Date : 2018-07-30 DOI: 10.1142/9789811200137_0002
Martins Bruveris
{"title":"Riemannian Geometry for Shape Analysis and Computational Anatomy","authors":"Martins Bruveris","doi":"10.1142/9789811200137_0002","DOIUrl":"https://doi.org/10.1142/9789811200137_0002","url":null,"abstract":"Shape analysis and compuational anatomy both make use of sophisticated tools from infinite-dimensional differential manifolds and Riemannian geometry on spaces of functions. While comprehensive references for the mathematical foundations exist, it is sometimes difficult to gain an overview how differential geometry and functional analysis interact in a given problem. This paper aims to provide a roadmap to the unitiated to the world of infinite-dimensional Riemannian manifolds, spaces of mappings and Sobolev metrics: all tools used in computational anatomy and shape analysis.","PeriodicalId":367095,"journal":{"name":"Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133469686","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
The Geometry, Topology and Physics of Moduli Spaces of Higgs Bundles 希格斯束模空间的几何、拓扑和物理
Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore Pub Date : 2018-06-21 DOI: 10.1142/10683
R. Wentworth, Graeme Wilkin
{"title":"The Geometry, Topology and Physics of Moduli Spaces of Higgs Bundles","authors":"R. Wentworth, Graeme Wilkin","doi":"10.1142/10683","DOIUrl":"https://doi.org/10.1142/10683","url":null,"abstract":"","PeriodicalId":367095,"journal":{"name":"Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125415035","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Diffeomorphic Registration of Discrete Geometric Distributions 离散几何分布的微分同胚配准
Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore Pub Date : 2018-01-29 DOI: 10.1142/9789811200137_0003
Hsi-Wei Hsieh, N. Charon
{"title":"Diffeomorphic Registration of Discrete Geometric Distributions","authors":"Hsi-Wei Hsieh, N. Charon","doi":"10.1142/9789811200137_0003","DOIUrl":"https://doi.org/10.1142/9789811200137_0003","url":null,"abstract":"This paper proposes a new framework and algorithms to address the problem of diffeomorphic registration on a general class of geometric objects that can be described as discrete distributions of local direction vectors. It builds on both the large deformation diffeomorphic metric mapping (LDDMM) model and the concept of oriented varifolds introduced in previous works like [Kaltenmark 2017]. Unlike previous approaches in which varifold representations are only used as surrogates to define and evaluate fidelity terms, the specificity of this paper is to derive direct deformation models and corresponding matching algorithms for discrete varifolds. We show that it gives on the one hand an alternative numerical setting for curve and surface matching but that it can also handle efficiently more general shape structures, including multi-directional objects or multi-modal images represented as distributions of unit gradient vectors.","PeriodicalId":367095,"journal":{"name":"Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore","volume":"65 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125938578","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 7
Variational Second-Order Interpolation on the Group of Diffeomorphisms with a Right-Invariant Metric 具有右不变度量的微分同胚群上的变分二阶插值
Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore Pub Date : 2018-01-12 DOI: 10.1142/9789811200137_0001
Franccois-Xavier Vialard
{"title":"Variational Second-Order Interpolation on the Group of Diffeomorphisms with a Right-Invariant Metric","authors":"Franccois-Xavier Vialard","doi":"10.1142/9789811200137_0001","DOIUrl":"https://doi.org/10.1142/9789811200137_0001","url":null,"abstract":"In this note, we propose a variational framework in which the minimization of the acceleration on the group of diffeomorphisms endowed with a right-invariant metric is well-posed. It relies on constraining the acceleration to belong to a Sobolev space of higher-order than the order of the metric in order to gain compactness. It provides the theoretical guarantee of existence of minimizers which is compulsory for numerical simulations.","PeriodicalId":367095,"journal":{"name":"Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore","volume":"2553 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127482973","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
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