Organizers
UPDATE!
Additional conference materials can be found at: https://www.asc.ohiostate.edu/kurtek.1/cbms.html
Topic Area
This Conference Board of the Mathematical Sciences (CBMS) conference will feature an intensive lecture series on elastic methods for statistical analysis of functional and shape data, using tools from Riemannian geometry, Hilbert space methods, and computational science. The main focus of this conference is on geometric approaches, especially on using elastic Riemannian metrics with desired invariance properties, and squareroot representations that simplify computations. These approaches allow joint registration and statistical analysis of functional data, and are termed elastic for that reason. The statistical goals include comparisons, summarization, clustering, modeling, and testing of functional and shape data objects.
There is no travel/accomodation funding remaining, however we are still accepting applications to participate.
Travel and Lodging Info
 Lodging  There are several great hotel and lodging options available near the Ohio State University Campus. For a full list of options and more information go here. The MBI is located in Jennings Hall at 1735 Neil Avenue on the 3rd floor and most OSU hotels should offer shuttle transportation to get you to and from the MBI on campus for the workshop each day.
 Airport  When you arrive at John Glenn Columbus International airportCMH you can take a taxi to your hotel (or find your hotel shuttle if offered) by going to the ground transportation area of the terminal where they offer 24hour Airport taxi service.
 Driving to MBI & Campus Parking  If you are driving to the workshop, the closest public parking garage near the MBI is the 12th Avenue Garage. The MBI is just a short walk east from here on 12th Ave. to the Intersection of Neil Ave. where we are located in Jennings Hall on the 3rd floor. Here is a Google walking map.
Primary Lecturer
Prof. Anuj Srivastava is a Professor of Statistics and a Distinguished Research Professor at Florida State University (FSU) in Tallahassee, FL. His main expertise lies in the use of techniques from algebra and differential geometry in deriving statistical inferences on nonlinear manifolds. Specifically, along with his colleagues, he has developed comprehensive Riemannian frameworks for shape analysis of objects, including scalar functions, Euclidean curves, 2D surfaces, and neuronal trees. He is an author, along with Prof. Eric Klassen of FSU, of a recently published Springer textbook on Functional and Shape Data Analysis. He has also published more than 200 papers in refereed journals and proceedings of refereed international conferences. He is a fellow of the IEEE, IAPR, and ASA.
Additional Lecturers
Prof. Eric Klassen, Department of Mathematics, Florida State University
Prof. Veera Baladandayuthapani, Department of Biostatistics, University of Texas MD Anderson Cancer Center
Prof. Laurent Younes, Department of Applied Mathematics and Statistics, Johns Hopkins University
Prof. Zhengwu Zhang, Department of Biostatistics and Computational Biology, University of Rochester
We gratefully acknowledge funding and support from the National Science Foundation CBMS grant, the Mathematics Research Institute, the Mathematical Biosciences Institute, the Department of Statistics at Ohio State, and the NSF TRIPODS grant.
Accepted Speakers
Monday, July 16, 2018  

Time  Session 
08:30 AM 09:15 AM  Breakfast 
09:15 AM 09:30 AM  Opening Remarks 
09:30 AM 12:00 PM  Anuj Srivastava  Introduction and Background

12:00 PM 02:00 PM  Lunch Break 
02:00 PM 04:00 PM  Anuj Srivastava  Elastic Functional Data Analysis

04:30 PM 06:30 PM  Reception 
Tuesday, July 17, 2018  

Time  Session 
08:45 AM 09:30 AM  Breakfast 
09:30 AM 12:00 PM  Anuj Srivastava  Elastic Shape Analysis of Curves

12:00 PM 02:00 PM  Lunch Break 
02:00 PM 04:00 PM  Anuj Srivastava, Eric Klassen  Fundamental Mathematical Formulations, Recent Progress and Open Problems

04:30 PM 05:30 PM  Discussion Session 
Wednesday, July 18, 2018  

Time  Session 
08:45 AM 09:30 AM  Breakfast 
09:30 AM 12:00 PM  Anuj Srivastava  Elastic Shape Analysis of Surfaces

12:00 PM 02:00 PM  Lunch Break 
02:00 PM 04:00 PM  Anuj Srivastava, Karthik Bharath  Statistical Models

04:30 PM 05:30 PM  Software Demonstrations in Matlab 
Thursday, July 19, 2018  

Time  Session 
08:45 AM 09:30 AM  Breakfast 
09:30 AM 12:00 PM  Eric Klassen, Anuj Srivastava  Generalizations of the Square Root Velocity Framework to Trajectories in Manifolds In previous talks, SRVF method has been discussed as a powerful and efficient way to analyze collections of curves in a Euclidean space. However, in many applications the data to be analyzed consists of trajectories in a manifold, rather than in a Euclidean space. Examples include hurricane paths on the surface of the earth, paths of covariance matrices that arise in the study of brain connectivity, and paths of images that lie in a shape space. The comparison of curves in a manifold is more subtle than in a Euclidean space, because one cannot subtract velocity vectors that lie in two different tangent spaces! In this talk, we discuss several methods of adapting the SRVF method to this situation, and comment on the advantages and disadvantages of each method. 
12:00 PM 02:00 PM  Lunch Break 
02:00 PM 04:00 PM  Laurent Younes  Introduction to Metric Registration Registration (for curves, surfaces or images) can be seen as a representation of a shape dataset as a subset of the diffeomorphism group, each shape in the dataset being associated with an optimal deformation of a template. We will in particular focus on methods that compute this deformation by optimizing a distance over diffeomorphisms under the constraint of mapping a template to a target, and such that the minimized distance is in turn a metric in shape space. These “metric registration” methods include a large spectrum of algorithms deriving from the “large deformation diffeomorphic metric mapping” (LDDMM) framework, and “metamorphosis” in which nondiffeomorphic shape variations are also allowed. We will describe mathematical foundations and algorithms, and the various forms that these methods may take in relation to applications. 
04:30 PM 05:30 PM  Software Demonstrations in Matlab 
Friday, July 20, 2018  

Time  Session 
08:45 AM 09:30 AM  Breakfast 
09:30 AM 12:00 PM  Veera Baladandayuthapani  Bayesian Models for Richly Structured Data in Biomedicine Modern scientific endeavors generate highthroughput, multimodel datasets of different sizes, formats, and structures at a single subjectlevel. In the context of biomedicine, such data include multiplatform genomics, proteomics and imaging; and each of these distinct data types provides a different, partly independent and complementary, highresolution view of various biological processes. Modeling and inference in such studies is challenging, not only due to high dimensionality, but also due to presence of rich structured dependencies such as serial, spatial, graphical, functional and shapebased correlations. This talk will cover probabilistic frameworks that acknowledge and exploit these inherent complex structural relationships to develop regression and clustering models, that extract maximal information from such data. These approaches will be illustrated using several biomedical case examples especially in oncology. 
12:00 PM 02:00 PM  Lunch Break 
02:00 PM 04:00 PM  Zhengwu Zhang  Geometrybased Brain Structural Connectome Analysis Advanced brain imaging techniques make it possible to measure individuals' structural connectomes in large cohort studies noninvasively. The structural connectome is initially shaped by genetics and subsequently refined by the environment. It is extremely interesting to study structural connectomes and their relationships to environmental factors or human traits, which motivates the routine collection of highresolution connectomes in large human studies (e.g., the Human Connectome Project and UK Biobank). However, there is a fundamental gap between the state of the art in image acquisition and the tools available to reconstruct and analyze the connectome data, due to the complexity of data. This lecture aims at introducing our recent effort in the thread. More specifically, we will introduce a populationbased structural connectome (PSC) mapping framework to reproducibly extract binary networks, weighted networks, and streamlinebased brain connectomes. In addition, various novel methods of analyzing the outputs of PSC will be introduced. We will also introduce a userfriendly software package that implements the PSC and the analysis methods. 
04:00 PM 04:15 PM  Closing Remarks 
Name  Affiliation  

Acharyya, Satwik  satwik91@gmail.com  Statistics, Texas A & M University 
Baladandayuthapani, Veera  veera@mdanderson.org  Department of Biostatistics, UT MD Anderson Cancer Center 
Benard, Efuelaka  efuelaka@yahoo.com  STATISTICS, UNIVERSITY OF HASSELT 
Bharath, Karthik  karthik.bharath@nottingham.ac.uk  Mathematical Sciences, University of Nottingham 
Chen, Chao  cc16w@my.fsu.edu  statistics, Florida State University 
Cho, Min Ho  cho.829@osu.edu  Statistics, 
Flaih, Ahmad  ahmad.flaih@qu.edu.iq  STATISTICS, UNIVERSITY OF ALQADISIYAH 
Guha, Aritra  aritra@umich.edu  Statistics, University of Michigan 
Guo, Mengmeng  mengmeng.guo@ttu.edu  Mathematics, Texas Tech University 
Honaker, John  honaker.32@osu.edu  Statistics, The Ohio State University 
Hong, Yi  hongyi.cs@gmail.com  Computer Science, University of Georgia 
Hu, Ziqing  zhu4@nd.edu  ACMS, University of Notre Dame 
Kakareko, Sylwia  sylwia.kakareko@gmail.com  Industrial and Manufacturing Engineering, Florida State University 
Kang, Hyun Bin  hbkang0823@gmail.com  Statistics, Pennsylvania State University 
Kausar, Rukhsana  rukhsana718@gmail.com  Department of Mathematics, University of Kaiserslautern 
Kim, Kyongwon  kyongwon.psu@gmail.com  Statistics, Pennsylvania State University 
Klassen, Eric  klassen@math.fsu.edu  Mathematics, Florida State University 
Kurtek, Sebastian  kurtek.1@stat.osu.edu  Statistics, The Ohio State University 
Li, Huazhang  hl5qd@virginia.edu  Statistics, University of Virginia 
Li, Tengfei  tengfeili2006@gmail.com  Biostatistics, University of Texas MD Anderson Cancer Center 
Lu, Yi  lu08stat@gmail.com  Mathematics and Computer Science, Drew University 
Maltsi, Anieza  maltsi@wiasberlin.de  PARTIAL DIFFERENTIAL EQUATIONS GROUP, WeierstrassInstitut f""ur Angewandte Analysis und Stochastik (WIAS) 
Manley, Kevin  kmanley1@nd.edu  Applied and Computational Math and Statistics, University of Notre Dame 
Matuk, James  matuk.3@osu.edu  Statistics, The Ohio State University 
Memoli, Facundo  memoli@math.osu.edu  Mathematics, The Ohio State University 
Miao, Ruizhong  rm9dd@virginia.edu  Statistics, University of Virginia 
Mitchell, Emily  emily.mitchell@nottingham.ac.uk  Mathematical Sciences, University of Nottingham 
Prematilake, Chalani  prematilakec17@ecu.edu  Mathematics, East Carolina University 
Qadir, Ghulam  ghulam.qadir@kaust.edu.sa  Statistics, King Abdullah University of Science and Technology (KAUST) 
Rao, Arvind  ukarvind.cmu@gmail.com  Bioinformatics, University of Michigan Health Systems 
Ronquist, Scott  scotronq@umich.edu  Bioinformatics, University of Michigan 
Rooks, Brian  btrooks88@gmail.com  Department of Biostatistics and Computational Biology, University of Rochester 
Saha, Abhijoy  saha.58@osu.edu  Statistics, The Ohio State University 
Shen, Luyi  lshen4@nd.edu  ACMS, University of Notre Dame 
Shieh, Denise  dshieh08@gmail.com  Biostatistics, Columbia University 
Shu, Hai  hshu@mdanderson.org  Biostatistics, University of Texas MD Anderson Cancer Center 
Soto, Carlos  cjs15g@my.fsu.edu  Statistics, Florida State University 
Srivastava, Anuj  anuj@stat.fsu.edu  Statistics, Florida State University 
Strait, Justin  strait.50@osu.edu  Statistics, The Ohio State University 
Wang, Yusu  yusu@cse.ohiostate.edu  Computer Science and Engineering, The Ohio State University 
Wang, Yuan  yuan.wang.stat@gmail.com  Mathematics and Statistics, Washington State University 
Wang, Boshi  boshiwang1993@gmail.com  Department of statistics, Florida State University 
Wang, Xuan  wangxuan209@hotmail.com  mathematics, Zhejiang University 
Younes, Laurent  laurent.younes@jhu.edu  Applied Mathematics and Statistics, Johns Hopkins University 
Zhang, Tingting  tz3b@virginia.edu  Statistics, University of Virginia 
Zhang, Zhengwu  zhengwu_zhang@urmc.rochester.edu  Department of Biostatistics and Computational Biology, University of Rochester 
Zhang, JianZhou  zhangjz@scu.edu.cn  College of Computer, Sichuan University 
Zohner, Ye Emma  emma.zohner@rice.edu  Biostatistics, MD Anderson Cancer Center 
Modern scientific endeavors generate highthroughput, multimodel datasets of different sizes, formats, and structures at a single subjectlevel. In the context of biomedicine, such data include multiplatform genomics, proteomics and imaging; and each of these distinct data types provides a different, partly independent and complementary, highresolution view of various biological processes. Modeling and inference in such studies is challenging, not only due to high dimensionality, but also due to presence of rich structured dependencies such as serial, spatial, graphical, functional and shapebased correlations. This talk will cover probabilistic frameworks that acknowledge and exploit these inherent complex structural relationships to develop regression and clustering models, that extract maximal information from such data. These approaches will be illustrated using several biomedical case examples especially in oncology.
 Statistical modeling of functional data: Karcher mean, multiple registration, fPCA in quotient space.
 Curves on manifolds: smoothing splines.
 Trajectories on Manifolds: issues; transported SRVFs, vector bundle representations, tangent bundle representation.
In previous talks, SRVF method has been discussed as a powerful and efficient way to analyze collections of curves in a Euclidean space. However, in many applications the data to be analyzed consists of trajectories in a manifold, rather than in a Euclidean space. Examples include hurricane paths on the surface of the earth, paths of covariance matrices that arise in the study of brain connectivity, and paths of images that lie in a shape space. The comparison of curves in a manifold is more subtle than in a Euclidean space, because one cannot subtract velocity vectors that lie in two different tangent spaces! In this talk, we discuss several methods of adapting the SRVF method to this situation, and comment on the advantages and disadvantages of each method.
 scalar FDA
 characterization of orbits
 existence of optimal matching for piecewiselinear curves
 C1 functions
In previous talks, SRVF method has been discussed as a powerful and efficient way to analyze collections of curves in a Euclidean space. However, in many applications the data to be analyzed consists of trajectories in a manifold, rather than in a Euclidean space. Examples include hurricane paths on the surface of the earth, paths of covariance matrices that arise in the study of brain connectivity, and paths of images that lie in a shape space. The comparison of curves in a manifold is more subtle than in a Euclidean space, because one cannot subtract velocity vectors that lie in two different tangent spaces! In this talk, we discuss several methods of adapting the SRVF method to this situation, and comment on the advantages and disadvantages of each method.
 Introduction and motivation.
 Function Spaces: norms, Hilbert space; L2 metric; complete orthonormal basis; sample mean, sample covariance; functional Principal Component Analysis (fPCA); functional regression models; generative models for functional data; least squares curve fitting.
 Background from geometry and algebra: manifolds, Riemannian metric, geodesics, exponential and inverse exponential map, Karcher/Frechet means; functional spaces of interest: set of probability density functions (pdfs), set of warping functions, group, group actions, quotient spaces.
 Phase variability and the registration problem; L2 metric and pinching problem; dynamic programming algorithm; penalized L2 metric.
 Invariance, squareroot velocity function (SRVF); FisherRao Riemannian metric; change of variables; registration using SRVFs; exact solution and approximation; quotient space metric, amplitude and phase distances.
 Goals and motivation; Past approaches in shape analysis; shapepreserving group actions; Kendall's shape analysis; active shape models; registration problem; nonelastic framework.
 Elastic Riemannian metric; SRVF; open curves and closed curves; shape geodesics.
 Statistics of shapes: sample mean, shape PCA, shape models, clustering and classification; symmetric shapes.
 scalar FDA
 characterization of orbits
 existence of optimal matching for piecewiselinear curves
 C1 functions
 Goals and motivation; past approaches; Iterative Closest Point (ICP) algorithm.
 Representations of surfaces: coordinate functions, gradient field, surface normal, 1nd fundamental form, 2nd fundamental form.
 Registration problem; elastic Riemannian metric; squareroot normal fields (SRNFs); inversion problem; shape geodesics.
 Statistics of shapes: sample mean, shape PCA, shape models, clustering and classification; symmetric shapes.
 Statistical modeling of functional data: Karcher mean, multiple registration, fPCA in quotient space.
 Curves on manifolds: smoothing splines.
 Trajectories on Manifolds: issues; transported SRVFs, vector bundle representations, tangent bundle representation.
Registration (for curves, surfaces or images) can be seen as a representation of a shape dataset as a subset of the diffeomorphism group, each shape in the dataset being associated with an optimal deformation of a template. We will in particular focus on methods that compute this deformation by optimizing a distance over diffeomorphisms under the constraint of mapping a template to a target, and such that the minimized distance is in turn a metric in shape space. These “metric registration” methods include a large spectrum of algorithms deriving from the “large deformation diffeomorphic metric mapping” (LDDMM) framework, and “metamorphosis” in which nondiffeomorphic shape variations are also allowed. We will describe mathematical foundations and algorithms, and the various forms that these methods may take in relation to applications.
Advanced brain imaging techniques make it possible to measure individuals' structural connectomes in large cohort studies noninvasively. The structural connectome is initially shaped by genetics and subsequently refined by the environment. It is extremely interesting to study structural connectomes and their relationships to environmental factors or human traits, which motivates the routine collection of highresolution connectomes in large human studies (e.g., the Human Connectome Project and UK Biobank). However, there is a fundamental gap between the state of the art in image acquisition and the tools available to reconstruct and analyze the connectome data, due to the complexity of data. This lecture aims at introducing our recent effort in the thread. More specifically, we will introduce a populationbased structural connectome (PSC) mapping framework to reproducibly extract binary networks, weighted networks, and streamlinebased brain connectomes. In addition, various novel methods of analyzing the outputs of PSC will be introduced. We will also introduce a userfriendly software package that implements the PSC and the analysis methods.
Introduction and Background
Anuj Srivastava
 Introduction and motivation.
 Function Spaces: norms, Hilbert space; L2 metric; complete orthonormal basis; sample mean, sample covariance; functional Principal Component Analysis (fPCA); functional regression m