{"title":"Modeling and Simulation for Collective Dynamics","authors":"W. Bao, P. Markowich, B. Perthame, E. Tadmor","doi":"10.1142/13136","DOIUrl":"https://doi.org/10.1142/13136","url":null,"abstract":"","PeriodicalId":367095,"journal":{"name":"Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123567997","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}
{"title":"Models and Methods for Quantum Condensation and Fluids","authors":"W. Bao, Yongyong Cai, I. Danaila, P. Markowich","doi":"10.1142/13134","DOIUrl":"https://doi.org/10.1142/13134","url":null,"abstract":"","PeriodicalId":367095,"journal":{"name":"Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115132040","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}
{"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}
{"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}
{"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}
{"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}
{"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}
{"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}
{"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}